The sooty shearwater (also known as the muttonbird, Titi, Puffinus griseus) is a long-lived super-abundant, burrow nesting petrel, harvested by Rakiura Maori from breeding colonies, located in southern New Zealand. The harvest is culturally defining and enormously important for Rakiura Maori. The work in this thesis contributes to the Kia Mau te Titi Mo Ake Tonu Atu Research Project being undertaken by Rakiura Maori and the University of Otago, towards assessing ongoing sustainability of the harvest and future threats. Analyses of eight muttonbirder harvest records spanning, 1938 to 2004, show that harvest rates demonstrate, systematic commonalities in seasonal patterns and broad-scale consistency in trends of chick abundance and quality across harvested islands. If co-ordinated and well replicated, harvest records offer Rakiura Maori a low-cost and effective monitoring tool of sooty shearwater reproductive success and long-term population abundance. Hunt tallies provide additional evidence of a dramatic reduction in sooty shearwater abundance from the late 1980s that was also detected by counts from boats off the western seaboard of the USA. A conservative estimate of overall decline in hunt success across diaries, for the period 1972 to 2004, is 1.89 % (CI₉₅ 1.14 to 2.65) per annum, a total reduction of 39.2%. The harvesting records show a sooty shearwater mortality event occurred just prior to the 1993-breeding season at the same time as a severe negative anomaly in both the Pacific Decadal Oscillation and Southern Oscillation Indices. The hunting diaries show a decoupling of chick size with harvest success in the early 1990s. This resulted from a decline in harvest success and an increase in its variability, while chick size remained correlated with changing chick abundance and maintained its pre-1990 average. Long- lived seabirds maintain high survival by skipping breeding and abandoning breeding attempts when oceanic conditions deteriorate, increasing variability in chick abundance is also evidence of pressure on adult survivorship. The multiple diaries confirm these were major demographic events not confined to a single island. My survival estimates for The Snares and Whenua Hou were very high 0.952 (0.896-0.979) compared to earlier estimates for this species. Transience at the colonies is high due to the presence ofjuvenile and pre-breeding birds. Both naturally high survival and the large number of transient pre-breeders indicate sooty shearwater are more resilient to harvest than earlier survival models suggested. There was no evidence for directional change in sooty shearwater breeding phenology over 49-years of harvest. Climate fluctuation/change is therefore apparently not altering egg-laying. Peak fledging occurred fairly consistently in the 2nd of May (IQR = 2.91 days). Yearly variability in emergence occurs primarily due to provisioning and localized fledging conditions. Larger chick size was strongly correlated with delayed fledging and is consistent with the traditional ecological knowledge of the birders. There was no evidence for chicks becoming smaller or that years with starving chicks were more common, so increasing mismatch of breeding with optimal forage was not indicated. The past proportion of birders over the last 20 years (1985 - 2005) has been ~2% all of Rakiura Maori. Approximately 376 birders participated in the 2006 season with an estimated of overall harvest intensity 19.4% (CI₉₅ = 13.8 - 24.2%) and a total catch of 381,000 (CI₉₅ = 262,257 - 487,186) chicks. This study found evidence that catch rates reduced with increasing birder competition partially mitigating effects on harvest pressure. The combined effects of potential climate change on bird abundance and increased harvester competition suggests that the proportion of Rakiura Maori whom choose to bird is likely to decrease as tallies reduce and cost recovery becomes more difficult. Rakiura Maori have for many years cherished and maintained their islands and implemented protective measures to safeguarded titi breeding habitat. Future harvest management will have additional issues to contend with, but Rakiura Maori are necessarily confronting these issues as the titi culture rests on the maintenance of their taonga. The information presented in this thesis shows that combining science and traditional knowledge is a powerful tool for managing harvest sustainability.

Bibliography: leaves 132-153. Spatially explicit models and computer intensive analysis were employed to explore how processes acting at the individual level scale up to population dynamics when processes are variable in space as well as the consequences of sampling spatially complex variability for drawing conclusions from limited ecological data. Dispersal and variation in marsupial mortality and development in relation to habitat selection and quality were studied, while evaluating spatially explicit models. The study of dynamics models of tick populations on sleepy lizards considered the effect of spatial and temporal variability, and demonstrated that counting ticks is a poor indicator of tick abundance. The "virtual ecologist" model is a useful method for linking the output of spatially explicit population models to reality, and will be a valuable approach for improving the design of ecological field research on spatially complex landscapes.

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior. Cholera remains a public health threat in many parts of the world and improved intervention strategies are needed. We investigate a key intervention strategy, vaccination, with optimal control applied to a cholera model. This system of differential equations has human compartments with susceptibles with different levels of immunity, symptomatic and asymptomatic infecteds, and two cholera vibrio compartments, hyperinfectious and non-hyperinfectious. The spread of the infection in the model is shown to be most sensitive to certain parameters, and the effect of varying these parameters on the optimal vaccination strategy is shown in numerical simulations. Our simulations also show the importance of the infection rate under various parameter cases.

Flowering dogwood (Cornus florida L.) populations have experienced severe declines caused by dogwood anthracnose in the past three decades. Mortality has ranged from 48 to 98%, raising the concern that genetic diversity of this native tree has been reduced significantly. Microsatellite data were used to evaluate the level and distribution of genetic variation throughout much of the native range of the tree. In the first conducted study, we found that genetic variation in areas affected by anthracnose was as high as or higher than areas without die-offs. We found evidence of four widespread, spatially contiguous genetic clusters. However, there was little relationship between geographic distance and genetic difference. These observations suggest that high dispersal rates and large effective population sizes have so far prevented rapid loss of genetic diversity. The effects of anthracnose on demography and community structure are likely to be far more consequential than short-term genetic effects. The second study examined levels and distribution of genetic variation of C. florida throughout Great Smoky Mountains National Park (GSMNP). Significant genetic structure at both landscape and local levels were found. We infer that two genetic clusters exist within the park, mostly separated by the main dividing ridge of the Great Smoky Mountains. The differentiation is statistically significant, but subtle, with gene flow evident through low-elevation corridors. It seems unlikely that recent demographic dynamics have resulted in a depletion of genetic variation in flowering dogwoods.

Species augmentation is a method of reducing species loss via augmenting declining or threatened populations with individuals from captive-bred or stable, wild populations. In this dissertation, species augmentation is analyzed in an optimal control setting to determine the optimal augmentation strategies given various constraints and settings. In each setting, we consider the effects on both the target/endangered population and a reserve population from which the individuals translocated in the augmentation are harvested. Four different optimal control formulations are explored. The first two optimal control formulations model the underlying population dynamics with a system of ordinary differential equations. Each of these two formulations utilizes a different function to model the cost of augmentation. For each optimal control formulation we find a characterization for the optimal control and show numerical results for scenarios of different illustrative parameter sets. The second two optimal control formulations model the underlying population dynamics with systems of discrete difference equations. The difference between these two optimal control formulations is the order in which events occur within each time step in the population models. In the first formulation the population is augmented before the natural growing season in each time step (augment then grow model), whereas in the second formulation the population is augmented after the natural growing season in each time step (grow then augment model). These two discrete time models, which differ only in their order of events, lead to structurally different models. The formulation with the augment then grow model cannot utilize discrete time optimal control theory and a brute force method of finding the optimal augmentation strategy is used. The formulation with the grow then augment model does utilize optimal control theory and we find the characterization of the optimal control. For both formulations, we explore several scenarios of different illustrative parameter sets. In each of the four optimal control formulations, the numerical results provide considerably more detail about the exact dynamics of optimal augmentation than can be readily intuited. The work presented here are the first steps toward building a general theory of population augmentation, which accounts for the complexities inherent in many conservation biology applications.

ABSTRACT One cause of declines and extinctions of island species is carnivore introduction. Four carnivores, including the small Indian mongoose (Herpestes auropunctatus), are on the IUCN’s list of 100 of the World's Worst Invasive Alien Species. My thesis summarizes global patterns of carnivore introductions and examines ecological, evolutionary, and management impacts of this mongoose. I study abundances of reptiles and amphibians on mongoose-infested and mongoose-free islands in the Adriatic Sea to determine if factors other than mongoose presence can account for abundance differences. For several reptiles and amphibians, the mongoose is implicated as causing differences. Additionally, I assess species abundance in the small mammal community and activity times of introduced ship rats (Rattus rattus) on the same islands. The mongoose is implicated in a shift in rat activity times, but it is difficult to separate mongoose impacts on small mammal abundance from rat impacts. To manage introduced carnivores, we can exclude, control, or eradicate them. I review literature data on mongoose eradication and control campaigns. I compiled a list of all islands with known mongoose populations and focused on assessing successes, failures, and challenges. The mongoose has been eradicated only on six very small islands. Management at low levels by various techniques has been attempted on many islands, with variable success. On almost all islands of introduction, the mongoose has no potential competitors of similar size. However, on three Adriatic islands where the mongoose was introduced, a similar-sized native carnivore, the stone marten (Martes foina), is present, while on one Adriatic island the small Indian mongoose is the sole carnivore. To see if character displacement occurs in the mongoose when the marten is present, and vice-versa, I examined size variation in the diameter of the upper canine tooth (the prey-killing organ) and skull length in these two species on these islands. Character displacement in both traits was evident for the mongoose but not the marten. Lastly, I developed a simulation model to examine genetic consequences of serial introductions of the small Indian mongoose and found that the potential for population genetic data to determine introduction pathways and sequences is limited.

Ever since Maynard-Smith and Price first introduced the concept of an evolutionary stable strategy (ESS) in 1973, there has been a growing amount of work in and around this field. Many new concepts have been introduced, quite often several times over, with different acronyms by different authors. This led to other authors trying to collect and collate the various terms (for example Lessard, 1990 & Eshel, 1996) in order to promote better understanding ofthe topic. It has been noticed that dynamic selection did not always lead to the establishment of an ESS. This led to the development ofthe concept ofa continuously stable strategy (CSS), and the claim that dynamic selection leads to the establishment of an ESSif it is a CSS. It has since been proved that this is not always the case, as a CSS may not be able to displace its near neighbours in pairwise ecological competitions. The concept of a neighbourhood invader strategy (NIS) was introduced, and when used in conjunction with the concept of an ESS, produced the evolutionary stable neighbourhood invader strategy (ESNIS) which is an unbeatable strategy. This work has tried to extend what has already been done in this field by investigating the dynamics of coexisting species, concentrating on systems whose dynamics are governed by Lotka-Volterra competition models. It is proved that an ESNIS coalition is an optimal strategy which will displace any size and composition of incumbent populations, and which will be immune to invasions by any other mutant populations, because the ESNIS coalition, when it exists, is unique. It has also been shown that an ESNIS coalition cannot exist in an ecologically stable state with any finite number of strategies in its neighbourhood. The equilibrium population when the ESNIS coalition is the only population present is globally stable in a n-dimensional system (for finite n), where the ESNIS coalition interacts with n - 2 other strategies in its neighbourhood. The dynamical behaviour of coexisting species was examined when the incumbent species interacted with various invading species. The different behaviour ofthe incumbent population when invaded by a coalition using either an ESNIS or an NIS phenotype underlines the difference in the various strategies. Similar simulations were intended for invaders who were using an ESS phenotype, but unfortunately the ESS coalition could not be found. If the invading coalition use NIS phenotypes then the outcome is not certain. Some, but not all of the incumbents might become extinct, and the degree to which the invaders flourish is very dependent on the nature ofthe incumbents. However, if the invading species form an ESNIS coalition, one is certain of the outcome. The invaders will eliminate the incumbents, and stabilise at their equilibrium populations. This will occur regardless of the composition and number of incumbent species, as the ESNIS coalition forms a globally stable equilibrium point when it is at its equilibrium populations, with no other species present. The only unknown fact about the outcome in this case is the number ofgenerations that will pass before the system reaches the globally stable equilibrium consisting ofjust the ESNIS. For systems whose dynamics are not given by Lotka-Volterra equations, the existence ofa unique, globally stable ESNIS coalition has not been proved. Moreover, simulations of a non Lotka-Volterra system designed to determine the applicability ofthe proof were inconclusive, due to the ESS coalition not having unique population sizes. Whether or not the proof presented in this work can be extended to non Lotka-Volterra systems remains to be determined. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2000.

Erratum pages inserted onto front end papers. / Bibliography: leaves 226-244. / vi, 244 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis developed mathematical models of commercially exploited fish populations, addressing the question of how to harvest a predator-prey metapopulation. Optimal harvesting strategies are found using dynamic programming and Lagrange multipliers. Rules about harvesting source/sink populations, more/less vulnerable prey subpopulations and more/less efficient predator subpopulations are explored. Strategies for harvesting critical prey subpopulations are suggested. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2000?

Bibliography: leaves 132-153. / viii, 153 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Spatially explicit models and computer intensive analysis were employed to explore how processes acting at the individual level scale up to population dynamics when processes are variable in space as well as the consequences of sampling spatially complex variability for drawing conclusions from limited ecological data. Dispersal and variation in marsupial mortality and development in relation to habitat selection and quality were studied, while evaluating spatially explicit models. The study of dynamics models of tick populations on sleepy lizards considered the effect of spatial and temporal variability, and demonstrated that counting ticks is a poor indicator of tick abundance. The "virtual ecologist" model is a useful method for linking the output of spatially explicit population models to reality, and will be a valuable approach for improving the design of ecological field research on spatially complex landscapes. / Thesis (Ph.D.)--University of Adelaide, Dept. of Environmental Science and Management, 1999?

[Truncated abstract] Most ecological research investigates the demography of organisms, which can be summarised by their population dynamics and structure. Population dynamics are the rates of birth, growth, reproduction and survival of individuals, which determine the number of individuals in different stage classes, or, the population structure. Understanding the demography of organisms is particularly difficult, and requires the application of different methods of investigation. A number of methods of investigation are required because each can only investigate particular aspects of population demography, and is subject to problems of inaccuracy and bias. Thus, population demography is best understood by simultaneously collecting complimentary data using different methods of analysis to quantify how and why the dynamics and structure of populations change with their environment. The need for complimentary methods of investigation to understand population demography is even greater for organisms that have complex life histories, such as corals. The life histories of corals are particularly complex because they display a variety of modes of sexual and asexual reproduction, and their rates of growth, reproduction and survival are strongly influenced by the size of the individual, which can change rapidly. Additionally, the rates of sexual recruitment to populations of corals are notoriously variable in space and time. Thus, corals are an ideal model to investigate the usefulness of combining methods of analysis to better understand the demography of organisms. In this thesis I demonstrate that combining data from a number of methods of analysis provides a much better understanding of the demography of populations of the mushroom coral Fungia fungites that were exposed to contrasting regimes of disturbance. I used methods of analysis that produce unique and complimentary results, in the form of genetic, size-structure, life history and experimental data. Genetic data confirmed that I was correctly identifying life history stages of polyps, indicated the extent to which a stock-recruitment relationship existed between the sexual recruits and the adult polyps at each population, and provided an estimate of the relative contribution of asexual recruitment to population maintenance. Changes in the size-structures of populations were quantified to determine the effects of different regimes of disturbance, and these changes in population structure were explained by quantifying the life history traits of polyps and their rates of transition through their life cycle. An experimental manipulation was conducted to specifically quantify the effects of sedimentation on the rates of survival and asexual recruitment of polyps, because sedimentation was an important disturbance whose effects were confounded by additional variables. Together, the set of complimentary data provided a good understanding of population demography in the context of varying levels of exposure to certain disturbances, and enabled the best possible predictions about the future of each population under a variety of conditions