20.2 Why do allele frequencies change in populations? Population genetics is the study of the properties of genes In algebraic terms, the Hardy-Weinberg principle is in populations. Genetic variation within natural popula written as an equation. Consider a population of 100 cats, tions was a puzzle to Darwin and his contemporaries. The with 84 black and 16 white cats. In statistics, frequency ray in which meiosis produces genetic segregation among is defined as the proportion of individuals falling within the progeny of a hybrid had not yet been discovered Selec certain category in relation to the total number of indi- tion,scientists then thought, should always favor an opti- viduals under consideration. In this case, the respective mal form, and so tend to eliminate variation. Moreover, the frequencies would be 0.84(or 84%)and 0. 16(or 16%) theory of blending inheritance--in which offspring were Based on these phenotypic frequencies, can we deduce expected to be phenotypically intermediate relative to their the underlying frequency of genotypes? If we assume that rents-was widely accepted. If blending inheritance were the white cats are homozygous recessive for an allele we orrect,then the effect of any new genetic variant would designate b, and the black cats are therefore either ho- quickly be diluted to the point of disappearance in subse- mozygous dominant BB or heterozygous Bb, we can cal- quent generations culate the allele frequencies of the two alleles in the population from the proportion of black and white indi- The Hardy-Weinberg Principle viduals. Let the letter p designate the frequency of one al- lele and the letter g the frequency of the alternative al Following the rediscovery of Mendels research, two people lele. Because there are only two alleles, p plus g must 1908 independently solved the puzzle of why genetic variation persists--G. H. Hardy, an English mathemati The Hardy-Weinberg equation can now be expressed in cian, and G. Weinberg, a German physician. They pointed the form of what is known as a binomial expansion out that the original proportions of the genotypes in a pop- p+q)2=p2 2pq ulation will remain constant from generation to generation as long as the following assumptions are met: Individuals (Individuals (Individuals azygous heterozygous monozygous 1. The population size is very large allele B) with alleles B+b) for allele b) 2. Random mating is occurring 3. No mutation takes place If g2= 0. 16(the frequency of white cats), then g=0.4 4. No genes are input from other sources(no immig Therefore, P, the frequency of allele B, would be 0.6(1.0 tion takes place) 0. 4=0.6). We can now easily calculate the genotype fre- 5. No selection occurs quencies: there are p=(0.6)x 100(the number of cats in the total population), or 36 homozygous dominant BB indi Dominant alleles do not, in fact, replace recessive ones. viduals. The heterozygous individuals have the Bb gen Because their proportions do not change, the genotypes are type, and there would be 2pg, or(2 X 0.6 0.4)X100,or said to be in Hardy-Weinberg equilibrium. 48 heterozygous Bb individuals Sperr p=0.6 Phenotypes p2=0.36 q=0.4 Genotypes BB bb pq=0.24 pq=0.24 genotype in population 0.36 0.48 0.16 q2=0.16 Frequency of gametes 0.36+0.24=0.6B 024+0.16=0.4b FIGURE 20.4 The Hardy-Weinberg equilibrium. In the absence of factors that alter them, the frequencies of gametes, genotypes, and phenotypes remain constant generation after generation 424 Part vi EvolutionPopulation genetics is the study of the properties of genes in populations. Genetic variation within natural popula￾tions was a puzzle to Darwin and his contemporaries. The way in which meiosis produces genetic segregation among the progeny of a hybrid had not yet been discovered. Selec￾tion, scientists then thought, should always favor an opti￾mal form, and so tend to eliminate variation. Moreover, the theory of blending inheritance—in which offspring were expected to be phenotypically intermediate relative to their parents—was widely accepted. If blending inheritance were correct, then the effect of any new genetic variant would quickly be diluted to the point of disappearance in subse￾quent generations. The Hardy–Weinberg Principle Following the rediscovery of Mendel’s research, two people in 1908 independently solved the puzzle of why genetic variation persists—G. H. Hardy, an English mathemati￾cian, and G. Weinberg, a German physician. They pointed out that the original proportions of the genotypes in a pop￾ulation will remain constant from generation to generation, as long as the following assumptions are met: 1. The population size is very large. 2. Random mating is occurring. 3. No mutation takes place. 4. No genes are input from other sources (no immigra￾tion takes place). 5. No selection occurs. Dominant alleles do not, in fact, replace recessive ones. Because their proportions do not change, the genotypes are said to be in Hardy–Weinberg equilibrium. In algebraic terms, the Hardy–Weinberg principle is written as an equation. Consider a population of 100 cats, with 84 black and 16 white cats. In statistics, frequency is defined as the proportion of individuals falling within a certain category in relation to the total number of indi￾viduals under consideration. In this case, the respective frequencies would be 0.84 (or 84%) and 0.16 (or 16%). Based on these phenotypic frequencies, can we deduce the underlying frequency of genotypes? If we assume that the white cats are homozygous recessive for an allele we designate b, and the black cats are therefore either ho￾mozygous dominant BB or heterozygous Bb, we can cal￾culate the allele frequencies of the two alleles in the population from the proportion of black and white indi￾viduals. Let the letter p designate the frequency of one al￾lele and the letter q the frequency of the alternative al￾lele. Because there are only two alleles, p plus q must always equal 1. The Hardy-Weinberg equation can now be expressed in the form of what is known as a binomial expansion: (p + q)2 = p2 + 2pq + q2 (Individuals (Individuals (Individuals homozygous heterozygous homozygous for allele B) with alleles B + b) for allele b) If q2 = 0.16 (the frequency of white cats), then q = 0.4. Therefore, p, the frequency of allele B, would be 0.6 (1.0 – 0.4 = 0.6). We can now easily calculate the genotype fre￾quencies: there are p2 = (0.6)2 100 (the number of cats in the total population), or 36 homozygous dominant BB indi￾viduals. The heterozygous individuals have the Bb geno￾type, and there would be 2pq, or (2 0.6 0.4) 100, or 48 heterozygous Bb individuals. 424 Part VI Evolution 20.2 Why do allele frequencies change in populations? Sperm Eggs Phenotypes Genotypes BB Bb bb 0.36 0.48 0.16 0.36 + 0.24 = 0.6B 0.24 + 0.16 = 0.4b Frequency of genotype in population Frequency of gametes b B BB Bb Bb bb q2 = 0.16 pq = 0.24 pq = 0.24 p2 = 0.36 p = 0.6 q = 0.4 p = 0.6 q = 0.4 b B FIGURE 20.4 The Hardy–Weinberg equilibrium. In the absence of factors that alter them, the frequencies of gametes, genotypes, and phenotypes remain constant generation after generation.