# The Hardy Weinberg law is a logical consequence of Mendel s

Last updated: 1/15/2024

The Hardy Weinberg law is a logical consequence of Mendel s first law of segregation af expresses the tendency toward equilibrium inherent in Mendelian heredity Let us select for our example a population having a single locus bearing just two alleles T and r The phenotypic expression of this gene might be for example the ability to taste a chemical compound called phenylthiocarba mide Individuals in the population will be of three genotypes for this locus T T T t both tasters and t t nontasters In a sample of 100 individuals let us suppose that we have 20 of T T genotype 40 of T t genotype and 40 of t t genotype We could then make a table showing the allelic frequencies remember that every individual has two copies of the gene Genotype T T T t 1 1 Total Number of Individuals 20 40 40 100 Sperm T 0 4 1 0 6 Copies of the T Allele 40 40 0 80 Of the 200 copies the proportion of the T allele is 80 200 0 4 40 and the proportion of the rallele is 120 200 0 6 60 It is customary to use p and q to represent the two allelic frequencies The genetically dominant allele is represented by p and the genetically recessive by q Thus T 0 4 TIT 0 16 Tlt 0 24 p frequency of 7 0 4 q frequency of 1 0 6 Therefore p q 1 Copies of the t Allele 0 40 80 120 Having calculated allelic frequencies in the sample let us determine whether these frequencies will change spontaneously in a new genera tion of the population Assuming that mating is random gametes are sampled independently in pairs each individual contributes an equal number of gametes to the common pool from which the next genera tion is formed Frequencies of gametes in the pool then equal the al lelic frequencies in the sample 40 of the gametes are T and 60 are r ratio of 0 4 0 6 Both ova and sperm of course show the same frequen cies The next generation is formed hic05193 cho vg3 136 indd 129 1 0 6 Tlt 0 24 tt 0 36 contain copies of the allele The term inclusive fitness pertains to cases where the average effect of an allele on its own propagation in the gene pool would be calculated incorrectly if its effects on sur vival of its possessors relatives were ignored For example natural selection might favor an allele for a behavior through which an indi vidual dies in saving the lives of many relatives Some traits and combinations of traits are advantageous for Collecting genotypes we have frequency of T T 0 16 frequency of T t 0 48 frequency of t t 0 36 Next we determine the values of p and q from the randomly mated pop ulations From the table above we see that the frequency of T is the sum of genotypes T T which is 0 16 and one half of the genotype T t which is 0 24 T p 0 16 5 0 48 0 4 Similarly the frequency of t is the sum of genotypes 1 t which is 0 36 and one half the genotype T t which is 0 24 t q 0 36 5 0 48 0 6 The new generation bears exactly the same allelic frequencies as the parent population Note that there has been no increase in the frequency of the genetically dominant allele T Thus in a freely interbreeding sexually reproducing population the frequency of each allele would re main constant generation after generation in the absence of natural se lection migration recurring mutation and genetic drift see text A mathematically minded reader should recognize that the genotype fre quencies T T T t and t t are actually a binomial expansion of p q p q p 2pq q 1 Note that the equilibrium calculations give expected frequencies which are unlikely to be realized exactly in a population of finite size For this reason finite population size is a cause of evolutionary change Most genes have more than just a single pair of alleles especially when we measure genetic variation at the DNA sequence level The bi nomial expansion shown above can be used for any number of alleles Suppose that we have three alleles T T T whose frequencies are denoted p q and r respectively We now have six possible genotypes with the following Hardy Weinberg equilibrium frequencies O TT TT TT TT TT TT p q r p 2pg q 2 pr 2gr As the number of alleles at a gene increases the proportion of the popu lation having heterozygous genotypes also increases disadvantageous for others Darwin used the term sexual selection to denote the selection of traits that are advantageous for obtaining mates but not for survival Bright colors and elaborate feathers can enhance a male bird s competitive ability in obtaining mates while simultaneously increasing his visibility to predators see Figure 6 31 Environmental changes such as extinction of a predator population can alter the selective values of alternative traits The action of selec