Some resources are essentially heterogeneous; biological resources (forests, fish, etc.), for instance, are structured by their size/age. In particular, size/age heterogeneity leads to asymmetric competition between individuals. For example, higher trees shade smaller trees, depriving the latter of some of their sunlight, but not vice versa. Models of optimal control of heterogeneous resources are therefore an important tool in advising policy on the exploitation of biological resources.
Methodologically, size/age-structured population dynamics models are expressed in the form of partial differential equations, in which the exploitation and recovery rates are control variables. A diversity of assumptions on how individuals respond to changing environmental conditions (for example, how growth and mortality rates depend on competition) as well as on how competition is actually formalized, gives rise to a diversity of specific models describing the dynamics of populations of heterogeneous individuals competing for the resource. A decision maker aims to optimize the economic profit from resource exploitation or may have other goals, for example, ones that take environmental degradation into account.
 Davydov A, Nassar AF (2014a). Stationary Regime of Exploitation of Size-Structured Population with Hierarchical Competition. Problems of Mathematical Analysis, 77: 71-75 (in Russian; English version in preparation)
 Davydov A, Nassar AF (2014b). On stationary solution in dynamic of population with hierarchical competition. Russian Mathematical Survey. Article in press (Published online November 2014) (in Russian; English version to appear)
 Davydov AA, Platov AS (2014). Optimal exploitation of two competing size-structured populations, Proceedings of the Steklov Institute of Mathematics, 287(1): 49-54
See also: Davydov A, Nassar AF (2015). Stationary Regime of Exploitation of Size-Structured Population with Hierarchical Competition. Journal of Mathematical Sciences, 205(2): 199-204
The photograph at the top of the page is a false-color image of a rainforest, where each color represents a certain degree of tree diversity.
Last edited: 12 March 2015
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