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The Mahalanobis distance is a statistical technique that has been used in statistics and data science for data classification and outlier detection, and in ecology to quantify species-environment relationships in habitat and ecological niche models. Mahalanobis distances are based on the location and scatter of a multivariate normal distribution, and can measure how distant any point in space is from the centre of this kind of distribution. Three different methods for calculating the multivariate location and scatter are commonly used: the sample mean and variance-covariance, the minimum covariance determinant, and the minimum volume ellipsoid. The minimum covariance determinant and minimum volume ellipsoid were developed to be robust to outliers by minimising the multivariate location and scatter for a subset of the full sample, with the proportion of the full sample forming the subset being controlled by a user-defined parameter. This outlier robustness means the minimum covariance determinant and the minimum volume ellipsoid are highly relevant for ecological niche analyses, which are usually based on natural history observations that are likely to contain errors. However, natural history observations will also contain extreme bias, to which the minimum covariance determinant and the minimum volume ellipsoid will also be sensitive. To provide guidance for selecting and parameterising a multivariate location and scatter method, a series of virtual ecological niche modelling experiments were conducted to demonstrate the performance of each multivariate location and scatter method under different levels of sample size, errors, and bias. The results show that there is no optimal modelling approach, and that choices need to be made based on the individual data and question. The sample mean and variance-covariance method will perform best on very small sample sizes if the data are free of error and bias. At larger sample sizes the minimum covariance determinant and minimum volume ellipsoid methods perform as well or better, but only if they are appropriately parameterised. Modellers who are more concerned about the prevalence of errors should retain a smaller proportion of the full data set, while modellers more concerned about the prevalence of bias should retain a larger proportion of the full data set. I conclude that Mahalanobis distances are a useful niche modelling technique, but only for questions relating to the fundamental niche of a species where the assumption of multivariate normality is reasonable. Users of the minimum covariance determinant and minimum volume ellipsoid methods must also clearly report their parameterisations so that the results can be interpreted correctly.

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BACKGROUND: The páramos, the high-elevation ecosystems of the northern Andes, are well-known for their high species richness and provide a variety of ecosystem services to local subsistence-based communities and regional urbanizations. Climate change is expected to negatively affect the provision of these services, but the level of this impact is still unclear. Here we assess future climate change impact on the ecosystem services provided by the critically important páramos of the department of Boyacá in Colombia, of which over 25% of its territory is páramo. METHODS: We first performed an extensive literature review to identify useful species of Boyacá, and selected 103 key plant species that, based on their uses, support the provision of ecosystem services in the páramos. We collated occurrence information for each key species and using a Mahalanobis distance approach we applied climate niche modelling for current and future conditions. RESULTS: We show an overall tendency of reduction in area for all ecosystem services under future climate conditions (mostly a loss of 10% but reaching up to a loss of 40%), but we observe also increases, and responses differ in intensity loss. Services such as Food for animals, Material and Medicinal, show a high range of changes that includes both positive and negative outcomes, while for Food for humans the responses are mostly substantially negative. Responses are less extreme than those projected for individual species but are often complex because a given ecosystem service is provided by several species. As the level of functional or ecological redundancy between species is not yet known, there is an urgency to expand our knowledge on páramos ecosystem services for more species. Our results are crucial for decision-makers, social and conservation organizations to support sustainable strategies to monitor and mitigate the potential consequences of climate change for human livelihoods in mountainous settings.

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Interpolation techniques provide a method to convert point data of a geographic phenomenon into a continuous field estimate of that phenomenon, and have become a fundamental geocomputational technique of spatial and geographical analysts. Natural neighbour interpolation is one method of interpolation that has several useful properties: it is an exact interpolator, it creates a smooth surface free of any discontinuities, it is a local method, is spatially adaptive, requires no statistical assumptions, can be applied to small datasets, and is parameter free. However, as with any interpolation method, there will be uncertainty in how well the interpolated field values reflect actual phenomenon values. Using a method based on natural neighbour distance based rates of error calculated for data points via cross-validation, a cross-validation error-distance field can be produced to associate uncertainty with the interpolation. Virtual geography experiments demonstrate that given an appropriate number of data points and spatial-autocorrelation of the phenomenon being interpolated, the natural neighbour interpolation and cross-validation error-distance fields provide reliable estimates of value and error within the convex hull of the data points. While this method does not replace the need for analysts to use sound judgement in their interpolations, for those researchers for whom natural neighbour interpolation is the best interpolation option the method presented provides a way to assess the uncertainty associated with natural neighbour interpolations.

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The Mahalanobis distance is a statistical technique that can be used to measure how distant a point is from the centre of a multivariate normal distribution. By measuring Mahalanobis distances in environmental space ecologists have also used the technique to model: ecological niches, habitat suitability, species distributions, and resource selection functions. Unfortunately, the original description of the Mahalanobis distance technique for ecological modelling contained an error describing how Mahalanobis distances could be converted into probabilities using a chi-squared distribution. This error has been repeated in the literature, and is present in popular modelling software. In the hope of correcting this error to maximise the potential application of the Mahalanobis distance technique within the ecological modelling community, I explain how Mahalanobis distances are calculated, and through a virtual ecology experiment demonstrate how to correctly produce probabilities and discuss the implications of the error for previous Mahalanobis distance studies.

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Limiting the impact of wildlife damage in a cost effective manner requires an understanding of how control inputs change the occurrence of damage through their effect on animal density. Despite this, there are few studies linking wildlife management (control), with changes in animal abundance and prevailing levels of wildlife damage. We use the impact and management of wild pigs as a case study to demonstrate this linkage. Ground disturbance by wild pigs has become a conservation issue of global concern because of its potential effects on successional changes in vegetation structure and composition, habitat for other species, and functional soil properties. In this study, we used a 3-year pig control programme (ground hunting) undertaken in a temperate rainforest area of northern New Zealand to evaluate effects on pig abundance, and patterns and rates of ground disturbance and ground disturbance recovery and the cost effectiveness of differing control strategies. Control reduced pig densities by over a third of the estimated carrying capacity, but more than halved average prevailing ground disturbance. Rates of new ground disturbance accelerated with increasing pig density, while rates of ground disturbance recovery were not related to prevailing pig density. Stochastic simulation models based on the measured relationships between control, pig density and rate of ground disturbance and recovery indicated that control could reduce ground disturbance substantially. However, the rate at which prevailing ground disturbance was reduced diminished rapidly as more intense, and hence expensive, pig control regimes were simulated. The model produced in this study provides a framework that links conservation of indigenous ecological communities to control inputs through the reduction of wildlife damage and suggests that managers should consider carefully the marginal cost of higher investment in wildlife damage control, relative to its marginal conservation return.

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Dispersal costs need to be quantified from empirical data and incorporated into dispersal models to improve our understanding of the dispersal process. We are interested in quantifying how landscape features affect the immediately incurred direct costs associated with the transfer of an organism from one location to another. We propose that least-cost modelling is one method that can be used to quantify direct transfer costs. By representing the landscape as a cost-surface, which describes the costs associated with traversing different landscape features, least-cost modelling is often applied to measure connectivity between locations in accumulated-cost units that are a combination of both the distance travelled and the costs traversed. However, we take an additional step by defining an accumulated-cost dispersal kernel, which describes the probability of dispersal in accumulated-cost units. This novel combination of cost-surface and accumulated-cost dispersal kernel enables the transfer stage of dispersal to incorporate the effects of landscape features by modifying the direction of dispersal based on the cost-surface and the distance of dispersal based on the accumulated-cost dispersal kernel. We apply this approach to the common brushtail possum (Trichosurus vulpecula) within the North Island of New Zealand, demonstrating how commonly collected empirical dispersal data can be used to calibrate a cost-surface and associated accumulated-cost dispersal kernel. Our results indicate that considerable improvements could be made to the modelling of the transfer stage of possum dispersal by using a cost-surface and associated accumulated-cost dispersal kernel instead of a more traditional straight-line distance based dispersal kernel. We envisage a variety of ways in which the information from this novel combination of a cost-surface and accumulated-cost dispersal kernel could be gainfully incorporated into existing dispersal models. This would enable more realistic modelling of the direct transfer costs associated with the dispersal process, without requiring existing dispersal models to be abandoned.

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Wild deer populations in Great Britain are expanding in range and probably in numbers, and relatively high prevalence of bovine tuberculosis (bTB, caused by infection with Mycobacterium bovis) in deer occurs locally in parts of southwest England. To evaluate the M. bovis exposure risk posed to cattle by wild deer relative to badgers in England and Wales, we constructed and parameterized a quantitative risk model with the use of information from the literature (on deer densities, activity patterns, bTB epidemiology, and pathology) and contemporary data on deer, cattle, and badger (Meles meles) distribution and abundance. The median relative risk score for each of the four deer species studied--red (Cervus elaphus), fallow (Dama dama), and roe (Capreolus capreolus) deer, and muntjac (Muntiacus reevesi)--was lower than unity (the relative risk set for badgers, the putative main wildlife reservoir of M. bovis in England and Wales). However, the 95th percentiles associated with risk estimates were large, and the upper limits for all four deer species exceeded unity. Although M. bovis exposure risks to cattle from deer at pasture are likely to be lower than those from badgers across most areas of England and Wales where cattle are affected by bTB because these areas coincide with high-density badger populations but not high-density deer populations, we predict the presence of localized areas where relative risks posed by deer may be considerable. Moreover, wherever deer are infected, risks to cattle may be additive to those posed by badgers. There are considerable knowledge gaps associated with bTB in deer, badgers, and cattle, and data available for model parameterization were generally of low quality and high variability, and consequently model output were subject to some uncertainty. Improved estimates of the proportion of time that deer of each species spend at pasture, the likelihood and magnitude of M. bovis excretion, and local badger and deer densities appear most important for improving estimates of relative risk in this system.

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The Eurasian badger (Meles meles) is implicated in the transmission of bovine tuberculosis (TB) to cattle in the UK and Republic of Ireland. Badger culling has been employed for the control of TB in cattle in both countries, with varying results. Social perturbation of badger populations following culling has been proposed as an explanation for the failure of culling to consistently demonstrate significant reductions in cattle TB. Field studies indicate that culling badgers may result in increased immigration into culled areas, disruption of territoriality, increased ranging and mixing between social groups. Our analysis shows that some measures of sociality may remain significantly disrupted for up to 8 years after culling. This may have epidemiological consequences because previous research has shown that even in a relatively undisturbed badger population, movements between groups are associated with increases in the incidence of Mycobacterium bovis infection. This is consistent with the results from a large-scale field trial, which demonstrated decreased benefits of culling at the edges of culled areas, and an increase in herd breakdown rates in neighbouring cattle.

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