Theoretical Ecology

, Volume 12, Issue 1, pp 31–48 | Cite as

Accounting for environmental change in continuous-time stochastic population models

  • Geoffrey LegaultEmail author
  • Brett A. Melbourne


The demographic rates (e.g., birth, death, migration) of many organisms have been shown to respond strongly to short- and long-term environmental change, including variation in temperature and precipitation. While ecologists have long accounted for such nonhomogeneous demography in deterministic population models, nonhomogeneous stochastic population models are largely absent from the literature. This is especially the case for models that use exact stochastic methods, such as Gillespie’s stochastic simulation algorithm (SSA), which commonly assumes that demographic rates do not respond to external environmental change (i.e., assumes homogeneous demography). In other words, ecologists are currently accounting for the effects of demographic stochasticity or environmental variability, but not both. In this paper, we describe an extension of Gillespie’s SSA (SSA + ) that allows for nonhomogeneous demography and examine how its predictions differ from a method that is partly naive to environmental change (SSAn) for two fundamental ecological models (exponential and logistic growth). We find important differences in the predicted population sizes of SSA + versus SSAn simulations, particularly when demography responds to fluctuating and irregularly changing environments. Further, we outline a computationally inexpensive approach for estimating when and under what circumstances it can be important to fully account for nonhomogeneous demography for any class of model.


Demographic stochasticity Environmental change Stationary Non-stationary Homogeneous Nonhomogeneous Environment-dependent demography Stochastic simulation algorithm Poisson process 



GL conceived of the study and ran the simulations. Authors GL and BAM did the analysis of the simulations and wrote the paper. The Janus supercomputer is a joint effort of the University of Colorado Boulder, the University of Colorado Denver and the National Center for Atmospheric Research. We thank the ESA Theoretical Ecology section for a poster award to GL, which provided early support for the project.

Funding information

In this study, preliminary simulation work used the Janus supercomputer, which is supported by the National Science Foundation (DEB, award number 1457660) and the University of Colorado Boulder.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Ecology and Evolutionary BiologyUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of BiologyUniversity of North Carolina at Chapel HillChapel HillUSA

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