New methods for understanding the intersection of evolution and ecology
Multi-player dynamic game methods
I developed a modeling approach based on dynamic state variable games (Mangel & Clark, 1988; Clark & Mangel, 2000; Houston & McNamara, 1999) that makes it possible to examine simultaneously the effect of interactions within and between the sexes (Alonzo & Warner, 2000a; Alonzo & Warner, 2000b). I have extended this method to examine interactions within and between species simultaneously (Alonzo 2002, Alonzo, Switzer and Mangel 2003a, 2003b). These methods are based on dynamic state-variable models that are solved numerically using a best-response method to find the behavior matrix (as a function of state and time) that is stable against invasion. To extend this method to multi-player games it is necessary to solve multiple dynamic programming equations simultaneously to find the behavior patterns that are predicted to be stable against changes in the behavior patterns of all “player” in the game. I currently have a National Science Foundation Grant (Emerging Frontiers: Advancing Theory in Biology Program) to develop new methods to examine evolutionary, behavioral and ecological dynamics simultaneously (for more details see Alonzo SH. 2010 Trends in Ecology and Evolutionary Biology).