# 8. Analyzing BAMM output with BAMMtools¶

**Note: documentation for BAMM and BAMMtools 2.0 is still under construction; some sections may be incomplete.**

## 8.1. Brief¶

The R package **BAMMtools** contains almost everything you need to analyze and visualize evolutionary rate dynamics from BAMM output. You will need to install this package. To install BAMMtools, type the following in your R console:

```
install.packages("BAMMtools")
```

The information below is a brief overview to get you started - there is much more than can be done. We first cover a sample BAMMtools workflow for analyzing rates and rate shifts. The general analyses described in this section apply both to **speciation-extinction** and **phenotypic evolution** studies. As such, they are not treated separately. The primary difference is the name of the parameters ( and for speciation and extinction, and for trait evolution).

In case you missed it, you really should read this section before proceeding. Having a solid understanding of *distinct shift configurations*, *marginal shift probabilities*, and *the overall best shift configuration* is critical to appreciating what BAMMtools can do.

The sections below include:

**BAMMtools quickstart guide**- This is a one sentence guide to major
*BAMMtools*functions, covering several common analyses.

**BAMM output and the *bammdata* object**- A quick overview of
**BAMM**output files.

**Assessing MCMC convergence**- Standard tests you should do to check BAMM convergence.

**Analysis of rate shifts**- This section describes how to analyze the number and location of rate shifts from a Bayesian perspective.

**Bayes factors for model comparison**- Robust model selection with Bayes factors.

**Clade-specific evolutionary rates**- Estimating mean rates for specific clades.

**Branch and tip-specific evolutionary rates**- Estimate marginal densities of rates for individual branches and tips.

**Rate-through-time analysis**- Analyze and plot macroevolutionary rates through time.

**Macroevolutionary cohort analysis**- Visualize sets of taxa with shared rate dynamics.

## 8.2. BAMMtools quickstart guide¶

This is a quickstart guide to some of the analyses discussed below (and many more are possible). Additional ideas are illustrated in the R code samples available on the BAMM graph gallery, and the **BAMMtools** package contains functions for a number of additional analyses.

- Test for convergence using the MCMC output with the
`coda`

package for R - Load event data with
`getEventData(....)`

- Generate a phylorate plot with
`plot.bammdata(....)`

- Compute the 95%
*credible set of rate shift configurations*using`credibleShiftSet`

- Extract the rate shift configuration with the highest posterior probability with
`getBestShiftConfiguration`

- Visualize random samples from the posterior distribution of rate shifts using
`plot.bammshifts`

- Generate phylorate plots for the distinct rate shift configurations in your 95% credible set using
`plot.credibleshiftset`

- Evaluate evidence for diversification shifts on each branch with
`marginalOddsRatioBranches`

- Plot rates through time with
`plotRateThroughTime(...)`

- Compute clade-specific marginal distributions of rates with
`getCladeRates(...)`

## 8.3. BAMM output and the *bammdata* object¶

### 8.3.1. BAMM output¶

BAMM generates three primary output files. The first is the *mcmc data file*, which contains several pieces of information about the MCMC simulation that may be useful in diagnosing convergence. The most important pieces of information from this file are the number of shift events, the log-likelihood of the data, and the log-prior probability of the data, for each sample from the posterior.

The second is the *event data file*, which contains all of the actual model parameters. Each sample from the posterior can be described with complete knowledge of all of the shift events on the tree, including their location and evolutionary rate parameters. The *event data file* is just a long list of all the shift events and associated parameters that were sampled, as well as the MCMC generation in which they were sampled. **You will not directly do anything with this file**. BAMMtools has a function for extracting all the relevant information from the file and for mapping the rate shift configurations to phylogenetic trees. A detailed explanation of the event data file can be found here.

Finally, BAMM will (optionally) generate a second MCMC output file that contains the results of a prior-only simulation. This file can be used to reconstruct the prior distribution of the number of shift events and is important for the estimation of Bayes factors.

### 8.3.2. The *bammdata* object¶

The *bammdata* object is the core of most analyses discussed below. This is a complex data structure that includes a phylogenetic tree and a mapping of all macroevolutionary rate parameters sampled using BAMM. Many of the methods in BAMMtools operate directly on objects of class *bammdata*. This object is created in R using the BAMMtools function `getEventData`

. Here’s sample code where we create the bammdata object (assume your phylogeny is in a file *mytree.tre*, and your event data file from a BAMM run is in file *bammrun_eventdata.txt*:

```
library(BAMMtools)
tree <- read.tree("mytree.tre")
edata <- getEventData(tree, eventdata = "event_data.txt", burnin=0.1)
```

*edata* is now a “BAMM-data” object, which has all the attributes of a class “phylo” object, plus many more. Please be patient with *getEventData* - this function can take some time to run for large datasets.

**Note**: The function `getEventData`

incurs significant memory overhead in R. It will likely give you trouble with trying to process more than 2000 samples. See graph gallery for more information on how often to sample. Most importantly, never try to read in all of your event data without first doing a trial run to get a feeling for how long it will take. You can read in a subset of your samples with the `nsamples`

option in `getEventData`

.

## 8.4. Assessing MCMC convergence¶

The first question after running any MCMC simuluation should always be: *did my run converge?* While it may be difficult to prove convergence in an absolute sense, there are a few simple checks you can do. First, you can plot the log-likelihood trace of your MCMC output file:

```
mcmcout <- read.csv("mcmc_out.txt", header=T)
plot(mcmcout$logLik ~ mcmcout$generation)
# Also, remember that comments in R are lines that start with
# a pound sign. We'll occasionally use them here.
# R will not execute these lines - they are only for reference!
```

This can give you a ballpark idea of whether your run has converged. The next step is to discard some as burnin. Here we’ll discard the first 10% of samples as burnin:

```
burnstart <- floor(0.1 * nrow(mcmcout))
postburn <- mcmcout[burnstart:nrow(mcmcout), ]
```

And using these samples, it is good to check the *effective sample sizes* of the log-likelihood and the number of shift events present in each sample. We’ll do this using the *coda* library for R:

```
library(coda)
effectiveSize(postburn$N_shifts)
effectiveSize(postburn$logLik)
```

In general, we want these to be at least 200 (and 200 is on the low side, but might be reasonable for very large datasets).

As an additional test for convergence, we recommend analyzing multiple independent BAMM runs. You can test whether the runs are converging on similar distributions by analyzing the branch-specific marginal rate shift probabilities (see `marginalShiftProbsTree`

).

If you are having trouble with convergence, please see the section on troubleshooting convergence issues.

## 8.5. Analysis of rate shifts¶

In the BAMM framework, many different shift configurations may be (more-or-less) equally plausible. BAMM samples shift configurations in proportion to their posterior probability. In principle, this means that each sample from your posterior contains a potentially unique configuration of regime shift events.

A conceptual discussion of the meaning of rate shifts is included in this documentation and it is **strongly recommended** that you read this section before continuing. Approaches that identify a single best shift configuration (e.g., stepwise AIC, or other approaches that simply maximize the likelihood) are inherently limited by their assumption that the model with the best information theoretic score (AIC etc) is **the** model, given the candidate set of models. However, for most real datasets, the best rate shift configuration is merely one of a large number of possible rate shift configurations that have similar probabilities. The BAMM philosophy is largely oriented around addressing this. To understand the following examples, you must understand what we mean by **distinct shift configurations**, **credible sets of rate shift configurations**, and **marginal shift probabilities**. These are also defined in the glossary.

### 8.5.1. How many rate shifts?¶

The first step in the analysis of BAMM output is to ask some basic questions about the number of macroevolutionary rate regimes on our phylogenetic tree. We can do this directly using the post-burn *MCMC output file*. Here, we’ll compute the posterior probabilities of models sampled using BAMM:

```
post_probs <- table(postburn$N_shifts) / nrow(postburn)
```

*post_probs* is now a vector of model posterior probabilities. We can look at these, we can plot them, we can compute posterior odds ratios, and so on. To see which models are part of the set that were sampled, you can just look at the names of this vector:

```
names(post_probs)
```

And to compute the posterior odds ratio for (say) two models ‘X’ and ‘Y’ (X and Y must be integers), you would do:

```
post_probs['X'] / post_probs['Y']
```

In general, any model that is not included in *names(post_probs)* was so lousy that it was never even sampled. Thus, if you fail to observe a model ‘0’ in this set, this means that you have such overwhelming evidence for diversification rate heterogeneity in your data that this model probability is effectively 0 (bear in mind that a model with name ‘0’ is model , or a model with no rate shifts). The probability of model ‘0’ is the posterior probability of a model with just a single evolutionary rate dynamic (no rate shifts). We’ll discuss the use of Bayes factors in gauging model support a little further down in this document, because Bayes factors – unlike model posterior probabilities – are theoretically invariant to the prior on the number of shifts (and should should always be preferred when they can be computed).

Alternatively, if we have our *bammdata* object, we can summarize the posterior distribution of the number of shifts using summary methods:

```
library(BAMMtools)
tree <- read.tree("mytree.tre")
edata <- getEventData(tree, eventdata = "bammrun_eventdata.txt", burnin=0.1)
shift_probs <- summary(edata)
```

`shift_probs`

is now a dataframe giving the posterior probabilities of each rate shift count observed during simulation of the posterior.

## 8.6. Bayes factors for model comparison¶

There is a critical issue that arises in model comparisons using BAMM: inferences on the posterior distribution of models are not independent of the prior. This is generally not an issue if you are using a conservative prior (`expectedNumberOfShifts = 1`

, for example), because a model with zero rate shifts will have a high prior probability. However, if you set `expectedNumberOfShifts = 0.1`

(or some other value < 1), your expected number of diversification shifts under the prior alone will increase. Hence, simply by manipulating the prior, you can potentially achieve a posterior distribution that is quite different from zero, even in the absence of evidence for diversification rate heterogeneity.

The solution that we advocate is to explicitly compare the evidence for models with at least one diversification shift to the evidence for the *null* model. Formally, there isn’t really a null model in BAMM, but for our purposes, it makes sense to think about model with zero rate shifts as the null hypothesis. In a Bayesian framework, we can do this by computing the Bayes factor associated with two models. This is computed as

where is the probability of the data given model and is the prior probability of model . Bayes factors are notoriously difficult to compute for many applications, but they are trivial from BAMM output.

**We suggest that (usually) the overall best model from a BAMM analysis is the model with the highest Bayes factor relative to the null model**, .

There is one complication that can arise, and it is that – in many cases – you wish to perform a Bayes factor comparison between models where one model is never sampled. For example, you might be running a BAMM analysis on a large phylogenetic dataset with lots of rate heterogeneity, and you find that you never sample a model with 0 shifts in the posterior. Hence, you’ll formally be unable to compute Bayes factor comparisons involving this model. There are several possible solutions to this scenario, none of which are implemented in BAMMtools. One strategy is to compute a **minimum Bayes factor**, by setting the posterior probability of the unsampled model equal to its maximum possible value. Suppose you have a posterior of 1000 samples and have never sampled , the “null” model with 0 shifts (e.g., all samples have at least one shift). You can approximate an upper bound on the probability of as roughly 1 / 1000 (as you have 1000 samples and no observations of ), and you could substitute this value into the equation used to compute the Bayes factor. Note that the true posterior probability of could have been **vastly lower** (but probably not much higher); hence, any Bayes factors where the posterior probability of is in the denominator will be underestimates. This is an acceptable practical solution to describing the evidence against when is so unlikely as to never be sampled. However, a Bayes factor computed in this fashion is a minimum estimate, and cannot be used to argue that rate heterogeneity is unlikely (because it is almost certain that the true Bayes factor evidence against is greater).

### 8.6.1. Prior distribution in BAMM¶

The primary goal of BAMM is to understand rate heterogeneity in a phylogeny without having to pre-specify the number or location of rate regimes. Rather than putting a prior on the number of shifts (*k*) directly, BAMM uses a weaker prior on the rate of the Poisson process that produces *k* (the Poisson rate prior: ). Understanding how much evidence there is for *k* shifts along your tree therefore requires that you determine the prior probability of *k* shifts under the specified Poisson rate prior used, which is calculated analytically as

Even a weak prior will have an effect on the posterior, so it is important to assess the evidence in favor of each number of shifts by taking the prior into account using Bayes Factors. BAMMtools makes it easy to compute Bayes factor evidence in favor of one model relative to another. The analysis described below assumes that you have generated an *MCMC output file* from a full BAMM run and that you know the `expectedNumberofShifts`

specified in the *control file*:

```
postfile <- "post_mcmc_out.txt"
bfmat <- computeBayesFactors(postfile, expectedNumberOfShifts=1, burnin=0.1)
```

and this will return a pairwise matrix of Bayes factors. For the whales dataset, you can do this as:

```
data(mcmc.whales)
computeBayesFactors(mcmc.whales, expectedNumberOfShifts=1, burnin=0.1)
```

It is very important to recognize that model probabilities for rarely sampled models are likely to be inaccurate. Hence, BAMMtools will not attempt to compute a Bayes factor for any model comparison where either model has a posterior or prior probability of (approximately) zero. The default output of computeBayesFactors is a matrix of pairwise Bayes Factors comparing all models with a posterior/prior greater than zero. In general, the first column of this output matrix is the comparison of all the models relative to the model with the lowest number of supported shifts (often zero).

In the case of the whales example dataset, the Bayes factors for a model with *k* shifts relative to a null model with *0* shifts is

```
shifts Bayes factor
0 1.0
1 17.2
2 10.9
3 4.5
4 2.3
5 0.9
```

For the whale example dataset, the Bayes factor evidence in favor of a model with a rate shift, relative to the null model, is moderate (BF > 17). This tells us that a model with a single diversification shift is the best overall model, at least by comparison to the null model with zero shifts. Bayes factors greater than 20 generally imply strong evidence for one model over another; values greater than 50 are *very strong* evidence in favor of the numerator model. Here, these data suggest that a model with a single rate shift is better than a model that lacks rate shifts, but the one shift model is is not decisively better. There is no definitive Bayes factor criterion for “significance”, but many researchers consider values greater than 12 to be consistent with at least some effect.

As discussed above, you may encounter a dataset where the posterior probability of the null model is so low that it cannot be estimated (e.g., it is never sampled during simulation of the posterior). Likewise, the prior probability of the models with high posterior probability might be very (i.e., inestimably) low, depending on your value for expectedNumberOfShifts. In this case, you will not be able to compute a Bayes factor. However, you can explicitly show the posterior and prior distributions recovered through your analysis to make it clear that the posterior distribution is shifted relative to the prior. We are actively working on strategies to address the problem of model selection when the posterior and/or prior probabilities approach zero (see also the previous section).

BAMMtools also has a function for visualizing the prior and posterior simultaneously. This is useful to see what models are not being sampled in the posterior, and also to evaluate how far from the prior the posterior has moved. To use it

```
data(mcmc.whales)
plotPrior(mcmc.whales, expectedNumberOfShifts=1)
```

### 8.6.2. Mean phylorate plot¶

The remainder of this section will use one of the example datasets included with BAMMtools. You should be able to run this code directly:

```
library(BAMMtools)
data(whales, events.whales)
edata <- getEventData(whales, events.whales, burnin=0.1)
summary(edata)
```

We will now generate a mean phylorate plot. This is a way of visualizing mean, model-averaged diversification rates at any point along every branch of a phylogenetic tree:

```
plot.bammdata(edata, lwd=2)
```

And we can add an interactive legend with `legend = T`

(this will enable us to add a frequency histogram of rates by clicking on the graphics window):

```
plot.bammdata(edata, lwd=2, legend=T)
```

You can also view a phylorate plot for any sample from the posterior. For example, here is the 25th sample from our `bammdata`

object:

```
# Here we will plot the 25th sample from the whale posterior:
index <- 25
e2 <- subsetEventData(edata, index = index)
plot.bammdata(e2, lwd=2)
addBAMMshifts(e2, cex=2)
```

### 8.6.3. Bayesian credible sets of shift configurations¶

The central goal of BAMM is to identify the relative evidence across a phylogeny for rate heterogeneity. Part of the modeling process involves placing a number of shifts at specific locations through the tree (shift configurations), however the precise location of each shift should not be overinterpreted. Evolution is complicated, it is highly unlikely that an empirical tree will have unambiguous evidence for the precise location of a shift. The more likely scenario is that several positions, both along a single branch or on successive branches, will have evidence for rate shifts.

BAMM enables us to identify the 95% credible set of distinct shift configurations (for more on distinct shift configurations, see here). Each sample from the posterior simulated using BAMM is a potentially unique configuration of rate shifts and parameters across a phylogeny. The *95% credible set* is the set of distinct shift configurations that account for 95% of the probability of the data. First, we need to estimate the expected frequency of observing rate shifts on each branch under the prior. We won’t worry about why we are doing this for the moment; you can read more here. Core shift locations are identified based on the shift’s marginal odds. Please read the special documentation on core and non-core shifts, because this is a confusing topic.

To plot the credible shift set, we need the **prior distribution** on the number of rate shifts (this is generated internally by BAMMtools). We can then estimate the credible set of rate shifts using the BAMMtools function `credibleShiftSet`

:

```
css <- credibleShiftSet(edata, expectedNumberOfShifts=1, threshold=5, set.limit = 0.95)
```

Here is the number of distinct shift configurations in the data:

```
css$number.distinct
```

Let’s think about what this means. In traditional analyses (e.g., stepwise AIC approaches), we strive to identify **the** single best rate shift configuration. We perform an analysis and return only the single overall best rate shift configuration. However, even in this simple example analysis, we find that there are a large number of distinct rate shift configurations in the credible set. We can view more information about the credible set with `summary`

:

```
summary(css)
```

Here we see that, even though there are many distinct configurations in the 95% credible set, just two of these account for most of the probability of the data. Here, we will generate phylorate plots for each of the N shift configurations with the highest posterior probabilities:

```
plot.credibleshiftset(css)
```

The text above each phylorate plot gives the posterior probability of each shift configuration. Because many samples from the posterior can be assigned to each distinct shift configuration, the phylorate plots generated by `plot.credibleshiftset`

are model-averaged mean rate parameters across all samples assignable to a given configuration. The shifts themselves are indicated with circles on branches (red = rate acceleration, blue = rate slowdown).

### 8.6.4. Finding the single *best* shift configuration¶

From the above plot, we can see that a single rate shift configuration has a higher posterior probability than any other. This shift configuration is the one with the *maximum a posteriori* (MAP) probability. This is one estimate of the overall best rate set of rate shifts given our data. If you are to show a single set of rate shifts on a phylogeny for publication, this would be a good one to go with:

```
best <- getBestShiftConfiguration(edata, expectedNumberOfShifts=1)
plot.bammdata(best, lwd = 2)
addBAMMshifts(best, cex=2.5)
```

Here, we have generated a phylorate plot for the best overall shift configuration and manually added the corresponding rate shifts for this configuration. This should match the first plot from the panel of plots we obtained with `plot.credibleshiftset`

.

Related to this, we could have pulled out any *specific sample* from a particular shift configuration for plotting using the `credibleShiftSet`

object. The assignments of individual samples to specific shift configurations are stored in the `indices`

component of the `credibleshiftset`

object. This is a list, and you can access the full vector of the *most-probable* shift configuration as follows:

```
css <- credibleShiftSet(edata, expectedNumberOfShifts=1, set.limit = 0.95)
css$indices[[1]]
```

The samples that can be assigned to the second most-probable shift configuration can be identified by `css$indices[[2]]`

, and the indices for the k’th most-probable configuration are `css$indices[[k]]`

. You could plot any specific sample from any shift configuration as follows by first pulling out the relevant sample index, then using `subsetEventData`

:

```
index <- css$indices[[1]][5]
rsample <- subsetEventData(edata, index=index)
plot.bammdata(rsample)
addBAMMshifts(rsample, cex=2)
```

In the example above, we’ve pulled out the 5’th sample that was assigned to the most-probable shift configuration:

```
first <- subsetEventData(edata, index=1)
second <- subsetEventData(edata, index = 2)
# Plotting the second most probable configuration:
plot.bammdata(second)
addBAMMshifts(second, cex=2)
```

**Alternative to the credible shift set for summarizing the overall best shift configuration:** For some datasets with large numbers of taxa and rate shifts (e.g., trees with thousands of taxa), all shift configurations may have low probability. There are simply too many parameters in the model to allow a single shift configuration to dominate the credible set. An alternative approach is to extract the shift configuration that maximizes the marginal probability of rate shifts along individual branches. This is very similar to the idea of a *maximum clade credibility tree* in phylogenetic analysis. BAMM has a function *maximumShiftCredibility* for extracting this shift configuration:

```
msc.set <- maximumShiftCredibility(edata, maximize='product')
```

A number of samples from the posterior potentially have identical credibility scores, and the object `msc.set`

now tells us which they are. We can pull out a single representative and plot it as follows:

```
msc.config <- subsetEventData(edata, index = msc.set$sampleindex)
plot.bammdata(msc.config, lwd=2)
addBAMMshifts(msc.config, cex = 2)
```

In this case, the maximum shift credibility configuration closely matches the MAP shift configuration. But for most datasets, **we recommend** using `credibleShiftSet`

and not `maximumShiftCredibility`

.

### 8.6.5. Viewing some random shift configurations¶

To give you some intuition for the distinct shift configurations in your dataset, we have included a function to plot random samples from the posterior and the associated shifts. Here, we will plot random samples from the posterior that are assignable to one of the distinct shift configurations that we have identified:

```
dsc <- distinctShiftConfigurations(edata, expectedNumberOfShifts=1, threshold=5)
# Here is one random sample with the BEST shift configuration
plot.bammshifts(dsc, edata, rank=1, legend=F)
# Here is another (read the label text):
plot.bammshifts(dsc, edata, rank=1, legend=F)
```

And we can plot some random examples of the second-best shift configuration:

```
plot.bammshifts(dsc, edata, rank=2, legend=F)
# Here is another
plot.bammshifts(dsc, edata, rank=2, legend=F)
```

You can see that, in each case, the same **distinct shift configuration** is being plotted, but a different sample. Hence, you should notice that the actual positions of shifts will move around.

### 8.6.6. Plotting rate shifts using `plot.phylo`

¶

We will also cover how you can visualize rate shifts using `plot.phylo`

and associated functions from the **ape** package. As we did previously, we can visualize just a single rate shift configuration from our *bamm-data* object:

```
mysample <- 25 # this is the sample we'll plot
```

To get the total number of rate regimes on the tree for this sample, you can do:

```
nrow(edata$eventData[[ mysample ]])
```

If there is only one rate regime, then you have no rate shifts: the single rate regime starts at the root and describes the entire tree. Assuming you have more than 1, we can get the node numbers (in **ape** format), as follows:

```
shiftnodes <- getShiftNodesFromIndex(edata, index = mysample)
```

And we can plot these nodes on the tree like this:

```
plot.phylo(whales)
nodelabels(node = shiftnodes, pch=21, col="red", cex=1.5)
```

This highlights the *downstream node* (e.g., “tipwards”, as opposed to “rootwards”) at the end of each branch on which a shift occurs in the specified sample. In contrast, `plot.bammdata`

shows the exact position along a branch where a shift occurred. You should be able to repeat this exercise again with a different value for *mysample*, and sooner or later, you should be able to see that different shift configurations will “light up” on your tree. Note that if there are no shifts in a given sample, there are no nodes to plot, which will lead to an error message.

In general, the BAMMtools plotting functions are better for visualizing shift configurations and rates along trees. However, understanding how to move between **BAMMtools** and **ape** can potentially facilitate a number of advanced data visualizations.

### 8.6.7. Marginal shift probabilities¶

BAMMtools enables the user to summarize *marginal shift probabilities*. This is nothing more than the marginal probability that each branch contains one or more shift events (see here for why these can be difficult to interpret). The next few lines of code will compute the marginal shift probabilities for each branch, then plot a new phylogenetic tree where the branch lengths are scaled by the probability that they contain a shift event:

```
marg_probs <- marginalShiftProbsTree(edata)
plot.phylo(marg_probs)
```

The variable *marg_probs* becomes a copy of our phylogenetic tree, but where each branch length has been transformed into the corresponding marginal shift probability. The marginal shift probabilities can be a little misleading, because we might have relatively low confidence in precisely which branch a shift occurred on, but nonetheless have extremely high confidence that a shift occurred *somewhere* in the vicinity.

### 8.6.8. Marginal odds for rate shift locations¶

As explained here and in this Evolution article, we can compute the marginal odds that a shift is associated with a particular branch. To be clear, this method is not meant to identify the *number* of shifts, to do that see this page. Here, we are discussing how to compute the evidence for a shift that is independent of the prior. This is used in BAMM to distinguish between core and non-core shifts, in the estimation of the 95% credible set of rate shifts. But it is not the same as identifying the best location of one or more rate shifts.

To compute marginal odds, we find the ratio between the probability of a shift along that branch in the posterior and the prior odds of a shift along that branch. This **marginal odds ratio** is superficially similar to a Bayes Factor, and we have previously used that term in the Evolution article. However, because the marginal odds of a shift along the tree are a *summary statistic* and not a component of *model selection*, they are not formal Bayes Factors.

This is an important point: **you cannot use the marginal odds ratios for branches to select the number of shifts along a tree.** To understand why, consider the whale tree where Bayes Factors support a single shift, but the marginal odds are over 20 for three separate branches leading up to the dolphin clade. These high marginal odds show the relative support each of those three branches has for the **one** shift supported by the Bayes Factor, and is not evidence of three shifts. To see this, plot the credible shift set from the posterior distribution of the whale tree (as in the preceding sections) and note that you only ever have **one** shift on each of those three branches. You do not find evidence for a shift on all three branches on the trees in the posterior. **The only strong evidence for a shift on a specific branch is when that shift occurs in >95% of the posterior**, which we find to be fairly rare in empirical data. As stated in here the primary goal of BAMM is not to specify the exact location of shifts, as due to both the reality of the amount of data present in a phylogeny and the complex nature of biological evolution, it will rarely be possible to have high confidence in a specific shift magnitude and location.

What the marginal odds **do** provide is an estimate of the “density” of shifts on a particular branch, independent of the length of the branch. But note that this can conflict directly with the *marginal shift probabilities*. In the whale dataset, for example, the branch with the highest marginal odds of a shift is not the branch with the highest marginal shift probability. When there is a conflict, we suggest that the marginal shift probabilities are your overall best measure of the location of a shift. But the marginal odds ratio is critical for distinguishing core and non-core rate shifts.

## 8.7. Clade-specific evolutionary rates¶

Estimating clade-specific rates with BAMMtools is straightforward. To compute the overall rate of speciation, extinction, or trait evolution, you can use the function `getCladeRates`

, which computes the average rate for the focal clade. Here we will use an example from the `whales`

example dataset that is included with BAMMtools:

```
library(BAMMtools)
data(whales)
data(events.whales)
edata <- getEventData(whales, events.whales, burnin=0.1)
#and here we get the rates
allrates <- getCladeRates(edata)
```

`allrates`

is a list with speciation and extinction components, with the mean rate across all whales for each sample in the posterior. It is important to realize that this function is *averaging* over any rate heterogeneity that occurs within your focal clade. Still, we can compute the mean speciation rate for whales and estimate the 90% highest posterior density (HPD):

```
mean(allrates$lambda)
quantile(allrates$lambda, c(0.05, 0.95))
```

To compute rates for **a specific clade**, just specify the node you’d like to compute the mean rate for. In the whales example, node 140 is the node number of the dolphin clade (you can find identify node numbers using `plot.phylo`

and `nodelabels`

from the `ape`

package). We can estimate the mean of the marginal density of speciation rates for dolphins as follows:

```
dolphinrates <- getCladeRates(edata, node=141)
mean(dolphinrates$lambda)
```

which should be a bit higher than the overall rate, an effect that you can clearly visualize in some of the sample phylorate plots for whales (or just generate your own, with `plot.bammdata(ed)`

).

You can also use the `node`

argument to `getCladeRates`

to **exclude** all the descendants of a particular node, thus computing the mean rate only for the *background* lineages. This is extremely useful in the present example. We have an evolutionary rate estimate for dolphins, and good evidence that their diversification dynamics are different from the background rate. We can thus compute a mean rate for *non-dolphin whales*, as follows:

```
nondolphinrate <- getCladeRates(edata, node = 141, nodetype = "exclude")
mean(nondolphinrate$lambda)
quantile(nondolphinrate$lambda, c(0.05, 0.95))
```

And you can see that the non-dolphin (background) rate is much lower than the dolphin rate. These are *mean time-averaged clade-specific rates*. If diversification rates have changed dramatically through the history of a particular clade, a single overall mean rate might not be particularly informative.

## 8.8. Branch & tip-specific evolutionary rates¶

BAMM can estimate marginal distributions of evolutionary rates for any point in time along a phylogenetic tree (this is what the the function `plot.bammdata`

is going to generate a phylorate plot). Sometimes, however, it is useful to have mean rates for individual branches. To pull out the mean rates for individual branches, you can use the function `getMeanBranchLengthTree`

(see the `?getMeanBranchLengthTree`

for help on this function). The function generates a copy of your original phylogenetic tree, but where each branch length is replaced by the mean of the marginal distribution of evolutionary rates on each branch. The function can be used to extract branch-specific mean rates of speciation, extinction, net diversification, and trait evolution.

You can also estimate individual tip-specific rates. For the whale example, this is actually included as part of your bammdata object. If `edata`

is the bammdata object for whales, the components `edata$meanTipLambda`

and `edata$meanTipMu`

are the relevant model-averaged mean rates of speciation and extinction at the tips of the tree.

## 8.9. Rate-through-time analysis¶

Plotting a rate-through-time curve (example here) is trivial. BAMM’s built-in function `plotRateThroughTime`

makes it easy to generate plots of rates through time:

```
plotRateThroughTime(edata, ratetype="speciation")
```

should produce a plot with density shading on confidence regions for your speciation-through-time curve. See help on this function for more details about tweaking the plot. This function can take awhile to run, because it generates a rate-through-time matrix that includes all samples in the posterior distribution.

You can also use `plotRateThroughTime`

to plot speciation through time curves for just a portion of your phylogeny. We can do this by feeding a node number in to `plotRateThroughTime`

, and the function will just compute and plot the rates for this subtree. To find a particular node number for your tree, you can plot the tree (using ape), and then plot your node numbers directly on the tree, like this:

```
plot.phylo(whales)
nodelabels()
```

Another way of doing this is to extract the most recent common ancestor (MRCA) node for your clade, by specifying the names of 2 descendant species from the clade that span the focal clade:

```
species1 <- "Tursiops_truncatus"
species2 <- "Orcinus_orca"
```

Now to get the *tip node numbers* in ape format:

```
tipnode1 <- which(whales$tip.label == species1)
tipnode2 <- which(whales$tip.label == species2)
```

And now the MRCA node:

```
mrca <- getMRCA(whales, tip = c(tipnode1, tipnode2))
```

Now we feed this in to `plotRateThroughTime`

:

```
plotRateThroughTime(edata, node = mrca, nodetype="include", ylim=c(0,0.7))
```

And we can also plot the entire rate through time curve after we **exclude** this clade (as in: just plot the background rates, without the focal clade):

```
plotRateThroughTime(edata, node = mrca, nodetype="exclude", ylim=c(0,0.7))
```

There are many other options available through `plotRateThroughTime`

, so please see the R help on this function:

```
?plotRateThroughTime
```

That’s the quick and dirty way of plotting rates through time. Often, you will want more control over the plotting process. The core BAMM operation for plotting a rate-through-time curve involves the generation of a rate-through-time matrix, like this:

```
data(primates, events.primates)
edata <- getEventData(primates, events.primates, burnin=0.1, nsamples=1000, type='trait')
rtt <- getRateThroughTimeMatrix(edata)
```

which returns a list of rate-through-time matrices plus a vector of the time points at which the rates were computed. If your rate matrix was for trait evolution, you will have a component *rtt$beta* in your rtt object (components *rtt$lambda* and *rtt$mu* if you are modeling speciation-extinction). To get the mean rates at any point in time:

```
meanTraitRate <- colMeans(rtt$beta)
```

and to do a simple no-frills plot:

```
plot(meanTraitRate ~ rtt$times)
```

You can also include and exclude nodes from the calculation of the rate-through-time matrix (assuming you know the node to exclude or include):

```
plot(primates, cex=0.5)
nodelabels(node=370)
rtt_subtree <- getRateThroughTimeMatrix(edata, node = 370)
```

Please see code underlying some BAMM graph gallery plots for more on working with these objects.

## 8.10. Macroevolutionary cohort analysis¶

Macroevolutionary cohort analysis provides a way of summarizing the extent to which species share correlated macroevolutionary dynamics. The method is explained in this Systematic Biology article. The basic idea is to visualize the pairwise probabilities that any two species share a common macroevolutionary rate regime. The first step is to generate a cohort matrix, which contains the pairwise probabilities of shared macroevolutionary dynamics. This is then passed to the `cohorts`

function, which generates the plot:

```
data(events.whales, whales)
edata <- getEventData(whales, events.whales, burnin=0.1)
cmat <- getCohortMatrix(edata)
cohorts(cmat, edata)
```

A macroevolutionary cohort matrix for whales is shown here.

## 8.11. Cumulative shift probabilities¶

The *cumulative shift probability tree* shows the cumulative probability, on each branch, that a shift occurred somewhere between the focal branch and the root of the tree. This option is a potentially useful complement to cohort analysis. The occurrence of such a shift implies that evolutionary dynamics on the focal branch are decoupled from the “background” diversification or trait evolutionary process at the root of the tree. We can compute and plot the cumulative shift probability tree as follows:

```
cst <- cumulativeShiftProbsTree(edata)
plot.phylo(cst)
```

Or, showing shift probs in color:

```
cst <- cumulativeShiftProbsTree(edata)
edgecols <- rep('black', length(mytree$edge.length))
is_highprobshift <- cst$edge.length >= 0.95
edgecols[ is_highprobshift ] <- "red"
plot.phylo(mytree, edge.color = edgecols)
```

And this should plot your tree (*mytree*) such that all branches with cumulative shift probabilities of 0.95 or higher are identified in red.