Depensation Growth

Depensation growth corresponds to a kinetic term F p) 0 a 1, i.e., to setting = a, 02 = — a, and = find the three branches of steady states  

In this case there exists a critical patch size. In the following we truncate the expansion in (9.39) at the first order for simplicity, p q with q given by (9.44). The nontrivial branches collide at a saddle-node bifurcation point or turning point that 

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Fig. 9.5 (a) Bifurcation diagram for depensation growth for a = 0.1 and D = r =. Solid lines correspond to stable branches and the dotted lines to unstable branches. Symbols depict numerical results. Vertical dashed lines separate the extinction, relative extinction/survival, tind survival regions, (b) Plot of the critical initial density vs the patch size for the relative extinction/survival region... 

The steady state is stable if the term in brackets is positive, and unstable if it is negative. To be specific, we consider explicitly some examples of ecological interest, namely compensation and depensation population growth. In Fig. 9.3 we plot typical growth functions. 

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