Consider a community of various species newly introduced into a stable environment. Evolutionary processes acting on this community will produce, over time, a community of surviving species. Methods for predicting the evolutionarily stable strategies (ESSs) used by the surviving species are now available for a large class of dynamic population models. Here we expand a previously developed evolutionary game theory, which can be used to predict ESSs in a large class of models, by introducing strategy dynamics. By so doing, a more complete description of the evolutionary process is obtained. One not only obtains a convenient way of determining evolutionarily stable strategies, but interesting features about the evolutionary process itself can be observed. of particular interest here, we show that the number of strategies which are evolutionarily stable can change as certain environmental factors involved with the model change. The process by which the ESS is formed is examined in terms of an “adaptive landscape” formed by our fitness generating function (G-function). The G-function has properties that enhance the likelihood that the various adaptive peaks will be occupied.