## chronopl.R (2011-07-04) ## Molecular Dating With Penalized Likelihood ## Copyright 2005-2011 Emmanuel Paradis ## This file is part of the R-package `ape'. ## See the file ../COPYING for licensing issues. chronopl <- function(phy, lambda, age.min = 1, age.max = NULL, node = "root", S = 1, tol = 1e-8, CV = FALSE, eval.max = 500, iter.max = 500, ...) { n <- length(phy$tip.label) ROOT <- n + 1 if (length(node) == 1 && node == "root") node <- ROOT if (any(node <= n)) stop("node numbers should be greater than the number of tips") zerobl <- which(phy$edge.length <= 0) if (length(zerobl)) { if (any(phy$edge[zerobl, 2] <= n)) stop("at least one terminal branch is of length zero: you should remove it to have a meaningful estimation.") else { warning("at least one internal branch is of length zero: it was collapsed and some nodes have been deleted.") if (length(node) == 1 && node == ROOT) phy <- di2multi(phy) else { tmp <- FALSE if (is.null(phy$node.label)) { tmp <- !tmp phy$node.label <- paste("node", 1:phy$Nnode) } node.lab <- phy$node.label[node - n] phy <- di2multi(phy) node <- match(node.lab, phy$node.label) + n if (tmp) phy$node.label <- NULL } } } m <- phy$Nnode el <- phy$edge.length e <- phy$edge N <- dim(e)[1] TIPS <- 1:n EDGES <- 1:N ini.rate <- el el <- el/S ## `basal' contains the indices of the basal edges ## (ie, linked to the root): basal <- which(e[, 1] == ROOT) Nbasal <- length(basal) ## `ind' contains in its 1st column the index of all nonbasal ## edges, and in its second column the index of the edges ## where these edges come from (ie, this matrix contains pairs ## of contiguous edges), eg: ## ___b___ ind: ## | | | | ## ___a___| | b | a | ## | | c | a | ## |___c___ | | | ind <- matrix(0L, N - Nbasal, 2) ind[, 1] <- EDGES[-basal] ind[, 2] <- match(e[EDGES[-basal], 1], e[, 2]) age <- numeric(n + m) ##ini.time <- node.depth(phy)[-TIPS] - 1 ini.time <- node.depth(phy) - 1 ## first, rescale all times with respect to ## the age of the 1st element of `node': ratio <- age.min[1]/ini.time[node[1]] ini.time <- ini.time*ratio ## because if (!is.null(age.max)), 'node' is modified, so we copy it in case CV = TRUE: node.bak <- node if (length(node) > 1) { ini.time[node] <- age.min real.edge.length <- ini.time[e[, 1]] - ini.time[e[, 2]] while (any(real.edge.length <= 0)) { for (i in EDGES) { if (real.edge.length[i] > 0) next if (e[i, 1] %in% node) { ini.time[e[i, 2]] <- ini.time[e[1, 2]] - 2 * real.edge.length[i] next } if (e[i, 2] %in% node) { ini.time[e[i, 1]] <- ini.time[e[1, 1]] + 2 * real.edge.length[i] next } ##browser() ini.time[e[i, 2]] <- ini.time[e[1, 2]] - real.edge.length[i] ini.time[e[i, 1]] <- ini.time[e[1, 1]] + real.edge.length[i] } real.edge.length <- ini.time[e[, 1]] - ini.time[e[, 2]] ##print(min(real.edge.length)) } } ## `unknown.ages' will contain the index of the nodes of unknown age: unknown.ages <- n + 1:m ## define the bounds for the node ages: lower <- rep(tol, length(unknown.ages)) upper <- rep(1/tol, length(unknown.ages)) if (!is.null(age.max)) { # are some nodes known within some intervals? lower[node - n] <- age.min upper[node - n] <- age.max interv <- which(age.min != age.max) node <- node[-interv] if (length(node)) age[node] <- age.min[-interv] } else age[node] <- age.min if (length(node)) { unknown.ages <- unknown.ages[n - node] lower <- lower[n - node] upper <- upper[n - node] } ## `known.ages' contains the index of all nodes (internal and ## terminal) of known age: known.ages <- c(TIPS, node) ## concatenate the bounds for the rates: lower <- c(rep(tol, N), lower) upper <- c(rep(1 - tol, N), upper) minusploglik.gr <- function(rate, node.time) { grad <- numeric(N + length(unknown.ages)) age[unknown.ages] <- node.time real.edge.length <- age[e[, 1]] - age[e[, 2]] if (any(real.edge.length < 0)) { grad[] <- 0 return(grad) } ## gradient for the rates: ## the parametric part can be calculated without a loop: grad[EDGES] <- real.edge.length - el/rate if (Nbasal == 2) { # the simpler formulae if there's a basal dichotomy grad[basal[1]] <- grad[basal[1]] + lambda*(rate[basal[1]] - rate[basal[2]]) grad[basal[2]] <- grad[basal[2]] + lambda*(rate[basal[2]] - rate[basal[1]]) } else { # the general case for (i in 1:Nbasal) grad[basal[i]] <- grad[basal[i]] + lambda*(2*rate[basal[i]]*(1 - 1/Nbasal) - 2*sum(rate[basal[-i]])/Nbasal)/(Nbasal - 1) } for (i in EDGES) { ii <- c(which(e[, 2] == e[i, 1]), which(e[, 1] == e[i, 2])) if (!length(ii)) next grad[i] <- grad[i] + lambda*(2*length(ii)*rate[i] - 2*sum(rate[ii])) } ## gradient for the 'node times' for (i in 1:length(unknown.ages)) { nd <- unknown.ages[i] ii <- which(e[, 1] == nd) grad[i + N] <- sum(rate[ii] - el[ii]/real.edge.length[ii])#, na.rm = TRUE) if (nd != ROOT) { ii <- which(e[, 2] == nd) grad[i + N] <- grad[i + N] - rate[ii] + el[ii]/real.edge.length[ii] } } grad } minusploglik <- function(rate, node.time) { age[unknown.ages] <- node.time real.edge.length <- age[e[, 1]] - age[e[, 2]] if (any(real.edge.length < 0)) return(1e50) B <- rate*real.edge.length loglik <- sum(-B + el*log(B) - lfactorial(el)) -(loglik - lambda*(sum((rate[ind[, 1]] - rate[ind[, 2]])^2) + var(rate[basal]))) } out <- nlminb(c(ini.rate, ini.time[unknown.ages]), function(p) minusploglik(p[EDGES], p[-EDGES]), function(p) minusploglik.gr(p[EDGES], p[-EDGES]), control = list(eval.max = eval.max, iter.max = iter.max, ...), lower = lower, upper = upper) attr(phy, "ploglik") <- -out$objective attr(phy, "rates") <- out$par[EDGES] attr(phy, "message") <- out$message age[unknown.ages] <- out$par[-EDGES] if (CV) ophy <- phy phy$edge.length <- age[e[, 1]] - age[e[, 2]] if (CV) attr(phy, "D2") <- chronopl.cv(ophy, lambda, age.min, age.max, node.bak, n, S, tol, eval.max, iter.max, ...) phy } chronopl.cv <- function(ophy, lambda, age.min, age.max, nodes, n, S, tol, eval.max, iter.max, ...) ### ophy: the original phylogeny ### n: number of tips ### Note that we assume here that the order of the nodes ### in node.label are not modified by the drop.tip operation { cat("Doing cross-validation\n") BT <- branching.times(ophy) D2 <- numeric(n) for (i in 1:n) { cat("\r dropping tip ", i, " / ", n, sep = "") tr <- drop.tip(ophy, i) j <- which(ophy$edge[, 2] == i) if (ophy$edge[j, 1] %in% nodes) { k <- which(nodes == ophy$edge[j, 1]) node <- nodes[-k] agemin <- age.min[-k] agemax <- age.max[-k] } else node <- nodes if (length(node)) { chr <- chronopl(tr, lambda, age.min, age.max, node, S, tol, FALSE, eval.max, iter.max, ...) tmp <- if (Nnode(chr) == Nnode(ophy)) BT else BT[-(ophy$edge[j, 1] - n)] D2[i] <- sum((tmp - branching.times(chr))^2 / tmp) } else D2[i] <- 0 } cat("\n") D2 }