Bayesian Predictive Probability Functions for Count Data that are Subject to Misclassification

We develop three Bayesian predictive probability functions based on data in the form of a double sample. One Bayesian predictive probability function is for predicting the true unobservable count of interest in a future sample for a Poisson model with data subject to misclassification and two Bayesian predictive probability functions for predicting the number of misclassified counts in a current observable fallible count for an event of interest. We formulate a Gibbs sampler to calculate prediction intervals for these three unobservable random variables and apply our new predictive models to calculate prediction intervals for a real‐data example. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An empirical comparison of models for the phenology of bird migration

Bird migration phenology shows strong responses to climate change. Studies of trends and patterns in phenology are typically based on annual summarizing metrics, such as means and quantiles calculated from raw daily count data. However, with irregularly sampled data and large day‐to‐day variation, such metrics can be biased and noisy, and may be analysed using phenological functions fitted to the data. Here we use count data of migration passage from a Finnish bird observatory to compare different models for the phenological distributions of spring migration (27 species) and autumn migration (57 species). We assess parsimony and goodness‐of‐fit in a set of models, with phenological functions of different complexity, optionally with covariates accounting for day‐to‐day variability. The covariates describe migration intensities of related species or relative migration intensities the previous day (autocovariates). We found that parametric models are often preferred over the more flexible generalized additive models with constrained degrees of freedom. Models corresponding to a mixture of two distinct passing populations were frequently preferred over simpler ones, but usually no more complex models are needed. Slightly more complex models were favoured in spring compared to autumn. Related species’ migration activity effectively improves the model by accounting for the large day‐to‐day variation. Autocovariates were usually not that relevant, implying that autocorrelation is generally not a major concern if phenology is modelled properly. We suggest that parametric models are relatively good for studying single‐population migration phenology, or a mix of two groups with distinct phenologies, especially if daily variation in migration intensity can be controlled for. Generalized additive models may be useful when the migrating population composition is unknown. Despite these guidelines, choosing an appropriate model involves case‐by‐case assessment or the biological relevance and rationale for modelling phenology.     

Land use improves spatial predictions of mountain plant abundance but not presence‐absence

Question: Does a land‐use variable improve spatial predictions of plant species presence‐absence and abundance models at the regional scale in a mountain landscape? Location: Western Swiss Alps. Methods: Presence‐absence generalized linear models (GLM) and abundance ordinal logistic regression models (LRM) were fitted to data on 78 mountain plant species, with topo‐climatic and/or land‐use variables available at a 25‐m resolution. The additional contribution of land use when added to topo‐climatic models was evaluated by: (1) assessing the changes in model fit and (2) predictive power, (3) partitioning the deviance respectively explained by the topo‐climatic variables and the land‐use variable through variation partitioning, and (5) comparing spatial projections. Results: Land use significantly improved the fit of presence‐absence models but not their predictive power. In contrast, land use significantly improved both the fit and predictive power of abundance models. Variation partitioning also showed that the individual contribution of land use to the deviance explained by presence‐absence models was, on average, weak for both GLM and LRM (3.7% and 4.5%, respectively), but changes in spatial projections could nevertheless be important for some species. Conclusions: In this mountain area and at our regional scale, land use is important for predicting abundance, but not presence‐absence. The importance of adding land‐use information depends on the species considered. Even without a marked effect on model fit and predictive performance, adding land use can affect spatial projections of both presence‐absence and abundance models.     

Selecting discriminant function models for predicting the expected richness of aquatic macroinvertebrates

1. The predictive modelling approach to bioassessment estimates the macroinvertebrate assemblage expected at a stream site if it were in a minimally disturbed reference condition. The difference between expected and observed assemblages then measures the departure of the site from reference condition. 2. Most predictive models employ site classification, followed by discriminant function (DF) modelling, to predict the expected assemblage from a suite of environmental variables. Stepwise DF analysis is normally used to choose a single subset of DF predictor variables with a high accuracy for classifying sites. An alternative is to screen all possible combinations of predictor variables, in order to identify several ‘best’ subsets that yield good overall performance of the predictive model. 3. We applied best‐subsets DF analysis to assemblage and environmental data from 199 reference sites in Oregon, U.S.A. Two sets of 66 best DF models containing between one and 14 predictor variables (that is, having model orders from one to 14) were developed, for five‐group and 11‐group site classifications. 4. Resubstitution classification accuracy of the DF models increased consistently with model order, but cross‐validated classification accuracy did not improve beyond seventh or eighth‐order models, suggesting that the larger models were overfitted. 5. Overall predictive model performance at model training sites, measured by the root‐mean‐squared error of the observed/expected species richness ratio, also improved steadily with DF model order. But high‐order DF models usually performed poorly at an independent set of validation sites, another sign of model overfitting. 6. Models selected by stepwise DF analysis showed evidence of overfitting and were outperformed by several of the best‐subsets models. 7. The group separation strength of a DF model, as measured by Wilks’Λ, was more strongly correlated with overall predictive model performance at training sites than was DF classification accuracy. 8. Our results suggest improved strategies for developing reliable, parsimonious predictive models. We emphasise the value of independent validation data for obtaining a realistic picture of model performance. We also recommend assessing not just one or two, but several, candidate models based on their overall performance as well as the performance of their DF component. 9. We provide links to our free software for stepwise and best‐subsets DF analysis.     

Assessing intervention efficacy on high‐risk drinkers using generalized linear mixed models with a new class of link functions

Unhealthy alcohol use is one of the leading causes of morbidity and mortality in the United States. Brief interventions with high‐risk drinkers during an emergency department (ED) visit are of great interest due to their possible efficacy and low cost. In a collaborative study with patients recruited at 14 academic ED across the United States, we examined the self‐reported number of drinks per week by each patient following the exposure to a brief intervention. Count data with overdispersion have been mostly analyzed with generalized linear mixed models (GLMMs), of which only a limited number of link functions are available. Different choices of link function provide different fit and predictive power for a particular dataset. We propose a class of link functions from an alternative way to incorporate random effects in a GLMM, which encompasses many existing link functions as special cases. The methodology is naturally implemented in a Bayesian framework, with competing links selected with Bayesian model selection criteria such as the conditional predictive ordinate (CPO). In application to the ED intervention study, all models suggest that the intervention was effective in reducing the number of drinks, but some new models are found to significantly outperform the traditional model as measured by CPO. The validity of CPO in link selection is confirmed in a simulation study that shared the same characteristics as the count data from high‐risk drinkers. The dataset and the source code for the best fitting model are available in Supporting Information.     

Parametric Models for Estimating the Number of Classes

We consider parametric distributions intended to model heterogeneity in population size estimation, especially parametric stochastic abundance models for species richness estimation. We briefly review (conditional) maximum likelihood estimation of the number of species, and summarize the results of fitting 7 candidate models to frequency‐count data, from a database of >40000 such instances, mostly arising from microbial ecology. We consider error estimation, goodness‐of‐fit assessment, data subsetting, and other practical matters. We find that, although the array of candidate models can be improved, finite mixtures of a small number of components (point masses or simple diffuse distributions) represent a promising direction. Finally we consider the connections between parametric models for abundance and incidence data, again noting the usefulness of finite mixture models. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Validation of species–climate impact models under climate change

Increasing concern over the implications of climate change for biodiversity has led to the use of species–climate envelope models to project species extinction risk under climate‐change scenarios. However, recent studies have demonstrated significant variability in model predictions and there remains a pressing need to validate models and to reduce uncertainties. Model validation is problematic as predictions are made for events that have not yet occurred. Resubstituition and data partitioning of present‐day data sets are, therefore, commonly used to test the predictive performance of models. However, these approaches suffer from the problems of spatial and temporal autocorrelation in the calibration and validation sets. Using observed distribution shifts among 116 British breeding‐bird species over the past ～20 years, we are able to provide a first independent validation of four envelope modelling techniques under climate change. Results showed good to fair predictive performance on independent validation, although rules used to assess model performance are difficult to interpret in a decision‐planning context. We also showed that measures of performance on nonindependent data provided optimistic estimates of models' predictive ability on independent data. Artificial neural networks and generalized additive models provided generally more accurate predictions of species range shifts than generalized linear models or classification tree analysis. Data for independent model validation and replication of this study are rare and we argue that perfect validation may not in fact be conceptually possible. We also note that usefulness of models is contingent on both the questions being asked and the techniques used. Implementations of species–climate envelope models for testing hypotheses and predicting future events may prove wrong, while being potentially useful if put into appropriate context.     

A new multivariate zero‐adjusted Poisson model with applications to biomedicine

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log‐normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero‐vectors; (ii) The multivariate zero‐inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero‐truncated/deflated count data and it is difficult to apply to high‐dimensional cases; (iii) The Type I multivariate zero‐adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative. In this paper, we first introduce a new multivariate ZAP distribution, based on a multivariate Poisson distribution, which allows the correlations between components with a more flexible dependency structure, that is some of the correlation coefficients could be positive while others could be negative. We then develop its important distributional properties, and provide efficient statistical inference methods for multivariate ZAP model with or without covariates. Two real data examples in biomedicine are used to illustrate the proposed methods.     

Does accounting for imperfect detection improve species distribution models?

Models of species distributions are increasingly being used to address a variety of problems in conservation biology. In many applications, perfect or constant detectability of species, given presence, is assumed. While this problem has been acknowledged and addressed through the development of occupancy models, we still know little regarding whether addressing the potential for imperfect detection improves the predictive performance of species distribution models in nature. Here, we contrast logistic regression models of species occurrence that do not correct for detectability to hierarchical occupancy models that explicitly estimate and adjust for detectability, and maximum entropy models that attempt to circumvent the detectability problem by using data from known presence locations only. We use a large‐scale, long‐term monitoring database across western Montana and northern Idaho to contrast these models for nine landbird species that cover a broad spectrum in detectability. Overall, occupancy models were similar to or better than other approaches in terms of predictive accuracy, as measured by the Area Under the ROC Curve (AUC) and Kappa, with maximum entropy tending to provide the lowest predictive accuracy. Models varied in the types of errors associated with predictions, such that some model approaches may be preferred over others in certain situations. As expected, predictive performance varied across a gradient in species detectability, with logistic regression providing lower relative performance for less detectable species and Maxent providing lower performance for highly detectable species. We conclude by discussing the advantages and limitations to each approach for developing large‐scale species distribution models.     

Improving predictive mapping in Swiss mire ecosystems through re‐calibration of indicator values

Question: How may Landolt indicator values be re‐calibrated to improve the performance of predictive models? Location: Mires Gross Moos Schwändital (1250 m a.s.l.) in the Prealps, Burgmoos (465 m. a.s.l.) on the Central Plateau and La Burtignière (1000 m a.s.l.) in the Jura, Switzerland. Methods: Habitat distribution models based on high resolution remotely sensed data and vegetation field data are applied to monitor 130 mires. Instead of plant species or communities we used mean indicator values of vegetation records as response variables. To improve the differential power of indicator values for wetland habitat conditions, we calibrated these values using field data. Different methods were tested with our predictive models in three mires to see which calibration method is best in enhancing model performance. To assess the effect of the uneven distribution of vegetation records along environmental gradients, calibrations based on random and evenly distributed samples were compared. As a test of the predictive power of the models we used r² between ground truth and model prediction. This approach is illustrated through an application with nutrient indicator values in the mire La Burtignière. Results: Model performances were not the same for the three mires. The predictive power was better for the nutrient values, soil reaction and humus values than for light and moisture values. 2000 records were sufficient as basis for re‐calibration. Models based on original Landolt indicator values were overall the weakest compared with re‐calibrated values. By comparing the predictive power of Models based on randomly or evenly selected records were about equally predictive. Conclusions: 1. Ahabitat‐specific re‐calibration of the Landolt indicator values enhances the predictive mapping of the Swiss mire ecosystems. 2. The re‐calibration based on weighted averaging gives a better performance than the one based on Gaussian logistic regression. 3. The uneven distribution of indicator values due to the over‐representation of mire habitats does not hamper model performance. 4. 2000 vegetation records are a sufficient basis for an optimal re‐calibration of the vegetation types. An illustration of the method is given by using the soil fertility pattern of the mire La Burtignière.     

Improved species‐occurrence predictions in data‐poor regions: using large‐scale data and bias correction with down‐weighted Poisson regression and Maxent

Species distribution modelling (SDM) has become an essential method in ecology and conservation. In the absence of survey data, the majority of SDMs are calibrated with opportunistic presence‐only data, incurring substantial sampling bias. We address the challenge of correcting for sampling bias in the data‐sparse situations. We modelled the relative intensity of bat records in their entire range using three modelling algorithms under the point‐process modelling framework (GLMs with subset selection, GLMs fitted with an elastic‐net penalty, and Maxent). To correct for sampling bias, we applied model‐based bias correction by incorporating spatial information on site accessibility or sampling efforts. We evaluated the effect of bias correction on the models’ predictive performance (AUC and TSS), calculated on spatial‐block cross‐validation and a holdout data set. When evaluated with independent, but also sampling‐biased test data, correction for sampling bias led to improved predictions. The predictive performance of the three modelling algorithms was very similar. Elastic‐net models have intermediate performance, with slight advantage for GLMs on cross‐validation and Maxent on hold‐out evaluation. Model‐based bias correction is very useful in data‐sparse situations, where detailed data are not available to apply other bias correction methods. However, bias correction success depends on how well the selected bias variables describe the sources of bias. In this study, accessibility covariates described bias in our data better than the effort covariate, and their use led to larger changes in predictive performance. Objectively evaluating bias correction requires bias‐free presence–absence test data, and without them the real improvement for describing a species’ environmental niche cannot be assessed.     

Complexity is costly: a meta‐analysis of parametric and non‐parametric methods for short‐term population forecasting

Short‐term forecasts based on time series of counts or survey data are widely used in population biology to provide advice concerning the management, harvest and conservation of natural populations. A common approach to produce these forecasts uses time‐series models, of different types, fit to time series of counts. Similar time‐series models are used in many other disciplines, however relative to the data available in these other disciplines, population data are often unusually short and noisy and models that perform well for data from other disciplines may not be appropriate for population data. In order to study the performance of time‐series forecasting models for natural animal population data, we assembled 2379 time series of vertebrate population indices from actual surveys. Our data were comprised of three vastly different types: highly variable (marine fish productivity), strongly cyclic (adult salmon counts), and small variance but long‐memory (bird and mammal counts). We tested the predictive performance of 49 different forecasting models grouped into three broad classes: autoregressive time‐series models, non‐linear regression‐type models and non‐parametric time‐series models. Low‐dimensional parametric autoregressive models gave the most accurate forecasts across a wide range of taxa; the most accurate model was one that simply treated the most recent observation as the forecast. More complex parametric and non‐parametric models performed worse, except when applied to highly cyclic species. Across taxa, certain life history characteristics were correlated with lower forecast error; specifically, we found that better forecasts were correlated with attributes of slow growing species: large maximum age and size for fishes and high trophic level for birds. Synthesis Evaluating the data support for multiple plausible models has been an integral focus of many ecological analyses. However, the most commonly used tools to quantify support have weighted models’ hindcasting and forecasting abilities. For many applications, predicting the past may be of little interest. Concentrating only on the future predictive performance of time series models, we performed a forecasting competition among many different kinds of statistical models, applying each to many different kinds of vertebrate time series of population abundance. Low‐dimensional (simple) models performed well overall, but more complex models did slightly better when applied to time series of cyclic species (e.g. salmon).     

Logistic regression models for predicting occurrence of terrestrial molluscs in southern Sweden – importance of environmental data quality and model complexity

We compared the performance of four logistic regression models of different complexity with different environmental data quality, in predicting the occurrence of 49 terrestrial mollusc species in southern Sweden. Performance of models derived from an explanatory data set was evaluated on a confirmatory data set. The overall predictive success of our models (>80% for the three best model approaches), is as good as in other studies, despite the fact that we had to transform a text database into quantitative habitat variables. Simple models (no variable interactions), with forward selection, and detailed habitat data (from field visits) showed the best overall predictive success (mean=84.8%). From comparisons of model approaches, we conclude that data quality (map‐derived data vs habitat mapping) had a stronger impact than model complexity on model performance. However, most of these models showed relatively low values (mean=0.29) for Kappa (statistic for model evaluation), suggesting that the models need to be improved before they would be applied. Predictive success was strongly associated with species incidence but also Kappa was positively correlated with species incidence in univariate tests. Predictive success for true absences was negatively correlated with predictive success for true presences (R²=0.69) and most models failed to give a good prediction of both categories. Models for species with a high incidence in “Open dry sites” or “Mesic interior forests” had a better performance than expected, suggesting that occurrences of species with preference for “narrow” habitats are most easy to predict. Tree layer variables (openness and species abundance) were included in 48 of the 49 final predictive models, suggesting that these variables were good “indicators” of habitat conditions for ground‐living molluscs. Twenty‐four species models included distance to coast and altitude, and we interpret these associations as partly being related to differences in climate. In the final models, true presences (36.9% correctly classified) were much more difficult to predict than true absences (89.7% correct). Possible explanations might be that important habitat variables (e.g. chemical variables and site history) were not included. On the other hand, all suitable sites would not be expected to be occupied due to dynamics in local extinctions (meta‐population theory).     

Effect of species rarity on the accuracy of species distribution models for reptiles and amphibians in southern California

Aim Several studies have found that more accurate predictive models of species’ occurrences can be developed for rarer species; however, one recent study found the relationship between range size and model performance to be an artefact of sample prevalence, that is, the proportion of presence versus absence observations in the data used to train the model. We examined the effect of model type, species rarity class, species’ survey frequency, detectability and manipulated sample prevalence on the accuracy of distribution models developed for 30 reptile and amphibian species. Location Coastal southern California, USA. Methods Classification trees, generalized additive models and generalized linear models were developed using species presence and absence data from 420 locations. Model performance was measured using sensitivity, specificity and the area under the curve (AUC) of the receiver‐operating characteristic (ROC) plot based on twofold cross‐validation, or on bootstrapping. Predictors included climate, terrain, soil and vegetation variables. Species were assigned to rarity classes by experts. The data were sampled to generate subsets with varying ratios of presences and absences to test for the effect of sample prevalence. Join count statistics were used to characterize spatial dependence in the prediction errors. Results Species in classes with higher rarity were more accurately predicted than common species, and this effect was independent of sample prevalence. Although positive spatial autocorrelation remained in the prediction errors, it was weaker than was observed in the species occurrence data. The differences in accuracy among model types were slight. Main conclusions Using a variety of modelling methods, more accurate species distribution models were developed for rarer than for more common species. This was presumably because it is difficult to discriminate suitable from unsuitable habitat for habitat generalists, and not as an artefact of the effect of sample prevalence on model estimation.     

Land-cover data improve bioclimatic models for anurans and turtles at a regional scale

Aim We investigated whether accounting for land cover could improve bioclimatic models for eight species of anurans and three species of turtles at a regional scale. We then tested whether accounting for spatial autocorrelation could significantly improve bioclimatic models after statistically controlling for the effects of land cover. Location Nova Scotia, eastern Canada. Methods Species distribution data were taken from a recent (1999–2003) herpetofaunal atlas. Generalized linear models were used to relate the presence or absence of each species to climate and land‐cover variables at a 10‐km resolution. We then accounted for spatial autocorrelation using an autocovariate or third‐order trend surface of the geographical coordinates of each grid square. Finally, variance partitioning was used to explore the independent and joint contributions of climate, land cover and spatial autocorrelation. Results The inclusion of land cover significantly increased the explanatory power of bioclimatic models for 10 of the 11 species. Furthermore, including land cover significantly increased predictive performance for eight of the 11 species. Accounting for spatial autocorrelation improved model fit for rare species but generally did not improve prediction success. Variance partitioning demonstrated that this lack of improvement was a result of the high correlation between climate and trend‐surface variables. Main conclusions The results of this study suggest that accounting for the effects of land cover can significantly improve the explanatory and predictive power of bioclimatic models for anurans and turtles at a regional scale. We argue that the integration of climate and land‐cover data is likely to produce more accurate spatial predictions of contemporary herpetofaunal diversity. However, the use of land‐cover simulations in climate‐induced range‐shift projections introduces additional uncertainty into the predictions of bioclimatic models. Further research is therefore needed to determine whether accounting for the effects of land cover in range‐shift projections is merited.     

Quantifying intraclass correlations for count and time‐to‐event data

The intraclass correlation is commonly used with clustered data. It is often estimated based on fitting a model to hierarchical data and it leads, in turn, to several concepts such as reliability, heritability, inter‐rater agreement, etc. For data where linear models can be used, such measures can be defined as ratios of variance components. Matters are more difficult for non‐Gaussian outcomes. The focus here is on count and time‐to‐event outcomes where so‐called combined models are used, extending generalized linear mixed models, to describe the data. These models combine normal and gamma random effects to allow for both correlation due to data hierarchies as well as for overdispersion. Furthermore, because the models admit closed‐form expressions for the means, variances, higher moments, and even the joint marginal distribution, it is demonstrated that closed forms of intraclass correlations exist. The proposed methodology is illustrated using data from agricultural and livestock studies.     

Comparison of regression methods for spatially‐autocorrelated count data on regularly‐ and irregularly‐spaced locations

It has long been known that insufficient consideration of spatial autocorrelation leads to unreliable hypothesis‐tests and inaccurate parameter estimates. Yet, ecologists are confronted with a confusing array of methods to account for spatial autocorrelation. Although Beale et al. (2010) provided guidance for continuous data on regular grids, researchers still need advice for other types of data in more flexible spatial contexts. In this paper, we extend Beale et al. (2010)‘s work to count data on both regularly‐ and irregularly‐spaced plots, the latter being commonly encountered in ecological studies. Through a simulation‐based approach, we assessed the accuracy and the type I errors of two frequentist and two Bayesian ready‐to‐use methods in the family of generalized mixed models, with distance‐based or neighbourhood‐based correlated random effects. In addition, we tested whether the methods are robust to spatial non‐stationarity, and over‐ and under‐dispersion – both typical features of species distribution count data which violate standard regression assumptions. In the simplest of our simulated datasets, the two frequentist methods gave inflated type I errors, while the two Bayesian methods provided satisfying results. When facing real‐world complexities, the distance‐based Bayesian method (MCMC with Langevin–Hastings updates) performed best of all. We hope that, in the light of our results, ecological researchers will feel more comfortable including spatial autocorrelation in their analyses of count data.     

Modeling spatiotemporal abundance of mobile wildlife in highly variable environments using boosted GAMLSS hurdle models

Modeling organism distributions from survey data involves numerous statistical challenges, including accounting for zero‐inflation, overdispersion, and selection and incorporation of environmental covariates. In environments with high spatial and temporal variability, addressing these challenges often requires numerous assumptions regarding organism distributions and their relationships to biophysical features. These assumptions may limit the resolution or accuracy of predictions resulting from survey‐based distribution models. We propose an iterative modeling approach that incorporates a negative binomial hurdle, followed by modeling of the relationship of organism distribution and abundance to environmental covariates using generalized additive models (GAM) and generalized additive models for location, scale, and shape (GAMLSS). Our approach accounts for key features of survey data by separating binary (presence‐absence) from count (abundance) data, separately modeling the mean and dispersion of count data, and incorporating selection of appropriate covariates and response functions from a suite of potential covariates while avoiding overfitting. We apply our modeling approach to surveys of sea duck abundance and distribution in Nantucket Sound (Massachusetts, USA), which has been proposed as a location for offshore wind energy development. Our model results highlight the importance of spatiotemporal variation in this system, as well as identifying key habitat features including distance to shore, sediment grain size, and seafloor topographic variation. Our work provides a powerful, flexible, and highly repeatable modeling framework with minimal assumptions that can be broadly applied to the modeling of survey data with high spatiotemporal variability. Applying GAMLSS models to the count portion of survey data allows us to incorporate potential overdispersion, which can dramatically affect model results in highly dynamic systems. Our approach is particularly relevant to systems in which little a priori knowledge is available regarding relationships between organism distributions and biophysical features, since it incorporates simultaneous selection of covariates and their functional relationships with organism responses.     

Community‐level vs species‐specific approaches to model selection

A topic of particular current interest is community‐level approaches to species distribution modelling (SDM), i.e. approaches that simultaneously analyse distributional data for multiple species. Previous studies have looked at the advantages of community‐level approaches for parameter estimation, but not for model selection – the process of choosing which model (and in particular, which subset of environmental variables) to fit to data. We compared the predictive performance of models using the same modelling method (generalised linear models) but choosing the subset of variables to include in the model either simultaneously across all species (community‐level model selection) or separately for each species (species‐specific model selection). Our results across two large presence/absence tree community datasets were inconclusive as to whether there was an overall difference in predictive performance between models fitted via species‐specific vs community‐level model selection. However, we found some evidence that a community approach was best suited to modelling rare species, and its performance decayed with increasing prevalence. That is, when data were sparse there was more opportunity for gains from “borrowing strength” across species via a community‐level approach. Interestingly, we also found that the community‐level approach tended to work better when the model selection problem was more difficult, and more reliably detected “noise” variables that should be excluded from the model.     

Evaluating model transferability for a threatened species to adjacent areas: Implications for rock‐wallaby conservation

When modelling the distribution of a species, it is often not possible to comprehensively sample the whole distribution of the species and managers may have habitat models based on data from one area that they want to apply in other areas. Hence, an important question is: how accurate are models of the distributions of species when applied beyond the areas where they were developed? A first step in measuring model transferability could be testing models in adjacent areas. We predicted the habitat associations of the brush‐tailed rock‐wallaby (Petrogale penicillata) across two spatial scales in two neighbouring study areas in eastern Australia, south‐east Queensland and north‐east New South Wales. We used classification trees for exploratory data analysis of habitat relationships and then applied logistic regression models to predict species occurrence. We assessed the within‐area discriminative ability of the habitat models using cross‐validation and threshold plots, and tested the predictive ability of the models for adjacent areas using the receiver operating characteristic statistic to determine the area under the curve. We found that models performed well within an area and extrapolating them to adjacent areas resulted in good predictive performance at the site scale but substantially poorer predictive performance at the landscape scale. We conclude that distribution models for wildlife species should only be extrapolated to neighbouring areas with caution when using landscape‐scale environmental variables. Alternatively, only key habitat associations predicted by the models at this scale should be transferred across adjacent areas once verified against local knowledge of the ecology of the study species.