skip to main content

Title: A unifying framework for quantifying and comparing n‐dimensional hypervolumes

The quantification of Hutchinson's n‐dimensional hypervolume has enabled substantial progress in community ecology, species niche analysis and beyond. However, most existing methods do not support a partitioning of the different components of hypervolume. Such a partitioning is crucial to address the ‘curse of dimensionality’ in hypervolume measures and interpret the metrics on the original niche axes instead of principal components. Here, we propose the use of multivariate normal distributions for the comparison of niche hypervolumes and introduce this as the multivariate‐normal hypervolume (MVNH) framework (R package available on

The framework provides parametric measures of the size and dissimilarity of niche hypervolumes, each of which can be partitioned into biologically interpretable components. Specifically, the determinant of the covariance matrix (i.e. the generalized variance) of a MVNH is a measure of total niche size, which can be partitioned into univariate niche variance components and a correlation component (a measure of dimensionality, i.e. the effective number of independent niche axes standardized by the number of dimensions). The Bhattacharyya distance (BD; a function of the geometric mean of two probability distributions) between two MVNHs is a measure of niche dissimilarity. The BD partitions total dissimilarity into the components of Mahalanobis distance (standardized Euclidean distance with correlated variables) between hypervolume centroids and the determinant ratio which measures hypervolume size difference. The Mahalanobis distance and determinant ratio can be further partitioned into univariate divergences and a correlation component.

We use empirical examples of community‐ and species‐level analysis to demonstrate the new insights provided by these metrics. We show that the newly proposed framework enables us to quantify the relative contributions of different hypervolume components and to connect these analyses to the ecological drivers of functional diversity and environmental niche variation.

Our approach overcomes several operational and computational limitations of popular nonparametric methods and provides a partitioning framework that has wide implications for understanding functional diversity, niche evolution, niche shifts and expansion during biotic invasions, etc.

more » « less
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Date Published:
Journal Name:
Methods in Ecology and Evolution
Page Range / eLocation ID:
p. 1953-1968
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Adaptive radiations are typically characterized by niche partitioning among their constituent species. Trophic niche partitioning is particularly important in predatory animals, which rely on limited food resources for survival.

    We test for trophic niche partitioning in an adaptive radiation of HawaiianTetragnathaspiders, which have diversified in situ on the Hawaiian Islands. We focus on a community of nine species belonging to two different clades, one web‐building and the other actively hunting, which co‐occur in wet forest on East Maui. We hypothesize that trophic niches differ significantly both: (a) among species within a clade, indicating food resource partitioning, and (b) between the two clades, corresponding to their differences in foraging strategy.

    To assess niches of the spider species, we measure: (a) web architecture, the structure of the hunting tool, and (b) site choice, the physical placement of the web in the habitat. We then test whether differences in these parameters translate into meaningful differences in trophic niche by measuring (c) stable isotope signatures of carbon and nitrogen in the spiders’ tissues, and (d) gut content of spiders based on metabarcoding data.

    We find significant interspecific differences in web architecture and site choice. Importantly, these differences are reflected in stable isotope signatures among the five web‐building species, as well as significant isotopic differences between web‐builders and active hunters. Gut content data also show interspecific and inter‐clade differences. Pairwise overlaps of web architecture between species are positively correlated with overlaps of isotopic signature.

    Our results reveal trophic niche partitioning among species within each clade, as well as between the web‐building and actively hunting clades. Based on the correlation between web architecture and stable isotopes, it appears that the isotopic signatures of spiders’ tissues are influenced by architectural differences among their webs. Our findings indicate an important link between web structure, microhabitat preference and diet in the HawaiianTetragnatha.

    A freePlain Language Summarycan be found within the Supporting Information of this article.

    more » « less
  2. Abstract

    While trait‐based approaches have been effectively leveraged by plant ecologists to advance our understanding of community responses to major global challenges, such as climate change and invasive species, the study of marine macroalgae is still mired in a functional group (FG) framework developed in the 1980s.

    In this paper, we used predominantly categorical data for 18 macroalgal traits that were accessible in public databases and/or the literature to explore their usefulness in a trait‐based framework for marine macroalgae. Species were clustered into emergent, data‐driven groups using a Gower dissimilarity matrix, then a k‐medoid clustering approach called partitioning around the medoids.

    We identified 14 emergent groups (EGs) that captured a spectrum of strategies used by different macroalgal species. However, significant ‘gaps’ in trait space may identify evolutionary constraints to algal adaptive strategies. Multivariate analysis showed how the 18 traits created trait space and drove the clustering. A spectrum of strategies and the influence of multiple traits imply that algal strategies are likely governed by complex multivariate, not bivariate, trade‐offs. Finally, we found that our EGs appeared to reflect multivariate trade‐offs and diverse ecological strategies more than the traditional FG model for macroalgae. We tested the usefulness of our EGs by comparing real‐world spatial distributions of species across habitats with known strong environmental filters to their area occupied in trait space. We found significant separation in trait space and divergent occupancy patterns across global distributions, attachment substrates and elevational zones. These results support the use of categorical data accessible in the literature as a useful step towards developing trait‐based ecology for marine macroalgae.

    Synthesis. Our findings indicate that readily accessible categorical traits produce emergent FGs that reflect environmental filtering and therefore demonstrate the power of trait‐based approaches over the current FG framework. Furthermore, we posit that categorical traits are a valuable and potentially complementary addition to a newly developing database of continuous traits because they encompass a broader, more globally accessible set of traits.

    more » « less
  3. Summary

    The expansion of angiosperm‐dominated forests in the Cretaceous and early Cenozoic had a profound effect on terrestrial biota by creating novel ecological niches. The majority of modern fern lineages are hypothesized to have arisen in response to this expansion, particularly fern epiphytes that radiated into the canopy. Recent evidence, however, suggests that epiphytism does not correlate with increased diversification rates in ferns, calling into question the role of the canopy habitat in fern evolution.

    To understand the role of the canopy in structuring fern community diversity, we investigated functional traits of fern sporophytes and gametophytes across a broad phylogenetic sampling on the island of Moorea, French Polynesia, including > 120 species and representatives of multiple epiphytic radiations.

    While epiphytes showed convergence in small size and a higher frequency of noncordate gametophytes, they showed greater functional diversity at the community level relative to terrestrial ferns.

    These results suggest previously overlooked functional diversity among fern epiphytes, and raise the hypothesis that while the angiosperm canopy acted as a complex filter that restricted plant size, it also facilitated diversification into finely partitioned niches. Characterizing these niche axes and adaptations of epiphytic ferns occupying them should be a priority for future pteridological research.

    more » « less
  4. Abstract

    Governments around the world rely on environmental impact assessment (EIA) to understand the environmental risks of proposed developments.

    To examine the basis for these appraisals, we examine the output of EIA processes in jurisdictions within seven countries, focusing on scope (spatial and temporal), mitigation actions and whether impacts were identified as ‘significant’.

    We find that the number of impacts characterized as significant is generally low. While this finding may indicate that EIA is successful at promoting environmentally sustainable development, it may also indicate that the methods used to assess impact are biased against findings of significance. To explore the methods used, we investigate the EIA process leading to significance determination.

    We find that EIA reports could be more transparent with regard to the spatial scale they use to assess impacts to wildlife. We also find that few reports on mining projects consider temporal scales that are precautionary with regard to the effects of mines on water resources. Across our sample of reports, we find that few EIAs meaningfully consider the different ways that cumulative impacts can interact.

    Across countries, we find that proposed mitigation measures are often characterized as effective without transparent justification, and sometimes are described in ways that render the mitigation measure proposal ambiguous.

    Across the reports in our sample, professional judgement is overwhelmingly the determinant of impact significance, with little transparency around the reasoning process involved or input by stakeholders.

    We argue that the credibility and accuracy of the EIA process could be improved by adopting more rigorous assessment methodologies and empowering regulators to enforce their use.

    A freePlain Language Summarycan be found within the Supporting Information of this article.

    more » « less
  5. Abstract

    It is standard statistical practice to provide measures of uncertainty around parameter estimates. Unfortunately, this very basic and necessary enterprise is often absent in macroevolutionary studies using maximum likelihood estimates (MLEs).

    dentist is an R package that allows an approximation of confidence intervals (CI) around parameter estimates without an analytic solution to likelihood equations. This package works by ‘denting’ the likelihood surface by sampling points a specified distance around the MLE following what is essentially a Metropolis‐Hastings walk.

    We describe the importance of estimating uncertainty around parameter estimates, as well as demonstrate the ability of dentist to accurately approximate CI.

    We introduce several plotting tools to visualize the results of a dentist analysis. dentist is freely available from, written in the R language, and can be used for any given likelihood function.

    more » « less