Age-structured models with density-dependent recruitment

Abstract

This chapter examines age-structured models with density-dependent recruitment. In particular, it focuses on populations with over-compensatory density dependence, such as may occur due to cannibalism or some types of space competition. When the slope (at the equilibrium point) of the relationship between egg production and subsequent recruitment is declining in an over-compensatory way, the population may exhibit unstable limit cycles with period twice the generation time (2T). These cycles occur when that slope is steeply negative and the spawning age distribution has a high mean and low width. These results are applied to study the behavior of cycles in the U.S. west coast Dungeness crab fishery, variability in populations of an intertidal barnacle, and cycles in populations of a pest, the flour beetle. Additionally, it is shown how single-sex harvesting and compensatory growth affect population cycles and equilibria.