Phylogenetics

A heritable feature represented by distinct states in a comparative analysis. State definitions, homology assumptions, uncertainty and correlations among characters affect the reconstruction.

A branching diagram representing a hypothesis of relationships. Branch geometry need not encode elapsed time or amount of anatomical change.

A lineage outside the focal group used to inform rooting and character polarity. An extant outgroup is not an unchanged ancestor.

Naming clades by explicit ancestry-based definitions. A definition fixes the rule connecting a name to ancestry; an inferred phylogenetic tree determines which organisms satisfy that rule.

A named organism, species or other specified reference used to anchor a clade definition. Internal specifiers are included and external specifiers excluded.

A definition selecting the largest clade containing specified internal reference taxa but excluding specified external reference taxa. With one of each, it includes organisms more closely related to the internal than to the external specifier.

A definition selecting the smallest clade containing specified internal reference taxa: their last common ancestor and every descendant. The specifiers need not be living.

Inference combining evidence types such as morphological characters and molecular sequences, with explicit assumptions about homology, missing data and evolution.

Inference of evolutionary relationships from molecular data. Structural correspondence is most persuasive when evaluated alongside alignments, sequence profiles and taxonomic distributions.

Correlation among species observations caused by shared evolutionary history. Comparative tests must distinguish replicated evolutionary changes from repeated sampling of the same ancestral trait.

The historical difficulty of placing turtles among reptiles, including conflict between a roofed temporal skull and evidence for diapsid ancestry. It exposes the difference between character similarity and inferred descent.

Assembly of separate lineages without including their relevant connecting ancestry, often using independently acquired similar features. Selected tips alone do not always distinguish this from paraphyly; the ancestry included and the interpretation of characters matter.

Inclusion of an ancestor while excluding some descendants. Traditional reptiles with birds excluded provide an example; the status depends on the stated group definition.

In the cladistic sense, inclusion of an ancestor and all its descendants. Such a group is a clade.

A shared derived character supporting a particular branch of a phylogenetic tree. Its level depends on inferred character polarity; a trait shared ancestrally across a wider group need not diagnose a smaller clade.

Similarity of character states not explained simply by inheritance of that state from the relevant common ancestor. Independent origins and evolutionary reversals can make a single feature misleading.

The most recent ancestor shared by the stated descendant lineages. In population history it is important to distinguish a shared ancestral population from the common ancestor of copies at a particular genetic locus.

Extinct lineages more closely related to the specified crown group than to its living sister group, but outside that crown. Its membership depends on the crown and sister group specified.

The clade comprising the last common ancestor of a stated set of living lineages and all its descendants. An older fossil closely related to that group may instead belong to its stem group.

An inference criterion selecting histories or trees minimizing the stated cost of character changes. A minimum-change history is not automatically the most probable history under a stochastic evolutionary model.

Inference of characters at ancestral nodes from observed relatives and an evolutionary model. Historical hypotheses should carry uncertainty in trees, rates, character coding and root states into subsequent tests.

The inferred ancestral or derived status of a character state relative to a particular comparison. A state can be derived at one node and ancestral at another.

Sampling evolutionary character histories conditional on observations, a tree and transition assumptions. Histories can include multiple unobserved events along a branch, rather than only changes implied by endpoints.

Joint inference of evolutionary times, rates and related parameters using Bayesian inference. Sequence distances identify products of rates and durations; absolute ages require additional time information and assumptions.

Inference of a posterior distribution over phylogenetic trees and model parameters by combining a sequence likelihood function with a prior distribution. Integrating nuisance parameters is distinct from maximizing the likelihood.

A recursive calculation of the likelihood function on a phylogenetic tree, summing over unknown ancestral states while reusing partial calculations from descendant subtrees.^[ref]

A probabilistic model of sequence changes along a phylogenetic tree. A continuous-time Markov chain rate matrix gives branch transition probabilities through a matrix exponential; assumptions about composition and rate variation affect inference.

Persistence of ancestral variation through successive lineage splits, allowing the ancestry of one genomic region to disagree with the population branching history. Such disagreement is not by itself evidence of introgression.

A molecular clock relates accumulated nucleotide substitutions to elapsed evolutionary time through an assumed rate. Two lineages evolving at the same constant rate $r$ for time $T$ have total expected substitution count $2rT$ per site before accounting for repeated changes obscured in endpoint sequences. Rate variation among sites or branches requires a more general clock model.

A molecular branch length is expected substitutions per site, the product of evolutionary rate and elapsed time. Without external calibration, simultaneous rescaling of rate and time preserves the sequence likelihood. Fossil or geological bounds, or informative sampling dates, supply time information; relaxed clocks allow rate variation. Calibration uncertainty, saturation and gene/species-tree discordance must be propagated rather than turned into an exact historical date.

Use of dated fossil evidence to constrain evolutionary times. Geological age, phylogenetic placement, stem versus crown assignment and uncertainty all affect the constraint.

A calibration constraint allowing a small nonzero probability outside its principal range. It represents uncertainty but still needs biologically defensible tail probabilities.

A calibration constraint assigning zero probability to ages beyond a specified limit. Sequence data cannot overcome an excluded age under that prior.

A model allowing evolutionary rates to vary among branches. The distribution and dependence of rates affect inferred times and must be distinguished from absolute-time calibration.

A model assigning the same evolutionary rate to the relevant branches. Expected branch length is rate multiplied by duration; scaling times and inverse-scaling the rate preserves the sequence likelihood.

A clade comprises an ancestor and all its descendants. Membership is about common descent, not a taxonomic rank or a degree of cellular complexity. In a two-domain system, the nuclear lineage of eukaryotes nests within archaea; a group containing only the prokaryotic members excludes descendants and is therefore not that complete clade. See OpenStax Biology 2e, 20.2: clades and shared ancestry.

A specified crown group together with its stem group. fossil occurrences must be assigned at the correct level before they are used for fossil calibration.

A phylogenetic tree describes ancestral relationships. In a probabilistic graphical model on a rooted tree, latent variables at ancestral vertices are inferred from observations at leaves using belief propagation.

A phylogenetic epoch is an interval between successive branching or merging events during which the number of extant ancestral branches is constant. Its expected duration with $k$ branches is denoted $E_k$.

A representation of the branching history of species lineages. Individual gene trees can differ, so a well-supported tree for one gene is not automatically a complete species history.

A phylogenetic tree describing the ancestry of sampled gene copies or a genomic region. It need not match a species tree, because lineage sorting, duplication or introgression can produce a different history.

The Felsenstein pruning algorithm computes a site likelihood function by sum-product belief propagation from leaves to root. For a finite-state Markov kernel $K$, the subtree likelihood function obeys $L_v(a)={\prod }_{w\text{ child of }v}{\sum }_{b}K(a,b)L_w(b)$, with observed-state indicators at leaves. Summing against the root probability distribution gives the site likelihood function. An outward pass gives edge posterior probabilities and expected transition counts for the expectation-maximization algorithm.