runs.test.decel: Applying the runs test to the decelerated evolution model

In klvoje/adePEM: Evaluate the adequacy of within-lineage phenotypic evolution models

Applying the runs test to the decelerated evolution model

Description

Investigates if the decelerated evolution model is an adequate statistical description of an evolutionary time series by applying the runs test.

Usage

runs.test.decel(y, r = NULL, vstep = NULL, nrep = 1000,
  conf = 0.95, plot = TRUE, save.replicates = TRUE)

Arguments

y	a paleoTS object
r	parameter describing the decreasing rate change through time. r is restricted to values smaller than zero (the model reduces to the BM model when r = 0).
vstep	the variance of the step distribution estimated from the observed data.
nrep	number of iterations in the parametric bootstrap (number of simulated time series); default is 1000.
conf	confidence level for judging whether a model is an adequate statistical description of the data. Number must be between 0 and 1. A higher number means less strict judgment of whether a model is adequate; default is 0.95. Tests are two-tailed, which means a model is judged adequate if the observed test statistic is within the 2.5 percent of the extreme values of the calculated test statistics on the simulated data given the default confidence value of 0.95.
plot	logical; if TRUE, the value of the test statistic calculated based on the observed fossil time series is plotted on the distribution of test statistics calculated on the simulated time series; default is TRUE.
save.replicates	logical; if TRUE, the values of the test statistic calculated on the simulated time series is saved and can be accessed later for plotting purposes; default is TRUE.

Details

This function applies a runs test in order to investigate if the random walk model can be judged an adequate statistical description of the data. After detrending, there should be no tendency in the data to successively deviate from the average in the same direction and the runs test is applied to the sign of the residuals (i.e. θ – trait value) to identify series that have non-random patterns in the sign of deviations. For a time series of length n, the number of runs (one run is a sequence of consecutive numbers with same sign), is approximately normal with mean μ=(2(n_+ n_-))/n+1 and variance (μ-1)(μ-2)/(n-1), where n+ and n- are the number of residuals above and below the optimum respectively. The mean and variance are used to calculate the standard/Z-score implemented as the test statistic.

Value

First part of the output summarizes the number of iterations in the parametric bootstrap and the confidence level for judging whether a model is an adequate statistical description of the data. The last part of the output is:

estimate	The calculated test statistic on the observed data.
min.sim	The smallest test statistic calculated on the simulated data.
max.sim	The largest test statistic calculated on the simulated data.
p-value	Not a real p-value, but is calculated as the fraction of simulated test statistics that is larger (or smaller) than the calculated test statistic on the observed data divided by 0.5. A value of 1 means 50 percent of the test statistics on the simulated data are larger and smaller than the calculated statistic on the observed data. A value of 0.10 means 90 percent of the test statistics on the simulated data are larger or smaller than the test statistic on the observed time series.
result	Whether the model PASSED or FAILED the adequacy test. The outcome depends on the confidence level.

Author(s)

Kjetil L. Voje

References

Voje, K.L. 2018. Assessing adequacy of models of phyletic evolution in the fossil record. Methods in Ecology and Evoluton. (in press).

Voje, K.L., Starrfelt, J., and Liow, L.H. 2018. Model adequacy and microevolutionary explanations for stasis in the fossil record. The American Naturalist. 191:509-523.

See Also

runs.test.stasis, runs.test.RW, fit3adequasy.trend

Examples

## generate a paleoTS objects by simulating early burst
x <- sim.accel_decel(ns=40, r=-1, vs=0.1)

## investigate if the time series pass the adequacy test
runs.test.decel(x)

klvoje/adePEM documentation built on Feb. 24, 2023, 1:28 p.m.