Calculates the Core Ancestor Cost (CAC) for sets of tips on a phylogeny. The CAC is calculated by identifying the node in the tree that is the most recent common ancestor of at least chi proportion of the tips in the set. The CAC is the distance of this node from the root of the tree. The same function can also calculate the standardized value of this measure under three different null models which maintain species richness.

1 2 |

`tree` |
A phylo tree object |

`matrix` |
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. |

`chi` |
A number in the interval (0.5,1] |

`standardize` |
Specifies whether the function should standardize the CAC value according to the variation in species richness. For each input tip set R, the CAC value for R is standardized by subtracting the mean CAC and dividing by the standard deviation of this measure. The mean and standard deviation are calculated among all tip sets that have the same number of elements as set R (default = FALSE) |

`null.model` |
A character vector (string) that defines which null model is used for computing the standardized values of the measure. There are two possible null models that can be used for computing the standardized values: these are "uniform", and "sequential". Both models maintain species richness. More specifically, the available models are defined as follows: -
**"uniform"**considers samples with equal (uniform) probability among all possible tip samples of the same richness. -
**"sequential"**is an abundance-weighted null model where species samples are chosen based on the same method as R's*sample*function. Unlike the other model (which is computed analytically), this model uses Monte-Carlo randomization.
This argument is optional, and its default value is set to "uniform". |

`abundance.weights` |
A vector of positive numeric values. These are the abundance weights that will be used if option "sequential" is selected. The names stored at the vector must match the names of the tips in the tree. This argument is redundant if the "uniform" model is selected. |

`reps` |
An integer that defines the number of Monte-Carlo random repetitions that will be performed when using the "sequential" model. This argument is redundant if the "uniform" model selected. |

`seed` |
A positive integer that defines the random seed used in the Monte-Carlo randomizations of the "sequential" model. This argument is optional, and becomes redundant if this model is not selected. |

A vector which stores the computed (standardized) CAC values. The i-th entry in this vector stores the CAC value of the i-th row in the input matrix.

Constantinos Tsirogiannis (tsirogiannis.c@gmail.com)

Tsirogiannis, C. and B. Sandel. 2015. PhyloMeasures: A package for computing phylogenetic biodiversity measures and their statistical moments. Ecography, doi: 10.1111/ecog.01814, 2015.

Tsirogiannis, C., B. Sandel and A. Kalvisa. 2014. New algorithms for computing phylogenetic biodiversity. Algorithms in Bioinformatics, LNCS 8701: 187-203.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
#Load phylogenetic tree of bird families from package "ape"
data(bird.families, package = "ape")
#Create 100 random communities with 50 families each
comm = matrix(0,nrow = 100,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 cac values for each community
cac.query(bird.families,comm,0.8)
#Calculate standardized versions under the uniform model
cac.query(bird.families,comm,0.8,TRUE)
# Create random abundance weights
weights = runif(length(bird.families$tip.label))
names(weights) = bird.families$tip.label
#Use query function to calculate standardized versions under the sequential model
cac.query(bird.families,comm,0.8,TRUE,null.model="sequential",
abundance.weights=weights, reps=1000)
``` |

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