The likelihood is computed on the basis of contrasts between the observed standardized gene frequencies. The covariance matrix of these contrasts is returned by function covpred. Two arguments are required; the name of the migration model FUN, the parameter vector theta.
Function covobs estimates the covariances from the observations directly using the estimator
(4) |
The predicted and observed covariances can be compared through plotting them with the covplot function. Arguments are the computed predicted and observed covariance matrices. The following call
> covplot(covpred(steppingstone,fit1$par),covobs(p))produced the plot shown in Figure 2. Two additional optional arguments can be given; mfcol specifying the number of rows and columns in the plot, and file specifying the name of a postscript file (used as alternative output). The interpretation of these type of plots is discussed in Tufto et al. (1998).
Function covpred computes (an approximation) of the covariances under a given model, conditioned on the observed gene frequency means at each locus. The unconditional covariances may also be of interest. These can be computed by function courgeau, called with the migration matrix M and the vector of effective population sizes Ne as arguments. This function rewrites the matrix equation (Tufto et al., 1996, eq. 7) to a system of equations (Tufto et al., 1996, eq. A.4 and A.5) and solves these. It may be noted that the returned unconditional covariances (which are exact to the extent that the order of the events in the life cycle can be ignored) can differ greatly from the conditional ones, especially if the long range rate of migration is low such that the gene frequency vector is in one of the states or for long periods of time.