I am having a difficult time finding information about a minimum threshold for number of individuals to use in wgs pop gen analyses. Are there software or formulas/theory available to determine what number total number of haplotypes/individuals you need to get theta estimates, make a linkage map, run mk tests etc based on inputs such as genome size, read depth per individual, sequencing platform? Obviously there can be financial constraints and considerations to make for non-model organisms when choosing how many individuals to sequence. Any advice would be appreciated. Thanks!
I think that many of the applications that you mention require wildly different numbers of individuals. It would help to know more about goals, questions, organism details, etc.
For example, for simple population statistic estimates, you can depend on the large number of sites in the genome to get an accurate estimates (such as Watterson) from a single individual, if you are working in a diploid organism, as you can use heterozygosity. See the first Neandertal genome paper for what you can do with one single not very good sequence.
For applications such as linkage maps, you will need a rather larger number of individuals, as you need to sample a large number of recombinations. However, "large" is relative, as a centimorgan-level resolution of the human genome was achieved with a mere 110 humans and ~6000 loci. For finer linkage analysis you may need more individuals; however, with WGS your loci will be much less limited.
For McDonald-Kreitman tests or such-like, it is possibly more important to have more individuals. But you don't need WGS of every individual, in principle you could just find the gene(s) of interest and Sanger it for every individual, which is in most cases still much cheaper.