adiv (version 2.2.1)

PADDis: Functional Dissimilarity Measures for Presence-Absence Data

Description

Functions PADDis, DJac and Jac calculate the dissimilarity coefficients introduced in Ricotta et al. (2016). These dissimilarity coefficients use traditional mismatching components a, b and c of the 2 x 2 contingency table expressed as to include functional or phylogenetic differences among species and noted A, B, C. Components B and C represent the functional or phylogenetic uniqueness of community X compared with community Y and vice versa. Component A represents the functional or phylogenetic similarities between communities X and Y.

Usage

PADDis(comm, dis, method = NULL, diag = FALSE, upper = FALSE)
DJac(comm, dis, diag = FALSE, upper = FALSE)
Jac(comm, diag = FALSE, upper = FALSE)

Value

In function PADDis, if method=0, then the function PADDis returns 6 matrices corresponding to the a, b, c, A, B, and C values per pair of communities. Otherwise, it returns an object of class dist corresponding to the dissimilarities among communities.

Functions DJac and Jac return a list of three objects of class dist:

J

for the full dissimilarities between communities;

JRepl

for the turnover component of the dissimilarities;

JRich

for the component of difference in richness.

Arguments

comm

a matrix or a data frame with communities (or plots, assemblages, etc.) as rows and species as columns containing the incidence (0/1) of all species in the communities.

dis

an object of class dist containing the (functional) dissimilarities among species.

method

an integer between 0 and 6. If NULL the choice is made with a console message. See details.

diag

a logical value indicating whether the diagonal of the distance matrix should be printed by function print.dist.

upper

a logical value indicating whether the upper triangle of the distance matrix should be printed by function print.dist.

Author

Sandrine Pavoine

Details

In PADDIS, dissimilarities among communities are calculated with the following formulas:

Generalized Jaccard dissimilarity, with method = 1 $$\frac{B+C}{a+b+c}$$

Generalized Sorensen dissimilarity, with method = 2 $$\frac{B+C}{2a+b+c}$$

Generalized Sokal and Sneath dissimilarity, with method = 3 $$\frac{2(B+C)}{a+2(b+c)}$$

Generalized Ochiai dissimilarity, with method = 4 $$\frac{\sqrt{A+B}\sqrt{A+C}-A}{\sqrt{a+b}\sqrt{a+c}}$$

Generalized Simpson dissimilarity, with method = 5 $$\frac{min\{B+C\}}{a+min\{b+c\}}$$

Generalized Kulczynski dissimilarity, with method = 6 $$0.5*(\frac{B}{a+b}+\frac{C}{a+c})$$

DJac and Jac use the additive decomposition of the Jaccard index into turnover and richness difference. DJac takes into account the (functional or phylogenetic) dissimilarities among species while Jac does not.

References

Ricotta, C., Podani, J., Pavoine, S. (2016) A family of functional dissimilarity measures for presence and absence data. Ecology and Evolution, 6, 5383--5389

Examples

data(RPP16EE)
Com <- RPP16EE$Com
Dis <- as.dist(RPP16EE$Dis)
J <- Jac(Com)
DJ <- DJac(Com, Dis)

plot(c(as.matrix(DJ$J)[1,]), ylab="Dissimilarity", 
xlab="Plot-to-plot comparison", pch=15, type="b", 
ylim=c(0,1), main="Jaccard")

lines(c(as.matrix(J$J)[1,]), type="b", pch=18)

legend("bottomright", legend=c("P/A scores", "functional data"), 
pch=c(15,18), lty=1)

plot(c(as.matrix(DJ$JRepl)[1,]), ylab="Dissimilarity",
xlab="Plot-to-plot comparison", pch=15, type="b", 
ylim=c(0,1), main="Species replacement")

lines(c(as.matrix(J$JRepl)[1,]), type="b", pch=18)

legend("bottomright", legend=c("P/A scores", "functional data"), 
pch=c(15,18), lty=1)


#Use the following instruction to obtain all components:

PADDis(Com, Dis, method=0)