I have SNP data from several cultivars of rice which I have used to produce alignments, but I don't think that the usual models and algorithms used for generating phylogenetic trees are appropriate, because these cultivars are not the result of speciation events and have been interbred in their histories. How can I best calculate and visualize their degree of relatedness?
Even with inbreeding and other genetic phenomena that might mask actual evolution of these cultivars, any phylogenetic methodology would be capable of determining relationships accurately.
Try creating a Neighbour Joining tree with MEGA, which is one of the simplest methods available. This should give you enough to check the relationships of the cultivars.
Wait, you are right, but trees don't work here.
This is the area of population genetics. You will generate allele frequencies for each locus. The allele frequenceies will be used to perform Hardy-Weinberg equilibrium, F statistics, Fst and Fis
H-W start by using Structure API to work out how many populations you have. This is vital information for the next two analyses:
Fis is particularly useful here because it is the inbreeding co-efficient, the nearer 1 it is the more inbreeding the data has been through.
The Fst distances can be used to generate a tree, but this is not a model of point mutations, rather a model of migration between populations. You can input the distance matrix in MEGA and make a tree from it, Fstat API (I think) will do it for you.
Pop gen is difficult to get your head around at first, but you'll get use to it.