Lecture 12 Quantitative Genetics 12 Thurs 12 Feb

Lecture 12: Quantitative Genetics 12. Thurs. , 12 Feb. 2015 - Quantitative Genetics Vitzthum, V. J. 2003. A number no greater than the sum of its parts: the use and abuse of heritability. Human Biology 75: 539 -558. 1

"A central question in biology is whether observed variation in a particular trait is due to environmental factors or biological factors — sometimes expressed as the nature–nurture debate. Heritability is a concept which summarizes how heritable a phenotype of interest is, in particular with reference to the resemblance of offspring and parents. Heritability is both a word that is used in common speech and a technical term in genetics, thereby causing confusion. " Visscher, P. M. , W. G. Hill, and N. R. Wray. 2008. Heritability in the genomics era — concepts and misconceptions. Nature Reviews Genetics 9: 255 -266. 2

Now let's work towards the definition of "heritability" used in quantitative genetics … 3

Mendel first sorted out the "particulate" or discrete nature of inheritance. He was lucky and insightful to study traits that allowed him to see this. 4

Mendel worked with traits that came in discrete forms, either/or traits: traits e. g. , round/wrinkled, yellow/green Different alleles gave clearly distinguishable phenotypes. "Heritability" was clear. 5

But variation in most phenotypic traits is continuous or quantitative, not discrete like Mendel's peas. Height distribution of 486 children measured at age 5 and 8 years. http: //adc. bmj. com/content/79/4/318. full 6

We can reconcile "Mendelian inheritance" with quantitative trait variation if we assume that many different genes affect the trait (and also that variation in environmental factors may cause "smear" among the genetic categories of trait variation). 7

Let's imagine that 3 loci (A, B, C), each with 2 alleles, affects the quantitative trait of human skin color. Assuming completely independent assortment (no linkage) Purely additive effects of alleles, i. e. , heterozygotes are exactly intermediate between the two homozygotes at every locus (no dominance or epistasis) "Punnett square" 7 different categories that grade into each other http: //www. tokresource. org/tok_classes/biobiobio/biomenu/polygenic_inheritence/index. htm 8

Let's imagine that 3 loci (A, B, C), each with 2 alleles, affects the quantitative trait of human skin color. Assuming completely independent assortment (no linkage) Purely additive effects of alleles (no dominance or epistasis) 7 different categories that grade into each other http: //www. tokresource. org/tok_classes/biobiobio/biomenu/polygenic_inheritence/index. htm 9

For quantitative or continuous-valued traits, like skin color, variation among individuals within a population is caused by: 1. genetic differences at multiple loci 2. environmental differences experienced since fertilization of egg (or even before) Phenotypic variance of a population is calculated as: (Xi - Xmean)2 ---------------- N-1 Standard deviation is square root of variance 10

Although standard deviations are more intuitive, because they have the same units as the mean (average), quantitative genetics works with variances because variances can be added. 11

Phenotypic variance of a population can be partitioned into various components. Simplest partitioning: VP = VG + VE 12

Phenotypic variance of a population can be partitioned into various components. Simplest partitioning: VP = VG + VE May also have Genotype-Environment interaction a. which genotype has the higher phenotype depends on the environment in which rearing occurs b. "reaction norm" or "norm of reaction" = set of phenotypes produced by a given genotype across a range of environments (phenotypic plasticity) 13

Phenotypic variance of a population can be partitioned into various components. Simplest partitioning: VP = VG + VE May also have Genotype-Environment interaction a. which genotype has the higher phenotype depends on the environment in which rearing occurs b. "reaction norm" or "norm of reaction" = set of phenotypes produced by a given genotype across a range of environments (phenotypic plasticity) So, can add term: VP = VG + VE + V G X E 14

Also may have genotype-environment correlation, i. e. , different genotypes tend to occur in different environments or microenvironments: a. genotypes might differentially select microenvironments b. strongest individuals obtain best territories c. farmer takes better care of the best calves If so, then need VP = VG + VE + VG X E + VGEcorr This can be avoided by making measurements in controlled environments, with little or no variation among where individuals live, hence eliminating sources of variance. 15

However, resulting numbers may or may not be relevant to natural populations. Some workers do make estimates in nature, especially for sessile organisms, such as plants, or animals that use nests. Many bird populations have been studied with artificial nest boxes. In many cases, for practical reasons, workers often just lump VG X E and VGEcorr into VE, i. e. , they do not try to estimate them separately. 16

Broad-sense heritability = VG/VP But not all genetic variance can be passed on to offspring, only the additive genetic variance. So, a more useful partitioning for some purposes is: VP = VA + VD + VI + VE + VG X E + VGEcorr VA = variance caused by additive effects of alleles at all relevant loci VD = variance caused by dominance deviations, i. e. , non-additive interactions between alleles at a single locus VI = variance caused by epistatic deviations, i. e. , non-additive interactions between alleles at different loci 17

What do we mean by additive effects of alleles? ● Many different genetic loci affect a complex trait ● At each locus, we might have multiple alleles: "+" alleles "–" alleles "o" alleles ● For body mass, + alleles might be those that increase appetite, increase secretion of growth hormone, reduce activity levels, etc. ● ● – alleles would tend to do the opposite o alleles would have no effect on these lowerlevel (subordinate) traits 18

What do we mean by additive effects of alleles? ● The effects of an allele at one locus do not depend on what alleles are at other loci ● A large individual will have mostly + alleles at most loci ● A small individual will have mostly – alleles at most loci ● Next slide shows hypothetical examples for 14 loci … 19

What do we mean by additive effects of alleles? ● Genotype of Large Individual (genetic score = +21) +–++o++++ ++o+++–+++++++ ● Genotype of an "Average" Individual (genetic score = 0) –+ooooo–oooooo oo+oooo–oooo+o ● Genotype of Small Individual (genetic score = – 18) – – + o – – – o – – +–––o–––+–o––– These would be the genetic propensities of these individuals. Could be masked or amplified by environmental effects. 20

Narrow-sense heritability = VA/VP Narrow-sense heritability is viewed as the single most important descriptive statistic about the quantitative genetics of a given trait in a given population. To a first approximation, it indicates the (shortterm) evolutionary potential of the trait. How do we estimate narrow-sense heritability? Resemblance of relatives: phenotypic similarity will be correlated with genetic relatedness. 21

Fisher, R. A. 1918. The correlation between relatives on the supposition of Mendelian inheritance. Transactions of the Royal Society of Edinburgh 52: 399 -433. Fisher_Young_Man_Photograph courtesy of Professor A W F Edwards by kind permission of Joan Fisher Box. jpg 22

Fraction of Shared Influence Different kinds of relatives share different kinds of genetic effects to varying degrees. Relatives VA VD VI clones 1 1 full sibs 1 1/2 1/4 1/1 6 1/6 4 half sibs 1/4 0 first cousins 1/8 0 double first cousins 1/1 1/4 6 one parent-offspring grandparentgrandchild 1/2 0 1/4 1/1 6 1/1 23

Fraction of Shared Influence By comparing how strongly different kinds of relatives resemble each other for some trait, you can, by subtraction, estimate other variance components, such as dominance. Relatives VA VD VI clones 1 1 full sibs 1 1/2 1/4 1/1 6 1/6 4 half sibs 1/4 0 first cousins 1/8 0 double first cousins 1/1 1/4 6 one parent-offspring grandparentgrandchild 1/2 0 1/4 1/1 6 1/1 24

Fraction of Shared Influence Relatives VA VD VI clones 1 1 full sibs A common way to estimate additive genetic effects is to comparents with their offspring (measured at the same age). 1 1/2 1/4 1/1 6 1/6 4 half sibs 1/4 0 first cousins 1/8 0 double first cousins 1/1 1/4 6 one parent-offspring grandparentgrandchild 1/2 0 1/4 1/1 6 1/1 25

Least-squares linear regression slope = estimate of narrow-sense heritability = 0. 5615 in this example N = 50 If have no epistasis, and also no maternal effects or commonfamily environmental effects. 26

Repeatability Generally Sets an Upper Limit to Heritability Low repeatability would add a lot of "jitter" to the data points and reduce the slope. Low repeatability can be caused by high measurement error per se, as well as biological factors that cause a trait to fluctuate over time (e. g. , blood pressure). 27

Narrow-sense heritability would be estimated as 0. 18 (assuming no maternal effects or common-family environmental effects, and no epistasis). 95% confidence interval ranges from 0. 057 to 0. 311. Swallow, J. G. , P. A. Carter, and T. Garland, Jr. 1998. Artificial selection for increased wheel-running behavior in house mice. Behavior Genetics 28: 227 -237. 28

Heritability of beak size in a Darwin's Finch (Geospiza fortis) Boag, P. T. 1983. The heritability of external morphology in Darwin's ground finches (Geospiza) on Isla Daphne Major, Galapagos. Evolution 37: 877 -894. Darwin's Finches in the Galapagos islands include Geospiza fortis (nutcracker finch), which has evolved a deep bill for cracking seeds. Each point shows the mean offspring bill depth and its corresonding midparent value (the average of the two parents). The relation between these measures in 1976 (red circles) had a slope of 0. 82 (red line). A drought in 1978 produced tougher seeds with lower water content: finches with larger beaks (hence greater cracking strength) were more likely to survive. Heritability remains quite similar in 1978 (slope of blue line = 0. 74, which is approximately parallel to red line): the mean beak size increased (blue line displaced upward ~0. 5 mm) and no birds with beaks <9 mm survived (blue circles). Although beak size has constant high heritability, this does not mean that the trait is constant: beak size in any one year is highly variable (note ranges of axes), and varies when the environment changes 29 (upward displacement of slope beween years). [Modified from text material © 2010 by Steven M. Carr]

In principle, can use any relatives, just need to know the expected causes of resemblance. For example, in an organism that had no paternal care, might measure offspring and only the fathers: double the regression slope to estimate narrow-sense heritability. 30

Another common "breeding design" is to mate each father (sire) with multiple mothers (dams) and measure trait of interest in the offspring only. This half-sib, full-sib breeding design allows estimation of narrow-sense heritability. In particular, the among-sire component of variance is proportional to additive genetic effects (if have no non-genetic paternal effects). 31

Current state-of-the-art analytical techniques allow use of pedigrees to determine the expected resemblances for any sorts of relatives ("animal model"). The dairy cattle industry has millions of animals in pedigrees, along with measures of milk produciton. http: //1. bp. blogspot. com/-KZt. THg. TZh. SA/UZG 73 jom 5_I/AAAABr. M/tte 0 a. Tmq 7 z. E/s 1600/Darwin. Pedigree. gif http: //phylonetworks. blogspot. com/2013/05/charles-darwins-family-pedigree-network. html 32

Narrow-sense heritability can also be estimated from a selective breeding experiment. Let's see how … 33

The breeder's equation says adaptive phenotypic evolution consists of two parts: r = h 2 s r = response to selection = evolution from one generation to the next = change in the phenotypic mean of a population from one generation to the next 34

r = h 2 s h 2 = narrow-sense heritability = how much of the phenotypic variation in a population is caused by genetic effects that can be passed on from parents to their offspring additive genetic variance = -------------------total phenotypic variance 35

r = h 2 s s = directional selection differential = difference in mean phenotype between the original whole population before selection and the mean of the individuals who actually breed to produce the next generation 36

r = h 2 s Now let's look at this whole equation graphically … 37

Population Before Selection Consider the distribution of a phenotypic trait within a population Mean. Before 38

Population Before Selection Mean. Before Population After Selection Mean. After Now imagine that a selective event occurs, e. g. , a winter ice storm that kills most of the individuals in a bird population (Bumpus 1899). In this example, the larger birds survive. s = Mean. After - Mean. Before 39

Population Before Selection Mean. Before Population After Selection Mean. After This subset of "selected" individuals survives to breed 40

Population Before Selection Mean. Before Population After Selection Mean. After Next Generation Mean. Next Generation The distribution of the trait in their offspring might look like this Exactly where depends on inheritance because r = h 2 s 41

Population Before Selection r = h 2 s Mean. Before Population After Selection Mean. After Next Generation s = Mean. After - Mean. Before r = Mean. Next Generation Mean. Before h 2 = r/s So this is one way to estimate the narrow-sense heritability. Mean. Next Generation Usually called the realized heritability. 42

Realized heritability estimated from a selective breeding experiment for wheel running in mice Swallow, J. G. , P. A. Carter, and T. Garland, Jr. 1998. Artificial selection for increased wheelrunning behavior in house mice. Behavior Genetics 28: 227 -237. We will go into this later. 43

Can we see any general patterns in estimates of heritabilities for different types of traits? 44

"The data set comprises 1, 120 narrow sense heritability estimates collected from 140 sources, representing 75 species. … estimates for the Drosophila genus were excluded from the present study as they are treated elsewhere (Roff and Mousseau, 1987). " Life History (lowest) Morphology (highest) "The results indicate that [heritabilities of] life history traits are generally much lower than morphological traits, and that behavioural and physiological traits tend to fall in the middle. " Mousseau, T. A. , and D. A. Roff. 1987. Natural selection and the heritability of fitness components. Heredity 59: 181 -197. 45

Why might morphological traits tend to have high heritabilities? Life History (lowest) Morphology (highest) More genetic influence (maybe because they are not so selectively important) Less day-to-day fluctuation caused by biological factors Less measurement error Mousseau, T. A. , and D. A. Roff. 1987. Natural selection and the heritability of fitness components. Heredity 59: 181 -197. 46

"on average, heritability estimates are larger for morphological traits than for fitness-related traits, and that heritability tends to be larger in better environments when compared with poorer environments. " Visscher, P. M. , W. G. Hill, and N. R. Wray. 2008. Heritability in the genomics era — concepts and misconceptions. Nature Reviews Genetics 9: 255 -266. 47

Box 4 | The heritability of IQ controversy Nowhere has the debate about nature and nurture been so controversial as in the study of mental ability in humans. In one meta-analysis of a number of twin studies the modelling of maternal effects implied a narrow-sense heritability of only 0. 3 and an estimate of broad-sense heritability of 0. 5. Therefore, we can conclude from the wealth of empirical data currently available that the resemblance between relatives is large and consistent with the hypothesis that a large proportion of the variation in IQ between individuals within a population is associated with additive genetic factors. So, about half of the among-individual variation in IQ in a given human population is probably related to non-genetic factors. Thus, potentially we could do a lot to improve IQ by manipulating relevant environmental factors (e. g. , early-life nutrition, education). Visscher, P. M. , W. G. Hill, and N. R. Wray. 2008. Heritability in the genomics era — concepts and misconceptions. Nature Reviews Genetics 9: 255 -266. 48

When selection acts on a trait, it will tend to: 1. increase frequency of alleles with additive effects in the favored direction 2. decrease frequency of alleles with additive effects in the "wrong" direction 3. increase frequency of alleles with dominance effects in the favored direction This leads to predictions about the genetic architecture of traits. . . 49

Traits that have been under (strong) directional selection should exhibit relatively low narrow-sense heritabilities. This could explain why life-history traits tend to have low heritabilities. If we cross a population that has been under selection for high values of a particular trait with a population that has not been under selection, then the F 1 offspring should tend to resemble the parents from the selected population. 50

It is presumed that wild house mice have generally been under directional selection for high activity levels. A cross of wild house mice with laboratory house mice found that, after the first few days, wheel running of the F 1 animals was the same as that of the wild mice, thus indicating net dominance in the direction of high wheel running. Dohm, M. R. , C. S. Richardson, and T. Garland, Jr. 1994. Exercise physiology of wild and random-bred laboratory house mice and their reciprocal hybrids. American Journal of Physiology 267 (Regulatory Integrative Comp. Physiol. 36): R 1098 -R 1108. 51

VO 2 max of the F 1 animals was also the same as that of the wild mice, indicating net dominance in the direction of high VO 2 max. That makes sense, as it would go along with high activity levels. It is not clear what body size selection may have favored in wild house mice, but the population studied was smaller in size than the lab house mice with which they were crossed. Body mass of the F 1 animals was intermediate between wild and lab mice, indicating no net dominance. Dohm, M. R. , C. S. Richardson, and T. Garland, Jr. 1994. Exercise physiology of wild and random-bred laboratory house mice and their reciprocal hybrids. American Journal of Physiology 267 (Regulatory Integrative Comp. Physiol. 36): R 1098 -R 1108. 52

This equation describes the response to directional selection of a single phenotypic trait, given its narrow-sense heritability and the intensity of selection: r = h 2 s However, organisms comprise many phenotypic traits, and they may be correlated. Therefore, selection that affects one may affect another. 53

Trait B Imagine two traits that are positively correlated in a population before selection. Trait A 54

Survive Imagine that selection eliminates all individuals with values < 1. 0 for Trait A. Trait B Die Trait A 55

Trait B Die Survive Imagine that selection eliminates all individuals with values < 1. 0 for Trait A. These survivors will also have values for trait B that tend to be greater than the mean for the whole population before selection. Trait A 56

Trait B in Offspring In addition, traits may be genetically correlated, i. e. , tend to run together in families Therefore, to understand phenotypic evolution, we need to consider both phenotypic and additive genetic correlations between traits. We need a multi-trait version of the breeder's equation. Trait A in Parents 57

We will discuss the multivariate version of the breeder's equation when we talk about Measuring Selection in the Wild (174 -15 -Winter_17_3 -March_Selection_in_the_Wild. ppt). For now, just be aware that it includes genetic correlations between traits instead of just the heritability of a single trait. Stopped here 12 Feb. 2015 = end of material for 2 nd Exam. 58

Genetic correlations can either slow (constrain) or accelerate (facilitate) phenotypic evolution, depending on whether they are in the same direction as selection. Genetic correlations are caused by pleiotropy (one gene affects > 1 trait) and/or by linkage disequilibrium (nonrandom associations among alleles at different loci during the gametic phase), one cause of which is physical linkage on chromosomes. Pleiotropy is generally thought to be the more important cause. Genetic correlations can themselves evolve in response to selection because alleles with different pleiotropic effects may be favored. Thus, a genetic correlation between two traits might indicate the action of past correlated selection on the two traits (http: //www. bio. tamu. edu/users/ajones/gmatrixonline. html). 59

Definitions: Phenotype = any measurable trait (height, metabolic rate, I. Q. ) Genotype = genetic material, usually DNA, actual set of genes on chromosomes Genotype (zygote) is translated into phenotype (adult) through development during an organism's ontogeny, and subject to many environmental effects 60

Definitions: Natural Selection = individual variation in Darwinian fitness that is correlated with variation in one or more phenotypic traits. Darwinian Fitness (simply) = number of offspring left to the next generation by a given individual (measure at same stage, zygote-to-zygote best, difficult in practice) Components of Darwinian Fitness, e. g. , survivorship, fecundity, # of mates These are often studied because it is too difficult to measure lifetime reproductive success. 61

This lecture was too short by about 15 minutes in 2011. I added about 6 slides, and it was too short by about 20 minutes in 2012! This lecture was too short by about 15 minutes in 2013, but I had not yet moved the definitions slides in here!!!! This is end of material for Midterm Exam #2 in Spring 2012. Extra Slides Follow Add more on examples of genetic correlations, pleiotropy, hormonal pleiotropy, etc. --> but that is in the next lecture … Add modern examples with animal model analyses? 62

Updates to be Done for 2011 Spring for QG: M: Power. PointQuantitative_Genetics_from_NIU. ppt Visscher, P. M. , W. G. Hill, and N. R. Wray. 2008. Heritability in the genomics era — concepts and misconceptions. Nature Reviews Genetics 9: 255 -266. http: //www. husdyr. kvl. dk/htm/kc/popgen/genetics/6/4. htm http: //www. mun. ca/biology/scarr/2900_Natural_Selection_in_the_Wild. html George W Gilchrist and Raymond B Huey. 1999. The direct response of Drosophila melanogaster to selection on knockdown temperature. Heredity 83: 15 -29. doi: 10. 1038/sj. hdy. 6885330 http: //www. nature. com/scitable/topicpage/multifactorial-inheritanceand-genetic-disease-919 Citation: Lobo, I. (2008) Multifactorial inheritance and genetic disease. Nature Education 1(1): 5 http: //www. tutorvista. com/content/biology-iii/heredity-andvariation/quantitative-inheritance. php 63

Nice figures: Gary T Miller, William T Starmer and Scott Pitnick. 2001. Quantitative genetics of seminal receptacle length in Drosophila melanogaster. Heredity 87: 25 -32. doi: 10. 1046/j. 1365 -2540. 2001. 00903. x Fig. 1 Response in (a) the first and (b) the second high (squares) and low (circles) SR selection lines, and the response in (c) the first and (d) the second experiments as a function of cumulative selection differential. The heritability is twice the slope (m) of the regression. Asterisks indicate the first generation of relaxed selection (see text for details). 64

Population Before Selection Mean. Before Population After Selection These Individuals Breed Mean. After Next Generation Mean. Next Generation 65

Midterm 1 Fall 2004 N Mean SD Min Max 21 UG 82. 6 11. 64 58. 5 98. 0 8 Grads 87. 5 6. 84 74. 5 94. 0 All 29 84. 0 10. 65 ANOVA of UG vs. Grads, 2 -tailed P = 0. 278 Levene’s test to compare variances, 2 -tailed P = 0. 063 66

Boag, P. T. 1983. The heritability of external morphology in Darwin's ground finches (Geospiza) on Isla Daphne Major, Galapagos. Evolution 37: 877 -894. 67

Boag, P. T. 1983. The heritability of external morphology in Darwin's ground finches (Geospiza) on Isla Daphne Major, Galapagos. Evolution 37: 877 -894. 68

3. for higher-level phenotypic traits, many allelic variants must be almost selectively neutral, because: a. most phenotypic traits are affected by many genes = polygenic characters, polygenic inheritance b. any individual gene (and its alleles) has a small effect c. if stabilizing selection is usually operating, then an allele that increases body size will be advantageous in a small individual, and vice versa, and so neutral overall d. environment and hence selection may fluctuate, almost stochastically, so net selection over many generations may be around zero 69

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Variation in most phenotypic traits is continuous or quantitative, not discrete like Mendel's peas. 71