Caribbean spiny lobster (Panulirus argus) is a popular and heavily exploited seafood throughout its range. This species supports the primary fishery in many Caribbean countries, especially in the Bahamas, which reports the highest catches and where spiny lobster serves as the number one food export. P. argus possesses one of the longest pelagic larval durations of any marine species, ranging from 6-12 months. This allows for the possibility of long-range dispersal, which would make it difficult to determine if local adult populations originate from areas close-by or within the same countries/jurisdictions, thus presenting implications for conservation and management of the species. This project seeks to explore the policy implications of lobster larval dispersal in the Bahamas by examining the larval connectivity of locally spawned P. argus in order to determine the mean dispersal kernel and to identify hotspots of settlement within the area. A coupled biophysical model was used to simulate larval transport from scaled egg production of 47 release locations within the Bahamas. The model was initialized bi-weekly from April through May, the highest months of larvae production in the Bahamas, with each model run occurring for a maximum of 180 days. The dispersal kernel for the Bahamas was calculated to be an average of 100-300 km, indicating that the larvae released within its boundaries typically settled there as well. Due to the long pelagic larval duration, larval particles were able to travel extensive distances, averaging trajectories covering distances of 4000 km and greater from the source locations. Yet, those same larval particles still settled in locations within the Bahamas, suggesting local retention, which varies from the common perception that lobster in the Bahamas originate elsewhere. This knowledge can be used to assess and perhaps reevaluate conservation and management strategies related to the Bahamian P. argus fishery, including the implementation of MPAs and/or MPA networks, input and output management controls, and other management tools.

Orientador: Wilson Castro Ferreira Junior / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-22T04:48:33Z (GMT). No. of bitstreams: 1 LouVega_Salvador_D.pdf: 14692586 bytes, checksum: f745ca7fb3da3cfa09dfb8a8dd9f37bb (MD5) Previous issue date: 2013 / Resumo: Apresentamos um modelo integro - recursivo para a dispersão de uma planta que acopla uma dinâmica de reprodução, com efeito, Allee e uma dinâmica de dispersão em um meio heterogêneo. Propomos um modelo de difusão e sedimentação para derivar núcleos de dispersão teóricos, que representem o padrão de dispersão de sementes gerado por pássaros frugívoros em um meio heterogêneo. O núcleo gerado através do modelo _e capaz de reproduzir o padrão espacial de agregação de sementes gerado pelos pássaros frugívoros sob condições naturais. Enquanto _a dinâmica de reprodução, consideramos um efeito Allee devido à limitação de pólen, que reduz a produção de sementes. Introduzimos o efeito Allee através de uma função de probabilidade que depende da densidade local de plantas. Analisa-se o comportamento da expansão da planta, e estima-se a velocidade média de expansão. O modelo mostra uma invasão através de pulsos, que atribuímos ao efeito Allee e ao comportamento de dispersão da planta / Abstract: We present an integro-difference model for a plant dispersal, which couples a reproductive dynamic with Allee effect and dispersal dynamic in a heterogeneous environment. We propose diffusion and settling model to derive theoretical dispersal kernels that represent the seed dispersal pattern generated by frugivores birds in a heterogeneous environment. The dispersal kernel derived through the model is able to reproduce the aggregate seed dispersal pattern generated by the frugivores birds under field conditions. As for the reproductive dynamic, we consider an Allee effect due to pollen limitation, which reduces seed production. We introduce the Allee effect through a probability function, which depends on the local plant density. The plant expansion behavior is analyzed, and the average expansion speed is estimated. The model shows a pulsed invasion, which we attribute to the Allee effect and the plant dispersal behavior / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Cette thèse porte sur l'analyse mathématique de modèles de réaction-dispersion de la forme [delta]tu=D(u) +f(x,u). L'objectif est de comprendre l'influence du terme de réaction f, de l'opérateur de dispersion D, et de la donnée initiale u0 sur la propagation des solutions de ces équations. Nous nous sommes intéressés principalement à deux types d'équations de réaction-dispersion : les équations de réaction-diffusion où l'opérateur de dispersion différentielle est D=[delta]2z et les équations intégro-différentielles pour lesquelles D est un opérateur de convolution, D(u)=J* u-u. Dans le cadre des équations de réaction-diffusion en milieu homogène, nous proposons une nouvelle approche plus intuitive concernant les notions de fronts progressifs tirés et poussés. Cette nouvelle caractérisation nous a permis de mieux comprendre d'une part les mécanismes de propagation des fronts et d'autre part l'influence de l'effet Allee, correspondant à une diminution de la fertilité à faible densité, lors d'une colonisation. Ces résultats ont des conséquences importantes en génétique des populations. Dans le cadre des équations de réaction-diffusion en milieu hétérogène, nous avons montré sur un exemple précis comment la fragmentation du milieu modifie la vitesse de propagation des solutions. Enfin, dans le cadre des équations intégro-différentielles, nous avons montré que la nature sur- ou sous-exponentielle du noyau de dispersion J modifie totalement la vitesse de propagation. / This thesis deals with the mathematical analysis of reaction-dispersion models of the form [delta]tu=D(u) +f(x,u). We investigate the influence of the reaction term f, the dispersal operator D and the initial datum u0 on the propagation of the solutions of these reaction-dispersion equations. We mainly focus on two types of equations: reaction-diffusion equations (D=[delta]2z and integro-differential equations (D is a convolution operator, D(u)=J* u-u). We first investigate the homogeneous reaction-diffusion equations. We provide a new and intuitive explanation of the notions of pushed and pulled traveling waves. This approach allows us to understand the inside dynamics the traveling fronts and the impact of the Allee effect, that is a low fertility at low density, during a colonisation. Our results also have important consequences in population genetics. In the more general and realistic framework of heterogeneous reaction-diffusion equations, we exhibit examples where the fragmentation of the media modifies the spreading speed of the solution. Finally, we investigate integro-differential equations and prove that emph{fat-tailed} dispersal kernels J, that is kernels which decay slower than any exponentially decaying function at infinity, lead to acceleration of the level sets of the solution u.