Coalescent simulation of genealogies

A Genealogy (tree) consist of Topology and coalescent times.

• Topology can be isochronous (all tips are “sampled” at time 0) or heterochronous (tips have different “sampling times”). Lineages merge (coalesce) at random between the existant lineages at the coalescent times.
• Coalescent times are exponentially distributed random variables with a rate that depends on the number of lineages and the population size trajectory.

The main function for simulation of genealogies in phylodyn is . In all our simulations, time is measured in units of \(N_{0}\) generations.

gene = coalsim(samp_times = samp_times, n_sampled = n_sampled, traj = traj, lower_bound = 1/20)

Examples

The following example generates an isochronous genealogy from a constant effective population size (Ne=1) with 10 tips.

library("phylodyn")

constant<-function(x){
  return (rep(1,length(x)))
}

simulation1<-coalsim(0,10,constant)
tree1<-generate_newick(simulation1)
plot(tree1$newick)

tree1$newick

## 
## Phylogenetic tree with 10 tips and 9 internal nodes.
## 
## Tip labels:
##  t1_0, t2_0, t3_0, t4_0, t5_0, t6_0, ...
## 
## Rooted; includes branch lengths.

In the following example we simulate a genealogy with constant effective population size with 10 tips at time 0 and 40 other tips with uniform sampling times

samp_times = c(0, sort(runif(40, 0, 8)))
n_sampled = c(10, rep(1, 40))

simulation2<-coalsim(samp_times = samp_times, n_sampled = n_sampled, traj = constant)
tree2<-generate_newick(simulation2)
plot(tree2$newick,show.tip.label = F)

tree2$newick

## 
## Phylogenetic tree with 50 tips and 49 internal nodes.
## 
## Tip labels:
##  t49_0, t50_0, t33_0, t34_0, t28_0, t26_0, ...
## 
## Rooted; includes branch lengths.

Here, we consider a more general demographic model such as bottleneck. We specify our trajectory through the function and simulate via the thinning method (see Palacios and Minin, 2013)

bottleneck_traj<-function(t){
  result=rep(0,length(t))
  result[t<=0.5]<-1
  result[t>0.5 & t<1]<-.1
  result[t>=1]<-1
  return(result)
}

simulation3<-coalsim(samp_times = samp_times, n_sampled = n_sampled, traj = bottleneck_traj,method="thin",val_upper=11)
tree3<-generate_newick((simulation3))
plot(tree3$newick,show.tip.label = F)

Note: Other R packages such as Ape and phyclust (ms) have functions that simulate isochronous genealogies under the coalescent model for specific demographic scenarios such as exponential growth and piece-wise constant functions.