evodiss_family {adiv}

A Family of Indices Dedicated to Pair-wise Phylogenetic Dissimilarities between Communities

Description

The function evodiss_family was written thanks to function dist.binary of package ade4. Function dist.binary calculates specific compositional distances. The new function here replaces species with evolutionary units. It calculates Nipperess et al. (2010) parameters a, b, c, d (with incidence data), or A, B, C, D (with abundance data) and then use these parameters to compute pair-wise phylogenetic dissimilarities between communities.

The graphical function evodiss_ternaryplot displays Nipperess et al. (2010) parameters a, b, c (with incidence data), or A, B, C (with abundance data) on a ternary plot (see Koleff et al. 2003).

Usage

evodiss_family(phyl, comm, method = NULL, abundance = TRUE,
squareroot = TRUE, diag = FALSE, upper = FALSE, tol = 1e-08)

evodiss_ternaryplot(phyl, comm, abundance = TRUE, 
tol = 1e-08, ...)

Arguments

phyl

an object inheriting the class phylo (see package ape), phylo4 (see package phylobase) or hclust.

comm

a data frame typically with communities as rows, species as columns and presence/absence or an index of abundance as entries. Species should be labeled as in the phylogenetic tree where they are the tips.

method

either NULL or a number between 1 and 14. If NULL, the choice is made with a console message. See details.

abundance

a logical indicating whether abundance data (if TRUE) or incidence data (presence/absence if FALSE) must be used.

squareroot

a logical. First a similarity index (S) is calculated (see details). Then if squareroot=TRUE, the dissimilarity is calculated as \sqrt{1-S}. If squareroot=FALSE, it is calculated as 1-S. The square root is useful to obtain Euclidean properties for the PD-dissimilarity indices (with methods 1 to 10).

diag

logical argument passed to function as.dist (R base).

upper

logical argument passed to function as.dist (R base).

tol

numeric tolerance threshold: values between -tol and tol are considered equal to zero.

...

other arguments can be added and passed to the function triangle.plot of the ade4 package (labels cannot be changed and are defined thanks to the row names of comm).

Details

The function was written thanks to function dist.binary of package ade4. Function dist.binary calculates specific compositional distances. The new function here replaces species with evolutionary units and adds several indices. It calculates Nipperess et al. (2010) parameters a, b, c, d (with incidence data), or A, B, C, D (with abundance data). Then, the parameters are combined thanks to one out of 14 methods as defined below:

method = 1: Jaccard index (1901); S3 coefficient of Gower and Legendre (1986) = a / (a+b+c).

method = 2: Simple matching coefficient of Sokal and Michener (1958); S4 coefficient of Gower and Legendre (1986) = (a+d) / (a+b+c+d).

method = 3: Sokal and Sneath(1963); S5 coefficient of Gower and Legendre (1986) = a / (a + 2(b + c)).

method = 4: Rogers and Tanimoto (1960); S6 coefficient of Gower and Legendre (1986) = (a + d) / (a + 2(b + c) +d).

method = 5: Dice (1945) or Sorensen (1948); S7 coefficient of Gower and Legendre (1986) = 2a / (2a + b + c).

method = 6: Hamann coefficient; S9 index of Gower and Legendre (1986) = (a - (b + c) + d) / (a + b + c + d).

method = 7: Ochiai (1957); S12 coefficient of Gower and Legendre (1986) = a / sqrt((a + b)(a + c)).

method = 8: Sokal and Sneath (1963); S13 coefficient of Gower and Legendre (1986) = ad / sqrt((a + b)(a + c)(d + b)(d + c)).

method = 9: Phi of Pearson; S14 coefficient of Gower and Legendre (1986) = (ad - bc) / sqrt((a + b)(a + c)(d + b)(d + c)).

method = 10: S2 coefficient of Gower and Legendre (1986) = a / (a + b + c + d) (imposed unit self-similarity).

method = 11: Kulczynski index; S10 coefficient of Gower and Legendre (1986) = 0.5 * (a/(a+b) + a/(a+c))

method = 12: S11 coefficient of Gower and Legendre (1986) = 0.25 * (a/(a+b) + a/(a+c) + d/(b+d) + d/(c+d))

method = 13: S8 coefficient of Gower and Legendre (1986) = (a+d)/(a+0.5*(b+c)+d)

method = 14: Simpson coefficient = a/(a+min(b,c))

Value

Function evodiss_family returns an object of class dist containing the PD-dissimilarities (phylogenetic dissimilarities) between communities.

Function evodiss_ternaryplot returns a graph.

Author(s)

Sandrine Pavoine [e-mail]

References

The methodologies are presented in Pavoine, S. (2016) A guide through a family of phylogenetic dissimilarity measures among sites. Oikos, 125, 1719–1732.

They gather in a common framework and extend earlier work introduced in Koleff, P., Gaston, K.J., Lennon, J.J. (2003) Measuring beta diversity for presence-absence data. Journal of Animal Ecology, 72, 367–382.

Nipperess, D.A., Faith, D.P., Barton, K.(2010) Resemblance in phylogenetic diversity among ecological assemblages. Journal of Vegetation Science, 21, 809–820.

Dice, L.R. (1945) Measures of the amount of ecologic association between species. Ecology, 26, 297–302.

Gower, J.C., Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5–48.

Jaccard, P. (1901) Etude comparative de la distribution florale dans une portion des Alpes et des Jura. Bulletin de la Societe Vaudoise des Sciences Naturelles, 37, 547–579.

Ochiai, A. (1957) Zoogeographic studies on the soleoid fishes found in Japan and its neighbouring regions. Bulletin of the Japanese Society of Scientific Fisheries, 22, 526–530.

Rogers, J.S. and Tanimoto, T.T. (1960) A computer program for classifying plants. Science, 132, 1115–1118.

Sokal, R.R. and Michener, C.D. (1958) A Statistical Method for Evaluating Systematic Relationships. The University of Kansas Science Bulletin, 38, 1409–1438.

Sokal, R.R. and Sneath, P.H.A. (1963) Principles of numerical taxonomy. San Francisco: W. H. Freeman.

Sorensen, T. (1948) A method of establishing groups of equal amplitude in plant sociology based on similarity of species content. Kongelige Danske Videnskabernes Selskabs Biologiske Skrifter, 5, 1–34.

See Also

evodiss

Examples

## Not run: 
if(require(ape)){

data(batcomm)
phy <- read.tree(text=batcomm$tre)
ab <- batcomm$ab[,phy$tip.label]

# PD-dissimilarity indices that use Nipperess et al. (2010)
# parameters can be obtained thanks to function evodiss_family. 
# For example, with incidence data, 
# indices evoDJaccard, evoDSorensen, and evoDOchiai 
# (supplementary Appendix 1 in Pavoine 2016) 
# can be obtained as follows:

evodiss_family(phy, ab, method=1, abundance=FALSE) # Jaccard
evodiss_family(phy, ab, method=5, abundance=FALSE) # Sorensen
evodiss_family(phy, ab, method=7, abundance=FALSE) # Ochiai

# With abundance data, indices evoDTJ, evoDTS, evoDTO 
# (supplementary Appendix 1 in Pavoine 2016) 
# can be obtained as follows:

evodiss_family(phy, ab, method=1) # evoDTJ
evodiss_family(phy, ab, method=5) # evoDTS
evodiss_family(phy, ab, method=7) # evoDTO

# Ternary plots can be obtained for Nipperess et al. (2010) 
# parameters a, b, c (incidence data) 
# (see Supplementary material Appendix 4 in Pavoine 2016):

evodiss_ternaryplot(phy, ab, abundance = FALSE)

# and for Nipperess et al. (2010) parameters A, B, C 
# (abundance data):

evodiss_ternaryplot(phy, ab, abundance = TRUE)

# The ternary plots can be adjusted thanks 
# to the arguments of function triangle.plot (package ade4). 
# For example, full triangles can be obtained as follows 
# (previous graphs were zoomed on the smallest principal 
# equilateral triangle that contained the points, 
# as indicated by the embedded close grey triangle 
# at the left-hand corner of ternary plot given above):

evodiss_ternaryplot(phy, ab, abundance = FALSE, adjust=FALSE, showposition=FALSE)
# Incidence data

evodiss_ternaryplot(phy, ab, abundance = TRUE, adjust=FALSE, showposition=FALSE)
# abundance data

}

## End(Not run)