Using the Hardy-Weinberg Equation Table 20.1 Agents of Evolutionary Change The Hardy-Weinberg equation is a simple extension of the Facto Punnett square described in chapter 13, with two alleles as- signed frequencies p and g. Figure 20.4 allows you to trace Mutation The ultimate source of variation. Individual mutations occur so rarely that mutation genetic reassortment during sexual reproduction and se alone does not change allele frequency how it affects the frequencies of the B and b alleles durin the next generation. In constructing this dhar hese cats is Gene flow A very potent agent of change. Populations assumed that the union of sperm and egg in random. so that all combinations of b and b alleles occur. For this reason, the alleles are mixed randomly and repre- sented in the next generation in proportion to their original eration has a 0.6 chance of receiving a B allele(p=0.6)and g om Inbreeding is the most common form. It representation. Each individual egg or sperm in each gen Nonrandom does not alter allele frequency but a 0.4 chance of receiving a b allele(=0.4 decreases the proportion of heterozygotes. In the next generation, therefore, the chance of combin ing two B alleles is p2, or 0.36(that is, 0.6 X0.6),and proximately 36% of the individuals in the population will Genetic drift Statistical accidents Usually occurs only in continue to have the BB genotype. The frequency of bb in dividuals is g2(0.4 X 0.4)and so will continue to be about 16%, and the frequency of Bb individuals will be 2pg(2X Selection The only form that produces adaptive 0.6 X 0.4), or approximately 48%. Phenotypically, if the evolutionary changes population size remains at 100 cats, we will still see approx- imately 84 black individuals(with either BB or Bb geno- types)and 16 white individuals(with the bb genotype)in ment are important. In fact, they are the key to the im the population. Allele, genotype, and phenotype frequen ortance of the Hardy-Weinberg principle, because indi cies have remained unchanged from one generation to the vidual allele frequencies often change in natural popula ions with some alleles becoming more common and This simple relationship has proved extraordinarily others decreasing in frequency. The Hardy-Weinberg useful in assessing actual situations. Consider the recessive principle establishes a convenient baseline against which allele responsible for the serious human disease cystic fi- to measure such changes. By looking at how various fac- brosis. This allele is present in North Americans of Cau- tors alter the proportions of homozygotes and heterozy- casian descent at a frequency g of about 22 per 1000 indi- gotes, we can identify the forces affecting particular situa viduals, or 0.022. What proportion of North American tions we observe Caucasians, therefore, is expected to express this trait Many factors can alter allele frequencies. Only five The frequency of double recessive individuals(o)is ex- however, alter the proportions of homozygotes and het pected to be 0.022 0.022, or 1 in every 2000 individu- erozygotes enough to produce significant deviations from als. What proportion is expected to be heterozygous car- the proportions predicted by the Hardy-Weinberg princi riers? If the frequency of the recessive allele q is 0.022, ple: mutation, gene flow(including both immigration into then the frequency of the dominant allele p must be and emigration out of a given population), nonrandom is(2pq) is thus expected to be 2 0.978 X 0.022, or 43 which is more likely in small populations), and selection in every 1000 individuals (table 20.1). Of these, only selection produces adaptive evo- How valid are these calculated predictions? For many lutionary change because only in selection does the result genes, they prove to be very accurate. As we will see, fo depend on the nature of the environment. The other some genes the calculated predictions do not match the ac- tors operate relatively independently of the environment, tual values. The reasons they do not tell us a great deal so the changes they produce are not shaped by environ about evolution mental demands Why Do Allele Frequencies Change The Hardy-Weinberg principle states that in a large According to the Hardy-Weinberg principle, both the al population mating at random and in the absence of lele and genotype frequencies in a large, random-mating other forces that would change the proportions of the cOpulation will remain constant from generation to gen- different alleles at a given locus, the process of sexual ation if no mutation, no gene flow, and no selection reproduction(meiosis and fertilization) alone will not occur. The stipulations tacked onto the end of the state hange these proportions. Chapter 20 Genes within Populations 425Using the Hardy–Weinberg Equation The Hardy–Weinberg equation is a simple extension of the Punnett square described in chapter 13, with two alleles as￾signed frequencies p and q. Figure 20.4 allows you to trace genetic reassortment during sexual reproduction and see how it affects the frequencies of the B and b alleles during the next generation. In constructing this diagram, we have assumed that the union of sperm and egg in these cats is random, so that all combinations of b and B alleles occur. For this reason, the alleles are mixed randomly and repre￾sented in the next generation in proportion to their original representation. Each individual egg or sperm in each gen￾eration has a 0.6 chance of receiving a B allele (p = 0.6) and a 0.4 chance of receiving a b allele (q = 0.4). In the next generation, therefore, the chance of combin￾ing two B alleles is p2, or 0.36 (that is, 0.6 0.6), and ap￾proximately 36% of the individuals in the population will continue to have the BB genotype. The frequency of bb in￾dividuals is q2 (0.4 0.4) and so will continue to be about 16%, and the frequency of Bb individuals will be 2pq (2 0.6 0.4), or approximately 48%. Phenotypically, if the population size remains at 100 cats, we will still see approx￾imately 84 black individuals (with either BB or Bb geno￾types) and 16 white individuals (with the bb genotype) in the population. Allele, genotype, and phenotype frequen￾cies have remained unchanged from one generation to the next. This simple relationship has proved extraordinarily useful in assessing actual situations. Consider the recessive allele responsible for the serious human disease cystic fi￾brosis. This allele is present in North Americans of Cau￾casian descent at a frequency q of about 22 per 1000 indi￾viduals, or 0.022. What proportion of North American Caucasians, therefore, is expected to express this trait? The frequency of double recessive individuals (q2) is ex￾pected to be 0.022 0.022, or 1 in every 2000 individu￾als. What proportion is expected to be heterozygous car￾riers? If the frequency of the recessive allele q is 0.022, then the frequency of the dominant allele p must be 1 – 0.022, or 0.978. The frequency of heterozygous individu￾als (2pq) is thus expected to be 2 0.978 0.022, or 43 in every 1000 individuals. How valid are these calculated predictions? For many genes, they prove to be very accurate. As we will see, for some genes the calculated predictions do not match the ac￾tual values. The reasons they do not tell us a great deal about evolution. Why Do Allele Frequencies Change? According to the Hardy–Weinberg principle, both the al￾lele and genotype frequencies in a large, random-mating population will remain constant from generation to gen￾eration if no mutation, no gene flow, and no selection occur. The stipulations tacked onto the end of the state￾ment are important. In fact, they are the key to the im￾portance of the Hardy–Weinberg principle, because indi￾vidual allele frequencies often change in natural popula￾tions, with some alleles becoming more common and others decreasing in frequency. The Hardy–Weinberg principle establishes a convenient baseline against which to measure such changes. By looking at how various fac￾tors alter the proportions of homozygotes and heterozy￾gotes, we can identify the forces affecting particular situa￾tions we observe. Many factors can alter allele frequencies. Only five, however, alter the proportions of homozygotes and het￾erozygotes enough to produce significant deviations from the proportions predicted by the Hardy–Weinberg princi￾ple: mutation, gene flow (including both immigration into and emigration out of a given population), nonrandom mating, genetic drift (random change in allele frequencies, which is more likely in small populations), and selection (table 20.1). Of these, only selection produces adaptive evo￾lutionary change because only in selection does the result depend on the nature of the environment. The other fac￾tors operate relatively independently of the environment, so the changes they produce are not shaped by environ￾mental demands. The Hardy–Weinberg principle states that in a large population mating at random and in the absence of other forces that would change the proportions of the different alleles at a given locus, the process of sexual reproduction (meiosis and fertilization) alone will not change these proportions. Chapter 20 Genes within Populations 425 Table 20.1 Agents of Evolutionary Change Factor Description Mutation The ultimate source of variation. Individual mutations occur so rarely that mutation alone does not change allele frequency much. Gene flow A very potent agent of change. Populations exchange members. Nonrandom Inbreeding is the most common form. It mating does not alter allele frequency but decreases the proportion of heterozygotes. Genetic drift Statistical accidents. Usually occurs only in very small populations. Selection The only form that produces adaptive evolutionary changes.