The Cost of Mismatch: Optimal Traits, Plasticity, and Mutation Interactions in Variable Environments

A fixed trait may face several demands within a single lifetime. How much reproductive output can an organism gain by tracking each demand? Suppose a trait p facing a demand e pays a reciprocal mismatch cost J(p/e) = (p/e + e/p)/2 − 1 from a common reproductive budget. If A and H are the exposure-weighted arithmetic and harmonic means of the demand, the best fixed trait is √(AH). Its unavoidable cost is √(A/H) − 1, which gives the exact break-even price of perfect tracking. The same budget predicts the one-generation selection response and the magnitude and sign of interactions between mutations that multiply one trait. We give a bacterial expression experiment that can distinguish these predictions from those of a cost quadratic in log expression.