Environmental Engineering Reference
In-Depth Information
Fig. 9.2 Results of two simulation runs with the projection matrix given in Table
9.1
. The initial
population was ten individuals, all in age class 1 (
solid line
) and uniformly distributed over all ten
age classes (
dotted line
), respectively
The sum of individuals in all age classes for every time point is shown in Fig.
9.2
.
Apart from small differences at the beginning the population dynamics is the same for
both initial populations. Because the maximal eigenvalue of L is greater than one, the
population will grow exponentially. The normed right eigenvector belonging
l
1
describes the stable age distribution of the deer population (i.e. the proportions of
individuals belonging to the different age classes), which finally will be reached no
matter what initial distribution is assumed (Fig.
9.3
).
Elasticity Analysis
The impact of small changes in the life history parameters on the population
dynamics is of special interest for ecologists when making recommendations for
species management. For example, a specific age class should be a target for
conservation or control, if a small change in survival of this age class markedly
affects the population growth. Whether an increase or decrease in survival is desired
depends on the population being at risk or a pest, respectively. The effects of small
changes in the parameters on the growth rate can be assessed by an elasticity
analysis of the projection matrix (see also sensitivity analysis Chap. 23). Elasticity
is a measure of the effect of a proportional change in the life history parameters on
