The application of life-history and predation allometry to population dynamics to predict the critical density of extinction

Abstract

Strong Allee effects entail the existence of the Allee threshold A, a population density, below which the population will go extinct, even in absence of environmental stochasticity. To examine Allee effects by observation or experiment is, however, very difficult. This study provides a mechanistic model to quantify Allee effects by breaking down population dynamics into three density-dependent ecological processes: the biomass fluxes due to production, natural death, and predation. The model is calibrated by empirical life-history scalings to species body mass M with a temperature of 20°C. Calibration reveals three new findings: (i) a single scaling of biomass production at the optimal or steady status, smooth across body mass regardless of reproduction pattern, (ii) a positive response of biomass production to population density, and (iii) allometry regarding predation process. Calculations demonstrate a new A scaling to M with an identical exponent of carrying capacity K scaling. In particular, a constant ratio A/K is of order 0.01, relatively stable to environmental stochasticity. This new protocol could be of wide applicability to invasion biology and conservation biology. The modeling methodology and revealed A–K linearity would be broadly applicable beyond Tuesday Lake, which is used as a reference of carrying capacity in this study. This provides a convenient way to estimate a system-dependent Allee threshold given specific carrying capacity. As a specific example, we show its implication for evaluating ballast water discharge standards in temperate mesotrophic water.