Botkin Environmental Science Earth as Living Planet 8th txtbk

262 CHAPTER 13 Wildlife, Fisheries, and Endangered Species
Population size (thousands)
100
90
80
70
60
50
40
30
20
10
Logistic curve
0
0 20 40 60 80 100
Time
(a)
MSY
population
size
Carrying capacity
Population estimated correctly
Population overestimated
120 140 160
No harvest MSY overharvest MSY correct
FIGURE 13.3 (a) The logistic growth curve,
showing the carrying capacity and the maximum
sustainable yield (MSY) population (where the
population size is one-half the carrying capacity).
The figure shows what happens to a population
when we assume it is at MSY and it is not. Suppose
a population grows according to the logistic
curve from a small number to a carrying capacity
of 100,000 with an annual growth rate of 5%.
The correct maximum sustainable yield would be
50,000. When the population reaches exactly the
calculated maximum sustainable yield, the population
continues to be constant. But if we make a
mistake in estimating the size of the population
(for example, if we believe that it is 60,000 when
it is only 50,000), then the harvest will always
be too large, and we will drive the population to
extinction. (b) Another view of a logistic population.
Growth in the population here is graphed
against population size. Growth peaks when the
population is exactly at one-half the carrying
capacity. This is a mathematical consequence
of the equation for the curve. It is rarely, if ever,
observed in nature.
Surplus of recruitment over loss
(potential sustainable harvest)
Maximum
sustainable
yield
Population size
(b)
MSY level
Original level, or
carrying capacity
carrying capacity is an abundance at which a population
can sustain itself without any detrimental effects that would
lessen the ability of that species—in the abstract, treated as
separated from all others—to maintain that abundance. The
third, the optimum sustainable population, already discussed,
leads to a population size between the other two.
An Example of Problems
with the Logistic Curve
Suppose you are in charge of managing a deer herd for
recreational hunting in one of the 50 U.S. states. Your
goal is to maintain the population at its MSY level,
which, as you can see from Figure 13.3, occurs at exactly
one-half of the carrying capacity. At this abundance, the
population increases by the greatest number during any
time period.
To accomplish this goal, first you have to determine
the logistic carrying capacity. You are immediately in
trouble because, first, only in a few cases has the carrying
capacity ever been determined by legitimate scientific
methods (see Chapter 2) and, second, we now know that
the carrying capacity varies with changes in the environment.
The procedure in the past was to estimate the carrying
capacity by nonscientific means and then attempt
to maintain the population at one-half that level. This
method requires accurate counts each year. It also requires