Indicator Power of Species

Indicator power calculation of Halme et al. (2009) or the congruence between indicator and target species.

Usage

indpower(x, type = 0)

Arguments

x

Community data frame or matrix.

type

The type of statistic to be returned. See Details for explanation.

Details

Halme et al. (2009) described an index of indicator power defined as \(IP_I = \sqrt{a \times b}\), where \(a = S / O_I\) and \(b = 1 - (O_T - S) / (N - O_I)\). \(N\) is the number of sites, \(S\) is the number of shared occurrences of the indicator (\(I\)) and the target (\(T\)) species. \(O_I\) and \(O_T\) are number of occurrences of the indicator and target species. The type argument in the function call enables to choose which statistic to return. type = 0 returns \(IP_I\), type = 1 returns \(a\), type = 2 returns \(b\). Total indicator power (TIP) of an indicator species is the column mean (without its own value, see examples). Halme et al. (2009) explain how to calculate confidence intervals for these statistics, see Examples.

Value

A matrix with indicator species as rows and target species as columns (this is indicated by the first letters of the row/column names).

References

Halme, P., Mönkkönen, M., Kotiaho, J. S, Ylisirniö, A-L. 2009. Quantifying the indicator power of an indicator species. Conservation Biology 23: 1008--1016.

Author

Peter Solymos

Examples

data(dune)
## IP values
ip <- indpower(dune)
## and TIP values
diag(ip) <- NA
(TIP <- rowMeans(ip, na.rm=TRUE))
#> i.Achimill i.Agrostol i.Airaprae i.Alopgeni i.Anthodor i.Bellpere i.Bromhord 
#>  0.3186250  0.3342800  0.2168133  0.3416198  0.3567884  0.3432281  0.3665632 
#> i.Chenalbu i.Cirsarve i.Comapalu i.Eleopalu i.Elymrepe i.Empenigr i.Hyporadi 
#>  0.2095044  0.2781640  0.1713273  0.2414787  0.3263516  0.2016196  0.2378197 
#> i.Juncarti i.Juncbufo i.Lolipere i.Planlanc  i.Poaprat  i.Poatriv i.Ranuflam 
#>  0.2915850  0.3331330  0.3998442  0.3426064  0.4094319  0.3929520  0.2663080 
#> i.Rumeacet i.Sagiproc i.Salirepe i.Scorautu i.Trifprat i.Trifrepe i.Vicilath 
#>  0.3484684  0.3788905  0.2898512  0.4362493  0.3145854  0.4503764  0.2605349 
#> i.Bracruta i.Callcusp 
#>  0.4252676  0.2070766 

## p value calculation for a species
## from Halme et al. 2009
## i is ID for the species
i <- 1
fun <- function(x, i) indpower(x)[i,-i]
## 'c0' randomizes species occurrences
os <- oecosimu(dune, fun, "c0", i=i, nsimul=99)
#> Warning: nullmodel transformed 'comm' to binary data
## get z values from oecosimu output
z <- os$oecosimu$z
## p-value
(p <- sum(z) / sqrt(length(z)))
#> [1] -1.316112
## 'heterogeneity' measure
(chi2 <- sum((z - mean(z))^2))
#> [1] 80.28942
pchisq(chi2, df=length(z)-1)
#> [1] 0.9999994
## Halme et al.'s suggested output
out <- c(TIP=TIP[i], 
    significance=p,
    heterogeneity=chi2,
    minIP=min(fun(dune, i=i)),
    varIP=sd(fun(dune, i=i)^2))
out
#> TIP.i.Achimill   significance  heterogeneity          minIP          varIP 
#>      0.3186250     -1.3161122     80.2894187      0.0000000      0.2142097