Anthony Lehmann

Sample selection bias and presence‐only distribution models: implications for background and pseudo‐absence data

Most methods for modeling species distributions from occurrence records require additional data representing the range of environmental conditions in the modeled region. These data, called background or pseudo-absence data, are usually drawn at random from the entire region, whereas occurrence collection is often spatially biased toward easily accessed areas. Since the spatial bias generally results in environmental bias, the difference between occurrence collection and background sampling may lead to inaccurate models. To correct the estimation, we propose choosing background data with the same bias as occurrence data. We investigate theoretical and practical implications of this approach. Accurate information about spatial bias is usually lacking, so explicit biased sampling of background sites may not be possible. However, it is likely that an entire target group of species observed by similar methods will share similar bias. We therefore explore the use of all occurrences within a target group as biased background data. We compare model performance using target-group background and randomly sampled background on a comprehensive collection of data for 226 species from diverse regions of the world. We find that target-group background improves average performance for all the modeling methods we consider, with the choice of background data having as large an effect on predictive performance as the choice of modeling method. The performance improvement due to target-group background is greatest when there is strong bias in the target-group presence records. Our approach applies to regression-based modeling methods that have been adapted for use with occurrence data, such as generalized linear or additive models and boosted regression trees, and to Maxent, a probability density estimation method. We argue that increased awareness of the implications of spatial bias in surveys, and possible modeling remedies, will substantially improve predictions of species distributions.

Predicting species spatial distributions using presence-only data: a case study of native New Zealand ferns

Abstract Identification of areas containing high biological diversity (‘hotspots’) from species presence-only data has become increasingly important in species and ecosystem management when presence/absence data is unavailable. However, as presence-only data sets lack any information on absences and as they suffer from many biases associated with the ad hoc or non-stratified sampling, they are often assumed problematic and inadequate for most statistical modeling methods. In this paper, this supposition is investigated by comparing generalized additive models (GAM) fitted with 43 native New Zealand fern species presence/absence data, obtained from a survey of 19 875 forested plots, to GAM models and ecological niche factor analysis (ENFA) models fitted with identical presence data and, in the case of GAM models, computer generated ‘pseudo’ absences. By using the same presence data for all models, absence data is isolated as the varying factor allowing different techniques for generating ‘pseudo’ absences used in the GAM models to be analyzed and compared over three principal levels of investigation. GAM models fitted with an environmentally weighted distribution of ‘pseudo’ absences and ENFA models selected environmental variables more similar to the GAM presence/absence models than did the GAM models fitted with randomly distributed ‘pseudo’ absences. Average contributions for the GAM presence/absence model showed mean annual temperature and mean annual solar radiation as the most important factors followed by lithology. Comparisons of prediction results show GAM models incorporating an environmentally weighted distribution of ‘pseudo’ absences to be more closely correlated to the GAM presence/absence models than either the GAM models fitted with randomly selected ‘pseudo’ absences or the ENFA models. ENFA models were found to be the least correlated to the GAM presence/absence models. These latter models were also shown to give the most optimistic predictions overall, however, as ENFA predicts habitat suitability rather than probability of presence this was expected. Summation of species predictions used as a measure of species potential biodiversity ‘hotspots’ also shows ENFA models to give the highest and largest distribution of potential biodiversity. Additionally, GAM models incorporating ‘pseudo’ absences were more highly correlated to the GAM presence/absence model than was ENFA. However, ENFA identified more areas of potential biodiversity ‘hotspots’ similar to the GAM presence/absence model, than either GAM model incorporating ‘pseudo’ absences.

GRASP: generalized regression analysis and spatial prediction

We present generalized regression analysis and spatial prediction (GRASP) conceptually as a method for producing spatial predictions using statistical models, and introduce and demonstrate a specific implementation in Splus that facilitates the process. We put forward GRASP as a new name encapsulating an existing concept that aims at making spatial predictions using generalized regression analysis. Regression modeling is used to establish relationships between a response variable and a set of spatial predictors. The regression relationships are then used to make spatial predictions of the response. The GRASP process requires point measurements of the response, as well as regional coverages of predictor variables that are statistically (and preferably causally) important in determining the patterns of the response. This approach to spatial prediction is becoming more commonplace, and it is useful to define it as a general concept. For instance, GRASP could use a survey of the abundance of a species (the response), and existing spatial coverages of environmental (e.g. climate, landform) variables (the predictors) for a region. A multiple regression can be used to establish the statistical relationship between the species abundance and the environmental variables. These regression relationships can then be used to predict the species abundance from the environmental surfaces. This process defines relationships in environmental space and uses these relationships to predict in geographic space. We introduce GRASP (the implementation) as an interface and collection of functions in Splus designed to facilitate modern regression analysis and the use of these regressions for making spatial predictions. GRASP standardizes the modeling process and makes it more reproducible and less subjective, while preserving analysis flexibility. The set of functions provides a toolbox that allows quick and easy data checking, model building and evaluation, and calculation of predictions. The current version uses generalized additive models (GAMs), a modern non-parametric regression technique the advantages of which are discussed. We demonstrate the use of the GRASP implementation to model and predict the natural distributions of two components of New Zealand fern biodiversity: (1) the natural distribution of an icon species, silver fern (Cyathea dealbata); and (2) the natural pattern of total fern species richness. Key steps are demonstrated, including data preparation, options setting, data exploration, model building, model validation and interpretation, and spatial prediction.

Modeling spatial distribution of amphibian populations: a GIS approach based on habitat matrix permeability

Predictions of occurrence of two amphibian species, the common toad and the alpine newt, were made using information on land use surrounding breeding ponds. A geographical information system (GIS) was used to compile a landuse map, from which permeability estimates (friction) were derived. Potential migration zones based on friction and maximum migration distance were then modeled. Contacts between several migration zones suggest the potential for migration between ponds by adult individuals. The ability of the migration zones to enhance predictions of species occurrence was tested using generalized additive models (GAMs), and several landscape variables were selected as determinants of amphibian presence. The area of a migration zone and the number of ponds within that zone were positively related to both toad and newt presence, suggesting the importance of buffer habitats around each pond in amphibian conservation. Toad presence declined with cultivated field area and newt presence declined with vineyard area, suggesting the negative effect of agricultural activity on amphibians. The friction-based modeling approach improved the prediction of toad presence when compared to a more classical analysis of habitat composition within a circular zone centered on the focal pond. Prediction of newt presence was, however, less accurate than prediction of toad presence. Despite its exploratory nature and the subjectivity of permeability estimates, this study shows the usefulness of GIS in the functional analysis of a landscape, with potential applications in biological conservation. It also highlights the need for improving our knowledge of habitat use by animals.

Regression models for spatial prediction: their role for biodiversity and conservation

This paper is an introduction to a Special Issue on ‘regression models for spatial predictions’ published in Biodiversity and Conservation following an international workshop held in Switzerland in 2001 (http://leba.unige.ch/workshop). This introduction describes how the exponential growth in computing power has improved our ability to reach spatially explicit assessment of biodiversity and to develop cost-effective conservation management. New questions arising from these modern approaches are listed, while papers presenting examples of applications are briefly introduced.

GIS modeling of submerged macrophyte distribution using Generalized Additive Models

The distribution of submerged macrophytes in the littoral zone of Lake Geneva (Switzerland) was modeled from bathymetry, wave exposure, current strength, water quality, soil type and harvesting practice. Generalized Additive Models (GAM) were used to identify the responses of three Potamogeton species and Chara sp. to these environmental parameters. The maps of original data and the spatial predictions were processed in a Geographic Information System (GIS) database. The effect of the selected environmental variables on plant distribution is discussed in relation to species adaptive strategies. GIS and GAM appear as powerful tools to proceed from the description of species response curves to environmental gradients toward the spatial predictions of species distribution under changing environmental conditions.

Assessing New Zealand fern diversity from spatial predictions of species assemblages

The utility of explicit spatial predictions for biodiversity assessment is investigated with New Zealand fern flora. Distributions of 43 species were modelled from climatic and landform variables and predicted across New Zealand using generalised additive models (GAM). An original package of functions called generalised regression analysis and spatial prediction (GRASP) was developed to perform the analyses. On average, for the 43 models, the contributions of environmental variables indicate that mean annual temperature is the most important factor at this broad regional scale. Both annual solar radiation and its seasonality had higher correlations than temperature seasonality. Measures of water availability such as ratio of rainfall to potential evapotranspiration, air saturation deficit and soil water deficit presented significant contributions. Lithology was a better predictor than slope and drainage. These results are similar to those obtained from analyses of the distributions of New Zealand tree species and are consistent with the hypothesis that both tree and fern diversity are highest on sites conducive to high productivity. In order to identify hotspots of fern diversity, spatial predictions of individual species were summed up. The resulting map gave a very similar result to the direct prediction of their corresponding richness (number of species by plot out of 43 spp.). As a consequence, and where individual species models were not all available, the number of species within different species assemblages was directly modelled. Predicted richness hotspots of total species (out of 122 spp.), selected species (out of 43 and 21 spp.) and common species (out of 23 spp.) present very similar spatial patterns and are highly correlated. Richness of uncommon species (out of 39 spp.) was also accurately predicted, but presented a different spatial pattern. The number of rare species (out of 60 spp.) was not correctly modelled. Even though the lack of data for rare species clearly limits the application of this approach, fern community composition of more common species can be partially reconstructed from individual species predictions. This case study offers therefore a consistent approach not only for biodiversity hotspots identification, but also for setting targets to biodiversity assessment and restoration programs.

A parallelization framework for calibration of hydrological models

Large-scale hydrologic models are being used more and more in watershed management and decision making. Sometimes rapid modeling and analysis is needed to deal with emergency environmental disasters. However, time is often a major impediment in the calibration and application of these models. To overcome this, most projects are run with fewer simulations, resulting in less-than-optimum solutions. In recent years, running time-consuming projects on gridded networks or clouds in Linux systems has become more and more prevalent. But this technology, aside from being tedious to use, has not yet become fully available for common usage in research, teaching, and small to medium-size applications. In this paper we explain a methodology where a parallel processing scheme is constructed to work in the Windows platform. We have parallelized the calibration of the SWAT (Soil and Water Assessment Tool) hydrological model, where one could submit many simultaneous jobs taking advantage of the capabilities of modern PC and laptops. This offers a powerful alternative to the use of grid or cloud computing. Parallel processing is implemented in SWAT-CUP (SWAT Calibration and Uncertainty Procedures) using the optimization program SUFI2 (Sequential Uncertainty FItting ver. 2). We tested the program with large, medium, and small-size hydrologic models on several computer systems, including PCs, laptops, and servers with up to 24 CPUs. The performance was judged by calculating speedup, efficiency, and CPU usage. In each case, the parallelized version performed much faster than the non-parallelized version, resulting in substantial time saving in model calibration.

Vegetation and peat characteristics in the development of lowland restiad peat bogs, North Island, New Zealand

A chronosequence of restiad peat bogs (dominated by Restionaceae) in the lowland warm temperate zone of the Waikato region, North Island, New Zealand, was sampled to identify the major environmental determinants of vegetation pattern and dynamics. Agglomerative hierarchical classification of vegetation data from 69 plots in nine different-aged bogs, initiated from c. 600 to c. 15,000 cal yr BP, identified eight groups. Six of these groups formed a sequence from sedges through Empodisma minus, the main peatforming restiad species, to phases dominated by a second restiad species, Sporadanthus ferrugineus. The sequence reflected bog age and paralleled patterns of temporal succession over the last 15,000 years (from early successional sedges through mid-successional Empodisma to late successional Sporadanthus) derived from previous studies of plant macrofossils and microfossils in peat cores. This indicated that different-aged bogs in the Waikato region could be used to interpret temporal succession. The remaining two classificatory groups comprised plots from sites modified by drainage, fire, or weed invasion and currently dominated by non-restiad species. The relationships between environmental variables and the six groups representing restiad bog succession indicated that, as succession proceeds, von Post decomposition index and nutrients in the top 7.5 cm peat zone decrease. The most useful indicators of successional stage were von Post, total P, total N, and % ash. Environmental response curves of the dominant plant species separated the species along nutrient and peat decompositional gradients, with early successional species having wider potential environmental ranges than late successional species. Empodisma minus, a mid-successional species, also had a relatively wide environmental range, which probably contributes to its key role in restiad bog development.

A GIS approach of aquatic plant spatial heterogeneity in relation to sediment and depth gradients, Lake Geneva, Switzerland

A georeferenced database was constructed for a section of the littoral zone of Lake Geneva in order to investigate aquatic plant spatial heterogeneity at a community level, by exploring the relationships between species distribution and: (i) depth and sediment characteristics; and (ii) plant traits. This database includes information layers on vegetation, sediment and bathymetry. Vegetation was mapped from a digital photo interpretation coupled with field observation of species distribution and cover index. An abundance index was calculated for each species by multiplying the surface area of each stand by the species relative percentage and its cover index. Bathymetry was established from echosounder profiles and sediment maps were obtained from point interpolation between sediment core samples. Measured sediment characteristics include texture, nutrient and organic matter contents. Multiple regression models were developed in a related article (Lehmann et al., 1997) in order to estimate species biomass and maximum shoot length from depth and sediment characteristics. These models are applied in this article between the corresponding GIS layers to give a spatial estimation of these plant traits for three species of Potamogeton. Macrophyte stands, wherein a given species was dominant at more than 80%, were selected by a spatial selection together with the underlying depth and sediment characteristics and the estimated plant traits. When compared, P. lucens L. appeared to have the best competitive ability in relation to the observed plant traits, but it was dominated by a species more tolerant to wave disturbance in shallower depth (P. pectinatus L.) and a species more tolerant to the stress of light attenuation and nutrient availability in deeper sites (P. perfoliatus L.).