# Efficient PIC algorithm for multiple traits

### Description

Following the function prep_multipic, this function efficiently performs the PIC algorithm for multiple traits simultaneously, allowing for rapid repeated calls using different datasets (e.g., for bootstrap simulations). NOTE: this function is intended for use via the do.call function (see example).

### Usage

1 2 | ```
multipic(ntip, nnode, edge1, edge2, edge_len, phe, contr,
var_contr, scaled, pic_len, pic_recon)
``` |

### Arguments

`ntip` |
This quantity is computed by the function prep_multipic |

`nnode` |
This quantity is computed by the function prep_multipic |

`edge1` |
This quantity is computed by the function prep_multipic |

`edge2` |
This quantity is computed by the function prep_multipic |

`edge_len` |
This quantity is computed by the function prep_multipic |

`phe` |
This quantity is computed by the function prep_multipic |

`contr` |
This quantity is computed by the function prep_multipic |

`var_contr` |
This quantity is computed by the function prep_multipic |

`scaled` |
This quantity is computed by the function prep_multipic |

`pic_len` |
This quantity is computed by the function prep_multipic |

`pic_recon` |
This quantity is computed by the function prep_multipic |

### Value

`contrasts ` |
A matrix of PICs, one column for each trait (rows correspond to node numbers on a postorder tree) |

`sum_invV ` |
Sum of the inverse of the phylogenetic covariance matrix: sum(solve(vcv(tree))) |

`log_detV ` |
The natural log of the determinant of the phylogenetic covariance matrix |

`root ` |
Vector of estimated root values for each trait |

`pic_len ` |
Vector of PIC-rescaled branch lengths |

`pic_recon ` |
Matrix of PIC-reconstructed ancestral values. NOTE: this is not equivalent to the ML ancestral estimates except for the root value! |

### References

Felsenstein, J. (1985) Phylogenies and the comparative method. American Naturalist, 125, 1-15.

Paradis, E., Claude, J. and Strimmer, K. (2004) APE: analyses of phylogenetics and evolution in R language. Bioinformatics, 20, 289-290.

Paradis, E. (2012) Analysis of Phylogenetics and Evolution with R (Second Edition). New York: Springer.

### See Also

pic

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | ```
require(phylocurve)
require(ape)
nspecies <- 1000
ntraits <- 500
tree <- rtree(n = nspecies) # Simulate a random 1000-species phylogeny
Y <- matrix(rnorm(nspecies*ntraits),ncol=ntraits) # Generate random data
rownames(Y) <- tree$tip.label
# Call prep_multipic
prep.Y <- prep_multipic(x = Y,phy = tree)
# Calculate phylogenetically independent contrasts using pic (ape package)
Y.pics.ape <- apply(X = Y,MARGIN = 2,FUN = pic,phy = tree)
# Calculate PICs using multipic
# returns a list with contrasts, sum_invV, log_detV, root
# 'contrast' is a matrix of PICs
# 'sum_invV' is equal to sum(solve(vcv(tree)))
# 'log_detV' is equal to log(det(vcv(tree)))
# 'root' is the maximum likelihood phenotypic value at the root
Y.pics.phylocurve <- do.call(multipic,prep.Y)
# Verify that results are identical
range(Y.pics.ape - Y.pics.phylocurve$contrasts)
# Generate 50 random datasets (NOT RUN)
#niter <- 50
#randomY <- vector(mode = "list",length = niter)
#for(i in 1:niter)
#{
# randomY[[i]] <- matrix(rnorm(nspecies*ntraits),ncol=ntraits)
# rownames(randomY[[i]]) <- tree$tip.label
#}
###########################################################################
# Compare time to calculate PICs on 50 random datasets using pic vs multipic
#
##### pic function (NOT RUN)
#system.time(for(i in 1:niter) apply(X = randomY[[i]],MARGIN = 2,FUN = pic,phy = tree))
##### user system elapsed
##### 18.35 0.23 18.61
##### multipic function (NOT RUN)
#system.time(for(i in 1:niter)
#{
# prep.Y$phe[1:nspecies,] <- randomY[[i]] # update prep.Y$phe with new data
# do.call(multipic,prep.Y)
#})
##### user system elapsed
##### 1.38 0.14 1.52
#
###########################################################################
``` |

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