Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Optimal migratory behavior in spatially-explicit seasonal environments

Pages: 3359 - 3378, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3359

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Timothy C. Reluga - Department of Mathematics, Penn State University, University Park, PA 16802, United States (email)
Allison K. Shaw - Division of Evolution, Ecology, and Genetics, The Australian National University, Canberra ACT 0200, Australia (email)

Abstract: Mass migrations of vertebrate and arthropod species have long been perceived as some of the most mystical phenomena in nature. And for eons, we have been asking ourselves why animals migrate. Ecologically, migration provides benefits in currencies of survival, growth, and reproduction, allowing animals to exploit environmental heterogeneities in space and time. Yet for a given environment, different species respond with different behaviors -- some travelling large distances, while others shelter in place. Part of the explanation of this distinction is the physiological differences between species and their ability to move. But is physiological difference a necessary pre-condition? Or can environmental heterogeneity itself be sufficient for bifurcations in movement behavior?
    In this paper, we address this last question using a model for the evolution of migration in a density-independent, spatially-explicit setting when movement is costly based on the harvesting a single resource that varies in space and time. We use optimal control methods to calculate the optimal movement patterns in several different situations. In this framework, optimal movement strategies can be classified into six different regimes, based on the cost of movement, the strength and scale of seasonal resource variation, and the degree of trade-off between short-term and long-term benefits. We show that a migratory niche emerges in response to inseparable spatio-temporal environmental heterogeneity, and that this niche can bifurcate from changes to the resource distribution without need for physiological divergence.

Keywords:  Migration, evolution, seasonal variation, optimal movement.
Mathematics Subject Classification:  92D40, 92D15, 70K42, 70H12.

Received: July 2013;      Revised: February 2014;      Available Online: October 2014.