Bayesian Parameter Estimation of Cannibalism Dynamics in Larval Atractosteus tropicus Under Different Feeding Conditions

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Abstract
In this work, Bayesian estimation is performed for the parameters of a mathematical model, formulated as a system of ordinary differential equations, that describes cannibalism dynamics in a larval populations of Atractosteus tropicus were reared in a pond. The model divides the population into three subclasses: vulnerable, cannibalistic, and non-vulnerable individuals. Parameter estimation is conducted under two scenarios: a fed population and an unfed population. Correlation matrices are calculated for both cases. For the fed population, the most influential parameters are food quality and the time devoted to managing cannibalistic individuals. In contrast, for the unfed population, the strongest correlation occurs between the mortality rate and the transition rate of cannibalistic individuals to the non-vulnerable class. Therefore, providing larvae with high-quality food substantially reduces cannibalism and the handling time required and, consequently, increases the survival of the species.

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