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Home , Additive genetic effects, Quantitative genetics

Quantitative : I: Traits controlled my many loci Traits controlled my many loci

So far in our discussions, we have focused on Learning Objectives: understanding how selection works on a small number of 1. To describe how segregation at multiple loci can produce a loci (1 or 2). pattern of quantitative variation in a trait. However in many cases, evolutionary biologists ask 2. To define the breeding value (A) and relate it to the average questions about traits or (for example…) effects of . Many factors may affect a trait, including the action of 3. To define and differentiate broad and narrow sense . alleles at one or more loci, and the environment in which 4. To describe the components of trait (phenotypic) variation and an individual exists. describe how and why additive is the key component of variation relevant to narrow sense heritability and Quantitative genetics provides the framework for the response to selection. understanding how evolutionary forces act on complex Readings: Chapter 9 in Freeman traits. 336-9 1 336-9 2

Quantitative genetics vs. Sir (1890-1962): Linking quantitative traits variation and Mendelian genetics

• In 1918, Fisher showed that a large number of Mendelian factors () influencing a trait would cause a nearly continuous distribution of trait values. Therefore, mendelian genetics can lead to an approximately normal distribution

336-9 3 336-9 4 Wheat kernel colour variation Wheat kernel colour variation With three loci, each This figure shows with two alleles, six measured phenotypes in a phenotypic classes are population of F2 plants obtained, and the from parents that differ distribution of in kernel colour. phenotypes begins to We can see that more look like a normal than two or three curve. phenotypes are seen in

the F2. This pattern is explained by the action of three loci. 336-9 5 336-9 6

Population genetics Quantitative genetics

What are the conditions that will lead to a shift in the mean value of a trait under selection? 336-9 7 336-9 8 Human Height: An example of a quantitative trait Breeder’s equation

Breeder’s equation: R = h2S 336-9 9 336-9 10

The first big question in Building a Quantitative Genetics quantitative genetics: Model: lessons from agriculture • How much phenotypic variation among In quantitative genetics, the phenotypic value (P) of an individual (e.g. height) is attributed to the of individuals is due to the presence and the individual and to its environment: interaction of different alleles, and how P = G + E much is due to differences in the The genotypic value (G) reflects the influence of every environment? carried by the individual on the phenotypic value. The environmental deviation (E) is a measure of the • Answers to this question will determine influence of the environment of the phenotypic value of the degree to which traits can respond an individual. to selection. We can see how these components are estimated in an example from crop yield in wheat.

336-9 11 336-9 12 Average Yield of three wheat strains over Average Yield of three wheat strains over a ten year period (bushels/acre) a ten year period (bushels/acre)

Year Roughrider Seward Agassiz Year Roughrider Seward Agassiz Environmental values (E) 1986 47.9 55.9 47.5 1986 47.9 55.9 47.5 1987 63.8 72.5 59.5 1987 63.8 72.5 59.5 63.8 - 45.63 = 18.17 1988 23.1 25.7 28.4 1988 23.1 25.7 28.4 1989 61.6 66.5 60.5 1989 61.6 66.5 60.5 1990 0.0 0.0 0.0 1990 0.0 0.0 0.0 1991 60.3 71.0 55.4 1991 60.3 71.0 55.4 1992 46.6 49.0 41.5 1992 46.6 49.0 41.5 49.0 - 52.18 = -3.18 1993 58.2 62.9 48.8 1993 58.2 62.9 48.8 1994 41.7 53.2 39.8 1994 41.7 53.2 39.8 1995 53.1 65.1 53.5 1995 53.1 65.1 53.5 Mean 45.63 52.18 43.49 Mean 45.63 52.18 43.49 Genetic values (G)

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Using Genetic values in breeding: Using Genetic values in breeding: The Breeding Value The Breeding Value

Mean yield of population Genetic value of a parent Mean yield of population Genetic value of a parent (60 bushels/acre) (80 bushels/acre) (60 bushels/acre) (80 bushels/acre) Expected genetic value of Actual genetic value of offspring (70 bushels/acre) offspring (67 bushels/acre) The genetic value of a genotype reflects the sum total In reality, the yield of the offspring may differ from effect of all alleles at the loci that affect the trait of that predicted on the basis of the genetic value of the interest. parent. Given that a parent in a sexual species passes half of Why? its alleles to the offspring, what is the expected - (interactions among alleles at a locus) genetic value of the offspring? (assume a randomly - (interactions among alleles at different loci) 3chosen36-9 mate) 15 336-9 16 Using Genetic values in breeding: Breeding Value Example 1 The Breeding Value d d To increase milk yield, dairy farmers estimate the breeding value of bulls from the average dairy Mean yield of population Breeding Value (A) production of each bull’s daughters. (60 bushels/acre) of the parent genotype When a particular bull is mated to several cows, Actual genetic value of (74 bushels/acre) offspring (67 bushels/acre) his daughters produce an average of 100 liters of milk per day, in a herd with an average production of 75 liters. The breeding value of a genotype (A) is obtained by In terms of dairy production, adding twice the deviation of the mean (d) of the offspring from the population mean. ...what is the breeding value (A) of the bull?(125) ...what is the phenotypic value of the bull? (!!)

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Breeding Value Example 2 Effects of Dominance Now say that a particular cow produces 100 liters of milk per day, compared to a herd average of 75 liters per Dominance relationships among alleles at a locus affect day. the way in which a trait is transmitted to the When mated to different bulls, this cow’s daughters offspring. produce an average of 80 liters of milk per day. A parent that is homozygous (e.g. BB) at a locus that In terms of dairy production, affects a trait cannot transmit this condition to its ...what is the breeding value (A) of the cow? (85) offspring. ...what is the phenotypic value of the cow? (100) What contributes to this difference (assuming no If B is recessive to b, a high fitness BB parent mated to environmental effects)? a low fitness bb parent produces only Bb (low fitness) If alleles at some loci affect traits differently offspring. depending on the rest of the genotype (Interactions) Such dominance effects have an impact on trait Dominance (D) (interactions at the same locus) expression of the offspring from any cross. Epistasis (I) (interactions at different loci) 336-9 19 336-9 20 Effects of Gene Interactions Average Effect /Epistasis Similarly, good interaction among the alleles at different Because of dominance and epistasis, a given allele may not loci are not faithfully transmitted, as illustrated in these always have the same effect of the . card hands. Even though Mom and Dad have good combinations, they may not combine well in the offspring. The average effect of an allele accounts for the difference in the effect of an allele paired with any 5 6 7 8 9 6 4 A A A 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 Mom Dad background). The breeding value of an individual (A) represents the 6 4 7 A 9 average effects of all of his/her alleles. ! " " $ "

336-9 Offspring 21 336-9 22

Expanding the basic quantitative From individuals to populations: genetics equation patterns of phenotypic variation We earlier described the relationship, With an understanding of factors P = G + E, that determine the phenotype of an Which describe the factors that determine an individual’s individual, we can move back up to phenotype, but we now understand that the component G can be the level of the population to develop our understanding of how to further broken down into: estimate the genetic component of G= A + D + I, quantitative trait variation. to describe the components of Genetic effects on the phenotype Q: How much of the phenotypic attributed to (as measured by he variation that we observe is due to Breeding value), Dominance effects and Interaction effects genetic variation? (Epistasis). How much of this genetic variation contributes to the response to Our description of the Breeding value (A) showed that the selection? phe33n6o-9type of an individual’s offspring is mainly determined by t2h3e 336-9 24 breeding value of its parents. From individuals to populations: From individuals to populations: patterns of phenotypic variation patterns of phenotypic variation

V = V + V The phenotypic variance (VP) P G E measures the extent to which The genetic variance (VG) can be individuals vary in phenotype for a further broken down into additive, particular trait. dominance and interaction components, analogous to those The phenotypic variance within a used to describe an individual population may be due to genetic phenotype: and/or environmental differences among individuals: VG = VA + VD + VI VP = VG + VE

(Ignoring interactions between The additive genetic variance (VA) genes & environment) equals the variance in breeding values within a population and measures the degree to which 336-9 25 336-9 offspring resemble their parents.26

Calculating phenotypic and Calculating phenotypic and additive genetic variances additive genetic variances Example: Milk yield in cows Example: Milk yield in cows

Variance: Cow yield Variance: Cow yield Offspring A = (offspring- _ 1 75 _ Yield mean) X 2 + mean V = ! (X – X)2 2 88 V = ! (X – X)2 1 75 74.5 x i i V = (75-75)2 + (88-75)2 +… x i i 2 88 81.5 ------3 52 P ------4 83 n-1 3 52 65.5 (n – 1) 5 82 (n – 1) 4 83 79 A = 83 = 425.6 6 43 5 82 78.5 7 100 6 43 66 8 48 7 100 84 A = 93 9 79 8 48 64.5 10 100 9 79 79.5 mean 75 10 100 78 336-9 27 336-9 mean 75 28 Calculating Phenotypic and Calculating Phenotypic and Additive Genetic Variance Additive Genetic Variance Example: Milk yield in cows Knowledge of the phenotypic

Variance: Cow yield Offspring A variance and additive genetic VP = 425.6 _ Yield variance allows us to predict VA = 205.5 V = ! (X – X)2 1 75 74.5 74 how similar we expect the x i i 2 88 81.5 88 ------phenotypes of parents and In the previous example, 3 52 65.5 56 offspring to be. 4 83 79 83 nearly half of the (n – 1) VP = 425.6 5 82 78.5 82 phenotypic variance was V = 205.5 It will also allow us to 6 43 66 57 A the result of additive predict the magnitude of the 7 100 84 93 genetic variance. 8 48 64.5 54 response to selection when 9 79 79.5 84 individuals with different 10 100 78 81 phenotypic means have

336-9 mean 75 75.2 29 3differen36-9 t probabilities of 30 survival or reproduction.

Narrow-Sense Heritability Broad-Sense Heritability 2 2 h = VA / VP H = VG / VP

Narrow sense heritability describes the Broad sense heritability describes the proportion of phenotypic variance due to proportion of phenotypic variance due to total additive genetic variance among individuals, or genetic variance among individuals.

the extent to which variation in phenotype is 2 H = VG / VP caused by genes transmitted from parents. 2 Broad-sense heritability will be 1 if all of the phenotypic h = VA / (VA + VD + VI + VE) variation within a population is due to genotypic

Heritability can be low due to: differences among individuals (VG = VP). Broad-sense heritability will be 0 if all of the phenotypic Conversely, h2 will be 1 only if there is no variation is caused by environmental differences. variation due to dominance, epistasis, or 336-9 environmental effects. When h2 = 1, P = G = A. 31 336-9 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 4. 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. 336-9 33