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Advisor(s)
Abstract(s)
Os modelos ecológicos descrevem a dinâmica de uma determinada população que
habita num ecossistema e num período de tempo determinado. Este trabalho tem
por principal objectivo estudar os modelos ecológicos unidimensionais. Os modelos considerados neste trabalhos são os modelos de Beverton-Holt, Ricker, Maynard
Smith-Slatkin e Hassel. Para tal, começamos por introduzir algumas definições e
resultados que servem de base ao estudo do comportamento assintótico dos modelos
propostos. De seguida, fazemos a derivação dos modelos do ponto de vista
biológico. Faz-se também a derivação dos modelos modificados de Beverton Holt e Ricker, bem como o estudo do comportamento assintótico destes modelos. De
seguida, os modelos de Maynard Smith-Slatkin e Hassel são usados para obtermos
modelos unidimensionais de captura e discutir o efeito de hidra, efeito que por vezes
ocorre nestes modelos. Obtemos ainda um modelo de captura generalizado, o
modelo de Seno, e desenvolve-se de seguida um novo modelo que ´e alternativo ao
modelo de Seno com função de Beverton-Holt. Finalmente, descrevem-se alguns aspectos que foram considerados aquando da elaboração de uma ação de divulgação
em Biomatemática na Academia Júnior de Ciências.
Ecological models describe the dynamics of a given population that inhabits in some ecosystem and over a given period of time. The main objective of this work is to study one-dimensional ecological models. The models considered in this work are the Beverton-Holt, the Ricker, the Maynard Smith-Slatkin and the Hassel models. To do this, we start by introducing some definitions and results that are the main tools we will use to study the asymptotic behavior of the proposed models. After this, we derive the models from the biological point of view. We also derive the modified Beverton-Holt and Ricker models and study of their asymptotic behavior. After, the models of Maynard Smith-Slatkin and Hassel are used to develop unidimensional capture models and to discuss the hydra effect, frequently found in capture models. Additionaly, we consider a generalized capture model, the Sine model, and develop a new model that is alternative to the Sine model with Beverton-Holt function. Finally, we describe some aspects that were discussed in the elaboration of a talk in Biomathematics given at the “Academia J´unior de Ciˆencias” (Junior Academy of Sciences).
Ecological models describe the dynamics of a given population that inhabits in some ecosystem and over a given period of time. The main objective of this work is to study one-dimensional ecological models. The models considered in this work are the Beverton-Holt, the Ricker, the Maynard Smith-Slatkin and the Hassel models. To do this, we start by introducing some definitions and results that are the main tools we will use to study the asymptotic behavior of the proposed models. After this, we derive the models from the biological point of view. We also derive the modified Beverton-Holt and Ricker models and study of their asymptotic behavior. After, the models of Maynard Smith-Slatkin and Hassel are used to develop unidimensional capture models and to discuss the hydra effect, frequently found in capture models. Additionaly, we consider a generalized capture model, the Sine model, and develop a new model that is alternative to the Sine model with Beverton-Holt function. Finally, we describe some aspects that were discussed in the elaboration of a talk in Biomathematics given at the “Academia J´unior de Ciˆencias” (Junior Academy of Sciences).
Description
Keywords
Acção de Divulgação Em Matemática Comportamento Assintótico Efeito de Hidra Modelo de Maynard Smith-Slatkin Modelo de Ricker Modelo de Seno Modelo Debeverton-Holt Modelo Dehassel Modelos de Captura Modelos Unidimensionais Pontos Fixos