Abstract
A fitness-ranking compares the fitness of 2 genotypes or traits. A species'' fitness-ranking describes the relative fitness of genotypes in an aggregated species as a whole. An environmental fitness-ranking describes the relative fitness of genotypes in a particular population of the species in a particular environment. A set of axioms is proposed to describe what might plausibly be desired of the relation between a species'' fitness-ranking and environmental fitness-rankings. There is no way to construct a species'' fitness-ranking that satisfies all of these axioms. Hope that a single natural measure of the fitness of genotypes exists for a species as a whole must be replaced by attention to the dynamics of multiple populations in multiple environments.

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