Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical modelling of seasonal migration
John Gerard Donohue, Petri Tomas Piiroinen

Last modified: 2014-03-28


The breeding success of many species depends on the synchronisation of the period of maximum demand of offspring with a period of food abundance. The trend towards higher spring temperatures in recent decades has caused such windows to advance [1]. The cue for migrating populations to depart their wintering quarters is often independent of temperature, preventing individuals from arriving in their breeding quarters early enough to react to the warmer climate and advance their breeding [2].

In this work, we propose a population-based dynamical system framework in which the interplay of different seasonal factors both within and between years can be better understood. The breeding and survival stages are modelled as separate annual regimes in a time-dependent switching system. Having developed a novel method for representing seasonal migration problems, we then use a simple switching model to illustrate some possible effects of and responses to climate change. Steady state solutions are used to measure the extent to which the population can sustain itself over long time-scales and repeated breeding events.

We show the negative effect that an advance in the food peak, relative to a fixed reproduction window and migration schedule, can have on population size, with a sufficiently severe shift bringing about a total collapse. By advancing both migration and breeding accordingly, the population can compensate for these environmental changes and maintain the population size corresponding to no climate change. Two obstacles to achieving this resynchronisation are considered - a shortage of food early in the breeding season [3] and a constraint on arrival date to the breeding quarters [2]. In both cases, the population reaches a point at which it no longer able to shift its breeding schedule forward. It is shown that manipulating the hatching distribution so that a higher proportion of pairs hatch at the earliest possible date is not sufficient to recover the original steady state size.

The model therefore agrees qualitatively with the population declines associated with ecological systems subjected to climate change. Furthermore, it predicts that persistent climate change could result in population collapses. The representation of seasonal breeding in a dynamical systems context is a foundation upon which a new class of time-dependent population models can be developed. The framework outlined is well-suited to deal with both seasonal interactions and the propagation of recruitment failures from one year to the next, enabling us to assess the impact of persistent temporal mismatches brought about by changing climatic conditions.



[1] Gian-Reto Walther, Eric Post, Peter Convey, Annette Menzel, Camille Parmesan, Trevor J. C. Beebee, Jean-Marc Fromentin, Ove Hoegh-Guldberg, and Franz Bairlein. Ecological responses to recent climate change. Nature, 416:389-395, 2002.

[2] Christiaan Both and Marcel E. Visser. Adjustment to climate change is constrained by arrival date in a long-distance migrant bird. Nature, 411:296-298, 2001.

[3] I.R. Stevenson and D.M. Bryant. Climate change and constraints on breeding. Nature, 406:366-367, 2000.


seasonality; migration; phenology; populations; breeding; climate change;