even if an equilibrium is asymptotically stable, that is no guarantee that the system will reach that equilibrium unless we know that the system's initial state is sufficiently close to the equilibrium. Global stability of an equilibrium, when we have it, gives the equilibrium a much more powerful explanatory role. An equilibrium is globally asymptotically stable if the dynamics carries every possible initial state in the interior of the state space to that equilibrium. If an equilibrium is globally stable, it (...) can have.. (shrink)

This paper applies the theoretical criteria laid out by D’Arms et al. to various aspects of evolutionary models of signalling. The question that D’Arms et al. seek to answer can be formulated as follows: Are the models that we use to explain the phenomena in question conceptually adequate? The conceptual adequacy question relates the formal aspects of the model to those aspects of the natural world that the model is supposed to capture. Moreover, this paper extends the analysis of D’Arms (...) et al. by asking the following additional question: Are the models that we use sufficient to explain the phenomena in question? The sufficiency question asks what formal resources are minimally required for the model to get the right results most of the time. (shrink)

Most current modeling for evolution of communication still underplays or ignores the role of local action in spatialized environments: the fact that it is immediate neighbors with which one tends to communicate, and from whom one learns strategies or conventions of communication. Only now are the lessons of spatialization being learned in a related field: game-theoretic models for cooperation. In work on altruism, on the other hand, the role of spatial organization has long been recognized under the term ‘viscosity’.Here we (...) offer some simple simulations that dramatize the importance of spatialization for studies of both cooperation and communication, in each case contrasting a model dynamics in which strategy change proceeds globally, and a spatialized model dynamics in which interaction and strategy change both operate purely locally. Local action in a spatialized model clearly favors the emergence of cooperation. In the case of communication, spatialized models allow communication to arise and flourish where the global dynamics more typical in the literature make it impossible.Simulations make a dramatic case for spatialized modeling, but analysis proves difficult. In a final section we outline some of the surprises of spatial dynamics but also some of the complexity facing attempts at deeper analysis. (shrink)