Effective population size

Introduction

• Given a clock-like tree, one of the quantities we can estimate is the effective population size over time assuming a coalescent model.
• This captures the rate at which the tree branches:
  • Small effective population size = high branching rate and short branches
  • Large effective population size = low branching rate and long branches

What is the effective population size?

• Not simply the number of infected individuals
• For simple models

$N_e=I \tau /2$

$I$ = number of infected individuals $\tau$ = average time between infections in the population ('generation time')

• As both change over the course of an epidemic, it is often hard to interpret effective population size epidemiologically
• However, during the epidemic growth phase, the rate of change of $N_e$ reflects the exponential growth rate of infected individuals

Coalescent models, birth-death-sampling models, and beyond

• Coalescent models assume the population size is changing deterministically
  • R package rcolgem
• Birth-death models allow for stochastic fluctuations in the population, but have not yet been extended to complex, nonlinear, structured populations
  • R package TreePar
• Stochastic epidemiological models are the most realistic, but have only been implemented for very simple cases
  • R package expoTree