Log-Rate, Log-Interval (LRI) method of Gingerich

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Description

Gingerich (1993) introduced a method that plots on log-log scale, the rate and interval for each pair of samples in an evolutionary sequence. On this plot, the slope is interpreted as an indicator of evolutionary mode (-1 for stasis, 0.5 for random walk, 0 for directional), and the intercept is interpreted as a measure of the rate of evolution over one generation.

Usage

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LRI(x, gen.per.t = 1e+06, draw = TRUE)

Arguments

x

a paleoTS object

gen.per.t

the number of generations per unit time (e.g., 1e6 for yearly generations and time in x is in Myr)

draw

logical, if TRUE, a plot is produced

Details

Following Gingerich (1993), a robust line is fit through the points by minimizing the sum of absolute deviations.

Value

A named vector of three elements: Intercept, slope and GenerationalRate

Note

This method was important in attempts to disentangle evolutionary tempo and mode. I view likelihood-based methods as more informative, and in particular the estimation of 'Generational Rates' using LRI is compromised by sampling error (see Hunt [2012] and the example below).

Author(s)

Gene Hunt

References

Gingerich, P.D. 1993. Quantification and comparison of evolutionary rates. American Journal of Science 293-A:453–478.
Gingerich, P.D. 2009. Rates of evolution. Annual Review of Ecology Evolution and Systematics 40:657–675. Hunt, G. 2012. Fitting and comparing models of phyletic evolution: random walks and beyond. Paleobiology 38:351–373.

See Also

fit3models

Examples

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	xFast<- sim.GRW(ns=20, ms=0.5, vs=0.2)   # fast evolution
	xSlow<- sim.Stasis(ns=20, theta=10, omega=0)   # strict stasis! rates are actually zero
	wFast<- LRI(xFast, draw=FALSE)
	wSlow<- LRI(xSlow, draw=FALSE)
	## LRI usually assigns faster generational rate to Strict Stasis!
	print(wFast[3],4)
	print(wSlow[3],4)

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