Does averaging overestimate or underestimate population growth? It depends

Dmitrii O. Logofet

Ecological Modelling, 2019, vol. 411, issue C

Abstract: When a matrix population model is nonautonomous, i.e., when it represents a set of single-time-step ("annual") PPMs, L(t), t = 0, 1, …, T – 1, each corresponding to a fixed life cycle graph, then each of the annual matrices generates its own set of model results to characterize the population. In particular, λ1(t), the asymptotic growth rate, varies with t and may result in alternating predictions of population viability. A logical way to characterize the population over the total period of observations is to average the given set of T PPMs, and I have proved the correct mode of averaging to be the pattern-geometric average. It means finding a matrix, G, such that its Tth power equals the product of T annual matrices (in the chronological order), while its pattern does correspond to the given life cycle graph. In practical cases however, the mathematical problem of pattern-geometric average has no exact solution for a fundamental mathematical reason. Nevertheless, the approximate solutions have revealed a fair precision of approximation in recent case studies of alpine short-lived perennials (Eritrichium caucasicum and Androsace albana), resulting in quite certain predictions of population viability by means of λ1(G), the dominant eigenvalue of the average matrix.

Keywords: Discrete-structured population; Life cycle graph; Matrix calibration; Pattern-geometric average; Dominant eigenvalue; Reproductive uncertainty; Stochastic growth rate; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:411:y:2019:i:c:s0304380019302522

DOI: 10.1016/j.ecolmodel.2019.108744

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