A competitive coexistence principle?

Competitive exclusion n species cannot coexist on fewer than n limiting resources in a constant and isolated environment has been a central ecological principle for the past century. Since empirical studies cannot universally demonstrate exclusion, this principle has mainly relied on mathematical proofs. Here we investigate the predictions of a new approach to derive functional responses in consumer/resource systems. Models usually describe the temporal dynamics of consumer/resource systems at a macroscopic level i.e. at the population level. Each model may be pictured as one time-dependent macroscopic trajectory. Each macroscopic trajectory is, however, the product of many individual fates and from combinatorial considerations can be realized in many different ways at the microscopic or individual level. Recently it has been shown that, in systems with large enough numbers of consumer individuals and resource items, one macroscopic trajectory can be realized in many more ways than any other at the individual or microscopic level. Therefore, if the temporal dynamics of an ecosystem are assumed to be the outcome of only statistical mechanics that is, chance a single trajectory is near-certain and can be described by deterministic equations. We argue that these equations can serve as a null to model consumer-resource dynamics, and show that any number of species can coexist on a single resource in a constant, isolated environment. Competition may result in relative rarity, which may entail exclusion in finite samples of discrete individuals, but exclusion is not systematic. Beyond the coexistence/exclusion outcome, our model also predicts that the relative abundance of any two species depends simply on the ratio of their competitive abilities as computed from and only from their intrinsic kinetic and stoichiometric parameters.