The adePEM package allows assessing the adequacy of models of within-lineage phenotypic evolution.
The package contains tests to assess the adequacy of the following models: stasis, unbiased random walk (with fixed or decelerating rates of evolution), biased random walk (trend model), and various versions of Ornstein-Uhlenbeck models. These models are available in the R packages paleoTS and evoTS.
Models fit in paleoTS and evoTS are evaluated using AICc. However, the best model among a list of candidates according to an information criterion may not describe the data particularly well. This is true because any set of candidate models will only reflect a subset of ways of portraying evolutionary dynamics in a lineage.
Passing adequacy tests suggests the model provides an adequate statistical description of the trait dynamics in the data and that meaningful inferences can be drawn from the estimated model parameters.
The adePEM package includes functions to simulate data sets, calculate summary statistics and plot results.
The manuscript where the adePEM package is presented:
Voje, K.L. 2018. Assessing adequacy of models of phyletic evolution in the fossil record. Methods in Ecology and Evolution 9:2402-2413. https://doi.org/10.1111/2041-210X.13083
The methods for assessing adequacy of the stasis model were first described in this paper: 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. https://doi.org/10.1086/696265
Adequacy tests for OU models and the unbiased random walk with a decelerating rate of evolution were published in this paper: Voje, K.L. 2020. Testing eco‐evolutionary predictions using fossil data: Phyletic evolution following ecological opportunity. Evolution 74:188-200. https://doi.org/10.1111/evo.13869.
Install the package from github using devtools:
install.packages("devtools")
devtools::install_github("klvoje/adePEM")
library(adePEM)
The adePEM package tests the adequacy of models implemented in the paleoTS and evoTS packages. Both packages are available on CRAN:
install.packages("paleoTS")
install.packages("evoTS")
library(paleoTS)
library(evoTS)
We are interested in analyzing the evolution of element length (measured in mm) in the conodont Pterospathodus. The data is available as part of the adePEM package and was originally published by Jones (2009). The data (element.length) is already a paleoTS object. We first plot the data.
plot.paleoTS(element.length)
Time (the x-axis) is in millions of years and the trait is measured in millimeters. Error bars represent one standard error.
We then run the fit3models function from the paleoTS package to check the relative fit of the stasis, random walk and trend models to the data.
fit3models(element.length, pool=TRUE)
Comparing 3 models [n = 31, method = Joint]
logL K AICc Akaike.wt
GRW 25.38445 3 -43.88002 0.262
URW 25.12370 2 -45.81882 0.690
Stasis 22.47400 2 -40.51943 0.049
The random walk (URW) model has the best fit to the data according to the AICc scores. However, the difference in the AICc score is small (<2 units) relative to the trend model (GRW).
Let's investigate if the random walk represents an adequate statistical description of the trait dynamics in the data. To do that, we run the function fit3adequacy.RW from the adePEM package. This is a wrapper function that runs 3 adequacy tests at the same time.
# Run adequacy tests for the random walk model:
fit3adequacy.RW(element.length)
$info
Value
replications 1000.00
confidence level 0.95
$summary
estimate min.sim max.sim p-value result
auto.corr -0.318 -0.66474 0.36931 0.494 PASSED
runs.test 1.09003 -2.0057 4.09368 0.68 PASSED
slope.test 0.01199 -0.02635 0.04576 0.498 PASSED
The first part of the output summarizes the number of bootstrap replications (the number of simulated data sets) used for assessing model adequacy and the confidence level. 1000 replications and a confidence level of 0.95 are the default settings, but both can be defined by the user when running the fit3adequacy.RW function.
The second part of the output contains information on the results of the adequacy tests. The first column names the adequacy tests. The second column gives the test statistic computed on the real data. From the second column, we see that the autocorrelation is calculated to be negative and the slope test (which is the least-squares slope of how the (detrended) data changes with time) is positive.
The third and fourth columns reports the smallest and largest test statistics calculated on the simulated data sets. As we can see, all the three test statistics computed on the real data (second column) are not close to the extreme values reported in columns three and four.
The fifth column is not a real p-value, but is 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, respectively. 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.
The sixth column indicates whether our model passed the adequacy tests. Since we set our confidence level to 0.95 and all values in the fifth column is larger than 0.05, this means the random walk model passed all tests for our data set.
That the random walk model passed all tests can also be seen in the visual representation of the distributions of test statistics, where the test statistics computed for the real data is indicated with a broken (red) line. These plots are generated automatically if plot = TRUE (which is the default setting) when we run the fit3adequacy.RW function.
To summarize: Among the three candidate models stasis, random walk and directional change, random walk has the best relative model fit to the data based on AICc. However, a relative better fit for a model (in this case, the random walk model) to a phyletic fossil time series is no guarantee that the model represents a sufficiently good statistical explanation for the trait dynamics. We therefore assessed to what extent the random walk model also fitted the data in an absolute sense by running adequacy models. The random walk model passed all adequacy tests, which suggest the random walk model represents an adequate statistical description of the phyletic time series.
If we take a look at the plot of how the trait changes over 6 million years, it seems to suggest a trend towards becoming bigger. Therefore, let's assess the adequacy for the trend model on the data. This model did indeed show a quite similar fit to the data based on their AICc scores. We run the wrapper function fit3adequacy.trend to run all three adequacy tests simultaneously.
# Run adequacy tests for the trend model:
fit3adequacy.trend(element.length)
$info
Value
replications 1000.00
confidence level 0.95
$summary
estimate min.sim max.sim p-value result
auto.corr 0.0464 -0.02127 0.97608 0.004 FAILED
runs.test -0.54272 -5.29741 0.23802 0.028 FAILED
slope.test 0.00637 -0.13183 0.2477 0.934 PASSED
The trend model fails the autocorrelation test and the runs test, and passes the slope test. This suggests that the trend model is not an adequate statistical description of the data.
Functions for running each adequacy test alone are provided in the package (e.g. auto.corr.test.stasis, runs.test.RW, slope.test.trend). The wrapper function for investigating the adequacy of the stasis model is fit4adequacy.stasis. This function runs a fourth adequacy test that is only implemented for testing the adequacy of the stasis model. A low amount of net evolution is part of the verbal definition of stasis, but not for random walk and directional trend. The fit4adequacy.stasis function therefore runs a test to check if the amount of net evolution is larger than expected given the model parameters the stasis model. The function net.change.test.stasis runs this test alone on the data.
Kjetil Lysne Voje [email protected]
Hunt, G. 2006. Fitting and Comparing Models of Phyletic Evolution: Random Walks and beyond. Paleobiology 32:578–601. link
Jones, D. 2009. Directional evolution in the conodont Pterospathodus. Paleobiology 35: 413-431. link
Voje, K.L. 2018. Assessing adequacy of models of phyletic evolution in the fossil record. Methods in Ecology and Evoluton 9:2402–2413. PDF
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. PDF
Voje, K.L. 2020. Testing eco‐evolutionary predictions using fossil data: Phyletic evolution following ecological opportunity. Evolution 74:188-200. PDF