Probabilistic Gompertz model of irreversible growth |
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Authors: | D C Bardos |
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Institution: | (1) School of Physics, The University of Melbourne, Victoria, 3010, Australia |
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Abstract: | Characterizing organism growth within populations requires the application of well-studied individual size-at-age models,
such as the deterministic Gompertz model, to populations of individuals whose characteristics, corresponding to model parameters,
may be highly variable. A natural approach is to assign probability distributions to one or more model parameters. In some
contexts, size-at-age data may be absent due to difficulties in ageing individuals, but size-increment data may instead be
available (e.g., from tag-recapture experiments). A preliminary transformation to a size-increment model is then required.
Gompertz models developed along the above lines have recently been applied to strongly heterogeneous abalone tag-recapture
data. Although useful in modelling the early growth stages, these models yield size-increment distributions that allow negative
growth, which is inappropriate in the case of mollusc shells and other accumulated biological structures (e.g., vertebrae)
where growth is irreversible.
Here we develop probabilistic Gompertz models where this difficulty is resolved by conditioning parameter distributions on
size, allowing application to irreversible growth data. In the case of abalone growth, introduction of a growth-limiting biological
length scale is then shown to yield realistic length-increment distributions. |
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Keywords: | |
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