Pushed beyond the brink: Allee effects, environmental stochasticity, and extinction

To understand the interplay between environmental stochasticity and Allee effects, we analyse persistence, asymptotic extinction, and conditional persistence for stochastic difference equations. Our analysis reveals that persistence requires that the geometric mean of fitness at low densities is gre...

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Bibliographic Details
Published inJournal of biological dynamics Vol. 8; no. 1; pp. 187 - 205
Main Authors Roth, Gregory, Schreiber, Sebastian J.
Format Journal Article
LanguageEnglish
Published England Taylor & Francis 01.01.2014
Taylor & Francis Ltd
Subjects
Animals
demographic Allee effect
Environment
Extinction
Extinction, Biological
Fitness
Humans
Models, Biological
Original
persistence
Population
Population density
Population Dynamics
positive and negative density dependence
Predation
Species extinction
stochastic difference equations
Stochastic Processes
Stochasticity
demographic Allee effect
persistence
stochastic difference equations
extinction
population dynamics
positive and negative density dependence
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Summary:To understand the interplay between environmental stochasticity and Allee effects, we analyse persistence, asymptotic extinction, and conditional persistence for stochastic difference equations. Our analysis reveals that persistence requires that the geometric mean of fitness at low densities is greater than one. When this geometric mean is less than one, asymptotic extinction occurs with high probability for low initial population densities. Additionally, if the population only experiences positive density-dependent feedbacks, conditional persistence occurs provided the geometric mean of fitness at high population densities is greater than one. However, if the population experiences both positive and negative density-dependent feedbacks, conditional persistence only occurs if environmental fluctuations are sufficiently small. We illustrate counter-intuitively that environmental fluctuations can increase the probability of persistence when populations are initially at low densities, and can cause asymptotic extinction of populations experiencing intermediate predation rates despite conditional persistence occurring at higher predation rates.
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Author Email: sschreiber@ucdavis.edu
ISSN:1751-3758
1751-3766
DOI:10.1080/17513758.2014.962631