skyline {ape} | R Documentation

## Skyline Plot Estimate of Effective Population Size

### Description

`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`).

### Usage

    skyline(x, ...)
    ## S3 method for class 'phylo'
    skyline(x, ...)
    ## S3 method for class 'coalescentIntervals'
    skyline(x, epsilon=0, ...)
    ## S3 method for class 'collapsedIntervals'
    skyline(x, old.style=FALSE, ...)
    find.skyline.epsilon(ci, GRID=1000, MINEPS=1e-6, ...)

### Arguments

`x` | 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 `"collapsedIntervals"`).
`epsilon` | 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.
`old.style` | Parameter to choose between two slightly different variants of the generalized skyline plot (Strimmer and Pybus, pers. comm.). The default value `FALSE` is recommended.
`ci` | coalescent intervals (i.e. an object of class `"coalescentIntervals"`)
`GRID` | Parameter for the grid search for `epsilon` in `find.skyline.epsilon`.
`MINEPS` | Parameter for the grid search for `epsilon` in `find.skyline.epsilon`.
`...` | Any of the above parameters.

### Details

`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).

### Value

`skyline` returns an object of class `"skyline"` with the following entries:

`time` | A 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.length` | A vector with the length of each interval.
`population.size` | A vector with the effective population size of each interval.
`parameter.count` | Number of free parameters in the skyline plot.
`epsilon` | The value of the underlying smoothing parameter.
`logL` | Log-likelihood of skyline plot (see Strimmer and Pybus, 2001).
`logL.AICc` | AICc corrected log-likelihood (see Strimmer and Pybus, 2001).

`find.skyline.epsilon` returns the value of the `epsilon` parameter that maximizes `logL.AICc`.

### Author(s)

Korbinian Strimmer

### References

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`.

### Examples

    # get tree
    data("hivtree.newick") # example tree in NH format
    tree.hiv <- read.tree(text = hivtree.newick) # load tree

    # corresponding coalescent intervals
    ci <- coalescent.intervals(tree.hiv) # 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(tree.hiv)   # from tree
    sk1

    plot(skyline(tree.hiv))
    skylineplot(tree.hiv) # 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(tree.hiv, 0.0119) # from tree
    sk2

    plot(sk2)

    # 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
    find.skyline.epsilon(ci)

    sk3 <- skyline(ci, -1) # negative epsilon also triggers estimation of epsilon
    sk3$epsilon

[Package ape version 3.5 Index]