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:

- Population is infinitely large -– or large enough to minimize the effect of genetic drift, which is change in allele frequencies due entirely to random chance (and not selection).
- No selection occurs - so all the individuals in the population have an equal chance of surviving and reproducing.
- Mating is random – so that an individual is equally likely to mate with any potential mate in the population, regardless of genotype or phenotype.
- No migration - so no alleles enter or leave the population.
- No mutation - so allelic characteristics do not change

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:

- 0.64 AA
- 0.32 Aa
- 0.04 aa

That is, if there were a thousand offspring, there would be:

- 640 AA
*individuals* - 320 Aa
*individuals* - 40 aa
*individuals*

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*) = *p*^{2} + 2*pq* + *q*^{2} as the
distribution of the genotypes.

- The frequency of AA individual
will be
*p*^{2}. - The frequency of Aa individuals will
be 2
*pq*. - The frequency of aa individuals will
be
*q*^{2}.

Furthermore, the frequency of A alleles will be
*p*^{2} + *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 *p*^{2} + *pq*, which equals *p*^{2}
+ *p* (1 —* p*) = *p*^{2} + *p* —* p*^{2} = *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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