Optimal Harvesting in Stream Networks: Maximizing Biomass and Yield

In this study, we develop a metapopulation model framework to identify optimal harvesting strategies for a population in a stream network. We consider two distinct optimization objectives: maximization of total biomass and maximization of total yield, under the constraint of a fixed total harvesting effort. We examine in detail the special case of a two-patch network and fully characterize the optimal strategies for each objective. We show that when the population growth rate exceeds a critical threshold, a single harvesting strategy can simultaneously maximize both objectives. For general $n$-patch networks with homogeneous growth rates across patches, we focus on the regime of large growth rates and demonstrate that the optimal harvesting strategy selects patches according to their intraspecific competition rates and an effective net flow metric determined by network connectivity parameters.

💡 Research Summary

This paper develops a spatially explicit metapopulation framework for a species inhabiting a stream network composed of interconnected habitat patches. The authors consider two management objectives under a fixed total harvesting effort: (1) maximization of the long‑term total biomass (the sum of equilibrium densities across patches) and (2) maximization of the sustainable total yield (the sum of harvest rates multiplied by equilibrium densities). The total effort H is allocated among patches as non‑negative harvest rates h_i with ∑ h_i = H.

The underlying population dynamics are based on a modified logistic equation u′ = u(r − c u), allowing the intrinsic growth rate r to be positive or negative. Extending this to n patches yields the system

u′i = u_i(r_i − c_i u_i) − h_i u_i + ∑j (a{ij} u_j − a{ji} u_i),

where a_{ij} ≥ 0 are dispersal rates and the movement matrix A is assumed irreducible. The authors first analyze the special case of two patches (upstream and downstream) with biased movement: downstreamward rate d + q, upstreamward rate d (d, q > 0). Harvesting effort is parameterized by θ∈