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Distance-based functional diversity measures and their decomposition: a framework based on Hill numbers.

ABSTRACT: Hill numbers (or the "effective number of species") are increasingly used to characterize species diversity of an assemblage. This work extends Hill numbers to incorporate species pairwise functional distances calculated from species traits. We derive a parametric class of functional Hill numbers, which quantify "the effective number of equally abundant and (functionally) equally distinct species" in an assemblage. We also propose a class of mean functional diversity (per species), which quantifies the effective sum of functional distances between a fixed species to all other species. The product of the functional Hill number and the mean functional diversity thus quantifies the (total) functional diversity, i.e., the effective total distance between species of the assemblage. The three measures (functional Hill numbers, mean functional diversity and total functional diversity) quantify different aspects of species trait space, and all are based on species abundance and species pairwise functional distances. When all species are equally distinct, our functional Hill numbers reduce to ordinary Hill numbers. When species abundances are not considered or species are equally abundant, our total functional diversity reduces to the sum of all pairwise distances between species of an assemblage. The functional Hill numbers and the mean functional diversity both satisfy a replication principle, implying the total functional diversity satisfies a quadratic replication principle. When there are multiple assemblages defined by the investigator, each of the three measures of the pooled assemblage (gamma) can be multiplicatively decomposed into alpha and beta components, and the two components are independent. The resulting beta component measures pure functional differentiation among assemblages and can be further transformed to obtain several classes of normalized functional similarity (or differentiation) measures, including N-assemblage functional generalizations of the classic Jaccard, Sørensen, Horn and Morisita-Horn similarity indices. The proposed measures are applied to artificial and real data for illustration.

SUBMITTER: Chiu CH

PROVIDER: S-EPMC4085071 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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Distance-based functional diversity measures and their decomposition: a framework based on Hill numbers.

Chiu Chun-Huo CH Chao Anne A

PloS one 20140707 7

Hill numbers (or the "effective number of species") are increasingly used to characterize species diversity of an assemblage. This work extends Hill numbers to incorporate species pairwise functional distances calculated from species traits. We derive a parametric class of functional Hill numbers, which quantify "the effective number of equally abundant and (functionally) equally distinct species" in an assemblage. We also propose a class of mean functional diversity (per species), which quantif ...[more]

PMID: 25000299

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Project description:The identification of phenotypic associations in high-dimensional brain connectivity data represents the next frontier in the neuroimaging connectomics era. Exploration of brain-phenotype relationships remains limited by statistical approaches that are computationally intensive, depend on a priori hypotheses, or require stringent correction for multiple comparisons. Here, we propose a computationally efficient, data-driven technique for connectome-wide association studies (CWAS) that provides a comprehensive voxel-wise survey of brain-behavior relationships across the connectome; the approach identifies voxels whose whole-brain connectivity patterns vary significantly with a phenotypic variable. Using resting state fMRI data, we demonstrate the utility of our analytic framework by identifying significant connectivity-phenotype relationships for full-scale IQ and assessing their overlap with existent neuroimaging findings, as synthesized by openly available automated meta-analysis (www.neurosynth.org). The results appeared to be robust to the removal of nuisance covariates (i.e., mean connectivity, global signal, and motion) and varying brain resolution (i.e., voxelwise results are highly similar to results using 800 parcellations). We show that CWAS findings can be used to guide subsequent seed-based correlation analyses. Finally, we demonstrate the applicability of the approach by examining CWAS for three additional datasets, each encompassing a distinct phenotypic variable: neurotypical development, Attention-Deficit/Hyperactivity Disorder diagnostic status, and L-DOPA pharmacological manipulation. For each phenotype, our approach to CWAS identified distinct connectome-wide association profiles, not previously attainable in a single study utilizing traditional univariate approaches. As a computationally efficient, extensible, and scalable method, our CWAS framework can accelerate the discovery of brain-behavior relationships in the connectome.

Dataset Information

Distance-based functional diversity measures and their decomposition: a framework based on Hill numbers.

Publications

Distance-based functional diversity measures and their decomposition: a framework based on Hill numbers.

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