Structured Populations

Abstract

So far, we have treated populations as homogeneous: all individuals were assumed to be identical with respect to reproduction and dispersal. We only modeled the dynamics of a single density function. In reality, most populations are heterogeneous in many ways. Individuals differ with respect to age, size, gender, and other attributes, and their reproductive and dispersal behavior may depend on these attributes. The nonspatial dynamics of populations with complex life cycles have been successfully described by matrix models. In this chapter, we introduce and study spatially explicit matrix models to generalize the simple IDE to stage-structured populations. We present an in-depth analysis of the critical patch-size problem and the spreading speed for these equations, including several proofs that we omitted in the scalar case in earlier chapters. Throughout the chapter, we use a simple two-stage model for juveniles and adults to illustrate the theory. We close with an overview of the rich literature of applications of structured IDEs to real-world systems, in particular to species invasions.