Mathematical Modelling of Ecological Systems in Patchy Environments

In this thesis, we incorporate spatial structure into different ecological/epidemiological systems by applying the patch model. Firstly, we consider two specific costs of dispersal: (i) the period of time spent for migration; (ii) deaths during the dispersal process. Together with the delayed logistic growth, we propose a two-patch model in terms of delay differential equation with two constant time delays. The costs of dispersal, by themselves, only affect the population sizes at equilibrium and may even drive the populations to extinction. With oscillations induced by the delay in logistic growth, numerical examples are provided to illustrate the impact of loss by dispersal. Secondly, we study a predator-prey system in a two-patch environment with indirect effect (fear) considered. When perceiving a risk from predators, a prey may respond by reducing its reproduction and decreasing or increasing (depending on the species) its mobility. The benefit of an anti-predation response is also included. We investigate the effect of anti-predation response on population dynamics by analyzing the model with a fixed response level and study the anti-predation strategies from an evolutionary perspective by applying adaptive dynamics. Thirdly, we explore the short-term or transient dynamics of some SIR infectious disease models over a patchy environment. Employing the measurements of reactivity of equilibrium and amplification rates previously used in ecology to study the response of an ecological system to perturbations to an equilibrium, we analyze the impact of the dispersals/travels between patches and other disease-related parameters on short term dynamics of these spatially structured disease models. This contrasts with most existing works on modelling the dynamics of infectious disease which are only interested in long-term disease dynamics in terms of the basic reproduction number

Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction number R0 which is defined through the spectral radius of a linear integral operator. If R0 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given

Interaction of human foraging behaviour and prey life-history traits

Mestrado em Ecologia, Biodiversidade e Gestão de EcossistemasO presente trabalho propõe-se divulgar a pesquisa passada e recente no âmbito das consequências da exploração de recursos costeiros pelo homem na biologia das espécies alvo e na comunidade onde estas estão inseridas. A ênfase das pesquisas aqui apresentadas recai principalmente sobre moluscos bentónicos e lapas em particular, dada a ocorrência de protandria (mudança de sexo de macho para fêmea ao longo do ciclo de vida) em algumas das espécies usadas como recurso alimentar. Questões relacionadas modos de reprodução, hermafroditismo e mudança de sexo no mundo animal são igualmente focadas como introdução aos últimos capítulos da dissertação onde se aborda essas questões mais profundamente. No capítulo final são apresentados trabalhos científicos que retratam a importância das áreas marinhas protegidas na conservação de espécies costeiras. ABSTRACT: The present work aims to bring to public, past and present research in the costal resources exploitation by Man and its consequences upon target species and the surrounding community. Particular attention is given to benthic molluscs and limpets in particular due to the occurrence of protandry (sex change from male to female during the life cycle) in some of the harvested species. The issues related to reproduction mode, hermaphroditism and sex change in animals are presented first as to introduce later chapters where these subjects are deepened. The final chapter presents relevant research of the use marine protected areas to the conservation of coastal species

Qualitative Theory of Switched Integro-differential Equations with Applications

Switched systems, which are a type of hybrid system, evolve according to a mixture of continuous/discrete dynamics and experience abrupt changes based on a switching rule. Many real-world phenomena found in branches of applied math, computer science, and engineering are naturally modelled by hybrid systems. The main focus of the present thesis is on hybrid impulsive systems with distributed delays (HISD). That is, studying the qualitative behaviour of switched integro-differential systems with impulses. Important applications of impulsive systems can be found in stabilizing control (e.g. using impulsive control in combination with switching control) and epidemiology (e.g. pulse vaccination control strategies), both of which are studied in this work. In order to ensure the models are well-posed, some fundamental theory is developed for systems with bounded or unbounded time-delays. Results on existence, uniqueness, and continuation of solutions are established. As solutions of HISD are generally not known explicitly, a stability analysis is performed by extending the current theoretical approaches in the switched systems literature (e.g. Halanay-like inequalities and Razumikhin-type conditions). Since a major field of research in hybrid systems theory involves applying hybrid control to problems, contributions are made by extending current results on stabilization by state-dependent switching and impulsive control for unstable systems of integro-differential equations. The analytic results found are applied to epidemic models with time-varying parameters (e.g. due to changes in host behaviour). In particular, we propose a switched model of Chikungunya disease and study its long-term behaviour in order to develop threshold conditions guaranteeing disease eradication. As a sequel to this, we look at the stability of a more general vector-borne disease model under various vaccination schemes. Epidemic models with general nonlinear incidence rates and age-dependent population mixing are also investigated. Throughout the thesis, computational methods are used to illustrate the theoretical results found

Assessing variations in water availability to vegetation and its consequences on the riparian forest of the arid southwestern USA in service of ecosystem conservation

As Earth’s climate changes, a solid understanding of ecosystems’ sensitivity and reactivity to climatic and environmental controls is critical. Vegetation is considered a key structural element of habitats and ecosystems. By studying changes in vegetation communities’ (specific species assemblages) distribution, health, and timing of main life events, compared with potential controls, such as water availability, it is possible to infer important information on the interactions between vegetation communities (an indicator of habitat integrity) and a changing climate. This comprehension of vegetation dynamics is also crucial for the conservation of species vulnerable to changes and their habitat, even more so in the case of species that are already considered endangered. To fulfil their conservation mission, natural resources managers of lands, regardless of ownership, need a regional-scale understanding of climatic and environmental controls on habitat distribution, condition and vulnerability to climate change. They also need to be able to monitor habitat condition and distribution efficiently and accurately with limited resources. This thesis examines the case of riparian habitats in drylands. Intermittent streams and their streamside vegetation act as moist and cool refuges, support a high species richness and buffer sensitive populations from drought. But they are also rare, isolated, and highly sensitive to changes in water availability. My goal is to reconstruct the complex links between water distribution, water availability to vegetation, and vegetation distribution across a diverse landscape covering a range of elevation, topography and geology, supporting diverse ecosystems. To achieve this landscape-scale overview, I use remote sensing to map the main vegetation communities distribution, their long-term evolution, health, and sensitivity to drought, and conductivity sensors to detect flow and open water presence in-non perennial streams. These methods provide high spatiotemporal resolution datasets that can cover wide areas. The resulting information on vegetation and flow is then compared to climatic and environmental factors, including local geology and rainfall, to better understand their potential vulnerability to drought. This work is focused on applied research and is set in a wider context of providing knowledge and tools for natural resources managers to keep track of rare and sensitive habitats’ condition and extent. The methods and tools used were chosen to test their suitability as accessible and efficient monitoring tools. This thesis focuses on an area in the Southwest USA, covering the upper basin of the San Pedro River (an intermittent river of the Colorado basin), the Huachuca Mountains (an isolated mountain range) and the semi-arid valley in between. My research was conducted on military lands and, as such, the natural resources management side of this work is seen through the lens of military installations and their specific approach to ecosystem conservation. However, the findings of my thesis, both on the ecosystem functioning and the management implications sides, can be more widely applied to monitoring of isolated ecosystems in drylands. This work provides an overall understanding of water availability to vegetation across a diverse landscape, and how this availability controls vegetation distribution and health, from rainfall-supported grassland to groundwater-fed dense riparian forests. I study the differences in long-term, interannual vegetation density variations between ephemeral and perennial reaches along a dryland river, showing how local geology and groundwater levels can buffer riparian ecosystems against drought. I also describe the spatiotemporal distribution of flow in mountain ephemeral streams, from perennial springs to rainfall-fed washes. I link flow permanence to underlying geology, consider how different reaches might be impacted by prolonged drought, and the consequences on local flora and fauna. Finally, I look at short-term, intra-annual changes in vegetation phenology along mountain streams and show how droughts, with higher temperatures and lower precipitation, might shorten the growing season and negatively impact vegetation leaf density. Throughout the thesis, I relate my findings to natural resources management questions and needs, with the goal of providing tools and conclusions useful for endangered and critical habitat monitoring

Plant Community Development in Storm-induced Overwash Fans of the Otis Pike Fire Island High Dune Wilderness Area, New York

Barrier island systems are driven by disturbance, climate, and geomorphology. Previously, barrier island vegetation communities were primarily described by microclimate variability. The purpose of this dissertation is to better understand effects of white-tailed deer on developing plant communities on barrier islands after a catastrophic disturbance. I used distance-based Moran\u27s eigenvector maps to identify spatial structures in vegetation communities of overwash fans in the third and fourth years after Hurricane Sandy. Spatial structures were present and significant at two or more frequencies in all overwash fans and explained the greatest amount of variation in vegetation community composition. Induced spatial dependence was predominantly controlled by proximity to foredune. I identified five biotic and abiotic influences to community composition in overwash fans and ranked their importance through canonical correspondence analysis. Gradients in productivity and elevation were primarily responsible for community composition and deer effects were not identifiable at the plot level. I identified effects of deer on vegetation cover and richness through a paired exclosure experiment, though only cover effects were statistically significant. Deer effects on cover were starker than those observed on species richness, suggesting assessments of deer effects on depauperate communities should focus on richness and cover. Lastly, I assessed effects of white-tailed deer on the rate of vegetation recovery in overwash fans through imagery classification and assessments of local white-tailed deer density. Though deer affect vegetation cover through trampling, grazing, and browsing in overwash fans, their effects on recovery rates were minimal and not statistically significant. Two overwash fans are expected to recover to pre-Sandy conditions within the decade since a nascent foredune is present and growing. Two overwash fans may never recover due to continued disturbance. The five remaining overwash fans have a slowly-forming nascent foredune, and changes in climate and frequency of storm events make their futures uncertain. Though deer do not pose a threat to the resilience of the barrier island, selective foraging behaviors may change composition and developmental trajectories of recovering vegetation communities over time