Stochastic differential equations mixed model for individual growth with the inclusion of genetic characteristics

  • Nelson T. Jamba Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora, Portugal and Liceu nº 918 do município dos Gambos, Angola https://orcid.org/0000-0003-3270-0928
  • Patrícia A. Filipe Iscte-Instituto Universitário de Lisboa, Iscte Business School, Quantitative Methods for Management and Economics Department, Lisboa and Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora, Évora, Portugal https://orcid.org/0000-0003-3664-7239
  • Gonçalo Jacinto Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora and Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora, Évora, Portugal https://orcid.org/0000-0002-3292-2208
  • Carlos A. Braumann Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora and Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora, Évora, Portugal https://orcid.org/0000-0003-2721-9750
DOI: https://doi.org/10.19139/soic-2310-5070-1829
Keywords: Genetic traits, Individual Growth, Mixed Models, Stochastic Differential Equations

Abstract

In early work we have studied a class of stochastic differential equation (SDE) models, for which the Gompertz and the Bertalanffy-Richards stochastic models are particular cases, to describe individual growth in random environments, and applied it to model cattle weight evolution using real data. We have started to work on these type of models considering that the model parameters are fixed, i.e. the same for all the animals. Aiming to incorporate variability among individuals, we consider that the model parameters can be random variables, resulting in SDE mixed models. In additon, here we consider SDE mixed models, allowing the parameters to be random and propose to incorporate each animal's genetic characteristics considering the transformed animal's weight at maturity to be a function of its genetic values. The main objective is to extend the SDE mixed model to the more realistic case where the individual genetic value becomes an important component in the estimated growth curve. For the estimation of the model parameters we have used maximum likelihood estimation theory. Estimates and asymptotic confidence intervals of the parameters are presented. A comparison with SDE non-mixed model and SDE mixed model without the inclusion of genetic characteristics is shown with the conclusion that the incorporation of some genetic characteristics in the model parameters improves the estimation of the animal's growth curve.

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Published
2023-12-19
How to Cite
Jamba, N. T., Filipe, P. A., Jacinto, G., & Braumann, C. A. (2023). Stochastic differential equations mixed model for individual growth with the inclusion of genetic characteristics. Statistics, Optimization & Information Computing, 12(2), 298-309. https://doi.org/10.19139/soic-2310-5070-1829
Issue
Vol 12 No 2 (2024)
Section
Research Articles
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