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Choosing classes for size projection matrix models

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  • Picard, Nicolas
  • Ouédraogo, Dakis
  • Bar-Hen, Avner

Abstract

Projection matrix models are intensely used in ecology to model the dynamics of structured populations. When dealing with size-structured populations, there is no satisfactory algorithm to partition size into discrete classes. We show that the Vandermeer–Moloney algorithm for choosing classes is inconsistent with the Usher model, and systematically selects the finest classes. Considering that the matrix model is a discrete approximation of a continuous model, we define an approximation error as the sum of a distribution error (the difference between the discrete distribution and its continuous counterpart), and a sample error. The optimal partition of size into classes is the one that minimizes the approximation error. This method for choosing classes also shows that the choice of the class width cannot be disconnected from the choice of the time step. When applied to 520 trees of Dicorynia guianensis in French Guiana, this algorithm identified 8 classes of 11.4cm in width, which is in agreement with the empirical choice of foresters.

Suggested Citation

  • Picard, Nicolas & Ouédraogo, Dakis & Bar-Hen, Avner, 2010. "Choosing classes for size projection matrix models," Ecological Modelling, Elsevier, vol. 221(19), pages 2270-2279.
    • Handle: RePEc:eee:ecomod:v:221:y:2010:i:19:p:2270-2279
    DOI: 10.1016/j.ecolmodel.2010.06.010
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    References listed on IDEAS

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    1. Picard, Nicolas & Mortier, Frédéric & Chagneau, Pierrette, 2008. "Influence of estimators of the vital rates in the stock recovery rate when using matrix models for tropical rainforests," Ecological Modelling, Elsevier, vol. 214(2), pages 349-360.
    2. Logofet, Dmitrii O., 2008. "Convexity in projection matrices: Projection to a calibration problem," Ecological Modelling, Elsevier, vol. 216(2), pages 217-228.
    3. López Torres, I. & Fullana Belda, C. & Ortuño Pérez, S.F. & Martín Fernández, A.J., 2008. "Choosing Fagus sylvatica L. matrix model dimension by sensitivity analysis of the population growth rate with respect to the width of the diameter classes," Ecological Modelling, Elsevier, vol. 218(3), pages 307-314.
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    Cited by:

    1. Smith, Phoebe & Guiver, Chris & Adams, Ben, 2022. "Quantifying the per-capita contribution of all components of a migratory cycle: A modelling framework," Ecological Modelling, Elsevier, vol. 471(C).

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