On the net reproduction rate of continuous structured populations with distributed states at birth

Details On the net reproduction rate of continuous structured populations with distributed states at birth On the net reproduction rate of continuous structured populations with distributed states at birth

2012-02-16

arxiv.org/abs/1202.3800v1

Biology

Quantitative Biology

Populations and Evolution

Scientific paper

We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral properties of a parametrized family of unbounded operators. The alternative approach, on which we focus here, is based on the reformulation of the problem as an integral equation. In this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity. Finally, we briefly discuss a third approach, which is based on the finite rank approximation of the recruitment operator.

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