The thesis describes various modifications of the predator-prey model. The modifications are considering several harvesting methods. At the beginning a solution and a sensitivity analysis of the basic model are provided. The first modification is the percentage harvesting model, which could be easily converted to the basic model. Secondly a constant harvesting including a linearization is derived. A significant part is devoted to regulation models with special a focus on environmental applications and the stability of the system. Optimization algorithms for one and both species harvesting are derived and back-tested. One species harvesting is based on econometrical tools; the core of two species harvesting is the modified Newton's method. The economic applications of the model in macroeconomics and oligopoly theory are expanded using the methods derived in the thesis.

Dans cette thèse nous nous sommes intéressés à la formation des bancs de poissons et à l'étude des interactions proies-prédateurs en présence de comportements collectifs par une approche de modélisation. Ce phénomène, bien qu'il soit le résultat d'interactions qui ont lieu à l'échelle individuelle, il engendre des conséquences à plus grande échelle, spatiale ou temporelle. L'objectif principal de cette thèse a été celui de comprendre l'influence du processus d'agrégation sur la réponse fonctionnelle. Nous avons élaboré un modèle centré sur l'individu (IBM) qui décrit les interactions intra-spécifiques ainsi que celle entre proies et prédateurs. Les agents peuvent ou pas avoir du comportement collectif.Dans un premier modèle les prédateurs sont attirés par les proies qu'ils voient. Ensuite, nous avons ajouté une composante à la vitesse du prédateur dépendante du bruit émis par les proies. Pour les deux cas, nous avons comparé les réponses fonctionnelles dans quatre configurations différentes. Nos résultats suggèrent que la prédation est plus efficace lorsque les proies s'agrègent. De plus, deux différents types de réponse fonctionnelle émergent : celle de Holling type II si les proies ne forment pas des bancs, celle de Holling type III autrement.Ensuite, nous nous sommes focalisés sur les conséquences à l'échelle de la population d'un phénomène (l'agrégation) se déroulant à l'échelle individuelle. Nous avons cherché un indice capable de détecter les bancs dans l'espace. Ensuite, en suivant une démarche mathématique, nous avons écrit une équation aux dérivées partielles représentant l'évolution spatio-temporelle de la densité des proies. / This thesis deals with the modelling of schooling phenomena and its consequences on predator-prey dynamics. Many marine species exhibit collective behaviour. While this phenomenon depends on individual interactions, it can have important effects at larger spatial and temporal scales.The main goal of this work is to understand the influence of aggregation on functional response, which represents predator feeding behaviour. We elaborated an individual-based model (IBM) describing schooling behaviour as well as predator-prey interactions. Predators can either be attracted towards visible prey, or hear, and so move towards, the noise produced by prey at a larger distance and then attack once they are close enough to see them. We analysed four different configurations, in which prey and/or predators can school or just move randomly. Our results shown an increased predation efficiency when prey school, and also different functional response shapes: Holling type II emerges if prey do not aggregate, while Holling type III emerges when prey school. Then, we focused on schooling consequences at higher scale. In particular, we analysed how to fit classical models to our emergent functional responses. Moreover, we found out a possible way to detect aggregates. Finally, we wrote a model representing the spatio-temporal evolution of prey density.

Ce travail est consacré à l’étude de la dynamique d’un système proie-prédateur de type Leslie-Gower défini par un système d’équations différentielles ordinaires (EDO) ou d’équations différentielles stochastiques (EDS), ou par des systèmes couplés d’EDO ou d’EDS. L’objectif principal est de faire l’analyse mathématique et la simulation numérique des modèles construits. Cette thèse est divisée en deux parties : La première partie est consacrée à un système proie-prédateur où les proies utilisent un refuge, le modèle est donné par un système d’équations différentielles ordinaires ou d’équations différentielles stochastiques. Le but de cette partie est d’étudier l’impact du refuge ainsi que la perturbation stochastique sur le comportement des solutions du système. Dans la deuxième partie, nous considérons un système proie-prédateur couplé en réseau. Il s’agit d’étudier comment des couplages plus ou moins forts entre plusieurs systèmes affectent l’existence et la position des points d’équilibre, et la stabilité de ces systèmes. / This work is devoted to the study of the dynamics of a predator-prey system of Leslie-Gower type defined by a system of ordinary differential equations (EDO) or stochastic differential equations (EDS), or by coupled systems of EDO or EDS. The main objective is to do mathematical analysis and numerical simulation of the models built. This thesis is divided into two parts : The first part is dedicated to a predator-prey system where the prey uses a refuge, the model is given by a system of ordinary differential equations or stochastic differential equations. The purpose of this part is to study the impact of the refuge as well as the stochastic perturbation on the behavior of the solutions of the system. In the second part, we consider a networked predator-prey system. We show that symmetric couplings speed up the convergence to a stationary distribution.

In introductory biology, college students are taught to predict how populations will grow and change over time by using population growth models. These models are commonly represented as mathematical equations. However, students consistently struggle when math and biology concepts intersect in the classroom, and these struggles lead to suboptimal understanding of how mathematical population models are designed and used. Education literature suggests that students may struggle with population modeling because of math anxiety, the high cognitive load of the task, and the lack of scaffolding for abstract concepts. In our study, we sought to improve student mastery modeling exponential growth, logistic growth, and Lotka-Volterra predator-prey interactions through using pictorial diagrams in modeling pedagogy. We predicted that these diagrams would reduce the amount of triggered math anxiety, lower the cognitive load of the task through reducing element interactivity, and allow for a more scaffolding for abstract symbols through a pictorial representation bridge. To test the effectiveness of population diagrams, we created two versions of a population modeling lesson plan: one version taught using diagrams then equations, while the other taught using purely equations. We also designed practice and assessment questions that tested calculation and model-building ability. We assessed math anxiety, scientific reasoning ability, and math ability at the beginning of the semester and state anxiety, effort of tasks, and difficulty of tasks during each lesson. Over 200 students from a non-major biology course were randomly assigned to each group, and all were given a pre-assessment, four lessons, a practice test, and a unit test on population modeling. Our findings show that while the addition of pictorial models to the traditional pedagogy did not have a significant effect on exponential and logistic growth model mastery, students that were exposed to predator-prey diagrams were more able to create a new model for a three-level predator-prey interaction than students that were only given traditional pedagogy. In addition, students who were exposed to predator-prey interaction diagrams before they derived equations reported a lower cognitive load than students who were only exposed to equations. Although diagrams were not a more helpful calculation tool for students than traditional equations, using population diagrams before to equation derivation may help improve student mastery of growth model creation.

Predators often have strong top-down effects on ecosystems and are considered a priority for conservation and management. Predator activity can influence prey distribution, abundance, and foraging behaviors and are likely to influence habitat by impacting ecological and environmental characteristics as well as presence of competitor species. There are knowledge gaps of the functional diversity of fish assemblages, non-consumptive predator effects, and environmental effects on fish assemblages. With this study, effects of top marine predators, such as sharks and great barracuda, on diversity and abundance of prey communities were examined in putative low (north side of South Bimini = lagoon) and high-risk (south side of South Bimini = flat) areas around South Bimini, The Bahamas. Baited remote underwater video surveys (BRUVs) deployed in the nearshore habitat captured abundance and potential predator-prey interactions. Predator and prey abundances at each site were compared to determine potential risk affect within high and low risk environments. A general baseline of predator and prey species was established throughout six months of observation (January- June 2018). Results showed a difference in prey communities between high and low risk habitats. Teleost abundance was highest on the south side of South Bimini. There were no differences in flight behavior of prey from predator (sharks vs barracuda). Longitude, depth, temperature, salinity, and dissolved oxygen were significantly linked to biotic assemblages. The identification of significant factors influencing predator-prey interaction is important in understanding community composition and for future implementation of conservation and management practices pertaining to nearby mangrove and seagrass habitats.

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Cyclic and extreme ecological disturbances have the capacity to alter resources and thereby animal populations. Interactions between disturbance and resource availability can influence predator-prey interactions. Predator-prey responses to ecological disturbance may be more pronounced in herbivores and their predators as herbivores track food resources that are often augmented by ecological disturbance. My objective with this dissertation was to examine how various forms of ecological disturbance influence predator-prey interactions through the lens of a case study – white-tailed deer (Odocoileus virginianus) and Florida panther (Puma concolor coryi) in southwestern Florida public and conservation lands. I quantified species-specific behavior of deer to an extreme disturbance event (i.e., Hurricane Irma), examined behavior of females with different fate outcomes to varied ecological disturbances and predation, investigated how ecological disturbance mediates the influence of human disturbance on predator-prey interactions, and quantified deer spatial ecology in response to fire, hydrology, panther and human activity. I found that deer behaviorally mediated the negative fitness impacts of Hurricane Irma. Further, I found that female deer with different fate outcomes selected areas of different ecological disturbance and the ecological disturbance type conferred different fitness costs (through differences in predation risk). Finally, I found that South Florida deer utilize diurnal times when humans are the most active to temporally reduce predation risk as panthers were more nocturnal in response to humans. My work here suggests that ecological disturbance regimes have the capacity to influence predator-prey interactions through nuanced mechanisms. Outcomes of these nuanced species-specific and predator-prey responses should be examined further. More practically, if disturbance influences aspects of animal fitness, a deeper understanding of species-specific and predator-prey responses to disturbance will improve management and conservation efforts as some regimes can be manipulated (e.g., prescribed fire). More broadly, consideration of ecological disturbance when examining predator-prey interactions may yield novel insight that deviates from predictions based on inference suggested in systems without disturbance. Highlighting nuanced predator-prey interactions mediated by ecological disturbances will improve predictions regarding species and community responses to global changes such as climate change and ecological restoration. / Doctor of Philosophy / Events that cause temporary changes to ecosystem structure and function (ecological disturbances) have the capacity to influence resources (i.e., food and shelter) for wild animals. Changes in resources as a function of ecological disturbance has the capacity to influence prey and predator species interactions. Predator-prey responses to ecological disturbance may be more pronounced in plant-eating animals (herbivores) and their predators as herbivores utilize food resources that are often altered by ecological disturbance. My objective with this dissertation was to examine how various forms of ecological disturbance influence interactions between predators and prey by using the white-tailed deer (Odocoileus virginianus) and Florida panther (Puma concolor coryi) in southwestern Florida wildlands as a case study. I quantified species-specific behavior of deer to an extreme climate event (i.e., Hurricane Irma). Next, I quantified and compared behavioral differences in responses to ecological disturbance (flooding and fire) and panther predation risk between female deer that survived and those killed by panthers during the offspring rearing season. I also investigated how ecological disturbance and human use of wildlands influenced predator-prey interactions. Finally, I characterized deer behavior in response to fire, hydrology, and panther and human activity. I found that deer changed their behavior during Hurricane Irma, presumably to offset the negative impacts of the storm as all our monitored deer survived the event. Further, I found that different ecological conditions generated by fire and flooding, respectively, influenced female behavior during the offspring rearing season in response to predation risk, and those behavioral differences may explain differences in mortality outcomes. Finally, I found that South Florida deer utilize daylight hours when humans are the most active to minimize encounters with predators as panthers were shown to be more active at night in areas with greater human use. My findings suggest that ecological disturbances have the capacity to influence predator-prey interactions in novel ways not suggested elsewhere. Outcomes of novel predator and prey interactions in response to ecological disturbance should be investigated further. More practically, if disturbance influences aspects of animal livelihood, a deeper understanding of species-specific and predator-prey responses to disturbance will improve management and conservation efforts as some disturbances can be manipulated (e.g., prescribed fire). More broadly, consideration of ecological disturbance when examining predator-prey interactions may yield novel insight that deviates from predictions based on inference suggested in systems without disturbance. Highlighting novel predator-prey interactions that is changed as a result of ecological disturbances will improve predictions regarding species and community responses to global changes through climate change and ecological restoration.