Quantitative Genetics: Traits controlled my many loci So far in our discussions, we have focused on understanding how selection works on a small number of loci (1 or 2). However in many cases, evolutionary biologists ask questions about traits or phenotypes (for example ) Many factors may affect a trait, including the action of alleles at one or more loci, and the environment in which an individual exists. Quantitative genetics provides the framework for understanding how evolutionary forces act on complex traits. 1 Quantitative Genetics I: Traits controlled my many loci Learning Objectives: 1. To describe how segregation at multiple loci can produce a pattern of quantitative variation in a trait. 2. To define the breeding value () and relate it to the average effects of alleles. 3. To define and differentiate broad and narrow sense heritability.. To describe the components of trait (phenotypic) variation and describe how and why additive genetic variation is the key component of variation relevant to narrow sense heritability and the response to selection. Readings: Chapter in Freeman 2 Quantitative genetics vs. population genetics Sir Ronald Fisher (10-12): Linking quantitative traits variation and Mendelian genetics In 11, Fisher showed that a large number of Mendelian factors (genes) influencing a trait would cause a nearly continuous distribution of trait values. Therefore, mendelian genetics can lead to an approximately normal distribution 3
Wheat kernel colour variation Wheat kernel colour variation This figure shows measured phenotypes in a population of F 2 plants from parents that differ in kernel colour. We can see that more than two or three phenotypes are seen in the F 2. This pattern is explained by the action of three loci. With three loci, each with two alleles, six phenotypic classes are obtained, and the distribution of phenotypes begins to look like a normal curve. Population genetics Quantitative genetics What are the conditions that will lead to a shift in the mean value of a trait under selection?
Breeder s equation Human Height: n example of a quantitative trait The first big question in quantitative genetics: Breeder s equation: R = h2s 10 Building a Quantitative Genetics Model: lessons from agriculture How much phenotypic variation among individuals is due to the presence and interaction of different alleles, and how much is due to differences in the environment? nswers to this question will determine the degree to which traits can respond to selection. In quantitative genetics, the phenotypic value (P) of an individual (e.g. height) is attributed to the genotype of the individual and to its environment: P = G + E The genotypic value (G) reflects the influence of every gene carried by the individual on the phenotypic value. The environmental deviation (E) is a measure of the influence of the environment of the phenotypic value of an individual. We can see how these components are estimated in an example from crop yield in wheat. 11 12
verage Yield of three wheat strains over a ten year period (bushels/acre) verage Yield of three wheat strains over a ten year period (bushels/acre) Year 1 1 1 1 10 11 12 13 1 1 Mean Roughrider. 3. 23.1 1. 0.3..2 1. 3.1.3 Seward. 2. 2.. 1.0.0 2. 3.2.1 2.1 gassiz.. 2. 0.. 1.. 3. 3. 3. Year 1 1 1 1 10 11 12 13 1 1 Mean Roughrider. 3. 23.1 1. 0.3..2 1. 3.1.3 Seward. 2. 2.. 1.0.0 2. 3.2.1 2.1 gassiz.. 2. 0.. 1.. 3. 3. 3. Environmental values (E) 3. -.3 = 1.1.0-2.1 = -3.1 Genetic values (G) 13 1 Using Genetic values in breeding: The Breeding Value Using Genetic values in breeding: The Breeding Value Mean yield of population (0 bushels/acre) Expected genetic value of offspring (0 bushels/acre) Genetic value of a parent (0 bushels/acre) The genetic value of a genotype reflects the sum total effect of all alleles at the loci that affect the trait of interest. Given that a parent in a sexual species passes half of its alleles to the offspring, what is the expected genetic value of the offspring? (assume a randomly chosen mate) 1 Mean yield of population (0 bushels/acre) ctual genetic value of offspring ( bushels/acre) Genetic value of a parent (0 bushels/acre) In reality, the yield of the offspring may differ from that predicted on the basis of the genetic value of the parent. Why? - Dominance (interactions among alleles at a locus) - Epistasis (interactions among alleles at different loci) 1
Using Genetic values in breeding: The Breeding Value Mean yield of population (0 bushels/acre) ctual genetic value of offspring ( bushels/acre) d Breeding Value () of the parent genotype ( bushels/acre) The breeding value of a genotype () is obtained by adding twice the deviation of the mean (d) of the offspring from the population mean. d 1 Breeding Value Example 1 To increase milk yield, dairy farmers estimate the breeding value of bulls from the average dairy production of each bull s daughters. When a particular bull is mated to several cows, his daughters produce an average of liters of milk per day, in a herd with an average production of liters. In terms of dairy production,...what is the breeding value () of the bull?(12)...what is the phenotypic value of the bull? (!!) 1 Breeding Value Example 2 Effects of Dominance Now say that a particular cow produces liters of milk per day, compared to a herd average of liters per day. When mated to different bulls, this cow s daughters produce an average of 0 liters of milk per day. In terms of dairy production,...what is the breeding value () of the cow? ()...what is the phenotypic value of the cow? () What contributes to this difference (assuming no environmental effects)? If alleles at some loci affect traits differently depending on the rest of the genotype (Interactions) Dominance (D) (interactions at the same locus) Epistasis (I) (interactions at different loci) 1 Dominance relationships among alleles at a locus affect the way in which a trait is transmitted to the offspring. parent that is homozygous (e.g. BB) at a locus that affects a trait cannot transmit this condition to its offspring. If B is recessive to b, a high fitness BB parent mated to a low fitness bb parent produces only Bb (low fitness) offspring. Such dominance effects have an impact on trait expression of the offspring from any cross. 20
Effects of Gene Interactions /Epistasis Similarly, good interaction among the alleles at different loci are not faithfully transmitted, as illustrated in these card hands. Even though Mom and Dad have good combinations, they may not combine well in the offspring. Mom! $! # Dad $ verage llele Effect Because of dominance and epistasis, a given allele may not always have the same effect of the phenotype. The average effect of an allele accounts for the difference in the effect of an allele paired with any other alleles /genes currently found within the population (e.g., accounting for the chance that it is found in a heterozygote or homozygote, in any particular genetic background). The breeding value of an individual () represents the average effects of all of his/her alleles. Offspring 21 22 Expanding the basic quantitative genetics equation We earlier described the relationship, P = G + E, Which describe the factors that determine an individual s phenotype, but we now understand that the component G can be further broken down into: G= + D + I, to describe the components of Genetic effects on the phenotype attributed to dditive genetic effects (as measured by he Breeding value), Dominance effects and Interaction effects (Epistasis). Our description of the Breeding value () showed that the phenotype of an individual s offspring is mainly determined by the 23 breeding value of its parents. From individuals to populations: patterns of phenotypic variation With an understanding of factors that determine the phenotype of an individual, we can move back up to the level of the population to develop our understanding of how to estimate the genetic component of quantitative trait variation. Q: How much of the phenotypic variation that we observe is due to genetic variation? How much of this genetic variation contributes to the response to selection? 2
From individuals to populations: patterns of phenotypic variation From individuals to populations: patterns of phenotypic variation The phenotypic variance (V P ) measures the extent to which individuals vary in phenotype for a particular trait. The phenotypic variance within a population may be due to genetic and/or environmental differences among individuals: V P = V G + V E (Ignoring interactions between genes & environment) 2 V P = V G + V E The genetic variance (V G ) can be further broken down into additive, dominance and interaction components, analogous to those used to describe an individual phenotype: V G = V + V D + V I The additive genetic variance (V ) equals the variance in breeding values within a population and measures the degree to which offspring resemble their parents. 2 Calculating phenotypic and additive genetic variances Variance: _ V x =! i (X i X) 2 --------------- (n 1) Cow 1 2 3 10 mean yield 2 3 2 3 Example: Milk yield in cows V P = (-) 2 + (-) 2 + n-1 = 2. 2 Calculating phenotypic and additive genetic variances Variance: _ V x =! i (X i X) 2 --------------- (n 1) Cow 1 2 3 10 mean yield 2 3 2 3 Example: Milk yield in cows Offspring Yield. 1..... = (offspringmean) X 2 + mean = 3 = 3 2
Calculating Phenotypic and dditive Genetic Variance Variance: _ V x =! i (X i X) 2 --------------- (n 1) Cow 1 2 3 10 mean yield 2 3 2 3 Example: Milk yield in cows Offspring Yield. 1..... 3 2 3 1.2 V P = 2. V = 20. 2 Calculating Phenotypic and dditive Genetic Variance Knowledge of the phenotypic variance and additive genetic variance allows us to predict how similar we expect the phenotypes of parents and offspring to be. It will also allow us to predict the magnitude of the response to selection when individuals with different phenotypic means have different probabilities of survival or reproduction. V P = 2. V = 20. In the previous example, nearly half of the phenotypic variance was the result of additive genetic variance. 30 Narrow-Sense Heritability h 2 = V / V P Broad-Sense Heritability H 2 = V G / V P Narrow sense heritability describes the proportion of phenotypic variance due to additive genetic variance among individuals, or the extent to which variation in phenotype is caused by genes transmitted from parents. h 2 = V / (V + V D + V I + V E ) Heritability can be low due to: Conversely, h 2 will be 1 only if there is no variation due to dominance, epistasis, or environmental effects. When h 2 = 1, P = G =. 31 Broad sense heritability describes the proportion of phenotypic variance due to total genetic variance among individuals. H 2 = V G / V P Broad-sense heritability will be 1 if all of the phenotypic variation within a population is due to genotypic differences among individuals (V G = V P ). Broad-sense heritability will be 0 if all of the phenotypic variation is caused by environmental differences. 32
Important points about heritability 1. When we use the term heritability, we are almost always referring to narrow sense heritability. 2. Estimates of heritability are not transferable. They are specific to the population and the environment in which they are estimated. 3. Heritability estimates are for populations, not individuals. Heritability does not indicate the degree to which a trait is genetically based. Rather, it measures the proportion of the phenotypic variance that is the result of genetic factors. 33