6.1 What is being optimised #
6.1.1 A tree is a hypothesis about columns #
A phylogenetic tree of sequences is a hypothesis about splitting order, with branch lengths in substitutions, time, or both. The data are alignment columns. The tree is no better than those columns, and a guide tree used to build the alignment is not an independent test of itself.
Rooted Phylogenetic Tree & Evolutionary Cladogram
Sequences alone give an unrooted tree. An outgroup, or a rate assumption such as a clock, supplies the root. A distant or long-branched outgroup can distort the ingroup, and midpoint rooting quietly assumes a rough clock. A clade is a claim about a rooted tree. Name the method, the model, the alignment, and the root. Evolutionary Biology reads the tree as history. These notes ask only what was optimised, and which artefacts look like an answer.
6.2 Four families of method #
6.2.1 Distance #
A distance method collapses each pair to one number, then builds a tree from the matrix. Which sites changed is discarded, including a signal that sits only in a misaligned region. What remains is speed, which is why distances still build guide trees and first looks at large collections.
Raw percent difference hides multiple hits. Under Jukes–Cantor, where every nucleotide change is equally likely, d = −(3/4) ln(1 − 4p/3), with p the observed proportion of differences. Ten percent difference corrects only to about 0.11 substitutions per site. Fifty percent corrects to about 0.82. As p approaches 75% the distance goes to infinity and the pair is saturated. UPGMA forces equal root-to-tip lengths, a clock, and should not be used when rates differ. Neighbour joining does not assume a clock. Neither looks back at the alignment once the numbers exist.
6.2.2 Parsimony #
Parsimony prefers the tree that explains the columns with the fewest changes. Constant columns, and columns in which only one sequence differs, cost the same on every tree and separate none of them.
No explicit rate model is required. That simplicity is also how long-branch attraction gets in. Parsimony is reasonable when change is rare and branches are short. It is a poor default for a deep alignment with unequal rates.
6.2.3 Maximum likelihood #
Maximum likelihood prefers the tree and parameter values that give the alignment the highest probability under a substitution model. The model is part of the hypothesis. Nucleotide models run from one rate, through a transition/transversion distinction, to a general time-reversible model with six rates. Protein models are empirical matrices. A gamma distribution of rates across sites, often plus a class of invariant sites, stops every column being treated as equally free to change. Branch lengths are substitutions per site, not years.
A badly wrong model can make the most likely tree historically wrong, and more columns then make the error more confident. Omitting rate variation is the common case. The reported tree is the maximum, not a sample of near-equals. Support is a separate calculation.
6.2.4 Bayesian inference #
A Bayesian analysis puts a prior on trees and parameters and targets the posterior, proportional to likelihood times prior. A Markov chain Monte Carlo sample, once it has converged, visits clades in proportion to that posterior. Two runs that disagree have not converged, and a posterior with no convergence check is unfinished.
Priors show through on short branches and on clocks. A wrong model yields a tight posterior on the wrong tree. Justifying the prior and the calibrations is Evolutionary Biology. The sampler only enforces the model it was given.
6.3 Support, artefacts, and the clock #
6.3.1 Bootstraps and posterior probabilities #
The bootstrap resamples columns with replacement, rebuilds the tree, and counts how often a clade returns. It asks whether many columns agree, or a few carry the signal. It does not ask whether the model or the alignment is true. A bias present in every column is present in every resample, so support can be high on a wrong tree.
There is no universal cutoff. A classroom habit treats proportions above about 70% as some support and above about 90% as strong, for that data and method. A bootstrap of 80% is not an 80% chance the clade is true. Posterior probabilities are a different quantity and are often numerically higher. Support is not accuracy. Accuracy is a match to history, and systematic error produces supported inaccuracy. The remedies are the alignment, the model, the root, and loci that do not share the artefact.
6.3.2 Long-branch attraction #
Long-branch attraction is a named inconsistency. In the four-taxon case the true tree pairs A with B and C with D, but A and C have evolved much faster. Chance matches along those long branches look, to parsimony, like shared changes, so A is grouped with C. More sites add more coincidences, and the estimate locks.
A likelihood model that expects multiple hits resists that classical case, and fails in turn if rates vary and the model ignores the variation. Suspect a clade that unites the two longest branches and nothing else. Support that rises toward 100% as genes are added is what an artefact does.
6.3.3 The molecular clock #
The molecular clock is the hypothesis, associated with Zuckerkandl and Pauling in the 1960s, that substitutions per unit time are roughly constant across lineages. It is a hypothesis, not a fact about genomes. A relative-rate test against an outgroup can reject it, and forcing a strict clock onto data that reject it turns rate differences into false dates.
Relaxed clocks let the rate change along the tree and still connect change to time. Years enter only through calibrations: fossils or dated biogeographic events, each with uncertainty. Sequences do not contain the year. Without a calibration the result is relative time only. A misplaced calibration yields a narrow interval around the wrong date. Evolutionary Biology owns the fossils and the biological causes of rate change.
6.4 Genes are not species #
6.4.1 Orthologues and paralogues #
Fitch’s distinction is the event that split two homologous genes. Orthologues split at a speciation. Paralogues split at a duplication. Two copies in one genome are paralogues, and a pair drawn from two species can still be paralogues if the duplication was earlier and each species kept a different copy.
In-paralogues duplicated after the speciation of interest; out-paralogues duplicated before it, so several mouse genes may form one set orthologous to a single human gene. Xenologues arrived by horizontal transfer. A reciprocal best hit — each gene is the other’s best match in the other genome — is a screen, not the definition. Within one search, bit score and E-value agree on which hit is best. The screen fails when the true partner is missing, when a recent duplicate wins, or when several co-orthologues exist and only one is kept.
6.4.2 Why the gene tree disagrees with the species tree #
A correctly estimated gene tree need not match the species tree. After duplication and loss, one gene kept per species can be a paralogue, and the tree then groups species by which copy survived.
Martial Arts Blue Belt With Yellow Stribes
Incomplete lineage sorting is different. The ancestor carried more than one allele, and speciation happened before those alleles sorted to a single lineage. Which allele is fixed in which daughter need not follow the speciation order. This is expected when internodes are short relative to population size. Nothing in the estimation has failed, and a high bootstrap only makes a true disagreement look settled.
Horizontal transfer means the gene’s history is not a species branching at all. One gene, one alignment, and a large support value are therefore not a species tree. That question needs many loci, and a model that expects discordance (the multispecies coalescent, which these notes do not derive).
6.5 Key terms, summary, and self-check #
Key terms. Unrooted tree; outgroup; distance; Jukes–Cantor; UPGMA; neighbour joining; parsimony; maximum likelihood; posterior; bootstrap; long-branch attraction; molecular clock; relaxed clock; calibration; orthologue; paralogue; reciprocal best hit; incomplete lineage sorting.
Summary. Sequence trees are unrooted until an outgroup or a clock roots them. Distances throw away which sites changed; UPGMA assumes a clock and neighbour joining does not. Parsimony minimises changes. Likelihood maximises the probability of the data under a model. Bayesian sampling targets a posterior and needs a convergence check. Neither bootstraps nor posterior probabilities are accuracy, and long-branch attraction is the classic confident error, worsened by more data. A strict clock can be rejected; relaxed clocks still need calibrations for years. Orthology is speciation and paralogy is duplication. Duplication and loss, incomplete lineage sorting, and transfer let a true gene tree differ from the species tree.
Self-check.
1. Why does Jukes–Cantor turn an observed 50% difference into about 0.82, and what happens as the difference approaches 75%?
2. What does likelihood maximise, and why can the maximum be the wrong tree?
3. A clade with bootstrap 100% joins the two longest branches. Why is “add sites” not the remedy?
4. What ingredient of a dated relaxed clock is not in the sequences?
5. Reciprocal best hits succeed. Why is that not proof of one-to-one orthology? Name a process that separates a correct gene tree from the species tree.
