INTERPLAY BETWEEN FORAGING CHOICES AND POPULATION GROWTH DYNAMICS

The paper formalizes an MDP-based adaptive logistic model and reports (via simulation) that optimal foraging time rises with population size and that adaptive population trajectories are attenuated relative to the classical logistic, but it gives no rigorous proofs of these claims and leaves key shape assumptions about PFF(f,P) implicit. In particular, the paper states as a qualitative finding that the optimal foraging time increases with population size (Discussion), without a structural theorem or clear conditions under which this is guaranteed ; the Bellman equations are specified but suppress the explicit P-dependence in PFF in (2.1), (2.2) and do not analyze comparative statics . The candidate model provides a rigorous framework (existence, a clean V^NFF recursion independent of P, ΔV_t nonincreasing in P, attenuation of adaptive logistic via a logit-transform comparison) and, under a natural “decreasing-differences” congestion condition on PFF(f,P) suggested by the paper’s Appendix description (“increase speed becomes lower as population grows”) , proves the opposite monotonicity: optimal foraging time is weakly decreasing in P. That said, the model’s ν-comparative statics step invokes an incorrect monotonicity claim about B(f)^ν differences; the stated Milgrom–Shannon argument needs refinement. Net: the paper’s conclusions are numerically illustrated but unproven (incomplete), and the model’s structural program is broadly correct on the main points (well-posedness, ΔV monotonicity, logistic attenuation), but one comparative-statics step (in ν) is under-justified, so we judge both incomplete. Meanwhile, the paper’s monotonicity direction (f*(P) increasing) conflicts with the model’s direction under assumptions that the paper itself appears to endorse for PFF; resolving this requires the paper to state and analyze the shape conditions explicitly (e.g., decreasing vs increasing differences) rather than rely on simulations .