untitled

Note that we have set a condition to ensure that the population never declines below

zero. We use a random number generator drawn from a normal distribution with

mean =0 and standard deviation (σ) =0.10, appropriate to the observed data, to

generate population dynamics, starting from the average carrying capacity (N=1600)

recorded in the Ontario study. We use the observed fluctuations in prey recorded

during 1973 – 87 to generate environmental variation in food supply for the martens.

The results (Figs 19.5 and 19.6) demonstrate that the marten population cannot sus-

tain a constant quota at the MSY for any appreciable length of time.

The important lesson we obtain from this example is this: given that all harvested

wildlife species live in stochastic environments in which weather conditions and food

supplies are expected to vary widely, wildlife managers should keep the harvesting

rate well below MSY. A margin of error of about 25% below the estimated maximum

N

gN Z

t gN Z

ttt

ttt

+ =

≤

(^1) −

0

( , , )

(, , )

if MSY

MSY otherwise

ε

ε

340 Chapter 19

800

600

400

200

0

(^051015)
Year
Predicted marten abundance
Fig. 19.5Predicted
variation in marten
abundance under a
constant quota harvest
policy, with annual
marten harvests set at
the maximum
sustainable yield (H=
423 martens per year),
starting from a
population size of 400
animals in 1973.
500
400
300
200
100
0
0 5 10 15
Year
Predicted marten harvest
Fig. 19.6Predicted
variation in marten
harvests under a
constant quota harvest
policy, with annual
marten harvests set at
the maximum
sustainable yield (H=
423 martens per year),
starting from a
population size of 400
animals in 1973.