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Resumen del producto
Ornelas, A., F., Delgado-Vences, E., Morales-Bojórquez, V.H., Cruz-Escalona, E., Marín-Enríquez & C.J., Hernández-Camacho
(2023).
Modeling the biological growth with a random logistic differential equation.
Environmental and Ecological Statistics.
30: 233-260.
DOI: 10.1007/s10651-023-00561-y.
Modeling the biological growth with a random logistic differential equation
Arelly Ornelas 1, Francisco Delgado-Vences 2, Enrique Morales-Bojórquez 3, Víctor Hugo Cruz-Escalona 4, Emigdio Marín-Enríquez 5 y Claudia J. Hernández-Camacho 4
1 Instituto Politécnico Nacional, Centro Interdisciplinario de Ciencias Marinas, Centro Interdisciplinario de Ciencias Marinas, Conacyt - Instituto Politécnico Nacional, La Paz, Mexico
2 Instituto de Matemáticas, Conacyt - Universidad Nacional Autónoma de México, Oaxaca, Mexico
3 Centro de Investigaciones Biológicas del Noroeste SC., La Paz, Mexico
4 Instituto Politécnico Nacional, Centro Interdisciplinario de Ciencias Marinas, Centro Interdisciplinario de Ciencias Marinas, Instituto Politécnico Nacional, La Paz, Mexico
5 Facultad de Ciencias del Mar, Conacyt - Universidad Autónoma de Sinaloa, Mazatlán, Mexico
We modeled biological growth using a random differential equation (RDE), where the initial condition is a random variable, and the growth rate is a suitable stochastic process. These assumptions let us obtain a model that represents well the random growth process observed in nature, where only a few individuals of the population reach the maximal size of the species, and the growth curve for every individual behaves randomly. Since we assumed that the initial condition is a random variable, we assigned a priori density, and we performed Bayesian inference to update the initial condition’s density of the RDE. The Karhunen–Loeve expansion was then used to approximate the random coefficient of the RDE. Then, using the RDE’s approximations, we estimated the density f(p, t). Finally, we fitted this model to the biological growth of the giant electric ray (or Cortez electric ray) Narcine entemedor. Simulations of the solution of the random logistic equation were performed to construct a curve that describes the solutions’ mean for each time. As a result, we estimated confidence intervals for the mean growth that described reasonably well the observed data. We fit the proposed model with a training dataset, and the model is tested with a different dataset. The model selection is performed with the square of the errors.
Palabras clave: ecology; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Math. Appl. in Environmental Science; Statistics for Life Sciences, Medicine, Health Sciences; Theoretical Ecology/Statistics
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