CH22 Quantitative Genetics BIOL 2416 Genetics CH22 Quantitative Genetics

Quantitative Genetics Study of traits that exhibit a wide range of possible phenotypes Known as continuous traits (grayscale) As opposed to regular Mendelian discontinuous/discrete traits (black vs. white) Caused by multiple genes (a.k.a polygenic inheritance) Individual contributing loci called QTL = Quantitative Trait Loci May be additive Often multifactorial Due to genotype + environment

The simplest case: a trait determined by two loci RRCC (dark red) x rrcc (white) F1= all RrCc (intermediate red kernel color)

F1 x F1 Might expect a typical 9:3:3:1… Instead, with both R and C contributing to the same phenotype, will observe phenotypes falling into five different classes: 1:4:6:4:1 Obviously, not a case of simple Mendelian inheritance…

Note that 1:4:6:4:1 corresponds to the coefficients in the Binomial expansion (a+b)4: RRCC rrcc RRCc or RrCC RRcc or rrCC or RrCc rrCc or Rrcc

In reality… Much more complicated Many more genes 2 contributing genes > 5 phenotypic classes 3 contributing genes > 7 phenotypic classes etc Plus environmental factors Requires lots of statistics

Will want to ask the question: how much phenotypic variation (VP) is due to genetic variation (VG), and how much is due to environmental variation (VE)? Where VP = VG + VE

How do we measure traits in big populations? Pick a subset Must be LARGE enough to avoid sampling errors Must be RANDOMLY picked!!! Extrapolate to describe the entire population

How do we describe variation? Normal, (phenotypic) distributions look like symmetrical, bell-shaped curves All we need to describe these are the Mean ( ) A.k.a. average Center of the curve Add up values and divide by the number of values (n) Variance (S2) For each value add up deviation from the mean; square the sum of the deviations, and divide by n-1 Width of the curve

Same mean, three different variances (S2): Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

Standard Deviation

A theoretical normal distribution: within 3 std deviations from mean within 2 std deviations from mean within 1 std deviation from mean Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

Correlation Organisms are composites of many traits Some traits may be related, e.g. height and weight are measurements of size Genes and environmental factors that affect development likely to affect both height and weight There is a correlation between height and weight

Covariance Shows to what extent two variables change together Covariance values span a wide range of numbers: Zero means the two variables are uncorrelated Negative means they change out-of-sync: if one is above the expected value, the other will be below the expected value Positive means they change in-sync: if one is above the expected value, the other will also be above the expected value

Covariance Very similar to calculating variance, except instead of squaring the deviation from the mean for one of the variables, you multiply the deviation from the mean of one variable (x) by the deviation from the mean of the other variable (y): “co” means dealing with TWO variables

Correlation Coefficient (r) Covariance can be turned into a unitless, standardized version called the correlation coefficient Narrows the range of possible values (-1 to +1) Still measures the strength of the association between 2 variables, usually within a given individual Positive r = both variables increase The closer to +1, the stronger the positive correlation Zero r = no correlation/relationship Negative r = one increases, the other decreases The closer to -1, the stronger the negative correlation -1 0 +1 strong none strong negative positive

(n = 12) (mean x) (mean y) (square root of variance) (square root of variance) (positive number means x and y change in-sync) (close to +1 means a strong positive correlation: when one goes up, the other goes up as well)

(The closer r is to 0, the weaker the correlation) Fig. 23.6 Scatter diagrams showing the correlation of x and y variables none + weak + + - + strong (The closer r is to 0, the weaker the correlation) Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

Beware… Correlations say NOTHING about cause and effect!

To answer these quantitative questions, we must do regression analysis Correlation coefficient r is a qualitative, NOT a quantitative measure… can tell us about the strength of the association between variables, and whether the relationship is positive or negative, that’s IT Once we know there is a correlation, we may want to ask more specific questions E.g. if a father is 6 ft tall, what is the most likely height for his son? To answer these quantitative questions, we must do regression analysis Involves plotting real father-son height data points Finding line of best fit through the data The slope of this regression line is the regression coefficient shows how much son height is expected to increase for e.g. every 1 inch increase in dad height (0.5 inches if slope = 0.5)

Fig. 23.7 Regression of sons’ height on fathers’ height one father-son pair data point slope b Also equal to Regression line minimizes distance of individual data points to the line: y = a + bx y intercept a Peter J. Russell, iGenetics: Copyright © Pearson Education, Inc., publishing as Benjamin Cummings.

But to what extent is variation seen in a given trait genetic?

ANOVA ANalysis Of VAriance Powerful statistical technique “partitions” the variance into genetic and environmental variance Can answer questions like “How much of the variation in milk production among cows results from genotype differences, and how much results from environmental differences? Depending on the answer, we may want to focus on selective breeding or on optimizing the environment to try and increase milk production

Heritability The proportion of a population’s phenotype that is attributable to genetic factors Remember VP = VG + VE?

Broad-Sense Heritability Symbolized by H2 The proportion of the total phenotypic variance that is genetic Ranges from 0 to 1 0 means none of phenotypic trait variation in the population is due to (any kind of) genetic differences between individuals 1 means the phenotypic trait variation in the population is genetically determined

Broad-Sense Heritability Why do we care about this number? Used to estimate the importance of the environment Can tell if breeding programs in general might result in e.g. a herd of top milk-producers, or if you should concentrate on controlling the environment instead E.g. “(broad) heritability of IQ” is shorthand for “heritability of variations in IQ” Cannot answer meaningless question: “To what extent is an individual person’s IQ genetic?” (questions need to be population-specific) But can be used to answer meaningful (difficult…) question: “How much of the differences in IQ between people in a particular country at a particular time are caused by their genetic differences of any kind, and how much by their environments and life histories?” Heritability is NOT a fixed value. Again, it is population-specific: in a society where everyone has access to education, IQ will have a higher broad heritability (genetic component of IQ variation) than in a society where certain groups of people do not have equal access

Further partitioning the genetic component of phenotypic variance (VG): VG = VA + VD + VI VA = additive genetic variance Predicts how much additive alleles contribute to phenotypic variation in the next generation. (E.g. g = 2cm, G = 4cm, GG = 8cm, Gg = 6cm, gg = 4cm) VD = dominance variance Predicts how much non-additive dominant alleles contribute to phenotypic variation in the next generation. (E.g. BB and Bb individuals might have the exact same phenotype. But Bb would create greater phenotypic variation than BB in the next generation; if the B trait is more desirable, BB individuals would be more useful to the breeder). VI = interaction variance Predicts how much epistasis contributes to phenotypic variation in the next generation (e.g. BBee, Bbee, bbee = all yellow labs).

Narrow-Sense Heritability Recall that And recall that VG = VA + VD + VI But out of these, only VA (additive genetic variance) is under the direct control of natural selection VD: cannot select e.g. BB over Bb VI: cannot select e.g. BBee over bbee Natural selection “selects” the next generation’s phenotype We can use the VA part of VG to help us predict how similar a baby will be to its parents it is used for breeding purposes, to help select phenotypes for the next generation Narrow-sense heritability =

If narrow-sense heritability = 1 VP = VA phenotypic selection for producing the best next generation should be 100% effective

It is possible… that broad heritability = 1, but narrow heritability < 1 So this trait would be under strictly genetic control, but that does not mean phenotypic selection will be 100% effective Recap: broad heritability can tell us what proportion of the phenotypic variation in the population is due to variation in the genotypes narrow heritability can tell us how much a baby will look like its parents