Quantitative Genetics: Approaches and Definitions

Biology 105 - Evolution Dr. Theodore Garland, Jr. 17 Nov. 2015: "Quantitative Genetics" Reading is pages 293-8, 318-331, 7, 43-5, 49, 179, 325-9, 667 in Bergstrom, C. T., and L. A. Dugatkin. 2012. Evolution. W.W. Norton and Company.

Four Approaches for Studying Adaptation: • 1. Comparisons of Species (or populations) • Shows what has happened in past evolution • 2. Biology of Natural Populations: • extent of individual variation (repeatability)heritability and genetic correlationnatural and sexual selectionfield manipulations and introductions • Shows present evolution in action • 3. Selection Experiments • Shows, experimentally, what might happen during future evolution • 4. Comparison of Real Organisms with Theoretical Models • Shows how close selection can get to producing optimal solutions Evolution

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 Fitness, e.g., survivorship,age at first reproduction, fecundity, # of mates

Definitions: • Phenotype = any measurable trait (height, metabolic rate, I.Q., milk yield, litter size) • Genotype = genetic material, 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

Adaptive phenotypic evolution consists of two parts: r = h2s The “breeders equation”

Adaptive phenotypic evolution consists of two parts: r = h2s 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

r = h2s h2 = 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 We will define this later.

r = h2s 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

X r = h2s Distribution of a trait within a population, before selection Body Mass

Select a subset to breed X X r = h2s before selection after selection Body Mass s Difference between mean before and after selection = s, the directional selection differential. s indicates strength of selection acting to change (increase) the average value of a trait.

Select a subset to breed X X r = h2s before selection after selection Body Mass What will their offspring look like? It depends on h2

Select a subset to breed Body Mass X X X r = h2s before selection after selection Body Mass offspring h2 = 0

Select a subset to breed Body Mass X X X r = h2s before selection after selection Body Mass offspring h2 = 1

Select a subset to breed Body Mass X X X r = h2s before selection after selection Body Mass Difference between mean before selection and mean of offspring = r,the response to selection= evolution across one generation. offspring h2 = 0.5

Select a subset to breed Body Mass X X X r = h2s before selection after selection Body Mass Realized heritability can be estimated be rearranging equation as: r/s = h2 So, if you selectively breedfor a trait for one or moregenerations then you canestimate heritability. offspring h2 = 0.5

Variation in most phenotypic traits is continuous or quantitative, not discrete like Mendel's peas. Among individuals within a population, some of the variation is caused by: 1. environmental differences experienced since fertilization of egg (or even before) 2. genetic differences at multiple loci

Variation in most phenotypic traits is continuous or quantitative, not discrete like Mendel's peas. Among individuals within a population, some of the variation is caused by: 1. environmental differences experienced since fertilization of egg (or even before) 2. genetic differences at multiple loci Phenotypic variance of a population is calculated as:  (Xi - X)2 ---------------------- N - 1 (standard deviation is square root of variance)

Variances are additive, but standard deviations are not. So, quantitative genetics uses variances, even though the units (squared) are not so intuitive. It also tends to deal with ratios of variances,such as “heritabilities.”

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 highest 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) c. the "environmental sensitivity" of a genotype

Phenotypic variance of a population can be partitioned into various components. Simplest partitioning: VP = VG+ VE So, can add term for G-E interaction: VP = VG+ VE+ VG X E

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 d. you always rent apartments near an all-you-can-eat buffet

Phenotypic variance of a population can be partitioned into various components. Simplest partitioning: VP = VG+ VE Add term for G X E interaction: VP = VG+ VE+ VG X E Add another term for GE correlation: VP = VG+ VE+ VG X E+ VGEcorr Thus, easiest to make measurements in controlled environments, with little or no variation among where individuals live, and hence eliminate these variance components.

However, resulting narrow-sense heritabilities may or may not be so relevant to natural populations. Hypothetical example: Narrow-sense heritability is higher when Environmental variation is reduced, as it might be in a laboratory vs. in the wild.

What do the data say for narrow-sense heritabilities measured in lab versus wild? 1996, Evolution 50:2149-2157.

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 practice, for practical reasons, workers often just lump VG X E and VGEcorr into VE,i.e., they do not try to estimate them separately.

Broad-sense heritability = VG/VP Common for studies of human beings But not all genetic variance can be passed onto offspring, only the additive genetic variance. So, a more useful partitioning for some purposes is: VP = VA+ VD+ VI + VE+ VG X E+ VGEcorr 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

Dominance Additivity Phenotype Phenotype PartialDominance Overdominance Phenotype Phenotype

Narrow-sense heritability = VA/VP This is the heritability in the breeder's equation: r = h2s Narrow-sense heritability is viewed as the single most important descriptive statistic about the quantitative genetics of a given trait in a given population. It indicates the evolutionary potential of the trait. How do we estimate narrow-sense heritability? Examine the resemblance of relatives ...

Least-squares linear regression slope = narrow-sense heritability N = 50 If have no maternal effects or common-family environ-mental effects

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

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. This would avoid complications of maternal effects. Studies of Galapagos finches have estimated heritability in several ways …

Body Mass Wing Length Tarsus Length Bill Length Bill Depth Bill Width @ 4 mm Boag, P. T. 1983. The heritability of external morphology in Darwin's ground finches (Geospiza) on Isla Daphne Major, Galapagos. Evolution 37:877-894.

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 design" allows estimation of narrow-sense heritability. Specifically, the among-sire component of variance is proportional to additive genetic effects (if have no non-genetic paternal effects). Can also estimate realized narrow-sense heritability from a selective breeding experiment because:r/s = h2

Biology 105 - Evolution Dr. Theodore Garland, Jr. 17 Nov. 2015: "Selection Experiments & Experimental Evolution - 1"

Four Approaches for Studying Adaptation: • 1. Comparisons of Species (or populations) • Shows what has happened in past evolution • 2. Biology of Natural Populations: • extent of individual variation (repeatability)heritability and genetic correlationnatural and sexual selectionfield manipulations and introductions • Shows present evolution in action • 3. Selection Experiments • Shows, experimentally, what might happen during future evolution • 4. Comparison of Real Organisms with Theoretical Models • Shows how close selection can get to producing optimal solutions

Types of Experimental Manipulations Surgical manipulations Hormonal manipulations Pharmacological manipulations Organ or embryo transplants Mutagenesis Transgenesis, Knockouts Selective breeding Experimental evolution "phenotypic engineering" "genetic engineering"

Selection Experiments: • The earliest form of “genetic engineering” • An experimental way to study “evolution in action” • A way to produce “useful” organisms • The most direct and convincing test of whether a trait shows any additive genetic variance in the population • A way to probe the interrelations among traits • A way to test hypotheses about trade-offs and constraints

Selection Experiments: 7. A way to find the genes that underlie phenotypic variation. Crossing a selected population with a non-selected or oppositely-selected population facilitates genetic mapping.

Selection Experiments: 8. A powerful way to demonstrate mechanism, i.e., how organisms work: a. Select on an organismal trait b. Observe correlated response in lower- level trait that you hypothesize causes the organismal difference c. Test that hypothesis by performing a second experiment, selecting on the lower-level trait d. Does the organismal trait change as predicted?

Hypothetical Example a. Select for long life span in mice b. Observe correlated increase in anti-oxidant enzyme activities c. Select for high anti-oxidant enzyme activities (e.g., biopsy individuals to score their phenotype and then choose breeders) d. Does life span increase as predicted?

Types of "Selection Experiments" Artificial Selection (Selective Breeding): Captive populations in which individuals in each generation are measured for a phenotypic trait (or combination of traits) that is of interest. Some top or bottom fraction of individuals is then chosen as the breeders to produce the next generation. This is called truncation selection or mass selection. One variation is taking the highest-scoring (or lowest-scoring) male and female from within each family ("within-family selection"). Within-family selection increases the effective population size, reduces rate of inbreeding, and helps to eliminate confounding influences of some maternal effects. But, it also reduces the possible intensity of selection as compared with "mass selection," which involves choosing breeders without regard to their family membership.

Laboratory Natural Selection (Experimental Evolution): Individual phenotypes are not measured each generation, nor are breeders specifically chosen by the investigator. Rather, a freely breeding population is exposed to altered environmental conditions, such as different temperatures or salinities, or to altered husbandry conditions, which could favor changes in demographic schedules. Assuming that additive genetic variance exists for relevant traits, the population will adapt to the new conditions. Most common with non-vertebrates, including Drosophila, bacteria, and viruses, but have also been employed with vertebrates: Barnett and Dickson housed mouse colonies at room temperature or around 0o Celsius.

Barnett, S. A., and R. G. Dickson. 1984b. Milk production and consumption and growth of young of wild mice after ten generations in a cold environment. Journal of Physiology 346:409-417. This is in 174 2016 so should replace with a bacteria or fly example. In only 10 generations, "Eskimo mice" evolved to be larger and to have more body fat for their body size.

Intentional Field Introductions & Manipulations: David Reznick's guppies and their predators in Trinidad Anolis lizards or their predators introduced to Caribbean islands (Schoener, Losos, Spiller) "Accidental" Introductions & Manipulations: Drosophila cline studied by Ray Huey and colleagues House Sparrows Adaptations of fishes to ponds heated by nuclear power plants Adaptations of plants to living on mine tailings

Premise of Selective Breeding 1 • Many different genetic loci affect a complex trait • At each locus, we might have multiple alleles: "+" alleles "–" alleles "o" alleles • For body mass at a given age, + alleles might be those that increased birth mass, appetite, growth rate, masses of individual organs, amount of body fat, or reduced basal metabolic rate • – alleles would tend to do the opposite • o alleles would have no effect

Premise of Selective Breeding 2 • Ignoring environmental effects to keep this example simple. • 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 …

Premise of Selective Breeding 3 + – + + o + + + + o+ + + ++ + o + + + – + + + + + + + • Genotype of Large Individual(genetic score = +21) • Genotype of an "Average" Individual(genetic score = 0) • Genotype of Small Individual(genetic score = –18) – + o o o o o – o o o o o oo o + o o o o – o o o o + o – – – –+ o – – – – –o – –+ – – – o – – – + – o – – –

Premise of Selective Breeding 4 • Summing across all loci and all individuals in the population, let's assume we have about: 1/3 + alleles 1/3 o alleles 1/3 –alleles

Premise of Selective Breeding 5 • Hypothetical "Gene Pool" of Population: + – o + – o + – o + – o + – o + – o + – o + – o + – o + – o + – o + – o+ – o + – o+ – o+ – o+ – o+ – o • Now we could choose the largest individuals to be the parents of the next generation, whose gene pool will thus be altered …

Quantitative Genetics: Approaches and Definitions