Atlas / Biology / The Tree of Life Thread

Field · Emerged 1950 – 2001

Phylogenetics

Given only the organisms alive now, how can the branching order of their ancestry be reconstructed, and how confident may we be in the answer?

5 chapters7 min read6 turning points 2 open problems

Branched from: Systematics + Evolutionary Biology
Branched into: Macroevolution + Microbial Phylogenomics
Figures: Willi Hennig, Emile Zuckerkandl, Linus Pauling, Robert Sokal, Joseph Camin, Margaret Dayhoff, Walter Fitch, Joseph Felsenstein, John Huelsenbeck, Fredrik Ronquist, Wayne Maddison

In brief

If all life descends from common ancestors, there is one true tree, and every classification is a hypothesis about it. Phylogenetics is the business of inferring that tree from evidence — originally from anatomy, since the 1960s mostly from sequences — and of saying how much of the inferred tree is supported by the data and how much is an artefact of the method.

Two ideas made it a science rather than a craft. Willi Hennig's, in 1950, was that only shared novelties carry information about grouping: the fact that birds and crocodiles both have scales says nothing, because their common ancestor had scales too. Emile Zuckerkandl and Linus Pauling's, in 1962, was that molecules are documents — the number of differences between two proteins measures the time since their lineages parted. From there the problem became statistical, and in some of its forms provably hard: the number of possible trees for fifty species exceeds the number of atoms in the Earth.

Key ideas

SynapomorphyEnters 1950 – 1966: A character state that is new in the common ancestor of a group and inherited by its descendants. Only these group things. A state retained unchanged from a remoter ancestor — a plesiomorphy — is shared by too many organisms to delimit anything.
MonophylyEnters 1950 – 1966: A group containing an ancestor and all of its descendants. On this criterion birds belong inside the reptiles, and "reptiles excluding birds" is not a group. Groups that omit some descendants are paraphyletic; groups assembled from convergence are polyphyletic.
Molecular clockEnters 1962 – 1965: Over long intervals, substitutions in a protein or gene accumulate at a roughly steady rate, so sequence difference is a measure of elapsed time. The rate differs between genes and between lineages, which is what makes calibration the hard part.
ParsimonyEnters 1965 – 1971: Prefer the tree that requires the fewest character changes. It needs no model of substitution, which is its appeal, and it is biased when change is fast, which is its weakness.
Likelihood and posterior supportEnters 1996 – 2001: Specify a probabilistic model of substitution, and every tree acquires a likelihood: the probability of the observed sequences given that tree. Maximising it selects a tree; sampling from the posterior with Markov chain Monte Carlo attaches a probability to every branch.
Long-branch attractionEnters 1978 – 1985: Two rapidly evolving lineages accumulate so many changes that some coincide, and parsimony reads the coincidences as shared novelty. The two are drawn together on the tree however distant they really are, and adding more data makes the error more confident, not less.

Draws on other domains

↙ Mathematics
Bayesian Statistics
Bayesian family trees

Chapter I

Only Novelties Group

By the 1950s everyone agreed that classification should reflect descent. Nobody could say how to get from characters to descent without judgement. Willi Hennig, a specialist in flies who drafted his theory in an Allied prisoner-of-war camp, supplied the missing rule in 1950, and it is almost embarrassingly simple: a shared character groups organisms only if it is new.

Birds and crocodiles both lay shelled eggs, but so did their remote ancestors, and so do turtles and lizards; the character cannot separate any group from any other. Birds and crocodiles also share a four-chambered heart and a particular arrangement of skull openings that their common ancestor acquired and that lizards never had. Those are evidence. Hennig called a shared novelty a synapomorphy and a retained ancestral state a plesiomorphy, and insisted that only the former counts. From the rule follows a severe consequence: a named group must contain all of its ancestor's descendants. Reptilia without birds fails that test and is therefore not a group at all — which is why, in every modern classification, birds are reptiles.

Published in German, the book went unread for sixteen years. Its 1966 translation arrived at the moment when systematics was tearing itself apart over method, and it won, comprehensively and acrimoniously.

Chapter II

Molecules as Documents

The second idea came from chemistry. Emile Zuckerkandl and Linus Pauling lined up haemoglobin sequences from several mammals and counted differences. Horse and human differ in about 18 of 141 residues in the alpha chain; the gorilla differs from the human in one. Plotted against divergence times estimated from fossils, the counts fell roughly on a line. In 1965 they drew the conclusion: a protein is a document of evolutionary history, and its rate of change is a clock that runs whether or not anything visible is happening to the organism.

Morphologists were unimpressed, and the claim was overstated — rates differ between genes, between lineages and between sites, and modelling that variation is still the hardest part of molecular dating. But the consequence was immediate and permanent. Every organism carries a record of its ancestry in a form that can be read without fossils, and the record is the same kind of data for a bacterium, an oak and a whale. Relationships that anatomy could never settle, because the organisms have no anatomy in common, became answerable.

Chapter III

From Counting Steps to Fitting Models

The first computational methods counted. Joseph Camin and Robert Sokal proposed in 1965 that the best tree is the one needing fewest character changes, and tested the idea on plasticine "caminalcules" whose true genealogy they had invented and therefore knew. Margaret Dayhoff and Richard Eck published the first protein tree computed by that principle in 1966. Walter Fitch and Emanuel Margoliash built trees from distance matrices in 1967, and Fitch's 1971 algorithm scored a tree against an alignment in a single pass over the sites.

Then Joseph Felsenstein showed that counting can fail in a specific and dangerous way. If two lineages on opposite sides of the tree both evolve fast, some of their changes will coincide by chance, and parsimony reads coincidence as shared novelty. In 1978 he proved that for some branch lengths the method is statistically inconsistent: more data make it more certain of the wrong tree. The fix was to model substitution explicitly, which he did in 1981 — a tree's likelihood is the probability of the observed sequences given the tree and the model, computed by pruning up from the tips. In 1985 he added the bootstrap: resample the sites, rebuild the tree a hundred times, and report for each branch how often it appears. For the first time a published phylogeny carried numbers that meant something about confidence.

By the end of the 1990s the Bayesian version was in place. Put a prior on trees, sample the posterior with Markov chain Monte Carlo, and read off a probability for each clade; John Huelsenbeck and Fredrik Ronquist's MrBayes made this a command line away in 2001. The machinery came straight from Bayesian statistics and Monte Carlo methods, and phylogenetics became one of their largest consumers.

Chapter IV

A Closer Look: Scoring Three Trees for Four Species

With four species there are exactly three possible unrooted trees, given by which pair is grouped: $(AB)(CD)$ , $(AC)(BD)$ , $(AD)(BC)$ . Take this alignment of eight sites:

Site	A	B	C	D	Pattern
1	G	G	A	A	supports $(AB)(CD)$
2	C	C	T	T	supports $(AB)(CD)$
3	T	T	G	G	supports $(AB)(CD)$
4	A	C	A	C	supports $(AC)(BD)$
5	G	T	G	T	supports $(AC)(BD)$
6	A	T	T	A	supports $(AD)(BC)$
7	C	C	C	C	constant
8	G	G	G	A	unique to D

For a four-taxon tree, a site with two taxa in one state and two in another needs one change if the split matches the tree's internal branch, and two if it does not. A constant site needs none; a site unique to one tip needs one on every tree. So:

\begin{aligned} (AB)(CD): &\quad 3(1) + 2(2) + 1(2) + 0 + 1 = 10,\\ (AC)(BD): &\quad 3(2) + 2(1) + 1(2) + 0 + 1 = 11,\\ (AD)(BC): &\quad 3(2) + 2(2) + 1(1) + 0 + 1 = 12. \end{aligned}

Parsimony picks $(AB)(CD)$ , by one step. That margin is the whole evidence: three sites for it, two against, one for the third topology. Resample those eight sites with replacement and the winner changes often — which is exactly what Felsenstein's bootstrap measures.

Now scale up. The number of unrooted binary trees on $n$ tips is $(2n-5)!!$ :

Tips	Trees
4	3
10	2,027,025
20	$2.2 \times 10^{20}$
50	$2.8 \times 10^{74}$

Fifty species — a modest study — give more trees than there are atoms in the Earth, which is about $10^{50}$ . No search can visit them, and deciding the best one is NP-hard, so every published tree is the end point of a heuristic walk through that space.

The deeper trouble is that more sites do not always help. Under the Jukes–Cantor model, if a fraction $p$ of sites differ between two sequences, the number of substitutions per site that actually happened is

d = -\tfrac{3}{4}\ln\!\left(1 - \tfrac{4}{3}p\right).

At $p = 0.05$ this gives $d = 0.052$ — observed difference and real change are nearly the same. At $p = 0.3$ , $d = 0.38$ : a quarter of the history is already hidden by sites that changed twice. At $p = 0.6$ , $d = 1.21$ , and at $p = 0.75$ the formula diverges, because two random sequences over four bases differ at three sites in four. Past that point the sequences carry no information about time at all — they are saturated — and two long branches will look alike simply because both have gone random. That is long-branch attraction in one line, and it is why the sister group of all other animals is still disputed with whole genomes in hand.

Chapter V

One Tree, or Many?

A tree assumes that a lineage splits and the parts stay separate. Real histories break the assumption in two ways. Wayne Maddison pointed out in 1997 that even with no gene flow at all, different genes can have genuinely different trees: a polymorphism present in the ancestor gets sorted into the descendant species in whatever order chance dictates, and when speciations follow one another quickly, that order often disagrees with the species tree. Concatenating hundreds of genes does not fix this; it can produce high confidence in the wrong answer. Modern analyses model the gene trees inside the species tree, using the coalescent, rather than hoping the conflict averages out.

The second break is worse, and it is not about statistics. Genes move sideways between lineages, and in microbes they move constantly — so constantly that the tree may not be the right shape for the history at all. That is the problem of microbial phylogenomics. Where the tree does hold, calibrating it against the dated strata of palaeontology turns branching order into a chronology, and what that chronology shows over hundreds of millions of years is the subject of macroevolution.

Turning points6

1950 – 1966CONSENSUS-OVERTURNED
Hennig's phylogenetic systematics
Willi Hennig, an entomologist who wrote much of his theory as a prisoner of war, argues that classification must express branching order and nothing else, and that branching order can only be inferred from shared derived characters. Published in German in 1950 and largely ignored outside it, the argument reached the English-speaking world in 1966 and within fifteen years had displaced both phenetics and evolutionary taxonomy. It is the reason modern classifications contain no Reptilia in the old sense.
Willi Hennig
› Sources (2)
- Hennig, W. (1950). Grundzüge einer Theorie der phylogenetischen Systematik. Deutscher Zentralverlag, Berlin.
- Hennig, W. (1966). Phylogenetic Systematics. University of Illinois Press.
1962 – 1965DISCOVERY
Molecules as documents of history
Emile Zuckerkandl and Linus Pauling compare haemoglobins from several mammals and find that the number of amino-acid differences between two species is roughly proportional to the time since they diverged, as estimated from fossils. They propose that a protein is a document of evolutionary history and that its rate of change is a clock. The claim was received badly by palaeontologists and morphologists, and it turned out to be approximately right, with rate variation that took thirty years to model.
Emile Zuckerkandl, Linus Pauling
› Sources (2)
- Zuckerkandl, E. & Pauling, L. (1965). Molecules as documents of evolutionary history. Journal of Theoretical Biology 8(2): 357–366.
- Morgan, G. J. (1998). Emile Zuckerkandl, Linus Pauling, and the molecular evolutionary clock, 1959–1965. Journal of the History of Biology 31: 155–178.
1965 – 1971TECHNIQUE-INVENTED
Trees computed from characters
Joseph Camin and Robert Sokal propose choosing the tree that requires the fewest character changes, and test it on artificial organisms whose true history they knew. Margaret Dayhoff and Richard Eck publish the first protein phylogeny computed this way in 1966; Walter Fitch and Emanuel Margoliash build trees from distance matrices in 1967; and Fitch's algorithm of 1971 scores any tree against any alignment in one pass. Inference of trees becomes something a computer does.
Robert Sokal, Joseph Camin, Margaret Dayhoff, Walter Fitch
› Sources (3)
- Camin, J. H. & Sokal, R. R. (1965). A method for deducing branching sequences in phylogeny. Evolution 19: 311–326.
- Fitch, W. M. & Margoliash, E. (1967). Construction of phylogenetic trees. Science 155: 279–284.
- Fitch, W. M. (1971). Toward defining the course of evolution: minimum change for a specific tree topology. Systematic Zoology 20: 406–416.
1978 – 1985TECHNIQUE-INVENTED
Likelihood, inconsistency and the bootstrap
Joseph Felsenstein shows in 1978 that parsimony can be statistically inconsistent: for certain branch lengths it converges on the wrong tree as data accumulate, because coincidental changes in two fast lineages mimic shared ancestry. In 1981 he gives a practical algorithm for the likelihood of a tree under an explicit substitution model, and in 1985 he adapts the bootstrap to phylogenies, so that each branch carries a number saying how often it survives resampling of the sites. Trees acquire error bars.
Joseph Felsenstein
› Sources (3)
- Felsenstein, J. (1978). Cases in which parsimony or compatibility methods will be positively misleading. Systematic Zoology 27: 401–410.
- Felsenstein, J. (1981). Evolutionary trees from DNA sequences: a maximum likelihood approach. Journal of Molecular Evolution 17: 368–376.
- Felsenstein, J. (1985). Confidence limits on phylogenies: an approach using the bootstrap. Evolution 39: 783–791.
1996 – 2001TECHNIQUE-INVENTED
Sampling trees with Markov chains
Bruce Rannala and Ziheng Yang, Bob Mau and Michael Newton, and Brian Larget and Donald Simon independently put phylogenetics in a Bayesian frame: treat the tree as a parameter, place a prior on it, and sample the posterior with Markov chain Monte Carlo. John Huelsenbeck and Fredrik Ronquist's MrBayes, released in 2001, made it routine. The method gives a posterior probability for every clade and can carry relaxed clocks, fossil calibrations and partitioned models at the same time.
John Huelsenbeck, Fredrik Ronquist
› Sources (2)
- Rannala, B. & Yang, Z. (1996). Probability distribution of molecular evolutionary trees. Journal of Molecular Evolution 43: 304–311.
- Huelsenbeck, J. P. & Ronquist, F. (2001). MRBAYES: Bayesian inference of phylogenetic trees. Bioinformatics 17(8): 754–755.
1997 – 2010CONSENSUS-OVERTURNED
One species tree, many gene trees
Wayne Maddison points out that different genes in the same organisms legitimately give different trees. Ancestral polymorphism can be sorted into descendants in an order that does not follow the species branching — incomplete lineage sorting — and the shorter the interval between speciations, the more often it happens. Concatenating genes to get a single answer can then be confidently wrong. Methods that model the coalescent inside the species tree followed, and genome-scale data made the problem unavoidable rather than theoretical.
Wayne Maddison
› Sources (2)
- Maddison, W. P. (1997). Gene trees in species trees. Systematic Biology 46(3): 523–536.
- Degnan, J. H. & Rosenberg, N. A. (2009). Gene tree discordance, phylogenetic inference and the multispecies coalescent. Trends in Ecology & Evolution 24(6): 332–340.

Applications

Where it is used

Public health
Reading an outbreak from its genomes
Pathogen genomes sampled during an epidemic form a phylogeny whose branch lengths are measured in weeks. The tree shows which introductions seeded which clusters, whether a hospital outbreak is one transmission chain or several, and when a new variant arose. During the COVID-19 pandemic millions of SARS-CoV-2 genomes were placed on a single growing tree, and lineage designations came out of it.
› Sources (2)
- Hadfield, J. et al. (2018). Nextstrain: real-time tracking of pathogen evolution. Bioinformatics 34(23): 4121–4123.
- Grubaugh, N. D. et al. (2019). Tracking virus outbreaks in the twenty-first century. Nature Microbiology 4: 10–19.
Combinatorics↗ Mathematics · Enumerative Combinatorics
Counting the trees
The number of distinct unrooted binary trees on $n$ labelled tips is the double factorial $(2n-5)!! = 1 \cdot 3 \cdot 5 \cdots (2n-5)$ . The formula, and the bijections used to derive and sample from it, are combinatorics; phylogenetics is the reason anyone needs to enumerate or search such a set.
› Sources (1)
- Felsenstein, J. (1978). The number of evolutionary trees. Systematic Zoology 27: 27–33.
Algorithms↗ Mathematics · Computational Complexity
Finding the best tree is NP-hard
Deciding the most parsimonious tree is equivalent to the Steiner tree problem in a Hamming space and is NP-hard; maximum-likelihood tree inference is too. Practical software therefore does heuristic search — branch swapping, stochastic restarts — and reports a local optimum. That phylogenetic software never promises the best tree is a statement about complexity, not about biology.
› Sources (2)
- Foulds, L. R. & Graham, R. L. (1982). The Steiner problem in phylogeny is NP-complete. Advances in Applied Mathematics 3: 43–49.
- Roch, S. (2006). A short proof that phylogenetic tree reconstruction by maximum likelihood is hard. IEEE/ACM Transactions on Computational Biology and Bioinformatics 3(1): 92–94.

Open problems

Where the map runs out

Open

The first split among animals

Open as of 2026; the answer still changes with the substitution model chosen.

Are sponges or comb jellies the sister group to all other animals? The two answers imply opposite histories for nerves and muscles: either they arose once after sponges branched off, or they arose early and were lost in sponges. Analyses of the same genomes support either topology depending on which genes are included, how saturated sites are treated, and which outgroup is used.

Why it is hard: The split is more than 600 million years old and was probably rapid, so the informative signal is a thin layer of substitutions under 600 million years of subsequent noise. Comb jellies evolve fast, which makes them a textbook candidate for long-branch attraction, and the models used to correct for it are themselves what the answer depends on.
What resolving it unlocks: The order in which nervous systems, muscle and gut arose, and therefore whether the animal body plan was assembled once or converged on twice.

› Sources (2)

Dunn, C. W. et al. (2008). Broad phylogenomic sampling improves resolution of the animal tree of life. Nature 452: 745–749.
Schultz, D. T. et al. (2023). Ancient gene linkages support ctenophores as sister to other animals. Nature 618: 110–117.

Open

Dating divergences without good fossils

Open as of 2026; molecular and fossil dates still disagree by tens of millions of years in several groups.

Molecular clocks put the origin of placental mammals and of flowering plants well before their first fossils, by margins of 30 million years or more. Either the fossil record is systematically missing early members, or the clocks run fast when applied across a change in body size, generation time or population size, or both. The disagreement has not converged despite twenty years of relaxed-clock models.

Why it is hard: Rate and time are multiplied together in the data, so separating them requires external information, which comes from fossils whose placement is exactly what is in dispute. Priors on calibration dates do a large share of the work in the result, and it is difficult to tell how large.
What resolving it unlocks: Whether major groups diversified before or after the end-Cretaceous extinction, which is the difference between ecological opportunity and gradual accumulation as the cause of modern diversity.