Optimal management of heterogeneous resources

The research focuses on using such models for a qualitative analysis: i) in order to better understand the consequences of various management strategies; and ii) to reveal management principles aimed at optimizing given economic and environmental objectives. It is often assumed that the steady state achieved in the long run in such models is more informative for policy than short-term non-stationary dynamics; that is why our research focuses on analyzing models’ steady states.

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ASA has recently started research on optimal control of size-structured populations. ASA researchers [1] [2] analyzed a fairly generic model of a one-species population of individuals that were heterogeneous in terms of size, in which asymmetric intra-species competition impacted vital parameters (growth, mortality, and fertility rates) and decreased the population density disproportionally, favoring bigger individuals. The inflow of newborn individuals is defined by a decreasing-return-to-scale function of the population density. Under these assumptions the existence of a stationary size distribution for any given exploitation rate is proven.

ASA researchers analyzed a model of two size-structured populations competing for a joint resource. The competition is assumed to be asymmetric with respect to two species, but symmetric with respect to individuals of different sizes [3]. Other assumptions are the same as in [1] and [2]. The existence of a unique stationary size distribution for any given harvesting rate was proved, as was the existence of optimal harvesting and planting rates maximizing the economic benefit of harvesting the population.