Assembly rules and community models for unicellular organisms: patterns in diatoms of boreal streams

1. Many studies have addressed either community models (e.g. Clementsian versus Gleasonian gradients) or assembly rules (e.g. nestedness, checkerboards) for higher plant and animal communities, but very few studies have examined different non‐random distribution patterns simultaneously with the same data set. Even fewer studies have addressed generalities in the distribution patterns of unicellular organisms, such as diatoms. 2. We studied non‐randomness in the spatial distribution and community composition of stream diatoms. Our data consisted of diatom surveys from 47 boreal headwater streams and small rivers in northern Finland. Our analytical approaches included ordinations, cluster analysis, null model analyses, and associated randomisation tests. 3. Stream diatom communities did not follow discrete Clementsian community types, where multiple species occur exclusively in a single community type. Rather, diatom species showed rather individualistic responses, leading to continuous Gleasonian variability in community composition. 4. Although continuous variability was the dominating pattern in the data, diatoms also showed significant nestedness and less overlap in species distribution than expected by chance. However, these patterns were probably only secondary signals from species’ individualistic responses to the environment. 5. Although unicellular organisms, such as diatoms, differ from multicellular organisms in several biological characteristics, they nevertheless appear to show largely similar non‐random distribution patterns previously found for higher plants and metazoans.     

Forecasting the future of biodiversity: a test of single‐ and multi‐species models for ants in North America

The geographic distributions of many taxonomic groups remain mostly unknown, hindering attempts to investigate the response of the majority of species on Earth to climate change using species distributions models (SDMs). Multi‐species models can incorporate data for rare or poorly‐sampled species, but their application to forecasting climate change impacts on biodiversity has been limited. Here we compare forecasts of changes in patterns of ant biodiversity in North America derived from ensembles of single‐species models to those from a multi‐species modeling approach, Generalized Dissimilarity Modeling (GDM). We found that both single‐ and multi‐species models forecasted large changes in ant community composition in relatively warm environments. GDM predicted higher turnover than SDMs and across a larger contiguous area, including the southern third of North America and notably Central America, where the proportion of ants with relatively small ranges is high and where data limitations are most likely to impede the application of SDMs. Differences between approaches were also influenced by assumptions regarding dispersal, with forecasts being more similar if no‐dispersal was assumed. When full‐dispersal was assumed, SDMs predicted higher turnover in southern Canada than did GDM. Taken together, our results suggest that 1) warm rather than cold regions potentially could experience the greatest changes in ant fauna under climate change and that 2) multi‐species models may represent an important complement to SDMs, particularly in analyses involving large numbers of rare or poorly‐sampled species. Comparisons of the ability of single‐ and multi‐species models to predict observed changes in community composition are needed in order to draw definitive conclusions regarding their application to investigating climate change impacts on biodiversity.     

Species and community responses to short‐term climate manipulation: Microarthropods in the sub‐Antarctic

Abstract: Both species and community‐level investigations are important for understanding the biotic impacts of climate change, because current evidence suggests that individual species responses are idiosyncratic. However, few studies of climate change impacts have been conducted on entire terrestrial arthropod communities living in the same habitat in the southern Hemisphere, and the effects of precipitation changes on them are particularly poorly understood. Here we investigate the species‐ and community‐level responses of microarthropods inhabiting a keystone plant species, on sub‐Antarctic Marion Island, to experimental reduction in precipitation, warming and shading. These climate manipulations were chosen based on observed climate trends and predicted indirect climate change impacts on this system. The dry‐warm and shade inducing treatments that were imposed effected significant species‐ and community‐level responses after a single year. Although the strongest community‐level trends included a dramatic decline in springtail abundance and total biomass under the dry‐warm and shade treatments, species responses were generally individualistic, that is, springtails responded differently to mites, and particular mite and springtail species responded differently to each other. Our results therefore provide additional support for the dynamic rather than static model for community responses to climate change, in the first such experiment in the sub‐Antarctic. In conclusion, these results show that an ongoing decline in precipitation and increase in temperature is likely to have dramatic direct and indirect effects on this microarthropod community. Moreover, they indicate that while at a broad scale it may be possible to make generalizations regarding species responses to climate change, these generalizations are unlikely to translate into predictable effects at the community level.     

Weak climatic associations among British plant distributions

Aim Species distribution models (SDMs) are used to infer niche responses and predict climate change‐induced range shifts. However, their power to distinguish real and chance associations between spatially autocorrelated distribution and environmental data at continental scales has been questioned. Here this is investigated at a regional (10 km) scale by modelling the distributions of 100 plant species native to the UK. Location UK. Methods SDMs fitted using real climate data were compared with those utilizing simulated climate gradients. The simulated gradients preserve the exact values and spatial structure of the real ones, but have no causal relationships with any species and so represent an appropriate null model. SDMs were fitted as generalized linear models (GLMs) or by the Random Forest machine‐learning algorithm and were either non‐spatial or included spatially explicit trend surfaces or autocovariates as predictors. Results Species distributions were significantly but erroneously related to the simulated gradients in 86% of cases (P < 0.05 in likelihood‐ratio tests of GLMs), with the highest error for strongly autocorrelated species and gradients and when species occupied 50% of sites. Even more false effects were found when curvilinear responses were modelled, and this was not adequately mitigated in the spatially explicit models. Non‐spatial SDMs based on simulated climate data suggested that 70–80% of the apparent explanatory power of the real data could be attributable to its spatial structure. Furthermore, the niche component of spatially explicit SDMs did not significantly contribute to model fit in most species. Main conclusions Spatial structure in the climate, rather than functional relationships with species distributions, may account for much of the apparent fit and predictive power of SDMs. Failure to account for this means that the evidence for climatic limitation of species distributions may have been overstated. As such, predicted regional‐ and national‐scale impacts of climate change based on the analysis of static distribution snapshots will require re‐evaluation.     

The role of climate,habitat, and species co‐occurrence as drivers of change in small mammal distributions over the past century

Species distribution models are commonly used to predict species responses to climate change. However, their usefulness in conservation planning and policy is controversial because they are difficult to validate across time and space. Here we capitalize on small mammal surveys repeated over a century in Yosemite National Park, USA, to assess accuracy of model predictions. Historical (1900–1940) climate, vegetation, and species occurrence data were used to develop single‐ and multi‐species multivariate adaptive regression spline distribution models for three species of chipmunk. Models were projected onto the current (1980–2007) environmental surface and then tested against modern field resurveys of each species. We evaluated models both within and between time periods and found that even with the inclusion of biotic predictors, climate alone is the dominant predictor explaining the distribution of the study species within a time period. However, climate was not consistently an adequate predictor of the distributional change observed in all three species across time. For two of the three species, climate alone or climate and vegetation models showed good predictive performance across time. The stability of the distribution from the past to present observed in the third species, however, was not predicted by our modeling approach. Our results demonstrate that correlative distribution models are useful in understanding species' potential responses to environmental change, but also show how changes in species‐environment correlations through time can limit the predictive performance of models.     

Do community‐level models describe community variation effectively?

Aim The aim of community‐level modelling is to improve the performance of species distributional models by taking patterns of co‐occurrence among species into account. Here, we test this expectation by examining how well three community‐level modelling strategies (‘assemble first, predict later’, ‘predict first, assemble later’, and ‘assemble and predict together’) spatially project the observed composition of species assemblages. Location Europe. Methods Variation in the composition of European tree assemblages and its spatial and environmental correlates were examined with cluster analysis and constrained analysis of principal coordinates. Results were used to benchmark spatial projections from three community‐based strategies: (1) assemble first, predict later (cluster analysis first, then generalized linear models, GLMs); (2) predict first, assemble later (GLMs first, then cluster analysis); and (3) assemble and predict together (constrained quadratic ordination). Results None of the community‐level modelling strategies was able to accurately model the observed distribution of tree assemblages in Europe. Uncertainty was particularly high in southern Europe, where modelled assemblages were markedly different from observed ones. Assembling first and predicting later led to distribution models with the simultaneous occurrence of several types of assemblages in southern Europe that do not co‐occur, and the remaining strategies yielded models with the presence of non‐analogue assemblages that presently do not exist and that are much more strongly correlated with environmental gradients than with the real assemblages. Main conclusions Community‐level models were unable to characterize the distribution of European tree assemblages effectively. Models accounting for co‐occurrence patterns along environmental gradients did not outperform methods that assume individual responses of species to climate. Unrealistic assemblages were generated because of the models’ inability to capture fundamental processes causing patterns of covariation among species. The usefulness of these forms of community‐based models thus remains uncertain and further research is required to demonstrate their utility.     

Integrating demography,dispersal and interspecific interactions into bird distribution models

Species’ ranges are primarily limited by the physiological (abiotic) tolerance of the species, described by their fundamental niche. Additionally, demographic processes, dispersal, and interspecific interactions with other species are shaping species distributions, resulting in the realised niche. Understanding the complex interplay between these drivers is vital for making robust biodiversity predictions to novel environments. Correlative species distribution models have been widely used to predict biodiversity response but also remain criticised, as they are not able to properly disentangle the abiotic and biotic drivers shaping species’ niches. Recent developments have thus focussed on 1) integrating demography and dispersal into species distribution models, and on 2) integrating interspecific interactions. Here, I review recent demographic and multi‐species modelling approaches and discuss critical aspects of these models that remain underexplored in general and in respect to birds, for example, the complex life histories of birds and other animals as well as the scale dependence of interspecific interactions. I conclude by formulating modelling guidelines for integrating the abiotic and biotic processes that limit species’ ranges, which will help to disentangle the complex roles of demography, dispersal and interspecific interactions in shaping species niches. Throughout, I pinpoint complexities of avian life cycles that are critical for consideration in the models and identify data requirements for operationalizing the different modelling steps.     

How complex should models be? Comparing correlative and mechanistic range dynamics models

Criticism has been levelled at climate‐change‐induced forecasts of species range shifts that do not account explicitly for complex population dynamics. The relative importance of such dynamics under climate change is, however, undetermined because direct tests comparing the performance of demographic models vs. simpler ecological niche models are still lacking owing to difficulties in evaluating forecasts using real‐world data. We provide the first comparison of the skill of coupled ecological‐niche‐population models and ecological niche models in predicting documented shifts in the ranges of 20 British breeding bird species across a 40‐year period. Forecasts from models calibrated with data centred on 1970 were evaluated using data centred on 2010. We found that more complex coupled ecological‐niche‐population models (that account for dispersal and metapopulation dynamics) tend to have higher predictive accuracy in forecasting species range shifts than structurally simpler models that only account for variation in climate. However, these better forecasts are achieved only if ecological responses to climate change are simulated without static snapshots of historic land use, taken at a single point in time. In contrast, including both static land use and dynamic climate variables in simpler ecological niche models improve forecasts of observed range shifts. Despite being less skilful at predicting range changes at the grid‐cell level, ecological niche models do as well, or better, than more complex models at predicting the magnitude of relative change in range size. Therefore, ecological niche models can provide a reasonable first approximation of the magnitude of species' potential range shifts, especially when more detailed data are lacking on dispersal dynamics, demographic processes underpinning population performance, and change in land cover.     

Niche width of above‐ and below‐ground organisms varied in predicting biodiversity profiling along a latitudinal gradient

Biodiversity is the foundation of all ecosystems across the planet, and having a better understanding of its global distribution mechanism could be important for biodiversity conservation under global change. A niche width model, combined with metabolic theory, has successfully predicted the increase of α‐diversity and decrease of β‐diversity in the below‐ground microbial community along an altitudinal mountain gradient. In this study, we evaluated this niche width model of above‐ground plants (mainly trees and shrubs) and below‐ground bulk soil microbial communities (i.e., bacteria and archaea) along a latitudinal gradient of forests in China. The niche widths of both plants and microbes increased with increasing temperature and precipitation, and with proximity to circumneutral pH. However, the α‐ and β‐diversities (observed richness and Bray–Curtis dissimilarity, respectively) could not be accurately predicted by a single niche width model alone, either temperature, precipitation or pH. Considering the interactions among different niche width models, all three niche width models were combined to predict biodiversity at the community level using structural equation modelling. The results showed that the niche width model of circumneutral pH was most important in predicting diversity profiling (i.e., α‐ and β‐diversity) for both plants and microbes, while niche width of precipitation and temperature showed both direct and indirect importance for microbe and plant biodiversity, respectively. Because the current niche width model neglects several scenarios related to taxon and environmental attributes, it still needs to be treated with caution in predicting biodiversity trends.     

Niche shifts during the global invasion of the Asian tiger mosquito, Aedes albopictus Skuse (Culicidae), revealed by reciprocal distribution models

Aim Niche‐based distribution models are often used to predict the spread of invasive species. These models assume niche conservation during invasion, but invasive species can have different requirements from populations in their native range for many reasons, including niche evolution. I used distribution modelling to investigate niche conservatism for the Asian tiger mosquito (Aedes albopictus Skuse) during its invasion of three continents. I also used this approach to predict areas at risk of invasion from propagules originating from invasive populations. Location Models were created for Southeast Asia, North and South America, and Europe. Methods I used maximum entropy (Maxent ) to create distribution models using occurrence data and 18 environmental datasets. One native model was created for Southeast Asia; this model was projected onto North America, South America and Europe. Three models were created independently for the non‐native ranges and projected onto the native range. Niche overlap between native and non‐native predictions was evaluated by comparing probability surfaces between models using real data and random models generated using a permutation approach. Results The native model failed to predict an entire region of occurrences in South America, approximately 20% of occurrences in North America and nearly all Italian occurrences of A. albopictus. Non‐native models poorly predict the native range, but predict additional areas at risk for invasion globally. Niche overlap metrics indicate that non‐native distributions are more similar to the native niche than a random prediction, but they are not equivalent. Multivariate analyses support modelled differences in niche characteristics among continents, and reveal important variables explaining these differences. Main conclusions The niche of A. albopictus has shifted on invaded continents relative to its native range (Southeast Asia). Statistical comparisons reveal that the niche for introduced distributions is not equivalent to the native niche. Furthermore, reciprocal models highlight the importance of controlling bi‐directional dispersal between native and non‐native distributions.     

Taxonomic relatedness and spatial structure of a shelf benthic gastropod assemblage

Aim Phylogenetically related species share attributes that lead to common responses to environmental conditions, but which could also produce the exclusion of species by its relatives. These processes could generate the patterns of phylogenetic attraction or repulsion in local communities, where related species would tend to coexist more or less than expected by chance. This paper aims to (1) analyse the phylogenetic structure of a benthic gastropod assemblage in the south‐western Atlantic Ocean (SAO); (2) explore the linkages between phylogenetic structure and spatial distribution patterns; (3) compare outcomes driven by the analysis of presence‐only data and predictive species distribution models; and (4) explore which aspects of the gained knowledge can be useful to the design of sound conservation and/or management actions. Location Uruguayan shelf and slope in the SAO. Methods Spatial patterns in taxonomical relatedness were assessed using (1) raw presence/absence data (i.e. realized niche approach) and (2) reconstruction of the potential composition of the assemblage from niche modelling (i.e. fundamental niche approach). Null models were used to test hypotheses on assemblage structure. Results Significant departures from the null hypothesis that all species were drawn from the same assemblage were observed irrespectively of the approach, indicating the existence of non‐random structures. However, a high proportion of local communities can be thought as random subsets of the regional species pool. This lack of a strong signal of a taxonomic effect could be related to the absence of a linkage between taxonomic distances and ecological similarities. Main conclusions Our results suggest a random assembly of local communities from the regional species pool and/or niche filtering independent of phylogeny as main determinants of local community composition. We also suggest that local assemblages displaying significantly higher (or lower) than expected taxonomic relatedness should be taken into consideration for designing spatially explicit conservation measures.     

Cetacean range and climate in the eastern North Atlantic: future predictions and implications for conservation

There is increasing evidence that the distributions of a large number of species are shifting with global climate change as they track changing surface temperatures that define their thermal niche. Modelling efforts to predict species distributions under future climates have increased with concern about the overall impact of these distribution shifts on species ecology, and especially where barriers to dispersal exist. Here we apply a bio‐climatic envelope modelling technique to investigate the impacts of climate change on the geographic range of ten cetacean species in the eastern North Atlantic and to assess how such modelling can be used to inform conservation and management. The modelling process integrates elements of a species' habitat and thermal niche, and employs “hindcasting” of historical distribution changes in order to verify the accuracy of the modelled relationship between temperature and species range. If this ability is not verified, there is a risk that inappropriate or inaccurate models will be used to make future predictions of species distributions. Of the ten species investigated, we found that while the models for nine could successfully explain current spatial distribution, only four had a good ability to predict distribution changes over time in response to changes in water temperature. Applied to future climate scenarios, the four species‐specific models with good predictive abilities indicated range expansion in one species and range contraction in three others, including the potential loss of up to 80% of suitable white‐beaked dolphin habitat. Model predictions allow identification of affected areas and the likely time‐scales over which impacts will occur. Thus, this work provides important information on both our ability to predict how individual species will respond to future climate change and the applicability of predictive distribution models as a tool to help construct viable conservation and management strategies.     

Cryptic diversity in a fig wasp community—morphologically differentiated species are sympatric but cryptic species are parapatric

A key debate in ecology centres on the relative importance of niche and neutral processes in determining patterns of community assembly with particular focus on whether ecologically similar species with similar functional traits are able to coexist. Meanwhile, molecular studies are increasingly revealing morphologically indistinguishable cryptic species with presumably similar ecological roles. Determining the geographic distribution of such cryptic species provides opportunities to contrast predictions of niche vs. neutral models. Discovery of sympatric cryptic species increases alpha diversity and supports neutral models, while documentation of allopatric/parapatric cryptic species increases beta diversity and supports niche models. We tested these predictions using morphological and molecular data, coupled with environmental niche modelling analyses, of a fig wasp community along its 2700‐km latitudinal range. Molecular methods increased previous species diversity estimates from eight to eleven species, revealing morphologically cryptic species in each of the four wasp genera studied. Congeneric species pairs that were differentiated by a key morphological functional trait (ovipositor length) coexisted sympatrically over large areas. In contrast, morphologically similar species, with similar ovipositor lengths, typically showed parapatric ranges with very little overlap. Despite parapatric ranges, environmental niche models of cryptic congeneric pairs indicate large regions of potential sympatry, suggesting that competitive processes are important in determining the distributions of ecologically similar species. Niche processes appear to structure this insect community, and cryptic diversity may typically contribute mostly to beta rather than alpha diversity.     

Invasive species distribution models – how violating the equilibrium assumption can create new insights

Aim Two core assumptions of species distribution models (SDMs) do not hold when modelling invasive species. Invasives are not in equilibrium with their environment and niche quantification and transferability in space and time are limited. Here, we test whether combining global‐ and regional‐scale data in a novel framework can overcome these limitations. Beyond simply improving regional niche modelling of non‐native species, the framework also makes use of the violation of regional equilibrium assumptions, and aims at estimating the stage of invasion, range filling and risk of spread in the near future for 27 invasive species in the French Alps. Innovation For each invader we built three sets of SDMs using a committee averaging method: one global model and two regional models (a conventional model and one using the global model output to weight pseudo‐absences). Model performances were compared using the area under the receiver operating characteristic curve, the true skill statistic, sensitivity and specificity scores. Then, we extracted the predictions for observed presences and compared them to global and regional models. This comparison made it possible to identify whether invasive species were observed within or outside of their regional and global niches. Main conclusions This study provides a novel methodological framework for improving the regional modelling of invasive species, where the use of a global model output to weight pseudo‐absences in a regional model significantly improved the predictive performance of regional SDMs. Additionally, the comparison of the global and regional model outputs revealed distinct patterns of niche estimates and range filling among the species. These differences allowed us to draw conclusions about the stage of invasion and the risk of spread in the near future, which both correspond to experts' expectations. This framework can be easily applied to a large number of species and is therefore useful for control of biological invasions and eradication planning.     

Modelle für den Wandel der Natur

Ecological Modelling – Scenarios of future environmental changes Climate change affects ecosystems at different levels. Changes in species phenology, distribution and interactions are today well described phenomena documenting species responses to increasing temperatures. Environmental niche models (ENMs) have developed as powerful tools to address various questions in macroecology. Aiming at a species environmental niche, statistical modelling can be employed to predict a species' potential occurrence by projecting environmental information recorded at locality records over space and time. In climate change biology, ENMs are used to identify individual species' fates as range expansions or retractions as well as features that affect the structure of species assemblages and species interactions within and across different taxonomic groups. ENMs help to promote the persistence of species by identifying spatial patterns of species richness or endangerment to target conservation priorities. Moreover, they are an essential part of risk assessments to set up preventive measures against non‐native species most likely to adversely impact native ecosystems.     

Using ecological niche modelling to evaluate niche stability in deep time

Aim To investigate relative niche stability in species responses to various types of environmental pressure (biotic and abiotic) on geological time‐scales using the fossil record. Location The case study focuses on Late Ordovician articulate brachiopods of the Cincinnati Arch in eastern North America. Methods Species niches were modelled for a suite of fossil brachiopod species based on five environmental variables inferred from sedimentary parameters using GARP and Maxent . Niche stability was assessed by comparison of (1) the degree of overlap of species distribution models developed for a time‐slice and those generated by projecting niche models of the previous time‐slice onto environmental layers of a second time‐slice using GARP and Maxent , (2) Schoener’s D statistic, and (3) the similarity of the contribution of each environmental parameter within Maxent niche models between adjacent time‐slices. Results Late Ordovician brachiopod species conserved their niches with high fidelity during intervals of gradual environmental change but responded to inter‐basinal species invasions through niche evolution. Both native and invasive species exhibited similar levels of niche evolution in the invasion and post‐invasion intervals. Niche evolution was related mostly to decreased variance within the former ecological niche parameters rather than to shifts to new ecospace. Main conclusions Although the species examined exhibited morphological stasis during the study interval, high levels of niche conservatism were observed only during intervals of gradual environmental change. Rapid environmental change, notably inter‐basinal species invasions, resulted in high levels of niche evolution among the focal taxa. Both native and invasive species responded with similar levels of niche evolution during the invasion interval and subsequent environmental reorganization. The assumption of complete niche conservatism frequently employed in ecological niche modelling (ENM) analyses to forecast or hindcast species geographical distributions is more likely to be accurate for climate change studies than for invasive species analyses over geological time‐scales.     

Phylogeny and species traits predict bird detectability

Avian acoustic communication has resulted from evolutionary pressures and ecological constraints. We therefore expect that auditory detectability in birds might be predictable by species traits and phylogenetic relatedness. We evaluated the relationship between phylogeny, species traits, and field‐based estimates of the two processes that determine species detectability (singing rate and detection distance) for 141 bird species breeding in boreal North America. We used phylogenetic mixed models and cross‐validation to compare the relative merits of using trait data only, phylogeny only, or the combination of both to predict detectability. We found a strong phylogenetic signal in both singing rates and detection distances; however the strength of phylogenetic effects was less than expected under Brownian motion evolution. The evolution of behavioural traits that determine singing rates was found to be more labile, leaving more room for species to evolve independently, whereas detection distance was mostly determined by anatomy (i.e. body size) and thus the laws of physics. Our findings can help in disentangling how complex ecological and evolutionary mechanisms have shaped different aspects of detectability in boreal birds. Such information can greatly inform single‐ and multi‐species models but more work is required to better understand how to best correct possible biases in phylogenetic diversity and other community metrics.     

Effect of habitat degradation on competition,carrying capacity,and species assemblage stability

Changes in species’ trophic niches due to habitat degradation can affect intra‐ and interspecific competition, with implications for biodiversity persistence. Difficulties of measuring species’ interactions in the field limit our comprehension of competition outcomes along disturbance gradients. Thus, information on how habitat degradation can destabilize food webs is scarce, hindering predictions regarding responses of multispecies systems to environmental changes. Seagrass ecosystems are undergoing degradation. We address effects of Posidonia oceanica coverage reduction on the trophic organization of a macroinvertebrate community in the Tyrrhenian Sea (Italy), hypothesizing increased trophic generalism, niche overlap among species and thus competition and decreased community stability due to degraded conditions. Census data, isotopic analysis, and Bayesian mixing models were used to quantify the trophic niches of three abundant invertebrate species, and intra‐ and interspecific isotopic and resource‐use similarity across locations differing in seagrass coverage. This allowed the computation of (1) competition strength, with respect to each other and remaining less abundant species and (2) habitat carrying capacity. To explore effects of the spatial scale on the interactions, we considered both individual locations and the entire study area (“‘meadow scale”). We observed that community stability and habitat carrying capacity decreased as P. oceanica coverage declined, whereas niche width, similarity of resource use and interspecific competition strength between species increased. Competition was stronger, and stability lower, at the meadow scale than at the location scale. Indirect effects of competition and the spatial compartmentalization of species interactions increased stability. Results emphasized the importance of trophic niche modifications for understanding effects of habitat loss on biodiversity persistence. Calculation of competition coefficients based on isotopic distances is a promising tool for describing competitive interactions in real communities, potentially extendible to any subset of ecological niche axes for which specimens’ positions and pairwise distances can be obtained.