# Analysis of Molecular Variance This function performs a hierarchical analysis of molecular variance as described in Excoffier et al. (1992). This implementation accepts any number of hierarchical levels. ```r amova(formula, data = NULL, nperm = 1000, is.squared = FALSE) ## S3 method for class 'amova' print(x, ...) getPhi(sigma2) write.pegas.amova(x, file = "") ``` ## Arguments - `formula`: a formula giving the AMOVA model to be fitted with the distance matrix on the left-hand side of the `~`, and the population, region, etc, levels on its right-hand side (see details). - `data`: an optional data frame where to find the hierarchical levels; by default they are searched for in the user's workspace. - `nperm`: the number of permutations for the tests of hypotheses (1000 by default). Set this argument to 0 to skip the tests and simply estimate the variance components. - `is.squared`: a logical specifying whether the distance matrix has already been squared. - `x`: an object of class `"amova"`. - `sigma2`: a named vector of variance components. - `file`: a file name. - ``...``: unused (here for compatibility. ## Details The formula must be of the form `d ~ A/B/...` where `d` is a distance object, and `A`, `B`, etc, are the hierarchical levels from the highest to the lowest one. Any number of levels is accepted, so specifying `d ~ A` will simply test for population differentiation. It is assumed that the rows of the distance matrix are in the same order than the hierarchical levels (which may be checked by the user). The function `getPhi()` is a convenience function for extracting a table of hierarchical Phi-statistics for reporting. This will be an N+1 by N matrix where N is the number of hierarchcial levels and GLOBAL is always the first row of the matrix. The matrix can read as COLUMN in ROW. If the variance components passed to getPhi() are not named, they will be reported as "level 1", "level 2", etc. ## Note If there are more than three levels, approximate formulae are used to estimate the variance components. If there is an error message like this: `Error in FUN(X[[1L]], ...) : 'bin' must be numeric or a factor` it may be that the factors you use in the formula were not read correctly. You may convert them with the function `factor`, or, before reading your data files, do this command (in case this option was modified): `options(stringsAsFactors = TRUE)` ## Returns An object of class `"amova"` which is a list with a table of sums of square deviations (SSD), mean square deviations (MSD), and the number of degrees of freedom, and a vector of variance components. ## Author(s) Emmanuel Paradis, Zhian N. Kamvar, and Brian Knaus ## References Excoffier, L., Smouse, P. E. and Quattro, J. M. (1992) Analysis of molecular variance inferred from metric distances among DNA haplotypes: application to human mitochondrial DNA restriction data. **Genetics**, 131 , 479--491. ## See Also `amova` in `ade4` for an implementation of the original Excoffier et al.'s model; `adonis` in `vegan` for a general (multivariate) implementation of an ANOVA framework with distances. ## Examples ```r ### All examples below have 'nperm = 100' for faster execution times. ### The default 'nperm = 1000' is recommended. require(ape) data(woodmouse) d <- dist.dna(woodmouse) g <- factor(c(rep("A", 7), rep("B", 8))) p <- factor(c(rep(1, 3), rep(2, 4), rep(3, 4), rep(4, 4))) (d_gp <- amova(d ~ g/p, nperm = 100)) # 2 levels sig2 <- setNames(d_gp$varcomp$sigma2, rownames(d_gp$varcomp)) getPhi(sig2) # Phi table amova(d ~ p, nperm = 100) # 1 level amova(d ~ g, nperm = 100) ## 3 levels (quite slow): ## Not run: pop <- gl(64, 5, labels = paste0("pop", 1:64)) region <- gl(16, 20, labels = paste0("region", 1:16)) conti <- gl(4, 80, labels = paste0("conti", 1:4)) dd <- as.dist(matrix(runif(320^2), 320)) (dd_crp <- amova(dd ~ conti/region/pop, nperm = 100)) sig2 <- setNames(dd_crp$varcomp$sigma2, rownames(dd_crp$varcomp)) getPhi(sig2) ## End(Not run) ```

amova function