Abstract
According to the IUCN, most sea turtles fall into one of the endangered categories. Since, sea turtles, like many other reptiles, present an unusual developmental process, marked by the determination of the sex of the offspring by environmental factors, more specifically by temperature. In the temperature sex determination (TSD) system the temperature of an embryo's environment during incubation period will dictate the embryo's sex development. This developmental process, together with the complex mating and nesting behavior and the vulnerability of sea turtles to threats of a natural or anthropogenic nature, naturally lead to the study of the population dynamics of the species.? For this reason, in this paper, we have developed a continuous model given by a system of three ordinary differential equations to study the dynamics of the green sea turtle population long-term, focusing the mathematical simulations on the data obtained for the nesting species of Galapagos Islands. Through the qualitative analysis of the model, the following is demonstrated: 1) The flow induced by the system is positively invariant on the region of biological interest and 2). The given condition on is necessary and sufficient for the unique nontrivial equilibrium point to be globally asymptotically stable in that region. When implementing the estimated values for our parameters in the numerical simulations, it was observed that indeed the population of Galapagos green sea turtles complies with the condition for which the nontrivial critical point is globally asymptotically stable.
Highlights
Sea turtles present a temperature sex determination (TSD) system, this is an evolutionary condition that turtles, like other reptiles, have adopted throughout time
The model developed in this paper is characterized by studying the population dynamics through a sex-structured continuous time model
From the above results of the qualitative analysis of the model, we infer that the condition established determine the persistence and stability of the green turtle population or its extinction
Summary
Sea turtles present a temperature sex determination (TSD) system, this is an evolutionary condition that turtles, like other reptiles, have adopted throughout time. Due to the complex nesting behavior of sea turtles and the mechanism by which the sex of the offspring is determined, it is reasonable to look into the factors that could be directly affecting the sex ratios of eggs, such as sand temperatures. The lack of males within the sea turtle population will eventually affect the population dynamics It is unknown the minimum proportion of males sufficient to support the sea turtle population in such a way to avoid population collapse or even extinction. This problem naturally lends itself to investigation via a sex-structured model to analyse the dynamic of the population
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