Calculates the Community Distance (CD) given paired sets of tips on a phylogeny. The Community Distance is the beta diversity version of Mean Pairwise Distance (MPD), giving the average phylogenetic distance between two communities. The same function can also calculate the standardized value of this measure for the given tip sets. The standardized calculations consider equal (uniform) probability among all possible tip samples of the same richness.

1 2 |

`tree` |
A phylo tree object |

`matrix.a` |
A matrix with binary (0/1) values, where each row represents a tip set. Each column name in the matrix must match a tip label on the input tree. If not all values in the matrix are binary, we consider two cases; if the matrix contains only non-negative values, all values are coerced to binary ones and a warning message is printed. If the matrix contains at least one negative value, the function throws an error |

`matrix.b` |
Optional, a second matrix with a similar format as matrix.a |

`query.matrix` |
Optional, a two-column matrix specifying the pairs of rows (tip sets) for which the function computes the CD values. Each row in query.matrix indicates a pair of tip sets for which we want to compute the CD value. Let k and r be the values that are stored in the i-th row of query.matrix, where k is the value stored in the first column and r is the value stored in the second column. If matrix.b is given, the function computes the CD value between the k-th row of matrix.a and the r-th row of matrix.b. If matrix.b is not given, the function computes the CD value between the k-th and r-th row of matrix.a (default = NULL) |

`standardize` |
Specifies whether the function should return the standardized value of the CD for each sample pair. The value is standardized by subtracting the mean and dividing by the standard deviation of the CD. The mean and standard deviation are calculated among all tip sets that have the same number of elements as the two samples (default = FALSE) |

Queries can be given in four ways. If neither matrix.b nor query.matrix are given, the function computes the CD values for all pairs of rows (tip sets) in matrix.a . If matrix.b is given but not query.matrix, the function computes the CD values for all combinations of a row in matrix.a with rows in matrix.b. If query.matrix is given and matrix.b is not, the function returns the CD values for the pairs of rows in matrix.a specified by query.matrix. If query.matrix and matrix.b are both given, CD values are computed for the rows in matrix.a specified by the first column of query.matrix against the rows in matrix.b specified in the second column of query.matrix.

The CD values for the requested pairs of tip sets. If query.matrix is provided, then the values are returned in an one-dimensional vector. The i-th element of this vector is the CD value for the pair of tip sets indicated in the i-th row of query.matrix. If query.matrix is not provided, the CD values are returned in a matrix object; entry [i,j] in the output matrix stores the CD value between the tip sets specified on the i-th and j-th row of matrix.a (if matrix.b is not specified), or the CD value between the i-th row of matrix.a and the j-th row of matrix.b (if matrix.b is specified)

Constantinos Tsirogiannis (tsirogiannis.c@gmail.com)

Graham, C.H. and P.V.A. Fine. 2008. Phylogenetic beta diversity: linking ecological and evolutionary processes across space and time. Ecology Letters 11: 1265:1277.

Swenson, N.G. 2011. Phylogenetic beta diversity metrics, trait evolution and inferring functional beta diversity of communities. PLoS ONE: 6: e21264.

Tsirogiannis, C. and B. Sandel. In prep. Fast computation of measures of phylogenetic beta diversity.

`cd.moments`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
#Load phylogenetic tree of bird families from package "ape"
data(bird.families, package = "ape")
#Create 10 random communities with 50 families each
comm = matrix(0,nrow = 10,ncol = length(bird.families$tip.label))
for(i in 1:nrow(comm)) {comm[i,sample(1:ncol(comm),50)] = 1}
colnames(comm) = bird.families$tip.label
#Calculate all pairwise CD values for communities in comm
cd.query(bird.families,comm)
#Calculate pairwise distances from
#the first two rows of comm to all rows
cd.query(bird.families, comm[1:2,],comm)
#Calculate the distances from the first two rows
#to all rows using the query matrix
qm = expand.grid(1:2,1:10)
cd.query(bird.families,comm,query.matrix = qm)
#Calculate standardized versions
cd.query(bird.families,comm,standardize = TRUE)
``` |

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