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  • 1.
    Brännström, Åke
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Sumpter, David J.T.
    Stochastic analogues of deterministic single-species population models2006Ingår i: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 69, nr 4, s. 442-451Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models—additive normally distributed noise and multiplicative lognormally distributed noise—generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.

  • 2.
    De Roos, André M
    et al.
    Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O.Box 94084, 1090 GB Amsterdam, The Netherlands.
    Schellekens, Tim
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för ekologi, miljö och geovetenskap.
    Van Kooten, Tobias
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för ekologi, miljö och geovetenskap.
    Van De Wolfshaar, Karen
    Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O.Box 94084, 1090 GB Amsterdam, The Netherlands.
    Claessen, David
    Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O.Box 94084, 1090 GB Amsterdam, The Netherlands.
    Persson, Lennart
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för ekologi, miljö och geovetenskap.
    Simplifying a physiologically structured population model to a stage-structured biomass model.2008Ingår i: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 73, nr 1, s. 47-62Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We formulate and analyze an archetypal consumer-resource model in terms of ordinary differential equations that consistently translates individual life history processes, in particular food-dependent growth in body size and stage-specific differences between juveniles and adults in resource use and mortality, to the population level. This stage-structured model is derived as an approximation to a physiologically structured population model, which accounts for a complete size-distribution of the consumer population and which is based on assumptions about the energy budget and size-dependent life history of individual consumers. The approximation ensures that under equilibrium conditions predictions of both models are completely identical. In addition we find that under non-equilibrium conditions the stage-structured model gives rise to dynamics that closely approximate the dynamics exhibited by the size-structured model, as long as adult consumers are superior foragers than juveniles with a higher mass-specific ingestion rate. When the mass-specific intake rate of juvenile consumers is higher, the size-structured model exhibits single-generation cycles, in which a single cohort of consumers dominates population dynamics throughout its life time and the population composition varies over time between a dominance by juveniles and adults, respectively. The stage-structured model does not capture these dynamics because it incorporates a distributed time delay between the birth and maturation of an individual organism in contrast to the size-structured model, in which maturation is a discrete event in individual life history. We investigate model dynamics with both semi-chemostat and logistic resource growth.

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