# Living Graph: Analyzing Demographic Stochasticity

In this exercise we examine a population in which we can specify the initial population size (${N}_{t}$) and the age-specific survivorship and the multiplicative growth rate ($\lambda $). Recall that we calculate the population at any time $t$ from $\lambda $ and the starting population, ${N}_{0}$:

$${N}_{t}={\lambda}^{t}{N}_{0}$$In the exercise you can specify the values of ${N}_{t}$ and $\lambda $. You can also specify the amount of variation that occurs in the value of $\lambda $.

- Analyze the effect of the value of $\lambda $. Hold the variation in $\lambda $ constant and examine the change in the population over time for different values of $\lambda $.
- Analyze the effect of variation in $\lambda $. Hold the value of $\lambda $ constant and examine the change in the population over time for different values of the variation in $\lambda $.
- Run each simulation several times and note any differences in outcomes.

**Range
of Time (T)**:

**Initial
Pop. (${N}_{t}$) #1**

**Growth
Rate ($\lambda $) #1**

**$\lambda $ variation (%) #1**

**Initial
Pop. (${N}_{t}$) #2**

**Growth
Rate ($\lambda $) #2**

**$\lambda $ variation (%) #2**

To compare two populations over the same Time (T), please enter values above. Click the items in the legend to hide or display the corresponding plotted points. Explore the plotted points by hovering over them with your cursor; you can zoom in on a section of the graph by clicking and dragging. When zoomed-in, you may explore the timeline by dragging the scroll bar at the top of the graph. Reset the graph by clicking "Show all".

The graph plots population size from 0 to 150,000 versus Time T from 0 to 10. Population Size 1: 2, 0; 6, 10,000; 8, 25,000; 10, 150,000. All values are estimated.