qage: Quantile-based age estimation

In josephwb/chronosCI: Molecular Dating by Penalised Likelihood and Maximum Likelihood

Quantile-based age estimation

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, 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, method = "StraussSadler", k = 5)

Arguments

p	The desired probability level (0 < p < 1). A vector of probabilities can be provided. Default p = 0.5
ages	Either a vector of fossil ages or a matrix with two columns: the first with the minimum age bounds (upper stratigraphic bounds) and the second with the maximum age bounds (lower stratigraphic bounds) of each fossil (in rows). A minimum of 2 are required
method	The method for modelling age uncertainty. A number of options is available: "StraussSadler" The (default) method of Strauss & Sadler (1989) assumes that the sampled fossil ages are uniformly distributed in time, and a warning is returned if a Kolmogorov-Smirnov test rejects the uniformity hypothesis. “Beta” The method is a different parameterization of the Strauss & Sadler method (Wang et al., 2009) that uses the qbeta function, since the ratio between the observed maximum fossil age and the clade age for the Strauss & Sadler model is distributed according to a Beta distribution with parameters N and 1 (Wang et al. 2009); this should give the same result as "StraussSadler". Solow The method of Solow (2003) does not assume uniformity in sampled fossil ages, but is based on the two oldest ages only. NorrisPenG or NorrisGLin The method of Norris et al. (2015) based on the two oldest fossils only and the log-logistic distribution. "NorrisPenG" is used when the precise phylogenetic placement of fossils is not known, whereas "NorrisGLin" is used when one fossil from each daughter lineage is used. "RobertsSolow" The method of Roberts & Solow (2003) does not assume uniformity in sampling and is based on the fact that the joint distribution of the k oldest fossil ages can be modeled with the same Weibull distribution.
k	The number of fossil ages to use in when method="RobertsSolow", in which only the k oldest fossils are used. Default k = 5.

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

Gingerich1998chronos

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Norris2015chronos

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Solow2003chronos

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Strauss1989chronos

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Wang2007chronos

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Wang2009chronos

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Wang2010chronos

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)

josephwb/chronosCI documentation built on Jan. 30, 2023, 5:34 a.m.