Problem Set #8: Logistic Growth

WLF 448: Fish & Wildlife Population Ecology
Lab Notes 9, Fall 2002

Problem Set #8: Logistic Growth

1.	A population of 100 pheasants are released on an island. It is estimated that the island can support N_eq = 1,000 pheasants. Assume the rate of change in lambda for this population is equal to 0.0025.

Given this information, what will the population size of pheasants on this island be over the first 5 years?

Based on the rate of change in lambda, and the estimated N_eq, predict how the population will behave as it approaches equilibrium (i.e., will it approach K smoothly, damped oscillations, stable oscillations, or chaotic fluctuations?).

You have just been hired as a fisheries consultant in Mississippi. Your client wishes to establish a catfish fishery in a newly created series of ponds. Each pond can support a maximum of 800 catfish. Assume the fish breed year around (i.e., birth-flow fertility). The ponds have all been stocked with 100 catfish. These catfish came from a low-density population with the following age-specific characteristics:

age (yrs)	l_x	m_x
0	1.0	0.0
1	0.5	2.0
2	0.4	3.0
3	0.01	0.0

What is the instantaneous rate of change for this population?

Calculate and report N and dN/dt for this population for the next 10 years.
Plot N_t versus time and dN/dt versus N_t. What was the general shape of the growth curve when N was plotted versus time. What is the plot of dN/dt versus N_t telling us?
What value of N would provide the maximum sustained yield for this population? Why might you set the maximum allowable harvest at some level below the MSY?

Given that all parameters for a continuously reproducing population are equal except for time lags, what trends do you see if the lag time is 0, 1, 2, and 3 time periods? Compare and contrast results for the following populations:

N₀ = 15, K = 1000, r = 0.62
N₀ = 15, K = 1000, r = 0.32
N₀ = 800, K = 1000, r = 0.62

Discuss possible explanations for the differences or similarities you observed.

Note: Use program POPULUS.EXE to help you answer this question.

4. Explore Ricker's discrete time logistic growth model using the program POPULUS.EXE and find the values of r (rate of increase) which produce each of the following patterns of population change: smooth S shaped increase to K, cyclic population changes, and chaotic population change.

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Revised: 22 October 2002