Читать книгу Ecology - Michael Begon - Страница 133

One simple modification that we can make is to relax the assumption that populations respond instantaneously to changes in their own density, i.e. that present density determines the amount of resource available to a population and this in turn determines the net reproductive rate within the population. Suppose instead that the amount of resource available is determined by the density one time interval previously. For example, suppose that the amount of grass in a field in spring (the resource available to cattle) might be determined by the level of grazing (and hence, the density of cattle) in the previous year. In such a case, the reproductive rate itself will be dependent on the density one time interval ago. Thus, since in Equations 5.7 and 5.12:

(5.16)

Equation 5.12 may be modified to:

(5.17)

time lags provoke population fluctuations

Now there is a time lag in the population’s response to its own density, caused by a time lag in the response of its resources. The behaviour of the modified model is as follows:

In comparison, the original Equation 5.12, without a time lag, gave rise to a direct approach to its equilibrium for all values of R. The time lag has provoked the fluctuations in the model, and it can be assumed to have similar, destabilising effects on real populations.