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1. What is the genetic architecture and molecular basis of phenotypic variation in natural populations?

2. Why is there phenotypic variation in natural populations?

An introduction to quantitative genetics

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Monogenic traits (rare)- discrete binary characters- but modified by genetic and environmental background

Polygenic traits (common)- discrete (bristle number) or continuous (height) or binary (disease)- binary traits with a polygenic basis are often described by a threshold model

Types of traits

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�Finally, that from the uninterrupted concurrence of these causes or from these laws of nature, together with much time and with an almost inconceivable diversity of influential circumstance, organic beings of all the orders have been successively formed.�

Jean-Baptiste Lamarck 1802 in Recherches sur l'Organisation des Corps Vivans

History and origins of quantitative genetics

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�The hypothesis of Pangenesis, as applied to the several great classes of facts just discussed, no doubt is extremely complex, but so are the facts. The chief assumption is that all of the units of the body, besides having the universally admitted power of growing by self-division, throw off minute gemmules which are dispersed through the system. Nor can this assumption be considered as too bold, for we know from the cases of graft-hybridization that formative matter of some kind is present in the tissues of plants, which is capable of combining with that included in another individual, and of reproducing every unit of the whole organism. But we have further to assume that the gemmules grow, multiply, and aggregate themselves into buds and the sexual elements; their development depending on their union with other nascent cells or units. They are also believed to be capable of transmission in a dormant state, like seeds in the ground, to successive generations.�

Charles Darwin, 1868 in The Variation of Animals and Plants Under Domestication

Pangenesis

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�The Twins have a special claim upon our attention; it is, that their history affords means of distinguishing between the effects of tendencies received at birth, and of those that were imposed by the special circumstances of their after lives; in other words, between the effects of nature and nurture.�

Galton, 1876 The History of Twins, as a Criterion of the Relative Powers of Nature and Nurture. The Journal of the Anthropological Institute of Great Britain and Ireland 5: 391-406.

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The Mendelians versus the Biometricians

Mendelian Theorists

Discontinuous variationMacromutations

BatesonDe VriesPunnettJohannsen

Biometricians

Continuous variationSlight changes

WeldonPearson

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Ronald Fisher 1918 The correlation between relatives on the supposition of Mendelian inheritance. Trans. R. Soc. Edinburgh 52: 399�433.

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Castle-Wright estimator

ne=[�P1�P2�

2�Var �P1��Var �P2�]

[8Var �S�]

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Heritability � the proportion of phenotypic variation that is attributable to genotypic variation

Penetrance - is the percentage of individuals with a specific genotype that possess an associated phenotype. Categorical, e.g. Huntington's disease.

Expressivity - is the degree to which individuals with a specific genotype display the associated phenotype. Quantitative, e.g. psoriasis.

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Heritability � the proportion of phenotypic variation that is attributable to genotypic variation

Phenotype (P) = Genotype (G) + Environment (E)

Var(P) = Var(G) + Var(E) + Cov(G,E)

Broad-sense Heritability (H2) = Var(G) / Var(P)

Broad-sense heritability includes additive, dominance, epistatic variance along with maternal and paternal effects.

Genetic (G) = Additive (A) + Dominance (D) + Interactions (I)

Var(G) = Var(A) + Var(D) + Var(I)

Narrow-sense heritability (h2) = Var(A) / Var(P)

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Analysis of variance or regression (correlation)

H2 = Var(G) / Var(P)

Var(G) = Var(P) � Var(E)Var(E) = Var(F

1)

Var(P) = Var(F2)

h2 = r / br = the correlation coefficient or

Cov(X,Y) / Var(X) Var(Y)b = the coefficient of relatedness or the probability that at a random locus, the alleles there will be identical by descent.

What is the heritability if the correlation between brothers is 50%? What if the correlation is >50%?

Estimating Heritability

The square of the sample correlation coefficient, the coefficient of determination, is the fraction of the variance in y that is accounted for by a linear fit of x to y.

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Heritability from Twins

For comparison of monozygotic (MZ) and dizygotic (DZ) twins:

rmz

= A + C

rdz

= 0.5 * A + C

A = 2*(rmz

- rdz

)

C = rmz

� A

E = 1 - rmz

Where the components of variance are A for additive, C for common environment and E for unique environment

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What explains heritable variation in natural populations?

Mutation and genetic drift

Mutation-selection balance

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What explains heritable variation in natural populations?

Mutation and genetic drift

Lynch and Hill (1986)2NV(m) < Var(G) < 4NV(m)N = effective population sizeV(m) = the new variance from mutation added to the population every generation

Mutation-selection balance

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What explains heritable variation in natural populations?

Mutation and genetic drift

Lynch and Hill (1986)2NV(m) < Var(G) < 4NV(m)N = effective population sizeV(m) = the new variance from mutation added to the population every generation

Mutation-selection balance

Mutation increases Var(G)Selection decreases Var(G)R = h2SS is the selection differential and R is the selection response.Var(G) = sqrt (2N Var(m) Var(s)) for mutations of small effectVar(G) = 4Nu Var(s) for mutations of large effect

Var(s) = variance in the fitness function 21

�If x be the proportion of haemophilic males in the population, and f their effective fertility, that is to say their chance, compared with a normal male, of producing offspring, then in a large population of 2N, (1�f )xN haemophilia genes are effectively wiped out per generation. The same number must be replaced by mutation. But as each of the N females has two X-chromosomes per cell, and each of the N males one, the mean mutation rate per X-chromosome per generation is 1/3(1�f )x, or if f is small, a little less than 1/3(x). Hence we have only to determine the frequency of haemophilia in males to arrive at the approximate mutation rate.�

JBS Haldane 1935 The rate of spontaneous mutation of a human gene. J. Genet. 31: 317-326.

Estimating the mutation rate for monogenic traits

AA = 1, Aa = 1, aa = 1-s, u = mutation rate from A to a, then

The equilibrium frequency: q = sqrt(u/s)If Aa = 1-hs: q = u/(hs)

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Estimating the mutation rate for polygenic traits

Mukai (1964) The genetic structure of natural populations of Drosophila melanogaster. I. Spontaneous mutation rate of polygenes controlling viability. Genetics 50: 1-19.

Mutation accumulation scheme

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Control viabilities

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Mutation accumulation causes a decline in viability

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Assuming a linear increase in the number of mutation over time and interactions between mutations are not large the rate of polygenic mutation for viability is:

a p=vo�v

�a2��a

2� p=�G

2

a = average effect sizev = viability indexsigma_G = among line genetic variancesigma_a = variance in effect sizep = average number of mutationsdifference in viabilities per generations = 0.126increase in variance per generation = 0.113

Estimating mutational parameters

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Conclusion:1. Mutation rate is very high, 20x that of lethals

supported by frequency of mutation free lines2. Mutations are predominantly of small effect

A high mutation rate for small effects