Diversity indices: Which ones are admissible?

Routledge, Richard

doi:10.1016/0022-5193(79)90015-8

Cited by 153 publications

(130 citation statements)

References 11 publications

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“…In a more general context, Routledge (1979) and Gregorius (1978) independently concluded that, among the wealth of diversity measures in use, this effective number deserves priority on both conceptual and intuitive grounds. It is given by v = where the ps's are the relative allele frequencies.…”

Section: Diversity and Fieterozygositymentioning

confidence: 99%

Spatial and temporal genetic differentiation among the seed in a stand of Fagus sylvatica L.

1986

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In a beech population composed of three parts (demes), the genetic structure of the seed (after dispersal) of each deme was recorded in two successive years and at five protein loci, four of which were polymorphic. Spatial and temporal differentiation, as evidenced in allele frequencies, genic diversity and heterozygosity, was studied. While no differentiation was found for diversity, allele frequencies and heterozygosity showed significant spatial differentiation at the genically most diverse loci in both years. Temporal differentiation measured as genetic differences between the seed production of the two years was distinctly lower. The total seed production over both years showed a tendency of homogenising spatial genetic differences present in each single year. This observation can be explained by local differences in flowering of the trees from one year to the next combined with non-random dispersal of the seed, where, however, the reproducing parts of the stand were genetically similar in both years.Comparisons with the results of related studies on ponderosa pine revealed remarkable similarities in the amounts of spatial subpopulation differentiation. Noticeable differences occur with respect to the individual deme levels of differentiation. Consequences for the interpretation of adaptive strategies of trees are briefly discussed.The data on diversities and conditional heterozygosities suggest that there is a tendency for rare alleles to occur preferentially in homozygous form among the seed. The significance of this phenomenon for the maintenance of genetic polymorphisms is demonstrated in the light of recent population genetic selection theories.

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Section: Diversity and Fieterozygositymentioning

confidence: 99%

Spatial and temporal genetic differentiation among the seed in a stand of Fagus sylvatica L.

1986

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“…Yet, they raise several issues. First, different indices can deliver very different results, and there is a debate on which diversity index is most appropriate (e.g., Routledge 1979). At this point, it appears that no particular index is always superior.…”

Section: Introductionmentioning

confidence: 99%

On the Productive Value of Crop Biodiversity: Evidence from the Highlands of Ethiopia

Chavas¹,

Falco²

2011

Land Economics

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“…The replication principle is best known in economics, where it has long been recognized as an important property of concentration and diversity measures (Hannah and Kay 1977). In ecology, the doubling property has been extensively discussed by many authors (MacArthur 1965(MacArthur , 1972Hill 1973;Whittaker 1972;Routledge 1979;Peet 1974;Jost 2006Jost , 2007Jost , 2009Ricotta and Szeidl 2009;Jost et al 2010) and has been extended to phylogenetic measures ); see below.…”

Section: Hill Numbers and The Replication Principlementioning

confidence: 99%

“…Hurlbert 1971;Routledge 1979;Patil and Taillie 1982;Purvis and Hector 2000;Jost 2006Jost , 2007Jost et al 2010). There have also been intense debates on the choice of diversity partitioning schemes; see Ellison (2010) and the Forum that follows it.…”

Section: Introductionmentioning

confidence: 99%

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

Chao

Chiu

Jost³

2016

Biodiversity Conservation and Phylogenetic Systematics

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Conservation biologists need robust, intuitive mathematical tools to quantify and assess patterns and changes in biodiversity. Here we review some commonly used abundance-based species diversity measures and their phylogenetic generalizations. Most of the previous abundance-sensitive measures and their phylogenetic generalizations lack an essential property, the replication principle or doubling property. This often leads to inconsistent or counter-intuitive interpretations, especially in conservation applications. Hill numbers or the "effective number of species" obey the replication principle and thus resolve many of the interpretational problems. Hill numbers were recently extended to incorporate phylogeny; the resulting measures take into account phylogenetic differences between species while still satisfying the replication principle. We review the framework of phylogenetic diversity measures based on Hill numbers and their decomposition into independent alpha and beta components. Both additive and multiplicative decompositions lead to the same classes of normalized phylogenetic similarity or differentiation measures. These classes include multiple-assemblage phylogenetic generalizations of the Jaccard, Sørensen, Horn and Morisita-Horn measures. For two assemblages, these classes also include the commonly used UniFrac and PhyloSør indices as special cases. Our approach provides a mathematically rigorous, self-consistent, ecologically meaningful set of tools for conservationists who must assess the phylogenetic diversity and complementarity of potential protected areas. Our framework is applied to a real dataset to illustrate (i) how to use phylogenetic diversity profiles to completely convey species abundances and phylogenetic information among species in an assemblage; and (ii) how to use phylogenetic similarity (or differentiation) profiles to assess phylogenetic resemblance or difference among multiple assemblages.

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Diversity indices: Which ones are admissible?

Cited by 153 publications

References 11 publications

Spatial and temporal genetic differentiation among the seed in a stand of Fagus sylvatica L.

Spatial and temporal genetic differentiation among the seed in a stand of Fagus sylvatica L.

On the Productive Value of Crop Biodiversity: Evidence from the Highlands of Ethiopia

Phylogenetic Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

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