Tuberculosis (TB) is an infectious respiratory disease caused by the bacterium Mycobacterium tuberculosis. TB is the second largest cause of mortality by infectious diseases and is a challenging disease to control. It spreads easily among people via droplets propagated by an infectious person. Treatment against TB has been available since the 1950s; however, various problems with treatment have led to the emergence of drug-resistance in TB bacteria, which further complicates disease control. Furthermore, TB is a disease that predominantly affects poor countries or countries with high population densities. With the generalization of travel and migration in the second half of the twentieth century, individuals infected in such countries are likely to move to or spend some time in richer countries, making TB a worldwide problem. In this thesis, we consider the role of population movement in the spread of tuberculosis by studying two different models. The first one is an extension to a spatialized context of a simple existing mathematical model for the spread of TB. We establish that, similarly to the original model, the equilibrium without disease is globally asymptotically stable when the basic reproduction number $\R_0$ is less than one. In the case that $\R_0>1$, we prove that the system is uniformly persistent. The second model considers the spread of drug-resistant TB in a population, then between connected populations. We establish that a backward bifurcation can occur and that the coupled system has more types of equilibria than the systems in isolation. Finally, we consider a general class of models including the previous two in isolation and after coupling. We investigate which dynamical properties of the isolated models are preserved when coupling the models through movement. Some new results are provided in that direction.

Genetically modified (GM) canola (Brassica napus L.) has been widely adopted in Canada since its commercial release in 1995 and now represents over 85% of the canola grown in western Canada. Concurrently, GM canola volunteers have become an increasing management problem in cultivated fields and are ubiquitous in adjacent ruderal (non-cropped disturbed) habitats. However, systematic post-release monitoring is lacking and the ecological and agronomic impacts of escaped GM canola are poorly understood. In this dissertation, I characterize the escape, demography and distribution of GM canola in ruderal habitats in southern Manitoba, at multiple spatial and temporal scales. I characterized GM herbicide tolerance traits in 16 escaped canola populations. The progeny of 129 plants were tested in herbicide trials; 74% of plants produced glyphosate-tolerant progeny, 63% produced glufosinate-tolerant progeny, and 34% produced multiple herbicide-tolerant progeny as a result of gene flow between escaped plants. At the population-scale, four escaped GM canola populations were monitored and periodic matrix models were constructed to describe the dynamics and persistence of flowering plants. Escaped populations were observed to flower in synchrony with adjacent crops and were projected to persist for 2 to 5 years, confirming the potential for gene flow between escaped and cultivated canola populations. At the landscape-scale, the distribution of escaped canola was surveyed in three agricultural regions. Regional factors were important determinants of distribution; escaped canola density was positively correlated with canola cropping intensity and with traffic intensity, and was negatively correlated with distance to grain distribution centres. Local seed dispersal had negligible impact on distribution compared to landscape-scale anthropogenic seed inputs resulting from agricultural transport. These findings suggest that escaped canola persists as a metapopulation, where long-distance dispersal and colonization compensate for frequent extinction of local populations. Escaped populations play an important role in the persistence and spread of GM traits at large spatial scales, with substantial implications for the coexistence of GM and non-GM crops, and especially for organic and reduced-tillage farming operations. Landscape-scale management approaches, designed and implemented collaboratively by multiple stakeholders, are necessary to mitigate the risks of contamination resulting from GM trait escape. Regulation and ongoing monitoring of GM crops must acknowledge and address the dynamic regional nature of seed- and pollen-mediated gene flow.

Tuberculosis (TB) is an infectious respiratory disease caused by the bacterium Mycobacterium tuberculosis. TB is the second largest cause of mortality by infectious diseases and is a challenging disease to control. It spreads easily among people via droplets propagated by an infectious person. Treatment against TB has been available since the 1950s; however, various problems with treatment have led to the emergence of drug-resistance in TB bacteria, which further complicates disease control. Furthermore, TB is a disease that predominantly affects poor countries or countries with high population densities. With the generalization of travel and migration in the second half of the twentieth century, individuals infected in such countries are likely to move to or spend some time in richer countries, making TB a worldwide problem. In this thesis, we consider the role of population movement in the spread of tuberculosis by studying two different models. The first one is an extension to a spatialized context of a simple existing mathematical model for the spread of TB. We establish that, similarly to the original model, the equilibrium without disease is globally asymptotically stable when the basic reproduction number $\R_0$ is less than one. In the case that $\R_0>1$, we prove that the system is uniformly persistent. The second model considers the spread of drug-resistant TB in a population, then between connected populations. We establish that a backward bifurcation can occur and that the coupled system has more types of equilibria than the systems in isolation. Finally, we consider a general class of models including the previous two in isolation and after coupling. We investigate which dynamical properties of the isolated models are preserved when coupling the models through movement. Some new results are provided in that direction.

Genetically modified (GM) canola (Brassica napus L.) has been widely adopted in Canada since its commercial release in 1995 and now represents over 85% of the canola grown in western Canada. Concurrently, GM canola volunteers have become an increasing management problem in cultivated fields and are ubiquitous in adjacent ruderal (non-cropped disturbed) habitats. However, systematic post-release monitoring is lacking and the ecological and agronomic impacts of escaped GM canola are poorly understood. In this dissertation, I characterize the escape, demography and distribution of GM canola in ruderal habitats in southern Manitoba, at multiple spatial and temporal scales. I characterized GM herbicide tolerance traits in 16 escaped canola populations. The progeny of 129 plants were tested in herbicide trials; 74% of plants produced glyphosate-tolerant progeny, 63% produced glufosinate-tolerant progeny, and 34% produced multiple herbicide-tolerant progeny as a result of gene flow between escaped plants. At the population-scale, four escaped GM canola populations were monitored and periodic matrix models were constructed to describe the dynamics and persistence of flowering plants. Escaped populations were observed to flower in synchrony with adjacent crops and were projected to persist for 2 to 5 years, confirming the potential for gene flow between escaped and cultivated canola populations. At the landscape-scale, the distribution of escaped canola was surveyed in three agricultural regions. Regional factors were important determinants of distribution; escaped canola density was positively correlated with canola cropping intensity and with traffic intensity, and was negatively correlated with distance to grain distribution centres. Local seed dispersal had negligible impact on distribution compared to landscape-scale anthropogenic seed inputs resulting from agricultural transport. These findings suggest that escaped canola persists as a metapopulation, where long-distance dispersal and colonization compensate for frequent extinction of local populations. Escaped populations play an important role in the persistence and spread of GM traits at large spatial scales, with substantial implications for the coexistence of GM and non-GM crops, and especially for organic and reduced-tillage farming operations. Landscape-scale management approaches, designed and implemented collaboratively by multiple stakeholders, are necessary to mitigate the risks of contamination resulting from GM trait escape. Regulation and ongoing monitoring of GM crops must acknowledge and address the dynamic regional nature of seed- and pollen-mediated gene flow.

The type of regional dynamics of a species can provide information on how to manage the species, and may be the only way that some rare species may persist in a given region. A metapopulation is a type of regional dynamic in which local extinction is counterbalanced by recruitment from nearby patches. Metapopulation studies were originally conducted on animals, but have been adapted to plants, and are generally restricted to single-season studies. Plant species may persist as a metapopulation in patchy habitats, such as in forest openings. Forest openings (commonly called barrens, hill prairies, or glades) are habitats found on ridgetops which are characterized by having thin or nutrient-poor soil, high sunlight exposure, and relatively low soil moisture when compared to nearby forest habitats. Forest openings commonly contain plant species more frequently found in prairies, and are often maintained by natural fires that prevents woody species encroachment. In the absence of natural fires due to human management and suppression, woody species have invaded some forest openings, dividing them into a series of patches. To determine whether it is possible for each species to persist as a metapopulation in forest openings, five studies were carried out at each of three sites within the Shawnee National Forest in southern Illinois: a plant survey and ordination using environmental variables, the use of incidence function models to determine which of the species had the potential to form a metapopulation, a metacommunity study to examine overall patterns at each site, a seed bank study, and a seed dispersal study. Forest openings were found to be separate habitats from the surrounding forest based upon canopy openness. Approximately 30% of the species fit the metapopulation model, and the metacommunities at each of the sites exhibited a Clementsian pattern, characterized by groups of co-occurring species that replace each other over the region due to turnover between the groups of species. Species that fit the metapopulation model tended to have seeds that emerge more frequently from the seed bank if annuals and less frequently in the seed bank than species not fitting the metapopulation model (non-metapopulation species) if longer-lived. Species fitting the metapopulation model dispersed equal numbers of seeds as non-metapopulation species at short (5m) and medium (10m) distances, and in some cases dispersed more seeds to longer distances than non-metapopulation species. These studies show that forest openings can be treated as islands of suitable habitat for some species, and that numerous (~30%) species (such as Scleria pauciflora, Stylosanthes biflora, and Manfreda virginica) may assume a metapopulation dynamic in any given year. Many species may have incidence patterns consistent with those of a metapopulation in multiple years; however, the exact habitat patches in which species occur in any given year may change from year to year. Species in forest openings tend to co-occur in groups (a Clementsian pattern), which means that management plans should consider the entire community rather than a single species.

Algumas metapopulações de espécies, como formigas, vivem em colônias que crescem durante algum tempo e depois colapsam. Após o colapso poucos indivíduos sobrevivem. Esses indivíduos se dispersam tentando fazer novas colônias que podem ou não se estabelecer dependendo do ambiente que encontram. Recentemente, Schinazi (2015) usou cadeias de nascimento e morte em ambientes aleatórios para modelar tais populações, e mostrou que a dispersão aleatória é uma boa estratégia para a sobrevivência da população. Nesta tese, introduzimos outros modelos estocásticos de colonização e colapso para os quais consideramos restrições espaciais e diferentes tipos de colapsos. Obtemos para esses novos modelos condições de sobrevivência e extinção. Debatemos algumas situações nas quais a dispersão nem sempre é uma boa estratégia de sobrevivência. Além disso, discutimos a relação destes modelos com outros conhecidos na literatura. Técnicas de percolação, acoplamento e comparação com processos de ramificação convenientemente definidos são usadas para obter os resultados aqui estabelecidos. / Some metapopulations, such as ants, live in colonies that grow for a while and then collapse. Upon collapse, very few individuals survive. These individuals disperse, trying to establish new colonies that may or may not settle, depending on the environment they encounter. Recently, Schinazi (2015) used birth and death chains in random environments to model such populations, and showed that random dispersion is a good strategy for the survival of the population. In this thesis, we introduce other stochastic models of colonization and collapse for which we consider spatial constraints and different kinds of collapse. We obtain conditions for survival and extinction in these new models. We discuss some situations in which dispersion is not always a good survival strategy. In addition, we discuss the relation of these models to others known in the literature. Percolation and coupling techniques and comparison with suitably defined branching processes are used to obtain the results set forth herein.

Algumas metapopulações de espécies, como formigas, vivem em colônias que crescem durante algum tempo e depois colapsam. Após o colapso poucos indivíduos sobrevivem. Esses indivíduos se dispersam tentando fazer novas colônias que podem ou não se estabelecer dependendo do ambiente que encontram. Recentemente, Schinazi (2015) usou cadeias de nascimento e morte em ambientes aleatórios para modelar tais populações, e mostrou que a dispersão aleatória é uma boa estratégia para a sobrevivência da população. Nesta tese, introduzimos outros modelos estocásticos de colonização e colapso para os quais consideramos restrições espaciais e diferentes tipos de colapsos. Obtemos para esses novos modelos condições de sobrevivência e extinção. Debatemos algumas situações nas quais a dispersão nem sempre é uma boa estratégia de sobrevivência. Além disso, discutimos a relação destes modelos com outros conhecidos na literatura. Técnicas de percolação, acoplamento e comparação com processos de ramificação convenientemente definidos são usadas para obter os resultados aqui estabelecidos. / Some metapopulations, such as ants, live in colonies that grow for a while and then collapse. Upon collapse, very few individuals survive. These individuals disperse, trying to establish new colonies that may or may not settle, depending on the environment they encounter. Recently, Schinazi (2015) used birth and death chains in random environments to model such populations, and showed that random dispersion is a good strategy for the survival of the population. In this thesis, we introduce other stochastic models of colonization and collapse for which we consider spatial constraints and different kinds of collapse. We obtain conditions for survival and extinction in these new models. We discuss some situations in which dispersion is not always a good survival strategy. In addition, we discuss the relation of these models to others known in the literature. Percolation and coupling techniques and comparison with suitably defined branching processes are used to obtain the results set forth herein.

Presently, eleven western states and two Canadian provinces utilize sport hunting as the primary mechanism for managing cougar (Puma concolor) populations. However, the impacts of sustained harvest on population dynamics and demographic structure arc not well understood. Additionally, the lack of cost-effective enumeration techniques and strongly conflicting societal values complicate effective management of this species. Given these concerns, the primary goals of this study were (I) to determine the effects of sustained harvest on cougar populations, and (2) estimate the level and extent of cougar harvest statewide. I monitored cougar populations on Monroe Mountain in south-central Utah, and in the Oquirrh Mountains of north-central Utah from 1999 to 2003. Over this interval the Monroe population was subjected to heavy annual removals and was characterized demographically by a younger age structure. low survival and fecundity, and declining density. In contrast , the Oquirrh Mountain population was partially protected and exhibited an older age distribution, relatively high survival and fecundity, and static density. To examine the statewide distribution of sport hunting, I mapped the locations of all cougars legally harvested from I 996-200 I, and calculated harvest rates by watershed (# cougars killed I yr I I 00 km2) . Population trends derived on the st udy sites under known harvest regimes were used as benchmarks and compared with rates calculated for occupied cougar habitat across the state. This provided an index of where cougar populations were stable or declining as a result of hunting pressure. Results from this research suggest heavy, sustained harvest can have significant impacts on cougar population dynamics and demographics. Patterns of recruitment resemble a source-sink population structure due in part to spatially variable management strategies. Moreover, these results indicate during the later I 990s, most of the statewide population was exploited at levels equal to or surpass ing those measured on Monroe Mountain. Because cougar density and habitat characteristics vary across management units, the temporal scale of population recovery will most likely depend on the interaction of harvest regime, productivity of unexploited populations, and landscape connectivity.

No description available.

Despite the two-fold advantage to asexual reproduction and its prevalence in a variety of organisms, sexual reproduction is prevalent across all taxa. The maintenance of two sexes is required to ensure genetic diversity and to prevent “evolutionary dead ends,” especially in clonal organisms. Many mechanisms have been proposed for the maintenance of two sexes, ranging from environmental variation and stochasticity, parasites and predators, and mutation rates. Spatial configuration, the size and location of populations with respect to other populations, can allow two competitors to coexist when one would normally be lost. This is especially important when the two competitors are the two sexes. In the clonal organism Marchantia inflexa, I determined that spatial configuration of populations can directly influence the maintenance of both sexes in a population and in an aggregate of populations (a metapopulation) using a combination of theoretical models and field studies. Based on field studies, population size has a significant influence on whether a subpopulation will contain both sexes, with populations smaller than 1m2 being more likely to contain only one sex while populations greater than 1m2 are more likely to contain both sexes. Based on mathematical models, the spatial arrangement of subpopulations within a metapopulation can greatly influence whether a metapopulation maintains both sexes as well as whether the metapopulation persists once one sex has been lost. Field data suggest that distance to nearest neighbor, a measurement of spatial arrangement, influences the maintenance of the sexes within subpopulations, but could affect maintenance differently depending on the metapopulation identity. In some metapopulations, both sexes are maintained when the nearest neighbor is close, while in other streams, one sex is lost when the nearest neighbor is close. When mathematical models are used to explicitly simulate natural metapopulations, the mathematical model predicts the observed sex ratios in one metapopulation, predicts the observed bias in another metapopulation, and fails to predicted observed values in two other metapopulations. Understanding spatial configuration helps us understand the maintenance and loss of sex, but other factors, such as environmental differences, may be required to accurately predict which sex will be lost.