# Quantitative Genetics Exercise

## Precis coenia eyespots

readings - introduction - exercise instructions - homework - instructor hints

Note: This project was originally conducted as part of a study by Fred Nijhout and Susan Paulsen at Duke University.  Butterfly wings were preserved in plastic and students were able to measure traits with a ruler.

http://www.treytronics.org/~paulsen/butterflyLab/butterflyLab.html

(PLEASE Email jvondras [at] mbc [dot] edu if you use this for a class)

Brakefield, P.M. et al. 1996. Development, plasticity and evolution of butterfly eyespot patterns. Nature. 384:236-242.

Nijhout, H.F. 1996. Focus on butterfly eyespot development. Nature. 384: 209-210.

### [Coming soon : more background for instructors & students]

Quantitative traits: do not follow simple Mendelian dominance patterns, but alleles interact to produce a range of phenotypes.

Today we will study how evolutionary biologists analyze selection for characters that are affected by a multitude of loci (continuous traits). Today's goal is to illustrate the mechanism for predicting the response to selection  when there are many genes affecting the character on which selection is occurring . This subject falls under the broad heading of Quantitative Genetics

Heritability is the proportion of phenotypic variance that is additive. If a character has no additive genetic variance in a population, it will not be inherited from parent to offspring. Your text describes the following intuitive explanation of heritability.

"Consider a parent that differs from the population by a certain amount. If its offspring also deviate by the same amount, heritability is 1.0; if the offspring have the same mean as the population, the heritability is 0.0; if the offspring deviate from the mean in the same direction as their parents but to a lesser extent, heritability is between 0.0 and 1.0. "

Because biologists often don’t know what alleles an individual has, or how those alleles contribute to phenotype, an indirect method of estimating additive genetic variance is used.
We will take the measurements necessary to calculate the heritability of characters in the wing pattern of the buckeye butterfly, Precis coenia .

### Exercise Instructions

• Choosing characters
• First familiarize yourself with the wing patterns of P. coenia using the sample wings provided. Learn to distinguish between the forewing and hindwing and between the dorsal and ventral surfaces.
• Choose the character for which you will estimate heritability. The character must be measurable with a ruler. Possible characters include the width of the various eyespots, the distance between spots, the distance from a spot to the edge of the wing etc.
• For a character to be heritable, it must be genetically variable. Therefore, try to ensure that your chosen character is variable by measuring a few of the sample individuals.
• Data collection
• There are 10 mother butterflies. Each mother has 10 offspring. Measure the phenotypes of all the mothers and 4 male and 4 female progeny from each mother.

### Calculations

For two variables x (parental value) and y (average value for the offspring of that parent), the regression coefficient (bxy ) is defined as the ratio:

where covxy is the covariance between x and y, and measures the degree to which parents and offspring "covary",  and var x = the variance of the parental measure x.

Use the formulas below to calculate the variances and covariances.

Variance is the average squared deviation from the population mean

Covariance is the product of the deviation from the mean of two different variables (x and y)

### Homework  (or in class)

• Compute the regression coefficient (bxy).
• Calculate the heritability. The heritability is equal to twice the slope of the regression line.
• For each character measured graph the mean value of the character in the offspring (y-axis) versus the value of the character in the mother (x-axis).
• The line of best fit for  the relationship between the parents and offspring has a slope equal to the regression coefficient and passes through the point (x = mean of mother's character values, y = mean of offspring mean character values). Draw this line on your graph.
• Succinctly answer the following questions:
• Imagine that 1/4 of your population with the largest characters could not reproduce.
• Describe a selective scenario which may result in this failure.
• Do you think that the method would be a valid way to predict selection on this character over the next 5 years? 50 years? 1000 years? Explain your reasoning.

### Instructor Hints

A similar project to measure heritability in parent/offspring regression could be done in conjunction with an artificial selection lab on Brassica or Drosophila, for example.