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#' Construct a Stochastic Sequenced Time-List from an Unsequenced Time-List
#'
#' This function randomly samples from a \code{timeList} object (i.e. a list composed of a matrix of interval start and end
#' dates and a matrix of taxon first and last intervals), to find a set of taxa and intervals that do not overlap,
#' output as a new \code{timeList} object.
#' @details
#' Many analyses of diversification and sampling in the fossil record require a dataset composed of sequential non-overlapping intervals,
#' but the nature of the geologic record often makes this difficult, with taxa from different regions, environments and sedimentary basins
#' having first and last appearances placed in entirely in-congruent systems of chronostratigraphic intervals. While one option is to convert
#' such occurrences to a single, global stratigraphic system, this may still result in overlapping intervals when fossil collections are poorly
#' constrained stratigraphically. (For example, this may often be the case in global datasets.)
#' This function offers an approach to avoid this issue in large datasets by randomly subsampling
#' the available taxa and intervals to produce stochastic
#' sets of ranges composed of data drawn from non-overlapping intervals.
#'
#' \code{seqTimeList} is stochastic and thus should be set for many runs to produce many such solutions. Additionally,
#' all solutions found are returned, and users may wish to sort amongst these to maximize the number of intervals and
#' number of taxa returned. A single solution which maximizes returned taxa and intervals may not be a precise enough approach
#' to estimating sampling rates, however, given the uncertainty in data. Thus, many runs should always be considered.
#'
#' By default, solutions are searched for without consideration to the length of intervals used (i.e. the selection of intervals is 'unweighted').
#' Alternatively, we can 'weight' selection toward the smallest intervals in the set, using the argument \code{weightSampling}. Smaller
#' intervals presumably overlap less and thus should retain more taxa and intervals of more equal length. However, in practice with empirical datasets,
#' the package author finds these approaches do not seem to produce very different estimates.
#'
#' For some datasets, many solutions found using \code{seqTimeList} may return infinite sampling values. This is often due to saving too many taxa
#' found in single intervals to the exclusion of longer-ranging taxa (see the example). This excess of single interval taxa is a clear artifact
#' of the randomized \code{seqTimeList} procedure and such solutions should probably be ignored.
#' @param timeList A list composed of two matrices, giving interval start and end
#' dates and taxon first and last occurrences within those intervals. Some intervals
#' are expected to overlap (thus necessitating the use of this function), and datasets
#' lacking overlapping intervals will return an error message.
#' @param nruns Number of new \code{timeList} composed of non-overlapping intervals produced.
#' @param weightSampling If \code{TRUE}, weight sampling of new intervals toward smaller intervals.
#' \code{FALSE} by default.
#' @return
#' A list, composed of three elements: \code{nIntervals}, a vector of the
#' number of intervals in each solution, \code{nTaxa}, a vector of the number of
#' taxa in each solution, and \code{timeLists}, a list composed of each new
#' \code{timeList} object as an element.
#' @seealso
#' Resulting time-lists can be analyzed with \code{\link{freqRat}}, \code{\link{durationFreq}}, etc.
#'
#' Additionally, \code{\link{binTimeData}} can be useful for simulating interval data.
#' @author David W. Bapst
#' @examples
#' # Simulate some fossil ranges with simFossilRecord
#' set.seed(444)
#' record <- simFossilRecord(
#' p = 0.1,
#' q = 0.1,
#' nruns = 1,
#' nTotalTaxa = c(60,80),
#' nExtant = 0
#' )
#' taxa <- fossilRecord2fossilTaxa(record)
#' # simulate a fossil record with imperfect sampling with sampleRanges()
#' rangesCont <- sampleRanges(taxa,r = 0.1)
#'
#' # Now let's use binTimeData to get ranges in discrete overlapping intervals
#' # via pre-set intervals input
#' presetIntervals <- cbind(
#' c(1000, 995, 990, 980, 970, 975, 960, 950, 940, 930, 900, 890, 888, 879, 875),
#' c(995, 989, 960, 975, 960, 950, 930, 930, 930, 900, 895, 888, 880, 875, 870)
#' )
#' rangesDisc1 <- binTimeData(rangesCont, int.times = presetIntervals)
#'
#' seqLists <- seqTimeList(rangesDisc1, nruns = 10)
#' seqLists$nTaxa
#' seqLists$nIntervals
#'
#' #apply freqRat as an example analysis
#' sapply(seqLists$timeLists, freqRat)
#'
#' # notice the zero and infinite freqRat estimates? What's going on?
#'
#' freqRat(seqLists$timeLists[[4]], plot = TRUE)
#'
#' # too few taxa of two or three interval durations for the ratio to work properly
#' # perhaps ignore these estimates
#'
#' # with weighted selection of intervals
#' seqLists <- seqTimeList(rangesDisc1, nruns = 10, weightSampling = TRUE)
#'
#' seqLists$nTaxa
#' seqLists$nIntervals
#' sapply(seqLists$timeLists, freqRat)
#'
#' # didn't have much effect in this simulated example
#' @export seqTimeList
seqTimeList <- function(
timeList,
nruns = 100,
weightSampling = FALSE
){
#############################################
timeList[[1]] <- as.matrix(timeList[[1]])
timeList[[2]] <- as.matrix(timeList[[2]])
#let's try to get sampling rates out of a timeList with overlapping intervals
#test for overlap
lap <- any(!apply(timeList[[1]],1,function(x)
2>sum(x[1]>(timeList[[1]][,2]) & x[2]<(timeList[[1]][,1]))))
if(!lap){stop("Your timeList doesn't have any overlap??")}
#let's make a list of valid intervals
#first, all non-overlapping intervals
noLap <- which(apply(timeList[[1]],1,function(x)
2>sum(x[1]>(timeList[[1]][,2]) & x[2]<(timeList[[1]][,1]))))
#now let's search iteratively for interval solutions
nInts <- nTaxa <- numeric()
savedLists <- list(1:nruns)
for(i in 1:nruns){
#set it up!
valid <- noLap
invalid <- numeric()
if(length(valid)>0){
candidate <- (1:nrow(timeList[[1]]))[-valid]
}else{
candidate <- (1:nrow(timeList[[1]]))
}
#LOOP
while(length(candidate)>1){
#next, let's pull out a random candidate interval
if(weightSampling){
weights <- order(apply(timeList[[1]][candidate,,drop = FALSE],1,diff))
weights <- weights/sum(weights)
draw <- sample(1:length(candidate),1,prob = weights)
}else{
draw <- sample(1:length(candidate),1)
}
#remove from candidate, add to valid
valid <- c(valid,candidate[draw])
drawInt <- timeList[[1]][candidate[draw],]
candidate <- candidate[-draw]
#add all overlapping to invalid and remove from candidate
candInt <- timeList[[1]][candidate,,drop = FALSE]
badInt <- apply(candInt,1,function(x) drawInt[1]>x[2] & drawInt[2]<x[1])
invalid <- c(invalid,candidate[badInt])
candidate <- candidate[!badInt]
#
#newInts <- timeList[[1]][valid,]
#if(any(!apply(newInts,1,function(x)
# 2>sum(x[1]>(newInts[,2]) & x[2]<(newInts[,1]))))){
# stop("WHAT!")}
}
if(length(candidate) == 1){valid <- c(valid,candidate)}
valid <- sort(valid)
newInts <- timeList[[1]][valid,]
# test that there be no overlaps
if(any(!apply(newInts,1,function(x)
2>sum(x[1]>(newInts[,2]) & x[2]<(newInts[,1]))))){stop("WHAT!")}
#
validTaxa <- apply(timeList[[2]],1,function(x) any(x[1] == valid) & any(x[2] == valid))
cropTaxa <- timeList[[2]][validTaxa,]
newTaxa <- cbind(sapply(cropTaxa[,1],function(x) which(x == valid)),
sapply(cropTaxa[,2],function(x) which(x == valid)))
nInts[i] <- nrow(newInts)
nTaxa[i] <- nrow(newTaxa)
savedLists[[i]] <- list(intTimes = newInts,taxonTimes = newTaxa)
}
results <- list(nIntervals = nInts,nTaxa = nTaxa,timeLists = savedLists)
return(results)
}
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