# Branch length in phylogenetic trees

I know this is a very basic question, but it is not too clear to me what is the unit of measure of branch length in phylogenetic trees. I have come to understand that it is usually expressed in number of substitutions/site/some unit of time. What is that "some unit of time"? Generations? Does it depend on what method of tree construction I am using (NJT, MP, ML)?

• It does depend greatly on the format, in some diagrams it is meaningless and just created by what is necessary to make the tree visibly clean. Make sure the diagram intends for it to mean something first.
– John
Jun 16, 2017 at 15:39
• @BeatriceBaldi See the chat for ongoing discussion. Jun 17, 2017 at 17:45

When you estimate a phylogenetic tree, be it by likelihood, parsimony, or distance (like NJ), the lengths will be given in units of substitutions per site, with no time information. For example from here:

The units of branch length are usually nucleotide substitutions per site – that is the number of changes or 'substitutions' divided by the length of the sequence (although they may be given as % change, i.e., the number of changes per 100 nucleotide sites).

To transform these lengths into a time scale, further information is necessary. For example assuming that the molecular clock is valid, or instead using relaxed clock models that describe how each branch length l=r x t can be decomposed into a rate r and a time t. Since in many cases the rate is not constant along the tree (i.e. the clock is not valid), an inferred phylogenetic tree is not ultrametric (i.e. the sum of branch lengths from the leaves to their MRCA is not constant).

There are software packages, most notably BEAST, that explicitly model a strict or relaxed clock for you, and then can return the branch lengths in arbitrary time units. "Arbitrary" means that the numbers by themselves do not have special meaning, and will reflect your choice for instance of the prior. In which case they can represent year, million years or generations (http://beast.bio.ed.ac.uk/faq#Evolutionary_rates_and_time_scales).

• I think it is important to separate the proxy used to estimate time with time itself. There's two solutions to the answer either "time" or "it depends upon the methodology used". However, in the second case one will note that whatever statistics is being used it is always a proxy for time. One will also note that many tree are being build as a congruent of various proxy so that the branch length are the best possible estimates of time. The overal goal of the tree representation is the time from lineage to their MRCA. Jun 17, 2017 at 14:43
• The branch length unit of a phylogenetic tree is always "substitutions per site" (the only info we have from sequences alone). No discussion there. Pls check the books by Felsenstein, by Ziheng Yang, the timetree resource, or the manual of any tree inference program. To interpret as time, usually you're assuming a (strict) molecular clock. In this case you are in fact claiming that the rate is constant (then branches are proportional to time). The lengths are NOT the best time estimates unless the sequences do follow a strict clock. (tests for clock-likeliness use this very fact BTW.) Jun 17, 2017 at 16:58
• How about phylogenetic trees based on phenotypic data and carbon14? Do you think it is wise to consider that there is no universal meaning to the length of a branch in a tree as it depends on the technic rather than saying that the length of the branches express some proxy for time? Jun 17, 2017 at 16:59
• I can't comment on wisdom, I am only answering the OP's question. Morphological data has the same interpretation as sequence data, and also need a model to disentangle rates and times, since the lengths describe only their product. I am happy to explain more through the chat. (By your comment on carbon14, for fossil ages, maybe you are thinking about "total evidence approach" and other dating methods? They are based on relaxed clock models.) And yes, there is a universal meaning for branch lengths -- that is my answer. Jun 17, 2017 at 17:18
• Thank you and @Remi.b your answers and chat were both helpful! What I was looking for was exactly what you said, that in all those methods of tree reconstruction that I mentioned (starting from sequence data), the branch lengths given are in units of substitution/site. Then of course, to have information about "absolute" time, we have to apply a molecular clock (be it strict or relaxed) and a calibration point (be it fossil data or biogeographical events). That way we can calculate time as branch length/mutation rate. Thank you both so much, it's great to find such a helpful community! Jun 18, 2017 at 11:47

This answer is mainly inspired by a long discussion in the chat with @LeoMartins.

Branch length represents some measurement of lineage divergence

Branch length represents some measurement of lineage divergence. The actual measurement depends upon the type of data considered. For genetic data, it is generally (if not always) a number of substitutions. In any case, those measures of lineage divergence are not a priori design to be best estimates of time, however they are often good proxy for time and often interpreted as being measurement of time.

Cases of meaningless branch length

Be careful that some trees use branches only to represent evolutionary relationships but do not convey meaning via branch lengths.

Total evidence approaches

More and more often, we make consideration of "total evidence approaches" (e.g. Arrigo et al. 2013) which can use sequence data, fossil data and morpho data to form a consensus and offer best estimate of lineage divergence.

• This is a good, generalized response that remains unbiased in perspective. +1.
– user22020
Oct 5, 2017 at 22:17

The length of branch indicate time in years (or whatever standard objective unit of time). It would make little sense (although one could argue that it'd be interesting to look at) to build a tree of life where time is in generation as the generation time varies so greatly among lineages.

It is important to not confuse the mean of estimating the length of a branch to the length of the branch itself. For this I will just give you two technics used to estimate such branch length.

Number of substitutions

Now, we estimate this time based on a number of method. One of them is the number of substitution at neutral sites. The number of substitution at neutral sites over $n$ generations is equal to the mutation rate $\mu \cdot t$. That's a classic result, it is due to the fact the there are $2 N \mu$ mutations at each generation, each of them having probability $\frac{1}{2N}$ to fix (given they are neutral) and therefore the neutral substitution rate is $\frac{2N\mu}{2N}=\mu$.

So, using substitution rate we can estimate the number of generations and by estimating the generation time, we can estimate real time (in years).

Most of the time the length of the branches are simply the number of observed substitutions but as not all phylogenetic trees are made from such data, one must consider the branch length in phylogenetic trees in general as being measure of time.

Fossil data

Other methods exist to estimate the length of branches such as fossil datation for example. Here we directly estimate the time in years, not in generation first.

It is important not to confound the mean of estimation of time with