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IV. Variation in Quantitative Traits A. Quantitative Effects

IV. Variation in Quantitative Traits A. Quantitative Effects. IV. Variation in Quantitative Traits A. Quantitative Effects - the more factors that influence a trait (genetic and environmental) , the more 'continuously variable' the variation in that trait will be.

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IV. Variation in Quantitative Traits A. Quantitative Effects

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  1. IV. Variation in Quantitative Traits A. Quantitative Effects

  2. IV. Variation in Quantitative Traits A. Quantitative Effects - the more factors that influence a trait (genetic and environmental) , the more 'continuously variable' the variation in that trait will be.

  3. IV. Variation in Quantitative Traits A. Quantitative Effects - For instance, a single gene trait, with two alleles and incomplete dominance, can only have three phenotypes (variants). A two gene trait with additive effects (height ‘dose’) can make 5 phenotypes (‘dose’ = 0, 1, 2, 3, 4), and so forth.

  4. IV. Variation in Quantitative Traits A. Quantitative Effects - the more genes that influence a trait, the more 'continuously variable' the variation in that trait will be. - For instance, a single gene trait, with two alleles and incomplete dominance, can only have three phenotypes (variants). AA, Aa, aa (Tall, medium, short) However, a two-gene trait with incomplete dominance at both loci can have nine variants: AA, Aa, aa X BB, Bb, bb - So, as the number of genes affecting a trait increase, the variation possible can increase multiplicatively.

  5. IV. Variation in Quantitative Traits • A. Quantitative Effects • - the more genes that influence a trait, the more 'continuously variable' the variation in that trait will be. • - For instance, a single gene trait, with two alleles and incomplete dominance, can only have three phenotypes (variants). AA, Aa, aa (Tall, medium, short) However, a two-gene trait with incomplete dominance at both loci can have nine variants: AA, Aa, aa X BB, Bb, bb • So, as the number of genes affecting a trait increase, the variation possible can increase multiplicatively. • If there are environmental effects, then the distribution of phenotypes can be continuous.

  6. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance

  7. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance - The phenotypic variation that we see in continuous traits is due to a number of factors that can be "lumped" as environmental or genetic. V(phen) = V(env) + V(gen)

  8. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance - The phenotypic variation that we see in continuous traits is due to a number of factors that can be "lumped" as environmental or genetic. V(phen) = V(env) + V(gen) - Actually, even this is a gross simplification, because it does not recognize the contribution that Genotype-by-Environment interactions can have. V(phen) = V(e) + V(g) + V(e*g)

  9. - Actually, even this is a gross simplification, because it does not recognize the contribution that Genotype-by-Environment interactions can have. V(phen) = V(e) + V(g) + V(e*g) AND THESE CAN BE VERY IMPORTANT: GENOTYPE 1 GENOTYPE 2 PHENOTYPE ENV 1 ENV 2

  10. The "direct effect" of environment would compare mean phenotype of organisms in Env 1 vs. mean phenotype in Env 2. There is no difference. GENOTYPE 1 GENOTYPE 2 PHENOTYPE ENV 1 ENV 2

  11. The "direct effect" of 'genotype' would compare mean phenotype of Genotype 1 vs. mean phenotype of Genotype 2. There is no difference. GENOTYPE 1 GENOTYPE 2 PHENOTYPE ENV 1 ENV 2

  12. But there is a SIGNIFICANT "genotype x environment" interaction. The effect of environment on the phenotype depends on the genotype. This important component of variation is often obscured in simplistic direct models. GENOTYPE 1 GENOTYPE 2 PHENOTYPE ENV 1 ENV 2

  13. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance - The phenotypic variation that we see in continuous traits is due to a number of factors that can be "lumped" as environmental or genetic. V(phen) = V(env) + V(gen) - Actually, even this is a gross simplification, because it does not recognize the contribution that Genotype-by-Environment interactions can have. V(phen) = V(e) + V(g) + V(e*g) - Ultimately, the goal of evolutionary studies is to determine the contribution of genetic variation, because this is the only variation that is heritable and can evolve. “Broad-sense” heritability = Vg/Vp

  14. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation

  15. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation - Even the genetic variation is more complex than one might think. There is variation due to 'additive' genetic variance, 'dominance' genetic variance, 'epistasis', and a variety of other contributors (sex linkage) that can be modeled. V(g) = V(a) + V(d) + V(ep)

  16. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation - Even the genetic variation is more complex than one might think. There is variation due to 'additive' genetic variance, 'dominance' genetic variance, 'epistasis', and a variety of other contributors that can be modeled. - We will concern ourselves with 'additive variation' Think of an individual that is AA. If the 'A' allele is adaptive, then their fitness will be higher than the mean fitness of the population. Their offspring, as a consequence of inheriting this adaptive gene, will also have a higher fitness than the population, as a whole. This allele 'adds' fitness. 2 A’s (AA) adds more…

  17. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Broad-sense (H) = V(g)/V(p) - difficult to measure

  18. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Broad-sense (H) = V(g)/V(p) - difficult to measure - Narrow-sense (h2) = V(a)/V(p)

  19. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Broad-sense (H) = V(g)/V(p) - difficult to measure - Narrow-sense (h2) = V(a)/V(p) – easier to measure

  20. Calculate the average phenotype of two parents, and calculate the average phenotype of their offspring. Graph these points across sets of parents and their offspring. The slope of the best-fit line (least-squares linear regression) describes the strength of the “heritability” of the trait.

  21. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Calculating Heritability from Selection Experiments - Consider a variable population, with mean phenotype = x.

  22. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Consider a variable population, with mean phenotype = x. - Select organisms with a more extreme phenotype (x + 5) to breed.

  23. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Consider a variable population, with mean phenotype = x. - Select organisms with a more extreme phenotype (x + 5) to breed. - The selection differential, S = (mean of breeding pop) - (mean of entire pop) S = (x + 5) - (x) = 5

  24. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Consider a variable population, with mean phenotype = x. - Select organisms with a more extreme phenotype (x + 5) to breed. - The selection differential, S = (mean of breeding pop) - (mean of entire pop) S = (x + 5) - (x) = 5 - Suppose the offspring mean phenotype = (x + 4)

  25. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Consider a variable population, with mean phenotype = x. - Select organisms with a more extreme phenotype (x + 5) to breed. - The selection differential, S = (mean of breeding pop) - (mean of entire pop) S = (x + 5) - (x) = 5 - Suppose the offspring mean phenotype = (x + 4) - The Response to Selection = R = difference between the whole original population and the offspring: R = (X + 4) - (x) = 4

  26. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Consider a variable population, with mean phenotype = x. - Select organisms with a more extreme phenotype (x + 5) to breed. - The selection differential, S = (mean of breeding pop) - (mean of entire pop) S = (x + 5) - (x) = 5 - Suppose the offspring mean phenotype = (x + 4) - The Response to Selection = R = difference between the whole original population and the offspring: R = (X + 4) - (x) = 4 - The heritability (narrow sense) = R/S = 4/5 = 0.8. because R = h s 2

  27. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Consider a variable population, with mean phenotype = x. - Select organisms with a more extreme phenotype (x + 5) to breed. - The selection differential, S = (mean of breeding pop) - (mean of entire pop) S = (x + 5) - (x) = 5 - Suppose the offspring mean phenotype = (x + 4) - The Response to Selection = R = difference between the whole original population and the offspring: R = (X + 4) - (x) = 4 - The heritability (narrow sense) = R/S = 4/5 = 0.8. - The closer the offspring are to their particular parents (in amount of deviation from the whole population), the greater the heritability and the more rapid the response to selection.

  28. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - Consider a variable population, with mean phenotype = x. - Select organisms with a more extreme phenotype (x + 5) to breed. - The selection differential, S = (mean of breeding pop) - (mean of entire pop) S = (x + 5) - (x) = 5 - Suppose the offspring mean phenotype = (x + 4) - The Response to Selection = R = difference between the whole original population and the offspring: R = (X + 4) - (x) = 4 - The heritability (narrow sense) = R/S = 4/5 = 0.8. - The closer the offspring get to their particular parents (in amount of deviation from the whole population), the greater the heritability and the more rapid the response to selection. - This quantifies the evolutionarily important genetic variance (heritability is also V(add)/V(phen), remember?

  29. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - This quantifies the evolutionarily important genetic variance (heritability is also V(add)/V(phen), remember)? - So, through a series of selection experiments, we can determine how responsive a trait is to selective pressure.

  30. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - This quantifies the evolutionarily important genetic variance (heritability is also V(add)/V(phen), remember)? - So, through a series of selection experiments, we can determine how responsive a trait is to selective pressure. As selection proceeds, most variation is environmental or dominance and response to selection slows.

  31. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability - This quantifies the evolutionarily important genetic variance (heritability is also V(add)/V(phen), remember)? - So, through a series of selection experiments, we can determine how responsive a trait is to selective pressure. As selection proceeds, most variation is environmental or dominance and response to selection slows. - So, counterintuitively, adaptive traits may show low heritability...they have already been selected for, and most of the phneotypic variation NOW is probably environmental. EXAMPLE: Polar bears all have genetically determined white fur - it has been adaptive and has become fixed in their population. But they still vary in coat color (phenotype) as a result of dirt, etc. But the offspring of dirty bears will be just as white as the offspring of clean bears... no response to selection for 'dirty bears' because all the variation is environmental at this point.

  32. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability 4. Misuses of Heritability: Heritability is a property of a trait, in a given population, in a given environment. It provides no insight for comparisons across populations in different environments…. Why?

  33. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability 4. Misuses of Heritability: Heritability is a property of a trait, in a given population, in a given environment. It provides no insight for comparisons across populations in different environments…. Why? Genotype x environment interactions…

  34. Consider the growth of these individual (and genetically different) plants in a common garden in Stanford, CA. These differences are GENOTYPIC DIFFERENCES, because the environmental variation is “0” (same environment).

  35. Can we use these data to predict how these genotypes would grow, relative to one another, in another environment? Consider the growth of these individual (and genetically different) plants in a common garden in Stanford, CA. These differences are GENOTYPIC DIFFERENCES, because the environmental variation is “0” (same environment).

  36. No. Although there is high heritability in BOTH populations for plant height. Can we use these data to predict how these genotypes would grow, relative to one another, in another environment? Consider the growth of these individual (and genetically different) plants in a common garden in Stanford, CA. These differences are GENOTYPIC DIFFERENCES, because the environmental variation is “0” (same environment).

  37. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability 4. Misuses of Heritability: Heritability DOES NOT equal “genetically based” Many traits that are determined genetically are fixed, with no genetic variation, and so have very low heritability.

  38. IV. Variation in Quantitative Traits A. Quantitative Effects B. Partitioning Variance 1. Partitioning Phenotypic Variance 2. Partitioning Genetic Variation 3. Heritability 4. Misuses of Heritability: Heritability DOES NOT equal “genetically based” Many traits that are determined genetically are fixed, with no genetic variation, and so have very low heritability. Finally, a take on twin studies: Some social psychologists beileve that we can determine “heritability” or “genetic contribution” to a triat by examining the degree of similarity between ‘monozygotic’ (identical) and ‘dizygotic’ (fraternal) twins.

  39. Finally, a take on twin studies: Some social psychologists beileve that we can determine “heritability” or “genetic contribution” to a triat by examining the degree of similarity between ‘monozygotic’ (identical) and ‘dizygotic’ (fraternal) twins. If twins are reared apart (so that the environments are presumed to be randomized and ‘equal’ across the populations), then traits that show greater correlations between mz twins suggest a greater degree of genetic involvement.

  40. Finally, a take on twin studies: Some social psychologists beileve that we can determine “heritability” or “genetic contribution” to a triat by examining the degree of similarity between ‘monozygotic’ (identical) and ‘dizygotic’ (fraternal) twins. If twins are reared apart (so that the environments are presumed to be randomized and ‘equal’ across the populations), then traits that show greater correlations between mz twins suggest a greater degree of genetic involvement. Problem: You don’t know that the environments are similar or different. The Jim twins: http://science.howstuffworks.com/genetic-science/twin1.htm

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