A few months ago, JP posted at GNXP that random mating is not necessary for Hardy-Weinberg Equilibrium (HWE). One round of random mating is still sufficient to achieve HWE genotype frequencies, but there are some non-random mating strategies that will also allow for HWE.
HWE is quite robust to violations of the assumptions. That makes it a poor test for things like natural selection, but it is commonly used to detect population structure. If you sample allele and genotype frequencies from a single population, the genotype frequencies should be in HWE. If, however, you sample from two separate populations and test for HWE as if you were sampling from one population, you should observe deviations from HWE. This strategy is often used to detect hybrid zones between populations because an overabundance of F1 hybrids will lead to deviations from HWE.
Anyway, JP's discovery isn't actually some huge paradigm shift in population genetics. But it is something to consider when interpreting the results of a test for HWE. It also goes to show you that a lot of the basic concepts you learn in undergraduate courses aren't entirely correct. Learning that random mating is a necessary condition for HWE isn't exactly wrong, but there are subtleties as described above.
Another fundamental concept covered in an introductory genetics course is the complementation test. In this analysis, two different true breeding mutants are crossed and the progeny are analyzed. If the progeny have the mutant phenotype, then the two mutations are in the same gene. If the progeny are wild type, the mutations are in different genes. But it's not always so simple.
Mutations in different genes can fail to complement each other (i.e., the progeny are mutant) if the gene products interact. My favorite researcher on the genetics of meiosis, Scott Hawley, discusses second-site noncomplementation (SSNC) in a recent paper in Genetics. Go there for the gory details and for some techniques that take advantage of SSNC to identify dominant enhancer mutations.
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One round of random mating is still sufficient to achieve HWE genotype frequencies
actually, the paper I linked to showed that one round of non-random mating can lead to HWE. along with previous results showing that HWE can be maintained by some non-random mating situations, there's essentially no need for random mating at any point for HWE.
But only certain non-random mating strategies can lead to HWE. One round of random mating will also lead to HWE (assuming equal allele frequencies in males and females). There are still limitations as to which mating situations lead to HWE.