Kingman Coalescent Tree Moments
Build genealogy moments from independent merger waits and explain mutation-count overdispersion.
Free theory articleBuild genealogy moments from independent merger waits and explain mutation-count overdispersion.
Concept & interpretation
The Kingman Coalescent models the backward-in-time genealogy of a sample of n lineages, assuming a neutrally evolving constant-size population. Pairs of lineages merge uniformly at random, with standard waiting times driven by independent Exponential distributions.
Experiment
You can interactively explore these properties in the module at https://riano.app/module/kingman-coalescent-tree-moments.
- Select Sample lineages to 6. Observe that the tree gains more stages and the Expected total branch length increases to approximately 4.566666666666666.
- Change the Mutation theta to 2. Notice that the Expected segregating sites doubles because mutations fall independently along the branches with rate proportional to theta.
- Change the Stage probe to 3. This highlights the tree where 3 ancestral lineages remain. The Merger Rate becomes 3.0 and the Mean Wait becomes 0.3333333333333333.