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Mathematical modelling of seasonal migration with applications to climate change

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  • Donohue, John G.
  • Piiroinen, Petri T.

Abstract

The breeding success of many species depends on the alignment of the period of maximum demand of offspring with a period of food abundance. In this paper, we use piecewise-smooth differential equations to model the variation in the size of a population that has a short interval each year during which successful reproduction is possible. An increase in spring-time temperatures in recent decades has caused these intervals to advance, leading to temporal mismatches between species on different trophic levels. We first consider a one-species model which illustrates the dynamics of a population of specialist feeders over the course of a single breeding season and use it to examine how reproductive success depends on the population's distribution of breeding dates. We then introduce time-dependent switches to extend the model to a broader class of species. Steady-state solutions are used to measure the extent to which a migratory population can sustain itself over long time scales and repeated breeding events. The model's predictions agree with the observed negative effect on population size associated with an advance in the food season if not adequately compensated for by the population. Finally, we discuss how this model can be extended in order to encompass a wider range of ecological systems and to highlight the mechanisms over which climate change may exert an influence.

Suggested Citation

  • Donohue, John G. & Piiroinen, Petri T., 2015. "Mathematical modelling of seasonal migration with applications to climate change," Ecological Modelling, Elsevier, vol. 299(C), pages 79-94.
    • Handle: RePEc:eee:ecomod:v:299:y:2015:i:c:p:79-94
    DOI: 10.1016/j.ecolmodel.2014.12.003
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    References listed on IDEAS

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    1. Christiaan Both & Marcel E. Visser, 2001. "Adjustment to climate change is constrained by arrival date in a long-distance migrant bird," Nature, Nature, vol. 411(6835), pages 296-298, May.
    2. Christiaan Both & Sandra Bouwhuis & C. M. Lessells & Marcel E. Visser, 2006. "Climate change and population declines in a long-distance migratory bird," Nature, Nature, vol. 441(7089), pages 81-83, May.
    3. Ian R. Stevenson & David M. Bryant, 2000. "Climate change and constraints on breeding," Nature, Nature, vol. 406(6794), pages 366-367, July.
    4. Gian-Reto Walther & Eric Post & Peter Convey & Annette Menzel & Camille Parmesan & Trevor J. C. Beebee & Jean-Marc Fromentin & Ove Hoegh-Guldberg & Franz Bairlein, 2002. "Ecological responses to recent climate change," Nature, Nature, vol. 416(6879), pages 389-395, March.
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