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Two paradigms in mathematical population biology: An attempt at synthesis

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Abstract

However popular the slogan of nonlinear ecological interactions has been in theory, practical ecology professes the projection matrix paradigm, which is essentially linear, i.e., the linear matrix model paradigm for discrete structured population dynamics. The dominant eigenvalue λ1 of projection matrix L is considered the growth potential of a population. It provides for a quantitative measure of species adaptation to the given environment, with the measure being adequate and precise, given data of the “identified individuals” type. The case of “identified individuals with uncertain parents” gives rise to uncertainty in the status-specific reproduction rates, which is eliminated in a unique way (for a broad class of structures and life cycle graphs) by maximizing λ1(L) under the constraints ensuing from the data on and knowledge about species biology. The paradigm of linearity gives way to the nonlinear models when species interactions such as competition for shared resources are to be modeled and where the outcome of interaction depends on the population structure of the competitors. This circumstance dictates the need for synthesis of the two paradigms, which is achieved in nonlinear matrix operators as models of interaction between the species whose populations are discrete-structured.

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  1. Laboratory of Mathematical Ecology, Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 119017, Russia

    D. O. Logofet & I. N. Belova

  2. Department of Geobotany, Biological Faculty, Moscow State University, Moscow, 119991, Russia

    N. G. Ulanova

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  1. D. O. Logofet
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  2. N. G. Ulanova
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Original Russian Text © D.O. Logofet, N.G. Ulanova, I.N. Belova, 2011, published in Zhurnal Obshchei Biologii, 2011, Vol. 72, No. 5, pp. 369–387.

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Logofet, D.O., Ulanova, N.G. & Belova, I.N. Two paradigms in mathematical population biology: An attempt at synthesis. Biol Bull Rev 2, 89–104 (2012). https://doi.org/10.1134/S2079086412010021

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