# Calculus for Biologists Lab Math 1180-002 Spring 2012

```Calculus for Biologists Lab
Math 1180-002
Spring 2012
Assignment #4 - Stochastic Population Growth
Report due date: Tuesday, February 14, 2012 at 9 a.m.
1. List the new R commands you used in the lab and describe, in general, what they do. Use your own words,
not mine!
2. Answer all ? bold ? questions (3 total).
3. Include Plot 4.1 for stochastic production from Lab 4.
(a) What do you notice about the r values that were randomly chosen for this particular population?
(b) What happens to the population size in the long run?
(c) Use your knowledge of r to help you explain the long term behavior of this population.
4. Include Plot 4.2 for stochastic immigration from Lab 4.
(a) What do you notice about the q values that were randomly chosen for this particular population?
(b) What happens to the population size in the long run?
(c) Use your knowledge of q to help you explain the long term behavior of this population.
5. Based on your observations from the two plots and from the lab, name at least two differences between
models describing stochastic production and those describing stochastic immigration. Be sure to give a
detailed description of how these differences affect the overall behavior of a population.
6. Modify the code you used in lab 4 to simulate a single population of your own.
(a) Choose the type of model you wish to use (production vs. immigration), the number of time steps
(N ), the necessary rates (r or q) and their min/max values or probabilities, and the initial population
size. Include these five pieces of information here. DO NOT include your code.
(b) Include a plot of the resulting population size over time.
(c) Make up a compelling story that defines your population and describes what happens to it throughout