Modeling and optimal management of size-structured biological populations

Advanced Systems Analysis (ASA) Program researchers develop and analyze stylized models of biological populations (e.g., fish or forests), in which individuals’ growth significantly depends on their size or age and on the size or age of others. The aim is to understand the consequences of various management strategies, and to identify those, which can optimize typical economic (e.g., profit) and environmental (e.g., biodiversity) objectives.

© Rixie | Dreamstime

© Rixie | Dreamstime

Some resources are essentially heterogeneous; biological resources (forests, fish, etc.), for instance, are structured by their size and age. In particular, heterogeneity in size and age leads to asymmetric competition between individuals. For example, taller trees shade shorter trees, depriving the latter of some of their sunlight, but not vice versa. Another important heterogeneity is the spatial distribution of a resource. Accounting for heterogeneity in models has the potential to increase the reliability of results; therefore, optimal control models of heterogeneous resources are an important tool for advising policymakers on the sustainable exploitation of biological resources.

ASA researchers analyzed a fairly generic model of a population of individuals that are heterogeneous in size, and in which asymmetric intra-species competition impacts vital parameters and decreases the population density disproportionally, favoring bigger individuals. The inflow of newborn individuals is defined by a decreasing-return-to-scale function of population density. Under these assumptions ASA researchers were able to prove the existence of a stationary size distribution for any given exploitation rate [1]. Spatially heterogeneity in the distribution of a renewable resource was the focus of another ASA study, in which the authors sought to optimize cyclic exploitation [2]. They proved the existence of an optimal management strategy and derived the necessary optimality conditions for harvesting rate.


[1] Davydov AA & Nassar AF (2015). Stationary regime of exploitation of size-structured population with hierarchical competition. Journal of Mathematical Sciences 205(2): 199-204.

[2] Belyakov AO, Davydov AA & Veliov VV (2015). Optimal cyclic exploitation of renewable resources. Journal of Dynamical and Control Systems 21(3): 475-494.


Vienna University of Technology, Austria

Moscow State University, Russia

Vladimir State University, Russia

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Last edited: 15 March 2016


Elena Rovenskaya

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Advancing Systems Analysis Program

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