What will happen in the next generation? To answer this question, we will use the Hardy-Weinberg principle, which applies basic rules of probability to a population to make predictions about the next generation. The Hardy-Weinberg principle predicts that allelic frequencies remain constant from one generation to the next, or remain in EQUILIBRIUM, if we assume certain conditions (which we will discuss below).
For example, if the allelic frequencies of alleles A and a in the initial population were p = 0.8 and q = 0.2, the allelic frequencies in the next generation will remain p = 0.8 and q = 0.2. The conditions for Hardy-Weinberg equilibrium are rarely (if ever) encountered in nature, but they are fundamental to understanding population genetics. When a population deviates from Hardy-Weinberg predictions, it is evidence that at least one of the conditions in not being met. Scientists can then determine why allelic frequencies are changing, and thus how evolution is acting on the population.
The conditions for Hardy-Weinberg equilibrium:
Because mating is random (Condition 3, above), we can think of these diploid individuals as simply mixing their gametes. We do not need to consider the parental origin of a given gamete (i.e. if it comes from a heterozygous or homozygous parent), but simply the proportion of alleles in the population. For example, for the population mentioned previously with p value of 0.8 and q value of 0.2, we can think of a bag of mixed gametes with 80% of which are A and 20% are a.
Therefore, on the paternal side (the sperm) we have the given proportions of the two alleles (0.8 of allele A and 0.2 of allele a) freely mixing with the eggs (the maternal contributions), which have the alleles in the same proportions (0.8 of A and 0.2 of a).
The probability of an A sperm meeting an A egg is 0.8 x 0.8 = 0.64. The probability of an A sperm meeting an a egg is 0.8 x 0.2 = 0.16. The probability of an a sperm meeting an A egg is 0.8 x 0.2 = 0.16. The probability of an a sperm meeting an a egg is 0.2 x 0.2 = 0.04.
Therefore in the following generation, we would expect to have the following proportion of genotypes:
That is, if there were a thousand offspring, there would be:
This in turn translates to 1600 A alleles (640 + 640 + 320), and 400 a alleles (320 + 40 + 40). 1600/2000 = 0.8 and 400/2000 = 0.2; that is, the allele frequencies are the same as in the parental generation.
To generalize: if the allele frequencies are p and q, then at Hardy-Weinberg Equilibrium you will have (p + q) X (p + q) = p2 + 2pq + q2 as the distribution of the genotypes.
Furthermore, the frequency of A alleles will be p2 + pq (equal to the frequency of AA individuals plus half the frequency of Aa individuals). Since p + q =1, then q = 1 - p. The frequency of A alleles is p2 + pq, which equals p2 + p (1 — p) = p2 + p — p2 = p ; that is, p stays the same from one generation to the next. The same can be shown for q.
So we see that with random mating, no selection, no migration or mutation, and a population large enough that the effects of random chance are negligible, the proportion of alleles in a population stays the same from generation to generation.
Let’s test your knowledge of this topic:
In a population that is in Hardy-Weinberg equilibrium, the frequency of the dominant allele A is 0.40. What is the frequency of individuals with each of the three allele combinations, AA, Aa and aa?
Frequency of AA individuals: _______
Frequency of Aa individuals: _______
Frequency of aa individuals: _______
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