Biology 0200
Week 2 Homework Assignment
Questions 1-3: Use a web-based simulation to answer a number of questions about
population growth. Open the Web Tutorial on Population Growth (there is a link on
the web page for Week 2. URL of the tutorial:
http://bcs.whfreeman.com/thelifewire/content/chp54/5402002.html
• Read the “Introduction” to logistic growth that appears as the window opens. Then
click on the “Graph” tab, and a window looking like this will open:
• Click on the New Plot button, and the simulation will immediate calculate a logistic
growth curve representing the growth of a population under the initial conditions that
appeared in the window: Those conditions are r = 1.00, N = 100, K = 1000. (Note: the
r value given in the simulation is actually rmax).
• As you may already have figured out, this window holds a program that allows you to
run Lotkka-Volterra growth simulations of the sort described in lecture on 1/28 and on
pages 1042--1046 of your textbook (Freeeman 4/e).
• Click the Clear button to erase the graph.
• Now run a new simulation by setting the carrying capacity (K) to 1/2 its initial value.
You can do this by hitting the “minus” button next to the K box to reduce the value of
1000 to just 500. Click New Plot to run the growth simulation.
• Then, run the curve twice more, the first time doubling K, to 1000 and the second time
returning K to its 1/2 maximum value (500) but doubling r (to 2.00). Each time, when
you have adjusted the parameters, hit New Plot The second and third plots should
appear on the graph in a different color, making it easy to distinguish them from the first.
If you’ve done all this properly, the parameters you’ve entered for the three simulations
should show up at the right side of the graph, like this:
Use your results from these simulations to answer these questions:
1) Which has a more pronounced effect on the early stages of growth? Doubling K
or r? (Note that the first curve was done with r = 1.0 and K = 500. In the second
simulation, we doubled K relative to the first simulation. In the third simulation,
we doubled r relative to the first simulation)
2) Why? Look at the equation that describes logistic growth (below) and provide a
mathematical reason for your answer to (1):
K-N
I = rmaxN K
3) • What will the value of population increase (I) be if N>K?
K-N
• What will the value of K
be if N is exactly one-half the value of K?
• Question 4 (on the next page) asks you to apply the population growth equations to a
problem in wildlife management.
4) You and a colleague have just been hired to manage the
population of ring-necked pheasant on a small island off the
Carolina coast. The island is approximately 1000 acres in
area. The pheasant population is now in the process of
recovering after a devastating hurricane in 2003. Population
counts during the summers of 2004 and 2005 gave the
following numbers of pheasants on the island:
2004: 110
2005: 132
A)
What rate of growth [r] has the population on the island displayed during this 1year period? Show your calculations.
B) Your colleague assures you that the value you have calculated in part A can also be
taken as the intrinsic [ro] rate of growth. She’s probably right (after all, she aced Bio
0200!). But how could you tell for sure? In other words, under what conditions could the
r value you calculated in (A) be reasonably taken as the intrinsic rate of growth [ro] for
the species? Be brief but specific.
C) Published estimates of the carrying capacity of habitats similar to your island suggest
that the ultimate carrying capacity [K] for ring-necked pheasants should be
approximately 100 birds per acre. You are uncertain of the validity of this value for K,
and propose an experiment in which you will stock the island with 40,000 birds (40 birds
per acre) and follow the rate of growth of the population over the next year.
Your colleague asks how many birds (per acre) you would expect to see on the island a
year from now if the 100 bird per acre value for K were correct. Calculate the total
number of birds expected on the island if a K value of 100 birds per acre is indeed
correct. Show your work!
Your homework must be submitted on line before 12
midnight, Friday, February 1.
(Well, technically, before 12:01 AM Saturday morning)
• Type your name and your Lab Section Number at the top of your
homework document. Submit your completed homework assignment
on the Canvas web site.