dorsal/arxiv
View SchemaDensity-Dependence as a Size-Independent Regulatory Mechanism
| Authors | Harold P. de Vladar |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0504022 |
| URL | https://arxiv.org/abs/q-bio/0504022 |
| DOI | 10.1016/j.jtbi.2005.05.014 |
| Journal | H.P. de Vladar. Density-dependence as a size-independent regulatory mechanism. J. Theor. Biol. (2006) vol. 238 (2) pp. 245-256 |
Abstract
The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the $\theta$-logistic, which generalises the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalises many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter $\rho$ and a competition coefficient $\theta$. Distinct sign combinations of these parameters reproduce not only the family of $\theta$-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.
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"abstract": "The growth function of populations is central in biomathematics. The main\ndogma is the existence of density dependence mechanisms, which can be modelled\nwith distinct functional forms that depend on the size of the population. One\nimportant class of regulatory functions is the $\\theta$-logistic, which\ngeneralises the logistic equation. Using this model as a motivation, this paper\nintroduces a simple dynamical reformulation that generalises many growth\nfunctions. The reformulation consists of two equations, one for population\nsize, and one for the growth rate. Furthermore, the model shows that although\npopulation is density-dependent, the dynamics of the growth rate does not\ndepend either on population size, nor on the carrying capacity. Actually, the\ngrowth equation is uncoupled from the population size equation, and the model\nhas only two parameters, a Malthusian parameter $\\rho$ and a competition\ncoefficient $\\theta$. Distinct sign combinations of these parameters reproduce\nnot only the family of $\\theta$-logistics, but also the van Bertalanffy,\nGompertz and Potential Growth equations, among other possibilities. It is also\nshown that, except for two critical points, there is a general size-scaling\nrelation that includes those appearing in the most important allometric\ntheories, including the recently proposed Metabolic Theory of Ecology. With\nthis model, several issues of general interest are discussed such as the growth\nof animal population, extinctions, cell growth and allometry, and the effect of\nenvironment over a population.",
"arxiv_id": "q-bio/0504022",
"authors": [
"Harold P. de Vladar"
],
"categories": [
"q-bio.PE"
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"doi": "10.1016/j.jtbi.2005.05.014",
"journal_ref": "H.P. de Vladar. Density-dependence as a size-independent\n regulatory mechanism. J. Theor. Biol. (2006) vol. 238 (2) pp. 245-256",
"title": "Density-Dependence as a Size-Independent Regulatory Mechanism",
"url": "https://arxiv.org/abs/q-bio/0504022"
},
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