Relative frequency function models for species distribution modeling

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

Using species distribution models for IUCN Red Lists of threatened species

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

Reserve selection using nonlinear species distribution models

Reserve design is concerned with optimal selection of sites for new conservation areas. Spatial reserve design explicitly considers the spatial pattern of the proposed reserve network and the effects of that pattern on reserve cost and/or ability to maintain species there. The vast majority of reserve selection formulations have assumed a linear problem structure, which effectively means that the biological value of a potential reserve site does not depend on the pattern of selected cells. However, spatial population dynamics and autocorrelation cause the biological values of neighboring sites to be interdependent. Habitat degradation may have indirect negative effects on biodiversity in areas neighboring the degraded site as a result of, for example, negative edge effects or lower permeability for animal movement. In this study, I present a formulation and a spatial optimization algorithm for nonlinear reserve selection problems in grid-based landscapes that accounts for interdependent site values. The method is demonstrated using habitat maps and nonlinear habitat models for threatened birds in the Netherlands, and it is shown that near-optimal solutions are found for regions consisting of up to hundreds of thousands grid cells, a landscape size much larger than those commonly attempted even with linear reserve selection formulations.     

Using species abundance distribution models and diversity indices for biogeographical analyses

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

Integrating species distribution models (SDMs) and phylogeography for two species of Alpine Primula

The major intention of the present study was to investigate whether an approach combining the use of niche-based palaeodistribution modeling and phylo-geography would support or modify hypotheses about the Quaternary distributional history derived from phylogeographic methods alone. Our study system comprised two closely related species of Alpine Primula. We used species distribution models based on the extant distribution of the species and last glacial maximum (LGM) climate models to predict the distribution of the two species during the LGM. Phylogeographic data were generated using amplified fragment length polymorphisms (AFLPs). In Primula hirsuta, models of past distribution and phylogeographic data are partly congruent and support the hypothesis of widespread nunatak survival in the Central Alps. Species distribution models (SDMs) allowed us to differentiate between alpine regions that harbor potential nunatak areas and regions that have been colonized from other areas. SDMs revealed that diversity is a good indicator for nunataks, while rarity is a good indicator for peripheral relict populations that were not source for the recolonization of the inner Alps. In P. daonensis, palaeo-distribution models and phylogeographic data are incongruent. Besides the uncertainty inherent to this type of modeling approach (e.g., relatively coarse 1-km grain size), disagreement of models and data may partly be caused by shifts of ecological niche in both species. Nevertheless, we demonstrate that the combination of palaeo-distribution modeling with phylogeographical approaches provides a more differentiated picture of the distributional history of species and partly supports (P. hirsuta) and partly modifies (P. daonensis and P. hirsuta) hypotheses of Quaternary distributional history. Some of the refugial area indicated by palaeodistribution models could not have been identified with phylogeographic data.     

Using species distribution models to identify suitable areas for biofuel feedstock production

The 2007 Energy Independence and Security Act mandates a five‐fold increase in US biofuel production by 2022. Given this ambitious policy target, there is a need for spatially explicit estimates of landscape suitability for growing biofuel feedstocks. We developed a suitability modeling approach for two major US biofuel crops, corn (Zea mays) and switchgrass (Panicum virgatum), based upon the use of two presence‐only species distribution models (SDMs): maximum entropy (Maxent) and support vector machines (SVM). SDMs are commonly used for modeling animal and plant distributions in natural environments, but have rarely been used to develop landscape models for cultivated crops. AUC, Kappa, and correlation measures derived from test data indicate that SVM slightly outperformed Maxent in modeling US corn production, although both models produced significantly accurate results. When compared with results from a mechanistic switchgrass model recently developed by Oak Ridge National Laboratory (ORNL), SVM results showed higher correlation than Maxent results with models fit using county‐scale point inputs of switchgrass production derived from expert opinion estimates. However, Maxent results for an alternative switchgrass model developed with point inputs from research trial sites showed higher correlation to the ORNL model than the corresponding results obtained from SVM. Further analysis indicates that both modeling approaches were effective in predicting county‐scale increases in corn production from 2006 to 2007, a time period in which US corn production increased by 24%. We conclude that presence‐only methods are a powerful first‐cut tool for estimating relative land suitability across geographic regions in which candidate biofuel feedstocks can be grown, and may also provide important insight into potential land‐use change patterns likely to be associated with increased biofuel demand.     

Irrigation as an important factor in species distribution models

Species distribution models (SDMs) that employ climatic variables are widely used to predict potential distribution of invasive species. However, climatic variables derived from climate datasets do not account for anthropogenic influences on microclimate. Irrigation is a major anthropogenic activity that influences microclimate conditions and alters the distribution of species in anthropogenic landuses. SDM-based studies appear to ignore the effects of irrigation on microclimatic conditions. This study incorporated irrigation as a correction to precipitation data, to improve the predictive capacity of SDM. As a case study, we examined a SDM of Wasmannia auropunctata, an invasive species that originates in South and Central America, which has invaded tropical and subtropical regions around the world. The potential distribution of W. auropunctata was predicted using Maxent. The model was built based on climatic variables and species records from non-irrigated sites in the native range and then projected on a global scale. Invasive species records were used to evaluate the performance of the model. Precipitation-related variables were modified to approximate actual water input in irrigated areas. Precipitation correction relied on an estimate of irrigation inputs. The model with irrigation correction performed better than the corresponding model without correction, on a global scale and when it was examined in five different geographical regions of the model. These results demonstrate the importance of irrigation correction for assessing the distribution of W. auropunctata in various geographical regions. Accounting for irrigation is expected to improve SDMs for a variety of species.     

Continuous versus discrete single species population models with adjustable reproductive strategies

We investigate population models with both continuous and discrete elements. Birth is assumed to occur at discrete instants of time whereas death and competition for resources and space occur continuously during the season. We compare the dynamics of such discrete-continuous hybrid models with the dynamics of purely discrete models where within-season mortality and competition are modelled directly as discrete events. We show that non-monotone discrete single-species maps cannot be derived from unstructured competition processes. This result is well known in the case of fixed reproductive strategies and our results extend this to the case of adjustable reproductive strategies. It is also shown that the most commonly used non-monotone discrete maps can be derived from structured competition processes.     

Swarming strategies for cooperative species

In this paper, we propose a model to investigate the relative efficiency of simple swarming strategies based on the interplay between spontaneous and recruitment-based emigration. We conduct a dynamical study of the model which combines inverse density dependence, saturation effects and induced vs. diffusion-like population transfer. The influence of the most relevant parameters is explored on a systematic basis, and transition values for which qualitative changes occur in the system's behaviour are given. The model is then used to study colonization of a multiple sites environment, as well as confrontation between species featuring different swarming strategies. Simulation results indicate that cooperative organisms should have an interest in evolving recruitment-based emigration. The corresponding population transfer patterns prove more efficient in invading new territories, eliminating competitors in the process. We suggest that this advantage could have promoted a simple form of coordinated swarming in species featuring a primitive type of cooperation.     

Assessing the accuracy of species distribution models to predict amphibian species richness patterns

1. Evaluating the distribution of species richness where biodiversity is high but has been insufficiently sampled is not an easy task. Species distribution modelling has become a useful approach for predicting their ranges, based on the relationships between species records and environmental variables. Overlapping predictions of individual distributions could be a useful strategy for obtaining estimates of species richness and composition in a region, but these estimates should be evaluated using a proper validation process, which compares the predicted richness values and composition with accurate data from independent sources. 2. In this study, we propose a simple approach to estimate model performance for several distributional predictions generated simultaneously. This approach is particularly suitable when species distribution modelling techniques that require only presence data are used. 3. The individual distributions for the 370 known amphibian species of Mexico were predicted using maxent to model data on their known presence (66,113 presence-only records). Distributions were subsequently overlapped to obtain a prediction of species richness. Accuracy was assessed by comparing the overall species richness values predicted for the region with observed and predicted values from 118 well-surveyed sites, each with an area of c. 100 km(2), which were identified using species accumulation curves and nonparametric estimators. 4. The derived models revealed a remarkable heterogeneity of species richness across the country, provided information about species composition per site and allowed us to obtain a measure of the spatial distribution of prediction errors. Examining the magnitude and location of model inaccuracies, as well as separately assessing errors of both commission and omission, highlights the inaccuracy of the predictions of species distribution models and the need to provide measures of uncertainty along with the model results. 5. The combination of a species distribution modelling method like maxent and species richness estimators offers a useful tool for identifying when the overall pattern provided by all model predictions might be representing the geographical patterns of species richness and composition, regardless of the particular quality or accuracy of the predictions for each individual species.     

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

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

Using species distributions models for designing conservation strategies of Tropical Andean biodiversity under climate change

Biodiversity in the Tropical Andes is under continuous threat from anthropogenic activities. Projected changes in climate will likely exacerbate this situation. Using species distribution models, we assess possible future changes in the diversity and climatic niche size of an unprecedented number of species for the region. We modeled a broad range of taxa (11,012 species of birds and vascular plants), including both endemic and widespread species and provide a comprehensive estimation of climate change impacts on the Andes. We find that if no dispersal is assumed, by 2050s, more than 50% of the species studied are projected to undergo reductions of at least 45% in their climatic niche, whilst 10% of species could be extinct. Even assuming unlimited dispersal, most of the Andean endemics (comprising ∼5% of our dataset) would become severely threatened (>50% climatic niche loss). While some areas appear to be climatically stable (e.g. Pichincha and Imbabura in Ecuador; and Nariño, Cauca, Valle del Cauca and Putumayo in Colombia) and hence depict little diversity loss and/or potential species gains, major negative impacts were also observed. Tropical high Andean grasslands (páramos and punas) and evergreen montane forests, two key ecosystems for the provision of environmental services in the region, are projected to experience negative changes in species richness and high rates of species turnover. Adapting to these impacts would require a landscape-network based approach to conservation, including protected areas, their buffer zones and corridors. A central aspect of such network is the implementation of an integrated landscape management approach based on sustainable management and restoration practices covering wider areas than currently contemplated.     

Behavioural context of multi-scale species distribution models assessed by radio-tracking

Incorporating ecological processes and animal behaviour into Species Distribution Models (SDMs) is difficult. In species with a central resting or breeding place, there can be conflict between the environmental requirements of the ‘central place’ and foraging habitat. We apply a multi-scale SDM to examine habitat trade-offs between the central place, roost sites, and foraging habitat in Myotis nattereri. We validate these derived associations using habitat selection from behavioural observations of radio-tracked bats. A Generalised Linear Model (GLM) of roost occurrence using land cover variables with mixed spatial scales indicated roost occurrence was positively associated with woodland on a fine scale and pasture on a broad scale. Habitat selection of radio-tracked bats mirrored the SDM with bats selecting for woodland in the immediate vicinity of individual roosts but avoiding this habitat in foraging areas, whilst pasture was significantly positively selected for in foraging areas. Using habitat selection derived from radio-tracking enables a multi-scale SDM to be interpreted in a behavioural context. We suggest that the multi-scale SDM of M. nattereri describes a trade-off between the central place and foraging habitat. Multi-scale methods provide a greater understanding of the ecological processes which determine where species occur and allow integration of behavioural processes into SDMs. The findings have implications when assessing the resource use of a species at a single point in time. Doing so could lead to misinterpretation of habitat requirements as these can change within a short time period depending on specific behaviour, particularly if detectability changes depending on behaviour.