Relative Selection Strength: Quantifying EffectSize in Habitat- and Step-Selection Inference

Habitat-selection analysis lacks an appropriate measure of the ecological significance of the statistical estimates-a practical interpretation of the magnitude of the selection coefficients. There is a need for a standard approach that allows relating the strength of selection to a change in habitat conditions across space, a quantification of the estimated effect size that can be compared both within and across studies. We offer a solution, based on the epidemiological risk ratio, which we term the relative selection strength (RSS). For a used-available design with an exponential selection function, the RSS provides an appropriate interpretation of the magnitude of the estimated selection coefficients, conditional on all other covariates being fixed. This is similar to the interpretation of the regression coefficients in any multivariable regression analysis. Although technically correct, the conditional interpretation may be inappropriate when attempting to predict habitat use across a given landscape. Hence, we also provide a simple graphical tool that communicates both the conditional and average effect of the change in one covariate. The average-effect plot answers the question: What is the average change in the space use probability as we change the covariate of interest, while averaging over possible values of other covariates? We illustrate an application of the average-effect plot for the average effect of distance to road on space use for elk (Cervus elaphus) during the hunting season. We provide a list of potentially useful RSS expressions and discuss the utility of the RSS in the context of common ecological applications

‘You shall not pass!’: quantifying barrier permeability and proximity avoidance by animals

1. Impediments to animal movement are ubiquitous and vary widely in both scale and permeability. It is essential to understand how impediments alter ecological dynamics via their influence on animal behavioural strategies governing space use and, for anthropogenic features such as roads and fences, how to mitigate these effects to effectively manage species and landscapes.2. Here, we focused primarily on barriers to movement, which we define as features that cannot be circumnavigated but may be crossed. Responses to barriers will be influenced by the movement capabilities of the animal, its proximity to the barriers, and habitat preference. We developed a mechanistic modelling framework for simultaneously quantifying the permeability and proximity effects of barriers on habitat preference and movement.3. We used simulations based on our model to demonstrate how parameters on movement, habitat preference and barrier permeability can be estimated statistically. We then applied the model to a case study of road effects on wild mountain reindeer summer movements.4. This framework provided unbiased and precise parameter estimates across a range of strengths of preferences and barrier permeabilities. The quality of permeability estimates, however, was correlated with the number of times the barrier is crossed and the number of locations in proximity to barriers. In the case study we found that reindeer avoided areas near roads and that roads are semi-permeable barriers to movement. There was strong avoidance of roads extending up to c. 1 km for four of five animals, and having to cross roads reduced the probability of movement by 68·6% (range 3·5–99·5%).5. Human infrastructure has embedded within it the idea of networks: nodes connected by linear features such as roads, rail tracks, pipelines, fences and cables, many of which divide the landscape and limit animal movement. The unintended but potentially profound consequences of infrastructure on animals remain poorly understood. The rigorous framework for simultaneously quantifying movement, habitat preference and barrier permeability developed here begins to address this knowledge gap

Appendix B. Mathematical details of the computation of the means, variances, and covariance of the nonstationary Gompertz process.

Mathematical details of the computation of the means, variances, and covariance of the nonstationary Gompertz process

An invariant approach to statistical analysis of shapes /

INTRODUCTIONA Brief History of MorphometricsFoundations for the Study of Biological FormsDescription of the data SetsMORPHOMETRIC DATATypes of Morphometric DataLandmark Homology and CorrespondenceCollection of Landmark CoordinatesReliability of Landmark Coordinate DataSummarySTATISTICAL MODELS FOR LANDMARK COORDINATE DATAStatistical Models in GeneralModels for Intra-Group VariabilityEffect of Nuisance ParametersInvariance and Elimination of Nuisance ParametersA Definition of FormCoordinate System Free Representation of FormEs

On using expert opinion in ecological analyses: a frequentist approach. Environmetrics 17:683{704

SUMMARY Many ecological studies are characterized by paucity of hard data. Statistical analysis in such situations leads to flat-likelihood functions and wide confidence intervals. Although, there is paucity of hard data, expert knowledge about the phenomenon under study is many times available. Such expert opinion may be used to strengthen statistical inference in these situations. Subjective Bayesian is one approach to incorporate expert opinion in statistical studies. This approach, aside from the subjectivity, also faces operational problems. Elicitation of the prior is the most difficult step. Another is the lack of a precise quantitative definition of what characterizes an expert. In this paper, we discuss a different approach to incorporating subjective expert opinion in statistical analyses. We argue that it is easier to elicit data than to elicit a prior. Such elicited data can then be used to supplement the hard, observed data to possibly improve precision of statistical analyses. The approach suggested here also leads to a natural definition of what constitutes a useful expert. We define a useful expert as one whose opinion adds information over and above what is provided by the observed data. This can be quantified in terms of the change in the Fisher information before and after using the expert opinion. One can, thus, avoid the real possibility of using an expert opinion that adds noise, instead of information, to the hard data. We illustrate this approach using an ecological problem of modeling and predicting occurrence of species. An interesting outcome of this analysis is that statistical thinking helps discriminate between a useful expert and a not so useful expert; expertness need not be decided purely on the basis of experience, fame, or such qualitative characteristics

Appendix B. An algorithm to obtain the bootstrap confidence intervals.

An algorithm to obtain the bootstrap confidence intervals