General representation theorems for efficient population behavior

摘要

A general efficiency principle for stochastic population behavior is formulated and analyzed. This principle asserts in essence that among all possible population states consistent with the same levels of activity, those states involving lower cost (or energy) expenditures are always at least as likely to occur as those states with higher expenditures. The central result of the paper is to show that, under quite general conditions on both activity and cost measures, such population behavior is always representable by probability distributions which are log-linear in both activity and cost variables, and in particular are nonincreasing in costs. In addition, it is shown that the continuity and differentiability properties of these functions are determined entirely by their associated mean-activity and mean-cost functions. The modeling implications of these results are illustrated in terms of three examples of population behavior drawn from the literature.