no evolution - as long as five conditions are met:
- No mutation (no change in the DNA sequence)
- No migration (no moving into or out of a population)
- Very large population size
- Random mating (mating not based on preference)
- No natural selection.
These five conditions rarely occur in nature. For example, it is highly unlikely that new
mutations are not constantly generated. If these five conditions are met, the frequencies of
genotypes within a population can be determined given the phenotypic frequencies.
The Hardy-Weinberg Equation
For example, let’s use a hypothetical rabbit population of 100 rabbits (200 alleles) to deter-
mine allele frequencies for color:
- 9 albino rabbits (represented by the alleles bb) and
- 91 brown rabbits (49 homozygous [BB] and 42 heterozygous [Bb]).
The gene pool contains 140 B alleles [49 + 49 + 42] (70%) and 60 b alleles [9 + 9 + 42]
(30%) – which have gene frequencies of 0.7 and 0.3, respectively.
If we assume that alleles sort independently and segregate randomly as sperm and eggs
form, and that mating and fertilization are also random, the probability that an offspring
will receive a particular allele from the gene pool is identical to the frequency of that allele
in the population:
- BB: 0.7 x 0.7 = 0.49
- Bb: 0.7 x 0.3 = 0.21
- bB: 0.3 x 0.7 = 0.21
- bb: 0.3 x 0.3 = 0.09
If we calculate the frequency of genotypes among the offspring, they are identical to the
genotype frequencies of the parents. There are 9% bb albino rabbits and 91% BB and Bb
brown rabbits. Allele frequency remains constant as well. The population is stable – at a
Hardy-Weinberg genetic equilibrium.
A useful equation generalizes the calculations we’ve just completed. Variables include
- p= the frequency of one allele (we’ll use alleleBhere) and
- q= the frequency of the second allele (bin this example).