BIO 5910: Homework Assignment 6
Due on November 26, 2013
1. An experiment testing flies for the ability to learn to fly toward the smell of potato is
repeated three times. In the first experiment the first fly to succeed is the 13th, in the
second experiment it is the 8th, and in the third experiment it is the 12th. Compare with
the likelihood of q = 0.1.
2. Color-blindness is due to a recessive allele that appears on the X chromosome. If the
color-blindness allele has frequency p, a fraction p of males will show the phenotype, and
a fraction p2 of females will show the phenotype (because they require two copies). We
wish to estimate the fraction p from a sample of 1000 males, 90 of whom are color blind,
and 1000 females, 13 of whom are color blind.
a. Estimate p using just the males.
b. Estimate p using just the females.
c. Write the likelihood function for males and females together.
d. Evaluate this likelihood function at a few interesting values of p you might have
encountered. Where do you think the maximum is? If you are very determined, it
is possible to solve for the maximum.
3. Consider the following data describing change in a bacterial population.
Colony Old population (bt ) New population (bt+1 )
1
0.47
0.95
2
3.3
6.4
3
0.73
1.5
4
2.8
5.6
5
1.5
3.1
6
0.62
1.2
a. Find r2 for the line bt+1 = 2bt . Graph the data and the line.
b. Find the best fitting line, and compare with mathematically idealized model. Which
makes more sense?