Chapter 14 Web Topics

14.1 Models for Environmental Signaling


Nearly all of the interactions between individuals discussed in Chapter 14 can be modeled with evolutionary game theory. It is instructive both for understanding the specific interactions and for getting a broader feel for game theoretical modeling to deconstruct the basic logic and outcomes of some of these models. We do not cover all the models cited in Chapter 14: those applicable to the evolution of crypsis, aposematism, and mimicry have been nicely reviewed elsewhere (Ruxton et al. 2004; Mappes et al. 2005; Skelhorn et al. 2010). However, the examples below provide a broad sampling of ESS approaches. They are presented in the order encountered in Chapter 14, and we classify the types of format used according to the schema outlined in Web Topic 10.5.

Predator notification (Bergstrom and Lachmann 2001)

The Question: When does it pay for a prey animal to notify a predator that it has been detected, and when does it pay for the predator to attend to such notification signals?

Background: If predators were to attend to such signals, what would keep a prey from giving the signal whether it has spotted a predator or not? In that case, predators would do better to ignore the signal and then there would be no selection for the prey to give it. There is clearly a conflict of interest between the two parties and some honesty guarantee will be required for communication to be favored. In this model the proposed cost that insures honesty is the risk that giving the signal will reveal the presence of the prey to a predator that had not yet detected it.

Game Format:

The game is obviously asymmetric (prey versus predator).

  • The model is based on discrete alternative strategies (prey: signal or don’t; predator: chase prey or don’t).
  • It is a single-shot model analyzed in extensive form with successive branch points: nature decides whether a predator is near a prey or not, the prey then decides whether to signal or not, and the predator (if present) then decides whether to chase or not.
  • Payoffs at the terminus of each tree branch are fixed (a contest).

Special Assumptions: Only a single prey is considered; this excludes alarm signaling to conspecifics and relative vulnerabilities of multiple prey as factors. The model also excludes signals that indicate prey unsuitability for reasons other than predator detection (e.g., aposematism or relative escape abilities).


  • Prey are exposed to stimuli that may or may not be generated by a nearby predator. They then use Bayesian updating to combine prior probabilities of predator presence with the conditional probabilities of perceiving these stimuli to generate an updated probability that a predator is present.
  • Prey can also estimate the risk of capture given the current context and likely predator. The product of this risk and the updated probability that a predator is present provides an overall measure of predation risk. Different stimuli and different occasions result in different overall risks.
  • Emitting a predator detection signal costs a prey by increasing its risk of detection by other predators. Prey should only emit the signal if these signal costs are less than the appropriately scaled overall risk of capture. For a fixed average cost, this defines a threshold stimulus level below which no signals should be emitted and above which they should.
  • The predator’s payoff depends on the probability of capturing a prey minus appropriately scaled costs of a chase.
  • The analysis sought equilibrium (ESS) strategies in which prey only signal if stimuli exceed the threshold, and predators avoid chasing prey that so signal. ESSs only exist if prey that estimate high overall risk (implying a predator is almost surely present) can use this information to reduce their risk of capture. That is, detecting a predator early in its hunt helps a prey to escape a subsequent chase. A related requirement is that prey that are exposed to stimuli below the threshold do not signal. If met, these conditions generate an ESS in which emission of a predator detection signal is relatively “honest” and thus valuable to both parties.
  • Two specific contexts were considered: in one case, predators always chased prey that did not signal. In the other, predators did not pursue prey until at least some signaled so that they could focus on the ones that did not.


The analysis for both contexts showed that predator detection signals are only likely to be honest if there is a cost to senders (in this case, the risk of attracting other predators). In addition, the benefit to prey of predator detection signals only accrue if a prey is relatively sure that a predator is present, and if this knowledge improves the prey’s chances of escaping if chased. This means that animals that cannot reduce their risks even if they detect a predator early (e.g., sessile or poorly mobile species, animals far from refuges, etc.) should not bother to give predator detection signals. The model also predicts that the threshold for giving predator detection signals should decrease when predators are more common, and the minimal cost that guarantees sender honesty can be smaller if the costs of pursuit to predators are higher.

Related Models:

  • Getty (2002) expanded on this model by noting that the prey face a signal detection problem in which each seeks to minimize costly false alarms; at the same time, the predator faces an optimal diet problem. Getty computed the relevant “red line” that the prey should adopt along the predator stimulus axis given a signal detection analysis. He also considers what happens when predators have alternative prey to pursue.
  • This model only considered a single prey animal. When multiple prey are present, a variety of consequences follow. Those relating to relative vulnerabilities are outlined in the models presented below. However, the simplest change is that instead of giving predator notification signals independently, a group of prey does so in concert. This usually takes the form of group predator inspection behavior. A relevant model for this tactic can be found in Dugatkin and Godin (1992).
  • A number of other models consider predator notification signals for other reasons. Readers may want to compare the above model to those in which prey signal to predators honest indications of their physical condition, stamina, palatability, or agility (Nur and Hasson 1984; Hasson 1991; Vega-Redondo and Hasson 1993; Maynard Smith and Harper 2003; Ruxton et al. 2004; Searcy and Nowicki 2005).

Vigilance behaviors (Sirot and Touzalin 2009)

The Question: What is the ESS level of vigilance in a foraging group if vigilant individuals are more likely to survive a predator attack than foraging individuals?

Background: Prey that are vigilant when a predator appears or attacks can often escape sooner and more effectively than prey that are foraging. This is because vigilant prey spot a predator first, know where it is, and thus know which direction would move them away from it. Foragers may only flee after vigilant animals have fled or given alarms, and then have no idea where the predator is. Given these differences, the risk to foragers increases as more and more members of their group become vigilant; the risk to vigilant animals decreases as more and more group members forage. The best strategy for escaping predation is always to be vigilant; however, the animal will then die of starvation. Is there an average level of vigilance which if adopted by all in the group optimizes the tradeoff between predation and starvation risks?

Game Format:

  • The strategy set is the fraction of time an individual spends being vigilant instead of foraging. It is thus continuous.
  • The game is a scramble because the payoff of adopting a given strategy depends on the mix of strategies adopted by a defined circle of neighbors.
  • Although relative location in a group may affect optimal strategy, all individuals in the same neighborhood begin the game with otherwise similar properties. The game is thus symmetric.

Special Assumptions: The game is spatially explicit; payoffs depend on abundances of different strategies adopted by local neighbors of a focal animal, not by the population as a whole. The game is played on cellular automoton grids such that each animal (at a node) has a fixed number of surrounding neighbors with which it shares predator detection ranges, alarms, and attack vulnerabilities. No coordination of vigilance based on mutualism, reciprocity, kin selection, or other cooperative economics is included in this game. Each animal just does what is best for itself (although noting what neighbors are doing is a key part of that process).


  • Prey animals need to acquire new energy through foraging and avoid being killed by predators. Vigilance is assumed to be incompatible with foraging and vice versa. There is thus a tradeoff in how to allocate actions.
  • The payoff currency in this model is the amount of energy reserves attained at the end of the game. This depends on how fast energy can be obtained when foraging and lost when not foraging, and the fraction of time that was spent foraging instead of being vigilant. The potential final reserves are then discounted by the probability of having survived all predator attacks.
  • Mortality risks due to a predator’s attack are varied along two axes. The first axis is the ratio between vigilant and foraging animal vulnerabilities: at one extreme, vigilant animals are never killed if there is at least one foraging animal in an attacked group; at the other extreme, vigilant and foraging group members have identical risks. The second axis is related to who, if anyone, first spots an approaching predator: risk is assumed to be least for an animal spotting and responding to an approaching predator, somewhat higher for animals who do not first spot the predator but are secondarily alerted by another member’s predator detection and response, and highest if nobody in the group spots the approaching predator.
  • Two models are considered. The first (static) model looked for the ESS average fraction of time that each individual in the group should be vigilant given its position in the group, its initial energy reserves, and the current probability of predator attacks. The second (dynamic) model acknowledges that different animals may elect to be vigilant at different times, thus making the number of vigilant neighbors a stochastic variable. The second model allows a focal animal to track these unpredictable variations and adjust its own vigilance accordingly.
  • The static model sought an overall ESS in which each group member adopted an average fraction of time spent vigilant that was optimal given their position in the group and the fractions adopted by other members in the group. At this mix of fractions, nobody benefited by adopting a different average fraction. These equilibria could not be identified analytically, but were identified for each set of initial conditions using asymptotic iterations. Of major interest was how ESS mixtures of fractions changed depending upon initial reserves at the start of the game, group size, and different relative vulnerabilities for foraging and vigilant group members.
  • The second model focused on a fixed number of relevant neighbors (12) and a fixed value for initial reserves, and played the cellular automaton game on a torus to eliminate world boundary effects. The optimal (ESS) fraction of time vigilant was computed using the equations for the first model and plotted against successively greater fractions of the group being vigilant. Equilibria occurred whenever the ESS fraction for an individual equaled the fraction of the group that was currently vigilant (using a method called rational reaction sets [Simaan and Cruz 1973]). Equilibria were stable if a slightly higher fraction of vigilant neighbors benefitted from a lower optimal (ESS) vigilance, and a slightly lower fraction benefitted from a higher optimal vigilance. Any drift away from a stable equilibrium would thus trigger individual adjustments back to the equilibrium point.
  • Even if all group members adopted the same optimal fraction of time vigilant, they might or might not synchronize their vigilance with that of neighbors. Simulations of the dynamic model were used to measure levels of spatial and temporal autocorrelation in vigilance for different conditions.


  • The static model predicted greater vigilance fractions for animals located on the outer edge of a group (since they had fewer neighbors to share the risk), for all neighbors given greater initial energy reserves (since they did not need to feed as much), when foragers were at higher risk than vigilant animals (since nobody wanted to be the straggler if attacked), and in contexts where predator attacks were more common.
  • The dynamic model made different predictions depending upon: a) the relative vulnerability of foragers and vigilant animals, and b) the differences in risk when at least one neighbor spotted the predator versus when nobody did:
    • Vigilant and foraging animals suffer similar capture probabilities, but detection of an approaching predator significantly reduces everyone’s risk. Here, an individual’s optimal vigilance decreased to an asymptote as the number of vigilant neighbors increased. An intermediate level of vigilance was the stable optimum. Instantaneous snap shots of such populations showed little spatial or temporal synchrony in being vigilant. An individual animal’s timing of activity was little affected by that of its neighbors.
    • Foraging animals suffer higher risks of being killed than vigilant animals, and detection of an approaching predator significantly reduces risk. High levels of vigilance were optimal when few neighbors were vigilant since this increased chances of the few vigilant animals spotting the predator and alerting all. High levels of vigilance were also favored when most group members were vigilant since being one of the few foraging animals greatly increased risk. When intermediate numbers of neighbors were vigilant, there were enough eyes and ears at work to lower one’s own vigilance, and enough other foragers around to reduce chances of being the only suitable prey if attacked. Stable equilibria occurred at a somewhat less than intermediate fraction of time being vigilant, and another when everyone was vigilant. Instantaneous snapshots of the population showed dense patches of synchronously vigilant animals (since nobody wanted to be the sole vulnerable forager) but no similar contagion of foraging.
    • Foraging animals suffer higher risks than vigilant animals of being killed, but early detection of a predator has little effect on anyone’s risk. The only relevant factor here was the greater risk of being killed while foraging when most of the neighbors were being vigilant. A stable ESS occurred at a low average vigilance fraction. These conditions generated contagious patches of synchronous vigilance as in the prior case, but also contagious patches of foraging.
  • See Figure 14.13 in the text for graphic comparisons of the three conditions.

Related Models:

  • This model built on the results of a number of prior publications on vigilance in groups of animals including Pulliam et al. 1982; Lima 1987; McNamara and Houston 1992; Lima 1995b, a; Lima and Zollner 1996; Bednekoff and Lima 1998b, a; Bahr and Bekoff 1999; Hilton et al. 1999; Lima and Bednekoff 1999; Beauchamp 2007; Pays et al. 2007a; Pays et al. 2007b. Readers may want to consult these earlier treatments after having worked through this one.
  • There are several parallel models examining the degree to which animals should coordinate vigilance by observing which neighbors are vigilant (Rodriguez-Girones and Vasquez 2002; Fernandez-Juricic et al. 2004; Jackson and Ruxton 2006).
  • Sirot and Pays (2011) recently published a paper using similar logic to identify the optimal amount of time a solitary forager should devote to scanning for predators.

Sentinel behaviors (Bednekoff 1997)

The Question: Why and when should an animal in a foraging group act as a sentinel?

Background: It is not initially obvious why any animal in a group would give up foraging and take on sentinel duty to the benefit of other group members. One answer is that, as suggested by the previous model, being a sentinel is often safer than being a forager. Also following the logic of the previous model, being a sentinel all the time would then be the safest anti-predator strategy, but the consequence would be death by starvation. Is there an optimal mix of foraging and sentinel duty and how might this mix vary depending upon the way in which sentinels and foragers do or do not alert each other when a predator is spotted?

Game Format:

  • The strategy set is discrete: individuals can either act as a sentinel or forage.
  • The game is a dynamic one: it consists of many successive bouts, during each of which each player decides to act as a forager or a sentinel for that bout. The goal is to identify the optimal choreography or “policy” to follow over a long series of bouts.
  • All group members start out with similar resources so the game is symmetric.
  • The payoffs are discrete: either an animal survived the series of bouts or it did not. It could die during any bout as a result of either predation or starvation.
  • Because the outcome of any bout depends not only on a focal player’s actions in that bout but also on the fractions of the foraging group that have adopted forager and sentinel roles, the game is a scramble.

Special Assumptions: Reciprocity and kin considerations are excluded from this model. By-product mutualism (in which doing what is best for oneself incidentally helps others) does come into play.


  • The model assumes that sentinels are less likely to be killed during a predator attack than are foragers. The ratio of relative vulnerabilities is a critical variable in the model.
  • ESS policies for a given set of conditions were derived using both forward and backward induction methods (see Web Topic 10.5 and Mangel and Clark (1988) for background).
  • ESS policies were independently derived for different patterns of “information sharing.” Three cases were considered: a) no sharing: detection of a predator by either a sentinel or forager never alerts other group members, either because the detector fails to give an alarm, or because its flight is not detectable by others; b) sentinel sharing: detection of a predator by sentinels but not foragers alerts other group members; and c) full sharing: detection of a predator by either sentinels or foragers alerts other group members. Being alerted reduces predation risk.
  • The median and distribution of fractions of the group acting as sentinels were computed for each ESS policy derived.
  • The initial model assumed a group size of five animals, four-fold lower vulnerability to attacks for sentinels than for foragers, and 90% probability that foragers would fail to detect approaching predators on their own. These values were later varied in a sensitivity analysis to determine the robustness of the initial results.


  • No information sharing: Here, predation risk for either sentinels or foragers increased as more of the individuals in a group became sentinels. This is because the risk to remaining foragers increases as they become more rare (same outcome as vigilance model of Sirot and Touzalin [2009] above), and once foragers are sufficiently rare, being a sentinel becomes just as risky and it no longer pays to be a sentinel. As a consequence, the threshold in energy reserve that was required before a forager switched to being a sentinel decreased as the number of sentinels in the group increased. The distribution in number of sentinels over time was highly variable with a mode at 0 sentinels. In short, sentinel behavior is unlikely to pay, even if sentinels have lower vulnerabilities than foragers, when there is no information sharing.
  • Sentinel sharing and full sharing: These two cases had very similar outcomes. Predation risk when no sentinels were present decreased dramatically to a very low value when one sentinel was present; adding additional sentinels further reduced risk for either foragers or sentinels but at a much decelerated rate. As a result, the threshold energy reserves required before an animal switched from foraging to being a sentinel rose dramatically once one other group member became a sentinel and increased only slightly when higher fractions acted as sentinels. Observed distributions of numbers of sentinels in multiple simulations showed a significantly narrow peak at one sentinel per group. Sentinel behavior can thus be favored as long as information is shared in some way.
  • Alternation: When information is shared, a threshold ratio between sentinel and forager vulnerabilities can be determined at which a well-fed animal could do equivalently well as a sentinel or forager. This sets the scene for alternation in which different individuals take successive turns in the sentinel role (a common observation in natural groups). Given the other parameters examined in these models, this threshold was always met if the conditions favoring being a sentinel at all were met.
  • Robustness of results: The optimal fraction of the group that should act as sentinels was independent of group size. Reduced mean food intake when foraging or greater unpredictability of food intake reduced the ESS fraction of the group serving as sentinels. Variation in other model parameters such as predator attack rates, failure of foragers to detect approaching predators, and initial energy reserves had only minor effects on predictions.
  • See Figure 14.14 in the text for graphic representation of some of these results.

Related Models:

  • This author developed the same model further, including the special, but common, case of pairs of animals in Bednekoff (2001).
  • The literature citing or building on this paper overlaps extensively with those papers cited for the prior game model (Sirot and Tourazin 2009).
  • A large number of field studies have since examined the assumptions and predictions of this model. Citations can be found in the main text.
  • Some authors have extended the information sharing aspect of sentinel behavior by noting that many sentinels emit repeated calls while on duty. The evidence that this enhances forager efficiency versus has some alternative function remains conflicting (Bednekoff et al. 2008; Hollen et al. 2008; Ellis 2009).

False alarm call rates (Beauchamp and Ruxton 2007)

The Question: Why and how often should members of a foraging group attend to false alarms?

Background: It is well known that foraging groups of some species experience frequent false predator alarms. Some false alarms are simply due to mistaken stimulus interpretation, but others may be intentional manipulations by some members of a group. Given the relative risks of predator attack and starvation, what is the optimal level of false alarms that can be tolerated by a foraging group, and are there other modulators of responses to false alarms (in particular, how many group members have taken flight) that alarm responders should consider?

Game Format:

  • The strategy set was discrete: individuals could either forage or be vigilant.
  • Individuals did not begin the game identically, but because their parameters were drawn from the same random distributions, the game was stochastically symmetric.
  • Payoffs were 0 if an individual starved or was killed by a predator, and equal to its accumulated energy reserves if a survivor. Because both factors could vary depending on what others in the group did, this game was a scramble.
  • Like the prior example, the game was dynamic: within a generation, each individual’s lifetime was divided into many successive bouts within each of which it could choose to be vigilant or forage.

Special Assumptions: As with prior examples, kin selection and reciprocity were not allowed in the models.


  • As in prior examples, individuals were assigned to groups. Different group sizes were examined but held constant for a given analysis.
  • Vigilant animals never erred in detecting an approaching predator or by fleeing or alarm signaling to innocuous stimuli (i.e., they never gave false alarms). Foragers however, could err in both ways. They could thus generate false alarms.
  • Each individual was haploid and carried three “genes” on a single chromosome: one specified the probability that the individual would be vigilant at any given time, one specified the probability that the individual would flee if it heard one group member’s alarm or saw one group member fleeing, and the third gene specified the probability that the individual would flee when it saw two or more group members fleeing. A model run began by assigning random values to each individual’s genes.
  • Unlike the prior example, evolution was then allowed to proceed through many successive generations. At the end of each generation, its members were ranked according to individual payoffs. The next generation was created by: a) replicating the top half of the ranks in the ending generation, and b) replacing the lower half of the prior generation by random choices of individuals from the top half of the rankings. Mutations were then added to each gene at a low rate.
  • After a sufficient number of generations, each of the three gene loci tended to converge on a stable distribution with a distinct mode and median. The combination of the three asymptotic medians for a given set of initial conditions defined an ESS. This type of multi-generational analysis is called genetic algorithm modeling (Vrugt and Robinson 2007).
  • ESS mixes were identified for a variety of different ambient conditions. Sensitivity analyses were then run to evaluate the robustness of these outcomes.


  • The median value of the vigilance gene decreased as group size was increased, and also when the rate at which foragers misclassified stimuli was increased.
  • The median value of the gene controlling the probability of fleeing after two group members fled was always higher than that for the probability of fleeing after only one member’s flight. The ESS thus favored reliance on more than one alarmed individual before fleeing.
  • The median value for both genes controlling the probability of flight decreased as group size increased, but the reduction was much smaller for the gene controlling flight after multiple alarms. Animals tend to rely on multiple flights or alarms at about the same rate regardless of group size or rates of forager misclassification of stimuli.
  • The average fraction of false alarms at the ESS was 20% for a group of six but as high as 55% for a group of 20 individuals. Larger groups thus tolerated surprisingly high rates of false alarms.

Related Models:

  • Lima (1994) and Proctor et al. (2001) consider similar questions, but include a number of constraints that are relaxed in this model.
  • Pollard (2011) models the degree to which identifying which group members produce the alerts might reduce false alarms, Bell et al. (2009) review refinement of alarm responses when animals integrate multiple sources of information such as recent surveillance outcomes, and Thompson and Hare (2010) show that where successive alarms are emitted can be used to predict an approaching predator’s trajectory.

Flower marking by bees (Stout and Goulson 2002)

Question: Why and when should foraging bees avoid nectar collection at a flower marked by an earlier forager?

Background: Bees visiting flowers remove most of the available nectar per visit. The flower then begins replenishing the nectar at a species-specific rate. The bee will obtain the largest subsequent nectar load if it postpones a return visit until the depleted flower has sufficiently replenished its nectar. Many bee species mark flowers with complex pheromone footprints whose components volatilize at different rates (Goulson et al. 2000). A bee can then monitor the changing composition of a footprint to determine how long a flower has had to replenish. Since different flower species have different nectar replenishment rates, optimal return times will differ for different species of flowers. Bumblebees have been shown to adjust return rates according to flower species. One cost of the time mark system is that other bees, even other species, detect and monitor the marks. A “cheater” bee can drain a flower before the marking bee would normally return. The cheater only gains a partial load, but they at least get this nectar before any competitor does. The resulting arms race could, in principle, undermine the entire marking strategy by forcing competitors to make earlier and earlier visits to marked flowers. For a given flower replenishment rate and density of competitors, is there an ESS that maximizes individual rates of nectar acquisition but preserves the flower marking strategy?

Game format:

  • The strategy set is the estimated time since a flower was last visited above which a bee will collect the nectar and below which it will reject the flower for now. The set is thus continuous.
  • The payoff to be maximized is the rate at which nectar is acquired per unit time.
  • All bees have equal access to the same set of flowers and the game is thus symmetric.
  • Because the nectar return for a bee adopting a given return time depends on the return times adopted by other bees foraging in the same neighborhood, the game is a scramble.

Special Assumptions: The authors further assumed that:

  • The time required to remove most of a flower’s nectar (the handling time) was independent of the amount of nectar being removed.
  • The bees always removed all the available nectar per visit.
  • The energetic costs of flight and handling were similar enough to use time spent as a common currency.
  • The interacting bees were unrelated excluding kin cooperation from playing a role.


  • The average rate of nectar acquisition was computed based on the search and handling times per flower, the relative fraction of flowers that were currently acceptable (above threshold nectar replenishment), and the average nectar load obtainable from those flowers.
  • It was assumed that there were enough bees and a finite number of flowers such that all flowers in the neighborhood had been visited recently. New flower production was thus assumed to be negligible over short time periods. The fraction of flowers that were acceptable thus depended on the rate of replenishment and return visit times used by the average bee.
  • If all bees cooperated by observing the same return time, a pareto optimal time could be computed that maximized individual forager intakes for a given flower species. No bee could do better without reducing the intake of others.
  • Assuming most bees had adopted the pareto return time, the rate of nectar accrual was then computed for a single “mutant” bee that visited flowers randomly without regard to return time marks. Using observed values for the relevant parameters, the rate of nectar accrual given random visits was usually higher than that for bees respecting the pareto rate of return. This meant that there was ample incentive for some bees to “cheat” by visiting flowers earlier than that proscribed by the pareto strategy.
  • An equilibrium occurs when bees using chemical marks to select or reject flowers adopt a return time that yields a nectar accrual rate equal to that enjoyed by bees that visit flowers randomly. If the bees relying on marking were to use a longer time, cheaters would be favored and increase in numbers; if cheaters were to use a shorter period, bees that relied on marks would do better. The equilibrium is thus stable and an ESS.
  • The study then compared the actual return times of wild bumblebees to the pareto optimal and ESS predicted values.


  • As expected, average return times to different flower species by wild bumblebees were inversely related to the rate of nectar replenishment.
  • For several combinations of bumble species and flower species, particularly flowers with rapid replenishment times, the pareto return time was considerably longer than the ESS time. Where this was the case, the average return time exhibited by the wild bumblebees was much closer to the ESS value than to the pareto value.
  • Where the pareto and ESS return times were very similar, the wild bumblebees exhibited average return times very close to the shared value of both predictions.

Related Models:

No related models since this publication were found. However, there remains much debate over whether the “footprint marks” of foraging bees are signals actively deposited on flowers to allow replenishment time monitoring or instead are inadvertent cues. Relevant citations are given in the text.

Literature cited

Bahr, D.B. and M. Bekoff. 1999. Predicting flock vigilance from simple passerine interactions: modelling with cellular automata. Animal Behaviour 58: 831–839.

Beauchamp, G. 2007. Vigilance in a selfish herd. Animal Behaviour 73: 449–472.

Beauchamp, G. and G.D. Ruxton. 2007. False alarms and the evolution of antipredator vigilance. Animal Behaviour 74: 1199–1206.

Bednekoff, P.A. 1997. Mutualism among safe, selfish sentinels: A dynamic game. The American Naturalist 150: 373–392.

Bednekoff, P.A. 2001. Coordination of safe, selfish sentinels based on mutual benefits. Annales Zoologici Fennici 38: 5–14.

Bednekoff, P.A., R. Bowman and G.E. Woolfenden. 2008. Do conversational gutturals help florida scrub-jays coordinate their sentinel behavior? Ethology 114: 313–317.

Bednekoff, P.A. and S.L. Lima. 1998a. Randomness, chaos and confusion in the study of antipredator vigilance. Trends in Ecology and Evolution 13: 284–287.

Bednekoff, P.A. and S.L. Lima. 1998b. Re-examining safety in numbers: interactions between risk dilution and collective detection depend upon predator targeting behaviour. Proceedings of the Royal Society of London, Series B 265: 2021–2026.

Bell, M.B.V., A.N. Radford, R. Rose, H.M. Wade and A.R. Ridley. 2009. The value of constant surveillance in a risky environment. Proceedings of the Royal Society of London, Series B 276: 2997–3005.

Bergstrom, C.T. and M. Lachmann. 2001. Alarm calls as costly signals of antipredator vigilance: the watchful babbler game. Animal Behaviour 61: 535–543.

Dugatkin, L.A. and J.G.J. Godin. 1992. Prey approaching predators: a cost–benefit perspective. Annales Zoologici Fennici 29: 233–252.

Ellis, J.M.S. 2009. Anti-predator signals as advertisements: evidence in white-throated magpie-jays. Ethology 115: 522–532.

Fernandez-Juricic, E., B. Kerr, P.A. Bednekoff and D.W. Stephens. 2004. When are two heads better than one? Visual perception and information transfer affect vigilance coordination in foraging groups. Behavioral Ecology 15: 898–906.

Getty, T. 2002. The discriminating babbler meets the optimal diet hawk. Animal Behaviour 63: 397–402.

Goulson, D., J.C. Stout, J. Langley and W.O.H. Hughes. 2000. Identity and function of scent marks deposited by foraging bumblebees. Journal of Chemical Ecology 26: 2897–2911.

Hasson, O. 1991. Pursuit deterrent signals—communication between prey and predator. Trends in Ecology and Evolution 6: 325–329.

Hilton, G., W. Cresswell and D.A. Ruxton. 1999. Intra-flock variation in the speed of response on an attack by an avian predator. Behavioral Ecology 10: 391–395.

Hollen, L.I., M.B.V. Bell and A.N. Radford. 2008. Cooperative sentinel calling? Foragers gain increased biomass intake. Current Biology 18: 576–579.

Jackson, A.L. and G.D. Ruxton. 2006. Toward an individual-level understanding of vigilance: the role of social information. Behavioral Ecology 17: 532–538.

Lima, J.T. 1987. Vigilance while feeding and its relation to the risk of predation. Journal of Theoretical Biology 124: 303–316.

Lima, J.T. 1994. Collective detection of predatory attack by birds in the absence of alarm calls. Journal of Avian Biology 25: 319–326.

Lima, S.L. 1995a. Back to the basics of antipredatory vigilance. Animal Behaviour 49: 11–20.

Lima, S.L. 1995b. Collective detection of predatory attack by social foragers-fraught with ambiguity. Animal Behaviour 50: 1097–1108.

Lima, S.L. and P.A. Bednekoff. 1999. Back to the basics of antipredatory vigilance: can nonvigilant animals detect attack? Animal Behaviour 58: 537–543.

Lima, S.L. and P.A. Zollner. 1996. Anti-predatory vigilance and the limits to collective detection: visual and spatial separation between foragers. Behavioral Ecology and Sociobiology 38: 355–363.

Mangel, M. and C.W. Clark. 1988. Dynamic Modeling in Behavioral Ecology. Princeton NJ: Princeton University Press.

Mappes, J., N. Marples and J.A. Endler. 2005. The complex business of survival by aposematism. Trends in Ecology and Evolution 20: 598–603.

Maynard Smith, J. and D. Harper. 2003. Animal Signals. Oxford UK: Oxford University Press.

McNamara, J.M. and A.I. Houston. 1992. Evolutionarily stable levels of vigilance as a function of group size. Animal Behaviour 43: 641–658.

Nur, N. and O. Hasson. 1984. Phenotypic plasticity and the handicap principle. Journal of Theoretical Biology 110: 275–297.

Pays, O., P.J. Jarman, P. Loisel and J.F. Gerard. 2007a. Coordination, independence or synchronization of individual vigilance in the eastern grey kangaroo? Animal Behaviour 73: 595–604.

Pays, O., P.C. Renaud, P. Loisel, M. Petit, J.F. Gerard and P.J. Jarman. 2007b. Prey synchronize their vigilant behaviour with other group members. Proceedings of the Royal Society of London, Series B 274: 1287–1291.

Pollard, K.A. 2011. Making the most of alarm signals: the adaptive value of individual discrimination in an alarm context. Behavioral Ecology 22: 93–100.

Proctor, C.J., M. Broom and G.D. Ruxton. 2001. Modelling antipredator vigilance and flight response in group foragers when warning signals are ambiguous. Journal of Theoretical Biology 211: 409–417.

Pulliam, H.R., G.H. Pyke and T. Caraco. 1982. The scanning behavior of juncos: a game-theoretic approach. Journal of Theoretical Biology 95: 89–103.

Rodriguez-Girones, M.A. and R.A. Vasquez. 2002. Evolutionary stability of vigilance coordination among social foragers. Proceedings of the Royal Society of London, Series B 269: 1803–1810.

Ruxton, G.D., T.N. Sherratt and M.P. Speed. 2004. Avoiding Attack: The Evolutionary Ecology of Crypsis, Warning Signals, and Mimicry. Oxford UK: Oxford University Press.

Searcy, W.A. and S. Nowicki. 2005. The Evolution of Animal Communication: Reliability and Deception in Signaling Systems. Princeton NJ: Princeton University Press.

Simaan, M. and J.B. Cruz. 1973. On the Stackelberg strategy in nonzero-sum games. Journal of Optimization Theory and Applications 11, Number 5.

Sirot, E. and O. Pays. 2011. On the dynamics of predation risk perception for a vigilant forager. Journal of Theoretical Biology 276: 1–7.

Sirot, E. and F. Touzalin. 2009. Coordination and synchronization of vigilance in groups of prey: the role of collective detection and predators’ preference for stragglers. The American Naturalist 173: 47–59.

Skelhorn, J., H.M. Rowland, M.P. Speed and G.D. Ruxton. 2010. Masquerade: camouflage without crypsis. Science 327: 51.

Stout, J.C. and D. Goulson. 2002. The influence of nectar secretion rates on the responses of bumblebees (Bombus spp.) to previously visited flowers. Behavioral Ecology and Sociobiology 52: 239–246.

Thompson, A.B. and J.F. Hare. 2010. Neighbourhood watch: multiple alarm callers communicate directional predator movement in Richardson’s ground squirrels, Spermophilus richardsonii. Animal Behaviour 80: 269–275.

Vega-Redondo, F. and O. Hasson. 1993. A game theoretic model of predator–prey signaling. Journal of Theoretical Biology 162: 309–319.

Vrugt, J.A. and B.A. Robinson. 2007. Improved evolutionary optimization from genetically adaptive multimethod search. Proceedings of the National Academy of Sciences of the United States of America 104: 708–711.

14.2 Videos of Echolocating Bats and Cetaceans


Approximately 760 species of bats echolocate as do 74 species of toothed (Odontocete) cetaceans (Nowak 1999). As we note in Chapter 14 of the text, both groups have exploited this sensory system to master an enormous variety of ecological niches (Thomas et al. 2002; Kunz and Fenton 2003). The degree of coordination that many species display to locate and capture prey is remarkable. Even for those videos that do not translate the ultrasonic echolocation sounds used by these animals down to frequencies that humans can hear, it is still valuable to see how various echolocating taxa use their unique sensory systems in natural and laboratory contexts. Below, we provide links to some illustrative videos across a wide variety of habitats and diets.

Echolocating bats:

Echolocating cetaceans

Literature cited

Cranford, T.W. 2000. In search of impulse sound sources in Odontocetes. In Hearing by Whales and Dolphins (Au, W.W.L., A.N. Popper and R.R. Fay, eds.). New York NY: Springer-Verlag. pp. 109–156.

Cranford, T.W. and M.E. Amundin. 2003. Biosonar pulse production in odontocetes: the state of our knowledge. In Echolcation in Bats and Dolphins (Thomas, J.A., C.F. Moss, M. Vater, eds.). Chicago IL: University of Chicago Press. pp. 27–35.

Cranford, T.W., M.E. Amundsin, and K.S. Norris. 1996. Functional morphology and homology in the odontocete nasal complex: implications for sound generation. Journal of Morphology 228:223–285.

Cranford, T.W., W.R. Elsberry, W.G. Van Bonn, J.A. Jeffries, M.S. Chaplin, D.J. Blackwood, D.A. Carder, T. Kamolnick, M.A. Todd and S.H. Ridgway. 2011. Observation and analysis of sonar signal generation in the bottlenose dolphin (Tursiops truncatus): evidence for two sonar sources. Journal of Experimental Marine Biology and Ecology 407: 81–96.

Kunz, T.H. and M.B. Fenton (eds.). 2003. Bat Ecology. Chicago IL: University of Chicago Press.

Nowak, R.M. 1999. Walker’s Mammals of the World, 6th Edition. Baltimore MD: Johns Hopkins University Press.

Reidenberg, J.S. and J.T. Laitman. 2007. Discovery of a low frequency sound source in mysticeti (Baleen whales): Anatomical establishment of a vocal fold homolog. Anatomical Record-Advances in Integrative Anatomy and Evolutionary Biology 290: 745–759.

Reidenberg, J.S. and J.T. Laitman. 2008. Sisters of the sinuses: cetacean air sacs. Anatomical Record-Advances in Integrative Anatomy and Evolutionary Biology 291: 1389–1396.

Thomas, J.A., C.F. Moss and M. Vater (eds.). 2002. Echolocation in Bats and Dolphins. Chicago IL: University of Chicago Press.