Читать книгу Ecology - Michael Begon - Страница 132

But what type or range of competition is this model able to describe? We can answer this question by tracing the relationship between k values and log N (as in Section 5.3). Each generation, the potential number of individuals produced (i.e. the number that would be produced if there were no competition) is N_t R. The actual number produced (i.e. the number that survive the effects of competition) is N_t R /(1 + aN_t ).

We have seen that:

(5.13)

Thus, in the present case:

(5.14)

or, simplifying:

(5.15)

Figure 5.21 shows a number of plots of k against log₁₀ N_t with a variety of values of a inserted into the model. In every case, the slope of the graph approaches and then attains a value of 1. In other words, the density dependence always begins by undercompensating and then compensates perfectly at higher values of N_t. The model is therefore limited in the type of competition it can produce. So far, we can only say that this type of competition leads to very tightly controlled regulation of populations.