Spatial Dynamics and Critical Patch Size of Annual Plant Populations

Abstract

Critical patch size is the minimum habitat size required for population persistence. The critical patch size of an annual plant population residing in a finite homogeneous habitat, using an integro-difference equation model is considered and this is found to be dependent on the basic population growth rate and dispersal characteristics. General analytical and numerical methods for the calculation of the critical patch size are presented with the inclusion of a simple new approximation technique. These methods are illustrated in the context of a species dispersing seeds on a Gaussian distribution. The approach is extended to incorporate a persistent seed-bank. Where the dispersion of seeds entering the seed-bank and those giving rise to adult plants is identical, the possession of a seed-bank influences the critical patch size through a scaling of the basic population growth rate. The wider implications of the approach are discussed in the context of metapopulation dynamics.