Population dynamics and competitive outcomes derive from resource allocation statistics: The governing influence of the distinguishability of individuals
Statistical mechanics reveals that seemingly deterministic events at the macroscopic level correspond to the most likely state at the stochastic microscopic level. To apply this insight to ecology, we develop a fundamental theoretical framework based on the notion that the observed dynamics at the population (macroscopic) level is the most likely outcome of stochastic resource allocation events at the individual (microscopic) level, which is solved by maximizing the Boltzmann entropy associated with each allocation pattern.
The method differs from information-theoretic MaxEnt methods previously applied in ecology in that it incorporates explicit birth and death processes and predicts how the rates of these demographic processes depend on population size. The theory highlights the governing role played by the relative distinguishability of individuals within species compared to that across species, an attribute that exerts a critical influence on predicted population dynamics and species coexistence patterns.
As relative individual distinguishability decreases, the theory predicts population dynamics to be subject to a stronger stabilizing mechanism (thus more chance for species to coexist) with respect to both steady state abundances and the time to reach steady state. When steady state is reached, the dependence of species abundance on its mean metabolic rate and relative individual distinguishability is analytically solved, from which the conditions for certain shapes of species abundance distributions to emerge and for the energy equivalence rule to hold are revealed. The theory can be easily modified to model predator-prey interactions and food web structure. Based on these findings, strategies for empirical testing of the theory are outlined.
Our theory establishes a comprehensive framework under which ecological interactions be studied. It gives a parsimonious explanation, based on attributes at the individual level, of when competitive exclusion should occur in nature, of the shape of abundance distributions, and of the relationship between the abundance and metabolic rate of species.