Virus Phylodynamics

"Skyline" coalescent model

The generalized skyline plot

Introduced by Pybus and Strimmer (2001).

Visual framework for exploring the demographic history of sampled DNA sequences
Input: a single estimated ancestral genealogy (a tree)
Output: nonparametric plot of the population size through time
Groups adjacent coalescent intervals
Converts information within these intervals to estimates of population size

for a single coalescent interval:

\[\hat{N}_k = \binom{k}{2}t_k\]

for \(j\) adjacent intervals:

\[\hat{N}_{k,j} = \frac{k(k-j)}{2j}\sum_{i=k-j+1}^k{t_i}\]

The generalized skyline plot - simulated data

Constant population size, \(N(t)=N_0\)

Exponential growth, \(N(t) = N_0 e^{-rt}\)

The generalized skyline plot - HIV-1 group M

The tree used here was estimated in Yusim et al (2001) Phil. Trans. Roy. Soc. Lond. B 356:855-866.

The black curve is a parametric coalescent estimate obtained from the same data under the expansion model, \(N(t) = (N_0-N_A)e^{-rt}+N_A\)

The Bayesian skyline plot

The Bayesian skyline plot (Drummond et al, 2005) estimates a demographic function that has a certain fixed number of steps (in this example 15) and then integrates over all possible positions of the break points, and population sizes within each epoch.