I am an evolutionary ecologist. I ask the question: How does natural selection acting as an optimization process determine feeding behaviors, population characteristics, and the properties of communities? My research includes the mathematical formulation and field tests of models and hypotheses based on foraging theory, consumer-resource models of species coexistence, and evolutionary game theory using the concept of evolutionary stable strategies (ESS).
To study foraging behaviors and link these behaviors to population and community level processes, I have extended Charnov's marginal value theorem of patch use, and developed giving-up density (GUD) approach for assaying foraging costs and benefits. A foraging animal should leave a depletable food patch when the harvest rate no longer exceeds the metabolic, predation, and missed opportunity costs of foraging. When harvest rates are related to the remaining abundance of food, then the amount of food remaining in experimental food patches, the GUD, estimates the point at which the animal has balanced costs and benefits. At present, I am using the giving-up density approach to examine the ecology of fear in fox squirrels, the community organization of desert granivores in the Negev Desert, Israel (with Dr. Burt Kotler), the effects of granivory, herbivory, and fire on prairie restorations (with Dr. Henry Howe
), and applications to the ecology of black rhinoceros (with Alina Kipchumba), show leopards preying upon blue sheep (with Mahesh Gurung), and mountain lions preying upon mule deer (with John Laundre).
Game theory and Maynard Smith and Price's pioneering concept of evolutionary stable strategies (ESS) provides a refreshing approach for modeling evolution by natural selection. To further the concept and its applications, Dr. Thomas Vincent and I have extended the ESS definition to parametric games (continuous vector-valued phenotypes) by developing the fitness generating function (G-function) and an associated 'ESS maximum principal'. This and others' research has recently discovered a range of outcomes and solutions to these evolutionary games. Solution concepts include local evolutionary maximum, unstable evolutionary maxima, stable evolutionary minima, and evolutionary Red Queens (non-equilibrium evolutionary dynamics). As an application, Dr. Mordachai Gersani, Dr. Zvika Abramsky, and I are using a split root technique (developed by Dr. Gersani) to test game theory models of root allocation in response to different habitats and competition.