Log-Rate, Log-Interval (LRI) method of Gingerich
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.
the number of generations per unit time (e.g., 1e6 for yearly generations and time in
Following Gingerich (1993), a robust line is fit through the points by minimizing the sum of absolute deviations.
A named vector of three elements:
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  and the example below).
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.
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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,4) print(wSlow,4)
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