diversity: Calculate a collection of diversity statistics from a...

In douglasgscofield/dispersalDiversity: Analyse individual and genetic diversity of dispersal processes in biological populations

Description

Given a sites-by-counts matrix, calculate a collection of diversity statistics. Statistics include PMI (probability of maternal inheritance) from Grivet et al. (2005) and Scofield et al. (2010, 2011) as well as alpha, beta, gamma and delta/omega from classical ecology and applied to a dispersal context by Scofield et al. (2012).

Calculate diversity for allele_divtables object using diversityMultilocus

Usage

## Default S3 method:
diversity(tab, ...)

## S3 method for class 'divtable'
diversity(tab, ...)

## S3 method for class 'allele_divtables'
diversity(x, ...)

Arguments

tab	divtable of sites-by-counts data. An attempt is make to convert it to class divtable if it is not already. Rows are not reordered.
x	Object of class allele_divtables
...	Additional arguments, currently ignored
...	Additional arguments passed to diversityMultilocus

Value

A list of class diversity containing three forms of diversity statistics, each returned as lists under separate named elements:

• q, based on squared frequencies, known to be biased at smaller sample sizes

• r, unbiased versions of q (Simpson, 1949), but singletons are dropped and values are nonsensical if a site contains only singletons

• q.nielsen, a better unbiased transformation of q following Nielsen et al. (2003) that does not have the singleton properties of r

Each such list q, r and q.nielsen contains several elements representing different diversity statistics. Several quantities are included:

• q.gg, vector of length number of sites, containing squared frequencies of groups in each site. In form q, these are untransformed, while in form r and q.nielsen, these are transformed accordingly

• q.bar.0, scalar, weighted mean of q.gg

• q.variance.0, scalar, weighted sample variance of q.bar.0

• q.unweighted.mean, mean of q.gg

• alpha.g, vector of length number of sites, containing reciprocals of q.gg

• alpha.unweighted.mean, scalar, mean of alpha.g

• d.alpha, scalar, reciprocal of q.unweighted.mean

• d.gamma, scalar, reciprocal of sum of grand squared frequencies

• d.beta, scalar, d.gamma / d.alpha

• diversity.mat, sites-by-sites matrix containing Chao pairwise divergences off-diagonal, alpha.g on-diagonal

• divergence.mat, sites-by-sites matrix matching diversity.mat but with with 0 on-diagonal

• overlap.mat, sites-by-sites matrix containing 1 - divergence.mat

• overlap, scalar, mean overlap, ∑{C} / ((G - 1) ∑{q_{gg}})

• divergence, scalar, mean divergence, 1 - overlap

The list also contains the original divtable passed to diversity, together with several descriptive quantities:

• table, the class divtable object passed in as tab

• num.groups, the number of rows in tab

• num.sources, the number of columns in tab

• num.samples, the sum of all elements in tab

• num.samples.group, a vector of length num.groups, the sum of elements in each row of tab

• num.sources.group, a vector of length num.groups, the number of distinct groups observed in each row of tab

• num.samples.source, a vector of length num.sources, the sum of elements in each column of tab

• num.groups.source, a vector of length num.groups, the number of distinct groups observed in each row of tab

Finally, some additional statistics representing pooled PMI measures (Scofield et al. 2010) and weighted overlaps (Scofield et al. 2011) are returned:

• y.gh, a pairwise matrix of counts of items in each group from any source that are shared with each other group

• prop.y.0.gh, a matrix of proportions of items in each group from any source that are shared with each other group, derived from y.gh

• q.0.gh, a matrix of probabilities that two items drawn from group g and h are from any of the sources shared between g and h

• q.bar.gh, weighted mean overlap (q_{gh}), probabilities that two items, one drawn from each of groups g and h, are from the same source, weighted by sample sizes

• q.variance.gh, weighted sample variance of q.bar.gh

The value from diversityMultilocus

References

Simpson, E. D. (1949) Measurement of diversity. Nature 163:688.

Chao, A., Jost, L., Chiang, S. C., Jiang, Y. H., and Chazdon, R. L. (2008) A two-stage probabilistic approach to multiple-community similarity indices. Biometrics 64:1178-1186.

Grivet, D., Smouse, P. E. and Sork, V. L. (2005) A novel approach to an old problem: tracking dispersed seeds. Molecular Ecology 14:3585-3595.

Nielsen, R., Tarpy, D. R. and Reeve, H. K. (2003) Estimating effective paternity number in social insects and the effective number of alleles in a population. Molecular Ecology 12:3157-3164.

Scofield, D. G., Sork, V. L. and Smouse, P. E. (2010) Influence of acorn woodpecker social behaviour on transport of coast live oak (Quercus agrifolia) acorns in a southern California oak savanna. Journal of Ecology 98:561-572.

Scofield, D. G., Alfaro, V. R., Sork, V. L., Grivet, D., Martinez, E., Papp, J., Pluess, A. R., Koenig, W. D. and Smouse, P. E. (2011) Foraging patterns of acorn woodpeckers (Melanerpes formicivorus) on valley oak (Quercus lobata N\'ee) in two California oak savanna-woodlands. Oecologia 166:187-196.

Scofield, D. G., Smouse, P. E., Karubian, J. and Sork, V. L. (2012) Use of alpha, beta and gamma diversity measures to characterize seed dispersal by animals. American Naturalist 180:719-732.

See Also

diversityMultilocus

Examples

## create table of random memberships from data frame of site-source pairs
n.sites <- 5
n.sources <- 10
n.samples <- 160
set.seed(75333)
t <- data.frame(site = sample(n.sites, n.samples, replace = TRUE),
                source = round(runif(n.samples) * n.sources + 0.5))
## diversity accepts table via default method, which applies as.divtable
div <- diversity(table(t))
div$q

douglasgscofield/dispersalDiversity documentation built on March 30, 2021, 9:50 a.m.