Species distribution models and ecological theory: A critical assessment and some possible new approaches

Given the importance of knowledge of species distribution for conservation and climate change management, continuous and progressive evaluation of the statistical models predicting species distributions is necessary. Current models are evaluated in terms of ecological theory used, the data model accepted and the statistical methods applied. Focus is restricted to Generalised Linear Models (GLM) and Generalised Additive Models (GAM). Certain currently unused regression methods are reviewed for their possible application to species modelling.A review of recent papers suggests that ecological theory is rarely explicitly considered. Current theory and results support species responses to environmental variables to be unimodal and often skewed though process-based theory is often lacking. Many studies fail to test for unimodal or skewed responses and straight-line relationships are often fitted without justification.Data resolution (size of sampling unit) determines the nature of the environmental niche models that can be fitted. A synthesis of differing ecophysiological ideas and the use of biophysical processes models could improve the selection of predictor variables. A better conceptual framework is needed for selecting variables.Comparison of statistical methods is difficult. Predictive success is insufficient and a test of ecological realism is also needed. Evaluation of methods needs artificial data, as there is no knowledge about the true relationships between variables for field data. However, use of artificial data is limited by lack of comprehensive theory.Three potentially new methods are reviewed. Quantile regression (QR) has potential and a strong theoretical justification in Liebig's law of the minimum. Structural equation modelling (SEM) has an appealing conceptual framework for testing causality but has problems with curvilinear relationships. Geographically weighted regression (GWR) intended to examine spatial non-stationarity of ecological processes requires further evaluation before being used.Synthesis and applications: explicit theory needs to be incorporated into species response models used in conservation. For example, testing for unimodal skewed responses should be a routine procedure. Clear statements of the ecological theory used, the nature of the data model and sufficient details of the statistical method are needed for current models to be evaluated. New statistical methods need to be evaluated for compatibility with ecological theory before use in applied ecology. Some recent work with artificial data suggests the combination of ecological knowledge and statistical skill is more important than the precise statistical method used. The potential exists for a synthesis of current species modelling approaches based on their differing ecological insights not their methodology.     

Spatial smoothing techniques for the assessment of habitat suitability

Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of observations is often violated in practice since the points at which the observations are collected are spatially aligned. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations.

Predicting tree distributions in an East African biodiversity hotspot: model selection, data bias and envelope uncertainty

The Eastern Arc Mountains (EAMs) of Tanzania and Kenya support some of the most ancient tropical rainforest on Earth. The forests are a global priority for biodiversity conservation and provide vital resources to the Tanzanian population. Here, we make a first attempt to predict the spatial distribution of 40 EAM tree species, using generalised additive models, plot data and environmental predictor maps at sub 1 km resolution. The results of three modelling experiments are presented, investigating predictions obtained by (1) two different procedures for the stepwise selection of predictors, (2) down-weighting absence data, and (3) incorporating an autocovariate term to describe fine-scale spatial aggregation. In response to recent concerns regarding the extrapolation of model predictions beyond the restricted environmental range of training data, we also demonstrate a novel graphical tool for quantifying envelope uncertainty in restricted range niche-based models (envelope uncertainty maps). We find that even for species with very few documented occurrences useful estimates of distribution can be achieved. Initiating selection with a null model is found to be useful for explanatory purposes, while beginning with a full predictor set can over-fit the data. We show that a simple multimodel average of these two best-model predictions yields a superior compromise between generality and precision (parsimony). Down-weighting absences shifts the balance of errors in favour of higher sensitivity, reducing the number of serious mistakes (i.e., falsely predicted absences); however, response functions are more complex, exacerbating uncertainty in larger models. Spatial autocovariates help describe fine-scale patterns of occurrence and significantly improve explained deviance, though if important environmental constraints are omitted then model stability and explanatory power can be compromised. We conclude that the best modelling practice is contingent both on the intentions of the analyst (explanation or prediction) and on the quality of distribution data; generalised additive models have potential to provide valuable information for conservation in the EAMs, but methods must be carefully considered, particularly if occurrence data are scarce. Full results and details of all species models are supplied in an online Appendix.     

Methods to empirically estimate direct and indirect rebound effect of energy-saving technological changes in households

Energy efficiency policies have a special importance within carbon emission reduction policies to mitigate the climate change effects. However, potential reductions of energy consumption and, consequently, its resulting emissions, can be offset through the so called “rebound effect”. The concept of “rebound effect” refers to a set of mechanisms whereby the improvement of efficiency reduces the cost of the energy service and this results in the household energy consumption rising and totally or partially negating the reduction achieved by the energy efficiency improvement. This paper provides a methodology to estimate the static direct plus indirect rebound effect of energy efficiency improvements in the use of energy in households. It is based on the combination of econometric estimations of energy demand functions, re-spending modelling and generalised intput-output of energy modelling. It also provides estimations for Catalonia.     

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.     

The effects of direct and indirect constraints on biological communities

Human activities are expected to result in a diversity of directional or stochastic constraints that affect species either directly or by indirectly impacting their resources. However, there is no theoretical framework to predict the complex and various effects of these constraints on ecological communities. We developed a dynamic model that mimics the use of different resource types by a community of competing species. We investigated the effects of different environmental constraints (affecting either directly the growth rate of species or having indirect effects on their resources) on several biodiversity indicators. Our results indicate that (i) in realistic community models (assuming uneven resource requirements among species) the effects of perturbations are strongly buffered compared to neutral models; (ii) the species richness of communities can be maximized for intermediate levels of direct constraints (unimodal response), even in the absence of trade-off between competitive ability and tolerance to constraints; (iii) no such unimodal response occurs with indirect constraints; (iv) an increase in the environmental (e.g., climatic) variance may have different effects on community biomass and species richness.     

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.     

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.     

Modelling plant species richness using functional groups

Conservation biologists increasingly rely on spatial predictive models of biodiversity to support decision-making. Therefore, highly accurate and ecologically meaningful models are required at relatively broad spatial scales. While statistical techniques have been optimized to improve model accuracy, less focus has been given to the question: How does the autecology of a single species affect model quality? We compare a direct modelling approach versus a cumulative modelling approach for predicting plant species richness, where the latter gives more weight to the ecology of functional species groups. In the direct modelling approach, species richness is predicted by a single model calibrated for all species. In the cumulative modelling approach, the species were partitioned into functional groups, with each group calibrated separately and species richness of each group was cumulated to predict total species richness. We hypothesized that model accuracy depends on the ecology of individual species and that the cumulative modelling approach would predict species richness more accurately. The predictors explained plant species richness by ca. 25%. However, depending on the functional group the deviance explained varied from 3 to 67%. While both modelling approaches performed equally well, the models of the different functional groups highly varied in their quality and their spatial richness pattern. This variability helps to improve our understanding on how plant functional groups respond to ecological gradients.     

Modelling species distributions with penalised logistic regressions: A comparison with maximum entropy models

An important aspect of species distribution modelling is the choice of the modelling method because a suboptimal method may have poor predictive performance. Previous comparisons have found that novel methods, such as Maxent models, outperform well-established modelling methods, such as the standard logistic regression. These comparisons used training samples with small numbers of occurrences per estimated model parameter, and this limited sample size may have caused poorer predictive performance due to overfitting. Our hypothesis is that Maxent models would outperform a standard logistic regression because Maxent models avoid overfitting by using regularisation techniques and a standard logistic regression does not. Regularisation can be applied to logistic regression models using penalised maximum likelihood estimation. This estimation procedure shrinks the regression coefficients towards zero, causing biased predictions if applied to the training sample but improving the accuracy of new predictions. We used Maxent and logistic regression (standard and penalised) to analyse presence/pseudo-absence data for 13 tree species and evaluated the predictive performance (discrimination) using presence-absence data. The penalised logistic regression outperformed standard logistic regression and equalled the performance of Maxent. The penalised logistic regression may be considered one of the best methods to develop species distribution models trained with presence/pseudo-absence data, as it is comparable to Maxent. Our results encourage further use of the penalised logistic regression for species distribution modelling, especially in those cases in which a complex model must be fitted to a sample with a limited size.     

What does ecological modelling model? A proposed classification of ecological niche models based on their underlying methods

Species distribution model is the term most frequently used in ecological modelling, but other authors used instead predictive habitat distribution model or species-habitat models. A consensual ecological modelling terminology that avoids misunderstandings and takes into account the ecological niche theory does not exist at present. Moreover, different studies differ in the type of niche that is represented by similar distribution models. I propose to use as standard ecological modelling terminology the terms “ecological niche”, “potential niche”, “realized niche” models (for modelling their respective niches), and “habitat suitability map” (for the output of the niche models). Therefore, the user can understand more easily that models always forecast species’ niche and relate more closely the different types of niche models.     

Toxicokinetic-toxicodynamic modelling in an individual based context—Consequences of parameter variability

Toxicokinetic-toxicodynamic (TKTD) models simulate the time-course of toxicant concentration in the organism and toxicity at the level of the organism. A link between TKTD models that simulate survival and individual based models for populations (IBMs) is proposed which allows TKTD parameters to vary between individuals. The TKTD-IBM predicts different survival in response to toxicants when TKTD parameters vary amongst individuals compared to the survival predicted with fixed TKTD parameters. The model with fixed parameters represents the concept of stochastic death whereas the model with variable parameters behaves, at least partly, according to the individual tolerance distribution concept. The whole set of TKTD parameters of an individual can be interpreted as constituting “individual tolerance”.     

Small-scale spatial and temporal interactions among benthic crustaceans and one fish species in the Bay of Biscay

In the summer of 2004, a video survey was carried out in the northern part of the central mud bank (Grande Vasière) of the Bay of Biscay to study the small scale relationship between the dominant crustacean megafauna Nephrops norvegicus, Munida rugosa and Goneplax rhomboides and juvenile hake (Merluccius merluccius). Using a towed body, high-resolution videos were recorded in six sampling sites. Statistical modelling using generalised additive models (GAM) revealed variations in activity patterns for two species. More N. norvegicus were observed outside their burrows at dawn and somewhat at dusk (no observations during night) while G. rhomboides was less observed in the morning. In addition, reduced spatial overlap between G. rhomboides and N. norvegicus suggested reduced competition for food but also space as both are burrowing species. The observed temporal and spatial activity patterns may contribute to regulating assemblage structure as competing species may be actively foraging at different times and locations thus reducing direct competition.     

An evaluation of environmental factors affecting species distributions

Many different models can be built to explain the distributions of species. Often there is no single model that is clearly better than the alternatives, and this leads to uncertainty over which environmental factors are limiting species’ distributions. We investigated the support for different environmental factors by determining the drop in model performance when selected predictors were excluded from the model building process. We used a paired t-test over 37 plant species so that an environmental factor was only deemed significant if it consistently improved the results for multiple species. Geology and winter minimum temperatures were found to be the environmental factors with the most support, with a significant drop in model performance when either of these factors was excluded. However, there was less support for summer maximum temperature, as other environmental factors could combine to produce similar model performance. Our method of evaluating environmental factors using multiple species will not be capable of detecting predictors that are only important for one or two species, but it is difficult to distinguish these from spurious correlations. The strength of the method is that it increases inference for factors that consistently affect the distributions of many species. We discourage the assessment of models against predefined benchmarks, such as an area under the curve (AUC) of more than 0.7, as many alternative models for the same species produce similar results. Therefore, the benchmarks do not provide any indication of how the performance of the selected model compares to alternative models, and they provide weak inference to accept any selected model.     

Model based grouping of species across environmental gradients

We present a novel approach to the statistical analysis and prediction of multispecies data. The approach allows the simultaneous grouping and quantification of multiple species’ responses to environmental gradients. The underlying statistical model is a finite mixture model, where mixing is performed over the individual species’ responses to environmental gradients. Species with similar responses are grouped with minimal information loss. We term these groups species archetypes. Each species archetype has an associated GLM that can be used to predict distributions with appropriate measures of uncertainty. Initially, we illustrate the concept and method using artificial data and then with application to real data comprising 200 species from the Great Barrier Reef (GBR) lagoon on 13 oceanographic and geological gradients from 12°S to 24°S. The 200 species from the GBR are well represented by 15 species archetypes. The model is interpreted through maps of the probability of presence for a fine scale set of locations throughout the study area. Maps of uncertainty are also produced to provide statistical context. The presence of each species archetype was strongly influenced by oceanographic gradients, principally temperature, oxygen and salinity. The number of species in each group ranged from 4 to 34. The method has potential application to the analysis of multispecies distribution patterns and for multispecies management.     

Implications of network particle tracking (NPT) for ecological model interpretation

Network particle tracking (NPT), building on the foundation of network environ analysis (NEA), is a new development in the definition of coherence relations within and between connected systems. This paper evaluates three ecosystem models in a comparison of throughflow- and storage-based NEA and NPT. Compartments in models with high indirect effects and Finn cycling showed low correlation of NEA storage and throughflow with particle repeat visits and numbers of particles in compartments at steady state. Conversely, the correlation between NEA and NPT results was high with two models having lower indirect effects and Finn cycling. Analysis of ecological orientors associated with NEA showed NPT to fully support conventional NEA results when the common conditions of donor control and steady state are satisfied. Particle trajectories are recorded in the new concept of a particle “passport”. Ability to track and record particle in-system histories enables views of multiple scales and opens the possibility of making pathway-dependent modeling decisions. NPT may also enable modeling of time, allowing integration of Newtonian, organismal and stochastic modeling perspectives in a single comprehensive analysis.     

Incorporating low-resolution historic species location data decreases performance of distribution models

Developing robust species distribution models is important as model outputs are increasingly being incorporated into conservation policy and management decisions. A largely overlooked component of model assessment and refinement is whether to include historic species occurrence data in distribution models to increase the data sample size. Data of different temporal provenance often differ in spatial accuracy and precision. We test the effect of inclusion of historic coarse-resolution occurrence data on distribution model outputs for 187 species of birds in Australian tropical savannas. Models using only recent (after 1990), fine-resolution data had significantly higher model performance scores measured with area under the receiver operating characteristic curve (AUC) than models incorporating both fine- and coarse-resolution data. The drop in AUC score is positively correlated with the total area predicted to be suitable for the species (R² = 0.163-0.187, depending on the environmental predictors in the model), as coarser data generally leads to greater predicted areas. The remaining unexplained variation is likely to be due to the covariate errors resulting from resolution mismatch between species records and environmental predictors. We conclude that decisions regarding data use in species distribution models must be conscious of the variation in predictions that mixed-scale datasets might cause.     

Constrained additive ordination

For several decades now, ecologists have sought to determine the shape of species' response curves and how they are distributed along unknown underlying gradients, environmental latent variables, or ordination axes. Its determination has important implications for both continuum theory and community analysis because many theories and models in community ecology assume that responses are symmetric and unimodal. This article proposes a major new technique called constrained additive ordination (CAO) that solves this problem by computing the optimal gradients and flexible response curves. It allows ecologists to see the response curves as they really are, against the dominant gradients. With one gradient, CAO is a generalization of constrained quadratic ordination (CQO; formerly called canonical Gaussian ordination or CGO). It supplants symmetric bell-shaped response curves in CQO with completely flexible smooth curves. The curves are estimated using smoothers such as the smoothing spline. Loosely speaking, CAO models are generalized additive models (GAMs) fitted to a very small number of latent variables. Being data driven rather than model driven, CAO allows the data to "speak for itself" and does not make any of the assumptions made by canonical correspondence analysis. The new methodology is illustrated with a hunting spider data set and a New Zealand tree species data set.     

Multivariate statistics as a tool for model-based prediction of floodplain vegetation and fauna

Robust prediction models for the spatial distribution of grassland vegetation, molluscs and carabids in a study area at the Middle Elbe (Germany) had to be generated by means of multivariate statistical methods. An appropriate study design has been developed. Data of all three taxons as well as numerous parameters of the abiotic environment were ascertained. Canonical correspondence analysis (CCA) detected clear dependencies between the occurrence of biotic objects and mainly hydrological parameters. By use of Arc/Info applications CANOGEN and CANORES, it was possible to extrapolate the models from the sample plots to the whole study area. The predicted spatial distribution of nearly all in the field studies examined species could be depicted with these instruments. Comparison between investigated and predicted distribution of species showed high correspondence.Robustness of the models was proved by interchanging model parameters for different study years and also in applying models at a second study area located 40 km upstream of the original study area.As a second method for further investigation, logistic regression was used to build generalised linear models (GLM) for potential indicator species in the study area.     

Use of Community‐Composition Data to Predict the Fecundity and Abundance of Species

Abstract: Species distribution models are critical tools for the prediction of invasive species spread and conservation of biodiversity. The majority of species distribution models have been built with environmental data. Community ecology theory suggests that species co‐occurrence data could also be used to predict current and potential distributions of species. Species assemblages are the products of biotic and environmental constraints on the distribution of individual species and as a result may contain valuable information for niche modeling. We compared the predictive ability of distribution models of annual grassland plants derived from either environmental or community‐composition data. Composition‐based models were built with the presence or absence of species at a site as predictors of site quality, whereas environment‐based models were built with soil chemistry, moisture content, above‐ground biomass, and solar radiation as predictors. The reproductive output of experimentally seeded individuals of 4 species and the abundance of 100 species were used to evaluate the resulting models. Community‐composition data were the best predictors of both the site‐specific reproductive output of sown individuals and the site‐specific abundance of existing populations. Successful community‐based models were robust to omission of data on the occurrence of rare species, which suggests that even very basic survey data on the occurrence of common species may be adequate for generating such models. Our results highlight the need for increased public availability of ecological survey data to facilitate community‐based modeling at scales relevant to conservation.