I did some math surrounding the number of mutations between two #nCoV2019 genomes and the distribution of the number of transmission steps that separate them. 1/9
First, I use the epidemiological parameters from this NEJM paper to sketch out two infections that are directly connected, finding an expectation of 9 days of viral replication from sample from index infection to sample from secondary infection: 2/9 
I use @arambaut's estimate of the evolutionary rate of the virus at 0.011 subs per site per year (virological.org/t/phylodynamic…) to derive a rate of 0.091 subs per genome per day and thus a rate of 0.88 subs per genome per sampling interval between direct infections. 3/9
@arambaut We can use a Poisson distribution to get the distribution of the number of mutations expected in the case of direct infection, finding 44% with 0 mutations, 36% with 1 mutation, 15% with 2 mutations and 4% with 3 mutations. 4/9
@arambaut With increasing numbers of transmission steps we get the following distribution of the number of mutations: 5/9
@arambaut We can also do out the Bayesian logic to get the distribution of the number of transmission steps given an observed number of mutations. 6/9
@arambaut Let's say we observe 0 mutations between two samples. This suggests a 56% chance of a direct infection (1 step), a 25% chance of 2 steps, a 11% of 3 steps and a 5% chance of 4 steps. 7/9
@arambaut Seems like a useful rule-of-thumb for contact tracing. Identical infections are about ~50% likely to be directly connected. 8/9
@arambaut This basic logic is what @XavierDidelot and @CarolineColijn's github.com/xavierdidelot/… uses with more rigor to infer transmission networks. 9/9
