The Caledonian pinewoods are a habitat of crucial environmental and cultural importance, and the sole home of many rare species. However, they have seen steady decline in recent centuries, through the establishment of hunting estates and forestry plantations. A recent trend in management is the attempted transformation of existing plantations (dense communities with a regular spatial structure and low variance in size and age) towards a state mimicking the perceived natural condition, which has a lower density, irregular spatial pattern, high variance in size and age. This presents a problem for traditional forestry practices, which were conceived primarily with “even-aged” plantation populations in mind. The shift towards management of an uneven-aged structure requires a more in-depth consideration of individual trees’ lifecycles and their effect upon long-term population dynamics. In recent years, great advances in computational and mathematical models for spatially interacting populations have been made. However, certain complications have prevented them from being utilised to their full potential for the purposes of forest management. Forest communities are not only spatially structured; the size of each tree plays a role in its ability to acquire resources for growth and survival. Existing models of population dynamics are discussed, and their extension to incorporate both size- and spatially- structured interactions is presented. The key aspects of populations’ structural development are studied. Data from both plantation and semi-natural Scots Pine stands in Scotland allow parameterisation of a stochastic individual-based model, which in turn provides insights into the behaviour of real populations, and the importance of spatial effects and heterogeneity in individuals. A partial differential equation (moment) approximation to the stochastic model is presented. While this is analytically intractable, numerical integration and heuristic analysis of the equations enable clearer identification of the drivers of population structure. Many results are concordant with existing models of both qualitative forest stand development and theoretical dynamics of spatially-structured populations, while others are specific to joint size-space structure. This deeper understanding of the population dynamics allows robust recommendations for diverse uneven-aged stand management objectives to be made. Approaches to accelerating the transformation of plantation stands towards a “natural” state (using two key operations: thinning – removal of trees, and planting) are investigated. Finally, approaches to so-called “continuous cover forestry” – the practice of maintaining a quasi-natural state while also obtaining economic value from a forest – are also considered. In both cases, the model’s simplicity enables clearer conclusions than would be possible using other approaches.

The present thesis deals with the related themes of mortality and growth in coral reef fishes. In the first chapter, a nine-year dataset from Bermuda is used to quantify how reef fish populations respond to the introduction of a trap-fishing ban, finding that herbivores exhibit extremely strong recovery, but that stock-recruitment relationships may be decoupled by a numerical response in a meso-predator. In the second chapter, a dataset from Bonaire is used to test the efficacy of the widely-used coefficient of natural mortality, M, in modelling a population of stoplight parrotfish (Sparisoma viride). As determined from simulation models, this statistical coefficient performs considerably less well than a novel mechanistic function that partitions mortality into size- and age-based processes and achieves extremely good fits to the field data. The third chapter presents a new approach to estimating growth parameters of reef fish from tagging data that exploits the disproportionate response of certain parameters to misestimates in the true age of the tagged individuals. The method works considerably better than the most widely used method when sample sizes are small, as is commonly the case in reef fish tagging studies where recapture rates tend to be low. The fourth and final chapter uses non-lethal stable isotope techniques to tease apart the invasion dynamics of Indo Pacific lionfish (Pterois spp.) that are currently colonising the wider Caribbean. The results show that lionfish exhibit habitat-specific ontogenetic shifts in prey selection, inflicting elevated mortality on small, bommie-dwelling fishes on forereefs but switching to seagrass-foraging invertivores as they grow. Lionfish also display ontogenetically shifting competition with native Nassau grouper (Epinephelus striatus), which may provide a greater barrier to invasion success on patch reefs than on fore reefs, where competitive overlap is diminished. The thesis concludes with a discussion of some lines of enquiry that could not be undertaken owing to time or data limitations, but which may hold as much interest for the reader as they do for the author.

The problem of changing scale in models of a system is relevant in many different fields. In this thesis we investigate the problem in models of biological systems, particularly infectious disease spread and population dynamics. We investigate this problem using the process algebra \emph{Weighted Synchronous Calculus of Communicating Systems} (WSCCS). In WSCCS we can describe the different types of individual in a population and study the population by placing many of these individuals in parallel. We present an algorithm that allows us to rigorously derive mean field equations (MFE) describing the average change in the population. The algorithm takes into account the Markov chain semantics of WSCCS such that as the system being considered becomes larger, the approximation offered by the MFE tends towards the mean of the Markov chain. The traditional approach to developing population level equations of a system involves making assumptions about the behaviour of the entire population. Our approach means that the population level dynamics explained by the MFE are a direct consequence of the behaviour of individuals, which is more readily observed and measured than the behaviour of the population. In this way we develop MFE models of several different systems and compare the equations obtained to the traditional mathematical models of the system.

No description available.

We study a discrete time, structured population dynamic model that is motivated by recent field observations concerning certain life history strategies of colonial- nesting gulls, specifically the glaucouswinged gull ( Larus glaucescens). The model focuses on mechanisms hypothesized to play key roles in a population's response to degraded environment resources, namely, increased cannibalism and adjustments in reproductive timing. We explore the dynamic consequences of these mechanics using a juvenile- adult structure model. Mathematically, the model is unusual in that it involves a high co- dimension bifurcation at R0 = 1 which, in turn, leads to a dynamic dichotomy between equilibrium states and synchronized oscillatory states. We give diagnostic criteria that determine which dynamic is stable. We also explore strong Allee effects caused by positive feedback mechanisms in the model and the possible consequence that a cannibalistic population can survive when a non- cannibalistic population cannot.

Mathematical modeling of population dynamics can provide novel insight to the growth and dispersal patterns for a variety of species populations, and has become vital to the preservation of biodiversity on a global-scale. These growth and dispersal stages can be modeled using integrodifference equations that are discrete in time and continuous in space. Previous studies have identified metrics that can determine whether a given species will persist or go extinct under certain model parameters. However, a need for computational tools to compute these metrics has limited the scope and analysis within many of these studies. We aim to create computational tools that facilitate numerical explorations for a number of associated integrodifference equations, allowing modelers to explore results using a selection of models under a robust parameter set.

Cette thèse a pour objet la modélisation individu-centrée des systèmes sociaux. Une première partie orientée aide à la décision présente un modèle d’évolution des populations rurales fortement inspiré des données. Une seconde partie, plus théorique, étudie divers mécanismes permettant à un individu d’accepter ou de résister à une influence sociale. Nous proposons tout d’abord un modèle individu-centré de la dynamique des municipalités rurales européennes, implémenté pour le département du Cantal. Nous proposons un nouvel algorithme de génération des populations initiales ne nécessitant pas d’échantillon de population (approche classique). Nous concevons et paramétrons un modèle de la dynamique de l’individu face au marché du travail basé sur les données de la « European Labour Force Survey ». Il inclut des heuristiques originales de transition d’états tel qu’actifs, inactifs, chômeurs, … prenant en compte l’âge, la profession et le secteur d’activité de l’individu. Nous déterminons les dynamiques non fondés sur des données individuelles en testant la capacité de dynamiques simples à produire des résultats proches des données agrégées disponibles. Est ainsi conçu un modèle de mobilité résidentielle, expliquant partiellement la migration et intégrant décision de déménager et choix d’une nouvelle résidence. La seconde partie de la thèse étudie les effets collectifs de différents mécanismes permettant aux individus de résister à ou d’accepter une influence sociale. Un premier mécanisme étudié est un filtre cognitif impliquant qu’un individu ne reçoit pas une information incongruente ou peu importante. Les individus « filtreurs » exhibent le biais de primauté car leur attitude n’est déterminée que par les premiers éléments reçus et se montrent négatifs alors que le message diffusé par un media est neutre. Le taux d’individus négatifs dans la population est accru ou diminuer par l’échange direct d’information entre les individus. Un second mécanisme est un rejet de la tentative d’influence qui mène l’individu à différencier davantage son attitude de celle de son interlocuteur. Il intervient lorsque l’individu éprouve un inconfort lié au fait qu’il est à la fois en accord et en désaccord avec son interlocuteur. Le couplage de ce rejet à un mécanisme d’attraction entre individus en accord entraîne un nombre moindre de groupes d’opinion différentes à l’échelle de la population (ie par rapport au nombre de groupes obtenus avec le seul mécanisme d’attraction). / This thesis is dedicated to individual-based modeling of social systems. While the first part is very practical, decision-support oriented, presenting a model which studies the evolution of a rural population, the second part is more theoretical, interested in various mechanisms allowing individual to accept or resist to social influence. Firstly, we propose an individual-based model of the European rural municipalities implemented for the French Cantal département. We use a new sample-free algorithm for generating the initial population, while classical methods require an initial sample. We design and parameterize the individual activity dynamics with data from the European Labour Force Survey database. The individual dynamics includes an original heuristic for labour statuses and employments changes, based on individual age, profession and activity sector when she is occupied. The last part of the model deals with dynamics that we have not been able to derive from data, mainly the demographic dynamics. Based on the Occam razor principle, we test very simple dynamics and choose them on their capacity to lead to model results close to reference data. In particular, we propose a simple residential mobility model, partly ruling the emigration, which integrates decision to move and location choice. Secondly, we study the collective effects of various mechanisms leading individuals to resist or accept social influence. A first mechanism leads individuals to neglect some features of an object if they are not important enough or incongruent. These individuals exhibit the primacy bias because their attitudes are determined by the first accepted feature. We show that this bias increases when individuals directly exchange about features compared to when they only get the features from the media, in a random order. The second mechanism is a rejection reaction that we suppose occurring because of the discomfort taking place when individuals are close on one dimension of attitude and far on another dimension. The main effect of this rejection mechanism is to lead to a lower number of clusters than with the attraction mechanism alone.

La palourde japonaise (Ruditapes philippinarum) a été introduite au début des années 1980 dans le bassin d’Arcachon à des fins aquacoles. Elle s’est rapidement répandue dans toute la zone intertidale de la lagune, créant actuellement le premier gisement français en terme de stock exploitable. Cependant, de récentes évaluations du stock ont démontré une structure en taille déséquilibrée avec un déficit en juvéniles et en adultes de taille supérieure à 38 mm. Ce constat alarmant a posé des questions sur le devenir des populations de palourdes japonaises dans le bassin d’Arcachon et a motivé la présente thèse. Cette étude vise à mieux comprendre la dynamique de population de cette espèce et certains facteurs contrôlant cette dynamique. Le but in fine était d’améliorer la gestion du stock exploitable de cette espèce dans la lagune grâce à un modèle, incrémenté des différents résultats obtenus lors de cette étude. Les paramètres de croissance K et L8 du modèle de Von Bertalanffy ont été déterminés d’une part par un suivi régulier des populations naturelles, et d’autre part par une expérience de marquage-recapture d’une durée de deux ans. Les résultats montrent une croissance lente avec un K homogène dans tout le bassin et un L8 variable suivant le site. Cette étude met aussi en évidence une mortalité naturelle normale mais une reproduction déficiente (indices de condition bas, mauvais recrutement). Parmi les facteurs pouvant expliquer cette dynamique, différents pathogènes ont été suivis durant deux ans : les trématodes digènes, la maladie de l’anneau brun, la perkinsose. De plus, une pathologie émergente (maladie du muscle marron, BMD) a été découverte. Seules la perkinsose et la BMD ont révélé de fortes prévalences et intensités. La perkinsose entraîne des effets mitigés sur la croissance tandis que la BMD entraîne une remontée des palourdes en surface puis leur mort. Les ressources trophiques sont également importantes pour expliquer la croissance et ont été étudiées ici grâce aux isotopes stables de l’azote et du carbone. Cette étude a révélé une hétérogénéité des sources trophiques au sein de la lagune et une alimentation dominée par du phytoplancton. La proportion de phytoplancton ingérée a été corrélée à L8. Les paramètres de croissance et de mortalité ont été ensuite intégrés dans un modèle de gestion qui nous a permis de voir que si rien n’était fait en terme de gestion, le stock de palourdes continuerait de se dégrader. Ce modèle nous a permis de simuler différentes situations de gestion et suite aux résultats obtenus, un certain nombre de mesures a ensuite été adopté par les organismes gestionnaires. / The Manila clam (Ruditapes philippinarum) was introduced into Arcachon Bay at the beginning of the 1980s for aquaculture purposes. It rapidly naturalized in all intertidal flats of the lagoon. Nowadays, Arcachon Bay ranks at the first French place in terms of exploitable stock. However, recent stock assessments have shown an unbalance size structure with a deficit in juvenile and adult clams (> 38 mm shell length). These alarming patterns asked many questions on the sustainability of Manila clam populations within Arcachon Bay and have motivated the present thesis. This study aimed to better understand the population dynamics of this species and also some factors controlling this dynamic. The final objective was to improve the Manila clam fishing management with a model raised with results of the study. Von Bertalanffy growth parameters (K and L8) were both determined by a field survey of populations and by a tagged-recapture experiment during two years. Growth appeared slow with a homogeneous K within the bay and different L8 according to the sites. This study also evidenced a normal natural mortality and an inefficient reproduction (low condition index, low recruitment). Among the factors that could explain these dynamics, different pathogens were monitored during two years: digenean trematodes, brown ring disease and perkinsosis. Moreover, an emergent pathology (brown muscle disease, BMD) has been discovered. Only perkinsosis and BMD revealed high prevalences and intensities. Perkinsosis induced mitigated effects on growth whereas BMD-infected clams rise to the surface of the sediment and died. Trophic sources were also important to explain growth and were studied with carbon and nitrogen stable isotopes. This study displayed a heterogeneous repartition of Manila clam trophic sources within the bay and a phytoplankton dominated diet. The proportion of ingested phytoplankton was correlated with L8. Growth and mortality parameters were integrated in a management model. If no new management measures were taken, the clam stock will continue to decrease. Different management situations have been simulated and new measures have been adopted by administrator organisms.

Much research debates whether properties of ecological networks such as nestedness and connectance stabilise biological communities while ignoring key behavioural aspects of organisms within these networks. Here, we computationally assess how adaptive foraging (AF) behaviour interacts with network architecture to determine the stability of plant-pollinator networks. We find that AF reverses negative effects of nestedness and positive effects of connectance on the stability of the networks by partitioning the niches among species within guilds. This behaviour enables generalist pollinators to preferentially forage on the most specialised of their plant partners which increases the pollination services to specialist plants and cedes the resources of generalist plants to specialist pollinators. We corroborate these behavioural preferences with intensive field observations of bee foraging. Our results show that incorporating key organismal behaviours with well-known biological mechanisms such as consumer-resource interactions into the analysis of ecological networks may greatly improve our understanding of complex ecosystems.

Student Number: 9811822T - MSc Dissertation - School of Computational and Applied Mathematics - Faculty of Science / This dissertation reviews population dynamic type models of viral infection and introduces some new models to describe strain competition and the infected cell lifecycle. Laboratory data from a recent clinical trial, tracking drug resistant virus in patients given a short course of monotherapy is comprehensively analysed, paying particular attention to reproducibility. A Bayesian framework is introduced, which facilitates the inference of model parameters from the clinical data. It appears that the rapid emergence of resistance is a challenge to popular unstructured models of viral infection, and this challenge is partly addressed. In particular, it appears that minimal ordinary differential equations, with their implicit exponential lifetime (constant hazard) distributions in all compartments, lack the short transient timescales observed clinically. Directions for future work, both in terms of obtaining more informative data, and developing more systematic approaches to model building, are identified.