horizonSampRate {paleotree}

Estimate Sampling Rate from Sampling Horizon Data (Solow and Smith, 1997)

Description

This function implements the exact maximum likelihood estimator for the instantaneous sampling rate from Solow and Smith (1997, Paleobiology), which is based on the relationship between the number of collections for a set of taxa and their durations (known precisely in continuous time).

Usage

horizonSampRate(sampOcc = NULL, durations = NULL, nCollections = NULL)

Arguments

sampOcc

A list with the number of elements equal to the number of taxa, and each element of the list being a numerical vector with the length equal to the number of collections for each taxon, and each value equal to the precise date of that fossil's time of collection. These dates do not need to be ordered. If not supplied, the elements durations and nCollections must be supplied.

durations

A vector of precise durations in continuous time, with the length equal to the number of taxa. If not supplied, this is calculated from SampOcc, which must be supplied.

nCollections

A vector of integers representing the number of collections for each taxon in the input durations. If not supplied this is calculated from SampOcc, which must be supplied.

Details

Given a dataset of taxa with a vector N, representing the number of collections for each taxon, and a vector D, giving the precise duration for each taxon, we can use the following maximum likelihood estimator from Solow and Smith (1997) to obtain the instantaneous sampling rate:

samplingRate = (sum(N-1)^2)/(sum(D)*sum(N))

This method is exclusively for datasets with very precisely dated horizons, such as microfossils from deep sea cores with very precise age models. The first and last appearance must be known very precisely to provide an equally precise estimate of the duration. Most datasets are not precise enough for this method, due to chronostratigraphic uncertainty. However, note that the age of individual collections other than the first and last appearance dates do not need to be known: its only the number of collections that matters.

Value

Returns the instantaneous sampling (in per lineage*time-units) as a single numerical value. Note that this is the instantaneous sampling rate and not the probability of sampling a taxon per interval.

References

Solow, A. R., and W. Smith. 1997. On Fossil Preservation and the Stratigraphic Ranges of Taxa. Paleobiology 23(3):271-277.

See Also

Duration frequency methods (Foote and Raup, 1996; Foote, 1997) use ranges alone to estimate sampling parameters, implemented in durationFreq.

Also see the conversion functions for sampling parameters at SamplingConv.

Examples

#can simulate this type of data with sampleRanges
    # just set ranges.only = FALSE
#let's try a simulation example:
set.seed(444)
record <- simFossilRecord(p = 0.1, q = 0.1, nruns = 1,
	nTotalTaxa = c(30,40), nExtant = 0)
taxa <- fossilRecord2fossilTaxa(record)
sampledOccurrences <- sampleRanges(taxa,r = 0.5,ranges.only = FALSE)

# now try with horizonSampRate
horizonSampRate(sampOcc = sampledOccurrences)

# but we could also try with the *other* inputs
   # useful because some datasets we may only have durations
   # and number of sampling events for
filtered <- sampledOccurrences[!is.na(sampledOccurrences)] 
dur <- sapply(filtered,max) - sapply(filtered,min)
nCol <- sapply(filtered,length)
# supply as durations and nCollections
horizonSampRate(durations = dur, nCollections = nCol)