Let $T_i$ be the time to coalesce from $n(t)=i+1$ to $n(t)=i$, where $n(t)$ is the number of sites that have not coalesced yet. In the below example the maximum $n(0)=6$.
As I understand it, many mathematical developments in coalescent theory depends on the fact that the random variables $T_i$ are independent (but not identically distributed). In other words...
$$f_{T_n, T_{n-1}, …. T_3, T_2}(t_n, t_{n-1},….,t_3, t_2) = \prod_{i=2}^n f_{T_i}(t_i)$$
What are the assumptions for this equation to hold true? Below are some suggestions
- No selection
- Selection is not varying through time
- Stable population size
- Random mating
- Both sexes have the same genetic background
- Both sexes have the same variance in fitness
- ...