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I am able to calculate frequencies for allele and genotype, but I don't understand how to tell if the population is at equilibrium. Or how to determine how many generations of random mating would be needed to reach HW equilibrium. I thought the proportions didn't change from generation to generation?

number of individuals: TT-200, Tc-200, cc-600 observed frequencies : TT-0.2, Tc-0.2, cc-0.6 HW frequencies : TT-0.05, Tc-0.35, cc-0.60

p=.33, q=.77

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The answer is logical if you understand the reasoning behind Hardy-Weinberg. I recommend that you to have a look at the post Solving Hardy Weinberg problems and try to answer the question yourself. Once you've done that, you can hover over the yellow zone below for the answer to compare against what you've understood.

The answer:

If the assumptions of Hardy-Weinberg are respected (see Assumptions of Hardy-Weinberg rule), incl. random mating, then a population is back to Hardy-Weinberg equilibrium at the beginning of any single generation. H-W equilibrium is directly caused by the random sampling of gametes. This random sampling is happening at every single generation and therefore a single generation is enough to get back to H-W equilibrium.

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