Revisiting Strategic Models of Evolution: The Concept of Neighborhood Invader Strategies

In game-theoretic or strategic models of species evolution, the phenotype of individual organisms in a population are regarded as alternate strategies for playing a competitive game. The evolutionary outcome is predicted to conform to the “solution” of that game. The most usual solution concept adopted for the evolutionary game is that of Maynard Smith, the so-called “evolutionary stable strategies” (ESS). In this paper we explore an alternative solution concept. We call it neighborhood invader strategy (NIS). A NIS is a phenotype which is capable of invading all established populations of its neighbors. This phenotype need not be, at the same time, an ESS; and the reverse is true as well. We shall analyze this concept for a single species whose evolutionary-possibility set is a one-dimensional continuum.