Within population biology, models are often analyzed for the net reproduction number or other generalized target reproduction numbers, which describe the growth or decline of the population based on specific mechanisms. This is useful in determining the strength and efficiency of control measures for inhibiting or enhancing population growth. The literature contains many algebraic and combinatorial approaches for deriving the net reproduction number and generalized target reproduction numbers from digraphs and associated matrices. Finding, categorizing, and counting the permutations of disjoint cycles, or cycles unions is a requirement of the Cycle Union approach by Lewis et al. (2019). These cycles and subsequent cycle unions can be found via the digraphs and associated matrices. We developed cycle counting patterns for targeting fertilities within Leslie Matrices, Lefkovitch Matrices, Sub-Diagonal Lower Triangle Transition Matrices, and Lower Triangle Transition Matrices to serve as a foundation for future work. Presented are the counting patterns and closed-form summations of the cycle unions.

The aim of this thesis is to define and study harvesting models of fish populations. These models are applied to particular fish species e.g., haddock and cod. The thesis is divided into five chapters: The first chapter is considered as an introductory one. In it, basics of fish biology and the recruitment process are defined. Two simple recruitment models known by the names Ricker and Beverton-Holt are used. In the second chapter the generalized Leslie model or Usher model is introduced. In section 2.2, some matrix theory is presented. For this matrix model, the net reproductive number is defined and studied in section 2.3. It turns out to be more useful than the spectral radius. In section 2.4, this study is extended to nonlinear matrix models. The nonlinearity, however, is defined only by the recruitment process. This allows to determine the equilibrium components. Finally section 2.5, the local stability of nonlinear matrix models is analyzed. Harvesting of such general matrix model is defined in chapter 3. We distinguish three different harvesting models (selective, net and semicontinuous harvesting models). In chapter 4, these harvesting models are then applied to concrete fish populations and analyzed with respect to its various parameters. In chapter 5, the stability is studied again along the lines of the paper of Levin, Goodyear [18]. The key results in this study are: 1) The maximum sustainable yields for selective harvesting and net harvesting are rather close. 2) Semicontinuous harvesting is more realistic harvesting models. 3) From a quantitative point of view, the choice of the recruitment function is important. 4) Harvesting process increases mortality and stability when we used Ricker recruitment model. 5) Stability of populations always holds if we use Beverton-Holt recruitment model.

Le fuligule milouin (Aythya ferina) est une espèce de canard plongeur répandue dans l’ensemble du Paléarctique. Montrant des signes de déclin de ses effectifs nicheurs en Europe depuis les années 2000, son statut de conservation IUCN a été réévalué de « Préoccupation Mineure » à « Vulnérable ». Etant une espèce chassée, la question du maintien de ces prélèvements cynégétiques est légitime. L’objectif de ce travail de thèse est donc de comprendre son fonctionnement démographique et les mécanismes sous-jacents à sa dynamique de population, pour proposer des mesures de gestion et de conservation. Pour cela, nous nous sommes attachés à estimer la tendance de ce déclin sur sa voie de migration nord-ouest européenne à partir des données de recensements de la mi-janvier. Puis, nous avons étudié la connectivité migratoire de cette voie de migration avec les autres voies préssuposées, afin de mieux comprendre l’origine de ce déclin. Enfin, nous avons estimé deux paramètres démographiques clés, la survie et le succès de nidification, pour les intégrer dans un cadre matriciel permettant d’estimer un taux de croissance asymptotique et comprendre quels sont les paramètres démographiques clés sur lesquels doivent reposer les actions de gestion. Il ressort de ce travail de thèse que le déclin du fuligule milouin est probalement dû surtout à une diminution de sa productivité en Europe de l’Est et en Russie. Le contrôle et la gestion de la productivité par l’Homme étant limités, uniquement des travaux de gestion autour des habitats liés à la nidification sont envisageables. Ces travaux pourraient être facilement menés en Europe mais beaucoup plus difficilement en Sibérie, principale aire de reproduction des milouins caractérisée par une vaste superficie et un fort isolement. Les taux de survie des oiseaux bagués en France sont plus faibles que pour les oiseaux bagués dans d’autres pays, potentiellement du fait d’une pression de chasse plus élevée. Amener le taux de survie en France au même niveau que dans les pays voisins (Suisse et Grande-Bretagne), par une modification de la réglementation sur la chasse, serait de nature à ramener le taux de croissance à l’équilibre. La mise en place de la gestion adaptative pourrait faciliter les objectifs de conservation fixés en adaptant annuellement ces prélèvements aux effectifs présents et aux connaissances dont on dispose. / The Common Pochard (Aythya ferina) is a regular diving duck species in the western Palearctic. However, a worrisome decline of its wintering population led to an up-listed IUCN status from “Least Concern” to “Vulnerable”. This species is still hunted in Europe despite this decline. Hence, one may wonder about the sustainability of its harvest. The aim of this work was to understand the population dynamics of this species, and the drivers of these mechanisms. For this purpose, we assessed the declining trend in northwestern Europe using the mid-january censuses. Then, we studied the migratory connectivity with the two others flyways, in order to better understand the origin of the decline. Finally, we assessed two main demographic parameters (survival rate and nesting success) and combined these into a matrix population model. This model allowed us to assess an asymptotic growth rate and to determine the key demographic parameters on which management actions should focus. The main results of this thesis indicate that the decrease in productivty in Europe and in Russia could have been the main reason of the decline. However, given the limited human action to improve Pochard productivity, only breeding habitat improvement could be considered. Such improvements could be easily considered in Europe, but not in Siberia, the main breeding region characterized by a large area and a strong geographic isolation. Survival rates were lower in France than in neighbouring countries, possibly owing to a greater hunting pressure. A more moderate hunting pressure could lead to higher survival rates, and a balanced growth rate. Setting up an adaptative harvest management scheme could help reaching defined management goals, by annually adapting hunting quotas to current knowledge and assessment of Pochard population size.

Presence of coastal aquaculture activities in marine landscapes is growing. However, there is insufficient knowledge on the subsequent ecological interactions between these activities and marine fish communities. The overall aim of this thesis was to evaluate the direct and indirect ecological effects of aquaculture activities on marine fish communities in Scotland. A combination of empirical and modelling approaches was employed to collect evidence of how aquaculture activities affect marine fish communities at the individual, population and ecosystem levels around coastal sea cages. The two fish farms evaluated in this research provided the wild fish sampled near the sea cages with a habitat rich in food resources which is reflected in an overall better biological condition. Results of the stomach content analysis indicated that mackerel (Scomber scombrus), whiting (Merlangius merlangus) and saithe (Pollachius virens) sampled near sea cages consumed wasted feed which was also reflected in their modified FA profiles. The overall effects of the two fish farms were more pronounced in young whiting and saithe than in mixed aged mackerel sampled near the sea cages. The phase space modelling approach indicated that the overall potential for fish farms to act at the extremes as either population sources (a habitat that is rich in resources and leads to an overall improved fitness) or ecological traps (a habitat that appears to be rich in resources but is not and leads to an overall poor fitness) are higher for juvenile whiting than for mackerel. Based on the empirical evidence and literature the two fish farms are more likely to be a population source for wild fishes. Using an ecosystem modelling approach indicated that fish farming impacts the food web in a sea loch via nutrient loading. Mussel farming relies on the natural food resources and has the potential to affect the food web in a sea loch via competing with zooplankton for resources which can affect higher trophic levels. The presence of both activities can balance the overall impact in a sea loch as compared to the impact induced if each of these activities were present on their own. Both activities have the potential do induce direct and indirect effects on the wild fish and the entire sea loch system. The results of this PhD identified several gaps in data and thus could be used to improve future sampling designs. It is important to evaluate the cumulative effect of the presence of aquaculture activities in terms of nutrient loading and physical structure in the environment. Using a combination of empirical and modelling approaches is recommended to gain further insight into the ecological impacts of aquaculture activities on wild fish communities. Results of this PhD study could lead to more informed decisions in managing the coastal aquaculture activities. Establishing coastal fish farms as aquatic sanctuaries can be of an advantage to increase fish production and conserve species that are endangered provided that no commercial and recreational fishing is allowed nearby. It would be useful to have long term monitoring of the fish stocks around the cages and if there is any production at the regional level. Additionally, information on behaviour, migration patterns should be collected to understand the impacts of aquaculture activities on fish stocks. From an aquaculture perspective, ecologically engineered fish farms in addition to careful site selection in new aquaculture developments may improve nutrient loading into the ecosystem.

Noteworthy species endemic to the Galapagos Islands off Ecuador are two flightless birds, the Galapagos Penguin (Spheniscus mendiculus) and Flightless Cormorant (Phalacrocrax harrisi). Both adapted increased swimming ability at the cost of flight. This however has limited their ability to find richer feeding grounds in times of low resource availability, or to escape potential predators. Their population numbers, though small, were stable. Stress on this stability has increased since human arrival. Various invasive species from pets, farm animals and rats to even mosquito vectors of avian disease accompanied humans. . El Nino Southern Oscillation or ENSO cycles of warm waters in the Pacific Ocean south of the Equator cause drastic drops in food sources for all Galapagos seabirds. Serious ENSO events in 1983 and 1998 caused some species’ populations to drop by as much as 77%. Periodic less severe cycles may help explain how population recovery has not rebounded to earlier numbers. Reduced chick survival and adult fecundity seem to occur in concert with mild events. With available data and use of a modeling approach, this study focuses and explores their situations. Restoring population stability may include use of models, species monitoring, conservation and limiting invasive species. Usher matrices based on different climate conditions were produced using data combined from current and past census counts and weather. Models are used to compare available census data and test reliable predictors. Climate data from National Oceanic and Atmospheric Administration and the University of Florida provides for testing predictions of current and probable future climate change. Life histories of both species are regarded. Results suggest the current Cormorant population is still stable. The Penguin, however, faces a 20% probability of extinction in 100 years if current conditions remain. Extinction probability rises to 60% if climate change continues to worsen. Interventions such as captive breeding could be suitable for population recovery.

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