Evolution frequently plays out over ecological timescales. Local adaptation under the joint action of evolutionary and ecological processes frequently leads to novel outcomes, as is evidenced by the theoretical work on adaptation at species' borders. However, to date this body of work does not have a theory for the effect of stochastic processes on local adaptation. The primary goal of this thesis is to show that demographic and genetic fluctuations can significantly impact upon local adaptation. In addition, the effect of polygenic evolution is also analysed. Specifically, three types of models are considered. First a deterministic mainland-island, subject to hard directional selection, maladaptive gene flow and density regulation is solved for two different trait architectures: an explicit multilocus trait and a quantitative trait. The maladaptive and adaptive steady states can be bistable. This depends on the underlying architecture of the trait, as well as locus number and ploidy. Sourcesink structure can emerge, accompanied by a novel, upper critical threshold above which maladaptation occurs. The most favourable condition for local adaptation occurs for few loci and low migration. Second, a stochastic version of the mainland-island model is analysed as a diffusion process. This is the central premise of the thesis and is explored by examining properties of the stationary distributions of both trait architectures, and the first-passage properties of the single locus case. It is found that across a range of migration rates that depend on locus number and migrant polymorphism, local adaptation may be reversed or escape from maladaptation becomes possible at varying transition rates. The diffusion model is compared to a similar discrete model. The continuous model is in good qualitative agreement with the discrete model. Third, the stochastic model is generalised to the infinite island model, which evolves deterministically. Under deterministic dynamics a range of equilibria are possible, depending on whether habitat size varies or is fixed. Multilocus dynamics restrict the conditions for polymorphism. Stochastic dynamics can have potentially detrimental consequences for the persistence of the island population when drift is strong. The relevance of the stochastic model to border populations is discussed. Although the diffusion process imposes severe constraints on the permissible parameter ranges, it is still able to provide a good qualitative understanding of the impact demographic and genetic fluctuations have on local adaptation.

The recent move to in situ conservation management world-wide is supported by, and stems from the 1992 International Convention on Biological Diversity. The Department of Conservation - charged with the conservation of New Zealand's natural resources - has directed efforts towards the restoration of natural processes as an avenue to halt local biodiversity decline. Ecosystem, habitat, and nature restoration programmes such as the Boundary Stream Mainland Island Project (BSMIP) represent the forefront of conservation management, combining intensive multi-species pest control, with broad-scale hierarchical monitoring programmes. Monitoring programmes confer information that is intended to support decision-making and management by the reduction of uncertainty, or by increasing knowledge. The validity of monitoring programmes depends on three key parts; the guiding objectives, biological relevance, and statistical reliability. Seven major long-term monitoring programmes established at the BSMIP were evaluated according to the above criteria. All monitoring programmes had appropriate guiding objectives, and were biologically relevant (outcome and result monitoring were balanced respective to each other and to the restoration intervention and efforts at BSMIP). The statistical reliability of the programmes was appraised with the use of the Computer programme MONITOR, which provided a calculated value for the statistical power of the monitoring programmes. All monitoring programmes except two (Lizard monitoring: which was initially designed as a short-term species survey, and Mustelid monitoring: which would be a good candidate for a double sampling methodology) had a robust design (evaluated using the actual initial data, and conservative criteria for the detection of population change). The monitoring programmes that did achieve a level of statistical robustness, provided a statistical power of 0.8 ( 80%) within appropriate timeframes for restoration of ecosystem processes (e.g. the timeframe for detection of a 10% change in the abundance, density, relative index, etc of the Result monitoring programmes: Rodents = three years, Possums = six years, and Outcome monitoring programmes: Weta = five years, Ground Invertebrates = four years, Birds (species nos.) = four years, Vegetation (Species, and sapling nos.) = 15 years). The guiding objectives for monitoring programmes must have clear, specific, measurable, and achievable goals, in-order to identify appropriate variables, in both spatial and temporal scales. The biological relevance or "linkage" between monitored groups is important and must be at least outlined, for monitoring programmes to be able to identify potential cause and effect. Statistical reliability (the balance between statistical significance, statistical power, and the timeframe for a conclusive result to be determined) is important, as it is the key method of detecting change. Statistical power can improve the design and efficiency of monitoring programmes and clarify research results. Power analysis has become readily available for researchers and managers with the development of computer programmes specifically designed for this task.

Thesis (M. For. Sc.)--University of Canterbury, 2003. / Typescript (photocopy). Includes bibliographical references (leaves 112-137). Also available via the World Wide Web.

Using trap data the Hawdon, Poulter and South Branch valleys, a spatial distribution model was created for Stoats (Mustela erminea), Ship Rats (Rattus rattus) and Weasels (Mustela nivalis) in the North Branch of the Hurunui River. Ten spatial attributes were analysed in this thesis as potential spatial predictors of Stoats, Ship rats or Weasels; four of which were distance related measurements (distance from ecotonal edge, distance from river, distance from river tributary and distance from trapping edge); three were climate based variables (mean maximum temperature, mean minimum temperature and mean precipitation) and three were topographical based variables (elevation, aspect and slope). Relationships that existed between each spatial attribute and the number of Stoats, Ship Rats and Weasels caught were quantified by comparing the significance of the mean trapping rate with each spatial attribute and expressed spatially as maps in a Geographical Information System (GIS). Results from this thesis found elevation, aspect and distance from ecotonal edge as potential spatial predictors of Stoat populations. Elevation and aspect were found to be potential predictors of Ship rat and Weasel populations. GIS is able to predict the spatial distribution of pest species to a similar (or better) level compared to more formal associative models. The potential of GIS is however, restrained by the same limitations associated with these models. By using a larger trapping data set and identifying a number of social interactions between Stoats, Ship Rats and Weasels, one can improve the accuracy of spatially modelling each species within a Beech forest environment. Therefore, improve our understanding how landscapes influence the distribution of each pest species.

Poison operations are a widely used technique for rodent control in the indigenous forests of New Zealand. This study examined the bait-take and rat monitoring data obtained for continuous poison operations at Boundary Stream Mainland Island (BSMI), Hawke’s Bay, between 1996 and 2007. Since the beginning of the Mainland Island project at BSMI in 1996, 800 ha of indigenous forest have been treated with an ‘Integrated Pest Management’ approach, in which rodents (primarily ship rats) have been targeted by consecutive ground poison operations. The aim of the intensive pest control was to allow the ecosystem to recover and provide a safe environment for threatened native bird species to recover or be re-introduced. Another important aim of this pest control is to provide experience and expert knowledge in management techniques especially applicable to the protection of indigenous habitat on the New Zealand mainland. This research study had two main aims: to identify spatial patterns of the rodent population at BSMI and to determine the efficacy of the different rodenticides applied for their control. The distribution of the rodent population was investigated by spatial analysis of bait-take across the reserve and through time. Visualisation of high and low bait-take areas revealed that there was a noticeable reinvasion from adjacent unmanaged native forests, but not markedly from exotic forest or pasture. Reinvasion from small and isolated adjacent forests ceased to be noticeable consistently after approximately four years of the poison operation, while a large scenic native reserve, as well as a narrow part of the treatment area surrounded by many native bush patches, were continuously affected by reinvasion through the entire project time. Bait-take was visibly higher after the bait had either been removed, or left in the field unserviced, over winter. No consistent areas of no bait-take were identified. Further statistical analysis of bait-take data revealed that bait-take was higher in bait stations within 150 m of the treatment edge than interior bait stations. Bait-take in broadleaf/tawa/podocarp forest was significantly higher than in kamahi/kanuka/rewarewa, beech and cloud-cap forest. The second aim of the study was to determine the efficacy of the various bait types with different active ingredients used during the operation. Rat monitoring data, namely rat tracking indices (RTI) obtained from tracking tunnels, were statistically modelled using Generalised Linear Models. Diphacinone cereal pellets (Pestoff® 50D, 0.05g/kg diphacinone) obtained the lowest RTI, followed by pindone cereal pellets (Pindone Pellets®, 0.5g/kg pindone), brodifacoum cereal pellets (Pestoff® 20p and Talon®, 0.02 g/kg brodifacoum), coumatetralyl paste (Racumin®, 0.375 g/kg) and diphacinone bait blocks (Ditrac®, 0.05 g/kg). Cereal pellet baits worked better than any other bait type used at this location. Season had no statistically significant effect on either RTI or bait-take estimates. The overall goal of the poison operation to decrease rat numbers, and to maintain low levels, has been met. However, the results of this study suggest that baiting needs to be done continuously and over the entire treatment area. Edge bait stations – particularly next to adjacent native forests – should be prioritised to target reinvading rodents. Poisons presented in cereal pellet baits should be preferred to other bait types. Both pindone and brodifacoum showed very good results, as well as diphacinone in cereal pellet baits.

Using trap data the Hawdon, Poulter and South Branch valleys, a spatial distribution model was created for Stoats (Mustela erminea), Ship Rats (Rattus rattus) and Weasels (Mustela nivalis) in the North Branch of the Hurunui River. Ten spatial attributes were analysed in this thesis as potential spatial predictors of Stoats, Ship rats or Weasels; four of which were distance related measurements (distance from ecotonal edge, distance from river, distance from river tributary and distance from trapping edge); three were climate based variables (mean maximum temperature, mean minimum temperature and mean precipitation) and three were topographical based variables (elevation, aspect and slope). Relationships that existed between each spatial attribute and the number of Stoats, Ship Rats and Weasels caught were quantified by comparing the significance of the mean trapping rate with each spatial attribute and expressed spatially as maps in a Geographical Information System (GIS). Results from this thesis found elevation, aspect and distance from ecotonal edge as potential spatial predictors of Stoat populations. Elevation and aspect were found to be potential predictors of Ship rat and Weasel populations. GIS is able to predict the spatial distribution of pest species to a similar (or better) level compared to more formal associative models. The potential of GIS is however, restrained by the same limitations associated with these models. By using a larger trapping data set and identifying a number of social interactions between Stoats, Ship Rats and Weasels, one can improve the accuracy of spatially modelling each species within a Beech forest environment. Therefore, improve our understanding how landscapes influence the distribution of each pest species.