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WILLIAM A. MITCHELL
Ph.D., The University of Arizona
Office: Science Building 354
Research Interests: behavioral ecology; community dynamics.
My research interests span several areas of ecology, from individual behavior to community interactions and large-scale patterns of biodiversity. In the pursuit of these interests, I have studied the behavioral and community ecology of birds and mammals in North America and Israel. I often use a quantitative approach, and much of my research is theoretical. My current research emphasizes understanding the determinants of species richness and spatial predator-prey games.
Ecological Determinants of Species Richness
Patterns of species richness across space and time have long intrigued ecologists. And, while there are many correlates of species richness (e.g. latitude, mean temperature, etc), there is a dearth of mechanistic theory to explain the patterns and correlations. One of the goals of my research is to provide such testable, mechanistic theory. Toward this end, I have developed mathematical models to investigate the effects of climate, resource productivity and travel cost on evolutionarily stable strategies and species richness (Mitchell 2000, Mitchell and Porter 2001, Mitchell et al. in press). My future research plans include, 1) addressing the effects of seasonality 2) compiling data to test competing theories for the ecological bases of species richness.
In some prey species individuals move frequently among widely distributed food patches. This movement may be costly in terms of foraging intake, especially if food patches are non-depleting. In addition, moving prey may be more likely to encounter predators, making movement appear to be a bad strategy, or one made necessary by food depletion. Current foraging and patch use models do not predict his type of movement.
Recently, I have collaborated with Dr. Steven L. Lima of Indiana State University to model large-scale foraging movements by prey (Mitchell and Lima, 2002). We propose that in these cases the prey and predator may be involved in a spatial "shell game", in which the predator attempts to learn prey locations, and prey attempt to be unpredictable in space. To understand this shell game, we developed an object-oriented, individual-based model in which we could vary a number of parameters characterizing the predator-prey interaction on a landscape. Our results show that the shell game is likely to occur when predators have good spatial memory and a low probability of killing prey on any given encounter.
Currently, I am modeling predator-prey games of movement using the technique of genetic algorithms. The motivation for using genetic algorithms is that they may allow us to find evolutionary stable strategies of interactions that are too complex to solve by traditional means, such as those involving multiple predators and multiple prey species.
Mitchell, W.A. and M.J. Angilletta. 2009. Thermal games: frequency-dependent models of thermal adaptation. Functional Ecology (In press).
Mitchell, W.A. 2009. Multi-behavioral strategies in a predator-prey game: an evolutionary algorithm analysis. Oikos (In press).
Mitchell, W.A. 2007. “Adaptive dynamics, resource conversion efficiency and species diversity”, pp. 287-303. In: Annals of the International Society of Dynamic Games, Vol 9:Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics; Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent (Eds.)
Kilpatrick, A.M., W.A. Mitchell, W.P. Porter, D.J. Currie. 2006. Testing a mechanistic explanation for the latitudinal gradient in mammalian species richness across North America. Evolutionary Ecology Research. 8:333-344.
Mitchell, W. A., B. Kotler, J. S.Brown, L. Blaustein, S. Dall. 2004. Species diversity in relation to habitat structure, environmental variability, and species interactions. Chapter 4 in M. Shachak, J. Gosz, S. T. A. Pickett and A. Perevolotsky (eds). Biodiversity in Drylands: Towards a Unified Framework. Oxford University Press, Oxford.
Lima, S. L., and W. A. Mitchell, and T. C. Roth. 2003. Predators feeding on behaviourally responsive prey: some implications for classical models of optimal diet choice. Evolutionary Ecology Research 5: 1083-1102.
Mitchell, W. A., and S. L. Lima. 2002. Predator-prey shell games: large-scale movement and its implications for decision-making by prey. Oikos 99: 249-259.
Mitchell, W. A. and W. P. Porter. 2001. Foraging games and species diversity. Annales Zoologici Fennici 38:89-98.
Mitchell, W. A. 2000. Limits to species richness in a continuum of habitat heterogeneity: an ESS approach. Evolutionary Ecology Research 2:293-316.
Brown, J. S., B. P. Kotler, and W. A. Mitchell. 1997. Competition between birds and mammals: A comparison of giving-up densities between crested larks and gerbils. Evolutionary Ecology 11: 757-771.
Brown, J. S., B. P. Kotler, and W. A. Mitchell. 1994. Foraging theory, patch use and the structure of a Negev Desert Granivore Community. Ecology 75:2286-2300
Mitchell, W. A. and T. J. Valone. 1990. The optimization research program: studying adaptations by their function. Quarterly Review of Biology 65:43-52.