R/perCapitaRates.R
In dwbapst/paleotree: Paleontological and Phylogenetic Analyses of Evolution
Defines functions
perCapitaRates
Documented in
perCapitaRates
#' Instantaneous \emph{per-Capita} Rates of Origination and Extinction from the Fossil Record
#'
#' Calculates and plots per-capita origination and extinction rates from
#' sequential discrete-time taxon ranges, following Foote (2000).
#'
#' @details
#' This function calculates the per-capita rates of taxonomic origination
#' and extinction from paleontological range data, as described by Foote
#' (2000). These values are the instantaneous rate of either type of event
#' occurring per lineage time-units. Although Foote (2001) also presents a
#' number of alternative rates collected from the prior literature such as
#' the 'Van Valen' rate metrics, these are not implemented here, but could be
#' estimated using the matrix invisibly output by this function (See Foote,
#' 2000, for the relevant equations for calculating these).
#'
#' The \code{timeList} object should be a list composed of two matrices, the first
#' matrix giving by-interval start and end times (in absolute time), the second
#' matrix giving the by-taxon first and last appearances in the intervals
#' defined in the first matrix, numbered as the rows. Absolute time should be
#' decreasing, while the intervals should be numbered so that the number
#' increases with time. Taxa alive in the modern should be either
#' (a) listed in \code{isExtant} or
#' (b) listed as last occurring in a time interval
#' that begins at time 0 and ends at time 0.
#' See the documentation for the time-scaling
#' function \code{\link{bin_timePaleoPhy}} and the simulation function
#' \code{\link{binTimeData}} for more information on formatting.
#'
#' Unlike some functions in \code{paleotree}, such as the diversity curve functions,
#' intervals must be both sequential and non-overlapping. The diversity curve
#' functions deal with such issues by assuming taxa occur from the base of the
#' interval they are first found in until the end of the last interval they
#' are occur in. This inflation of boundary crossers could badly bias estimates
#' of per-capita diversification rates.
#' @inheritParams DiversityCurves
#' @param plot If \code{TRUE}, the per-capita origination and extinctions rates are
#' plotted for each interval. Rates which cannot be calculated for an interval
#' will not be plotted, thus appearing as a gap in the plotted graph. The
#' author takes no responsibility for the aesthetics of this plot.
#' @param logRates If \code{TRUE}, rates plotted on log scale.
#' @param drop.extant Drops all extant taxa from a dataset before
#' calculating per-capita origination and extinction rates.
#' @param isExtant A vector of \code{TRUE} and \code{FALSE} values, same length as the
#' number of taxa in the second matrix of \code{timeList}, where \code{TRUE} values indicate
#' taxa that are alive in the modern day (and thus are boundary crossers which
#' leave the most recent interval). By default, this argument is \code{NULL} and instead
#' which taxa are extant is inferred based on which taxa occur in an interval
#' with start and end times both equal to zero. See details.
#' @param jitter If \code{TRUE} (default) the extinction rate will be plotted slightly
#' ahead of the origination rate on the time axis, so the two can be differentiated.
#' @param legendPosition The position of a legend indicating which line is
#' origination rate and which is extinction rate on the resulting plot. This
#' is given as the possible positions for argument \code{x} of the function
#'\code{\link{legend}}, and by default is \code{"topleft"}, which will be generally
#' useful if origination and extinction rates are initially low. If
#' \code{legendPosition = NA}, then a legend will not be plotted.
#' @return This function will invisibly return a ten column matrix,
#' where the number of rows is equal to the number of intervals. The
#' first two columns are interval start and end times and the third
#' column is interval length. The fourth through eighth column is the
#' four fundamental classes of taxa from Foote (2001):
#' \code{Nbt}, \code{NbL}, \code{NFt}, \code{NFL} and their sum, \code{N}.
#' The final two columns are the per-capita rates estimated for
#' each interval in units per lineage time-units;
#' the ninth column is the origination rate (\code{pRate}) and the tenth
#' column is the extinction rate (\code{qRate}).
#' @seealso \code{\link{DiversityCurves}}, \code{\link{SamplingConv}}
#' @references
#' Foote, M. 2000 Origination and extinction components of taxonomic diversity:
#' general problems. Pp. 74--102. In D. H. Erwin, and S. L. Wing, eds. Deep
#' Time: Paleobiology's Perspective. The Paleontological Society, Lawrence,
#' Kansas.
#' @examples
#'
#' \donttest{
#'
#' #with the retiolinae dataset
#' data(retiolitinae)
#' perCapitaRates(retioRanges)
#'
#' # Simulate some fossil ranges with simFossilRecord
#' set.seed(444)
#' record <- simFossilRecord(
#' p = 0.1, q = 0.1, nruns = 1, nTotalTaxa = c(80,100), nExtant = 0)
#' taxa <- fossilRecord2fossilTaxa(record)
#'
#' #simulate a fossil record with imperfect sampling with sampleRanges()
#' rangesCont <- sampleRanges(taxa,r = 0.5)
#'
#' #Now let's use binTimeData() to bin in intervals of 5 time units
#' rangesDisc <- binTimeData(rangesCont,int.length = 5)
#'
#' #and get the per-capita rates
#' perCapitaRates(rangesDisc)
#'
#' #on a log scale
#' perCapitaRates(rangesDisc,logRates = TRUE)
#'
#'
#' #get mean and median per-capita rates
#' res <- perCapitaRates(rangesDisc,plot = FALSE)
#'
#' apply(res[,c("pRate","qRate")],2,mean,na.rm = TRUE)
#'
#' apply(res[,c("pRate","qRate")],2,median,na.rm = TRUE)
#'
#' ##############################
#' #with modern taxa
#' set.seed(444)
#'
#' record <- simFossilRecord(
#' p = 0.1,
#' q = 0.1,
#' nruns = 1,
#' nExtant = c(10,50)
#' )
#'
#' taxa <- fossilRecord2fossilTaxa(record)
#'
#' #simulate a fossil record with imperfect sampling with sampleRanges()
#' rangesCont <- sampleRanges(taxa,r = 0.5,,modern.samp.prob = 1)
#'
#' #Now let's use binTimeData() to bin in intervals of 5 time units
#' rangesDisc <- binTimeData(rangesCont,int.length = 5)
#'
#' #and now get per-capita rates
#' perCapitaRates(rangesDisc)
#'
#' }
#' @export
perCapitaRates <- function(
timeList,
plot = TRUE,
logRates = FALSE,
drop.extant = FALSE,
isExtant = NULL,
jitter = TRUE,
legendPosition = "topleft"
){
#####################
#
# this function estimates per-capita rates
# for binned intervals from discrete interval range data
# based on Foote, 2000
# input is a list with (1) interval times matrix and (2) species FOs and LOs
# time interval starts and ends can be pre-input as a 2 column matrix
# HOWEVER this could be pretty misleading!
# standing richness may never be high as the apparent richness of some bins
# if there is a single interval that is start = 0 and end = 0,
# it is dropped and all appearances in this interval are either
# (a) melded onto the next most recent interval
# (b) dropped if drop.extant = TRUE
# output is a matrix of int-start, int-end, p, q
# example
# timeList <- rangesDisc;int.times = NULL;
# plot = TRUE;plotLogRates = FALSE;timelims = NULL
# drop.extant = FALSE;isExtant = NULL;split.int = TRUE
#
if(!inherits(timeList[[1]],"matrix")){
if(inherits(timeList[[1]],"data.frame")){
timeList[[1]] <- as.matrix(timeList[[1]])
}else{
stop("timeList[[1]] not of matrix or data.frame format")
}
}
if(!inherits(timeList[[2]],"matrix")){
if(inherits(timeList[[2]],"data.frame")){
timeList[[2]] <- as.matrix(timeList[[2]])
}else{
stop("timeList[[2]] not of matrix or data.frame format")
}
}
#the intervals the DATA is given in
intMat <- timeList[[1]]
timeData <- timeList[[2]]
timeData <- timeData[!is.na(timeData[,1]),,drop = FALSE]
if(any(is.na(timeData))){
stop("Weird NAs in Data??")
}
if(any(apply(intMat,1,diff)>0)){
stop("timeList[[1]] not in intervals in time relative to modern")
}
if(any(intMat[,2]<0)){
stop("Some dates in timeList[[1]] <0 ?")
}
if(any(apply(timeData,1,diff)<0)){
stop("timeList[[2]] not in intervals numbered from first to last (1 to infinity)")
}
if(any(timeData[,2]<0)){stop(
"Some dates in timeList[[2]] <0 ?")
}
#get rid of modern intervals
modInt <- which(intMat[,1] == 0)
if(length(modInt)>0){
if(drop.extant){
timeData <- timeData[!(timeData[,2] == modInt),]
}else{
if(is.null(isExtant)){isExtant <- timeData[,2] == modInt}
altMod <- which(!intMat[,1] == 0 & intMat[,2] == 0)
timeData[timeData[,1] == modInt,1] <- altMod
timeData[timeData[,2] == modInt,2] <- altMod
}
intMat <- intMat[-modInt,]
}
if(is.null(isExtant)){isExtant <- rep(FALSE,nrow(timeData))}
# make sure data is absolutely sequential and overlapping
isSequential_1 <- all(apply(intMat,2,function(x) identical(x,rev(sort(x)))))
isNonRep <- all(apply(intMat,2,function(x) identical(length(x),length(unique(x)))))
isSequential_2 <- all(sapply(2:nrow(intMat),function(x) intMat[x,1] == intMat[x-1,2]))
if(!(isSequential_1 & isSequential_2 & isNonRep)){
stop("Sorry, intervals need to be sequential, ordered and non-overlapping.")
}
#now get int length to modify rates with
intlen <- (-apply(intMat,1,diff))
#modify timeData if there are any extant taxa
if(any(isExtant)){timeData[isExtant,2] <- nrow(intMat)+1}
#get the four values
Nbt <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1]<x & timeData[,2]>x)
)
NbL <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1]<x & timeData[,2] == x)
)
NFt <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1] == x & timeData[,2]>x)
)
NFL <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1] == x & timeData[,2] == x)
)
N <- Nbt+NbL+NFt+NFL #total diversity
#now calculate rates
pRate <- ifelse(Nbt == 0,NA,-log(Nbt/(Nbt+NFt))/intlen)
qRate <- ifelse(Nbt == 0,NA,-log(Nbt/(Nbt+NbL))/intlen)
if(plot){
int.start <- intMat[,1];int.end <- intMat[,2]
times1 <- c(int.start,(int.end+((int.start-int.end)/100)))
#add a jigger so rates don't overlap
jigger <- min(diff(times1))/10
p1 <- c(pRate,pRate)[order(times1)]
q1 <- c(qRate,qRate)[order(times1)]
times1 <- sort(times1)
if(logRates){
p1[!(p1>0)] <- NA
q1[!(q1>0)] <- NA
ylims <- c(
min(c(p1,q1),na.rm = TRUE),
(max(c(p1,q1),na.rm = TRUE))*1.5
)
plot(
times1, p1,
type = "l", log = "y",
col = 4, lwd = 2, lty = 5,
xlim = c(max(times1),max(0,min(times1))),
ylim = ylims,
xlab = "Time (Before Present)",
ylab = "Instantaneous Per-Capita Rate (per Ltu)"
)
}else{
ylims <- c(
min(c(p1,q1),na.rm = TRUE),
(max(c(p1,q1),na.rm = TRUE))*1.2
)
plot(
times1, p1,
type = "l", col = 4, lwd = 2, lty = 5,
xlim = c(max(times1), max(0,min(times1))),
ylim = ylims,
xlab = "Time (Before Present)",
ylab = "Instantaneous Per-Capita Rate (per Ltu)"
)
}
if(jitter){
lines(times1+jigger,q1,col = 2,lwd = 2,lty = 2)
}else{
lines(times1,q1,col = 2,lwd = 2,lty = 2)
}
if(!is.na(legendPosition)){
legend(
x = legendPosition,
legend = c("Origination","Extinction"),
lty = c(5,2),
lwd = 2,
col = c(4,2)
)
}
}
res <- cbind(
intMat, intlen,
Nbt, NbL, NFt, NFL,
N, pRate, qRate
)
return(invisible(res))
}
dwbapst/paleotree documentation built on Aug. 30, 2022, 6:44 a.m.
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Defines functions perCapitaRates
Documented in perCapitaRates
#' Instantaneous \emph{per-Capita} Rates of Origination and Extinction from the Fossil Record
#'
#' Calculates and plots per-capita origination and extinction rates from
#' sequential discrete-time taxon ranges, following Foote (2000).
#'
#' @details
#' This function calculates the per-capita rates of taxonomic origination
#' and extinction from paleontological range data, as described by Foote
#' (2000). These values are the instantaneous rate of either type of event
#' occurring per lineage time-units. Although Foote (2001) also presents a
#' number of alternative rates collected from the prior literature such as
#' the 'Van Valen' rate metrics, these are not implemented here, but could be
#' estimated using the matrix invisibly output by this function (See Foote,
#' 2000, for the relevant equations for calculating these).
#'
#' The \code{timeList} object should be a list composed of two matrices, the first
#' matrix giving by-interval start and end times (in absolute time), the second
#' matrix giving the by-taxon first and last appearances in the intervals
#' defined in the first matrix, numbered as the rows. Absolute time should be
#' decreasing, while the intervals should be numbered so that the number
#' increases with time. Taxa alive in the modern should be either
#' (a) listed in \code{isExtant} or
#' (b) listed as last occurring in a time interval
#' that begins at time 0 and ends at time 0.
#' See the documentation for the time-scaling
#' function \code{\link{bin_timePaleoPhy}} and the simulation function
#' \code{\link{binTimeData}} for more information on formatting.
#'
#' Unlike some functions in \code{paleotree}, such as the diversity curve functions,
#' intervals must be both sequential and non-overlapping. The diversity curve
#' functions deal with such issues by assuming taxa occur from the base of the
#' interval they are first found in until the end of the last interval they
#' are occur in. This inflation of boundary crossers could badly bias estimates
#' of per-capita diversification rates.
#' @inheritParams DiversityCurves
#' @param plot If \code{TRUE}, the per-capita origination and extinctions rates are
#' plotted for each interval. Rates which cannot be calculated for an interval
#' will not be plotted, thus appearing as a gap in the plotted graph. The
#' author takes no responsibility for the aesthetics of this plot.
#' @param logRates If \code{TRUE}, rates plotted on log scale.
#' @param drop.extant Drops all extant taxa from a dataset before
#' calculating per-capita origination and extinction rates.
#' @param isExtant A vector of \code{TRUE} and \code{FALSE} values, same length as the
#' number of taxa in the second matrix of \code{timeList}, where \code{TRUE} values indicate
#' taxa that are alive in the modern day (and thus are boundary crossers which
#' leave the most recent interval). By default, this argument is \code{NULL} and instead
#' which taxa are extant is inferred based on which taxa occur in an interval
#' with start and end times both equal to zero. See details.
#' @param jitter If \code{TRUE} (default) the extinction rate will be plotted slightly
#' ahead of the origination rate on the time axis, so the two can be differentiated.
#' @param legendPosition The position of a legend indicating which line is
#' origination rate and which is extinction rate on the resulting plot. This
#' is given as the possible positions for argument \code{x} of the function
#'\code{\link{legend}}, and by default is \code{"topleft"}, which will be generally
#' useful if origination and extinction rates are initially low. If
#' \code{legendPosition = NA}, then a legend will not be plotted.
#' @return This function will invisibly return a ten column matrix,
#' where the number of rows is equal to the number of intervals. The
#' first two columns are interval start and end times and the third
#' column is interval length. The fourth through eighth column is the
#' four fundamental classes of taxa from Foote (2001):
#' \code{Nbt}, \code{NbL}, \code{NFt}, \code{NFL} and their sum, \code{N}.
#' The final two columns are the per-capita rates estimated for
#' each interval in units per lineage time-units;
#' the ninth column is the origination rate (\code{pRate}) and the tenth
#' column is the extinction rate (\code{qRate}).
#' @seealso \code{\link{DiversityCurves}}, \code{\link{SamplingConv}}
#' @references
#' Foote, M. 2000 Origination and extinction components of taxonomic diversity:
#' general problems. Pp. 74--102. In D. H. Erwin, and S. L. Wing, eds. Deep
#' Time: Paleobiology's Perspective. The Paleontological Society, Lawrence,
#' Kansas.
#' @examples
#'
#' \donttest{
#'
#' #with the retiolinae dataset
#' data(retiolitinae)
#' perCapitaRates(retioRanges)
#'
#' # Simulate some fossil ranges with simFossilRecord
#' set.seed(444)
#' record <- simFossilRecord(
#' p = 0.1, q = 0.1, nruns = 1, nTotalTaxa = c(80,100), nExtant = 0)
#' taxa <- fossilRecord2fossilTaxa(record)
#'
#' #simulate a fossil record with imperfect sampling with sampleRanges()
#' rangesCont <- sampleRanges(taxa,r = 0.5)
#'
#' #Now let's use binTimeData() to bin in intervals of 5 time units
#' rangesDisc <- binTimeData(rangesCont,int.length = 5)
#'
#' #and get the per-capita rates
#' perCapitaRates(rangesDisc)
#'
#' #on a log scale
#' perCapitaRates(rangesDisc,logRates = TRUE)
#'
#'
#' #get mean and median per-capita rates
#' res <- perCapitaRates(rangesDisc,plot = FALSE)
#'
#' apply(res[,c("pRate","qRate")],2,mean,na.rm = TRUE)
#'
#' apply(res[,c("pRate","qRate")],2,median,na.rm = TRUE)
#'
#' ##############################
#' #with modern taxa
#' set.seed(444)
#'
#' record <- simFossilRecord(
#' p = 0.1,
#' q = 0.1,
#' nruns = 1,
#' nExtant = c(10,50)
#' )
#'
#' taxa <- fossilRecord2fossilTaxa(record)
#'
#' #simulate a fossil record with imperfect sampling with sampleRanges()
#' rangesCont <- sampleRanges(taxa,r = 0.5,,modern.samp.prob = 1)
#'
#' #Now let's use binTimeData() to bin in intervals of 5 time units
#' rangesDisc <- binTimeData(rangesCont,int.length = 5)
#'
#' #and now get per-capita rates
#' perCapitaRates(rangesDisc)
#'
#' }
#' @export
perCapitaRates <- function(
timeList,
plot = TRUE,
logRates = FALSE,
drop.extant = FALSE,
isExtant = NULL,
jitter = TRUE,
legendPosition = "topleft"
){
#####################
#
# this function estimates per-capita rates
# for binned intervals from discrete interval range data
# based on Foote, 2000
# input is a list with (1) interval times matrix and (2) species FOs and LOs
# time interval starts and ends can be pre-input as a 2 column matrix
# HOWEVER this could be pretty misleading!
# standing richness may never be high as the apparent richness of some bins
# if there is a single interval that is start = 0 and end = 0,
# it is dropped and all appearances in this interval are either
# (a) melded onto the next most recent interval
# (b) dropped if drop.extant = TRUE
# output is a matrix of int-start, int-end, p, q
# example
# timeList <- rangesDisc;int.times = NULL;
# plot = TRUE;plotLogRates = FALSE;timelims = NULL
# drop.extant = FALSE;isExtant = NULL;split.int = TRUE
#
if(!inherits(timeList[[1]],"matrix")){
if(inherits(timeList[[1]],"data.frame")){
timeList[[1]] <- as.matrix(timeList[[1]])
}else{
stop("timeList[[1]] not of matrix or data.frame format")
}
}
if(!inherits(timeList[[2]],"matrix")){
if(inherits(timeList[[2]],"data.frame")){
timeList[[2]] <- as.matrix(timeList[[2]])
}else{
stop("timeList[[2]] not of matrix or data.frame format")
}
}
#the intervals the DATA is given in
intMat <- timeList[[1]]
timeData <- timeList[[2]]
timeData <- timeData[!is.na(timeData[,1]),,drop = FALSE]
if(any(is.na(timeData))){
stop("Weird NAs in Data??")
}
if(any(apply(intMat,1,diff)>0)){
stop("timeList[[1]] not in intervals in time relative to modern")
}
if(any(intMat[,2]<0)){
stop("Some dates in timeList[[1]] <0 ?")
}
if(any(apply(timeData,1,diff)<0)){
stop("timeList[[2]] not in intervals numbered from first to last (1 to infinity)")
}
if(any(timeData[,2]<0)){stop(
"Some dates in timeList[[2]] <0 ?")
}
#get rid of modern intervals
modInt <- which(intMat[,1] == 0)
if(length(modInt)>0){
if(drop.extant){
timeData <- timeData[!(timeData[,2] == modInt),]
}else{
if(is.null(isExtant)){isExtant <- timeData[,2] == modInt}
altMod <- which(!intMat[,1] == 0 & intMat[,2] == 0)
timeData[timeData[,1] == modInt,1] <- altMod
timeData[timeData[,2] == modInt,2] <- altMod
}
intMat <- intMat[-modInt,]
}
if(is.null(isExtant)){isExtant <- rep(FALSE,nrow(timeData))}
# make sure data is absolutely sequential and overlapping
isSequential_1 <- all(apply(intMat,2,function(x) identical(x,rev(sort(x)))))
isNonRep <- all(apply(intMat,2,function(x) identical(length(x),length(unique(x)))))
isSequential_2 <- all(sapply(2:nrow(intMat),function(x) intMat[x,1] == intMat[x-1,2]))
if(!(isSequential_1 & isSequential_2 & isNonRep)){
stop("Sorry, intervals need to be sequential, ordered and non-overlapping.")
}
#now get int length to modify rates with
intlen <- (-apply(intMat,1,diff))
#modify timeData if there are any extant taxa
if(any(isExtant)){timeData[isExtant,2] <- nrow(intMat)+1}
#get the four values
Nbt <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1]<x & timeData[,2]>x)
)
NbL <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1]<x & timeData[,2] == x)
)
NFt <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1] == x & timeData[,2]>x)
)
NFL <- sapply(1:nrow(intMat), function(x)
sum(timeData[,1] == x & timeData[,2] == x)
)
N <- Nbt+NbL+NFt+NFL #total diversity
#now calculate rates
pRate <- ifelse(Nbt == 0,NA,-log(Nbt/(Nbt+NFt))/intlen)
qRate <- ifelse(Nbt == 0,NA,-log(Nbt/(Nbt+NbL))/intlen)
if(plot){
int.start <- intMat[,1];int.end <- intMat[,2]
times1 <- c(int.start,(int.end+((int.start-int.end)/100)))
#add a jigger so rates don't overlap
jigger <- min(diff(times1))/10
p1 <- c(pRate,pRate)[order(times1)]
q1 <- c(qRate,qRate)[order(times1)]
times1 <- sort(times1)
if(logRates){
p1[!(p1>0)] <- NA
q1[!(q1>0)] <- NA
ylims <- c(
min(c(p1,q1),na.rm = TRUE),
(max(c(p1,q1),na.rm = TRUE))*1.5
)
plot(
times1, p1,
type = "l", log = "y",
col = 4, lwd = 2, lty = 5,
xlim = c(max(times1),max(0,min(times1))),
ylim = ylims,
xlab = "Time (Before Present)",
ylab = "Instantaneous Per-Capita Rate (per Ltu)"
)
}else{
ylims <- c(
min(c(p1,q1),na.rm = TRUE),
(max(c(p1,q1),na.rm = TRUE))*1.2
)
plot(
times1, p1,
type = "l", col = 4, lwd = 2, lty = 5,
xlim = c(max(times1), max(0,min(times1))),
ylim = ylims,
xlab = "Time (Before Present)",
ylab = "Instantaneous Per-Capita Rate (per Ltu)"
)
}
if(jitter){
lines(times1+jigger,q1,col = 2,lwd = 2,lty = 2)
}else{
lines(times1,q1,col = 2,lwd = 2,lty = 2)
}
if(!is.na(legendPosition)){
legend(
x = legendPosition,
legend = c("Origination","Extinction"),
lty = c(5,2),
lwd = 2,
col = c(4,2)
)
}
}
res <- cbind(
intMat, intlen,
Nbt, NbL, NFt, NFL,
N, pRate, qRate
)
return(invisible(res))
}
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