Skyline Plot Estimate of Effective Population Size

skyline computes the generalized skyline plot estimate of effective population size from an estimated phylogeny. The demographic history is approximated by a step-function. The number of parameters of the skyline plot (i.e. its smoothness) is controlled by a parameter epsilon. find.skyline.epsilon searches for an optimal value of the epsilon parameter, i.e. the value that maximizes the AICc-corrected log-likelihood (logL.AICc).

skyline(x, ...)
## S3 method for class 'phylo':
skyline(x, \dots)
## S3 method for class 'coalescentIntervals':
skyline(x, epsilon=0, \dots)
## S3 method for class 'collapsedIntervals':
skyline(x,, \dots)
find.skyline.epsilon(ci, GRID=1000, MINEPS=1e-6, ...)
Either an ultrametric tree (i.e. an object of class "phylo"), or coalescent intervals (i.e. an object of class "coalescentIntervals"), or collapsed coalescent intervals (i.e. an object of class "collapsedInterva
collapsing parameter that controls the amount of smoothing (allowed range: from 0 to ci$total.depth, default value: 0). This is the same parameter as in collapsed.intervals.
Parameter to choose between two slightly different variants of the generalized skyline plot (Strimmer and Pybus, pers. comm.). The default value FALSE is recommended.
coalescent intervals (i.e. an object of class "coalescentIntervals")
Parameter for the grid search for epsilon in find.skyline.epsilon.
Parameter for the grid search for epsilon in find.skyline.epsilon.
Any of the above parameters.

skyline implements the generalized skyline plot introduced in Strimmer and Pybus (2001). For epsilon = 0 the generalized skyline plot degenerates to the classic skyline plot described in Pybus et al. (2000). The latter is in turn directly related to lineage-through-time plots (Nee et al., 1995).


  • skyline returns an object of class "skyline" with the following entries:
  • timeA vector with the time at the end of each coalescent interval (i.e. the accumulated interval lengths from the beginning of the first interval to the end of an interval)
  • interval.lengthA vector with the length of each interval.
  • population.sizeA vector with the effective population size of each interval.
  • parameter.countNumber of free parameters in the skyline plot.
  • epsilonThe value of the underlying smoothing parameter.
  • logLLog-likelihood of skyline plot (see Strimmer and Pybus, 2001).
  • logL.AICcAICc corrected log-likelihood (see Strimmer and Pybus, 2001).
  • find.skyline.epsilon returns the value of the epsilon parameter that maximizes logL.AICc.


Strimmer, K. and Pybus, O. G. (2001) Exploring the demographic history of DNA sequences using the generalized skyline plot. Molecular Biology and Evolution, 18, 2298--2305.

Pybus, O. G, Rambaut, A. and Harvey, P. H. (2000) An integrated framework for the inference of viral population history from reconstructed genealogies. Genetics, 155, 1429--1437.

Nee, S., Holmes, E. C., Rambaut, A. and Harvey, P. H. (1995) Inferring population history from molecular phylogenies. Philosophical Transactions of the Royal Society of London. Series B. Biological Sciences, 349, 25--31.

See Also

coalescent.intervals, collapsed.intervals, skylineplot, ltt.plot.

  • skyline
  • skyline.phylo
  • skyline.coalescentIntervals
  • skyline.collapsedIntervals
  • find.skyline.epsilon
# get tree
data("hivtree.newick") # example tree in NH format <- read.tree(text = hivtree.newick) # load tree

# corresponding coalescent intervals
ci <- coalescent.intervals( # from tree

# collapsed intervals
cl1 <- collapsed.intervals(ci,0)
cl2 <- collapsed.intervals(ci,0.0119)

#### classic skyline plot ####
sk1 <- skyline(cl1)        # from collapsed intervals 
sk1 <- skyline(ci)         # from coalescent intervals
sk1 <- skyline(   # from tree

skylineplot( # shortcut

plot(sk1, show.years=TRUE, subst.rate=0.0023, present.year = 1997)

#### generalized skyline plot ####

sk2 <- skyline(cl2)              # from collapsed intervals
sk2 <- skyline(ci, 0.0119)       # from coalescent intervals
sk2 <- skyline(, 0.0119) # from tree


# classic and generalized skyline plot together in one plot
plot(sk1, show.years=TRUE, subst.rate=0.0023, present.year = 1997, col=c(grey(.8),1))
lines(sk2,  show.years=TRUE, subst.rate=0.0023, present.year = 1997)
legend(.15,500, c("classic", "generalized"), col=c(grey(.8),1),lty=1)

# find optimal epsilon parameter using AICc criterion

sk3 <- skyline(ci, -1) # negative epsilon also triggers estimation of epsilon
Documentation reproduced from package ape, version 2.6-3, License: GPL (>= 2)

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