Conservation of endangered species - Ecological Applications: Toward a Sustainable World - page 112

Fig. 5.1 (a) Population regulation with (i) density-independent death; (ii) density-dependent
birth and density-independent death; (iii) density-dependent birth and death. Population size
increases when the birth rate exceeds the death rate and decreases when the death rate
exceeeds the birth rate. N * is therefore a stable equilibrium population size. The actual value
of the equilibrium population size is seen to depend on both the magnitude of the density-
independent rate and the magnitude and slope of any density-dependent process.
(b) Population regulation with density-dependent birth, b , and density-independent death, d .
Death rates are determined by physical conditions which differ in three sites (death rates d 1 ,
d 2 and d 3 ). Equilibrium population size varies as a result ( N 1 *, N 2 *, N 3 *). (From Tow n send
et al., 2003.)

d n/ d t = rN {1 − ( N / K )}

This is known as the logistic equation. Now the rate at which the population increases declines as
the population size N approaches the carrying capacity K . When N and K are the same, the popula-
tion no longer increases but stabilizes at the carrying capacity. The carrying capacity can be for-
mally defi ned as the population size that the environment can just support (carry) without a
tendency to increase or decrease. Look again at Figure 5.1 and note that the equilibrium population
sizes ( N* ) can equally be described as carrying capacities ( K ).
Modelers have made the logistic equation (and others like it) progressively more realistic and
complex by incorporating elements that account for competition with individuals of other species,
mortality caused by predators, changes to reproduction and survivorship caused by parasites,
the way the population is arranged in space, the effects of random environmental changes, and
so on.
A different approach has been to build simulation models that can be run on a computer for
many generations, allowing us to follow the consequences for population dynamics of changing
the schedules of rates of birth and death of the various age classes that make up a real population,
or of incorporating density dependence or elements of environmental unpredictability.
Both algebraic and simulation approaches fi gure in the conservation management of endangered
populations.