Quantitative Genetics Multilocus traits Utility of Mendellian models for predicting phenotypic outcomes Measuring Heritable Variation Nature vs. Nurture Quantifying the strength of selection Measuring the response to selection (the Breeder’s equation) Modes of Selection – you know these

Quantitative Genetics Statistics review: Qualitative vs. Quantitative variables. Qualitative (Categorical) - An observation that can be assigned to one of several categories. Blood type – A, B, AB, O Sex – Male , Female Seed Shape – Wrinkled, Smooth Quantitative variable - A variable that records the amount of something. A continuous variable – a quantitative variable that measures something on a continuous scale. Biomass of an organism Absorption of a solution Concentration of cholesterol in a blood specimen We will focus on quantitative traits A discrete variable - a variable that is not continuous, but which falls on a discrete interval. Age of an item (in years as whole numbers), Number of pairs of Gill-over-the-ground in a square meter, Number of eggs in a bird’s nest.

Quantitative Genetics Height in humans is a quantitative trait. It is determined by: The genotype at many different loci. (Nature) The environment (Nurture) The resulting phenotypes are not discrete units, but continuous.

Quantitative Genetics An example of a quantitative trait from Evolutionary Biology lab

Quantitative Genetics Mendialian Genetics can explain qualitative traits but can they explain quantitative traits from multiple loci? Edward East – corolla length of Nicotiana longiflora) What we know from simple genetics. Genotypes aa aA AA are in what proportions? ¼ ½ ¼

Quantitative Genetics East knew that a single loci model was too simple. But a two loci model still yields discrete phenotypes (and genotypes) Genotypes – determined by a 4 x 4 Punnett square Phenotypes are: 1/4 , 4/16, 6/16, 4/16, 1/16 A step in the right direction, but - still too simple!

Quantitative Genetics East knew that a single loci model was too simple. A six loci model demonstrates that Mendellian genetics are capable of making correction predictions Genotypes – determined by a 64 x 64 Punnett square! In a six locus model, corolla length is still discrete. But in a 13 locus model, we would need a ruler. Corolla length is becoming more quantitative.

Quantitative Genetics East’s two predictions: In a six loci model, the range of F2 phenotypes identical to the parentals will be rare. 1 in 4,096 The parental phenotypes are not lost. The necessary alleles are in the heterozygotes. This leads to East’s second prediction-

Quantitative Genetics East’s two predictions: 2) With a few generations of selective breeding for either short or tall corollas, the original parental phenotypes can be recovered. Interesting outcome – the parentals were not identical – Why? Perhaps original parentals were not homozygous at all loci. Environmental variation - nurture

Quantitative Genetics – role of genetics Pure Polygenic Traits are those not influenced by the environment Range of phenotypes due to additive effects of loci, e.g. eye color.

Quantitative Genetics – influence of the environment Clausen, Keck and Heisey (1948) – Experimental studies on the nature of species. I. Effects of varied environments on western North American plants Achillea lanulosa (Wooly yarrow)

Quantitative Genetics – role of genetics Clausen, Keck and Heisey (1948) – Genetic variation in height of Achillea lanulosa.

Quantitative Genetics Both genetics and the environment play a role in phenotypic expression

Determination of Nature vs. Nurture Quantitative Genetics Determination of Nature vs. Nurture Question: What fraction of the trait is due to the environment and due to genes? Need to determine the Heritability (H or h2) [Variance components are squared – s2 –(sample) and δ2 – (population)] Heritability estimates the percentage of the phenotypic variation of a trait that is due to genes (nature) in a certain population. Ranges from 1.0 (gene completely control phenotype) to 0 (entirely caused by the environment)

Typically, this variation is considered as the phenotypic variation. Heritability – “the fraction of the total variation in a trait that is due to variation in genes.” (Freeman and Herron, 2007) Typically, this variation is considered as the phenotypic variation. Vp – the total variance in the phenotypic trait of a population. VP = VG + VE VG = Genetic variation VE = Environmental variation

Broad Sense Heritability h2 or H2 ℎ2= 𝑉𝐺 𝑉𝑃 ℎ2= 𝑉𝐺 𝑉𝐺+𝑉𝐸 The problem? VG represents all of the genetic variation as a single value.

Real genetic variation is complicated. V𝐺=V𝐴+V𝐷+V𝐼 VA = additive genetic variance VD = dominance genetic variance VI = variance due to epistatic interactions

Additive Variation –VA V𝐺=V𝐴+V𝐷+V𝐼 Important because it is why relatives resemble each other. Alleles act independently. The phenotype of an organism is the sum of the effect of each allele, hence additive. Additive alleles are not affected by the presence of other alleles. The effect of additive alleles allow biologists to follow evolution in a predictable way.

Additive Variation –VA V𝐺=V𝐴+V𝐷+V𝐼 A1 = 0.5, A2 = 0.5 Note: The best fit line (far right) explains all of the genetic variation. VG = VA.

Dominance Variation –VD V𝐺=V𝐴+V𝐷+V𝐼 The addition of alleles is not additive. Dominance is one type of variation where alleles interact (between sister alleles on other chromosome). The effect of an allele depends upon what it is paired with. Because of this dependence, the outcome of dominance variation is not entirely predictable - it is context dependent. This context disappears every generation because of meiosis. The pairing of an allele with a sister allele on another chromosome in forming a zygote is unpredictable. Because of this , the effects of dominance variation change every generation, and are not predictable.

Dominance Variation –VD V𝐺=V𝐴+V𝐷+V𝐼 A1 = 0.5, A2 = 0.5 Note: Adding a second copy of A2 does not change the phenotype. The Dominance Variation (VD) does not explain all of the Genetic Variation (VG). VG = VA + VD

Epistatic Effects –VI V𝐺=V𝐴+V𝐷+V𝐼 The effect of an allele at a locus is dependent the presence of an allele at another locus. The phenotype is dependent upon the allele at one locus interacting with an allele at another locus. Not a predictable outcome. Allele X may affect the phenotype one way in the presence of allele A, and affect the phenotype another way in the presence of allele B. Because of this dependence, the outcome of epistasis is not entirely predictable - it is context dependent. This context disappears every generation because of meiosis. When chromosomes independently assort and recombine, the pairings of alleles change. Because of this , the effects of epistasis change every generation, and are not predictable.

Narrow-Sense Heritability h2 or H2 ℎ2= 𝑉𝐴 𝑉𝑃 ℎ2= 𝑉𝐴 𝑉𝐺+𝑉𝐸 ℎ2= 𝑉𝐴 𝑉𝐴+𝑉𝐷+𝑉𝐼+𝑉𝐸 In determining heritability, only narrow-sense heritability is used, because only the variation due to additive effects permits predictions due to selection.

Heritability Determination Compare the best fit line of mid-parent trait to mid-offspring (mean) trait. How to determine heritability ℎ2= 𝑉𝐴 𝑉𝐺+𝑉𝐸 Heritability is considered in the narrow sense.

Very important in agricutlure Heritability Determination Very important in agricutlure

Heritability Determination But also useful in humans.

Selection of Quantitative Traits - Breeder’s eq. (R = h2S) Evolutionary Response (R = h2S) Allows us to predict how a trait will change over each generation R - the response to selection h2 – heritability (the superscript is symbolic, not functional) S – selection differential Bottom-line: Allows us to predict whether selection on a trait will cause a population to evolve Selection Differential: Fig 18a difference bw mean of populations and selected individuals Selection gradient: Fig 18b measures fitness vs trait of interest

Selection of Quantitative Traits - Breeder’s eq. (R = h2S) Need to determine differences in Reproductive Success and Survival Strength of Selection is the difference between selected individuals and the entire population Selection Differential (S): Difference between mean of selected individuals and the mean of entire population Selection for longer tails in a fictitious mouse population. Selection Differential: Fig 18a difference bw mean of populations and selected individuals Selection gradient: Fig 18b measures fitness vs trait of interest Selected individuals Non-breeders Entire population

Selection of Quantitative Traits - Breeder’s eq. (R = h2S) h2 – heritability – in the narrow sense – the fraction of the total phenotypic variation in the population that is due to the additive effects of genes. 1) Slope of the best fit line between the mid-parent value (x- axis) and the mid-offspring (mean) value (y- axis). 2) The rise over the run Selection Differential: Fig 18a difference bw mean of populations and selected individuals Selection gradient: Fig 18b measures fitness vs trait of interest Values on the x & y axes are the same as those in the body of the graph.

Selection of Quantitative Traits - Breeder’s eq. (R = h2S) Selection gradient - A measure of the strength of selection – related to the selection differential. 𝑺 𝒗𝒂𝒓 (𝒕𝒓𝒂𝒊𝒕) What is the variance? (see Phenotypic and Genetic variation in Brassica – Part I & II) 𝑠 2 = 𝑦 2 𝑛 Selection Differential: Fig 18a difference bw mean of populations and selected individuals Selection gradient: Fig 18b measures fitness vs trait of interest

Selection of Quantitative Traits - Breeder’s eq. (R = h2S) Selection gradient - A measure of the strength of selection Two ways to determine 1) 𝑷 𝒔 −𝑷 𝒗𝒂𝒓 (𝑷) where Ps = Mean of breeders and P = whole original population . 2) Slope of the line between the relative fitness of the breeders and the non-breeders. Selection Differential: Fig 18a difference bw mean of populations and selected individuals Selection gradient: Fig 18b measures fitness vs trait of interest Breeders have a fitness = 1 (n = 10) Non-breeders have a fitness = 0 (n = 20) Mean fitness of 30 mice = 0.33 Relative fitness is = 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 𝑚𝑒𝑎𝑛 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 For breeding mice- 1 0.33 = 3

Selection of Quantitative Traits - Breeder’s eq. (R = h2S) Directional: Fitness increases (or decreases) with value of trait Stabilizing: Intermediate individuals have the highest Fitness Disruptive: Extreme individuals have the highest Fitness Selection Differential: Fig 18a difference bw mean of populations and selected individuals Selection gradient: Fig 18b measures fitness vs trait of interest