Lattice models in ecology and social sciences

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Random matching between individuals, or the complete-mixing model, is often assumed in analyzing evolutionary or population dynamics in ecology and game theory or other models in social sciences. Making and analyzing a model is not difficult under this simple assumption. However spatial- or network-structured populations, including the lattice model and the power-law network, are more realistic for many ecological and social phenomena than the complete-mixing model. In this review, I will show first that a lattice model can be useful in investigating the effect of neighborhood interactions on the dynamics, not only of plants and forests, but also of animal and human societies. Second, the lattice model promotes the evolution of spiteful behavior, even though it is well-known that the lattice model promotes the evolution of cooperation. Finally, different social networks result in traits, such as social norms, spreading at different speeds.

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