Ecography

AimClimate is an essential element of species niche estimates in many current ecological applications such as species distribution models (SDMs). Climate predictors are often used in the form of long-term mean values. Yet, climate can also be described as spatial or temporal variability for variables like temperature or precipitation. Such variability, spatial or temporal, offers additional insights into niche properties. Here, we test to what degree spatial variability and long-term temporal variability in temperature and precipitation improve SDM predictions globally. LocationGlobal. Time period1979-2013 Major taxa studiesMammal, Amphibians, Reptiles MethodsWe use three different SDM algorithms, and a set of 833 amphibian, 779 reptile, and 2211 mammal species to quantify the effect of spatial and temporal climate variability in SDMs. All SDMs were cross-validated and accessed for their performance using the Area under the Curve (AUC) and the True Skill Statistic (TSS). ResultsMean performance of SDMs with climatic means as predictors was TSS=0.71 and AUC=0.90. The inclusion of spatial variability offers a significant gain in SDM performance (mean TSS=0.74, mean AUC=0.92), as does the inclusion of temporal variability (mean TSS=0.80, mean AUC=0.94). Including both spatial and temporal variability in SDMs shows similarly high TSS and AUC scores. Main conclusionsAccounting for temporal rather than spatial variability in climate improved the SDM prediction especially in exotherm groups such as amphibians and reptiles, while for endotermic mammals no such improvement was observed. These results indicate that more detailed information about temporal climate variability offers a highly promising avenue for improving niche estimates and calls for a new set of standard bioclimatic predictors in SDM research.

Predicting novel ranges of non-native species is a critical component to understanding the biosecurity threat posed by pests and diseases on economic, environmental and social assets. Species distribution models (SDMs) are often employed to predict the potential ranges of exotic pests and diseases in novel environments and geographic space. To date, researchers have focused on model complexity, data available for model fitting, the size of the geographic area to be considered and how the choice of model impacts results. These investigations are coupled with considerable examination of how model evaluation methods and test scores are influenced by these choices. An area that remains under-discussed is how to account for uncertainty in predictor selection while also selecting variables that increase a models ability to predict to novel environments (model transferability). Here we propose a novel method to finesse this problem by using multiple simple (bivariate) models to search for the candidate sets of predictor variables that are likely to produce transferable models. Once identified, each set is then used to construct 2-dimensional niche envelopes of pest presence/absence. This process ultimately results in a number of possible models that can be used to predict pest potential distributions, however, rather than relying on a single model, we ensemble these models in an attempt to account for predictor uncertainty. We apply this method to both virtual species and real species data, and find that it generally performs well against conventional approaches for statistically fitting numerous variables in a single model. While our methods only consider simple ecological relationships of species to environmental predictors, they allow for increased model transferability because they reduce the likelihood of over-fitting and collinearity issues. Simple models are also likely to be more conservative (over-predict potential distributions) relative to complex models containing many covariates - making them more appropriate for risk-averse applications such as biosecurity. The approach we have explored transforms a model selection problem, for which there is no true correct answer amongst the typically distal covariates on offer, to one of model uncertainty. We argue that increased model transferability at the expense of model interpretation is perhaps more important for effective rapid predictions and management of non-native species and biological invasions.

SDM describes a family of methods aiming to predict the geographic distribution of organisms using environmental data such as climate variables. It is a versatile tool in estimating ecological communities and interactions both spatially and through time. However, it has had limited utility in predicting the geographic distribution of fossil organisms. Due to preservation and sampling biases, fossil data does not satisfy the assumptions of species distribution models. Here is presented an analysis proposing a new methodology, which substitutes the conventional pseudoabsence data for fossil occurrences from non-target species. This approach eliminates variation in preservation and sampling, and returns a SDM which performs better than a conventional example. This model concludes that the ceratopsian Triceratops may have been widespread across North America, and beyond the region where its fossils have been recovered. The geographic distribution of Triceratops appears to have been governed by seasonality in temperature and temperature of the coldest month.

Metacommunity structure can be summarised by fitting joint species distribution models and partitioning the variance explained into environmental, spatial and codistribution components. Here we identify how these components respond through time with directed environmental change and propose this as an indicator of sustained directional pressure. Through simulations, we identify how declines in the codistribution component can diagnose ecological breakdown, while rises in environmental and spatial components may indicate losses in peripheral areas and dispersal limitations. We test the method in two well-studied systems. Butterflies are known to be strongly responding to climate change, and we show that over 21 years the codistribution component declines for butterfly communities in southern England. By contrast, birds in the same region are under less climate pressure and, despite high occupancy turnover, show minimal change in metacommunity structure. The approach has high potential to summarise and compare the impact of external drivers on whole communities.

AimPaleoclimate reconstructions have enhanced our understanding of how past climates may have shaped present-day biodiversity. We hypothesize that habitat stability in historical Afrotropical refugia played a major role in the habitat suitability and persistence of chimpanzees (Pan troglodytes) during the late Quaternary. We aimed to build a dynamic model of changing habitat suitability for chimpanzees at fine spatio-temporal scales to provide a new resource for understanding their ecology, behaviour and evolution. LocationAfrotropics. TaxonChimpanzee (Pan troglodytes), including all four subspecies (P. t. verus, P. t. ellioti, P. t. troglodytes, P. t. schweinfurthii). MethodsWe used downscaled bioclimatic variables representing monthly temperature and precipitation estimates, historical human population density data and an extensive database of georeferenced presence points to infer chimpanzee habitat suitability at 62 paleoclimatic time periods across the Afrotropics based on ensemble species distribution models. We mapped habitat stability over time using an approach that accounts for dispersal between time periods, and compared our modelled stability estimates to existing knowledge of Afrotropical refugia. Our models cover a spatial resolution of 0.0467 degrees (approximately 5.19 km2 grid cells) and a temporal resolution of every 1,000-4,000 years dating back to the Last Interglacial (120,000 BP). ResultsOur results show high habitat stability concordant with known historical forest refugia across Africa, but suggest that their extents are underestimated for chimpanzees. We provide the first fine-grained dynamic map of historical chimpanzee habitat suitability since the Last Interglacial which is suspected to have influenced a number of ecological-evolutionary processes, such as the emergence of complex patterns of behavioural and genetic diversity. Main ConclusionsWe provide a novel resource that can be used to reveal spatio-temporally explicit insights into the role of refugia in determining chimpanzee behavioural, ecological and genetic diversity. This methodology can be applied to other taxonomic groups and geographic areas where sufficient data are available.

AimUnderstanding whether invasive species retain or shift their ecological niches has traditionally relied on scalar overlap metrics that quantify the magnitude of niche change, but not its structure. Here, we test whether biological invasions involve a reorganisation of the environmental axes along which native and invasive ranges are differentiated, and whether the dominant axes of this reorganisation are consistently associated with invasion pathway type (intercontinental vs. within-continent). LocationGlobal (North America, Europe, Africa, Asia, Australasia). Time periodContemporary (environmental variables representing long-term averages, 1980-2021). Major taxa studiedFreshwater crayfish (Decapoda: Astacidea): Procambarus clarkii, Faxonius limosus, Pacifastacus leniusculus, Faxonius virilis, Faxonius rusticus. MethodsWe analysed native and invasive occurrences for five globally important crayfish invaders using [~]400 hydrologically resolved environmental variables from the Global Crayfish Database of Geospatial Traits. Classification models were used to quantify environmental differentiation between native and invasive ranges, and feature contributions were aggregated by environmental domain (climate, topography, soil, land cover). Patterns were evaluated across intercontinental and within-continent invasion pathways and assessed for robustness using cross-validation, permutation tests, sample-size sensitivity, and comparisons with classical niche overlap metrics. ResultsNative and invasive occurrences were consistently distinguishable across all species (accuracy 96.5-99.9%). A pathway-dependent pattern emerged: intercontinental invaders were primarily differentiated along climatic dimensions (58-76% of model importance), whereas within-continent invaders showed a more balanced contribution of climatic and topographic variables ([~]42% each), including strong signals from river network position. This contrast was stable across cross-validation folds (SD < 1.6%), and supported by permutation tests (P = 0.001). Classical niche overlap metrics (Schoeners D = 0.30-0.62) did not capture this qualitative distinction. Main conclusionsBiological invasions involve not only changes in niche position but a reorganisation of the environmental axes that distinguish species distributions. Our results suggest that the dominant axes of this reorganisation differ systematically with invasion pathway, reflecting whether species encounter novel climatic regimes or primarily shift within existing climatic space along topographic and network-position gradients. By resolving which environmental dimensions underpin native-invasive differentiation, this approach provides a complementary perspective to scalar overlap metrics and a basis for more mechanistic interpretations of invasion processes.

AimTo determine the degree to which assemblages of planktonic foraminifera track thermal conditions. LocationThe worlds oceans. Time periodThe last 700,000 years of glacial-interglacial cycles. Major taxa studiedPlanktonic foraminifera. MethodsWe investigate assemblage dynamics in planktonic foraminifera in response to temperature changes using a global dataset of Quaternary planktonic foraminifera, together with a coupled Atmosphere-Ocean General Circulation Model (AOGCM) at 8,000-year resolution. We use thermal deviance to assess assemblage responses to climate change, defined as the difference between the temperature at a given location and the bio-indicated temperature (i.e., the abundance-weighted average of estimated temperature optima for the species present). ResultsAssemblages generally tracked annual mean temperature changes through compositional turnover, but large thermal deviances are evident under certain conditions. The coldest-adapted species persisted in polar regions during warming but were not joined by additional immigrants, resulting in decreased assemblage turnover with warming. The warmest-adapted species persisted in equatorial regions during cooling. Assemblages at mid latitudes closely tracked temperature cooling and showed a modest increase in thermal deviance with warming. Main conclusionsPlanktonic foraminiferal assemblages were generally able to track or endure temperature changes: as climate warmed or cooled, bio-indicated temperature also became warmer or cooler, although to a variable degree. At polar sites under warming and at equatorial sites under cooling, the change in temperature predicted from assemblage composition was less than, or even opposite to, expectations based on estimated environmental change. Nevertheless, all species survived the accumulation of thermal deviance--a result that highlights the resilience and inertia of planktonic foraminifera on an assemblage level to the last 700,000 years of climate change, which might be facilitated by broad thermal tolerances or depth shifts.

Assessing the extinction risk of species through the IUCN Red List is key to guiding conservation policies and reducing biodiversity loss. This process is resource-demanding, however, and requires a continuous update which becomes increasingly difficult as new species are added to the IUCN Red List. The use of automatic methods, such as comparative analyses to predict species extinction risk, can be an efficient alternative to maintaining up to date assessments. Using amphibians as a study group, we predict which species were more likely to change status, in order to suggest species that should be prioritized for reassessment. We used species traits, environmental variables, and proxies of climate and land-use change as predictors of the IUCN Red List category of species. We produced an ensemble prediction of IUCN Red List categories by combining four different model algorithms: Cumulative Link Models (CLM), phylogenetic Generalized Least Squares (PGLS), Random Forests (RF), Neural Networks (NN). By comparing IUCN Red List categories with the ensemble prediction, and accounting for uncertainty among model algorithms, we identified species that should be prioritized for future reassessments due to high prediction versus observation mismatch. We found that CLM and RF performed better than PGLS and NN, but there was not a clear best algorithm. The most important predicting variables across models were species range size, climate change, and landuse change. We propose ensemble modelling of extinction risk as a promising tool for prioritizing species for reassessment while accounting for inherent models uncertainty.

The 19 standard bioclimatic variables available from the WorldClim dataset are some of the most used data in ecology and organismal biology. It is well known that many of the variables are correlated with each other, suggesting there are fewer than 19 independent dimensions of information in them. But how much information is there? Here I explore the 19 WorldClim bioclimatic variables from the perspective of the manifold hypothesis: that many high dimensional datasets are actually confined to a lower dimensional manifold embedded in an ambient space. Using a state-of-the-art generative probabilistic model (variational autoencoder) to model the data on a non-linear manifold reveals that only 5 uncorrelated dimensions are adequate to capture the full range of variation in the bioclimatic variables, with a clear data-driven separation between informative and redundant dimensions that eliminates arbitrary thresholds. I show that these 5 variables have meaningful structure and are sufficient to produce species distribution models (SDMs) nearly as good and in some ways better than SDMs using the original 19 bioclimatic variables. I have made the 5 synthetic variables available as a raster dataset at 2.5 minute resolution in an R package that also includes functions to convert back and forth between the 5 variables and the original 19.

AimWe aimed to determine the relationships between species association with humans, their levels of habitat specialisation, and the extent to which their geographic ranges have increased or decreased. LocationGreat Britain. Time periodPresent (1981-2020) Major taxa studiedTerrestrial invertebrates (n=1,722 species). MethodsWe determined the habitat associations for each of 1,722 species from 14 taxonomic groups in each of 18 land cover types in Great Britain. We used these values to calculate a human association index (based on whether species occupy human-modified land cover types, such as urban, suburban and coniferous plantation habitats, or occur in relatively unmodified land covers, such as several coastal habitats and marshlands) and habitat specialisation index (whether they are restricted to a few land cover types, or widely distributed across different land cover types) for each species. We then investigated the relationship between human association and habitat specialisation, as well as the relationship between human association and two metrics of range change between 1981-2000 and 2001-2020. ResultsContrary to previous hypotheses, we find no evidence that species associated with human-modified environments are more likely to be habitat generalists. Furthermore, human-associated species were more likely to increase. On average, the geographic distributions of the most human-associated third of species increased by 58% over the study period, whereas the least human associated third of species declined by 7.1%. Main conclusionsHumans have had increasingly large impacts on the worlds ecosystems, generating an intensity gradient of human-modification, including novel (anthropogenic) environments. Our findings show that new environments have provided opportunities for species to colonise, generating faunas which include species that have become human-associated specialists. The ongoing expansions of species in ecosystems with relatively high levels of human modification are key components of the future of biodiversity in the Anthropocene.

Reliable models of species niches and distributions depend on accurately matching occurrences to environments via spatial and temporal coordinates. For fossil occurrences, time-averaging and age uncertainty can create mismatches between fossils and their associated environments, distorting inferred niches and distributions. Using a virtual ecology approach, we assessed how temporal uncertainty ({+/-}200 years to the full late Quaternary) influences niche and distribution estimates for four virtual species centered on three periods: Holocene (6,000 y.b.p), deglacial (13,500 y.b.p.), and Last Glacial Maximum (18,000 k.y.b.p.). We compared uncertain estimates, derived by matching occurrences with environmental layers drawn from different times within each uncertainty window, against true niches and distributions. We found that during environmentally stable intervals, niches and distributions were robust to temporal uncertainty until it reached {+/-}2500 years. Higher environmental variability reduced accuracy, with the greatest mismatch occurring during the deglacial. These results demonstrate both the promise and limitations of paleodistribution reconstruction.

AimTo assess if and how species range size relates to range structure, if the observed geographic range properties can be retrieved from predicted maps based on species distribution modeling, and whether range properties are predictable from biogeophysical factors. LocationEurope Time periodCurrent Major taxa studied813 vascular plant species endemic to Europe MethodsWe quantified the size and spatial structure of species geographic ranges and compared ranges currently occupied with those predicted by species distribution models (SDMs). SDMs were constructed using complete occurrence data from the Atlas Florae Europaeae and climatic, soil and topographic predictors. We used landscape metrics to characterize range size, range division and patch shape structure, and analysed the phylogenetic, geographic and ecological drivers of species range size and structure using phylogenetic generalized least squares (pGLS). ResultsRange structure metrics were mostly decoupled from species range size. We found large differences in range metrics between observed and predicted ranges, in particular for species with intermediate observed range size and occupied area, and species with low and high observed patch size distribution, geographic range filling, patch shape complexity and geographic range fractality. Elevation heterogeneity, proximity to continental coasts, Southerly or Easterly geographic range positions and narrow ecological niche breadth constrained species observed range size and range structure to different extents. The strength and direction of the relationships differed between observed and predicted ranges. Main conclusionsSeveral range structure metrics, in addition to range size, are needed to adequately describe and understand species ranges. Species range structure can be well explained by geophysical factors and species niche width, albeit not consistently for observed and predicted ranges. As range structure can have important ecological and evolutionary consequences, we highlight the need to develop better predictive models of range structure than provided by current SDMs, and we identify the kinds of species for which this is most necessary.

Quantifying niche divergence is crucial to understanding the ecological and evolutionary processes underlying range limits, coexistence, speciation, biogeography, and macroevolution. Yet available approaches rely on low-dimensional climate summaries, are vulnerable to multiple biases, or struggle with high-dimensional collinear data. We introduce the R package NicheDiv, which adapts discriminant analysis of principal components (DAPC) to quantify pairwise niche divergence across any number of abiotic and biotic environmental variables associated with occurrence records. Our method first addresses correlations among environmental variables through principal component analysis. It then identifies a single discriminant axis that maximizes separation between predefined groups (species/lineages/populations), summarizing multivariate niche structure into one dimension. Significance is assessed by a permutation test that reshuffles group identities to mimic a shared niche. To characterize ecological differentiation, NicheDiv calculates Schoeners D as an overlap index and extends the niche divergence plane to multivariate space, providing metrics such as niche dissimilarity and exclusivity. Extracted variable contributions from the discriminant axis identify environmental variables that contribute most to divergence. Using simulations and empirical data together with a large set of environmental layers, we demonstrate that NicheDiv is computationally scalable, detects subtle divergence in high-dimensional space despite multicollinearity, distinguishes different forms of niche divergence (weighted, nested, soft, hard), and identifies the variables that potentially drive divergence. Compared with alternative divergence tests (PCA-env, hypervolumes, MVNH, PERMANOVA, PCA-space, and logistic regression), NicheDiv generally retains more variation, scales more consistently with increasing divergence, and returns more interpretable effect sizes. NicheDiv automatically extracts such environmental data from preconfigured and user-supplied GIS layers and implements a preprocessing pipeline that reduces known biases: delimiting accessible background space, spatially thinning occurrences, balancing sample sizes, filtering low-information variables, and screening predictors for between-group environmental analogy. We test our framework with empirical analyses of Hemileuca buck moths and demonstrate that their niches are structured by a range of seasonal abiotic and biotic variables rather than annual climatic averages. Overall, NicheDiv offers a robust framework for characterizing niche divergence across multiple environmental axes in support of species delimitation, local adaptation, community ecology, biogeography, and macroevolution.

Joint Species Distribution Models (jSDM) are increasingly used to explain and predict biodiversity patterns. By accounting for species co-occurrence patterns and potentially including species-specific information, jSDMs capture the processes that shape ecological communities. Yet, factors like missing covariates or omitting ecologically-important species may alter the interpretability and effectiveness of jSDMs. Additionally, while the specific formulation of a jSDM directly affects its performances, the effects of choices related to model structure, such as inclusion, or not of phylogeny or trait information, are not well-explored. Here, we developed a multifaceted framework to comprehensively assess performances of alternative jSDM formulations at both species and community levels. We applied this framework to four alternative models fitted on presence/absence and abundance data of a polychaete assemblage sampled in two coastal habitats over 500 km and 8 years. Relative to a benchmark jSDM only capturing the effects of abiotic predictors and residual co-occurrence patterns, we explored the performance of alternative formulations that also included species phylogeny, traits, or some additional 179 non-target species, which were sampled alongside the species of interest. For both presence/absence and abundance data, explanatory power was good for all models but their interpretability and predictive power varied. Relative to the benchmark model, predictive errors on species abundances decreased by 95% or 53%, when including non-target species, or phylogeny, respectively. These differences across models relate to changes in both species-environment relationships and residual co-occurrence patterns. While considering trait data did not improve explanatory or predictive power, it facilitated interpretation of trait-mediated species response to environmental gradients. This study demonstrates trade-offs in jSDM formulation for explaining or predicting species data, highlighting the importance of using a comprehensive framework to compare models. Furthermore, our study provides some guidance for model selection tailored to specific objectives and available data.

Accurately predicting species range shifts in response to environmental change is a central ecological objective and applied imperative. In synthetic analyses, traits emerge as significant but weak predictors of species range shifts across recent climate change. These studies assume linearity in the relationship between a trait and its function, while detailed empirical work often reveals unimodal relationships, thresholds, and other nonlinearities in many trait-function relationships. We hypothesize that the use of linear modeling approaches fails to capture these nonlinearities and therefore may be under-powering traits to predict range shifts. We evaluate the predictive performance of four different machine learning approaches that can capture nonlinear relationships (ridge-regularized linear regression, ridge-regularized kernel regression, support vector regression, and random forests). We validate our models using four multi-decadal range shift datasets in montane plants, montane small mammals, and marine fish. We show that nonlinear approaches perform substantially better than least-squares linear modeling in reproducing historical range shifts. In addition, using novel model observation and interrogation techniques, the trait classes (e.g. dispersal-or diet-related traits) that we identify as primary drivers of model predictions are consistent with expectations. However, disagreements among models in the directionality of trait predictors suggests limits to trait-based statistical predictive frameworks.

Ecosystems are constantly responding to shifting environmental conditions, and the observed structure of ecological communities at any given discrete observation timepoint is part of a larger dynamic response. However, we lack long-term time series of ecosystem responses allowing understanding of the processes driving community dynamics. Sedimentary ancient DNA (sed aDNA) offers novel opportunities to link empirical data with ecological processes, providing near continuous records of plant and animal community changes over millennia. Here, we analyzed metabarcoding data from 10 lakes from Northern Fennoscandia characterizing plant and mammal communities at temporal resolution of 100 years over several millenia. We used sed aDNA data to test how biotic processes, including temperature-dependent plant growth, competition, shading, and herbivory, may have driven the dynamics of Fennoscandic Holocene plant communities since the Last Glacial Maximum. We compared the explanatory power of ordinary differential equation-based models simulating community changes and including these processes. The fit of the models improved with the consideration of temperature dependent densification and biotic interactions, most notably shading. When considering individual taxa, the importance of shading and herbivory was greatest for the dwarf shrubs, while tree and shrub taxa were more often best predicted by models without competition. Our study demonstrates how using sed aDNA time series together with process-based inverse modelling can uncover the mechanisms of species response to climate change, offering potential for more realistic predictions.

Anticipating biodiversity change is critical in rapidly warming regions, yet challenging because these areas often coincide with poor sampling. Data gaps are widely understood to interfere with species distribution models (SDMs), but this is difficult to detect with biased data. We test SDM bias-correction methods with a new occurrence-checklist-range (OCR) validation approach and evaluate prediction discrepancy for [~]700 Canadian terrestrial vertebrate species. We found: 1) bias-correction improves model performance against independent (checklist and range) data, but not against typical occurrence cross-validation, 2) predicted richness differed among methods (up to 2.7-fold), especially in the north, and 3) counterintuitively, future projections varied less (by 28%) because well-sampled climate space will shift north. Our findings suggest potential widespread overconfidence in SDM predictions for the unevenly sampled world, with implications for the growing reliance on biodiversity estimates for planning and policy. OCR validation and methodological discrepancy measurements are relatively easy ways to address this.

O_LIPresence-only data used to develop species distribution models are often biased towards areas that are frequently surveyed. Furthermore, the size of calibration area with respect to the area covered by the species occurrences has been shown to affect model accuracy. However, existing assessments of the effect of data inadequacy and calibration size on model accuracy have predominately been conducted using empirical studies. These studies can give ambiguous results, since the data used to train and test the model can both be biased.\nC_LIO_LIThese limitations were addressed by applying simulated data to assess how inadequate data coverage and the size of calibration area affect the accuracy of species distribution models generated by MaxEnt and BIOCLIM. The validity of four presence-only performance measures, Contrast Validation Index (CVI), Boyce index, AUC and AUCratio, was also assessed.\nC_LIO_LICVI, AUC and AUCratio ranked the accuracy of univariate models correctly according to the true importance of their defining environmental variable, a desirable property of an accuracy measure. Contrastingly, Boyce index failed to rank the accuracy of univariate models correctly and a high percentage of irrelevant variables produced models with a high Boyce index.\nC_LIO_LIInadequate data coverage and increased calibration area reduced model accuracy by reducing the correct identification of the dominant environmental determinant. BIOCLIM outperformed MaxEnt models in predicting the true distribution of simulated species with a symmetric dominant response. However, MaxEnt outperformed BIOCLIM in predicting the true distribution of simulated species with skew and linear dominant responses. Despite this, the standard performance measures consistently overestimated the performance of MaxEnt models and showed them as always having higher model accuracy than the BIOCLIM models.\nC_LIO_LIIt has been acknowledged that research should be directed towards testing and improving species distribution modelling tools, particularly how to handle the inevitable bias and scarcity of species occurrence data. Simulated data, as demonstrated here, provides a powerful approach to comprehensively test the performance of modelling tools and to disentangle the effects of data properties and modelling options on model accuracy. This may be impossible to achieve using real-world data.\nC_LI

BackgroundNon-random species co-occurrence is of fundamental interest to ecologists. One approach to analysing non-random patterns is null modelling. This involves calculation of a metric for the observed dataset, and comparison to a distribution obtained by repeatedly randomising the data. Choice of randomisation algorithm, specifically whether null model species richness is fixed at that of the observed dataset, is likely to affect model results. This is particularly important in cases when there is high variation in species richness between sampling units in the observed data. MethodsHere I demonstrate the effects of accounting for variation in species richness. I use the C-score, a metric measuring species segregation as "checkerboard units", applied to 289 datasets. First, I run null models in which sites are equally likely to be occupied (fixed-equiprobable algorithm). I do this both for the original datasets, and for the same datasets where occurrences are randomised with the species richness distribution fixed (pre-randomised datasets). Second, I run null models that fix site species richness to that observed (fixed-fixed algorithm). ResultsFor real datasets, using the fixed-equiprobable algorithm (sites are equally likely to be colonised), C-score standardised effect size (SES) was positively related to variability in species richness between sites within a dataset. This effect was also found for pre-randomised datasets, indicating that variability in species richness can be exclusively responsible for detection of non-random species co-occurrence. When using the fixed-fixed algorithm (richness is constrained to that of real sites), there was no relationship between SES and variability in species richness. There was also a reverse in the effect direction, with 94% of significant tests indicating a lower C-score than expected for the fixed-equiprobable algorithm, but 98% of significant tests indicating a higher C-score than expected for the fixed-fixed algorithm. DiscussionI speculate that when variation in species richness is high, fewer checkerboard units are possible, regardless of segregation between species. Therefore, use of fixed-equiprobable algorithms in situations where real species richness is highly variable between sites within a dataset will yield significant results, even if species co-occur randomly within the constraints of the species richness distribution. Consequently, use of such tests makes the a priori assumption that high within-dataset variation in species richness indicates non-random species co-occurrence. I recommend using algorithms that explicitly take into account species richness distributions when one wants to eliminate the effect of richness variation in terms of producing significant but spurious positive co-occurrence results. Alternatively, non-null mechanistic models can be created, in which hypothesised species assembly processes must be explicitly stated and tested.

The linkage between environment, a species fitness and its abundance is central to the theory of evolution. So far, all studies of this linkage have been heuristic and empirical due to an inability to determine fitness either experimentally (independent of abundance) or theoretically (from species-environment interaction). One category of such studies involves the Abundant Centre Hypothesis which posits that a species abundance rises to a maximum at the centre of its range. We argue that the confusing mix of results from ACH studies arises from ignoring the central premise that the abundance distribution cannot be independent of the environment. First, we employed a theoretical framework to identify an environmental context (an elevational transect; 200-2800 m in the eastern Himalayas) likely to favour ACH. We then improved upon some previously identified conceptual and methodological shortcomings of ACH studies. Using systematically collected bird data (245 species; 15867 records) from that transect we found that the community average abundance profile is symmetric, as expected by ACH. Notwithstanding which, the abundance profiles of individual species showed a small degree of asymmetry which was correlated with elevation. This elevational dependence may be due to the hard elevational limits at the lower and upper ends of the mountain, as expected from theoretical considerations. We also showed that the average abundance profile shape is close to gaussian, while ruling out uniform and inverted-quadratic shapes. This work demonstrates that selecting a particular category of environmental contexts can help in integrating theoretical tools into a field dominated by empirical studies. Such a union should spur the development of more detailed and testable theoretical models for better insights in an important field.