The claim conflates correlation (environment and outcomes co-vary) with causation (environment causes non-binomial sampling) without specifying how equal fitness permits causal bias.
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causation(Lewis's counterfactual theory of causation)
Event C causes event E if and only if there exists a chain C, D1, …, Dn, E such that each member (except C) is counterfactually dependent on the preceding event; causation is the ancestral of counterfactual dependence
correlation(Skyrms's model of the evolution of justice)
A parameter measuring the degree to which interacting individuals are similar to one another genetically or culturally, influencing the basin of attraction for cooperative equilibria