How intra-stage and inter-stage competition affect overcompensation in density and hydra effects in single-species, stage-structured models

Abstract

Understanding and predicting responses to increased mortality is important for conservation biology and population management strategies. In stage-structured populations, increased mortality of a particular stage can have the counterintuitive effect of causing increased abundance in one or more stages (called stage-specific overcompensation in density) or the whole population (called a hydra effect). We analyzed an n-stage, single-species, ordinary differential equation model in order to explore the mechanisms driving overcompensation in density and hydra effects in stage-structured populations. We find that in the absence of inter-stage competition, overcompensation in density only occurs if intra-stage competition in one stage is sufficiently strong to cause overcompensation in the maturation or reproductive rate of that stage (i.e., increased input causes decreased output for that stage). When there is inter-stage competition, overcompensation in density can also be driven by sufficiently strong inter-stage competition, even in the absence of overcompensation in any ecological rate. Hydra effects arise under the same conditions and are more likely to be caused by sufficiently strong intra-stage competition. We interpret our results in terms of the direct and indirect effects between stages, which helps clarify the relationships between stage-specific overcompensation in density, overcompensation in ecological rates and hydra effects.