Biostat 551
Lab2

Genetic Covariance, Heritability, and Detection of Major Genes

Introduction: This lab covers several topics in chapters 7 and 13 of the Lynch and Walsh text. Problem 1 is a non-computer problem, but the others all require some computing (but no special statgen programs). The data sets appear in a companion document. I have worked through each of these problems. If you run into any problems or need help getting started, feel free to email me at amy@stat.washington.edu.

Problem 1: (Covers material in the Lynch and Walsh text, Ch. 7, pp 141- 145). A study of trait values found that, for the trait of interest, the additive genetic variance was 63, and the additive-additive genetic variance was 8.2.

1.Estimate the genetic covariance between the trait values for a pair of half-siblings in this population.
2. Estimate the genetic covariance between the trait values for a pair of second cousins from this population.
3. Consider estimating the genetic covariance between the trait values for a pair of full-sibs from this population. Is this possible with only the information given above? What other information would you need?

Problem 2: This problem concerns the material on pages 170-171 of the text. As part of a study investigating the genetics of height in Cairn Terriers (this is the breed of Toto in the Wizard of Oz), twenty sib-pairs (males) were measured.

1.Assuming that the additive genetic variance is the dominant source of phenotypic covariance for height in Cairn Terriers, estimate the (narrow-sense) heritability of this trait.
2. Now assume that the first ten sib-pairs (pairs 1-10) consisted of dogs
that been raised on a standard diet of dry dog food while the remaining pairs (11-20) were raised on "Dr. Bob's Miracle Grow Munchies". Use linear regression (or another technique) to estimate the effect of the "Miracle Grow" dog food, then subtract out that effect and redo the analysis you did in part A. What has happened to your estimate of the heritibility? Why?

Problem 3: This problem examines several of the methods for detecting major genes that appear in Chapter 13 of the text.

1.Commingling Analysis (Chapter 13, pp. 359-363 and Appendix 4, pp. 863-865) The data set for this problem consists of pest-resistance scores for 100 corn plants.

Perform a likelihood ratio test to determine whether there appears to be a major QTL associated with this trait. Specifically, you should be comparing a no-QTL model (i.e. all trait values come from a single normal distribution) with a one-QTL model (i.e. the trait values come from a mixture of three normal distributions). You will need to program an EM algorithm to get the maximum likelihood estimators for gene frequencies, means of the three normal distributions, and variance of the three normal distributions. This is explained in detail in Appendix 4 of the text. You may assume that the population is in Hardy-Weinburg equilibrium and that (in the case of the one-QTL model) all three normal distributions have the same variance.

When you have done the analysis, answer the following questions:

3.1.1. For the one-QTL model, what are the maximum-likelihood estimates for the proportions of individuals in each genotypic class (QQ, Qq, and qq)? What are the mean scores for corn plants in each class? Based on your findings, does the trait appear to be strictly additive?
3.1.2. What is the value of your chi-square test statistic? How many degrees of freedom?
3.1.3. What is the p-value for your test? What do you conclude?

2. Fains's Test (Chapter 13, pp. 355-357) The fictional Zuzububu plant produces one short-lived flower each year. The length of time the flower lasts seems to be a genetic trait of the plant that produces the flower. To investigate whether this trait seems to be controlled my one major gene 2 or many genes of small effect, horticulturists have collected flowering data from four sibling plants in each of twenty-five families. For each plant in the study, the horticulturist measured the time (in hours) that the flower bloomed. Perform Fain's test to see if the data appear to be consistent with a major gene model. You should turn in:

3.2.1. A scatterplot of the data you used in your regression, plotted along with the best fit quadratic function.
3.2.2. The equation of the best-fit quadratic and R2 value. 3.2.3. A test for significance and conclusion.

3. MGI (Chapter 13, p. 357). Hair color of the mythic Swamp Bear is always some shade of brown. Scientists studying the Swamp Bear are interested in color inheritance. To make the color quantitative, they have developed an index, I, that measures the strength of the coloration. Normal values of I range from 5 (light, sandy brown) to 15 (deep brown, almost black). The data set for this problem is a list of index values for ten parent-offspring Swamp Bear trios. Using that data set, calculate the Major-gene Index (MGI) for alpha = 0.5, 1, and 2. Are these data more consistant with a model in which there is a major gene segregating or a model in which the trait is influenced by many genes of small (additive) effect?