Branch length is the expected number of substitutions per site per time point. Each lineage evolves independently from the ancestor.
Paste a protein sequence, set a branch length and a number of time points, and this mutation simulator evolves several independent lineages from that ancestor under a real substitution model. Every new substitution is marked in red on the timeline, the results block sums them up, and the link you share reproduces the run exactly.
The simulator uses the continuous-time Markov model behind modern phylogenetics. From the chosen model’s exchangeability rates and equilibrium amino-acid frequencies it builds the rate matrix Q, scales it so that one unit of branch length equals one expected substitution per site, and computes the transition matrix P = exp(Qt) for the branch length t you set. At each time point every site of every lineage draws its next residue from the row of P belonging to its current residue. Time accumulates one branch length per point, so five points at 0.1 span a total distance of 0.5 substitutions per site from the ancestor.
The ancestor sits at the top. Below it, each time point lists one row per lineage with substitutions that happened in that step in bold red, earlier differences from the ancestor in faded red, and the mutation labels after the row, so I3V means isoleucine at position 3 became valine. The results block counts substitutions in total and per lineage, prints the expected number per sequence, which is the total branch length multiplied by the sequence length, the number of unique final sequences, the mean pairwise distance between lineages as differences per site, and the identity of the final sequences to the ancestor. Copy report puts the numbers and the final sequences on the clipboard.
The example sequence is the 21-residue A chain of insulin. With the defaults, branch length 0.1, five time points and five lineages, the total distance is 0.5 per site, so the expected count is 10.5 substitutions per lineage. Runs land around that value, and identity to the ancestor ends near 60 to 70 percent rather than 50, because a site that changes twice still counts as one difference and some sites revert. At branch length 1 the lineages diverge so far that almost every position differs from the ancestor, the regime where phylogenetic signal saturates.
Sequences are trimmed at 2,000 residues, FASTA header lines are stripped, and only the twenty standard amino acids are evolved. There are no insertions, deletions, rate variation between sites or selection beyond the conserved-site option: the output illustrates neutral substitution, it does not predict how a particular protein evolves.
JTT (Jones, Taylor and Thornton, 1992) and WAG (Whelan and Goldman, 2001), two empirical amino-acid models estimated from large sets of real protein alignments, plus a uniform model in which every amino acid is equally likely to change into any other. The empirical models make conservative changes such as isoleucine to valine far more likely than, say, tryptophan to glycine.
Branch length is evolutionary distance measured in expected substitutions per site, the unit used on phylogenetic trees. At 0.1 each site is expected to change about once in ten per time point, so a 100-residue protein accumulates roughly 10 substitutions per point, fewer where a site changes and changes back.
Each site draws its new residue at random from the model's probabilities, so two runs never match. Run again draws a fresh simulation; the share link carries the seed, and opening it reproduces the same timeline exactly.
The share of positions, averaged over all lineages, where the final sequence still has the ancestral residue. Multiple hits at one site count as one difference, which is why identity falls more slowly than the substitution count rises.
Only in one simple way: the Keep C, H, D, E option freezes cysteine, histidine, aspartate and glutamate, the residues most often found at active sites and disulfide bonds. Everything else evolves neutrally; there are no insertions or deletions, and sites evolve independently of one another.