Effects of sample size on the performance of species distribution models

A wide range of modelling algorithms is used by ecologists, conservation practitioners, and others to predict species ranges from point locality data. Unfortunately, the amount of data available is limited for many taxa and regions, making it essential to quantify the sensitivity of these algorithms to sample size. This is the first study to address this need by rigorously evaluating a broad suite of algorithms with independent presence–absence data from multiple species and regions. We evaluated predictions from 12 algorithms for 46 species (from six different regions of the world) at three sample sizes (100, 30, and 10 records). We used data from natural history collections to run the models, and evaluated the quality of model predictions with area under the receiver operating characteristic curve (AUC). With decreasing sample size, model accuracy decreased and variability increased across species and between models. Novel modelling methods that incorporate both interactions between predictor variables and complex response shapes (i.e. GBM, MARS-INT, BRUTO) performed better than most methods at large sample sizes but not at the smallest sample sizes. Other algorithms were much less sensitive to sample size, including an algorithm based on maximum entropy (MAXENT) that had among the best predictive power across all sample sizes. Relative to other algorithms, a distance metric algorithm (DOMAIN) and a genetic algorithm (OM-GARP) had intermediate performance at the largest sample size and among the best performance at the lowest sample size. No algorithm predicted consistently well with small sample size ( n  < 30) and this should encourage highly conservative use of predictions based on small sample size and restrict their use to exploratory modelling.     

BIOMOD – optimizing predictions of species distributions and projecting potential future shifts under global change

A new computation framework (BIOMOD: BIOdiversity MODelling) is presented, which aims to maximize the predictive accuracy of current species distributions and the reliability of future potential distributions using different types of statistical modelling methods. BIOMOD capitalizes on the different techniques used in static modelling to provide spatial predictions. It computes, for each species and in the same package, the four most widely used modelling techniques in species predictions, namely Generalized Linear Models (GLM), Generalized Additive Models (GAM), Classification and Regression Tree analysis (CART) and Artificial Neural Networks (ANN). BIOMOD was applied to 61 species of trees in Europe using climatic quantities as explanatory variables of current distributions. On average, all the different modelling methods yielded very good agreement between observed and predicted distributions. However, the relative performance of different techniques was idiosyncratic across species, suggesting that the most accurate model varies between species. The results of this evaluation also highlight that slight differences between current predictions from different modelling techniques are exacerbated in future projections. Therefore, it is difficult to assess the reliability of alternative projections without validation techniques or expert opinion. It is concluded that rather than using a single modelling technique to predict the distribution of several species, it would be more reliable to use a framework assessing different models for each species and selecting the most accurate one using both evaluation methods and expert knowledge.     

Mutualism influences species distribution predictions for a bromeliad‐breeding anuran under climate change

Ecological niche models, or species distribution models, have been widely used to identify potentially suitable areas for species in future climate change scenarios. However, there are inherent errors to these models due to their inability to evaluate species occurrence influenced by non‐climatic factors. With the intuit to improve the modelling predictions for a bromeliad‐breeding treefrog (Phyllodytes melanomystax, Hylidae), we investigate how the climatic suitability of bromeliads influences the distribution model for the treefrog in the context of baseline and 2050 climate change scenarios. We used point occurrence data on the frog and the bromeliad (Vriesea procera, Bromeliaceae) to generate their predicted distributions based on baseline and 2050 climates. Using a consensus of five algorithms, we compared the accuracy of the models and the geographic predictions for the frog generated from two modelling procedures: (i) a climate‐only model for P. melanomystax and V. procera; and (ii) a climate‐biotic model for P. melanomystax, in which the climatic suitability of the bromeliad was jointly considered with the climatic variables. Both modelling approaches generated strong and similar predictive power for P. melanomystax, yet climate‐biotic modelling generated more concise predictions, particularly for the year 2050. Specifically, because the predicted area of the bromeliad overlaps with the predictions for the treefrog in the baseline climate, both modelling approaches produce reasonable similar predicted areas for the anuran. Alternatively, due to the predicted loss of northern climatically suitable areas for the bromeliad by 2050, only the climate‐biotic models provide evidence that northern populations of P. melanomystax will likely be negatively affected by 2050.     

Modelling the occurrence of threatened plant species in taiga landscapes: methodological and ecological perspectives

Aim Understanding the spatial patterns of species distribution and predicting the occurrence of high biological diversity and rare species are central themes in biogeography and environmental conservation. The aim of this study was to model and scrutinize the relative contributions of climate, topography, geology and land‐cover factors to the distributions of threatened vascular plant species in taiga landscapes in northern Finland. Location North‐east Finland, northern Europe. Methods The study was performed using a data set of 28 plant species and environmental variables at a 25‐ha resolution. Four different stepwise selection algorithms [Akaike information criterion (AIC), Bayesian information criterion (BIC), adaptive backfitting, cross selection] with generalized additive models (GAMs) were fitted to identify the main environmental correlates for species occurrences. The accuracies of the distribution models were evaluated using fourfold cross‐validation based on the area under the curve (AUC) derived from receiver operating characteristic plots. The GAMs were tentatively extrapolated to the whole study area and species occurrence probability maps were produced using GIS techniques. The effect of spatial autocorrelation on the modelling results was also tested by including autocovariate terms in the GAMs. Results According to the AUC values, the model performance varied from fair to excellent. The AIC algorithm provided the highest mean performance (mean AUC = 0.889), whereas the lowest mean AUC (0.851) was obtained from BIC. Most of the variation in the distribution of threatened plant species was related to growing degree days, temperature of the coldest month, water balance, cover of mire and mean elevation. In general, climate was the most powerful explanatory variable group, followed by land cover, topography and geology. Inclusion of the autocovariate only slightly improved the performance of the models and had a minor effect on the importance of the environmental variables. Main conclusions The results confirm that the landscape‐scale distribution patterns of plant species can be modelled well on the basis of environmental parameters. A spatial grid system with several environmental variables derived from remote sensing and GIS data was found to produce useful data sets, which can be employed when predicting species distribution patterns over extensive areas. Landscape‐scale maps showing the predicted occurrences of individual or multiple threatened plant species may provide a useful basis for focusing field surveys and allocating conservation efforts.     

Indicating Soil Acidity Using Vegetation Relevés in Spatially Limited Areas – Case Study from the Považský Inovec, Slovakia

A fine-scaled approach for predicting soil acidity using plant species in a spatially limited area (?epú?ky Nature Reserve, Slovakia) is presented here. This approach copes with some specific limitations: i) a limited pool of vegetation data may make the predictions too sensitive to the lack of species information, and ii) the predictions may be sensitive to the narrow pH gradient. Vegetation relevés and soil reaction (pH-H₂O and pH-CaCl₂) were systematically recorded. A set of species indicator values and amplitudes was calibrated with physical pH data using the Weighted Averaging (WA), HOF modelling and Non-Metric Multidimensional Scaling (NMDS) methods, along with Ellenberg indicator values. Two prediction methods were tested: i) WA and ii) Amplitude Overlap (AO). WA prediction with Ellenberg’s and WA-calibrated species indicator values were the most powerful technique (R ²?=?68.4–68.7% and 53.4–59.1% for pH-CaCl₂ and pH-H₂O, respectively). WA-prediction with HOF-based indicator values was less effective (R ²?=?61.7% and 50.7%) due to the decrease in species’ information because with HOF modelling many species are assumed indifferent or too rare. The NMDS method does not bring any significant gain to the calibration, though it avoids the lack of species information. The AO method was proven to be less powerful under studied circumstances, because it is sensitive both to the lack of species’ information and to the truncation of species responses. The results prove that a spatially explicit approach can provide significant indices to estimate changes in soil acidity – pH-CaCl₂ better than pH-H₂O.     

Does the interpolation accuracy of species distribution models come at the expense of transferability?

Model transferability (extrapolative accuracy) is one important feature in species distribution models, required in several ecological and conservation biological applications. This study uses 10 modelling techniques and nationwide data on both (1) species distribution of birds, butterflies, and plants and (2) climate and land cover in Finland to investigate whether good interpolative prediction accuracy for models comes at the expense of transferability – i.e. markedly worse performance in new areas. Models’ interpolation and extrapolation performance was primarily assessed using AUC (the area under the curve of a receiver characteristic plot) and Kappa statistics, with supplementary comparisons examining model sensitivity and specificity values. Our AUC and Kappa results show that extrapolation to new areas is a greater challenge for all included modelling techniques than simple filling of gaps in a well‐sampled area, but there are also differences among the techniques in the degree of transferability. Among the machine‐learning modelling techniques, MAXENT, generalized boosting methods (GBM), and artificial neural networks (ANN) showed good transferability while the performance of GARP and random forest (RF) decreased notably in extrapolation. Among the regression‐based methods, generalized additive models (GAM) and generalized linear models (GLM) showed good transferability. A desirable combination of good prediction accuracy and good transferability was evident for three modelling techniques: MAXENT, GBM, and GAM. However, examination of model sensitivity and specificity revealed that model types may differ in their tendencies to either increased over‐prediction of presences or absences in extrapolation, and some of the methods show contrasting changes in sensitivity vs specificity (e.g. ANN and GARP). Among the three species groups, the best transferability was seen with birds, followed closely by butterflies, whereas reliable extrapolation for plant species distribution models appears to be a major challenge at least at this scale. Overall, detailed knowledge of the behaviour of different techniques in various study settings and with different species groups is of utmost importance in predictive modelling.     

Determinants of the biogeographical distribution of butterflies in boreal regions

Aim  We explored the relative contributions of climatic and land-cover factors in explaining the distribution patterns of butterflies in a boreal region.
Location  Finland, northern Europe.
Methods  Data from a national butterfly atlas survey carried out during 1991–2003, with a 10-km grain grid system, were used in these analyses. We used generalized additive models (GAM) and hierarchical partitioning (HP) to explore the main environmental correlates (climate and land-cover) of the realized niches of 98 butterfly species. The accuracy of the distribution models (GAMs) was validated by resubstitution and cross-validation approaches, using the area under the curve (AUC) derived from the receiver operating characteristic (ROC) plots.
Results  Predictive accuracies of the 98 individual environment–butterfly models varied from low to very high (cross-validated AUC values 0.48–0.99), with a mean of 0.79. The results of both the GAM and HP analyses were broadly concordant. Most of the variation in butterfly distributions is associated with growing degree-days, mean temperature of the coldest month and cover of built-up area in all six phylogenetic groups (butterfly families). There were no statistically significant differences in predictive accuracy among the different butterfly families.
Main conclusions  About three-quarters of the distributions of butterfly species in Finland appear to be governed principally by climatic, predominantly temperature-related, factors. This indicates that many butterfly species may respond rapidly to the projected climate change in boreal regions. By determining the ecological niches of multiple species, we can project their range shifts in response to changes in climate and land-cover, and identify species that are particularly sensitive to forecasted global changes.     

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

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

LIVES: a new habitat modelling technique for predicting the distribution of species’ occurrences using presence-only data based on limiting factor theory

Predictive modelling techniques using presence-only data have attracted increasing attention because they can provide information on species distributions and their potential habitat for conservation and ecosystem management. However, the existing predictive modelling techniques have several limitations. Here, we propose a novel predictive modelling technique, Limiting Variable and Environmental Suitability (LIVES), for predicting the distributions and potential habitats of species using presence-only data. It is based on limiting factor theory, which postulates that the occurrence of a species is only determined by the factor that most limits its distribution. LIVES predicts the suitability of a candidate grid cell for a species in terms of limiting environmental factor. It also predicts the most limiting factor or the potential limiting factor at the grid cell. The environmental factors can be climatic, geological, biological and any other relevant environmental factors, whether quantitative or qualitative. The predicted habitats consist of the current distribution of the species and the potentially suitable areas for the species where there is currently no record of occurrence. We also compare several properties of LIVES and other predictive modelling techniques. On the basis of 1,000 simulations, the average predictions of LIVES are more accurate than the two other commonly used modelling techniques (BIOCLIM and DOMAIN) for presence-only data.     

Method selection for species distribution modelling: are temporally or spatially independent evaluations necessary?

To assess the realism of habitat projections in the context of climate change, we conduct independent evaluations of twelve species distribution models, including three novel ecosystem‐based modelling techniques. Habitat hindcasts for 24 western North American tree species were validated against 931 palaeoecological records from 6000, 11000, 14000, 16000 and 21000 yr before present. In addition, we evaluate regional extrapolations based on geographic splits of >55000 sample plots. Receiver operating characteristic analyses indicated excellent predictive accuracy for cross‐validations (median AUC of 0.90) and fair accuracy for independent regional and palaeoecological validations (0.78 and 0.75). Surprisingly, we found little evidence for over‐parameterisation in any method. Also, given high correlations found between model accuracies in non‐independent and independent evaluations, we conclude that non‐independent evaluations are effective model selection tools. Ecosystem‐based modelling approaches performed below average with respect to model sensitivity but excelled in specificity statistics and robustness against extrapolations far beyond training data, suggesting that they are well suited to reconstruct historical biogeographies and glacial refugia.     

Predicting invasions in Australia by a Neotropical shrub under climate change: the challenge of novel climates and parameter estimation

Aim  To test how well species distributions and abundance can be predicted following invasion and climate change when using only species distribution and abundance data to estimate parameters.
Location  Models were developed for the species' native range in the Americas and applied to Australia.
Methods  We developed a predictive model for an invasive neotropical shrub ( Parkinsonia aculeata) using a popular ecophysiological bioclimatic modelling technique (CLIMEX) fitted against distribution and abundance data in the Americas. The effect of uncertainty in model parameter estimates on predictions in Australia was tested. Alternative data sources were used when model predictions were sensitive to uncertainty in parameter estimates. The resulting best-fit model was run under two climate change scenarios.
Results  Of the 19 parameters used, 9 could not be fitted using data from the native range. However, only parameters that lowered temperature or increased moisture requirements for growth noticeably altered the model prediction in Australia. Differences in predictions were dramatic, and reflect climates in Australia that were not represented in the Americas (novel climates). However, these poorly fitted parameters could be fitted post hoc using alternative data sources prior to predicting responses to climate change.
Conclusions  Novel climates prevented the development of a predictive model which relied only on native-range distribution and abundance data because certain parameters could not be fitted. In fact, predictions were more sensitive to parameter uncertainty than to climate change scenarios. Where uncertainty in parameter estimates affected predictions, it could be addressed through the inclusion of alternative data sources. However, this may not always be possible, for example in the absence of post-invasion data.     

Ensemble modelling of species distribution: the effects of geographical and environmental ranges

The aim of this study was to analyse the effects of species geographical and environmental ranges on the predictive performances of species distribution models (SDMs). We explored the usefulness of ensemble modelling approaches and tested whether species attributes influenced the outcomes of such approaches. Eight SDMs were used to model the current distribution of 35 fish species at 1110 stream sections in France. We first quantified the consensus among the resulting set of predictions for each fish species. Next, we created an average model by taking the average of the individual model predictions and tested whether the average model improved the predictive performances of single SDMs. Lastly, we described the ranges of fish species along four gradients: latitudinal, thermal, stream gradient (i.e. upstream‐downstream) and elevation. After accounting for the effects of phylogenetic relatedness and species prevalence, these four species attributes were related to the observed variations in both consensus among SDMs and predictive performances by using generalized estimation equations. Our results highlight the usefulness of ensemble approaches for identifying geographical areas of agreement among predictions. Although the geographical extent of species had no effect on the performances of SDMs, we demonstrated that more consensual and accurate predictions were obtained for species with low thermal and elevation ranges, validating the hypothesis that specialist species yield models with higher accuracy than generalist ones. We emphasized that significant improvements in the accuracy of SDMs can be achieved by using an average model. Furthermore, these improvements were higher for species with smaller ranges along the four gradients studied. The geographical extent and ranges of species along environmental gradients provide promising insights into our understanding of uncertainties in species distribution modelling.     

Which spatial distribution model best predicts the occurrence of dominant species in semi-arid rangeland of northern Iran?

Rangelands with more than 8000 plant species occupy nearly 54.6% of the land area of Iran and thus are accounted for a rich plant genetic storage. Mazandaran province has 378,000 ha of rangelands with high plant species richness and diversity due to its climate conditions but plants distribution is at risk because of non-principle management, land use change and as a result changing environmental factors. Vegetation management strategies can be guided by models that predict plant species distribution based on governing environmental variables. This is especially useful for the dominant species that determine ecosystem processes. In fact, modelling algorithm in each SDM determines its suitability for different ecosystems. Our aim was to compare the predictive power of a number of SDMs and to evaluate the importance of a range of environmental variables as predictors in the context of semi-arid rangeland vegetation. The selected study area, the Sarkhas rangelands (northern Iran, 36°10′ 42˝ N - 51°19′ 11˝ E), covers approximately 4358.9 ha of Mazandaran province. The efficacy of four different modelling techniques as well as Ensemble model was evaluated to predict the distribution of five dominant forage plant species (Vicia villosa, Stachys lavandulifolia, Coronilla balansae, Sanguisorba minor and Alopecurus textilis). The used models included artificial neural network (ANN), boosted regression trees (BRT), classification and regression trees (CART), and random forest (RF). Ensemble, RF and CART had the highest area under curve. The AUC obtained for Vicia villosa, Stachys lavandulifolia, Coronilla balansae, Sanguisorba minor and Alopecurus textilis, were 0.90, 0.72, 0.76, 0.69 and 0.75 respectively. Ensemble model was the model that most consistently demonstrated high predictive power across species in the rangeland context investigated here. BRT exhibited the least predictive power. An importance analysis of variables showed that soil organic C according to the CART model (0.396) and K according to the RF model (0.396) were the most important environmental variables.     

Sensitivity of predictive species distribution models to change in grain size

Predictive species distribution modelling (SDM) has become an essential tool in biodiversity conservation and management. The choice of grain size (resolution) of environmental layers used in modelling is one important factor that may affect predictions. We applied 10 distinct modelling techniques to presence-only data for 50 species in five different regions, to test whether: (1) a 10-fold coarsening of resolution affects predictive performance of SDMs, and (2) any observed effects are dependent on the type of region, modelling technique, or species considered. Results show that a 10 times change in grain size does not severely affect predictions from species distribution models. The overall trend is towards degradation of model performance, but improvement can also be observed. Changing grain size does not equally affect models across regions, techniques, and species types. The strongest effect is on regions and species types, with tree species in the data sets (regions) with highest locational accuracy being most affected. Changing grain size had little influence on the ranking of techniques: boosted regression trees remain best at both resolutions. The number of occurrences used for model training had an important effect, with larger sample sizes resulting in better models, which tended to be more sensitive to grain. Effect of grain change was only noticeable for models reaching sufficient performance and/or with initial data that have an intrinsic error smaller than the coarser grain size.     

GLM versus CCA spatial modeling of plant species distribution

Despite the variety of statistical methods available for static modeling of plant distribution, few studies directly compare methods on a common data set. In this paper, the predictive power of Generalized Linear Models (GLM) versus Canonical Correspondence Analysis (CCA) models of plant distribution in the Spring Mountains of Nevada, USA, are compared. Results show that GLM models give better predictions than CCA models because a species-specific subset of explanatory variables can be selected in GLM, while in CCA, all species are modeled using the same set of composite environmental variables (axes). Although both techniques can be readily ported to a Geographical Information System (GIS), CCA models are more readily implemented for many species at once. Predictions from both techniques rank the species models in the same order of quality; i.e. a species whose distribution is well modeled by GLM is also well modeled by CCA and vice-versa. In both cases, species for which model predictions have the poorest accuracy are either disturbance or fire related, or species for which too few observations were available to calibrate and evaluate the model. Each technique has its advantages and drawbacks. In general GLM will provide better species specific-models, but CCA will provide a broader overview of multiple species, diversity, and plant communities.     

Classification, assessment and trophic reconstruction of Danish lakes using chironomids

1. Surface-sediment assemblages of subfossil chironomid head capsules from fifty-four primarily shallow and nutrient-rich Danish lakes were analysed using multivariate numerical techniques. The species data, comprising forty-one chironomid taxa, were compared to environmental monitoring data in order to establish a relationship between chironomid faunal composition and lake trophic state.
2. The subfossil assemblages were compared to the chironomid bathymetric distributions along transects from four lakes. Correspondence analysis and similarity coefficients showed that the subfossil assemblages, sampled in the lake centre, reflect the chironomid communities in the littoral at a depth of 2–7 m.
3. Two-way indicator species analysis (TWINSPAN) was used to classify the Danish lakes into five groups defined by trophic state, lake depth and pH. Eighteen chironomid taxa showed significant differences in abundance among the five groups. Canonical correspondence analysis (CCA) showed the chlorophyll a concentration ([Chl a ]) and Secchi depth to be the variables best correlated to the faunal data, and fourteen taxa were significantly correlated to [Chl a ].
4. The strong correlation between chironomid data and the ln-transformed ([Chl a ]) was used to create a weighted averaging (WA) model to infer lake trophic state. Several models were tested by cross validation (leave-one-out jack-knifing), and a simple WA model using inverse de-shrinking had a RMSEP_jack of 0.65 (ln units) and a r ²_jack of 0.67.
5. The results can be used in the assessment and reconstruction of lake trophic state for long-term monitoring and palaeoecological investigations of shallow, temperate lakes in the mesotrophic to hypertrophic nutrient range.     

Dealing with Noisy Absences to Optimize Species Distribution Models: An Iterative Ensemble Modelling Approach

Species distribution models (SDMs) are widespread in ecology and conservation biology, but their accuracy can be lowered by non-environmental (noisy) absences that are common in species occurrence data. Here we propose an iterative ensemble modelling (IEM) method to deal with noisy absences and hence improve the predictive reliability of ensemble modelling of species distributions. In the IEM approach, outputs of a classical ensemble model (EM) were used to update the raw occurrence data. The revised data was then used as input for a new EM run. This process was iterated until the predictions stabilized. The outputs of the iterative method were compared to those of the classical EM using virtual species. The IEM process tended to converge rapidly. It increased the consensus between predictions provided by the different methods as well as between those provided by different learning data sets. Comparing IEM and EM showed that for high levels of non-environmental absences, iterations significantly increased prediction reliability measured by the Kappa and TSS indices, as well as the percentage of well-predicted sites. Compared to EM, IEM also reduced biases in estimates of species prevalence. Compared to the classical EM method, IEM improves the reliability of species predictions. It particularly deals with noisy absences that are replaced in the data matrices by simulated presences during the iterative modelling process. IEM thus constitutes a promising way to increase the accuracy of EM predictions of difficult-to-detect species, as well as of species that are not in equilibrium with their environment.     

Inferring the minimum pH of streams from macroinvertebrates using weighted averaging regression and calibration

1. Data on macroinvertebrates and stream chemistry were collected from sixty-four streams in Finland. Weighted averaging (WA) regression and calibration models were constructed to infer the minimum pH of streams from their invertebrate assemblages. The purpose was to develop an instrument for biological assessment and monitoring of stream acidification. The WA method was compared with simpler approaches, based on qualitative invertebrate data and pH tolerance limits, that are widely used.
2. Performance of the two approaches was assessed in terms of correlation between the inferred and observed minimum pH within the 'training set', and in terms of root mean squared differences (predicted – observed) (RMSEP) estimated by cross-validation or bootstrap resampling techniques. The models were further tested using independent data from the literature representative of a wide geographical range.
3. The predictive power of the WA models was reasonable (RMSEP 0.40–0.44 pH units) in the training set and consistently better than that of the tolerance limit method. In contrast to the latter, the WA models were able to infer a minimum pH above 5.5, suggesting they could detect the early stages of acidification.
4. The WA models performed better than the tolerance limit method in inferring pH from the independent literature, further demonstrating the superiority and generality of the WA approach.
5. The weighted averaging technique could be an effective and widely applicable tool for contemporary biological monitoring and assessment using aquatic invertebrates.     

Inferring the minimum pH of streams from macroinvertebrates using weighted averaging regression and calibration

1. Data on macroinvertebrates and stream chemistry were collected from sixty-four streams in Finland. Weighted averaging (WA) regression and calibration models were constructed to infer the minimum pH of streams from their invertebrate assemblages. The purpose was to develop an instrument for biological assessment and monitoring of stream acidification. The WA method was compared with simpler approaches, based on qualitative invertebrate data and pH tolerance limits, that are widely used.
2. Performance of the two approaches was assessed in terms of correlation between the inferred and observed minimum pH within the 'training set', and in terms of root mean squared differences (predicted – observed) (RMSEP) estimated by cross-validation or bootstrap resampling techniques. The models were further tested using independent data from the literature representative of a wide geographical range.
3. The predictive power of the WA models was reasonable (RMSEP 0.40–0.44 pH units) in the training set and consistently better than that of the tolerance limit method. In contrast to the latter, the WA models were able to infer a minimum pH above 5.5, suggesting they could detect the early stages of acidification.
4. The WA models performed better than the tolerance limit method in inferring pH from the independent literature, further demonstrating the superiority and generality of the WA approach.
5. The weighted averaging technique could be an effective and widely applicable tool for contemporary biological monitoring and assessment using aquatic invertebrates.