A semiparametric Bayesian method for detecting Allee effects

Abstract

The importance of Allee effects has long been recognized both in theoretical studies of population dynamics and in conservation sciences. Although the necessary conditions for Allee effects to occur (e.g., difficulty in finding mates and mortality driven by generalist predators at low density) would seem to apply to many species, evidence for Allee effects in natural populations is equivocal at best. This apparent scarcity might be an artifact driven by poor power to detect them with traditional parametric models. To circumvent this potential problem, we developed a semiparametric Bayesian method based on a Gaussian process prior. We validated the method using simulated data sets and applied it to three herring data sets.

Nonlinear dynamics and noise in fisheries recruitment: A global meta‐analysis

“…The GP approach extends the EDM toolkit by allowing automatic lag selection, incorporating information from multiple sources using hierarchical modelling and allowing for nonstationary dynamics (Munch et al., ). Gaussian process regression has been used in population modelling to estimate the form of density dependence (Munch, Kottas, & Mangel, ), test for the presence of Allee effects (Sugeno & Munch, ,b) and to assess model misspecification (Thorson, Ono, & Munch, ).…”

“…The natural comparison here would be to use a GP with the current stock size as the sole input (e.g. Munch et al., ; Sugeno & Munch, ,b). However, most readers will be unfamiliar with this method, so we also determined how much of the variation in recruitment could be explained by three commonly used stock–recruitment models: Ricker, Beverton‐Holt and Schnute (See Supporting Information Appendix S3 for model definitions and fitting methods).…”

Fluctuating effects of genetic and plastic changes in body mass on population dynamics in a large herbivore

“…The opposite effect we detect is due to the quadratic relationship between density and both survival and recruitment, which appeared in all but one of the top recruitment models. Although a quadratic relationship may oversimplify how density affects this population (Sugeno and Munch ), the shape of this curve suggests positive density dependence at low density (Courchamp et al. ).…”

“…The opposite effect we detect is due to the quadratic relationship between density and both survival and recruitment, which appeared in all but one of the top recruitment models. Although a quadratic relationship may oversimplify how density affects this population (Sugeno and Munch 2013), the shape of this curve suggests positive density dependence at low density (Courchamp et al 1999). This might reflect Allee effects, which have also been observed in another population of bighorn sheep, where probability to wean a lamb increased with density up to a threshold of around 90 sheep (Bourbeau-Lemieux et al 2011).…”

Variation in Allee effects: evidence, unknowns, and directions forward

“…Whether common phenomenological theoretical models truly are poor descriptors of real-world density-growth rate relationships, of course, should be rigorously evaluated with the goal of identifying the models and statistical techniques that best relect biological reality and ofer the most optimal balance between errors of omission and commission. Beyond the aforementioned approaches, recently developed Bayesian techniques are promising (Sugeno and Munch 2013;Stenglein and Van Deelen 2016). The growing accessibility of Bayesian and likelihood-based approaches may be particularly helpful to this area of research by better accounting for error and uncertainty, and by enabling the itting of more process-based models.…”