qage: Quantile-based age estimation

In evolucionario/cladeage: CladeAge: Estimating Clade Age Using The Fossil Record

Description

Quantile function that computes the age corresponding to a particular probability for the upper bound of a distribution of ages (Strauss & Sadler 1989, Gingerich & Uhen 1998, Solow 2003). The method of Strauss & Sadler (1989) assumes that the distribution of fossil ages is uniform and their formula depends on the fossil ages range and the number of fossil ages. The method of Solow (2003) is a general method for non-uniform distributions and depends on the temporal gap between the oldest and the second oldest fossil ages. Both methods assume that fossil ages are independent samples from the same distribution (only relevant for the two oldest ages for Solow's method), therefore, fossils should be as independent as possible (ideally from different geological formations and different regions).

In the particular case where there are only two fossil ages and no baseline age specified, Strauss & Sadler's and Solow's methods converge to the same result; the quantile functions are simply Xn/(1-P), and the likelihood function is 1/X.

Usage

qage(p = 0.5, ages, baseline = NULL, method = "StraussSadler")

Arguments

p	The desired probability level
ages	A vector of fossil ages. These do not need to be sorted
baseline	Youngest bound of the distribution that could be the present (=0) or some other geological age of reference. If a baseline is not provided, the minimum value of ages is used as baseline and n-1 is used for the sample size instead of n for calculations (Solow 2003).
method	Either "StraussSadler" for Strauss & Sadler's (1989) method (default) or "Solow" for Solow's (2003) method. A third option is to use the qbeta function (option "Beta"), since the ratio between the observed timespan and the real timespan for Strauss & Sadler's model is distributed according to a Beta distribution with parameters N and 1 (Wang et al. 2009); this should give the same results as "StraussSadler"

Value

A numeric value (or vector of numeric values, if multiple p values are provided) representing the age estimate of the clade origin given the method a p value provided

References

\insertRef

Claramunt2015cladeage

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Gingerich1998cladeage

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Norris2015cladeage

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Solow2003cladeage

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Strauss1989cladeage

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Wang2007cladeage

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Wang2009cladeage

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Wang2010cladeage

Examples

## Not run: 
  # The following demonstrates how inferences depend on p and method
  qage(p=c(0.1, 0.5, 0.9), ages=c(54, 30, 25, 14, 5));
  qage(p=c(0.1, 0.5, 0.9), ages=c(54, 30, 25, 14, 5), method="Beta");
  qage(p=c(0.1, 0.5, 0.9), ages=c(54, 30, 25, 14, 5), method="Solow");
  
## End(Not run)

evolucionario/cladeage documentation built on Dec. 31, 2021, 8:48 a.m.