Broad-Sense Heritability Index The heritability index estimates that part of variation due to all genetic influences, which is calculated as H2 = VG/VP Again, a heritability index close to 1.0 indicates that a large portion of the variation is due to genetic factors. Narrow-Sense Heritability Heritability and the heritability index is most useful as an estimate of the predicted response to selection. In order to make this estimate, VG must be subdivided to separate the effects of additive variance and dominance variance. VG= VA + VD (+ VI) (The interaction between the two is usually negligible and can be dropped from the equation) Narrow-Sense Heritability VA is that portion of the variance due to the average effect of additive components of genes. VD is the portion of variance that results when expression in heterozygotes is not precisely intermediate between that of homozygotes. h2 = VA/VP Putting It All Together Remember, heritability is due to the effects of environment and genetics. Having partitioned the effects of genetics into additive and dominance effects, we can put the equations together. VP = VE + VG and V G = V A + VD Heritability h2 = VA VE+ VA + VD Based on our knowledge of parental phenotypes, a value closer to 1.0 indicates a greater response to selection. Twin Studies How are heritability estimates created in humans? Study of identical (monozygotic) twins allows researchers to infer genetic and environmental effects. (Characteristics that remain similar are presumed to have a strong genetic component) Data can then be compared to fraternal (dizygotic) twins. Concordance Concordance values of phenotypic expression can also be used to make estimates. Twins are concordant for a trait if both express it or neither express it (i.e. are the same) Twins are discordant if one expresses it and the other does not. Concordance values for identical vs fraternal twins reared together then allows calculation of a heritability estimate. Concordance Estimates—Caveats Concordance estimates must be evaluated carefully to ensure that environmental effects are not in fact responsible for phenotypes observed. Concordance values are most useful when used to identify differences between identical and fraternal twins. Generally, a greater difference between monozygotic and dizygotic twins indicates a higher genetic component controlling the phenotype. Quantitative Trait Mapping Because most quantitative traits are controlled by multiple genes, researchers are interested in identifying where genes are located in the genome. Are they on the same chromosome? If so, how closely are they linked? Genes controlling a quantitative trait that are on the same chromosome are called quantitative trait loci (QTL). QTL are mapped relative to markers, or other known genes with known inheritance patterns. Population Genetics Basic observations by geneticists (Wallace, Darwin and Mendel) 1. Phenotypic variations exist among individuals within populations 2. These differences are passed on from parents to offspring 3. More offspring are born than will survive to reproduce 4. Some variants are more successful at surviving and reproducing than others. Population Genetics In populations where all four factors are in effect, the frequency of different phenotypes will change across generations. Changes in abundance of particular phenotypes in a population is tied to changes in abundance of the alleles that control the phenotype. Population Genetics is that portion of genetic research dedicated to study of changes in allele frequency. Forces that Alter Gene Frequencies 1. 2. 3. 4. Selection—Both natural and artificial Mutation Migration Random genetic drift Definitions 1. 2. Population: a group of individuals from the same species, living in the same geographic area and that can interbreed Gene pool: All gametes made by all the breeding members of a population in a single generation. (These gametes will combine to form zygotes that become the next generation) Remember, each gamete is haploid and only contains one allele for each locus, and different gametes carry different alleles. Definition 3. Allele frequency: The proportion of gametes in the gene pool that carries a particular allele. Populations are dynamic; they change over generations such that over time, the gene pool can change. Calculating Allele Frequency 1. 2. Genotypes may be inferred from phenotypes Protein or DNA sequences are analyzed 1. 2. 3. 4. Different protein forms (e.g. ABO blood type) Different size mRNA transcripts (splice variants) Small differences in DNA sequences that produce different size fragments when digested by enzymes (RFLP or restriction fragment length polymorphism) Single nucleotide differences (SNP or single nucleotide polymorphisms) Calculate Allele Frequency Populations are tested to determine the genotypes. When all the allele frequencies are added together and the total equals 1.0, then all possible alleles (for a given population) have been accounted for. The Hardy-Weinberg Law We are interested in determining or predicting changes in allele frequencies. The Hardy-Weinberg law is a mathematical model that shows what happens to alleles and genotypes in an ideal population (free of the complications that actually affect real populations). The Hardy-Weinberg law has a set of assumptions that must be kept in mind. Hardy-Weinberg Assumptions 1. 2. 3. 4. 5. Individuals of all genotypes are equal in capacity to survive and reproduce (no selection). No new alleles are created or converted from one to another (no mutation). Individuals do not migrate out or into a population The population is infinitely large such that sampling errors and random effects are negligible Individuals in a population mate randomly. Properties of an “Ideal” H-W Population 1. 2. The frequency of alleles does not change from generation to generation After one generation of random mating, offspring genotype frequencies can be predicted from the parent allele frequencies (and would be expected to remain constant from that point) Uses of H-W Assumptions and the “Ideal” Population By identifying and specifying the assumptions under which a population cannot evolve, the H-W law identifies the forces at work in the real world that cause allele frequencies to change. In other words, the H-W law holds some forces constant in order to identify and quantify other forces. Putting H-W to Work: An Example Consider the A locus, which has two alleles, A and a. The frequency of A is 0.7 and a is 0.3 in both eggs and sperm. 0.7 + 0.3 = 1.0, indicating all alleles are accounted for. Given the assumption that all individuals mate randomly, gametes are paired to make zygotes to create the next generation. The A Locus For any one zygote, the probability of the AA genotype (both egg and sperm donate A): 0.7 x 0.7 = 0.49 The probability of A from sperm and a from egg: 0.7 x 0.3 = 0.21 The probability of A from egg and a from sperm: 0.7 x 0.3 = 0.21 Overall, probability of the Aa genotype: 0.21 + 0.21 = 0.42 The A locus, continued Probability of the aa genotype (both egg and sperm donate a): 0.3 x 0.3 = 0.09 Added together, all probabilities add up to 1.0: 0.49 + 0.42 + 0.09 = 1.0 (All possible zygotes have been accounted for) What Happens in the Next Generation? Our zygotes are 49% AA, 42% Aa, and 9% aa. Remember, we assume all genotypes have an equal chance of surviving and reproducing. What will happen in the next generation? AA individuals are 49% of the population and the gametes they produce will constitute 49% of the gene pool, all containing the allele A. Frequency from homozygote = 0.49 The Next Generation, continued Likewise, the Aa individuals are 42% of the population, half (0.5) of which will contribute the A allele Frequency from heterozygotes = (0.5)0.42 The frequency of A is therefore 0.49 + (0.5)0.42 = 0.7 The Next Generation, Continued What about the frequency of the a allele? 9% were aa and will donate only the a allele 42% were Aa, half of which will donate the a allele Frequency of a = 0.09 + (0.5)0.42 = 0.3 So, after just one generation, genotype frequencies can be predicted. (The population does not evolve) The Hardy-Weinberg Law The example just used illustrates the law in general. The H-W law uses variables instead of numerical values for the allele frequencies: p and q The frequency of A = p and the frequency of a = q such that p + q = 1.0 The Hardy-Weinberg Law If we randomly draw a sperm and an egg from the gene pool, then pair them to make a zygote, the probability that both sperm and egg will carry the A allele = p x p, or p2. The Hardy-Weinberg Law Next, the probability that the egg carries A and the sperm carries a = p x q, and that the sperm carries A and the egg carries a =qxp Thus, the frequency of the Aa genotype is 2pq. The Hardy-Weinberg Law Lastly, the frequency at which both sperm and egg will carry the a allele is q x q, or q2. In total, the distribution of genotypes among the zygotes is p2 + 2pq + q2 = 1.0 The Hardy-Weinberg Law The Hardy-Weinberg law works for any frequencies of A and a, provided 1. The frequencies add up to 1.0 and 2. The five H-W assumptions are invoked. A population in which the allele frequencies remain constant from generation to generation and in which the genotype frequencies can be predicted from allele frequencies is said to be in Hardy- Weinberg equilibrium for that locus. Implications of the Hardy-Weinberg Law 1. 2. 3. Dominant traits do not necessarily increase in frequency from one generation to the next. Genetic variability can be maintained in a population since, once established, allele frequencies can remain unchanged. If the H-W assumptions are invoked, knowing the frequency of only one genotype allows calculation of all other genotypes. Implications, continued For example, by knowing the frequency of homozygous recessive individuals allows calculation of heterozygous carriers for the condition caused by the homozygous recessive genotype. Implications, continued The Hardy-Weinberg Law is the foundation upon which the entire study of population genetics is built. By demonstrating loci within populations that do not evolve, we can use the H-W law to identify forces that cause populations to evolve by examining loci that do show changes in allele frequencies over time. Implications, continued In other words, when the assumptions of the HardyWeinberg Law are broken, allele frequencies change over the generations. Therefore, the forces that are held constant in HardyWeinberg ideal populations are the very forces that cause genetic change. Implications, continued For example, non-random mating does not in and of itself change alter allele frequencies, but by altering genotype frequencies, it indirectly affects the course of evolution. The Hardy-Weinberg Law tells geneticists where to look to find sources driving evolution in populations.