Motivated by models from evolutionary population dynamics, we study a general class of nonlinear difference equations called matrix models. Under the assumption that the projection matrix is non-negative and irreducible, we prove a theorem that establishes the global existence of a continuum with positive equilibria that bifurcates from an extinction equilibrium at a value of a model parameter at which the extinction equilibrium destabilizes. We give criteria for the global shape of the continuum, including local direction of bifurcation and its relationship to the local stability of the bifurcating positive equilibria. We discuss a relationship between backward bifurcations and Allee effects. Illustrative examples are given

An Allee effect is a density-dependent process that can be responsible for the extinction of small populations. This thesis focuses on the detection of Allee effects, along with other density-dependent processes, and their influence on population synchrony. In chapter 2 I investigate the spatial variation in influential density-dependent processes and density-independent weather factors for the large skipper butterfly Ochlodes sylvanus across its British range. I find both qualitative and quantitative spatial variation in these processes and factors driving population dynamics. In chapter 3, I develop and test a Bayesian methodology, that I then use in chapter 4 to analyse local population level dynamics for 38 British butterfly species. For 35 of these species I found population level Allee effects and also found that phylogeny significant influenced a species’ susceptibility to Allee effects. Finally, in chapter 5 I examine the influence Allee effects have on network population synchrony in a theoretical framework.

Nearshore populations have been depleted and some have not yet recovered. Therefore, theoretical studies focus on improving fisheries management and designing marine protected areas (MPAs). Depleted populations may be undergoing an Allee effect, i.e. a decrease in fitness at low densities. Here, I constructed a marine metapopulation model that included pre- and post-dispersal Allee effects using a network theory approach. Networks represent metapopulations as groups of nodes connected by dispersal paths. With this model I answered four questions: What is the role of Allee effects on habitat occupancy? Are MPAs effective in recovering exploited populations? What is the importance of larval dispersal patterns in preventing local extinctions due to exploitation and Allee effects? Can exploitation fragment nearshore metapopulations? When weak Allee effects are included, habitat occupancy drops as larval retention decreases because more larvae are lost to unsuitable habitat. With strong Allee effects habitat occupancy also drops at high larval retention because more larvae are needed to overcome the Allee effect. Post-dispersal Allee effects seem more detrimental for nearshore metapopulations. MPA effectiveness seems also lower in a post-dispersal Allee effect scenario. In overexploited systems, local populations that go extinct are also less likely to recover even after protecting the whole coastline. In exploited nearshore metapopulations with Allee effects, local occupancy or the recovery of local populations depends not only on larval inflow from neighbor populations, but also on larval inflow for these neighbors. Nearshore metapopulations with intense fishing mortality and Allee effects may also suffer a decrease in dispersal strength and fragmentation. Population fragmentation occurs when large populations are split into smaller groups. A tool for detecting partitioning in a network is modularity. The modularity analysis performed for red abalone in the Southern California Bight showed that exploitation increases partitioning through time before the entire metapopulation collapses. These findings call for research effort in estimating the strength of potential Allee effects to prevent stock collapse and assess MPA effectiveness, evaluating the predictability of local occupancy by centrality metrics to help identify important sites for conservation, and using modularity analysis to quantify the health of exploited metapopulations to prevent their collapse. / text

The growing flow of people and goods around the globe has allowed new, non-native species to establish and spread in already fragile ecosystems. The introduction of invasive species can have a detrimental impact on the already established species. Thus, it is important that we understand the mechanisms that facilitate or prevent invasion. Since reaction-diffusion invasion models produce travelling waves we can study invasion by looking at the mechanisms that allow for wave propagation failure, or wave-blocking. In this thesis we consider a perturbed reaction-diffusion model in which the perturbation resides in either the reaction or diffusion term. In doing so we exploit the underlying symmetry of our problem to define a region in the appropriate parameter space that leads to wave blocking. As a demonstrative example we apply our theory to the bistable equation and consider the effects of various perturbations.

L’interaction de processus génétiques et démographiques peut générer des vortex d’extinction. Chez les Hyménoptères, les mâles sont haploïdes et les femelles diploïdes. Chez les espèces avec sl-CSD (single-locus complementary sex determination), les haploïdes, se développent en mâles et les diploïdes hétérozygotes au gène du CSD, en femelles. Les diploïdes homozygotes sont des mâles non viables ou stériles. Des études théoriques suggèrent que la production de mâles diploïdes peut entraîner les petites populations d’Hyménoptères dans un vortex d’extinction. Le premier objectif est d’encourager le dialogue entre génétique et démographie en proposant une définition des effets Allee élémentaires générés par des processus génétiques, dont nous avons identifié des exemples dans la littérature. Le deuxième objectif est de rechercher l’existence d’un effet Allee génétique dans des populations de Venturia canescens, un Hyménoptère parasitoïde avec sl-CSD. Des marqueurs microsatellites ont été élaborés et utilisés pour montrer une relation négative entre diversité génétique et proportion de mâles diploïdes dans des populations isolées ou goulotées. Les mâles diploïdes s’accouplent mais sont stériles. La dépression de consanguinité affectant les femelles est faible. Nous avons créé et suivi des populations expérimentales de V. canescens avec différents niveaux de diversité génétique. Un effet Allee génétique dû à la production de mâles diploïdes a été détecté mais il n’influençait ni le taux d’accroissement ni la probabilité d’extinction des populations. Les extinctions observées semblent surtout due à la stochasticité démographique. / Genetic and demographic processes can drive small populations to extinction. Their interaction can generate extinction vortices. In Hymenoptera, males are haploid and females are diploid. In species with single-locus complementary sex determination (sl-CSD), hemizygous at the CSD gene develop in males and heterozygous diploids, in females. Homozygous develop in diploids males, often unviable or sterile. Theoretical studies suggest that the production of diploid males associated with demographic and environmental stochasticity may drive small populations into an extinction vortex.The first objective is to stimulate collaboration between genetics and demography by proposing a definition for component Allee effects generated by genetic processes. Component and demographic genetic Allee effects were detected in the literature.The second objective was to investigate the presence of a genetic, and maybe demographic, Allee effect in populations of the parasitoid Venturia canescens, a Hymenoptera with sl-CSD. Microsatellite markers were developed and used to show a negative relationship between genetic diversity and proportion of diploid males in isolated and bottlenecked populations. Diploid males can mate but they are sterile. Inbreeding depression affecting females is negligible. We created and monitored experimental populations of V. canescens with different levels of genetic diversity. A genetic Allee effect due to the production of diploid males was detected but it did not influence the growth rate or the probability of extinction of populations. Extinction events observed thus seem mainly due to demographic stochasticity.

Of concern in this research were the ecological parameters associated with the establishment of a model invasive plant species, Imperata cylindrica, across a scale of ecological organization. Specifically, the study addressed the species’ ability to: differentially respond to abiotic and biotic constraints during seedling establishment, exhibit a novel underground competitive interference mechanism, and alter the decomposition dynamics in newly invaded ecosystems. Finally, the last portion of the research was centered around creating a predictive habitat model that will provide information on the most important variables responsible for creating habitat for this species. The population level seedling study indicated that soil characteristics and light availability play a significant role in seedling establishment. There were large trends in biomass allocation attributable to soil type with seedlings performing best in high nutrient soils representative of the Mississippi Alluvial Valley physiographic region. I. cylindrica seedlings also showed a positive response to increased seedling density during the initial stages of seedling establishment. The community level research examining a hypothesized novel interference mechanism deployed by I. cylindrica showed a significant and robust pattern of I. cylindrica damaging its own belowground tissue more often than that of its surrounding neighbors. Therefore, it is highly unlikely that I. cylindrica gains a competitive advantage by exposing the native plant assemblage to pathogen invasion (via ruptured tissue) as the plant would expose itself to these pathogens (to which it is evolutionarily naive) at much higher volumes. The ecosystem level examination of this globally important invasive species indicated that I. cylindrica invasion into native systems will significantly accelerate ambient rates of decomposition. Furthermore, fungal community composition in invaded areas was drastically altered as well as bacterial community functional activity in relation to several key enzymes responsible for the decomposition of plant tissue which were produced more abundantly in invaded areas.The landscape-scale analyses and modeling work validated decades of anecdotal evidence and indicated that anthropogenic disturbance factors associated with road maintenance and construction (soil disturbance and vegetation removal) are the principal factors responsible for creating habitat suitable for invasion by this species.