Pseudoabsence generation strategies for species distribution models

Background

Species distribution models require selection of species, study extent and spatial unit, statistical methods, variables, and assessment metrics. If absence data are not available, another important consideration is pseudoabsence generation. Different strategies for pseudoabsence generation can produce varying spatial representation of species.

Methodology

We considered model outcomes from four different strategies for generating pseudoabsences. We generating pseudoabsences randomly by 1) selection from the entire study extent, 2) a two-step process of selection first from the entire study extent, followed by selection for pseudoabsences from areas with predicted probability <25%, 3) selection from plots surveyed without detection of species presence, 4) a two-step process of selection first for pseudoabsences from plots surveyed without detection of species presence, followed by selection for pseudoabsences from the areas with predicted probability <25%. We used Random Forests as our statistical method and sixteen predictor variables to model tree species with at least 150 records from Forest Inventory and Analysis surveys in the Laurentian Mixed Forest province of Minnesota.

Conclusions

Pseudoabsence generation strategy completely affected the area predicted as present for species distribution models and may be one of the most influential determinants of models. All the pseudoabsence strategies produced mean AUC values of at least 0.87. More importantly than accuracy metrics, the two-step strategies over-predicted species presence, due to too much environmental distance between the pseudoabsences and recorded presences, whereas models based on random pseudoabsences under-predicted species presence, due to too little environmental distance between the pseudoabsences and recorded presences. Models using pseudoabsences from surveyed plots produced a balance between areas with high and low predicted probabilities and the strongest relationship between density and area with predicted probabilities ≥75%. Because of imperfect accuracy assessment, the best assessment currently may be evaluation of whether the species has been sufficiently but not excessively predicted to occur.     

Bayesian meta-analysis models for microarray data: a comparative study

Background

With the growing abundance of microarray data, statistical methods are increasingly needed to integrate results across studies. Two common approaches for meta-analysis of microarrays include either combining gene expression measures across studies or combining summaries such as p-values, probabilities or ranks. Here, we compare two Bayesian meta-analysis models that are analogous to these methods.

Results

Two Bayesian meta-analysis models for microarray data have recently been introduced. The first model combines standardized gene expression measures across studies into an overall mean, accounting for inter-study variability, while the second combines probabilities of differential expression without combining expression values. Both models produce the gene-specific posterior probability of differential expression, which is the basis for inference. Since the standardized expression integration model includes inter-study variability, it may improve accuracy of results versus the probability integration model. However, due to the small number of studies typical in microarray meta-analyses, the variability between studies is challenging to estimate. The probability integration model eliminates the need to model variability between studies, and thus its implementation is more straightforward. We found in simulations of two and five studies that combining probabilities outperformed combining standardized gene expression measures for three comparison values: the percent of true discovered genes in meta-analysis versus individual studies; the percent of true genes omitted in meta-analysis versus separate studies, and the number of true discovered genes for fixed levels of Bayesian false discovery. We identified similar results when pooling two independent studies of Bacillus subtilis. We assumed that each study was produced from the same microarray platform with only two conditions: a treatment and control, and that the data sets were pre-scaled.

Conclusion

The Bayesian meta-analysis model that combines probabilities across studies does not aggregate gene expression measures, thus an inter-study variability parameter is not included in the model. This results in a simpler modeling approach than aggregating expression measures, which accounts for variability across studies. The probability integration model identified more true discovered genes and fewer true omitted genes than combining expression measures, for our data sets.     

Relative frequency function models for species distribution modeling

A new approach to habitat distribution modeling is presented and tested with data on North American plants. The relative frequency function (RFF) algorithm compares the relative frequencies of a species’ sample points to that of random points or absence points on the landscape to compute a frequency ratio. The relative frequency ratio r is smoothed across the range of values using moving, overlapping windows. The ratio of frequencies at a sample point for each variable is used to compute the geometric mean score for all data with non‐missing values. Variables are added using a forward stepwise method. Confidence intervals are computed with bootstrap resampling. The method was tested with artificial and species habitat and geographic range data. The RFF method in all cases gave results comparable to other methods tested. For the species with good geographic range maps, the results were consistent with known biogeography. The RFF method is particularly well‐suited to irregularly shaped distributions and can classify sample points even when the data contain missing values. The method is extremely simple to use and comes with a free software tool, does not require a large sample size, does not require absence data, and is more interpretable and portable than certain other methods.     

Using species distribution models for IUCN Red Lists of threatened species

Red Lists have been used for years globally and regionally in many countries to highlight species that need special attention because of the rarity or rapid decline of their populations. To ensure homogenized classification at the global and regional level, the International Union for Conservation of Nature (IUCN) defined categories of threat, and criteria to attribute the taxa to these categories. Nevertheless, the strict application of the criteria is not always straightforward, especially for invertebrates, because of the difficulties associated with precise estimates of the size and viability of their populations. This paper presents a method for the estimation of extent of occurrence (EOO) and area of occupancy (AOO) based on species distribution models using multivariate adaptive regression splines. To achieve this, presence data have been modeled against topographical and climatic explanatory variables. Predictions from the statistical distribution models have then been cut using the minimal convex hull around (EOO) or the watersheds in which (AOO) the species have really been observed in recent years. This allows us to delimit the EOO and AOO according to the IUCN criteria, and better take into account the ecological requirements of the species. Furthermore, the method allows for the use of historical data (e.g. from museum’s collections) and the direct comparison of historical and recent distributions of species. The method has been tested on six species of butterflies. The results show the possibility of using species distribution models to define the Red Lists status according to the IUCN guidelines, and shows that the results are consistent with previous Red Lists assessments.     

Using unclassified continuous remote sensing data to improve distribution models of red-listed plant species

Remote sensing (RS) data may play an important role in the development of cost-effective means for modelling, mapping, planning and conserving biodiversity. Specifically, at the landscape scale, spatial models for the occurrences of species of conservation concern may be improved by the inclusion of RS-based predictors, to help managers to better meet different conservation challenges. In this study, we examine whether predicted distributions of 28 red-listed plant species in north-eastern Finland at the resolution of 25 ha are improved when advanced RS-variables are included as unclassified continuous predictor variables, in addition to more commonly used climate and topography variables. Using generalized additive models (GAMs), we studied whether the spatial predictions of the distribution of red-listed plant species in boreal landscapes are improved by incorporating advanced RS (normalized difference vegetation index, normalized difference soil index and Tasseled Cap transformations) information into species-environment models. Models were fitted using three different sets of explanatory variables: (1) climate-topography only; (2) remote sensing only; and (3) combined climate-topography and remote sensing variables, and evaluated by four-fold cross-validation with the area under the curve (AUC) statistics. The inclusion of RS variables improved both the explanatory power (on average 8.1 % improvement) and cross-validation performance (2.5 %) of the models. Hybrid models produced ecologically more reliable distribution maps than models using only climate-topography variables, especially for mire and shore species. In conclusion, Landsat ETM+ data integrated with climate and topographical information has the potential to improve biodiversity and rarity assessments in northern landscapes, especially in predictive studies covering extensive and remote areas.     

Intra-specific niche partitioning obscures the importance of fine-scale habitat data in species distribution models

Geographic information systems (GIS) allow researchers to make cost-effective, spatially explicit predictions of species’ distributions across broad geographic areas. However, there has been little research on whether using fine-scale habitat data collected in the field could produce more robust models of species’ distributions. Here we used radio-telemetry data collected on a declining species, the North American wood turtle (Glyptemys insculpta), to test whether fine-scale habitat variables were better predictors of occurrence than land-cover and topography variables measured in a GIS. Patterns of male and female occurrence were similar in the spring; however, females used a much wider array of land-cover types and topographic positions in the summer and early fall, making it difficult for GIS-based models to accurately predict female occurrence at this time of year. Males on the other hand consistently selected flat, low-elevation, riparian areas throughout the year, and this consistency in turn led to the development of a strong GIS-based model. These results demonstrate the importance of taking a more sex-specific and temporally dynamic view of the environmental niche.     

Disentangling the formation of contrasting tree-line physiognomies combining model selection and Bayesian parameterization for simulation models

Alpine tree-line ecotones are characterized by marked changes at small spatial scales that may result in a variety of physiognomies. A set of alternative individual-based models was tested with data from four contrasting Pinus uncinata ecotones in the central Spanish Pyrenees to reveal the minimal subset of processes required for tree-line formation. A Bayesian approach combined with Markov chain Monte Carlo methods was employed to obtain the posterior distribution of model parameters, allowing the use of model selection procedures. The main features of real tree lines emerged only in models considering nonlinear responses in individual rates of growth or mortality with respect to the altitudinal gradient. Variation in tree-line physiognomy reflected mainly changes in the relative importance of these nonlinear responses, while other processes, such as dispersal limitation and facilitation, played a secondary role. Different nonlinear responses also determined the presence or absence of krummholz, in agreement with recent findings highlighting a different response of diffuse and abrupt or krummholz tree lines to climate change. The method presented here can be widely applied in individual-based simulation models and will turn model selection and evaluation in this type of models into a more transparent, effective, and efficient exercise.     

A new method for dealing with residual spatial autocorrelation in species distribution models

Species distribution modelling (SDM) is a widely used tool and has many applications in ecology and conservation biology. Spatial autocorrelation (SAC), a pattern in which observations are related to one another by their geographic distance, is common in georeferenced ecological data. SAC in the residuals of SDMs violates the ‘independent errors’ assumption required to justify the use of statistical models in modelling species’ distributions. The autologistic modelling approach accounts for SAC by including an additional term (the autocovariate) representing the similarity between the value of the response variable at a location and neighbouring locations. However, autologistic models have been found to introduce bias in the estimation of parameters describing the influence of explanatory variables on habitat occupancy. To address this problem we developed an extension to the autologistic approach by calculating the autocovariate on SAC in residuals (the RAC approach). Performance of the new approach was tested on simulated data with a known spatial structure and on strongly autocorrelated mangrove species’ distribution data collected in northern Australia. The RAC approach was implemented as generalized linear models (GLMs) and boosted regression tree (BRT) models. We found that the BRT models with only environmental explanatory variables can account for some SAC, but applying the standard autologistic or RAC approaches further reduced SAC in model residuals and substantially improved model predictive performance. The RAC approach showed stronger inferential performance than the standard autologistic approach, as parameter estimates were more accurate and statistically significant variables were accurately identified. The new RAC approach presented here has the potential to account for spatial autocorrelation while maintaining strong predictive and inferential performance, and can be implemented across a range of modelling approaches.     

A class of Bayesian shared gamma frailty models with multivariate failure time data

For multivariate failure time data, we propose a new class of shared gamma frailty models by imposing the Box-Cox transformation on the hazard function, and the product of the baseline hazard and the frailty. This novel class of models allows for a very broad range of shapes and relationships between the hazard and baseline hazard functions. It includes the well-known Cox gamma frailty model and a new additive gamma frailty model as two special cases. Due to the nonnegative hazard constraint, this shared gamma frailty model is computationally challenging in the Bayesian paradigm. The joint priors are constructed through a conditional-marginal specification, in which the conditional distribution is univariate, and it absorbs the nonlinear parameter constraints. The marginal part of the prior specification is free of constraints. The prior distributions allow us to easily compute the full conditionals needed for Gibbs sampling, while incorporating the constraints. This class of shared gamma frailty models is illustrated with a real dataset.     

Using species abundance distribution models and diversity indices for biogeographical analyses

We examine whether Species Abundance Distribution models (SADs) and diversity indices can describe how species colonization status influences species community assembly on oceanic islands. Our hypothesis is that, because of the lack of source-sink dynamics at the archipelago scale, Single Island Endemics (SIEs), i.e. endemic species restricted to only one island, should be represented by few rare species and consequently have abundance patterns that differ from those of more widespread species. To test our hypothesis, we used arthropod data from the Azorean archipelago (North Atlantic). We divided the species into three colonization categories: SIEs, archipelagic endemics (AZEs, present in at least two islands) and native non-endemics (NATs). For each category, we modelled rank-abundance plots using both the geometric series and the Gambin model, a measure of distributional amplitude. We also calculated Shannon entropy and Buzas and Gibson's evenness. We show that the slopes of the regression lines modelling SADs were significantly higher for SIEs, which indicates a relative predominance of a few highly abundant species and a lack of rare species, which also depresses diversity indices. This may be a consequence of two factors: (i) some forest specialist SIEs may be at advantage over other, less adapted species; (ii) the entire populations of SIEs are by definition concentrated on a single island, without possibility for inter-island source-sink dynamics; hence all populations must have a minimum number of individuals to survive natural, often unpredictable, fluctuations. These findings are supported by higher values of the α parameter of the Gambin mode for SIEs. In contrast, AZEs and NATs had lower regression slopes, lower α but higher diversity indices, resulting from their widespread distribution over several islands. We conclude that these differences in the SAD models and diversity indices demonstrate that the study of these metrics is useful for biogeographical purposes.     

Assessing historical fish community composition using surveys, historical collection data, and species distribution models

Accurate establishment of baseline conditions is critical to successful management and habitat restoration. We demonstrate the ability to robustly estimate historical fish community composition and assess the current status of the urbanized Barton Creek watershed in central Texas, U.S.A. Fish species were surveyed in 2008 and the resulting data compared to three sources of fish occurrence information: (i) historical records from a museum specimen database and literature searches; (ii) a nearly identical survey conducted 15 years earlier; and (iii) a modeled historical community constructed with species distribution models (SDMs). This holistic approach, and especially the application of SDMs, allowed us to discover that the fish community in Barton Creek was more diverse than the historical data and survey methods alone indicated. Sixteen native species with high modeled probability of occurrence within the watershed were not found in the 2008 survey, seven of these were not found in either survey or in any of the historical collection records. Our approach allowed us to more rigorously establish the true baseline for the pre-development fish fauna and then to more accurately assess trends and develop hypotheses regarding factors driving current fish community composition to better inform management decisions and future restoration efforts. Smaller, urbanized freshwater systems, like Barton Creek, typically have a relatively poor historical biodiversity inventory coupled with long histories of alteration, and thus there is a propensity for land managers and researchers to apply inaccurate baseline standards. Our methods provide a way around that limitation by using SDMs derived from larger and richer biodiversity databases of a broader geographic scope. Broadly applied, we propose that this technique has potential to overcome limitations of popular bioassessment metrics (e.g., IBI) to become a versatile and robust management tool for determining status of freshwater biotic communities.     

A habitat quality indicator for common birds in Europe based on species distribution models

The EU 2020 Biodiversity Strategy requires the gathering of information on biodiversity to aid in monitoring progress towards its main targets. Common species are good proxies for the diversity and integrity of ecosystems, since they are key elements of the biomass, structure, functioning of ecosystems, and therefore of the supply of ecosystem services. In this sense, we aimed to develop a spatially-explicit indicator of habitat quality (HQI) at European level based on the species included in the European Common Bird Index, also grouped into their major habitat types (farmland and forest). Using species occurrences from the European Breeding Birds Atlas (at 50 km × 50 km) and the maximum entropy algorithm, we derived species distribution maps using refined occurrence data based on species ecology. This allowed us to cope with the limitations arising from modelling common and widespread species, obtaining habitat suitability maps for each species at finer spatial resolution (10 km × 10 km grid), which provided higher model accuracy. Analysis of the spatial patterns of local and relative species richness (defined as the ratio between species richness in a given location and the average richness in the regional context) for the common birds analysed demonstrated that the development of a HQI based on species richness needs to account for the regional species pool in order to make objective comparisons between regions. In this way, we proved that relative species richness compensated for the bias caused by the inherent heterogeneous patterns of the species distributions that was yielding larger local species richness in areas where most of the target species have the core of their distribution range. The method presented in this study provides a robust and innovative indicator of habitat quality which can be used to make comparisons between regions at the European scale, and therefore potentially applied to measure progress towards the EU Biodiversity Strategy targets. Finally, since species distribution models are based on breeding birds, the HQI can be also interpreted as a measure of the capacity of ecosystems to provide and maintain nursery/reproductive habitats for terrestrial species, a key maintenance and regulation ecosystem service.     

A Bayesian model for time-to-event data with informative censoring

Randomized trials with dropouts or censored data and discrete time-to-event type outcomes are frequently analyzed using the Kaplan-Meier or product limit (PL) estimation method. However, the PL method assumes that the censoring mechanism is noninformative and when this assumption is violated, the inferences may not be valid. We propose an expanded PL method using a Bayesian framework to incorporate informative censoring mechanism and perform sensitivity analysis on estimates of the cumulative incidence curves. The expanded method uses a model, which can be viewed as a pattern mixture model, where odds for having an event during the follow-up interval $$({t}_{k-1},{t}_{k}]$$, conditional on being at risk at $${t}_{k-1}$$, differ across the patterns of missing data. The sensitivity parameters relate the odds of an event, between subjects from a missing-data pattern with the observed subjects for each interval. The large number of the sensitivity parameters is reduced by considering them as random and assumed to follow a log-normal distribution with prespecified mean and variance. Then we vary the mean and variance to explore sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the expanded model, thus allowing exploration of the sensitivity to inferences as departures from the inferences under the MAR assumption. The proposed approach is applied to data from the TRial Of Preventing HYpertension.