Abstract
Modified versions of a wellknown model for coexistence are used to examine the conditions that determine the relative abundance of species that are in an evolutionarily stable state. Relative abundance is a term used to refer to the ranking of the number of individuals present within trophically similar species in an ecosystem. We use the G-function approach to understand why relative abundance relationships take the form so often found in field data. We assume that the ecosystem is at or near an evolutionary equilibrium and seek evolutionarily stable strategies to identify a coalition of individual species. In order to have a coalition greater than one, the G-function must produce frequency dependence, implying that the fitness of any given individual depends on the strategies used by all individuals in the population. This is an essential element of the evolutionary game. Otherwise, evolution would drive the population to a single strategy (i.e., a coalition of one) that is an optimal or group fitness strategy. We start with a classical version of the Lotka-Volterra competition equation that is not frequency dependent and make it frequency dependent in three different ways, thus allowing for the modeling of relative abundance. The first two methods involve a single resource niche and rely on modifications of the competitive effects to provide for a coalition of two or more. These models yield relative abundance distribution curves that are generally convex and are not typical of most field data. The third method creates several resource niches, and the simulated results generally create concave curves that are much closer to the field data obtained for natural systems.
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Vincent, T.L.S., Vincent, T.L. (2007). Evolutionarily Stable Relative Abundance Distributions. In: Jørgensen, S., Quincampoix, M., Vincent, T.L. (eds) Advances in Dynamic Game Theory. Annals of the International Society of Dynamic Games, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4553-3_15
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DOI: https://doi.org/10.1007/978-0-8176-4553-3_15
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