windex: Analyzing Convergent Evolution Using the Wheatsheaf Index in R.

SUMMARY: windex is a package developed for the R statistical environment to provide novel tools for the analysis of convergent evolution. The recently described Wheatsheaf index provides quantitative measures of the strength of convergence and opens up new possibilities for exploring this evolutionary phenomenon. The windex package allows implementation of this method with additional functions that can be used to create plots and perform statistical tests. R provides compatibility with other packages, and the R environment is familiar to many researchers. AVAILABILITY: The windex package is freely available from CRAN: http://cran.r-project.org/web/packages/windex/. Consequently, windex can be installed directly from R and is distributed under the GNU General Public License 2.0.

The use of phylogenetic comparative methods in evolutionary biology has seen a remarkable increase in recent years.1–4 Much of this growth has resulted from the proliferation of newly developed methods (eg, see Refs. 5–7) and a shift toward implementation of these methods in R, which has enhanced the flexibility and between-method compatibility of their implementation.

Convergent evolution, or the independent evolution of similar phenotypes, is a commonly observed phenomenon across the tree of life.8 Nevertheless, methods designed to study convergence have traditionally been limited to identifying its presence (eg, see Refs. 7 and 9), ie, whether convergence has or has not occurred in a given case. Recently, Arbuckle et al.10 developed a new method that aims to provide a quantitative measure of the strength of convergent evolution – the Wheatsheaf index. By quantifying convergence, this method allows an expanded range of questions we can ask, such as “Do life history traits show greater convergence than morphological traits?” or “Do limbs or eyes show stronger convergence in burrowing animals?” This more detailed understanding of how convergent evolution operates as a evolutionary mechanism can only be achieved once a suitable measure is available that can be used to analyze a wide range of traits.

Briefly, the Wheatsheaf index generates phenotypic (Euclidean) distances from any number of traits across species and penalizes these by phylogenetic distance before investigating similarity (in order to weight close phenotypic similarity higher for distantly related species). It also takes an a priori designation of focal species, which are defined as species belonging to a niche for which the traits are hypothesized to converge. The method then calculates a ratio of the mean (penalized) distances between all species to the mean (penalized) distances between focal species. In effect, the Wheat-sheaf index detects stronger convergence as the focal species diverge more in phenotypic space from the non-focal species and also as the focal species show a tighter clustering to each other.

Upon describing the Wheatsheaf index, Arbuckle et al.10 made available a MatLab script to implement the method, although this was quite inflexible and many potential users are not familiar with MatLab. Therefore, in this paper, we introduce a user friendly R package ( windex) with which researchers can use the Wheatsheaf index to analyze convergent evolution.

To illustrate the use of the R package windex, we analyze morphological convergence for burrowing in monitor lizards (Varanus) using the Wheatsheaf index applied to data taken from Thompson et al.11. windex contains three functions: plotTrait, windex, and test.windex (Table 1). These functions require up to two inputs, which we will herein refer to as the traits and the tree for convenience. The tree is a phylogenetic tree of the class phylo, as is standard for most phylogenetic packages in R. Traits is a data frame consisting of a few necessary columns. The first column must be named species and contains species names, which match the tip labels in the tree. One column must designate the focal taxa (see Ref. 10 for details of the method itself and further understanding of these terms) as 1 and non-focal taxa as 0. The focal taxa are those species for which you are interested in testing convergence (eg, burrowing species in our Varanus example). Other columns contain the trait values, typically (semi-)continuous traits, but if there are a large number of binary traits in the dataset, then they can also be used, as they would similarly allow the calculation of meaningful phenotypic distances. By (semi-)continuous, we mean ordinal or count data in addition to truly continuous measurements, as all of these types would generate a meaningful phenotypic distance. The data frame is then read into the R environment. The data frame for our example herein consists of three traits of interest: head depth ( headD), upper-fore limb length ( UforelimbL), and upper-hind limb length ( UhindlimbL). The first six rows are shown below to illustrate the format of the data frame (titled dat), called as follows:

Table 1

Brief summary of functions in the windex package.

FUNCTION	INPUT	OUTPUT
plotTrait	Traits	Aplot of phenotypic space for visualisation of raw (not phylogenetically corrected) data.
windex	Traits and tree	Wheatsheaf index along with 95% confidence intervals obtained by jackkniving the data.
test.windex	Traits and tree	P-value for a test of particularly strong convergence, including a graphical display of the result.

The plotTrait function only requires the traits (not the tree), and is intended as a tool for data exploration. It produces a plot that represents a phenotypic space with one to three dimensions (traits) with focal taxa highlighted to visualize where they appear relative to non-focals, although this plot does not take into account phylogenetic relationships. Nevertheless, it may often be a useful preliminary step for understanding how the data are structured.

For our monitor lizard example, we plot one-, two-and three-dimensional plots with the traits head depth ( headD), upper fore limb length ( UforelimbL), and upper hind limb length ( UforelimbL) (Fig. 1) using the following code:

Figure 1

An illustrative example of the plotTrait function for one-dimensional, two-dimensional and three-dimensional plots using the traits head depth (headD), upper fore limb length (UforelimbL), and upper hind limb length (UforelimbL).

> par(mfrow=c(1, 3))

> plotTrait(dat, traits=“headD”)

> plotTrait(dat, traits=c(“headD”, “UforelimbL”))

> plotTrait(dat, traits=c(“headD”, “UforelimbL”, “UhindlimbL”))

The core function of the package is windex, which takes both the tree and traits as input and calculates the Wheat-sheaf index. This function also performs jackknife resampling of the traits as per Ref. 10 and uses these samples to return 95% confidence intervals alongside the calculated index. The method requires that measurements for each trait are standardized by the standard error for the trait across species. Although this can be done as pre-treatment of the data file, the windex function includes an option that allows this step to be included as part of implementation, removing the need for any such pre-treatment of the data and, hence, increasing the method’s ease of use.

Here we use the function windex to calculate the Wheatsheaf index for a combination of three traits that are likely to be important in burrowing in our Varanus example: head depth ( headD), upper fore limb length ( UforelimbL), and upper hind limb length ( UforelimbL):

> windex(dat, tree, traits=c(“headD”, “UforelimbL”, “UhindlimbL”), SE=T)

$`Wheatsheaf Index`

[1] 1.322459

$`Lower 95% CI`

[1] 1.243233

$`Upper 95% CI`

[1] 1.389691

The final function in the package is test.windex, which implements the statistical test for exceptionally strong convergence, given the topological constraints of the tree (see Ref. 10 for more details). The function takes the same arguments as the windex function (as this is called internally by test.windex) plus two additional arguments. The first ( reps) specifies the number of bootstrap replicates from which the P-value is derived. The number of replicates is, of course, case dependent, but we have chosen 2000 in the example below as a compromise between computation time and accuracy. The user may wish to increase or decrease the number of replicates, though too few replicates may lead to unreliable results. The second additional argument ( plot) is an option to plot a visualization of the result in addition to returning the P-value for the test, and the default for this argument is set as plot = TRUE. The plot consists of a histogram of the distribution of the Wheatsheaf index from bootstrap replicates, with the calculated value and its 95% confidence interval marked on the plot. Additional arguments are passed to the basic hist function in R to allow the histogram to be customized. Since this function can take several minutes or longer on large datasets, we have incorporated a simple status bar to allow the user to monitor the progress of the function. To return to our monitor lizard example, we now illustrate the test.windex function on the same set of traits as were used above for the windex function:

> test.windex(dat, tree, traits=c(“headD”, “UforelimbL”, “UhindlimbL”),SE=TRUE, reps=2000, col=“light grey”)

$`

[1] 0.097

The P-value obtained here is 0.097, marginally non-significant and therefore indicating that although convergence is present in Varanus,11 it is not exceptionally strong in the selected traits for burrowing. The plot generated by the code above can be seen in Figure 2.

Figure 2

Histogram of the distribution of bootstrapped Wheatsheaf index values from our example of morphological convergence for burrowing in monitor lizards. The calculated Wheatsheaf index observed in the dataset is shown along with its jackknived 95% confidence interval.

We hope that windex will greatly increase the ease of using the Wheatsheaf index to analyze convergent evolution. The method is not intended to overshadow currently existing analyses for studying convergence but rather to complement them. Indeed, methods designed to test for the presence of convergence are strongly advised before using the Wheatsheaf index because it makes little sense to quantify the strength of something that does not exist in a given dataset. As such, we have developed windex as a component of the analytical toolbox available to investigators of convergent evolution that provides an easy to use and useful extension to the suite of methods available in R (eg, Refs. 7, 12, and 13).

> head(dat) species	focal	headD	UforelimbL	UhindlimbL
1 acanthurus	1	10.9	14.2	20.5
2 brevicauda	1	6.4	5.9	7.4
3 caudolineatus	0	6.8	7.8	11.3
4 eremius	1	9.6	11.3	16.8
5 giganteus	1	25.7	43.6	55.9
6 gilleni	0	7.3	8.7	11.7