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

### 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

1 |

### Arguments

`x` |
a |

`gen.per.t` |
the number of generations per unit time (e.g., 1e6 for yearly generations and time in |

`draw` |
logical, if |

### 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

1 2 3 4 5 6 7 | ```
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)
``` |