Browsing by Author "Chao, Anne"

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Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers
(2014-02-01)
Chiu, Chun-Huo
;
Jost, Lou
;
Chao, Anne
;
統計學研究所
;
Institute of Statistics
Until now, decomposition of abundance-sensitive gamma (regional) phylogenetic diversity measures into alpha and beta (within- and between-group) components has been based on an additive partitioning of phylogenetic generalized entropies, especially Rao's quadratic entropy. This additive approach led to a phylogenetic measure of differentiation between assemblages: (gamma - alpha)/gamma. We show both empirically and theoretically that this approach inherits all of the problems recently identified in the additive partitioning of non-phylogenetic generalized entropies. When within-assemblage (alpha) quadratic entropy is high, the additive beta and the differentiation measure (gamma - alpha)/gamma always tend to zero (implying no differentiation) regardless of phylogenetic structures and differences in species abundances across assemblages. Likewise, the differentiation measure based on the phylogenetic generalization of Shannon entropy always approaches zero whenever gamma phylogenetic entropy is high. Such critical flaws, inherited from their non-phylogenetic parent measures (Gini-Simpson index and Shannon entropy respectively), have caused interpretational problems. These flaws arise because phylogenetic generalized entropies do not obey the replication principle, which ensures that the diversity measures are linear with respect to species addition or group pooling. Furthermore, their complete partitioning into independent components is not additive (except for phylogenetic entropy). Just as in the non-phylogenetic case, these interpretational problems are resolved by using phylogenetic Hill numbers that obey the replication principle. Here we show how to partition the phylogenetic gamma diversity based on Hill numbers into independent alpha and beta components, which turn out to be multiplicative. The resulting phylogenetic beta diversity (ratio of gamma to alpha) measures the effective number of completely phylogenetically distinct assemblages. This beta component measures pure differentiation among assemblages and thus can be used to construct several classes of similarity or differentiation measures normalized onto the range [0,1]. We also propose a normalization to fix the traditional additive phylogenetic similarity and differentiation measures, and we show that this yields the same similarity and differentiation measures we derived from multiplicative phylogenetic diversity partitioning. We thus can achieve a consensus on phylogenetic similarity and differentiation measures, including N-assemblage phylogenetic generalizations of the classic Jaccard, SOrensen, Horn, and Morisita-Horn measures. Hypothetical and real examples are used for illustration.
Phylogenetic diversity measures based on Hill numbers
(2010-11-27)
Chao, Anne
;
Chiu, Chun-Huo
;
Jost, Lou
;
統計學研究所
;
Institute of Statistics
We propose a parametric class of phylogenetic diversity (PD) measures that are sensitive to both species abundance and species taxonomic or phylogenetic distances. This work extends the conventional parametric species-neutral approach (based on 'effective number of species' or Hill numbers) to take into account species relatedness, and also generalizes the traditional phylogenetic approach (based on 'total phylogenetic length') to incorporate species abundances. The proposed measure quantifies 'the mean effective number of species' over any time interval of interest, or the 'effective number of maximally distinct lineages' over that time interval. The product of the measure and the interval length quantifies the 'branch diversity' of the phylogenetic tree during that interval. The new measures generalize and unify many existing measures and lead to a natural definition of taxonomic diversity as a special case. The replication principle (or doubling property), an important requirement for species-neutral diversity, is generalized to PD. The widely used Rao's quadratic entropy and the phylogenetic entropy do not satisfy this essential property, but a simple transformation converts each to our measures, which do satisfy the property. The proposed approach is applied to forest data for interpreting the effects of thinning.
Phylogenetic diversity measures based on Hill numbers
(2010-11-27)
Chao, Anne
;
Chiu, Chun-Huo
;
Jost, Lou
;
統計學研究所
;
Institute of Statistics
We propose a parametric class of phylogenetic diversity (PD) measures that are sensitive to both species abundance and species taxonomic or phylogenetic distances. This work extends the conventional parametric species-neutral approach (based on 'effective number of species' or Hill numbers) to take into account species relatedness, and also generalizes the traditional phylogenetic approach (based on 'total phylogenetic length') to incorporate species abundances. The proposed measure quantifies 'the mean effective number of species' over any time interval of interest, or the 'effective number of maximally distinct lineages' over that time interval. The product of the measure and the interval length quantifies the 'branch diversity' of the phylogenetic tree during that interval. The new measures generalize and unify many existing measures and lead to a natural definition of taxonomic diversity as a special case. The replication principle (or doubling property), an important requirement for species-neutral diversity, is generalized to PD. The widely used Rao's quadratic entropy and the phylogenetic entropy do not satisfy this essential property, but a simple transformation converts each to our measures, which do satisfy the property. The proposed approach is applied to forest data for interpreting the effects of thinning.