Modeling species-habitat relationships with spatially autocorrelated observation data.

Spatial autocorrelation in wildlife observation data arises when extrinsic environmental processes and patterns that influence the spatial distribution of wildlife are themselves spatially structured, or when species are subject to intrinsic population processes, causing contagion or dispersion effects. Territoriality, Allee effects, dispersal limitations, and social clustering are examples of intrinsic processes. Both forms of autocorrelation can violate the assumptions of generalized linear regression models, resulting in biased estimation of model coefficients and diminished predictive performance. Such consequences may be avoided for extrinsic autocorrelation when autocorrelated environmental variables are available for use as model covariates, whereas intrinsic spatial autocorrelation requires an alternative modeling approach. The autologistic model provides an approach suited to the binary observations often obtained in wildlife surveys, but its performance has not been tested across widely varying sampling intensities or strengths of intrinsic spatial structure. Here we use simulated data to test the autologistic model under a range of sampling conditions. The autologistic model obtains better fits and substantially better predictive performance than the standard logistic regression model over the full range of sampling designs and intensities tested. We provide a simple Bayesian implementation of the autologistic model, which until now has not been achieved with standard statistical software alone. A step-by-step procedure is given for characterizing and modeling spatial autocorrelation in binary observation data, along with computer code for fitting autologistic models in WinBUGS, a freeware Bayesian analysis package. This approach avoids normal approximations to the pseudo-likelihood, in contrast to previous Bayesian applications of the autologistic model. We provide a sample application of the autologistic model, fitted to survey data for a gliding marsupial in southeastern Australia.     

Incorporating spatial autocorrelation into cellular automata model: An application to the dynamics of Chinese tamarisk (Tamarix chinensis Lour.)

Spatial autocorrelation (SAC) is frequently encountered in most spatial data in ecology. Cellular automata (CA) models have been widely used to simulate complex spatial phenomena. However, little has been done to examine the impact of incorporating SAC into CA models. Using image-derived maps of Chinese tamarisk (Tamarix chinensis Lour.), CA models based on ordinary logistic regression (OLCA model) and autologistic regression (ALCA model) were developed to simulate landscape dynamics of T. chinensis. In this study, significant positive SAC was detected in residuals of ordinary logistic models, whereas non-significant SAC was found in autologistic models. All autologistic models obtained lower Akaike's information criterion corrected for small sample size (AICc) values than the best ordinary logistic models. Although the performance of ALCA models only satisfied the minimum requirement, ALCA models showed considerable improvement upon OLCA models. Our results suggested that the incorporation of the autocovariate term not only accounted for SAC in model residuals but also provided more accurate estimates of regression coefficients. The study also found that the neglect of SAC might affect the statistical inference on underlying mechanisms driving landscape changes and obtain false ecological conclusions and management recommendations. The ALCA model is statistically sound when coping with spatially structured data, and the adoption of the ALCA model in future landscape transition simulations may provide more precise probability maps on landscape transition, better model performance and more reasonable mechanisms that are responsible for landscape changes.     

The importance of spatial autocorrelation,extent and resolution in predicting forest bird occurrence

Concerns about declines in forest biodiversity underscore the need for accurate estimates of the distribution and abundance of organisms at large scales and at resolutions that are fine enough to be appropriate for management. This paper addresses three major objectives: (i) to determine whether the resolution of typical air photo-derived forest inventory is sufficient for the accurate prediction of site occupancy by forest birds. We compared prediction success of habitat models using air photo variables to models with variables derived from finer resolution, ground-sampled vegetation plots. (ii) To test whether incorporating spatial autocorrelation into habitat models via autologistic regression increases prediction success. (iii) To determine whether landscape structure is an important factor in predicting bird distribution in forest-dominated landscapes. Models were tested locally (Greater Fundy Ecosystem [GFE]) using cross-validation, and regionally using an independent data set from an area located ca. 250 km to the northwest (Riley Brook [RB]). We found significant positive spatial autocorrelation in the residuals of at least one habitat model for 76% (16/21) of species examined. In these cases, the logistic regression assumption of spatially independent errors was violated. Logistic models that ignored spatial autocorrelation tended to overestimate habitat effects. Though overall prediction success was higher for autologistic models than logistic models in the GFE, the difference was only significantly improved for one species. Further, the inclusion of spatial covariates did little to improve model performance in the geographically discrete study area. For 62% (13/21) of species examined, landscape variables were significant predictors of forest bird occurrence even after statistically controlling for stand-level variability. However, broad spatial extents explained less variation than local factors. In the GFE, 76% (16/21) of air photo and 81% (17/21) of ground plot models were accurate enough to be of practical utility (AUC > 0.7). When applied to RB, both model types performed effectively for 55% (11/20) of the species examined. We did not detect an overall difference in prediction success between air photo and ground plot models in either study area. We conclude that air photo data are as effective as fine resolution vegetation data for predicting site occupancy for the majority of species in this study. These models will be of use to forest managers who are interested in mapping species distributions under various timber harvest scenarios, and to protected areas planners attempting to optimize reserve function.     

Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions

Two statistical modelling techniques, generalized additive models (GAM) and multivariate adaptive regression splines (MARS), were used to analyse relationships between the distributions of 15 freshwater fish species and their environment. GAM and MARS models were fitted individually for each species, and a MARS multiresponse model was fitted in which the distributions of all species were analysed simultaneously. Model performance was evaluated using changes in deviance in the fitted models and the area under the receiver operating characteristic curve (ROC), calculated using a bootstrap assessment procedure that simulates predictive performance for independent data. Results indicate little difference between the performance of GAM and MARS models, even when MARS models included interaction terms between predictor variables. Results from MARS models are much more easily incorporated into other analyses than those from GAM models. The strong performance of a MARS multiresponse model, particularly for species of low prevalence, suggests that it may have distinct advantages for the analysis of large datasets. Its identification of a parsimonious set of environmental correlates of community composition, coupled with its ability to robustly model species distributions in relation to those variables, can be seen as converging strongly with the purposes of traditional ordination techniques.     

Predictability of marine nematode biodiversity

In this paper, we investigated: (1) the predictability of different aspects of biodiversity, (2) the effect of spatial autocorrelation on the predictability and (3) the environmental variables affecting the biodiversity of free-living marine nematodes on the Belgian Continental Shelf. An extensive historical database of free-living marine nematodes was employed to model different aspects of biodiversity: species richness, evenness, and taxonomic diversity. Artificial neural networks (ANNs), often considered as “black boxes”, were applied as a modeling tool. Three methods were used to reveal these “black boxes” and to identify the contributions of each environmental variable to the diversity indices. Since spatial autocorrelation is known to introduce bias in spatial analyses, Moran's I was used to test the spatial dependency of the diversity indices and the residuals of the model. The best predictions were made for evenness. Although species richness was quite accurately predicted as well, the residuals indicated a lack of performance of the model. Pure taxonomic diversity shows high spatial variability and is difficult to model. The biodiversity indices show a strong spatial dependency, opposed to the residuals of the models, indicating that the environmental variables explain the spatial variability of the diversity indices adequately. The most important environmental variables structuring evenness are clay and sand fraction, and the minimum annual total suspended matter. Species richness is also affected by the intensity of sand extraction and the amount of gravel of the sea bed.     

Spatial residual analysis of six modeling techniques

In recent years alternative modeling techniques have been used to account for spatial autocorrelations among data observations. They include linear mixed model (LMM), generalized additive model (GAM), multi-layer perceptron (MLP) neural network, radial basis function (RBF) neural network, and geographically weighted regression (GWR). Previous studies show these models are robust to the violation of model assumptions and flexible to nonlinear relationships among variables. However, many of them are non-spatial in nature. In this study, we utilize a local spatial analysis method (i.e., local Moran coefficient) to investigate spatial distribution and heterogeneity in model residuals from those modeling techniques with ordinary least-squares (OLS) as the benchmark. The regression model used in this study has tree crown area as the response variable, and tree diameter and the coordinates of tree locations as the predictor variables. The results indicate that LMM, GAM, MLP and RBF may improve model fitting to the data and provide better predictions for the response variable, but they generate spatial patterns for model residuals similar to OLS. The OLS, LMM, GAM, MLP and RBF models yield more residual clusters of similar values, indicating that trees in some sub-areas are either all underestimated or all overestimated for the response variable. In contrast, GWR estimates model coefficients at each location in the study area, and produces more accurate predictions for the response variable. Furthermore, the residuals of the GWR model have more desirable spatial distributions than the ones derived from the OLS, LMM, GAM, MLP and RBF models.     

Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests

Forestry science has a long tradition of studying the relationship between stand productivity and abiotic and biotic site characteristics, such as climate, topography, soil and vegetation. Many of the early site quality modelling studies related site index to environmental variables using basic statistical methods such as linear regression. Because most ecological variables show a typical non-linear course and a non-constant variance distribution, a large fraction of the variation remained unexplained by these linear models. More recently, the development of more advanced non-parametric and machine learning methods provided opportunities to overcome these limitations. Nevertheless, these methods also have drawbacks. Due to their increasing complexity they are not only more difficult to implement and interpret, but also more vulnerable to overfitting. Especially in a context of regionalisation, this may prove to be problematic. Although many non-parametric and machine learning methods are increasingly used in applications related to forest site quality assessment, their predictive performance has only been assessed for a limited number of methods and ecosystems.In this study, five different modelling techniques are compared and evaluated, i.e. multiple linear regression (MLR), classification and regression trees (CART), boosted regression trees (BRT), generalized additive models (GAM), and artificial neural networks (ANN). Each method is used to model site index of homogeneous stands of three important tree species of the Taurus Mountains (Turkey): Pinus brutia, Pinus nigra and Cedrus libani. Site index is related to soil, vegetation and topographical variables, which are available for 167 sample plots covering all important environmental gradients in the research area. The five techniques are compared in a multi-criteria decision analysis in which different model performance measures, ecological interpretability and user-friendliness are considered as criteria.When combining these criteria, in most cases GAM is found to outperform all other techniques for modelling site index for the three species. BRT is a good alternative in case the ecological interpretability of the technique is of higher importance. When user-friendliness is more important MLR and CART are the preferred alternatives. Despite its good predictive performance, ANN is penalized for its complex, non-transparent models and big training effort.     

The performance of state-of-the-art modelling techniques depends on geographical distribution of species

We explored the effects of prevalence, latitudinal range and clumping (spatial autocorrelation) of species distribution patterns on the predictive accuracy of eight state-of-the-art modelling techniques: Generalized Linear Models (GLMs), Generalized Boosting Method (GBM), Generalized Additive Models (GAMs), Classification Tree Analysis (CTA), Artificial Neural Network (ANN), Multivariate Adaptive Regression Splines (MARS), Mixture Discriminant Analysis (MDA) and Random Forest (RF). One hundred species of Lepidoptera, selected from the Distribution Atlas of European Butterflies, and three climate variables were used to determine the bioclimatic envelope for each butterfly species. The data set consisting of 2620 grid squares 30′ × 60′ in size all over Europe was randomly split into the calibration and the evaluation data sets. The performance of different models was assessed using the area under the curve (AUC) of a receiver operating characteristic (ROC) plot. Observed differences in modelling accuracy among species were then related to the geographical attributes of the species using GAM. The modelling performance was negatively related to the latitudinal range and prevalence, whereas the effect of spatial autocorrelation on prediction accuracy depended on the modelling technique. These three geographical attributes accounted for 19–61% of the variation in the modelling accuracy. Predictive accuracy of GAM, GLM and MDA was highly influenced by the three geographical attributes, whereas RF, ANN and GBM were moderately, and MARS and CTA only slightly affected. The contrasting effects of geographical distribution of species on predictive performance of different modelling techniques represent one source of uncertainty in species spatial distribution models. This should be taken into account in biogeographical modelling studies and assessments of climate change impacts.     

Analyzing and modelling spatial distribution of summering lesser kestrel: The role of spatial autocorrelation

In modelling spatial distribution of species, ignoring spatial autocorrelation (SA) and multicollinearity may lead to false ecological conclusions. Here we take into account both issues for examining and modelling the spatial pattern of abundance of the globally threatened lesser kestrel (Falco naumanni) during summer in a 38,400 ha area of northwestern Spain where large premigratory aggregations of the species occur. Spatial pattern was examined using Moran's correlogram, and models were built including geographical coordinates and autocovariate terms (which account for SA) in generalized linear models (GLM) and hierarchical partitioning (HP) models. HP models allow to alleviate multicollinearity. A grid-based approach was used by dividing the study area in 24 contiguous 4 km × 4 km squares where birds were counted in 2–3 visits per square (response variable). Environmental coarse-grained variables were extracted from a geographic information system (GIS) at three spatial extents. Moran's correlogram showed that lesser kestrel mean abundance per square was spatially autocorrelated up to 4–8 km. The results from both GLM and HP analyses were roughly compatible. The GLM models explained 80.0% of the variation in kestrel abundance and were the same at the three spatial extents. Lesser Kestrel abundance was not significantly explained by landscape variables, but was negatively related to both the distance to the nearest communal roost and distance to the nearest breeding colony with more of 10 breeding pairs of lesser kestrel. An autocovariate term added later in the GLM models improved both their explanatory power (from 74.5 to 80.0%) and model residuals, which were not longer spatially autocorrelated, fulfilling thus the statistical assumption of independent errors. Findings suggest that the spatial distribution of abundance of summering lesser kestrel is, at least, partially driven by endogenous causes, such as conspecific attraction. Exogenous causes such as finer-scale variables (e.g. type of crops and food available) are yet likely needed for lesser kestrel-environment relationships.     

Analysis of environmental correlates of sexual segregation in northern elephant seals using species distribution models

Elephant seals are among the most sexually dimorphic and polygynous species of all mammals. Their foraging grounds occupy a wide area of the world oceans, where they show spatial segregation between males and females. The objective of this paper was to correlate female and male foraging distributions of Mirounga angustirostris with main climatic variables at a biogeographical scale. We used website and bibliographical sources to obtain information on adult elephant seal distribution and environmental predictors (surface and bottom sea temperatures, productivity and bathymetry) and three species distribution models [maximum entropy model, environmental niche factor analysis and based on climatic envelopes (BIOCLIM)] to predict the habitat suitability of ocean regions. BIOCLIM provided the best fit. Sea surface and bottom temperatures were the variables with the highest explanatory power for females, while bathymetry was for males. Predictive maps suggest that low temperatures constrain female, but not male, distribution at high latitudes. We suggest that large size increases foraging efficiency of males because, among other benefits, it augments thermal insulation, improving the use of cold, rich sectors of the ocean. Different thermoregulatory abilities between sexes due to size dimorphism should be a complementary explanation of sexual segregation in elephant seals.     

A heuristic approach to predicting water beetle diversity in temporary and fluctuating waters

An understanding of the causal mechanisms and processes that shape macroinvertebrate communities at a local scale has important implications for the management and conservation of freshwater biodiversity. Here we compare the performance of linear and non-linear statistics to explore diversity-environment relationships using data from 76 temporary and fluctuating ponds in two regions of southern England. We focus on aquatic beetle assemblages, which have been shown to be excellent surrogates of wider freshwater macroinvertebrate diversity. Ponds in the region contained a rich coleopteran fauna, totaling 68 species, which provided an excellent model system with which to compare the performance of two non-linear procedures (artificial neural networks—ANNs and generalised additive models—GAMs) and one more traditional linear approach (Multiple linear regression—MLR) to modelling diversity-environment relationships. Of all approaches employed, the best fit was obtained using an ANN model with only four input variables (conductivity, turbidity, magnesium concentration and depth). This model accounted for 82% of the observed variability in Shannon diversity index across ponds. In contrast, the best GAM and MLR models only explained 50% and 14% of this variation, respectively. Contribution profile analysis of conductivity, turbidity, magnesium concentration and depth, obtained from the best fit ANN through a hierarchical cluster analysis, allowed the identification of direct and proxy effects in relation to the environmental variables measured in this study. In each case, distinct clusters of ponds were identified in contribution profile analysis, suggesting that ponds across the two regions fall into a number of discrete groups, whose beetle faunas respond in subtly yet significantly different ways to key environmental variables. Aquatic coleopteran diversity in ponds in the two regions appears to be driven at a local scale by changes in relatively few physicochemical gradients, which are related to diversity in a clearly non-linear manner.     

Crustacean habitat potential mapping in a tidal flat using remote sensing and GIS

To make a macrofaunal (crustacean) habitat potential map, the spatial distribution of ecological variables in the Hwangdo tidal flat, Korea, was explored. Spatial variables were mapped using remote sensing and a geographic information system (GIS) combined with field observations. A frequency ratio (FR) and logistic regression (LR) model were employed to map the macrofauna potential area for the Ilyoplax dentimerosa, a crustacean species. Spatial variables affecting the tidal macrofauna distribution were selected based on abundance and biomass and used within a spatial database derived from remotely sensed data of various types of sensors. The spatial variables included the intertidal digital elevation model (DEM), slope, distance from a tidal channel, tidal channel density, surface sediment facies, spectral reflectance of the near infrared (NIR) bands and the tidal exposure duration. The relation between the I. dentimerosa and each spatial variable was calculated using the FR and LR. The species was randomly divided into a training set (70%) to analyse habitat potential using FR and LR and a test set (30%) to validate the predicted habitat potential map. The relations were overlaid to produce a habitat potential map with the species potential index (SPI) value for each pixel. The potential habitat maps were compared with the surveyed habitat locations such as validation data set. The comparison results showed that the LR model (accuracy is 85.28%) is better in prediction than the FR (accuracy is 78.96%) model. The performance of models gave satisfactory accuracies. The LR provides the quantitative influence of variables on a potential habitat of species; otherwise, the FR shows the quantitative influence of a class in each variable. The combination of a GIS-based frequency ratio and logistic regression models and remote sensing with field observations is an effective method to determine locations favorable for macrofaunal species occurrences in a tidal flat.     

Comparing discriminant analysis, neural networks and logistic regression for predicting species distributions: a case study with a Himalayan river bird

We assessed the occurrence of a common river bird, the Plumbeous Redstart Rhyacornis fuliginosus, along 180 independent streams in the Indian and Nepali Himalaya. We then compared the performance of multiple discrimant analysis (MDA), logistic regression (LR) and artificial neural networks (ANN) in predicting this species’ presence or absence from 32 variables describing stream altitude, slope, habitat structure, chemistry and invertebrate abundance. Using the entire data (=training set) and a threshold for accepting presence in ANN and LR set to P≥0.5, ANN correctly classified marginally more cases (88%) than either LR (83%) or MDA (84%). Model performance was assessed from two methods of data partitioning. In a ‘leave-one-out’ approach, LR correctly predicted more cases (82%) than MDA (73%) or ANN (69%). However, in a holdout procedure, all the methods performed similarly (73–75%). All methods predicted true absence (i.e. specificity in holdout: 81–85%) better than true presence (i.e. sensitivity: 57–60%). These effects reflect species’ prevalence (=frequency of occurrence), but are seldom considered in distribution modelling. Despite occurring at only 36% of the sites, Plumbeous Redstarts are one of the most common Himalayan river birds, and problems will be greater with less common species. Both LR and ANN require an arbitrary threshold probability (often P=0.5) at which to accept species presence from model prediction. Simulations involving varied prevalence revealed that LR was particularly sensitive to threshold effects. ROC plots (received operating characteristic) were therefore used to compare model performance on test data at a range of thresholds; LR always outperformed ANN. This case study supports the need to test species’ distribution models with independent data, and to use a range of criteria in assessing model performance. ANN do not yet have major advantages over conventional multivariate methods for assessing bird distributions. LR and MDA were both more efficient in the use of computer time than ANN, and also more straightforward in providing testable hypotheses about environmental effects on occurrence. However, LR was apparently subject to chance significant effects from explanatory variables, emphasising the well-known risks of models based purely on correlative data.     

Modelling the distribution of plant species using the autologistic regression model

For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida.     

Drivers of euphausiid species abundance and numerical abundance in the Atlantic Ocean

Mid-ocean ridges are common features of the world’s oceans but there is a lack of understanding as to how their presence affects overlying pelagic biota. The Mid-Atlantic Ridge (MAR) is a dominant feature of the Atlantic Ocean. Here, we examined data on euphausiid distribution and abundance arising from several international research programmes and from the continuous plankton recorder. We used a generalized additive model (GAM) framework to explore spatial patterns of variability in euphausiid distribution on, and at either side of, the MAR from 60°N to 55°S in conjunction with variability in a suite of biological, physical and environmental parameters. Euphausiid species abundance peaked in mid-latitudes and was significantly higher on the ridge than in adjacent waters, but the ridge did not influence numerical abundance significantly. Sea surface temperature (SST) was the most important single factor influencing both euphausiid numerical abundance and species abundance. Increases in sea surface height variance, a proxy for mixing, increased the numerical abundance of euphausiids. GAM predictions of variability in species abundance as a function of SST and depth of the mixed layer were consistent with present theories, which suggest that pelagic niche availability is related to the thermal structure of the near surface water: more deeply-mixed water contained higher euphausiid biodiversity. In addition to exposing present distributional patterns, the GAM framework enables responses to potential future and past environmental variability including temperature change to be explored.     

Predicting species distributions: use of climatic parameters in BIOCLIM and its impact on predictions of species’ current and future distributions

Bioclimatic models are widely used tools for assessing potential responses of species to climate change. One commonly used model is BIOCLIM, which summarises up to 35 climatic parameters throughout a species’ known range, and assesses the climatic suitability of habitat under current and future climate scenarios. A criticism of BIOCLIM is that the use of all 35 parameters may lead to over-fitting of the model, which in turn may result in misrepresentations of species’ potential ranges and to the loss of biological reality. In this study, we investigated how different methods of combining climatic parameters in BIOCLIM influenced predictions of the current distributions of 25 Australian butterflies species. Distributions were modeled using three previously used methods of selecting climatic parameters: (i) the full set of 35 parameters, (ii) a customised selection of the most relevant parameters for individual species based on analysing histograms produced by BIOCLIM, which show the values for each parameter at all of the focal species known locations, and (iii) a subset of 8 parameters that may generally influence the distributions of butterflies. We also modeled distributions based on random selections of parameters. Further, we assessed the extent to which parameter choice influenced predictions of the magnitude and direction of range changes under two climate change scenarios for 2020. We found that the size of predicted distributions was negatively correlated with the number of parameters incorporated in the model, with progressive addition of parameters resulting in progressively narrower potential distributions. There was also redundancy amongst some parameters; distributions produced using all 35 parameters were on average half the size of distributions produced using only 6 parameters. The selection of parameters via histogram analysis was influenced, to an extent, by the number of location records for the focal species. Further, species inhabiting different biogeographical zones may have different sets of climatic parameters limiting their distributions; hence, the appropriateness of applying the same subset of parameters to all species may be reduced under these situations. Under future climates, most species were predicted to suffer range reductions regardless of the scenario used and the method of parameter selection. Although the size of predicted distributions varied considerably depending on the method of selecting parameters, there were no significant differences in the proportional change in range size between the three methods: under the worst-case scenario, species’ distributions decrease by an average of 12.6, 11.4, and 15.7%, using all parameters, the ‘customised set’, and the ‘general set’ of parameters, respectively. However, depending on which method of selecting parameters was used, the direction of change was reversed for two species under the worst-case climate change scenario, and for six species under the best-case scenario (out of a total of 25 species). These results suggest that when averaged over multiple species, the proportional loss or gain of climatically suitable habitat is relatively insensitive to the number of parameters used to predict distributions with BIOCLIM. However, when measuring the response of specific species or the actual size of distributions, the number of parameters is likely to be critical.     

Hierarchical analysis of species distributions and abundance across environmental gradients

Abiotic and biotic processes operate at multiple spatial and temporal scales to shape many ecological processes, including species distributions and demography. Current debate about the relative roles of niche-based and stochastic processes in shaping species distributions and community composition reflects, in part, the challenge of understanding how these processes interact across scales. Traditional statistical models that ignore autocorrelation and spatial hierarchies can result in misidentification of important ecological covariates. Here, we demonstrate the utility of a hierarchical modeling framework for testing hypotheses about the importance of abiotic factors at different spatial scales and local spatial autocorrelation for shaping species distributions and abundances. For the two orchid species studied, understory light availability and soil moisture helped to explain patterns of presence and abundance at a microsite scale (<4 m2), while soil organic content was important at a population scale (<400 m2). The inclusion of spatial autocorrelation is shown to alter the magnitude and certainty of estimated relationships between abundance and abiotic variables, and we suggest that such analysis be used more often to explore the relationships between species life histories and distributions. The hierarchical modeling framework is shown to have great potential for elucidating ecological relationships involving abiotic and biotic processes simultaneously at multiple scales.     

Mapping water chemical variables with spatially correlated errors

One of the most important considerations in many environmental studies is need to allow for correlations among the variables. Monitoring and analyzing relationships between chemical environmental parameters using spatial correlation based regression modelling is the main motivation of this applied study. For this purpose, some noticeable environmental parameters of data sets obtained from two lakes have been considered and the concentrations of chemical variables such as cadmium and nitrate have been appraised by a regression-based geostatistical methodology. The modelling procedure consists of two stages. In the first stage, spatial variables are analyzed via multi-linear regression and some relationships are provided. Next, by using the spatial auto-correlations of the residuals, a type of regression-based kriging procedure is applied. The capacity of the model for appraising the water chemical variables is also tested and performance comparisons with ordinary kriging are conducted. Finally, the applications showed that analyzing water chemical variables with spatially correlated errors is a convenient and applicable approach for assessing the environmental systems.     

Modeling a spatially restricted distribution in the Neotropics: How the size of calibration area affects the performance of five presence-only methods

We here examine species distribution models for a Neotropical anuran restricted to ombrophilous areas in the Brazilian Atlantic Forest hotspot. We extend the known occurrence for the treefrog Hypsiboas bischoffi (Anura: Hylidae) through GPS field surveys and use five modeling methods (BIOCLIM, DOMAIN, OM-GARP, SVM, and MAXENT) and selected bioclimatic and topographic variables to model the species distribution. Models were first trained using two calibration areas: the Brazilian Atlantic Forest (BAF) and the whole of South America (SA). All modeling methods showed good levels of predictive power and accuracy with mean AUC ranging from 0.77 (BIOCLIM/BAF) to 0.99 (MAXENT/SA). MAXENT and SVM were the most accurate presence-only methods among those tested here. All but the SVM models calibrated with SA predicted larger distribution areas when compared to models calibrated in BAF. OM-GARP dramatically overpredicted the species distribution for the model calibrated in SA, with a predicted area around 10⁶ km² larger than predicted by other SDMs. With increased calibration area (and environmental space), OM-GARP predictions followed changes in the environmental space associated with the increased calibration area, while MAXENT models were more consistent across calibration areas. MAXENT was the only method that retrieved consistent predictions across calibration areas, while allowing for some overprediction, a result that may be relevant for modeling the distribution of other spatially restricted organisms.