Delineating environmental envelopes to improve mapping of species distributions, via a hurdle model with CART &/or MaxEnT

Species distribution modelling (SDM) typically analyses species’ presence together with some form of absence information. Ideally absences comprise observations or are inferred from comprehensive sampling. When such information is not available, then pseudo-absences are often generated from the background locations within the study region of interest containing the presences, or else absence is implied through the comparison of presences to the whole study region, e.g. as is the case in Maximum Entropy (MaxEnt) or Poisson point process modelling. However, the choice of which absence information to include can be both challenging and highly influential on SDM predictions (e.g. Oksanen and Minchin, 2002). In practice, the use of pseudo- or implied absences often leads to an imbalance where absences far outnumber presences. This leaves analysis highly susceptible to ‘naughty-noughts’: absences that occur beyond the envelope of the species, which can exert strong influence on the model and its predictions (Austin and Meyers, 1996). Also known as ‘excess zeros’, naughty noughts can be estimated via an overall proportion in simple hurdle or mixture models (Martin et al., 2005). However, absences, especially those that occur beyond the species envelope, can often be more diverse than presences. Here we consider an extension to excess zero models. The two-staged approach first exploits the compartmentalisation provided by classification trees (CTs) (as in O’Leary, 2008) to identify multiple sources of naughty noughts and simultaneously delineate several species envelopes. Then SDMs can be fit separately within each envelope, and for this stage, we examine both CTs (as in Falk et al., 2014) and the popular MaxEnt (Elith et al., 2006). We introduce a wider range of model performance measures to improve treatment of naughty noughts in SDM. We retain an overall measure of model performance, the area under the curve (AUC) of the Receiver-Operating Curve (ROC), but focus on its constituent measures of false negative rate (FNR) and false positive rate (FPR), and how these relate to the threshold in the predicted probability of presence that delimits predicted presence from absence. We also propose error rates more relevant to users of predictions: false omission rate (FOR), the chance that a predicted absence corresponds to (and hence wastes) an observed presence, and the false discovery rate (FDR), reflecting those predicted (or potential) presences that correspond to absence. A high FDR may be desirable since it could help target future search efforts, whereas zero or low FOR is desirable since it indicates none of the (often valuable) presences have been ignored in the SDM. For illustration, we chose Bradypus variegatus, a species that has previously been published as an exemplar species for MaxEnt, proposed by Phillips et al. (2006). We used CTs to increasingly refine the species envelope, starting with the whole study region (E0), eliminating more and more potential naughty noughts (E1–E3). When combined with an SDM fit within the species envelope, the best CT SDM had similar AUC and FPR to the best MaxEnt SDM, but otherwise performed better. The FNR and FOR were greatly reduced, suggesting that CTs handle absences better. Interestingly, MaxEnt predictions showed low discriminatory performance, with the most common predicted probability of presence being in the same range (0.00-0.20) for both true absences and presences. In summary, this example shows that SDMs can be improved by introducing an initial hurdle to identify naughty noughts and partition the envelope before applying SDMs. This improvement was barely detectable via AUC and FPR yet visible in FOR, FNR, and the comparison of predicted probability of presence distribution for pres/absence.

Role of behaviour in biological invasions and species distributions; lessons from interactions between the invasive Gammarus pulex and the native G-duebeni (Crustacea : Amphipoda)

In attempting to understand the distributions of both introduced species and the native species on which they impact, there is a growing trend to integrate studies of behaviour with more traditional life history/ecological approaches. The question of what mechanisms drive the displacement of the freshwater amphipod Gammarus duebeni by the often introduced G pulex is presented as a case study Patterns of displacement are well documented throughout Europe, but the speed and direction of displacement between these species can be varied. From early studies proposing interspecific competition as causal in these patterns, I review research progress to date. I show there has been no evidence for interspecific competition operating, other than the field patterns themselves, a somewhat tautological argument. Rather, the increased recognition of behavioural attributes with respect to the cannibalistic and predatory nature of these species gave rise to a series of studies unravelling the processes driving field patterns. Both species engage in 'intraguild predation' (IGP), with moulting females particularly vulnerable to predation by congeneric males. G pulex is more able both to engage in and avoid this interaction with G duebeni. However, several factors mediate the strength and asymmetry of this IGP, some biotic (e.g. parasitism) and others abiotic (e.g. water chemistry). Further, a number of alternative hypotheses that may account for the displacement (hybridization; parasite transmission) have been tested and rejected. While interspecific competition has been modelled mathematically and found to be a weak interaction relative to IGP, mechanisms of competition between these Gammarus species remain largely untested empirically. Since IGP may be finely balanced in some circumstances, I conclude that the challenge to detect interspecific competition remains and we require assessment of its role, if any, in the interaction between these species. Appreciation of behavioural attributes and their mediation should allow us to more fully understand, and perhaps predict, species introductions and resultant distributions.

A new statistical framework for the quantification of covariate associations with species distributions

Identifying processes that shape species geographical ranges is a prerequisite for understanding environmental change. Currently, species distribution modelling methods do not offer credible statistical tests of the relative influence of climate factors and typically ignore other processes (e.g. biotic interactions and dispersal limitation). We use a hierarchical model fitted with Markov Chain Monte Carlo to combine ecologically plausible niche structures using regression splines to describe unimodal but potentially skewed response terms. We apply spatially explicit error terms that account for (and may help identify) missing variables. Using three example distributions of European bird species, we map model results to show sensitivity to change in each covariate. We show that the overall strength of climatic association differs between species and that each species has considerable spatial variation in both the strength of the climatic association and the sensitivity to climate change. Our methods are widely applicable to many species distribution modelling problems and enable accurate assessment of the statistical importance of biotic and abiotic influences on distributions.

Fractal species distributions do not produce power-law species-area relationships

We derive the species-area relationship (SAR) expected from an assemblage of fractally distributed species. If species have truly fractal spatial distributions with different fractal dimensions, we show that the expected SAR is not the classical power-law function, as suggested recently in the literature. This analytically derived SAR has a distinctive shape that is not commonly observed in nature: upward-accelerating richness with increasing area (when plotted on log-log axes). This suggests that, in reality, most species depart from true fractal spatial structure. We demonstrate the fitting of a fractal SAR using two plant assemblages (Alaskan trees and British grasses). We show that in both cases, when modelled as fractal patterns, the modelled SAR departs from the observed SAR in the same way, in accord with the theory developed here. The challenge is to identify how species depart from fractality, either individually or within assemblages, and more importantly to suggest reasons why species distributions are not self-similar and what, if anything, this can tell us about the spatial processes involved in their generation.

Scenario-based assessment of future land use change on butterfly species distributions

Species distribution models (SDMs) are increasingly used to predict environmentally induced range shifts of habitats of plant and animal species. Consequently SDMs are valuable tools for scientifically based conservation decisions. The aims of this paper are (1) to identify important drivers of butterfly species persistence or extinction, and (2) to analyse the responses of endangered butterfly species of dry grasslands and wetlands to likely future landscape changes in Switzerland. Future land use was represented by four scenarios describing: (1) ongoing land use changes as observed at the end of the last century; (2) a liberalisation of the agricultural markets; (3) a slightly lowered agricultural production; and (4) a strongly lowered agricultural production. Two model approaches have been applied. The first (logistic regression with principal components) explains what environmental variables have significant impact on species presence (and absence). The second (predictive SDM) is used to project species distribution under current and likely future land uses. The results of the explanatory analyses reveal that four principal components related to urbanisation, abandonment of open land and intensive agricultural practices as well as two climate parameters are primary drivers of species occurrence (decline). The scenario analyses show that lowered agricultural production is likely to favour dry grassland species due to an increase of non-intensively used land, open canopy forests, and overgrown areas. In the liberalisation scenario dry grassland species show a decrease in abundance due to a strong increase of forested patches. Wetland butterfly species would decrease under all four scenarios as their habitats become overgrown

Pond-Breeding Amphibian Species Distributions in a Beaver-Modified Landscape, Acadia National Park, Mount Desert Island, Maine

In order to maintain pond-breeding amphibian species richness, it is important to understand how both natural and anthropogenic disturbances affect species assemblages and individual species distributions both at the scale of individual ponds and at a larger landscape scale. The goal of this project was to investigate what characteristics of ponds and the surrounding wetland landscape were most effective in predicting pond-breeding species richness and the individual occurrence of wood frog (Rana sylvatica), bullfrog (Rana catesbeiana) and pickerel frog (Rana palustris) breeding sites in a beaver-modified landscape and how this landscape has changed over time. The wetland landscape of Acadia National Park was historically modified by the natural disturbance cycles of beaver (Castor cazadensis), and since their reintroduction to the island in 1921, beaver have played a large role in creating and maintaining palustrine wetlands. In 2000 and 2001, I studied pond-breeding amphibian assemblages at 71 palustrine wetlands in Acadia National Park, Mount Desert Island, Maine. I determined breeding presence of 7 amphibian species and quantified 15 variables describing local pond conditions and characteristics of the wetland landscape. I developed a priori models to predict sites with high amphibian species and used model selection with Akaike's Information Criterion (AIC) to identify important variables. Single species models were also developed to predict wood frog, bullfrog and pickerel frogs breeding presence. The variables for wetland connectivity by stream corridors and the presence of beaver disturbance were the most effective variables to predict sites with high amphibian richness. Wood frog breeding was best predicted by local scale variables describing temporary, fishless wetlands and the absence of active beaver disturbance. Abandoned beaver sites provided wood frog breeding habitat (70%) in a similar proportion to that found in non beaver-influenced sites (79%). In contrast, bullfrog breeding presence was limited to active beaver wetlands with fish and permanent water, and 80% of breeding sites were large (≥2ha in size). Pickerel frog breeding site selection was predicted best by the connectivity of sites in the landscape by stream corridors. Models including the presence of beaver disturbance, greater wetland perimeter and greater depth were included in the confidence set of pickerel frog models but showed considerably less support. Analysis of historic aerial photographs showed an 89% increase in the total number of ponded wetlands available in the landscape between the years of 1944 and 1997. Beaver colonization generally converted forested wetlands and riparian areas to open water and emergent wetlands. Temporal colonization of beaver wetlands favored large sites low in the watersheds and sites that were impounded later were generally smaller, higher in the watershed, and more likely to be abandoned. These results suggest that beaver have not only increased the number of available breeding sites in the landscape for pond-breeding amphibians, but the resulting mosaic of active and abandoned beaver wetlands also provides suitable breeding habitat for species with differing habitat requirements.

Mapping species distributions : A comparison of skilled naturalist and lay citizen science recording

Acknowledgements We are grateful to Elaine O’Mahony, Imogen Pearce, Richard Comont, Anthony McCluskey and other BBCT staff for the many hours of BeeWatch species identification and for all people who submitted sightings to BeeWatch, OPAL, BWARS and the various local recording schemes and societies. We thank the NBN for allowing us to download the bumblebee records without strings attached, and the Essex, Greater London, Cumbria and Sussex based recording centres for providing records upon request. Finally, we are indebted to Tom August and two anonymous reviewers for their valuable critique on an earlier version of this work.

Climate-driven shifts in species' distributions may exacerbate the impacts of storm disturbances on North-east Atlantic kelp forests

Physical disturbance through wave action is a major determinant of kelp forest structure. The North-east Atlantic storm season of 2013–14 was unusually severe; the south coast of the UK was subjected to 6 of the 12 most intense storms recorded in the past 5 years. Inshore significant wave heights and periods exceeded 7 m and 13 s with two storms classified as ‘1-in-30 year’ events. We examined the impacts of the storm season on kelp canopies at three study sites. Monospecific canopies comprising Laminaria hyperborea were unaffected by storm disturbance. However, at one study site a mixed canopy comprising Laminaria ochroleuca, Saccharina latissima and L. hyperborea was significantly altered by the storms, due to decreased abundances of the former two species. Quantification of freshly severed stipes suggested that the ‘warm water’ kelp L. ochroleuca was more susceptible to storm damage than L. hyperborea. Overall, kelp canopies were highly resistant to storm disturbance because of the low vulnerability of L. hyperborea to intense wave action. However, if climate-driven shifts in kelp species distributions result in more mixed canopies, as predicted, then resistance to storm disturbance may be eroded.

Climate-driven shifts in species' distributions may exacerbate the impacts of storm disturbances on North-east Atlantic kelp forests

Physical disturbance through wave action is a major determinant of kelp forest structure. The North-east Atlantic storm season of 2013–14 was unusually severe; the south coast of the UK was subjected to 6 of the 12 most intense storms recorded in the past 5 years. Inshore significant wave heights and periods exceeded 7 m and 13 s with two storms classified as ‘1-in-30 year’ events. We examined the impacts of the storm season on kelp canopies at three study sites. Monospecific canopies comprising Laminaria hyperborea were unaffected by storm disturbance. However, at one study site a mixed canopy comprising Laminaria ochroleuca, Saccharina latissima and L. hyperborea was significantly altered by the storms, due to decreased abundances of the former two species. Quantification of freshly severed stipes suggested that the ‘warm water’ kelp L. ochroleuca was more susceptible to storm damage than L. hyperborea. Overall, kelp canopies were highly resistant to storm disturbance because of the low vulnerability of L. hyperborea to intense wave action. However, if climate-driven shifts in kelp species distributions result in more mixed canopies, as predicted, then resistance to storm disturbance may be eroded.

fuzzySim: Fuzzy similarity in species distributions

fuzzySim is an R package for calculating fuzzy similarity in species occurrence patterns. It includes functions for data preparation, such as converting species lists (long format) to presence-absence tables (wide format), obtaining unique abbreviations of species names, or transposing (parts of) complex data frames; and sample data sets for providing practical examples. It can convert binary presence-absence to fuzzy occurrence data, using e.g. trend surface analysis, inverse distance interpolation or prevalence-independent environmental favourability modelling, for multiple species simultaneously. It then calculates fuzzy similarity among (fuzzy) species distributions and/or among (fuzzy) regional species compositions. Currently available similarity indices are Jaccard, Sørensen, Simpson, and Baroni-Urbani & Buser.