OVERCOMPENSATORY RECRUITMENT AND GENERATION DELAY IN DISCRETE AGE-STRUCTURED POPULATION-MODELS

The effect of overcompensatory recruitment and the combined effect of overcompensatory recruitment and generation delay in discrete nonlinea r age-structured population models is studied. Considering overcompens atory recruitment alone, we present formal proofs of the supercritical nature of bifurcations (both flip and Hopf) as well as an extensive a nalysis of dynamics in unstable parameter regions. One important findi ng here is that in case of small and moderate year to year survival pr obabilities there are large regions in parameter space where the quali tative behaviour found in a general n+1 dimensional model is retained already in a one-dimensional model. Another result is that the dynamic s at or near the boundary of parameter space may be very complicated. Generally, generation delay is found to act as a destabilizing effect but its effect on dynamics is by no means unique. The most profound ef fect occurs in the n-generation delay cases. In these cases there is n o stable equilibrium X at all, but whenever X* small, a stable cycle of period n+1 where the periodic points in the cycle are on a very spe cial form. In other cases generation delay does not alter the dynamics in any substantial way.