11.1 A Detailed Description of Three Conflict Resolution Models

Introduction

War of attrition games provided the earliest models for conflict resolution that involved strings of successive displays or other actions per contest (see Web Topic 10.5). Although these contests involve repeated bouts, and are thus technically sequential games, the war of attrition models got around the sequential aspects by having each player select a persistence time at the outset, and then letting them display at each other until the shorter time bid had run out. Whichever individual picked the shorter time was then the loser. To prevent cheating that would undermine any ESS, players were not allowed to vary either the intensity or the rate of repetition of their display during the contest. The symmetric war of attrition assumed all players suffered the same rate of cost accrual during the contest and valued the contested commodity equally. Under these restrictive conditions, a mixed ESS was possible favoring settling of conflicts by repeated displays. Since player equality is unlikely to be the case in reality, the asymmetric war of attrition was proposed. Here, players were allowed to differ in cost accrual rates and/or contested commodity valuation. To achieve an ESS in this situation, the asymmetric war of attrition assumed that players could glean sufficient information about their own and their opponent’s fighting abilities before the contest to assign themselves to either “loser” or “winner” roles. Each player then drew a persistence time from a random distribution appropriate to that role. As with the symmetric war of attrition, players were not allowed to vary display intensity or repetition rates. This combination of assumptions and strategies did lead to a stable ESS.

One problem with the asymmetric war of attrition is that it assumes that players can assess cues in each other before the contest that are correlated with likely fighting abilities. While body size is an obvious factor that might both affect fight outcomes and be assessable by players before a contest, there are many other likely determinants of fight outcome that are not so assessable. Examples include physical condition, energy reserves, prior experience, and motivation. In addition, fight outcomes might also depend on relative stress or damage accumulated by players during an escalation; this might be very difficult to estimate before a contest but play a major role in outcomes. Clearly, the asymmetric war of attrition cannot handle any of these cases.

In this Web Topic, we review models in which each of three different types of initially non-assessable factors are assumed to play significant roles in the outcomes of contests with repeated and sequential displays. In the first example, the sequential assessment model, all of the same assumptions are made as for the asymmetric war of attrition except that no useful assessments are possible before the contest begins. Instead, players gradually extract information about their own and their opponent’s relative fighting abilities as the contest proceeds. At some point, these estimates become sufficiently accurate that the players can confidently identify who would be a “winner” and who a “loser” if they escalated; the contest then ends with the presumed loser quitting. In a second example, the critical factor that affects contests is the amount of stored energy or some equivalent resource prior to the contest. This resource gets “used up” as the contest proceeds, and eventually, one player reaches some ceiling or threshold beyond which it cannot afford to use up the remaining resource. It quits and the contest ends with it being the loser. The third type of model focuses on the role of damage accrual and/or other externally inflicted costs that might accumulate as a contest progresses. Again, each player will have its own threshold level of such costs that it can afford to suffer before it quits. The three models are similar in that each focuses on some state variable (information, energy reserves, or damage, respectively) that changes progressively as the contest proceeds. This raises a second issue that is normally associated with sequential games: what is the optimal policy for scheduling the rate of change in that state variable at different points in the contest? We take up this question for each of the three types of models (see Web Topic 10.5 for a review of terms and logic of game theory).

The sequential assessment model (SAM)

The sequential assessment model, like the asymmetric war of attrition, assumes that each player uses the same display repeatedly and does not vary either display intensity or instantaneous repetition rates (Enquist and Leimar 1983). Also like the asymmetric war of attrition, the goal of the interaction is to obtain an accurate estimate of the relative fighting abilities of the two parties. The state variable that changes during the course of the contest is the amount of error associated with those estimates. The sought ESS is a policy that identifies how accurate the estimates need be before one party assigns itself a “loser” role and quits.

The model assumes that the true fighting abilities of two contesting players (A and B) depend on the rate at which each accrues costs during an escalated contest, both from their own actions and from those of their opponent. If c_A is the true rate at which A accrues costs when contesting with B, and c_B is the equivalent rate for B, relative fighting ability from A’s point of view can be measured as

When θ_A > 0, B suffers higher cost accrual than A, and thus A can be considered to have higher relative fighting ability; when θ_A < 0, then A suffers more than B and has the lesser relative fighting ability. It should be obvious that θ_A = – θ_B.

When the contest begins, neither party has a good estimate of the true θ_i values. They then try to get more accurate estimates by observing each other’s displays during the contest. During each sample, an estimated value of θ_i will depend both on the true value and on some random error. Suppose the random error in any one sample i is z_i^A and that by B is z_i^B. The model assumes that these random errors are drawn from a normal distribution with mean zero and standard deviation σ. The best estimates at any step n in the contest would then be the cumulative average of the current and all prior samples. If at contest step n, A’s current estimate of θ_A is x_n^A, and B’s estimate of θ_B is x_n^B, then

At the beginning of the contest, each individual has only a crude estimate of the θ_i values. As the contest progresses, the effects of the random errors begin to average out to zero (e.g., the sampling error for the cumulative estimate after n steps is SE = σ/√n), and the current estimate approaches the true relative fighting ability. The model assumes that once one animal estimates that its θ_i is negative, it will end the contest by retreating or giving up. Since the standard error of the estimates should decrease as n increases, a smaller |θ_I| is necessary to trigger quitting as n increases. The evolutionarily stable policy can thus be described as a giving-up line on a graph of current estimates versus the number of steps so far, n. When one contestant’s current estimate crosses this line, it is sufficiently certain of its lower fighting ability that it makes the decision to quit (Figure 1).

Figure 1: Graphical solution for the sequential assessment game. Current estimates by each party of its relative fighting ability, x_A (red line) and x_B (blue line), are plotted on the vertical axis for successive numbers of steps n (horizontal axis). The solid horizontal line indicates equal estimated fighting abilities (e.g., x_i = 0). The dashed line shows the ESS policy for giving-up. Early in the fight, a player’s assessment of itself, x, must be quite low for it to give up because of the high level of uncertainty (e.g., large standard error of estimate). As the contest progresses and the estimates of true relative fighting ability become more accurate with repeated sampling, the giving-up line rises towards the 0 line. When an individual’s x crosses the line, it quits the fight. In this example, that was the blue player. (After Enquist and Leimar 1983.)

The smaller the difference in true fighting ability, and the higher the error of assessment, the longer the fight will be on average (Figure 2). Contests between near equals are also more variable in duration than those between unequal competitors and the (slightly) poorer contestant may sometimes win (Figure 3).

Figure 2: Average duration of a fight (in number of steps) as function of the absolute value of relative fighting ability. The three curves represent increasing (black to red to blue) standard deviations in the error levels of opponent assessment: higher levels of errors result in a slower decrease in fight durations. (After Enquist and Leimar 1983.)

Figure 3: The probability of victory (vertical axis) as a function of relative fighting ability. Losing or winning becomes more certain when contestants are more disparate in ability.

As the cost of fighting increases, the giving up line moves higher towards the x=0 line, meaning fight duration is shorter (Figure 4).

Figure 4: Giving-up line as a function of the cost of the interaction. The red curve is the giving-up line for a high level of interaction cost. Each line below it represents half the cost of the one above. As cost increases, the giving-up line moves up and contests are shorter. A similar series of curves is generated when the value of the resource decreases. As the value increases, the giving-up line is shifted down and contests are longer. (After Enquist and Leimar 1983.)

This game is a somewhat more realistic model than the asymmetric war of attrition, because it allows contestants to control the cost (duration) of the fight as it proceeds and to decide whether to continue or quit based on information gained during the fight. On the other hand, it yields some similar predictions to those of the asymmetric war of attrition, namely that contest length is short if the individuals are very different in size or fighting ability, and highly variable but generally longer when the contestants are similar.

In the original sequential assessment model, players were allowed to shift between multiple behaviors as long as these gave the same kind and amount of information. However, real animals often seem to have a sequence of escalating behaviors that are seen in conflicts. Enquist et al. (1990) later developed a different version of the sequential assessment game with several behavioral options that could be adopted in stages. Thus when the additional information provided by any given display stage became asymptotic, players could then switch to another display that provided more or different information. Usually, better information requires riskier or more expensive displays. In fish for example, lateral display may provide only partial information on size, tail beating leads to better but riskier size estimation, and mouth wrestling or head butting provides even better information. The model predicts that the alternative stages should be ordered so as to be maximally efficient in assessing relative fighting ability. This model thus provides an optimal policy for adjusting display type at different stages in the contest. In this extended model: (1) all contests should be organized into phases consisting of one or several behavior patterns with constant intensities and rates of repetition within a phase; (2) the contest should begin with the least costly behaviors that provide some information about fighting ability asymmetry, and after repetition with diminishing returns, switch to new, more costly but more effective behaviors in subsequent stages; (3) the division into phases should be independent of relative fighting ability; and (4) contests with great asymmetry in relative fighting ability should end in an early phase, whereas matched individuals may proceed through a series of escalations reaching a final phase of more dangerous fighting. Figure 5 shows a sample trajectory with three behaviors.

Figure 5: The sequential assessment game with three actions assigned to successive phases. In phase 1, only Action A is used until repetition provides no more useful information. In phase 2, Action B is added. In this example, the giving-up line is crossed during the second phase, so the contest ends before escalating to dangerous fighting, Action D. (After Enquist et al. 1990.)

Limited energy models

The sequential assessment game assumes that each time a combatant performs the same display, it provides additional information about its ability to fight should the contest escalate. This mechanism works best for assessing instantaneous attributes such as coordination or motivation. It may not be a good way to assess an opponent’s stamina and endurance, which could also play an important role in escalated contests. Like the asymmetric war of attrition and the sequential assessment game, the two models below focus on populations in which players do not share the same cost accrual rates or disputed commodity valuation. Both assume that each player has its own reserves (e.g., energy or some other limited resource) that get used up during the contest. No initial assessment of these reserves is possible, and players just display until one hits a threshold in cumulative costs beyond which it is not prepared to continue. It then quits and becomes the loser. Note that the outcomes of these contests are predetermined before the displays even begin; it is just that players cannot assess what these are. It is only after a contest has finished that this information is revealed. The first model below asks whether there can be an ESS in such contests if initial assessments are ignored and opponents just play out the endurance competition. The second model assumes that such an ESS exists and examines the optimal policy schedule for cost accumulation during such an endurance contest.

Limited energy models/War of attrition without assessment (WOAWA): The WOAWA model (Mesterton-Gibbons et al. 1996) assumes that individuals differ in the amount of energy or other limiting resource that is available for a protracted contest; distributions of maximal resources among the population’s individuals are assumed to be unimodal with a long tail at higher values. The longer a given player continues a contest, the less resource is available for other fitness-enhancing functions. Key parameters for this model are β, the rate at which a contest uses up this resource, and α, the efficiency with which residual resource after a contest can be turned into fitness. The cost/benefit ratio, β/α, is denoted by θ. A second key parameter is κ, the coefficient of variation in the amount of total resource held by different contestants in the population. Analysis of the model shows that an ESS can exist when players do not assess each other prior to initiating a contest as long as the relative cost/benefit ratio θ is small enough and/or the variation among contestants, κ, large enough (Figure 6A). In addition, the ESS identifies the maximal fraction, υ, of the total available resource at the start of the contest that an animal should commit before quitting (Figure 6B).

Figure 6: ESS outcomes of WOA model. (A) Combinations of coefficients of variation in initial resources (κ) and cost/benefit ratios of contests (θ) that preclude (blue) or favor (tan) a stable ESS in which contestants do not assess each other before beginning a contest, but just play out their resource until it hits a critical fraction, υ, of their total resource available. First opponent to hit this ceiling quits and is therefore loser. High cost/benefit ratios and/or low variation among combatants in initial resource level do not support this ESS. Combinations that favor the ESS may leave losers with less variation in residual resources after the contest than winners (light tan) or winners may show less variation than losers (dark tan). (B) ESS fraction of total available resource that should be assigned to a contest υ as a function of population variation in initial resources available (horizontal axis) and cost/benefit ratio (different colored lines). As cost/benefit ratio increases, average fraction of resources that should be allocated to a contest decreases. (After Mesterton-Gibbons et al. 1996.)

These authors also considered which statistical model best fit the distributions of resource identified in wild populations; the Weibull distribution (http://en.wikipedia.org/wiki/Weibull_distribution) appeared to give a better fit than a lognormal or gamma distribution. They also pointed out that while the asymmetric war of attrition predicts an inverse correlation between actual contest durations and the asymmetry in player fighting abilities, the WOAWA model predicts a positive correlation between contest duration and the residual resource remaining in losers of contests. This provides some interesting tests for comparing which of these two models, if either, fits a real system.

Limited energy models/Energetic war of attrition model (EWOA): The EWOA analysis looks for the optimal allocation of display effort during an endurance contest (Payne & Pagel 1996). Since the relative frequencies of players with different maximal endurance times are assumed to be fixed, and adoption of particular effort schedules by various players has no effect on those frequencies, this model is more of a simple optimization problem than a game. However, it provides some interesting predictions about when an endurance display system can or cannot pay for its costs.

In this model, players are competing for some commodity of value V, and each player has its own cost ceiling for a particular contest. This cost ceiling could be reached by performing high intensity or rapidly repeated displays throughout a short duration contest, or alternatively low intensity/infrequently repeated displays over a longer period. A focal animal’s instantaneous level of display (intensity, repetition rate, or both) at any time t in the contest is denoted by a(t) and the cumulative “signal” generated by this and all prior display in this contest is denoted by s(t). The cumulative cost of displays at point t in the contest is

C(t) = F(t) + T(t)

where F(t) is the cumulative energy cost and T(t) is the cumulative time lost (or fatigue acquired), both scaled in the same currency. At frequent intervals during the contest, each player compares its cumulative signal to its threshold value X. As long as its cumulative display is less than its X and its opponent is still displaying, it also continues to display. Once s(t) ≥ X, the player either flees (ending the contest), or escalates it into a more violent stage. Assuming no player escalates after s(t) ≥ X, denoting the average duration of a contest against an opponent B that has a threshold X_B by τ(X_B), and denoting the distribution of players with different values of X_B by N(X_B), the average payoff of endurance contests for a focal player A is:

The first term reflects cases where A won, and the second cases where B won.

Holding V and N(X_B) constant, the authors then examined how the costs C might vary with different emphases on display intensity versus contest duration for a given X. Replacing C with expressions defining its dependence on a(t), and setting the first derivative of that equation to zero and the second derivative to negative values identified the values of a(t) during a contest that maximized the payoff. Three types of outcomes were identified (Figure 7).

Figure 7: Possible outcomes for the EWOA analysis. A Type I outcome arises when cumulative time costs of continued display increase rapidly with contest duration whereas cumulative energy costs rise only minimally. Then a single high-intensity display is favored (maximal a(t) for the short duration of the contest). Type II contests arise when both cumulative energy and time costs increase during the contest. Type III contests arise when energetic costs rise rapidly with contest duration but time costs remain low. A minimally energetic display (low a(t)) is then given repeatedly for long periods as in the classical war of attrition. Whether a constant or changing display level is optimal during a contest depends on whether the cumulative time costs increase in accelerating (top dashed red line), linear (solid red line), or decelerating (lower dashed red line) manner. (Modified from Payne & Pagel 1996.)

In Type I contests, the optimal strategy is to produce a single maximum intensity signal; the duration of the contest then provides no information on player endurance. This situation can arise if the T(t) costs increase non-linearly with t but energetic costs, F(t), increase only slowly if at all during the contest. In Type III contests, the opposite occurs: it is best for each player to produce as costless a display as possible for as long a time as possible. In some respects, this is the classical war of attrition model. This is likely if energetic costs increase nonlinearly with contest duration, whereas time costs are minimal. Of greatest interest in this analysis are Type II contests. Here, a stable endurance game, in which each player’s stamina is honestly displayed by its maximal display duration, is only compatible with the relevant ESS if the cumulative energetic and cumulative time costs both increase significantly during the contest. In contrast with the sequential assessment game, in which each opponent should produce successive displays identically so that the average converges on their true fighting ability, the EWOA model can favor players increasing or decreasing the intensity or repetition rate of their displays as the contest proceeds: if time costs increase in an accelerating way, players should increase a(t) as t increases; if cumulative time costs increase in a decelerating way, players should decrease a(t) as t increases. This could explain changes in display intensity in natural examples for reasons other than escalating to obtain more information (as in staged sequential assessment games). Note however that for stable outcomes, all players have to adopt the same escalated or de-escalated display at the same time. How this “matching” might be achieved was not discussed in this paper, but is taken up in the next model.

Cumulative assessment model (CAM)

Whereas the sequential assessment model focused on cumulative acquisition of information, and the two prior models focused on the cumulative energy costs of protracted contests, the cumulative assessment model combines the accumulated effects of energy consumption and acquired damage during a contest. It focuses on a contestant’s successive decisions about whether to continue or quit given the cumulative sum of these combined costs (Payne 1998). It is most relevant to species that employ ritualized fighting in which only a certain amount of direct physical damage or stress can be tolerated. It can also be applied to non-contact interactions as long as the contestants are subject to external time costs not under their control, such as predation risk or lost foraging time. At no point are rivals assessed, and instead players only self-assess their own energetic expenditures and accumulated externally caused effects like damage.

As with the EWOA model, this analysis examines how contestants who differ in some fighting ability or intrinsic quality related to fighting, q, should alter the intensity, here denoted by R, of their actions over the course of a contest to maximize their expected payoffs. R can be a measure of the magnitude of a display and/or its instantaneous rate of repetition. All opponents are able to vary R during the course of a contest. It is assumed that each contestant persists in the interaction until the total costs including damage inflicted by the opponent surpass some threshold, and ignores the effects of its own attack upon the opponent, other than to note whether the opponent is still fighting or has fled. Like the EWOA model described earlier, this is a model of fighting tactics (how to perform optimally against a given opponent for a certain threshold) and not a strategy of how to choose the best threshold.

In this model, the overall cost suffered by each contestant over time is a combination of energetic costs F(t) and damage costs D(t):

C(t) = F(t) + D(t)

Consider a focal player with quality q that enters a contest with another player of quality q̂. The rate at which energy costs accrue to the focal player at any time t in the contest depends on the intensity of the actions R(q,t) that it chooses to adopt, and the rate that it accrues damage costs depends on the intensity of the actions R(q̂, t) adopted by its opponent over which the focal player has no control. The overall rate of cost accrual is then

where a and d are scaling parameters, and n is an exponent that allows for the possibility that energetic and damage costs do not accumulate with the same power of R over time.

The contest continues until one contestant flees at time T(q,q̂) which occurs when its tolerance threshold X(q) has been reached. The threshold reflects the costs an animal is willing to suffer in the contest, which in turn depend on contextual factors such as the value of the commodity being contested (V) and its own quality q. The overall expected payoff is given by

where p(q̂) is the probability density function of possible opponent qualities. As with the EWOA model, the first term accounts for contests that are won (opponent flees first), and the second term accounts for contests that are lost. The goal is to choose the optimal policy for each contestant as expressed by R(q,t) that maximizes E(q).

The author then examines a likely general case in which at least one party linearly escalates its R at which point the other should also increase its R and again is limited to linear increases. The question is then what the optimal intercept (initial R) and slope (rate of increase in R over time) should be for players with different quality (q) values. Stable policies are only present if the exponent n is greater than 1: energetic costs must rise in an accelerating manner as R is increased or no policy can be stable. The predicted ESS policy intercepts and slopes for contestants with linearly increasing R(t) are shown for high and low q individuals in Figure 8.

Figure 8: Optimal policies for increasing display intensity (R(t)) during a contest according to CAM model. In all cases, red line shows optimal policy (particularly intercept and slope) for high quality individuals and blue line indicates optimal policy for low quality individuals. High quality individuals should always adopt a higher initial value (intercept) than low quality ones. (A) When contests are likely to be brief, high quality individuals should adopt a high initial R and lower quality individuals a lower intensity. There is no time for the latter to catch up and damage the former enough to change outcome. They should just quit. (B) When contests are likely to be long, both parties should pick low initial intensities. Since high quality individuals can always afford to increase intensity at a steeper rate than low quality, the latter can never catch up. (C) For intermediate duration contests, high quality individuals again choose a high initial R. However, there is a chance low quality players can inflict sufficient damage on high quality opponents if they increase intensities faster and thus have a chance to win. Intermediate duration ensures that this strategy does not trap lower quality players into a long period of high costs. (After Payne 1998.)

Optimal policies differ depending on the likely duration of a contest. In all cases, higher q individuals should begin display at a higher R than lower q individuals. Thus the relevant linear trajectories always have a higher intercept for high q than for low q individuals. There are three general cases:

• Short contests: If contests are likely to be very brief (Figure 8A), cumulative costs are unlikely to be a concern and high q individuals should adopt a very high (and expensive) initial value of R. Because it starts at such a high R, these players subsequently can only increase R(t) slowly. They thus have a high intercept but gentle slope. Given this strong attack with little time left to increase its own R and inflict sufficient counter-damage on the opponent, a lower q individual should simply flee.
• Long contests: If contests are likely to be very long in duration, then both parties should adopt low initial R values (Figure 8B). Since the higher q individuals can endure cumulative costs better than low q individuals, the higher q individuals can afford to increase R(t) faster than can the low q individuals: thus the optimal slope for the high q individual line should be steeper than that for the low q individuals. Low q individuals can never catch up and will thus be forced to quit sooner than high q individuals.
• Intermediate duration contests: When contests are likely to be of intermediate length, the optimal policy for high q individuals is again to begin with a relatively high R, but because this is expensive, they can afford to increase R(t) at only a moderate slope (Figure 8C). Unlike the short contest situation, there may be enough time for lower q individuals to increase their R(t) at a fast enough rate (steeper slope) that they can inflict enough damage on the opponent to make it quit first. Sometimes it will succeed, and sometimes it will fail, but given sufficient time, it may be worth a shot.

A critical assumption of this model is that there needs to be some component of the cumulative costs that is beyond the control of each individual. Individuals can control their energy expenditures, but they cannot control the damage or stress imposed by the rival’s actions. Other possible external sources of cost include attraction of predators, increased vulnerability to parasites, lost foraging time, impaired ability to mate guard, and lost mating opportunities. The CAM model thus differs from the EWOA model primarily in the addition of cumulative costs due to external factors out of the focal animal’s control. Note that in addition to the escalation patterns illustrated in Figure 8, the cumulative assessment model predicts that contest duration will be positively correlated with the quality (energy reserves and defensive skill) of the loser. However, controlling for loser quality, contest duration should be negatively correlated with quality of the winner, since a higher quality winner will inflict costs on the loser at a higher rate. Depending on the relative importance of energetic and damage costs, these two predictive curves could vary in their strength.

Testing the models

The three models discussed above that predict contest trajectories (SAM, EWOA, and CAM), are sufficiently different that they generate divergent predictions that can be tested empirically. In the following table, different measures of relative fighting ability are all collected under a general term: resource holding potential (RHP) (see Chapter 11 in the text for more detailed definitions of this term). Below, we contrast a variety of predictions of these three trajectory models (an abbreviated version of this table also appears in the text):

Table 1. Summary of the predictions of the SAM, EWOA, and CAM models. (Sources: Briffa & Elwood 2009; Payne 1998.)

	Sequential Assessment (SAM)	Energetic War of Attrition (EWOA)	Cumulative Assessment (CAM)
Decision based on:	Difference between average opponent RHP	Sum of own actions	Sum of opponent’s actions
Assumes display level matching in population:	Depends on version	Yes	No
Assessment of opponent:	Yes	No	No
Escalation:	Not within a phase, but in sequential phases	Escalation and de-escalation possible	Escalation and de-escalation possible
Contest duration most strongly correlated with:	RHP asymmetry between opponents (–)	Loser RHP (+)	Loser RHP (+) and winner RHP (–)
Contest duration increases with increasing mean opponent RHP?	No	Yes	Possible
Display characteristics:	Non-dangerous index signals or ritualized fighting tactics	Energetically costly chasing or handicap signals with enforced intensity matching	Dangerous displays

It is easy to stage contests between known sized opponents and measure contest duration. This sort of data has been collected for a large number of species and used to test the contest duration predictions as a way to distinguish among the models. Taylor and Elwood (2003) importantly pointed out that these patterns can be misleading. They showed with simple simulations that if a pure self-assessment process such as the EWOA was in operation, and there was a perfect positive correlation between loser RHP and contest duration, a spurious negative correlation between RHP asymmetry and contest duration could arise. This occurs because in a population with a normal spread of body size or RHP, smaller individuals would usually have large opponents. Body size is thus negatively correlated with contestant size asymmetry, generating the spurious correlation between asymmetry and duration. Moreover, if true assessment is occurring, such that RHP asymmetry is negatively correlated with contest duration, a spurious positive correlation between loser RHP and duration, and a spurious negative correlation between winner RHP and duration, would be generated.

To make matters even more complex, if the CAM model is in operation, the same positive correlation with loser RHP, negative correlation with winner RHP, and negative correlation with RHP asymmetry will be generated. Although the CAM predicts that the loser and winner correlations should be stronger than the RHP asymmetry correlation, while the SAM predicts a stronger RHP asymmetry correlation, noisy data can obscure such subtle differences. Below, we show some of these primary versus spurious predictions of the three models:

Figure 9: Predicted relationships of contest duration as a function of winner and loser characteristics for the three fighting trajectory models. Contest duration is on the y-axis in each of these graphs. (1) indicates a primary prediction; (2) indicates a spurious correlation. (After Gammell & Hardy 2003; Taylor & Elwood 2003.)

As a consequence of these complications, it is essential in a study testing the fit to alternative models to examine the other differences among the models, including the dynamics of escalation, the presence of matching intensities, and the type of displays or fighting tactics employed (Briffa & Elwood 2009).

Literature cited

Briffa, M. & R.W. Elwood. 2009. Difficulties remain in distinguishing between mutual and self-assessment in animal contests. Animal Behaviour 77: 759–762.

Enquist, M. & O. Leimar. 1983. Evolution of fighting behavior — decision rules and assessment of relative strength. Journal of Theoretical Biology 102: 387–410.

Enquist, M., O. Leimar, T. Ljungberg, Y. Mallner & N. Segerdahl. 1990. A test of the sequential assessment game — fighting in the cichlid fish Nannacara anomala. Animal Behaviour 40: 1–14.

Gammell, M.P. & I.C.W. Hardy. 2003. Contest duration: sizing up the opposition? Trends in Ecology & Evolution 18: 491–493.

Mesterton-Gibbons, M., J.H. Marden, and L.A. Dugatkin. 1996. On wars of attrition without assessment. Journal of Theoretical Biology 181: 65–83.

Payne, R.J.H. and M. Pagel. 1996. Escalation and time costs in displays of endurance. Journal of Theoretical Biology 183: 185–193.

Payne, R.J.H. 1998. Gradually escalating fights and displays: the cumulative assessment model. Animal Behaviour 56: 651–662.

Taylor, P.W. & R.W. Elwood. 2003. The mismeasure of animal contests. Animal Behaviour 65: 1195–1202.

11.2 Resource Value and Ownership Asymmetries in Fighting Strategy Models

Introduction

In Web Topic 11.1, we focused on game and tactical models for contests in which outcomes are decided by the patterns of change in some state of a focal contestant: specifically, the states examined were information about the focal animal’s relative fighting ability, its energy reserves, and the accumulated damage that it might have sustained during the contest. Although these models usually included a term for the value of the contested commodity, this was held constant for all players. In this Web Topic, we examine similar games but where the contested commodity has different value for the two contestants. A special case occurs when one party has ownership of the commodity and is challenged by another. Again, we begin with the classic war of attrition models and relax or modify their assumptions to see when an ESS is possible and, if relevant, what scheduling policy of costs might be optimal to achieve that ESS. A final section reviews the mechanisms by which animals might assess resource value and ownership.

War of attrition with variable resource value

As we saw in Web Topic 10.5, the symmetric war of attrition model assumes that two animals compete for an indivisible commodity of value V, and that their only strategic choice is the length of time they will continue in a contest. The only ESS is a mixed one based on a random selection of a persistence time from the following probability density function:

The individual with the shorter time quits, and the other individual wins the commodity. All individuals are assumed to suffer the same rate of cost accrual per unit time, k, and place the same value V on the contested commodity. As long as –k is constant for all parties, we can replace t with investment cost x = kt.

One variant of this model, called the war of attrition with random rewards, considers the situation in which contestants may be in different commodity-requiring states on different occasions, and each individual only knows its own state and not that of its opponent (Bishop et al. 1978). For example, animals may differ in their hunger state; hungrier individuals should be willing to compete more strongly for food. The model assumes that being in a certain state is independent of the opponent’s state. The payoff to an individual in state u that selects an investment cost x against an opponent selecting y, or E_u (x,y), depends on whether x or y is larger:

If a focal animal selected the smaller investment x, it loses and its payoff is then just –x. If both parties picked the same investment x, they split the commodity or have equal chances of getting it and their net payoff is V_u/2 – x. If the focal animal is prepared to perform the larger investment x, its payoff is then V_u – y since it is the time selected by the loser that determines contest duration. The overall payoff for individual J of playing a given strategy a against opponent I is then

E_u (a,I) = P_a (V_u – a*) – (1 – P_a) a

where P_a is the probability of winning against I if J plays a; and a* is the expected investment cost if it wins, and a is its cost if it loses. The ESS is a probability density function G(x) with discrete sets of abutting curves depending on the number of need states. In the case of four different need states, the distribution of G(x) appears as in Figure 1 below.

Figure 1: Probability density function G(x) from which focal animal J should choose investment cost x. Four need states (e.g., hunger) are shown as separate colors with most needy state on far right. An animal in a given state should randomly select an investment cost (x) from the probability function defined by the line at the top of its colored segment. (After Bishop et al. 1978.)

The investment cost that an animal is prepared to make to win a contest will increase the more it values or needs the contested commodity. If there are differences of state between animals, the mean payoff given the ESS above is positive and greater for those animals for which the payoff of victory is higher. This means that hungrier individuals gain by being aggressive, and have a higher net payoff after allowing for the costs of aggression than less hungry individuals.

The sequential assessment model with asymmetric resource value

We saw in Web Topic 11.1 that the sequential assessment model assumed that contestants know little about each other’s fighting ability at the outset of the contest, and update this information as one or more types of displays are repeated over time. The ESS is based on a giving-up line that specifies a threshold estimate that one contestant is reasonably certain it will lose. This individual then quits and the contest is terminated. In the original model, contestants both knew the value of the resource (V) they were contesting at the outset and valued it to the same degree. As the value of the resource was increased, the giving-up line moved down and both contestants would persist for longer. This meant that contests over more valuable resources would be longer on average, everything else being equal.

A variant of this model allows the two contestants to place different values on the resource (Enquist and Leimar 1987). It is called the sequential assessment game with random rewards, and like the war of attrition with random rewards, assumes that animals vary in their resource valuation. The distribution of valuations in the population is assumed to be independent of the distribution of fighting abilities. The model then assumes that information about both relative fighting ability and opponent resource valuation can be acquired and updated during the contest. In practice, this might require different signals to indicate resource value and fighting ability. The model further assumes that as each contestant improves its estimates of its opponent’s valuation of the resource, it does not change its own valuation or fighting strategy as a result. The ESS then predicts separate giving-up lines for each opponent (Figure 2). Contestants with a high valuation will rely on a giving-up line that is below that of an opponent with a lower valuation. Thus contestants with higher valuations will tend to be more persistent in contests.

Figure 2: The sequential assessment model ESS giving-up lines for players with different resource valuations. (See Web Topic 11.1, Figure 4 for details on this type of graph.) Contestants with low valuation (e.g., red line) have giving-up lines higher in this graph than those with high valuation (blue line). If fighting abilities are similar, a contestant with the higher valuation is predicted to persist for longer and is therefore more likely to win against an opponent with a lower valuation. (After Enquist and Leimar 1987.)

Since relative fighting ability and resource value are drawn from independent distributions, the duration and outcome of a fight can vary in complex ways. For example, if contestant A has a greater valuation than an opponent B, the longest contests will occur when B is slightly stronger, and contests won by B will tend to be longer than those won by A. Figure 3 illustrates how variation in resource valuation against a random opponent affects the expected length of contests.

Figure 3: Expected contest durations for contests between focal animal and random member of population as function of resource valuation by focal animal. Opponent is a random draw from the population in both fighting ability and resource valuation. Contest durations always increase with focal animal’s valuation, but faster for contests it loses (blue) than ones it wins (red). Black line shows overall average relationship across all contests. (After Enquist and Leimar 1987.)

If the cost of acquiring information about relative fighting ability is decreased, either by decreasing fighting costs or decreasing the estimation error, the ESS changes so that the giving-up lines come closer together for opponents with different valuations. The consequence is that the outcome of fights will be more determined by relative fighting ability than by asymmetries in subjective resource value. Increasing cost or error will have the reverse effect of spreading out the giving-up lines. For sufficiently large cost or error, the ESS changes qualitatively, in that individuals with small valuations will decline to enter a contest. Increasing the range of variation of subjective resource valuations in the population or decreasing the range of variation of relative fighting ability has a similar effect on the ESS, making the outcome of fights more determined by asymmetry in subjective resource valuation than by asymmetry in fighting ability.

Sequential assessment model with asymmetric resource value information

An initial information asymmetry about resource value is most likely to occur for owner–intruder conflicts. The owner has spent some time with the resource and has more accurate information about its value than the intruder. This situation was modeled as a sequential assessment game in which the owner bases its decision to continue a contest or quit on both local resource value and information acquired about relative fighting ability, whereas the intruder bases its decision on fighting ability and an average estimate of resource valuation for the entire population (Enquist and Leimar 1987). This results in one ESS giving-up line for intruders, and a series of ESS giving-up lines for owners depending on their valuation of the resource. The respective giving-up lines are shown in Figure 4.

Figure 4: Owner–intruder game with information asymmetry. The black line is the intruder’s giving-up line, and the colored giving-up lines represent different possible valuations of the resource by the owner (higher values are lower on the plot). The shape of the intruder’s switching line is flatter, reflecting the fact that the owner’s behavior includes information about resource value. (After Enquist and Leimar 1987.)

The owner will become more persistent as its valuation of the resource increases. If the owner has a high resource valuation it will tend to persist and win against intruders, but if its valuation is less than the average for resources in this population, the intruder will win. Thus intruders will take over most poor resources but fail to acquire most high resources. A recent summary of whether this or the prior model predicts real animal contests can be found in Arnott and Elwood (2008).

Sequential assessment model with uncorrelated role asymmetry

Another variant of the sequential assessment model investigated the stability of fighting strategies based only on a role asymmetry that is uncorrelated with either fighting ability or resource valuation (Leimar and Enquist 1984). The logic is that both parties may do better to use some role asymmetry to settle a contest fairly quickly without enduring costs of a protracted contest. The invoking of the role asymmetry is thus a convention: which role tends to win and which lose may be completely arbitrary. In the context of a sequential assessment game in which both parties are trying to obtain more accurate estimates of their relative fighting ability, asymmetric roles would enter the model by specifying different giving-up lines for the two roles. The giving-up line for one of these roles would be crossed sooner on average than either would cross the shared line without invocation of role differences. The alternatives are best seen in the standard sequential assessment graph (Figure 5): 

Figure 5: ESS solutions for the sequential assessment game with an uncorrelated role asymmetry. The black line indicates the giving-up line when role asymmetries are ignored. This is in fact one ESS of this type of game. The alternative ESS is to invoke the role asymmetry by assigning one role to the blue giving-up line and the other to the red giving-up line. While chance always plays a role in sequential assessment games, the role assigned to the blue giving-up line will on average quit first. (After Leimar and Enquist 1984.)

Starting from a symmetric contestant situation, if one role is gradually made more favored with respect to fighting ability or resource value, the dichotomous solution becomes more likely. Thus the bourgeois strategy, in which resource owners typically win fights against intruders because intruders recognize the role asymmetry and back down, is more stable when owners either value the resource more, or are on average better fighters. Asymmetry in average strength is likely to appear when a resource is contested several times and stronger individuals have an advantage in such contests. Stronger individuals thus accumulate as territory owners, and owners will then be more persistent than intruders. Thus when the asymmetry involves resource ownership, the model predicts that: 1) owners will win when opponents are of equal strength, 2) contests won by the owner will tend to be shorter than those won by the intruder, and 3) the longest contests will occur when the intruder is slightly larger. These predictions have been realized in numerous lab and field studies. See Appendix A1 in Kokko (2006) for an extensive list of examples.

A self-consistent model of the bourgeois strategy

Previous models of territorial conflict resolution invoking an uncorrelated convention based on ownership have two serious problems. One is that the game invariably has two ESSs: one favors respecting the bourgeois convention (owners persist but intruders give up due to the asymmetry) and the other relies on the contrary convention in which intruders persist while owners retreat. This non-intuitive anti-bourgeois ESS would result in territories constantly changing owners, and if reproduction occurs on the territories, it would be continually interrupted. This solution has also been called a paradoxical ESS, in contrast to the common sense bourgeois ESS. It is certainly not what is usually seen in nature. A second problem is that when a population approaches fixation of the bourgeois strategy, all suitable habitat becomes filled with uncontestable territory owners, and territories become a rare and highly valuable resource. This situation will select for highly aggressive floaters who have nothing to lose if they take great risks in a takeover fight; this is called a desperado strategy. A better modeling approach is to acknowledge that there will be density dependent and population-level feedbacks on the payoffs of alternative strategies: the value of territories would then increase if they become rare and the mortality costs of searching and fighting for territories would also change. Such models are said to be self-consistent in that the payoffs can change in ways that are consistent with density dependence and population ecology (Houston and McNamara 2006). Another way to view this is that such games should really be treated as scrambles and not contests (see Web Topic 10.5).

Kokko et al. (2006) thus re-examined this type of game as a two-role continuous scramble. Unlike the prior models discussed in this Web Topic, this game was treated as single-bout interactions instead of long sequences. The two roles were territory owners and floaters without territories. Floaters interact with owners: either party can be aggressive and persistent (“daring”) or meek and non-persistent (“careful”). Each strategy in this game is a probability pair: one is the probability that a typical individual will be daring if an owner, and the other is the probability that it will be daring if a floater. The authors call these pairs of probabilities the “aggressiveness” scores for each role. Note that the two probability values in a strategy pair are assumed to be uncorrelated. The equations for single interaction payoffs explicitly incorporated possible density dependent effects making the game a scramble. The authors also considered cases in which relative fighting ability was versus was not a factor in interaction outcomes. The question was then what conditions might favor an ESS in which the uncorrelated asymmetry of territory ownership resolved an interaction.

The authors examined this model using evolutionary simulations. Populations were started at some combination of floater and owner aggressiveness values and many interactions were staged. Only owners were allowed to produce offspring, but all offspring began life as floaters. Mutants with a pair of probabilities different from the current population could invade and shift the current values if their levels of aggressiveness in the two roles were a better reply to the current strategy than the current strategy was to itself. The authors could then track the dynamic trajectories of a population over time for a given set of rates for mortality and territorial intrusion. Trajectories that ended at a fixed and convergently stable point were then ESSs.

Four general extreme outcomes are possible in this game (Figure 6). A no respect ESS can arise in which individuals always attack if in the floater role and always defend if in the owner role. This can be an ESS if baseline mortality for intruders is high, costs of fighting are low, and vacant territories are scarce, so that floaters have little to lose by acting as desperadoes. As the costs of fighting are increased, the ESS moves from a no respect pair strategy towards a complete respect one (e.g., the bourgeois strategy) in which individuals always respect ownership if in the floater role and always defend if owners. Depending on parameters, an intermediate partial respect ESS can arise in which individuals always defend if owners, and attack with some probability between 0 and 1 if floaters. A fourth outcome (called hippie world by the authors) involves no aggression by either party. This turns out never to be an ESS under reasonable parameters. The last possible outcome is the anti-bourgeois paradoxical case in which individuals always attack if in the floater role and always retreat if an owner. This is most likely when baseline mortality for owners is high, that of floaters is low, and mortality risks of fighting are high.

Figure 6: Evolutionary trajectories of the self-consistent feedback model for a particular set of mortality and intrusion rates. In this example, relative fighting ability had no effect on conflict outcomes. Of the possible ESSs (no respect, partial respect, full respect, and anti-bourgeois), evolutionary trajectories for this set of mortality and intrusion rates clearly lead to only two possible ESSs: partial respect and anti-bourgeois. This two-ESS outcome is the typical outcome if conflicts are dangerous. Including relative fighting ability leads to similar outcomes, but will usually move the partial respect ESS closer to the full respect corner of the plot. (After Kokko et al. 2006.)

For most reasonable parameters, this model results in two possible ESSs: one is the anti-bourgeois strategy and the other can be the no respect, the full respect, or the partial respect ESS. This again raises the question of which ESS is most likely when two are present. It is instructive to examine the evolutionary trajectories shown in Figure 6: the “basin of attraction” of any ESS is the relative size of the plot area in which points likely lead to that ESS. In the example shown, this clearly favors the partial respect ESS. This is because the frequency-dependent changes in single interaction payoffs as evolution proceeds often affect floater and owners in different directions. Floaters often experience negative selection on aggressiveness as the population level of floater aggressiveness increases. This is what favors intermediate floater aggressiveness in the partial respect ESS. Owners, on the other hand, do not experience negative frequency-dependence and thus should always be fully aggressive at the non-paradoxical ESSs.

Do animals assess resource value and use this in conflicts?

The above fighting strategy models assume that animals, at a minimum, assess a resource’s value for themselves before engaging in a contest over it. Resource valuation is implicit in uncorrelated asymmetry bourgeois models since owners should not defend their territory unless they value it sufficiently. But this raises the question of whether animals can also assess their opponent’s valuation of the resource. This would only be feasible if each animal adopts some state or behavior that reflects its personal valuation of a contested site or item and that can be detected and interpreted by others. Animals might or might not benefit by advertising their personal valuation. For example, a current owner of a resource that it valued highly might benefit by declaring its intentions to defend that resource without compromise; less motivated intruders would then give up without a contest. On the other hand, intruders often cannot evaluate a resource immediately upon encountering it, and thus must assume that it is of average quality. A current owner that declares an unlimited motivation to defend that resource suggests that it might be much more valuable than average. Intruders might then be attracted to such declarations. For researchers interested in whether resource valuation plays a role in conflict resolution, the absence of overt advertising might mean that the animal is hiding its valuation, or it could mean that resource valuation is not relevant or practiced by this animal. This poses a challenge to those who wish to test the predictions of the above models.

One set of indicators that an animal is evaluating the resource is the level of costs that they are willing to pay during an aggressive interaction. This level can be revealed during natural or induced conflicts as increases in contest duration, increases in vigor of certain activities, use of more risky displays and tactics, increases in the probability of injury, or increases in metabolic expenditure (measurable by researchers as increased oxygen consumption, lactate accumulation, or glucose depletion). One limitation to this approach is that measurements made at the end of a fight only reflect the loser’s resource valuation; they do not allow a full estimate of the costs that the winner was prepared to suffer (Arnott and Elwood 2008). An alternative technique for probing an animal’s subjective resource valuation during a contest is to interrupt the interaction at random points in time with a novel startling stimulus; this causes the attacker to break off the fight and hide; the speed with which it resumes the attack is then an indicator of its motivation (Elwood et al. 1998).

Suppose it is found that animals do evaluate the resource and this affects their behaviors. To investigate whether they can also assess their opponent’s resource value, researchers usually examine the degree to which a contestant varies its persistence, approach, and retreat behavior as a function of the opponent’s resource value. One can also search for potential cues or signals that may be associated with known variation in a sender’s resource value. Audio and video playback experiments using these potential motivational signals may be used to determine whether receivers adjust their approach, aggressive, and retreat behavior in response to these cues and signals.

Several studies examining animal resource valuation found no evidence of assessment by either party, despite a wide variation in resource value and clear benefits from higher-valued resources. For example, male scorpionflies (Harpobittacus nigriceps) provide females with an arthropod prey item as a nuptial gift during courtship. The larger the prey, the longer a male can copulate and the higher his fertilization success. Males sometimes attempt to steal another male’s prey item by engaging in aggressive contests. The duration of fights won by the usurper (because the owner gave up) was not influenced by prey size, which directly contradicts the theoretical predictions (see main text Figures 11.9B, C, and D) and suggests that the owner does not assess its own prey quality. Intruder persistence time in fights they lost also did not increase with prey quality, again indicating a lack of assessment (Thornhill 1984). Several other studies that failed to find evidence of resource assessment include contests over nest sites in male sand gobies (Pomatoschistus minutes) (Lindström 1992), contests over silk retreats and catch-nets in net-spinning caddisfly larvae (Arctopsyche ladogensis) (Englund and Olsson 1990), contests between female parasitic wasps (Pachycrepoideus vindemmiae) for dipteran pupa hosts of different quality (Goubault et al. 2007), contests over prey among group-living pholcid spiders (Holocnemus pluchei) (Jakob 1994), and contests between male fallow deer (Dama dama) during the rut (Jennings et al. 2004). In most of these species, however, assessment of relative fighting ability did affect contest duration and outcomes.

On the other hand, numerous food deprivation studies have shown that hungrier contestants fight harder for a food resource, as predicted by models of subjective resource valuation (see main text Figure 11.9A, and reviews by Arnott and Elwood, [2008] and Enquist and Leimar [1987]). Internal reproductive state also affects aggressive motivation, as demonstrated in shelter-related contests among brooding versus non-brooding red swamp crayfish (Procambarus clarkii) and American lobsters (Homarus americanus) (Figler et al. 1995a,b; 1997a,b; 1998), nest site contests in male cichlid fish (Tilapia zillii) with different testis weights (Neat et al. 1998), and contests over hosts between female parasitoid wasps (Goniozus nephantinis) with different egg loads (Stokkebo and Hardy 2000). The effect of resource scarcity was demonstrated in male cricket (Acheta domesticus) contests over females by subjects that had been deprived of female contact for different lengths of time (Brown et al. 2006, 2007).

Similarly, the predicted increase in contest duration when both parties value a resource highly has been found in a variety of species (see text Figure 11.9). One example involves sized-matched male red-spotted newts (Notophthalmus viridescens) fighting over females of different sizes (see text Figure 11.10). Larger females produce larger clutches and are therefore more valuable. Intruder males engage in wrestling contests with a male in possession of a female; contests are longer when the newts fight over a larger female. This positive correlation between duration and female size indicates that the intruder is able to assess female value. Intruders appear to use tactile and visual cues during the encounter to assess female size (Verrell 1986). A similar story was described for male wrestling contests over females in the amphipod Gammarus pulex, where intruders tug at the female and appear to rapidly assess female size and moult stage, which is associated with their fecundity (Dick and Elwood 1990).

Asymmetric information, where owners but not intruders have information about resource value, clearly affected contest dynamics in several well-described cases. Owners are expected to increase their persistence and defensive effort in relationship to increasing value of their resource, whereas intruders lacking precise information use an average value. This results in intruders fighting too hard for poor resources and not hard enough for good resources (text Figure 11.9D). In orb web spiders (Metellina spp), a male guards a female and waits for her to catch a large prey item, after which he initiates courtship. Larger females are more fecund. Intruder males will fight with a guarding male, but females remain in their retreats during these male contests. Guarding male persistence was positively correlated with female size, but intruder male persistence was not, indicating that intruders lacked information on female quality (Bridge et al. 2000; Hack et al. 1997). Similarly, in female-guarding male dung flies (Scatophaga stercoraria), the duration of fights lost by owners was positively correlated with the value of the female, whereas duration of fights lost by intruders was not (Sigurjónsdóttir and Parker, 1981).

In territorial owner–intruder conflicts, we expect intruders to have less information about the territory’s quality than the owner, but in some cases the intruder does appear to acquire resource value information. One example is the funnel-web spider Agelenopsis aperta, where the contestants are females (Riechert 1978, 1979, 1984). If the intruder is more than 10% larger than the owner, it will take over the web. But an owner that is only slightly smaller than an intruder usually prevails against a larger intruder, so ownership does confer some advantage. This species has a repertoire of 33 acts performed during contests, which escalate through the following phases of increasing cost and risk: locating with possible assessment of relative body size (6 acts); signaling (14 acts), threat (3 acts), and contact (4 acts). Webs have high value to the owner both because of the investment in constructing them, and because of their location in good prey capture areas. When a web is supplemented with food, increasing its perceived value to the owner, the signaling phase of the contest and the diversity of signals employed is greatly increased. In staged owner–intruder contests, both contestants increased their contest cost with increasing web quality, indicating that the intruder also assesses web quality. However, when contests were staged between two intruders on a web whose owner was removed, there was no relationship between contest cost and web quality. Taken together, these results suggest that intruders battling an owner obtain information about web quality from the owner’s behavior. At least some of the signals appear to provide intruders with website quality information.

Hermit crabs provide a unique situation for investigating the question of self and opponent resource value assessment, because two separate resources are involved—the gastropod shell currently occupied by each opponent (Arnott and Elwood 2008; Elwood and Briffa 2001). The value of a shell is determined by the size of the shell relative to the body size of the crab. If contestants differ in size, the value of a given shell will differ. A larger crab might fight another individual to obtain a better shell, which could leave a suboptimal shell for the loser. But if the loser had a shell that was too large for it, both individuals could benefit from exchanging shells. Contests are asymmetric with two roles: attacker and defender. In a typical interaction, two crabs encounter each other and perform a cheliped display to assess relative body size. The larger individual usually assumes the attacker role and approaches and grasps the defender’s shell, causing it to withdraw inside its shell. The attacker runs its claws over the exterior of the defender’s shell and turns the shell to feel the aperture, a better way to assess the shell’s interior volume. If the attacker decides to escalate, it rotates the defender’s shell and begins a vigorous rapping of its shell against the defender’s shell; rapping occurs in repeated bouts of rapid taps and continues until either the defender is evicted or the attacker becomes fatigued and gives up. In some species (Pagurus longicarpus), attackers base their decision to confront another individual only on the basis of the low quality of their own shell and apparently do not assess the quality of the defender’s shell (Gherardi 2006; Tricarico and Gherardi 2007).

Figure 7: Hermit crabs (Pagurus berhardus) fighting over shells. Note that larger animal has assumed attacker role and has rotated defender’s shell so that it can examine shell opening and begin rapping on shell to evict owner. (Photo by Mike Cursons.)

In the well-studied European hermit crab (Pagurus bernhardus), attackers gather information on the defender’s shell size after grasping and feeling it, and then make the decision whether or not to escalate (Figure 7) (Dowds and Elwood 1983; Elwood and Briffa 2001). The vigor of rapping is correlated with the attacker’s valuation of the opponent’s shell relative to its own, and successful eviction is associated with greater rapping intensity and duration (Figure 8). Defenders in this species are apparently unable to obtain any information about the attacker’s shell quality to modify their persistence and giving-up decision. However, in at least some species (Clibanarius spp, Calcinus tibicen), the defender apparently is able to assess the attacker’s shell size, possibly using the fundamental frequency of the rapping sound. Here, the defender gives up more quickly when the attacker’s shell is of higher value from the defender’s perspective. The attacker also assesses the defender’s shell fit during the aperture investigation and preferentially attacks small individuals with overlarge shells. Resource assessment by both parties in these latter species results in interactions characterized more by negotiation than by conflict; shells are primarily exchanged between crabs only when both individuals stand to benefit (Hazlett 1987, 1989, 1996).

Figure 8: Assessment of resource value in shell-exchanging hermit crabs. (A) Logarithm of the number of rapping bouts per contest by attacking hermit crabs (Pagurus bernhardus) when the larger crabs possessed shells that were 50% smaller or 80% of the optimal size, and the smaller crab occupied a shell that was optimally sized for the larger crab (Briffa et al. 1998). Blue bars reflect rapping bout number when the larger crab succeeded in evicting the smaller one; brown bars indicate larger crab gave up and smaller crab was able to retain shell. Eviction required more rapping than non-eviction, and the number of raps the larger crab was willing to perform was greater when the fit to its current shell was worse. (B) Logarithm of the number of rapping bouts required for a larger crab to evict a smaller defender housed in a high quality shell as a function of the quality of the contested shell (Arnott and Elwood 2007).

The owner–intruder role asymmetry appears to be readily assessed in most contests involving territories, prior residency in an area, and mate guarding systems. The primary evidence for this assertion is that ownership frequently confers a competitive advantage on the owner (Kokko et al. 2006). In a summary of 99 studies that examined the effects of both ownership and relative fighting ability on the outcome of contests, 77 studies found a positive effect of ownership on the probability of winning. In 58 of these studies, relative fighting ability also played a role, and ownership was the sole determinant of winning in 20 cases. Relative fighting ability was the sole determinant in 21 studies, indicating that ownership was not important or not assessed. Only one study concluded that neither ownership nor relative fighting ability affected contest outcome (Leimar and Enquist 1984). The species in these studies included sea urchins, spiders, crustaceans, insects, fish, amphibians, birds, and mammals, attesting to the ubiquity of the “owners usually win” phenomenon and to the fact that high cognitive skill is not required to achieve this assessment.

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11.3 Positive Allometry of Weapons and Ornaments

Introduction

Most non-scientists shown two breeds of cattle that differed two-fold in average length might surmise that the larger species had horns and penises that were twice as long as those of the small species, offspring and brains that were twice as heavy, a similar diet but a need to eat twice as much daily, and as a consequence, required access to twice the pasturage required by the small breed. They might even guess that the larger breed would live twice as long as the smaller one. In fact, most of these seemingly good guesses would be wrong. And while we used body length as the reference measure, most seemingly good guesses would have been as wrong had we used body mass, foot mass, blood volume, or running speed as the reference trait. The general finding is that the ratios between the magnitudes of two different organismal traits do not stay constant, (e.g., keep the same relative proportions), when compared in the same animal at different stages of development, different animals of the same age and species, or different animals at equivalent ages in different species (Huxley 1932; von Bertalanffy and Pirozynski 1952; Gould 1966). If the ratio for the two traits did stay constant when one was varied, we would call those traits isometric; if, on the other hand, the ratio varied as the magnitude of one of the traits varied, we would say the traits were allometric. The observation that many pairs of traits vary allometrically turns out to have major consequences for the organisms’ physiologies, behaviors, ecologies, and life histories (Schmidt-Nielsen 1984; Peters 1993; Brown and West 2000; Bonner 2006). These important consequences immediately raise the question of why some traits vary isometrically whereas others vary allometrically. In this Web Topic, we briefly review some basic background on biological allometry, note some of the more important general relationships, then turn to the specific role of allometry in the evolution of ornaments and weapons subject to sexual selection.

Fundamentals of allometric analysis

QUANTIFYING ALLOMETRY A measure of how two different biological traits might co-vary is called their scaling. Scalings can usually be quantified by relating the magnitude of one trait, say y, to the magnitude of the other, x, using a power law:

y = kx^a

where k is the scaling coefficient and a is the scaling exponent. If the best estimate for a = 1, then the two traits scale isometrically and their ratio will remain constant regardless of the value of x. If a > 1, then the magnitude of y is an accelerating function of x, and is said to be positively allometric in relation to x. If 0 < a < 1, then y still increases when x does, but at a decelerating rate. In this case, y has a negatively allometric relationship with x. Note that if y is positively allometric when compared to x, then x will be negatively allometric with respect to y.

What happens to the ratio between y and x when the two are related by a power law? If y = kx^a, then y/x = kx^a-1. If a=1, then y/x = k: this simply says that if two traits are isometric, their ratio is a constant. If a >1, then the ratio y/x is an increasing function of x; if 0 < a < 1, then y/x = k/x^1-a which means the ratio gets smaller as x gets bigger.

In practice, one collects a set of equivalent and independent sample pairs of x and y, and then uses a statistical method to obtain a best fit to the power equation variables k and a. It is much easier to do this if one compares the log y to the log x since if there is a power law fit

log y = log k + a log x

This is an equation for a straight line with intercept log k and slope a. Note that the only way that the slope a can be greater than 1 is if the range of values of y is greater than the range of values of x (Eberhard et al. 1998). This will have significance later.

Several statistical methods are available to find the best-fit line to such a data set (Harvey and Mace 1982). Ordinary least square regressions assume that there is no error in the measurement of the x variable. When the measurement errors for y are known to be significantly larger than those for measurements of x, least square regressions can be used to find best-fit lines. When it is known that the measurements of y and x have similar errors, least square regressions will underestimate the slope of the true relation between the variables. In these cases, alternative methods, such as reduced major axis analysis, should be used to find best-fit lines. Where the sample points might not be independent (e.g., if a large subset of the species in a multi-species comparison consists of species belonging to the same genus), various methods have been developed to control for these dependencies (Harvey and Pagel 1991). Once the relevant controls and methods have been applied, the slope of the resulting (hopefully) straight line provides an overall measure of a, the allometric exponent, and the intercept log k reflects the average ratio of the two traits across the entire sample. Where the function is clearly not linear on a log–log plot, more than one parameter will need to be extracted to describe the relationship between y and x.

DIFFERENT USES OF ALLOMETRIC MEASURES When traits are compared at different developmental stages in the same species, the resulting relationship reflects the ontogenetic allometry between the traits. A trait relationship based on variation among individuals of the same species and at the same life stages is called static allometry. Patterns based on comparisons between many different species reflect evolutionary allometry. Even where the same species are involved, these three different comparisons can result in quite different values of the scaling exponent a. Usually, allometric relationships are stronger (e.g., have steeper slopes) for ontogenetic than for static, and for static than for evolutionary contrasts.

Figure 1: Types of allometric relationships. Black dots show current values of the logarithms of traits x and y for different individuals at the same ontogenetic stage. Blue lines show ontogenetic allometric lines for each individual. If dots are from the same species, the red line characterizes static allometry, and if the dots are different species, the red line shows evolutionary allometry. Note the steeper slopes for the ontogenetic lines than for either static or evolutionary lines. (After Shingleton et al. 2007.)

Where one measures two traits in two different samples, say static contrasts for adult males and adult females, or multi-species contrasts for birds versus lizards, one can then compare both the intercept values (reflecting the average trait ratios) and the line slopes (corresponding to the scaling patterns) for the two data sets. Males and females might have similar intercepts but different scaling patterns; birds and lizards might have similar slopes but different intercepts. Another common use of allometry is to correct for body size effects when comparing other traits. For example, one might want to compare testis size in monogamous versus polygynous mammals. Absolute testis size will surely increase with body size regardless of the mating system. To control for this, one would first compute the allometric relationship between testis size and body size across the entire sample; the direction and magnitude of deviations above or below this line could then be correlated with mating system. This is called the comparative method (Harvey and Pagel 1991) and is discussed further in Web Topic 10.1.

Sources of allometric relationships

There are two general causes of the allometric relationships seen in biological systems:

• Physical laws: Basic geometric, physical, and chemical laws constrain all organisms. Combining a particular physical law and a particular geometry will often generate allometric relationships. For example, consider an animal that has to keep warm. The rate at which it can produce heat energy depends upon its total mass M which is proportional to its volume V. The rate at which it loses heat depends upon its surface area which is proportional to V^2/3. The energy that it has left over after thermoregulation is then kV - mV^2/3. For fixed k and m, this difference gets larger as V increases. An animal could thus gain several benefits from being larger. These include: a) reducing its foraging effort and thus risks until it just met its thermoregulation costs; b) switching to a lower quality but more abundant food; or c) continuing its current diet and foraging effort but using the extra energy for other activities such as soliciting mates or raising more offspring. This geometrical example led early researchers to the prediction that animal metabolisms should scale as the 2/3 power of their body mass with all the attendant advantages (Rubner 1883).
  

  In fact, nearly all organisms examined, including plants, protists, and animals, have metabolic exponents between 2/3 and 1 (McMahon 1975; Pennycuick 1992; Mcnab 2002; Brown et al. 2004; Glazier 2010). Resting birds and mammals tend to be on the low end of this range, whereas plants and very active animals tend to lie on the upper end. There remains considerable dispute about why this range of exponents is found. On one side is the “1/4 rule” school arguing that transport of energy, nutrients, blood, and sap, not the surface area of the organism, limits how much metabolism can be sustained; all critical functions of the organism are then predicted to scale as integer multiples of 1/4 (allowing for both positive and negative multipliers) (West et al. 1999; Savage et al. 2004; Banavar et al. 2010). Combined with the assumption that body mass sets the upper limit on energy/nutrient production, this approach predicts that metabolic rates should scale with the 3/4 power of body mass, whereas heart rate and respiration should scale as the –1/4 power of body mass. Reproductive rates and life expectancies are also predicted to scale as integer powers of 1/4. While a 3/4 value is often found for metabolism, there are many exceptions (hence the large observed range of exponent values).

  An alternative view is that whether the entire body mass or some transport factor is the limiting factor in metabolism can vary depending upon the current activity of the organism (Glazier 2010). An inactive organism (such as a plant or a resting animal) does not need a metabolic rate sufficiently high to be limited by its transport system or surface area. Thus its metabolic rate should scale according to its mass (an exponent of 1). The metabolic output of a moderately active animal is much more likely to be limited by its transport system or surface area as it must unload heat and wastes generated by the activity, and replace internal oxygen from outside sources. These activities should scale closer to the 2/3 exponent predicted by the surface area model. For very high activity bursts, most animals shift into an anaerobic metabolic state in which they rely on previously stored energy and oxygen and let wastes accumulate (e.g., lactic acid). Here again, the metabolism will depend on mass only and not on the transport system; the corresponding exponent for metabolic rate will again be 1. This model thus predicts that the range of exponents seen across taxa and contexts simply reflects a shifting of the limiting constraints between energy provision (body mass) and transport functions (circulatory systems or surface area). As evidence, they note that the intercept of the log–log plot lines should be higher as activity levels rise, and therefore the observed exponents should be correlated to some degree (but in a U-shaped manner) with the intercepts. Available data do tend to support these predictions.

  Once determined, the allometric scalings for metabolism can lead directly to predictions of allometric scalings for other traits such as behavior and reproduction. For example, one might expect home range size in animals to scale similarly to their metabolism (e.g., with exponents between 2/3 and 1). In general, this is what is found, but the range of variation is much greater than that found for most physiological or anatomical traits (Hendriks 2007; Hendriks et al. 2009). The increased variability appears to be due to the independent roles of an animal’s physiology and the abundance and spatial dispersion of food; the latter often follow fractal patterns in nature, and the observed scaling of home ranges with body sizes will thus depend both on the underlying metabolic needs and the fractal scaling of the food supply (Haskell et al. 2002; Buchmann et al. 2011). Metabolic scalings are also the basis of a prediction that the optimal lifetime reproductive effort of organisms should be a constant: assuming a metabolic exponent of 3/4, each female in a stable population should optimally produce a lifetime mass of offspring that is 1.43 times her own mass (Charnov et al. 2007). If this were true, there should be an inverse relationship between the average mass of an individual offspring and the total number produced. In fact, this is what is found: scaling exponents for individual offspring masses average 1/2 for heterotherms (plants and heterothermic animals) and range between 3/4 and 1 for homeotherms; offspring numbers for the same species have scaling exponents which are ranked inversely to those for offspring masses (Hendriks and Mulder 2008).

  For our purposes, it is not critical whether metabolic rates in organisms scale with 2/3, 3/4, or some other value between 2/3 and 1. As long as the metabolic scaling exponent is < 1, there will be more strategic options available to larger organisms than to smaller ones. This can have very significant consequences for social organization, mating systems, life histories, and even communication (Schmidt-Nielsen 1984; Reiss 1991; Peters 1993; Niklas 1994; Calder 1996; Brown and West 2000; Bonner 2006; Hendriks 2007; Weiner et al. 2009; Reiss and Schmid-Araya 2010).

• Selection: Most animals must compete for access to resources, refuges, and appropriate mates. This typically generates directional selection on any trait that might give their carrier an edge in competition (Green 1992). The simplest reason why such a trait might be positively allometric with respect to body size is that, for physical reasons, large animals have more spare resources to invest in competitive traits than small animals (Petrie 1992). This of course assumes that body size is under normalizing selection or at least a lower intensity of directional selection than the competitive trait. Alternatively, if selection favors greater among-individual variation in one trait than another, this will cause the first trait to show static positive allometry when compared to the second. Sexually selected traits are often found to be more variable than non-sexually selected traits (Pomiankowski and Møller 1995; Rowe and Houle 1996), and game theoretical models for some traits, such as personality, predict stable mixtures of many different phenotypes (McNamara et al. 2009; Botero et al. 2010; Dingemanse and Wolf 2010; Wolf and Weissing 2010). A third possible factor is that positive allometry of signal traits makes it easier to discriminate between individuals with large trait values (Wallace 1987). Given that measurement error in most sensory organs and brains tends to increase with mean stimulus magnitude (Weber’s Law; see Web Topic 8.6), positive allometry of signal traits would minimize receiver error and facilitate honest signaling.

  Since resources are limited for most animals, positive allometric investment in one trait will lead to reduced resources, and thus negative allometric investment, in other traits (Nijhout and Wheeler 1996; West-Eberhard 2003). The optimal distribution of available resources among competing traits will depend significantly on the relative contributions that each investment brings to overall fitness. One common tradeoff involves investment in a given trait versus that in further growth. Bonduriansky and Day (2003) have provided a useful model of this tradeoff that predicts whether a given pair of traits will have an isometric, positively allometric, or negatively allometric relationship. Given an assumption that body mass scales with an exponent < 1 as an animal ages and grows, these authors predict resulting relationships for the following contexts:

  • If fitness largely depends on the absolute size of the trait → isometry
  • If fitness largely depends on the size of the trait relative to body size → isometry
  • Given directional selection for larger traits and stabilizing selection on relative trait size due to survival costs → isometry
  • Given directional selection favoring both larger trait and body sizes but stronger selection on trait size → isometry
  • Given directional selection for larger traits, survival increasing with body size but decreasing with trait size → negative allometry
  • Given directional selection for larger traits, viability increasing with body size but in a decelerating manner; no viability consequences of trait →  positive allometry
  • Given stabilizing selection on the trait but directional selection on body size →  sigmoid allometric curve resulting in polymorphic populations

The basic point is that the type of allometric relationship arising from a tradeoff between investing resources in one trait versus in growth depends entirely on the shapes of the fitness functions for the trait and increased body size. In general, positive allometry only arises when the marginal increase in fitness by having a larger trait is greater in a larger animal than it would be in a smaller animal. This is similar to the requirement of the handicap principle for signal honesty: signals will only be honest if the fitness consequences of a high quality individual giving a signal for high quality are greater than that same signal given by a low quality individual (see Chapter 10).

The Bonduriansky and Day model identifies selective regimes that will favor different types of allometric relationships. But what mechanisms are available to respond to this selection? The generation of static allometries depends upon differences in the previous ontogenetic allometries of the sampled individuals. Here we shall define ontogeny broadly to include continuous maturational trajectories as well as periodic renewal investments by adults (such as the annual moulting of bird plumages or the recreation of antlers by male deer). What could have caused individuals to undertake different ontogenetic trajectories earlier in their lives that generate static allometries now?

The generally accepted answer is that most organisms show some degree of phenotypic plasticity during ontogeny: the same genetic makeup can result in different phenotypes depending upon external cues and conditions such as food abundance, temperature, population density, injury, parasite loads, and the like (Schlichting and Pigliucii 1998; West-Eberhard 2003). The function describing the probabilities of exhibiting different phenotypes for a given genotype is called that genotype’s norm of reaction. When two traits are considered concurrently, one can think of the norm of reaction for their combination as a policy for defining their ontogenetic allometry: a sample policy might favor focused investment in overall growth when food is scarce during ontogeny, but more investment in specific organs, at the expense of overall growth, when food is abundant (Emlen and Nijhout 2000; Shingleton et al. 2007). The points in Figure 1 represent individuals of the same age. The distance of each point from its vertical axis intercept represents the total resource it had available to invest in traits x and y during its ontogeny. The fact that different individuals adopted different relative allocations of resource to x and y (indicated by the different slopes for the points), presumably reflects how their norm of reaction policy reacted to the total amount of resource that was or seemed likely to be available. The physiological mechanisms by which these policies are implemented may simply depend on differences in the degree to which different traits are sensitive to the same cues and conditions: if overall growth is more sensitive to ambient food levels than growth of a particular trait, the two schedules can get out of synchrony and this can change the final allometry (Shingleton et al. 2007; Tobler and Nijhout 2010). It is also possible that a relevant policy allows for shifts between several alternative schedules at switching points depending on ambient cues and conditions (Tomkins et al. 2005). At least in insects, the norm of reaction of individual genotypes is not much narrower than the average allometric relationships seen in wild populations consisting of many genotypes (Emlen and Nijhout 2000). This makes analyses easier, but is not necessarily the case for all organisms. When we plot static allometry, we may be seeing the consequences of one norm of reaction and varying cue values (e.g., some insects), or many different norms of reaction corresponding to different genotypes in the population.

There is good evidence that allometric policies are associated with significant additive genetic variance, and can respond to selection by shifting to patterns above and beyond any physically-determined allometries. Male stalk-eyed flies (Diopsidae) show strong positive allometry between the width of their eye-stalks and body size; artificial selection in laboratory stocks can increase or decrease the allometric exponents, and natural variations in sexual selection and consequent viability are surely the reason for differences in the degree of allometry seen between species in this family (Wilkinson 1993). Similar artificial selection experiments altered the allometric relationships between horn and body size in scarab beetles (Emlen 1996). Studies of wild caught three-spined stickleback fish also suggest that allometric exponents are subject to selection independent of physical allometric effects on body size (McGuigan et al. 2010).

Allometry of ornaments and weapons

Given this prior background, we can now turn to recent studies of allometry in animal secondary sex characteristics such as weapons and ornaments. It is often observed that these traits show positive allometry relative to body size or at least have higher allometric exponents than other traits (Huxley 1932; Gould 1966, 1974; Echelle et al. 1978; Petrie 1988; Reiss 1991; Green 1992; Petrie 1992; Andersson 1994; Emlen and Nijhout 2000; Baker and Wilkinson 2001; Tomkins et al. 2005; Tomkins et al. 2010). A more recent review by Kodric-Brown et al. (2006) reported allometric exponents for weapons and ornaments in stag beetles, fiddler crabs, earwigs, and anoles ranging from 0.93–15.7, with modal values between 1.5 and 2.5. They then provided a model, described below, which they argued predicts positive allometry for all secondary sexual traits. Bonduriansky (2007) replied that neither his model nor the data supported this extreme a claim and cited a list of examples in which secondary sex characters did not show positive allometry, and others where non-sexual characters did (Bonduriansky 2007). Whereas some of Bonduriansky’s counter-examples have since been found to show positive allometry if reduced major axis analyses are used instead of ordinary least square regressions (Cuervo and Møller 2009), and traits associated with copulation such as penis length and claspers should be excluded since they routinely exhibit isometry or negative allometry (Eberhard et al. 1998; Eberhard 2009), there are still a number of species in which secondary sex traits are isometric or negatively allometric (e.g., anurans [Schulte-Hostedde et al. 2011] and feathers in some birds [Cuervo and Møller 2009]). Our reading of the literature is that most secondary sex characteristics do appear to show positive allometry, but enough do not that it would be unwise to use allometric relationships to predict trait functions or vice versa.

The Kodric-Brown et al. (2006) model builds on the earlier one by Bonduriansky and Day in that it also assumes that resources are limited, and thus investments in ornaments and weapons must trade off with investments in body growth. In their model, this tradeoff is linear: the investment available for general growth equals the total available minus that allocated to ornaments and weapons. Total fitness is equal to the sum of that contributed through body size effects and that contributed through the size of ornament/weapons relative to body size. It is assumed that either increased body size or increased relative ornament/weapon size increases fitness but with functions that are either asymptotic (body size effects) or rapidly decelerating (ornament/weapon size effects). As a result of these assumptions, combinations of body size and relative ornament/weapon size that would produce a given value of fitness plot as a hyperbola on a graph of relative ornament/weapon size versus the logarithm of body size. Different total fitnesses generate different hypberbolae. That hyperbola that just touches a species’ given tradeoff line is the optimal allocation (this is the fitness set analysis method of Levins [1968]). The authors then track the optimal allocations for a given individual over time, using the end point of its most recent growth as the starting point for the next stage. Interestingly, the resulting ontogenetic trajectories are almost always positively allometric. Also of interest, the steepness of the linear tradeoff has no effect on the allometric exponents; instead, it is the shape of the fitness hyperbolae that determines the degree of allometry. The tradeoff function, along with the disposition of the fitness hyperbolae, does affect the allometric intercept value.

Since there are exceptional species that exhibit isometry or negative allometry of sexually selected ornaments and weapons, there must be factors not included in the Kodric-Brown et al. model that need to be considered as well. Viability costs may not increase linearly with increases in ornament or weapon size, and thus the fitness generated by the weapon or ornament alone may not be a monotonically increasing function; after some threshold value, this component of fitness may decrease with increasing size due to physical constraints or nonlinear predation risks (Bonduriansky 2007). The separate contributions to fitness by body size and ornaments or weapons may not be additive and independent: multiplicative and interaction effects are certainly possible. Alternatively, the partitioning of tradeoffs into two components, ornament/weapons versus body size, may be too simplistic and multiple components may be at play. For example, it has been shown in stalk-eyed flies that the flight imbalances caused by large male eyestalks have selected for a variety of counter-balancing adaptations (Husak et al. 2011). These, and similar compensations in other sexually selected species, minimize the viability costs usually expected for an exaggerated ornament (Husak and Swallow 2011). No single pair of traits is likely to evolve independently of other traits (Emlen and Nijhout 2000; West-Eberhard 2003). Optimization when there are multiple components can lead to quite different outcomes than if components are examined only as dyads. In addition to ontogenetic and physiological linkages, traits may be genetically correlated in ways that complicate the independent effects assumed in the Kodric-Brown et al. model. Clearly, major progress has been made in understanding the observed patterns of allometry in animal weapons and ornaments, but there are still issues to be clarified.

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11.4 Songbird Territorial Negotiations

Introduction

Territorial songbirds use their songs to settle boundary disputes much like humans use words to negotiate business deals. Seventy-five percent of songbird species possess song-type repertoires ranging in size from a few to over 100 types, and many of the remaining species with one official song type vary their song structure in meaningful ways, such as by shifting the pitch or varying the duration with the number of repeated elements (Morton and Young 1986; Ritchison 1988; McGregor and Horn 1992; Shackleton and Ratcliffe 1994; Martin-Vivaldi et al. 1999). Most species also add or switch to call-like vocalizations, such as twitters, rattles, buzzes, or soft song, as contests escalate (Jarvi et al. 1980; Dabelsteen and Pedersen 1990; Lampe 1991; Rehsteiner et al. 1998; Poesel and Dabelsteen 2006; Anderson et al. 2008b). All songbirds learn the fine details of their species-specific song by listening to adult tutors, practicing the production of complex notes and note syntax, and crystallizing their songs at some point in early adulthood. Species differ greatly in when they learn, from whom they learn, and the degree to which they copy whole songs from other adults or innovate unique notes and song structures (Beecher and Brenowitz 2005; Brenowitz and Beecher 2005). In this Web Topics unit we discuss how birds (usually, but not always, the males) use their song types and other variable aspects of song structure and delivery pattern to make words and phrases that enable them to negotiate boundary disputes.

Variable song features and singing strategies

Male birds sing to attract mates as well as to defend territories. Females seek high-quality males that directly or indirectly maximize their fitness. As receivers, they compare males based on their signals and exert selective pressures on those aspects of singing behavior that reveal important differences in male health, genetic quality, and territory quality. Song traits preferred by females include high song rates or duty cycles, large or complex repertoires, high performance of difficult note structures, and songs of local, as opposed to foreign, population origin (Searcy and Nowicki 2005). Male receivers exert different selective pressures on singing behavior (Cardoso et al. 2007). Territorial rivals not only need information about relatively static male traits such as fighting ability and experience, but they also need to assess dynamic information about current motivation and valuation of particular patches of real estate. Thus song systems for territorial defense are designed to facilitate countersinging interactions: songs are relatively short and discrete and separated by silent gaps for listening to responses, repertoire sizes are small to intermediate, and the age window for learning may be timed so that males can acquire at least some song types that they share with their territorial neighbors. Short-term temporal patterns of song type delivery with respect to the neighbor’s singing are the key to assessment of relative motivation and negotiation of boundary locations (Todt and Naguib 2000; Vehrencamp et al. 2014).

Table 1 shows a list of the key singing strategies and song traits observed in songbirds. The table indicates whether the traits mainly vary between or within males; in some cases a trait may vary at both levels. While strategies such as song-type switching and matching obviously require males to possess song-type repertoires, others can be employed by species with a single song type. Also shown are the likely assignments of these song traits to categories of signals based on honesty-guaranteeing cost. Some of these features may be index signals associated with male age (repertoire size, song performance) (Mountjoy and Lemon 1995; Gil et al. 2001; Garamszegi et al. 2005; Forstmeier et al. 2006; Kiefer et al. 2006; Garamszegi et al. 2007; Nicholson et al. 2007; de Kort et al. 2009b), dominance (Christie et al. 2004; Botero et al. 2009; Vehrencamp et al. 2011), or local origin (song-type sharing with neighbors) (Wilson et al. 2000; Wilson and Vehrencamp 2001). Others are likely handicap signals of condition or need (song rate, song duration, amplitude, note structure and performance) (Ritchison 1988; Alatalo et al. 1990; Rehsteiner et al. 1998; Martin-Vivaldi et al. 1999; Bower 2005). Matching, overlapping, switching, and short-term diversity are probably conventional signals of aggressive or submissive motivation (Vehrencamp 2000). Switching rate was hypothesized to be a trait constrained by exhaustion, placing it in the category of a handicap or index signal of male quality. However, this idea has not been supported by recent evidence, and motivation appears to be the more likely explanation (Brumm et al. 2009). Soft song has been studied in several species and found to be strongly correlated with subsequent aggressive behavior, especially attack behavior when a taxidermic mount is presented to the territorial male (Searcy et al. 2006; Anderson et al. 2007; Laidre and Vehrencamp 2008; Ballentine et al. 2008; Anderson et al. 2008b; Hof and Hazlett 2010; Akçay et al. 2011). Most authors argue that such songs can only be detected when close to the receiver, so delivery of this signal comes with a proximity risk and we classify this singing style as a proximity signal.

Table 1: Variable song features of songbirds. Features may vary within and/or between males. Categories based on type of honesty-guaranteeing cost: C = conventional, I = index, H = handicap (quality or need), P = proximity.

Different species make use of a subset of these singing strategies, in combination with calls and/or visual displays, to form a graded system of aggressive escalation. Below we describe the escalation rules for four well-studied species.

Great tit (Parus major)

Great tit males have small repertoires of 1–8 song types. On average they share one song type with a given neighbor. Songs consist of two- or three-element phrases that are repeated a variable number of times to create songs (called strophes) of different duration. Figure 1 shows an example. The same song type is sung repeatedly for long periods of time before switching to another type, called the “eventual variety” mode of singing by repertoire species. The birds appear to be open-ended learners, as they can add new song types, and may increase or change their repertoire in response to stimulation from playback or new neighbors (Franco and Slabbekoorn 2009).

Figure 1: A series of song strophes by a male great tit. The number of times an element is repeated determines the duration of the song, which can be varied strategically during countersinging contests. (Photo courtesy of Danny Gibson; spectrograms from recordings provided by Greg Budney.)

The key variable song features used during countersinging interactions are song duration, overlapping, and matching. In escalated contests, a male first challenges a target neighbor by singing a shared song type. The neighbor may then respond by also singing this song type. Matching by senders is considered an aggressive intention signal, as the sender follows it with an aggressive approach response (Krebs et al. 1981). Overlapping also occurs in the early stages of a countersinging interaction when the birds are some distance apart (Dabelsteen et al. 1996; Langemann et al. 2000). When overlapped repeatedly, males sometimes shorten their song so that they can reverse the pattern and become the overlapper. At this point, variation in song duration becomes the mechanism of negotiation. Longer songs appear to be more threatening, and males that increase their song duration relative to the rival are subsequently more likely to approach the sound source (Lambrechts and Dhondt 1987; McGregor and Horn 1992; Amy et al. 2010). In other cases, males change their song duration in the opposite direction to the rival or playback, increasing duration when the rival decreases duration and vice versa. Matching is thus a necessary first step in these duration and overlapping contests, as the two birds must be singing the same song type with the same phrase duration to adequately match each other’s song duration and delay between song starts (McGregor et al. 1992). Figure 2 shows some basic rules of escalation for the great tit.

Figure 2: Stages of escalation in great tit countersinging contests. Each square represents a song element, several of which are combined to make a strophe or “song.” Song duration is determined by the number of times an element is repeated without pausing. Great tits escalate by first singing the same song type, and then increase song duration, followed by occasional overlapping. (After Langemann et al. 2000.)

Male great tits that are dominant in winter flocks sing longer songs on average than subordinates, and show less “positive drift” in the successive intervals between phrases in a song. Dominant males are more likely to respond to playback of long songs by increasing their own song duration, whereas subordinate males decrease their song duration (Lambrechts and Dhondt 1987). Moreover, the consistency of element frequency within strophes increases with age, and playback of more consistent songs elicits a stronger aggressive response compared to playback of less consistent songs (Rivera-Gutierrez et al. 2010, 2011). Dominant males also have wider black breast stripes (Järvi and Bakken 1984). These acoustic and plumage signal features are correlated with other measures of male quality such as survivorship and reproductive success (Lambrechts and Dhondt 1986; Rivera-Gutierrez et al. 2010).

Black-capped chickadee (Poecile atricapillus)

In the black-capped chickadee, a relative of the great tit, males possess a single song type consisting of a two-note whistle (fee-bee), but the entire song can be shifted up or down in absolute frequency to produce a continuous range of “frequency types.” Countersinging males employ two short-term singing features: overlapping and frequency matching (Figure 3).

Figure 3: Overlapping and frequency matching in black-capped chickadees. The two song features can be varied independently, as illustrated in the factorial design of a playback experiment shown here. White and black traces correspond to songs of different rival males. Territory owners subjected to these four interactive playback treatments inside their territories responded with very close approaches in all cases, but interrupted their singing more when overlapped by playback, and were more agitated when frequency-matched by playback. (From Mennill and Ratcliffe 2004. Photo courtesy of Dan Mennill.)

Observations of naturally occurring interactions recorded with a microphone array system revealed that overlapping is very common during contests (at least one instance of overlapping in 80% of contests) but not associated with closer approach. Frequency matching is less common (37% of contests), generally preceded by overlapping, and somewhat more frequent in contests where the rivals approached each other. Responses of receivers to different playback treatments generally show stronger responses and greater agitation to frequency matching than to overlapping. Thus overlapping and matching form a graded system of escalation, with matching associated with higher levels of escalation (Shackleton and Ratcliffe 1994; Otter et al. 2002; Mennill and Ratcliffe 2004; Fitzsimmons et al. 2008; Foote et al. 2008).

Chickadees form winter flocks with a dominance hierarchy, and dominance status in the prior winter’s flock affects some aspects of singing behavior and responses to playback (Mennill and Ratcliffe 2004; Ratcliffe et al. 2007). Dominance status is signaled by the brightness of the white head patch and song fine-structure: dominant males can maintain the same frequency ratio between the fee and bee notes when shifting absolute song frequency, whereas subordinate males exhibit a smaller frequency ratio when shifting to a higher absolute frequency (Christie et al. 2004; Doucet et al. 2005).

Song sparrow (Melospiza melodia)

Song sparrows are widespread throughout North America and subdivided into 34 morphological subspecies (Zink and Dittmann 1993). Males typically possess repertoires of about 8–10 discrete song types delivered repetitively in eventual variety mode. Song-type sharing varies among subspecies and populations. Males in some western subspecies are sedentary and share on average 20–40% of their repertoires, but for any two neighbors this value can range from 0 to 90% (Hill et al. 1999; Wilson et al. 2000). Song learning extends into the spring of a young male’s first year of life, when he has an opportunity to eavesdrop on singing neighbors, but the repertoire crystallizes after that point (Nordby et al. 2001, 2002; Burt et al. 2007; Nordby et al. 2007; Nulty et al. 2010). Migratory and eastern populations generally show very low song sharing, but a Nova Scotia population with notably high site fidelity by returning migratory males exhibits moderate song sharing levels similar to western populations (Hughes et al. 1998; Foote and Barber 2007). For the well-studied western populations with moderate song sharing, song matching is an important signal pattern (Figure 4). Song rate and switching rate may be more important in migratory eastern populations (Kramer and Lemon 1983; Kramer et al. 1985; Searcy et al. 2000; Anderson et al. 2008a). All populations appear to use soft song and wing-waving as close-distance aggressive intention signals (Anderson et al. 2008b).

Figure 4: Some shared song types between neighboring song sparrows. A singing male song sparrow from the southern California subspecies Melospiza melodia cooperi and examples of shared song types from this population. Each row shows a pair of song types shared by different sets of neighbors. Note that songs on the top row are not exactly identical, but the songs on the second and third rows show closely matched song structures. (After Wilson and Vehrencamp 2001. Photo courtesy of David Y. Allen.)

For song-sharing populations, type matching is an aggressive signal that predicts subsequent approach and elicits a strong aggressive approach response in receivers (Nielsen and Vehrencamp 1995; Beecher et al. 2000a; Burt et al. 2001; Vehrencamp 2001). Singing a non-matching but shared song type in the vicinity of a known neighbor, called repertoire matching, is considered a directed challenge but is less threatening than a type match (Beecher et al. 1996). At any point during an interaction, a bird may de-escalate the encounter by singing an unshared song type, which cannot be matched by the rival (Beecher and Campbell 2005). Rules of escalation are summarized in Figure 5. Birds initially challenge a known male neighbor by singing a song they share with that individual. The rival may then escalate by singing this same song type, remain neutral but engaged by singing a different shared song, or de-escalate by singing an unshared type. The first bird can then decide whether to continue type matching and persist with an aggressive approach, or switch to a different song type (Burt and Beecher 2008).

Figure 5: Escalation rules for neighboring song-sharing song sparrows. Behaviors by initiating male in green boxes, behaviors by target neighbor in purple boxes; red and blue arrows show escalating and de-escalating acts. Challenger begins by singing a shared song type, and target can respond by type matching, repertoire matching, or singing an unshared song type, which would end the interaction. If target type matches, challenger could escalate by staying on type match or de-escalate by switching to a different type. If both birds are type matching, target bird could escalate further by approaching and singing soft song, or de-escalate by singing a shared or unshared type. If target has approached with soft song, challenger could hold his ground and also sing soft song, which would likely result in the target attacking, or challenger could retreat. (After Searcy and Beecher 2009.)

Some males share no song types with one or more of their neighbors, and thus they are unable to make use of these matching strategies to negotiate boundaries. Their only option is to use the songs in their repertoire that contain some similar elements to the rival’s current song, especially similar introductory notes (Burt et al. 2002). Such partial matching appears to be less effective than whole song-type matching. In song-sharing populations, males that shared few or no songs with their neighbors had lower territory tenure than males that shared 2 or more song types (Beecher et al. 2000b; Wilson et al. 2000). Moreover, non-sharers had more frequent and more intense aggressive interactions with their neighbors compared to neighbors that shared several song types (Wilson and Vehrencamp 2001). Because song sparrows are age-restricted learners and cannot learn new songs after about six to nine months of age, non-sharers are generally individuals who were unable to acquire territories close to their tutors and dispersed farther away from their natal area (Nordby et al. 1999, 2002). Non-sharers may thus be less dominant birds, who must fight more intensely to gain a territory and suffer higher mortality as a result (Wilson et al. 2000). In eastern non-sharing populations, males will also sometimes reply to playback with a song type that is similar to the playback song (Anderson et al. 2005; Searcy et al. 2006). Birds that did give partial match replies approached the speaker more aggressively than those that did not match, indicating that even in these populations with little whole-song sharing, partial matching has some salience as a signal of aggressive intentions.

Banded wren (Thryothorus pleurostictus)

Males in this sedentary Neotropical species possess repertoires of 18–26 song types, 75% of which are typically shared with any given neighbor (range: 50–90%) (Molles and Vehrencamp 1999). Males can switch rapidly among song types in an immediate variety mode, or they can deliver the same song type repeatedly for a variable length of time. Variable song features used by this species include switching rate, song-type diversity, song matching, overlapping, trill note consistency, and trill performance (trade-off between frequency bandwidth and trill note rate). Most song types possess a terminal trill; trill types vary in their performance score (Figure 6).

Figure 6: Banded wren. Male working on the construction of his nest, a woven covered structure usually located in an ant acacia tree. Nine song types are illustrated here. Each song type has an introductory part consisting of various frequency sweeps and alternating notes, followed by a prominent and loud trill, and usually ending with a whip note. Trills vary in frequency bandwidth and note rate. Six of the song types contain a rattle or buzz element in the introductory part. (Song types after Trillo and Vehrencamp 2005. Photo courtesy of John Burt.)

Banded wrens use similar matching rules as described above for the song sparrow, using shared song types to initiate and continue an interaction, type matching for escalation, and unshared song types for de-escalation. But they add another layer of complexity on their song system with variation in switching rate and short-term diversity (Vehrencamp et al. 2014). Figure 7 below illustrates an example of a fairly lengthy countersinging interaction between two adjacent territorial males.

Figure 7: Countersinging interaction between two neighboring banded wren males (Male D in red, male J in green). Shared song types are shown in the white area, and unique song types for each male are shown in colored areas. Time sequence is depicted on the X axis. The birds began the interaction from the centers of their territories, each using a different subset of their shared song types (repertoire matching), but occasionally one bird type matched the other. At about song 45, male D sang a song type repetitively and the males approached their common boundary. At several points, male J delivered unshared song types. At song 65 they came even closer together and D sang another song type repeatedly, which J eventually started to type match repeatedly. The birds retreated without a fight in this instance. (After Molles 2006.)

In a follow-up study, many such interactions between neighboring males were analyzed to determine the general singing rules for escalating and de-escalating a countersinging contest. The results are summarized in a flow diagram (Figure 8) similar to the one presented earlier for song sparrows. Contests typically begin with rapid switching among a subset of shared song types and the use of rattle-buzz song types by the initiator (see Figure 6; rattles and buzzes are similar structurally to the alarm and aggressive calls given by these birds). If the neighbor approaches and responds with singing, he may overlap and match the initiator and negotiation begins, in which the birds compare each other’s song-type diversity. Aggressive motivation is signaled by more repetitive singing and lower song-type diversity. Either bird can de-escalate by keeping song diversity high, using unshared song types, and/or overlapping the other bird’s songs, as also demonstrated in playback studies (Molles and Vehrencamp 2001; Molles 2006; Hall et al. 2006; Vehrencamp et al. 2007). Males can also use song types with different structural features in different contexts. For example, they use songs with high-performance broadband trills during the dawn chorus and during countersinging interactions (Trillo and Vehrencamp 2005). Playback of song with high values of these trill features often cause receivers to remain farther from the speaker, even when the playback is performed in the center of the territory (Illes et al. 2006; de Kort et al. 2009a; de Kort et al. 2009b).

Figure 8: A flow diagram of escalation rules in the banded wren; time flows from left to right. The initiator’s actions are shown in blue boxes alternating with the responder’s actions in orange, and decisions to escalate or de-escalate are shown with green or red arrows, respectively. If both birds approach their boundary, they engage in a negotiation using higher or lower song type diversity and switching rates. A retreating bird may use unshared songs, overlapping, and high diversity singing. A persistent aggressor eventually stops singing and begins to utter aggressive calls, called grunting, and both birds may commence grunting if neither one retreats. A fight or chase may occur at that point. The defender signals he will hold his ground with highly repetitive singing, while the bird that backs off may resume singing with high diversity. (After Vehrencamp et al. 2014.)

Summaries of playback studies on matching, overlapping, switching, and performance

The signal value of different singing behaviors during male–male contests has been examined in a variety of songbird species using sound playback and observational techniques. Territorial birds are easy subjects for playback experiments because their movements are restricted to their territorial boundaries, and their individual histories (age, repertoire composition, song structure, mating success, reproductive behavior, etc.) are known if the study population has been individually color-marked. With the development of interactive playback methodologies in particular, researchers can finally examine the effects of matching, overlapping, and switching treatments on the responses of owners. In order to determine the signal value and function of some pattern of singing, three types of evidence should be examined (Vehrencamp et al. 2007): (1) the singing pattern should be given by senders in some contexts and not others, or by senders having a particular condition, status, age, or breeding stage. This information helps to establish whether the signal is given in aggressive contexts, or by more dominant birds, or by birds in better condition; (2) delivery of different singing patterns should predict or be associated with different subsequent behaviors by the sender. Signals that precede subsequent aggressive approach behavior would be classified as threat signals, whereas signals that precede retreat behavior would be classified as submissive or defensive signals; and (3) receivers of different singing patterns should respond differently. On-territory playback studies simulate the invasion of the territory by a potential rival male, and measuring the acoustic and spatial responses can help us interpret the likely function of the singing strategy. But such interpretations of responses are beset by the problem of the “peaked curve” of response strength versus signal intensity, in which low responses to a treatment are sometimes interpreted as a less threatening stimulus and sometimes interpreted as aversion to a highly threatening stimulus (see main text Figure 11.28). Details of the experimental protocol can also affect the results and interpretation—playbacks situated in the center of the territory generally elicit much stronger responses than playbacks situated on or outside the boundary. Treatments involving conventional signals may give different results from treatments involving index or handicap signals. Nevertheless, all three types of evidence should be combined to draw a consistent picture of the function of the singing pattern and its signal value. A detailed review of singing patterns by Searcy and Beecher (2009) using this approach provides a welcome assessment of the functions of song type matching, frequency matching, overlapping, low-amplitude song, song type switching, and vocal performance, and the interested reader should consult that source. In the sections below, we briefly summarize the results of playback experiments that investigated matching, overlapping, switching, and song performance, focusing in particular on playback studies that examined both the sender’s subsequent behavior after delivering certain signal variants and the receiver’s responses to these variants, i.e., points 2 and 3 above. Separate, differently designed experiments are usually required to assess these two points.

SONG MATCHING In songbird species with repertoires of learned song types or continuously varying song pitch, the birds in a neighborhood typically share at least some types with their neighbors. During countersinging interactions with a given neighbor, the particular song types shared with a that neighbor are used selectively, and matching rates typically increase above chance levels (Lemon 1968; Krebs et al. 1981; Schroeder and Wiley 1983; Falls 1985; Stoddard et al. 1992; Shackleton and Ratcliffe 1994; Beecher et al. 1996; Duguay and Ritchison 1998; Beecher et al. 2000a; Rogers 2004; Trillo and Vehrencamp 2005; Burt and Vehrencamp 2005; Rogers et al. 2006; van Dongen 2006). When a vocalizing individual hears another individual reply to its current song with a matching type, it can be relatively certain that the responder is attempting to grab its attention. Matching is an obvious way to acoustically point toward another individual in a network of individuals giving omnidirectional signals. Matching may also enable the birds to compare each other's performance skill, as proposed by Logue and Forstmeier (2008). Call or song matching has an affiliative function in some cases, such as coordinating nest visits between mated pairs or establishing contact in fission–fusion societies, but in male–male territorial interactions it typically serves an aggressive “challenge” function. In order for matching to evolve into a threat signal, senders must reliably follow a match with an increased display of aggression, such as approach, and receivers that are strong, dominant, and/or motivated must respond aggressively to impose a retaliation cost on potential buffers. If the threat is effective, truly weak or unmotivated receivers should retreat.

Table 2 summarizes playback studies of matching in species that have been examined from both the sender and receiver perspective. Experiments to assess sender perspective require broadcasting song types that the subject bird has in its own repertoire, to evaluate the relationship between its probability or rate of matching and its approach behavior. In all species shown in this table, if senders matched a playback stimulus, they were subsequently more likely to approach the playback speaker, regardless of where the speaker was located. Deeper analysis of banded wren and song sparrow responses showed that matching birds nearly always approached, but that some birds approached without first matching. Experiments to assess the receiver perspective necessarily involve interactive playback experiments that immediately match or do not match the subject’s songs. Among studies using this method, some found the predicted stronger approach when subjects were matched compared to when they were not matched, but others found no difference between treatments. A key protocol feature that differentiates these studies with these two outcomes is the stimulus source and playback location: studies showing stronger approach when matched employed neighbor song stimuli from an appropriate boundary location, whereas studies showing no difference employed stranger song stimuli from the territory center. These latter studies found extremely close approach and high levels of agitation to both treatments, suggesting a ceiling effect. Given that aggressive birds sometimes approach without matching first, this undifferentiated strong response to playback in the center of the territory is not surprising. Taken together, these results suggest that matching is a conventional threat signal that operates primarily between neighbors who know each other’s repertoires and facilitates the usually respectful “dear enemy” relationship. Searcy and Beecher (2009) conclude that type matching is lower level aggressive signal that may predict an increasing level of escalation but not attack, what we have called a challenge signal.

Table 2: Summary of experiments on song and frequency matching. Strength of sender aggressive behavior associated with matching or non-matching vocalizations during playback, and strength of receiver aggressive behavior in response to matching and non-matching interactive playback. Treatments: TM = type match, PM = partial match, FM = frequency match, RM = repertoire match, NM = nonmatch. Stimulus source: N = neighbor, S = stranger. Playback location: B = boundary, C = center.

SONG-TYPE SWITCHING Even birds with small song-type repertoires can vary the rate of switching between song types. Switching rate is measured as the number of switches per opportunity to switch (Searcy et al. 2000). Earlier adaptive hypotheses for the function of switching among song types included reducing habituation (Falls and Dagincourt 1982), deceiving intruders about the number of birds present (Krebs 1977), and reducing fatigue of the vocal muscles (Lambrechts and Dhondt 1988). These hypotheses have since been thoroughly tested and found to be insignificant (Yasukawa 1981; Dawson and Jenkins 1983; Yasukawa and Searcy 1985; Haftorn 1995; Brumm et al. 2009). Instead, evidence is accumulating that various switching strategies function as agonistic signals between countersinging males. Switching in bout singers can be synchronized with a countersinging rival’s switch to produce an acoustic pointing signal (Kramer and Lemon 1983; Horn and Falls 1991). The rate of change to new song types can vary continuously to form a graded signal (Kramer et al. 1985; Horn and Falls 1991; Molles and Vehrencamp 1999). Switching rate appears to be a truly conventional signal, in the sense that either a low or high switching rate can represent the more threatening signal variant depending on the species. Species that normally deliver song types in bouts (eventual variety) typically increase their switching rate in more aggressive contexts, and species that normally switch after every song (immediate variety) typically decrease their switching rate in more aggressive contexts (Vehrencamp 2000; Collins 2004). The red-winged blackbird is an exception; it is an eventual variety singer that reduces switching rate when confronted with a live male rival.

Few species have been the subject of both sender and receiver perspective playback experiments for switching patterns (Table 3). Song sparrows are bout singers that increase their switching rate in more aggressive contexts, and respond more aggressively to higher switching-rate playback, but there is no evidence that a high switching rate predicts subsequent approach. Ortolan buntings are also bout singers that increase their switching rate in more aggressive contexts; but young males respond less aggressively to high switching rate playback as if they are intimidated, whereas older birds respond aggressively to both switching treatments. As mentioned earlier, banded wrens are immediate variety singers that reduce their switching rate in more aggressive contexts. They respond more aggressively to low switching-rate playback. Low switching predicts aggressive behavior in some situations (males with fledglings). In countersinging interactions, repetitive singing occurs in the later stages of escalation when birds are close, but seems to indicate unwillingness to negotiate further with song switching and matching; it is also a victory signal by the winner of a close encounter.

Table 3: Summary of experiments on switching rate. Strength of sender and receiver aggressive responses to different switching rates. Singing mode: E = eventual variety, I = immediate variety. H = high switching rate, L = low switching rate. Stimulus sources: N = neighbor, S = stranger, L = live male. Playback location: C = center, B = boundary. Parentheses indicate evidence from other types of experiments or observations of natural encounters.

^a Receiver responses measured for older (2+ years) and younger (1 year) territory owners.
^b Treatments varied within-song and between-song switching rates in a factorial design.

SONG OVERLAPPING A repertoire of song types is not required for countersinging birds to use overlapping as an agonistic signal. In the first studies of song overlapping using European robins, European blackbirds, and nightingales, overlapping seemed to be an aggressive signal. These species appeared to overlap in more aggressive contexts. Robins and nightingales responded more aggressively to being overlapped, but blackbirds avoided song posts from which overlapping songs were played. More recent studies on other species have lead to a rather mixed picture about overlapping. While overlapping was initially believed to be an aggressive signal in great tits, intensive escalating playback on this species found that birds were more likely to overlap from a distance than when close. Studies on the black-capped chickadee ultimately found no particular evidence for overlapping as an aggressive or defensive strategy, but it may serve a pointing function and predict the next stage of escalation: frequency matching. Interactive studies on the corn bunting, yellowhammer, and banded wren all found an aversive response to being overlapped. This result was interpreted as overlapping being an intimidating aggressive signal. However, a sender-perspective study in the banded wren showed that overlapping by senders predicted their subsequent retreat, suggesting that overlapping instead might be a defensive threat signal, like a jamming signal in electric fish.

Searcy and Beecher (2009) concluded that there is little evidence of overlapping as an aggressive signal, largely because most positive results of increased overlapping by senders in more aggressive contexts can be accounted for by an increase in song rate and chance overlapping. Naguib and Mennill (2010) countered this view by arguing that despite the tendency for most birds to avoid overlapping or being overlapped, rare overlapping events could still be meaningful signals; moreover, many studies have found differential responses to different overlapping treatments. Eavesdropping experiments have been particularly informative. In these experiments, two speakers simulate overlapping and overlapped birds in earshot of a territorial subject. The subject often responds by showing more aggressive behavior toward the overlapping stimulus speaker. Searcy and Beecher (2011) countered again that most responses to being overlapped are interruption or shortening of the current song, which is a natural response by a vocalizing animal and not necessarily indicative of aggression. It is likely that overlapping may serve different functions in different species, aggressive in some cases, defensive in others, and not a signal in yet others. More studies are needed that examine overlapping and approach from both the sender and receiver perspective, making sure to correct for chance levels of overlapping as recommended by Searcy and Beecher (2009).

Table 4: Summary of overlapping experiments. Strength of sender and receiver responses to overlapping (O) and alternating (A) songs.

VOCAL PERFORMANCE Vocal performance includes various measures of note fine structure, such as note shape, repeated-note consistency, repeated-note drift, maximum or minimum pitch, and trill performance (bandwidth and note rate tradeoff) (see review by Podos et al. 2009). These song features usually vary within males on a slower time scale than matching, switching, and overlapping, and often differ among males as a function of age and condition (Janicke et al. 2008; Araya-Ajoy et al. 2009; Ballentine 2009; de Kort et al. 2009a). Several studies have demonstrated female preferences for high-performance songs (Vallet et al. 1998; Forstmeier et al. 2002; Ballentine et al. 2004; Cardoso et al. 2007; Holvek et al. 2008; Byers et al. 2010; Cramer et al. 2011). Thus song performance is likely to be an index signal of male age, experience, dominance, or general quality (Searcy and Beecher 2009). Nevertheless, males can choose to deliver higher performance songs in aggressive contexts, and in some cases may increase the vocal performance of a given song type in aggressive contexts (Trillo and Vehrencamp 2005; Kunc et al. 2006; Price et al. 2006; DuBois et al. 2009). Only a few playback studies have investigated the role of these features in male–male interactions. Most results indicate significant avoidance of high performance song playback, even by territorial males stimulated by playback in the center of their territory. In banded wrens, three performance level treatments were given and responses showed a peaked response for the middle level. In the nightingale, less successful males were intimated while more successful males behaved more aggressively toward the high-performance stimulus. Swamp sparrows responded more aggressively towards the higher performance stimulus.

Table 5: Summary of song performance experiments. Strength of aggressive response to high (H) versus low (L) performance songs. Song feature associated with older or more successful males. All playback experiments conducted in the center of the territory using stranger or modified song stimuli.

Species	Song feature	Sender age or quality	Receiver aggressive behavior	Ref
Nightingale	Trill bandwidth	H > L	L < H (successful males) L > H (unsuccessful males)	Schmidt et al. 2008
Redwinged blackbird	Trill bandwidth	H > L	L > H	Cramer and Price 2007
Banded wren	Trill bandwidth	H > L	L < M > H	Illes et al. 2006; de Kort et al. 2009b
	Trill consistency	H > L	L > H	de Kort et al. 2009a
Swamp sparrow	Trill bandwidth	H > L	H > L	DuBois et al. 2011

In conclusion, the variable song and singing features of bird song can signal a wide range of different types of information to rival males negotiating territorial boundaries, including: motivation to approach, attack, defend, and retreat; fighting ability, age, and experience; dominance and subordinance; current condition; and pairing status. These variable parameters can be considered “signals,” and can often be classified by their honesty-guaranteeing cost into handicap, index, conventional, and proximity signals. Species differ in their mix of variable parameters, and functions for the same signaling parameter may differ between species. Despite the tremendous progress in decoding the song systems of numerous species, much fieldwork remains to be done to verify the true function of some song signals.

For a game theoretic model of territory negotiation using a graded signal to indicate aggressive motivation, see Vehrencamp et al. 2014.

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