Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Age and temperature are two factors that affect mortality in adult tsetse flies. Both are found to be very important, but the simultaneous effect of these factors on the mortality rate have not been studied. This study seeks to address this, with an application to a population of female tsetse, using a model based on partial differential equations. Adult mortality is agedependent and is modelled as the sum of two exponentials, with four parameters (coefficients of each exponential): numerical analysis of a population model with this mortality structure predicts exponential growth. Analysis of each of the parameters through parameter variation shows that two of these parameters control the mortality of the nulliparous (ages 0 − 10 days) flies only while the other two only take care of flies of mature ages. Measurement of the impact of these parameters on the mortality of tsetse of different ages by the normalized forward sensitivity index method is also carried out. This is followed by fitting the model based on the age-dependent mortality along with a constant tsetse birth rate to data representing the catches of female Glossina pallidipes at Rekomitjie Research station, Zimbabwe. Considering a three parameter adult tsetse mortality, parameter analysis shows the effect of one of the parameters to affect the mortality of flies of all ages while a second controls only the mature tsetse flies of reproductive ages. A further analysis resulted in the estimate of these parameters as functions of temperature, thereby leading to the establishment of an age and temperature-dependent adult tsetse mortality. Using data for the daily average temperature records obtained in 1981 on Antelope Island, Lake Kariba, Zimbabwe, daily changes in the pupal duration (adult tsetse birth rate) changes negatively with temperature change. Incorporating this (temperature-dependent ) birth rate into the model, together with the established age and temperature-dependent adult mortality, the adult tsetse population dynamics is explored numerically. The latter model is then fitted to population data of female Glossina morsitans morsitans obtained from the same Island and for the same period as used for the temperature data. The data suggests peak tsetse population to be in the month of July and lowest in the month of December. The first quarter of the year is predicted to be most favorable for breeding tsetse while the second, showed a period of stable growth rate and a time of tsetse abundance. In addition, the dynamics with both age and temperature showed a non-uniform daily population growth contrary to that with age effect only. This study has enhanced our understanding of tsetse population dynamics for age and temperature-dependent adult mortality with temperature-dependent pupal duration and suggests the period of tsetse abundance on Antelope Island. / AFRIKAANSE OPSOMMING: Geen opsomming in Afrikaans.

A new strategy to fight mosquito-borne disease is based on infections of the maternally-transmitted, intracellular bacterium Wolbachia pipientis. Estimates predict that Wolbachia infects nearly half of all insect species, as well as other arthropods and some nematodes. Wolbachia manipulates the reproduction of its host to promote infection, most commonly causing a form of conditional sterility known as cytoplasmic incompatibility. Generally, Wolbachia infections are benign and do not inflict significant costs upon its host. However, studies demonstrate that some infections are associated with substantial costs to its host. These same infections can also induce pathogen interference and decrease vector competency of important disease vectors. Theory predicts that organisms that incur costs relative to conspecifics are less competitive and their competitive exclusion is expected. In the case of Wolbachia, the bacterium can influence reproduction such that phenotypes with lower fitness may still reach fixation in natural populations. In this dissertation, I describe theoretical and empirical experiments that aim to understand the invasion and stability of Wolbachia infections that impose costs on their host. Particular attention is paid to immature insect lifestages, which have been previously marginalized. These results are discussed in relation to ongoing vector control strategies that would use Wolbachia to manipulate vector populations. Specifically, I discuss the cost of novel Wolbachia infections in Aedespolynesiensis, which decreases larval survival and overall fitness relative to wild-type mosquitoes. Then, a theoretical framework was developed to determine the significance of reductions in larval viability in relation to the population replacement disease control strategy. Further theoretical studies determined that Wolbachia infections, once established, resist re-invasion by uninfected individuals despite relatively high costs associated with infection so long as the infection produces reproductive manipulations. Additional studies determined that larvae hatched from old eggs experience reduced survival in mosquito strains with novel Wolbachia infections when compared to the wild-type. To validate the theoretical studies, model predictions were tested empirically to determine the importance of the larval viability. Finally, a COPAS PLUS machine was evaluated and its role in understanding early larval development in mosquitoes is discussed. The importance of integrated research in disease control is highlighted.

Perissodus microlepis is a species of cichlid fish endemic to Lake Tanganyika (Africa). Adult P. microlepis are lepidophages, feeding on the scales of other living fish. As an adaptation for this feeding behavior P. microlepis exhibit lateral asymmetry with respect to jaw morphology: the mouth either opens to the right or left side of the body. Field data illustrate a temporal phenotypic oscillation in the mouth-handedness, and this oscillation is maintained by frequency-dependent selection. To better understand the oscillation, Takahashi and Hori model frequency-dependent selection in P. microlepis using a population genetic model. Their results are intriguing, and the purpose of this dissertation is to improve and extend their model, which fails to account for important biological aspects.We model P. microlepis with a novel approach that fuses the disparate modeling traditions of population genetics and population dynamics; we account for both processes since, in the case of P. microlepis, they occur on the same time scale (a case of microevolution). We construct our models using systems of difference equations. We prove the existence and uniqueness of a positive equilibrium, which corresponds to a 1 : 1 phenotypic ratio. Using a local stability and bifurcation analysis, we show that the equilibrium becomes unstable when frequency-dependent selection is sufficiently strong. We determine necessary and sufficient conditions for onset of oscillation. Local bifurcation analysis indicates key features of the oscillation that may suggest critical experiments.We determine the role of stage structure and the role of strong and weak intraspecific competition. We show that stage-structure is not necessary for, but enhances, oscillatory behavior. Finally we demonstrate the complicated interplay between population dynamic and population genetic processes. Our findings indicate that classical population genetic models can fail to elucidate complex dynamics.

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.