Stability and regularity results for a size-structured population model

In the present paper a nonlinear size-structured population dynamical model with size and density dependent vital rate functions is considered. The linearization about stationary solutions is analyzed by semigroup and spectral methods. In particular, the spectrally determined growth property of the linearized semigroup is derived from its long-term regularity. These analytical results make it possible to derive linear stability and instability results under biologically meaningful conditions on the vital rates. The principal stability criteria are given in terms of a modified net reproduction rate.