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A point mutation changes a nucleotide at one genomic position. Replication errors and chemical damage can generate substitutions; repair and other proofreading processes influence the retained mutation rate. A coding change may be synonymous or alter an amino acid, while a noncoding change can affect regulation. Its evolutionary effect depends on context, so mutation, functional consequence and eventual fixation are distinct events.

Mutation supplies new variants, while genetic drift, selection and population history determine their persistence. Under a simple neutral model, increasing population size raises the number of new variants but lowers each one's fixation probability; the neutral substitution rate is approximately the mutation rate. Selective constraint, generation time and lineage-specific processes can therefore complicate a universal molecular clock. Molecular evolution is not directed towards anticipated needs.

To infer a phylogeny, compare homologous positions in appropriately chosen orthologous sequences and estimate the tree and branch lengths under a substitution model. Shared derived characters support common ancestry, but reversals and parallel substitutions mean raw mismatches underestimate evolutionary distance. In a simple equal-rates four-state illustration, a mismatch fraction $p$ gives corrected pairwise distance $d=-(3/4)\log (1-4p/3)$. The formula's strong divergence as $p\to 3/4$ reflects saturation and loss of reliable historical information, not arbitrarily precise evidence for an ancient split.

The molecular-clock calibration and rate-time identifiability issue is fundamental: branch lengths first measure expected substitutions per site. A clock relates them to time by $d_i=r_i{t}_i$; for two equal-rate lineages separated for time $t$, pairwise distance is $d=2rt$, so $t=d/(2r)$. Absolute times require external information, such as independently dated fossils or geological constraints, or informative sampling dates when the data contain a temporal signal. Sequence differences alone generally identify only rate-times-time, not both quantities separately.

Time-calibrated inference should propagate uncertainty in topology, substitution rates, ancestral-state reconstruction and calibration bounds. Relaxed clocks permit different lineage rates. Fossil minima are not automatically exact split dates; orthology mistakes, incomplete lineage sorting, recombination, horizontal transfer and selection can cause discordance between one gene tree and species history. Multiple independent loci and well-justified calibrations make a stronger historical argument than a single uncalibrated sequence comparison. No unique numerical tree or date can be constructed here without actual sequence observations and calibration data.

A point mutation changes an individual nucleotide position, introducing heritable sequence variation. Replication errors and spontaneous chemical damage are possible origins; mutation does not occur because a future change would be useful. Natural selection changes the frequencies of variants through their effects on reproduction, while genetic drift causes random frequency changes, especially in small populations. A sequence difference fixed between lineages is a substitution; many new mutations disappear and never become substitutions. Under a simple neutral diploid model, $2N_e\mu$ new neutral variants per generation times fixation probability $1/(2N_e)$ gives substitution rate $\mu$, motivating a molecular clock for suitable neutral sites.

To infer a phylogenetic tree, compare homologous, preferably orthologous sequences and align corresponding sites. A nucleotide substitution model converts observed sequence differences into estimated evolutionary branch lengths, allowing for multiple changes at one site. For example, in the equal-frequency, equal-rate Jukes-Cantor model, a site changes to any alternative with rate $\mu /3$, where $\mu$ is its total substitution rate. The probability of matching its initial state after elapsed time $t$ is $1/4+(3/4)e^{-4\mu t/3}$. Thus for an evolutionary separation with expected substitutions per site $d$, the observed mismatch fraction is $p=(3/4)(1-e^{-4d/3})$ andFor small $p$, $d\simeq p$; near saturation $p=3/4$, large evolutionary distances become difficult to distinguish. The correction does not rescue fully saturated data. Real analyses may allow unequal nucleotide frequencies, transition biases and variation of rates between sites.

Tree topology and branch lengths can be estimated using maximum likelihood estimation or Bayesian phylogenetic inference, with support assessed from resampling or posterior uncertainty. A gene tree need not equal the species tree, because incomplete lineage sorting, genetic recombination and horizontal gene transfer can produce different histories. Rooting with an appropriate outgroup establishes ancestral direction; pairwise differences alone do not supply a root.

Branch lengths measured in substitutions per site are not yet calendar times. Under a strict molecular clock with rate $\mu$ per site per year, a branch of duration $t$ has length $\mu t$; two contemporaneously sampled descendants separated at time $t$ have total path length $d=2\mu t$, hence $\boxed{t=d/(2\mu )}$. Calibration comes from independently dated constraints such as fossil calibration, geological information or sufficiently informative sampling dates. A dated common ancestor is not automatically identical in age to the earliest observed fossil. A relaxed molecular clock permits branch-specific rates while imposing a statistical model on them.

Without an external temporal calibration or an independently known rate, multiplying all times by a constant and dividing all rates by that constant leaves expected sequence divergence unchanged. Absolute dates are therefore unidentifiable from sequence divergence alone. A useful time-calibrated phylogenetic tree reports uncertainty from sequence sampling, substitution models, rate variation, topology and calibration bounds, rather than displaying an unjustified exact date for each ancestor.

A point mutation affects a single base pair. Terminology varies: the broad usage includes a one-base pair insertion or deletion as well as a nucleotide substitution. Describing the actual sequence change avoids this ambiguity.^[ref]