Zeta.order.ex {zetadiv}

Expectation of zeta diversity for a specific number of assemblages or sites

Description

Computes the expectation of zeta diversity, the number of species shared by multiple assemblages, for a specific order (number of assemblages or sites) using a formula based on the occupancy of the species.

Usage

Zeta.order.ex(
  data.spec,
  order = 1,
  sd.correct = TRUE,
  rescale = FALSE,
  empty.row = "empty"
)

Arguments

data.spec

Site-by-species presence-absence data frame, with sites as rows and species as columns.

order

Specific number of assemblages or sites at which zeta diversity is computed.

sd.correct

Boolean value (TRUE or FALSE) indicating if the standard deviation must be computed with an unbiased estimator (using the number of site combinations - 1 as the denominator) or not (using the number of site combinations as the denominator).

rescale

Boolean value (TRUE or FALSE) indicating if the zeta values should be divided by \zeta_1, to get a range of values between 0 and 1.

empty.row

Determines how to handle empty rows, i.e. sites with no species. Such sites can cause underestimations of zeta diversity. Options are "empty" to let the data untreated or "remove" to remove the empty rows.

Details

Zeta.order.ex is much faster than Zeta.order.mc to compute the exact value of zeta diversity when the number of species is lower than C^N_{i}, where N is the total number of sites and i is the order of zeta.

sd.correct should be set to TRUE if the assemblages represent a subsample of the whole system. It can be set to FALSE if the sampling is exhaustive, for example in case of a continuous regular grid covering the whole study area.

Value

zeta.order.ex returns a list containing the following components:

zeta.order

The number of assemblages or sites for which the zeta diversity was computed.

combinations

The number of possible combinations of sites for the chosen order.

zeta.val

The zeta diversity values.

zeta.val.sd

The standard deviation of zeta diversity.

References

Hui C. & McGeoch M.A. (2014). zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

McGeoch M. A., Latombe G., Andrew N. R., Nakagawa S., Nipperess D. A., Roige M., Marzinelli E. M., Campbell A. H., Verges A., Thomas T., Steinberg P. D., Selwood K. E., Henriksen M. V. & Hui C. (2019). Measuring continuous compositional change using decline and decay in zeta diversity. Ecology, 100(11), e02832.

See Also

Zeta.order.mc, Zeta.decline.ex, Zeta.decline.mc

Examples

utils::data(bird.spec.coarse)
data.spec.bird <- bird.spec.coarse[,3:193]

zeta.bird <- Zeta.order.ex(data.spec.bird, order = 3)
zeta.bird

##########
s
utils::data(Marion.species)
data.spec.marion <- Marion.species[,3:33]

zeta.marion <- Zeta.order.ex(data.spec.marion, order = 3)
zeta.marion