# stairway: The Stairway Plot In pegas: Population and Evolutionary Genetics Analysis System

 stairway R Documentation

## The Stairway Plot

### Description

This function fits a model of population change using the site frequency spectrum (SFS). The default assumes THETA = 1. A model of population change estimates the temporal changes in THETA with respect to the value of this parameter at present time. The model is specified by the user with the option `epoch`.

### Usage

```stairway(x, epoch = NULL, step.min = 1e-6, step.max = 1e-3)
## S3 method for class 'stairway'
plot(x, type = "S", xlab = "Coalescent intervals",
ylab = expression(Theta), ...)
## S3 method for class 'stairway'
lines(x, type = "S", ...)
```

### Arguments

 `x` an object of class `site.spectrum` or of class `stairway`. `epoch` an optional vector of integers giving the periods of time (or epochs) with distinct THETA. `step.min` a single numeric value giving the smallest step size used during optimization. `step.max` id. for the largest step size (see `nlminb`). `type` the type of lines. `xlab, ylab` the default labels on the axes. `...` further arguments passed to other methods.

### Details

The basic method implemented in this function is similar to Polanski and Kimmel (2003). The temporal model with “epochs” is from Liu and Fu (2015).

### Value

By default, a single numeric value with the null deviance. If `epoch` is used, a list with the following components:

 `estimates` the maximum likelihood estimates. `deviance` the deviance of the fitted model. `null.deviance` the deviance of the null model. `LRT` the likelihood-ratio test comparing the null and the fitted models. `AIC` the Akaike information criterion of the fitted model.

### References

Liu, X. M. and Fu, Y. X. (2015) Exploring population size changes using SNP frequency spectra. Nature Genetics, 47, 555–559.

Polanski, A. and Kimmel, M. (2003) New explicit expressions for relative frequencies of single-nucleotide polymorphisms with application to statistical inference on population growth. Genetics, 165, 427–436.

`site.spectrum`, `nlminb`
```data(woodmouse)