perCapitaRates
Description
Calculates and plots percapita origination and extinction rates from sequential discretetime taxon ranges, following Foote (2000).
Usage
1 2 3 
Arguments
timeList 
A list composed of two matrices, giving interval start and end dates and taxon first and last occurrences within those intervals. See details. 
plot 
If true, the percapita 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. 
logRates 
If true, rates plotted on log scale. 
drop.extant 
Drops all extant taxa from a dataset before calculating percapita origination and extinction rates. 
isExtant 
A vector of TRUE and FALSE values, same length as the number of taxa in the second matrix of timeList, where 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 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. 
jitter 
If TRUE (default) the extinction rate will be plotted slightly ahead of the origination rate on the time axis, so the two can be differentiated. 
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 'x' of the function

Details
This function calculates the percapita 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 timeunits. Although Foote (2001) also presents a number of alternative rates collected from the prior literature such as the VanValen rate metrics, these are not implemented here, but could be estimated using the matrix invisibly output by this function.
The timeList object should be a list composed of two matrices, the first
matrix giving byinterval start and end times (in absolute time), the second
matrix giving the bytaxon 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 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 timescaling
function bin_timePaleoPhy
and the simulation function
binTimeData
for more information on formatting.
Unlike some functions in paleotree, such as the diversity curve functions, intervals must be both sequential and nonoverlapping. 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 percapita diversification rates.
Value
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): Nbt, NbL, NFt, NFL and their sum, N. The final two columns are the percapita rates estimated for each interval in units per lineage timeunits; the ninth column is the origination rate ('pRate') and the tenth column is the extinction rate ('qRate').
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.
See Also
DiversityCurves
, SamplingConv
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  #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 percapita rates
perCapitaRates(rangesDisc)
#on a log scale
perCapitaRates(rangesDisc,logRates=TRUE)
#get mean and median percapita 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,
nTotalTaxa=c(80,100))
#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 percapita rates
perCapitaRates(rangesDisc)

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