Evolution – Biology 4250 Hardy-Weinberg Problems

**SHOW ALL YOUR WORK ! ! !** Round answers to the nearest two significant
digits past the decimal point. Unless otherwise specified, assume populations
are in a fictitious H-W equilibrium.

1. In a population with 2 alleles for a particular locus (D and d), the frequency of the D allele is 0.91.

a) What is the frequency of the d allele? **
1 - .91 = ..09**

b) What is the frequency of homozygous dominant individuals
in the population? **.91 ^{2}
= .83**

c) What is the frequency of homozygous recessive individuals
in the population? **.09 ^{2}
= .0081**

d) What is the frequency of heterozygotes in the population? **
1 - .8381 = .16**

2. The fraggles are a population of mythical, mouselike creatures
that live in undergrown tunnels and chambers beneath a large vegetable
garden that supplies their food. Of the 154 fraggles in this population,
93 have green fur and **61*** have gray fur. Green fur is controlled by a
dominant allele F and gray fur by a recessive allele f.

a) What is the frequency of the gray allele f?
**
√61/154 = .63**

b) What is the frequency of the green allele F? **
1 - .63 = .37**

c) How many fraggles are heterozygous (Ff)? **
2(.63)(.37) = .47, so .47 x 154 = 72 Ff**

d) How many fraggles are homozygous recessive (ff)? **
61* (listed in the problem!)**

e) How many fraggles are homozygous dominant (FF)? **
154 - (72 + 61), so 21 FF**

3. One spring, a dust storm blankets the usually green garden of the
fraggles in gray. Under these conditions, the green fraggles become very
visible to the Gorgs, monstrous beasts who tend the gardens and try to
kill the fraggles to protect their crops. The gray fraggles, however,
blend into the dusty background and find that they can easily steal
radishes from the garden. How might this event affect microevolution in
this population of fraggles?

**Increase in gray, decrease in green, though
the dust would conceivably damage the CROPS as well!! Kinda' hard
to make a living on dead radishes!
**

4. In a population that is in Hardy-Weinberg equilibrium, 16% of the
individuals exhibit the recessive trait (ss).

**q = freq. s = √.16
= .4**

a) What is the frequency of the dominant allele (S) in the
population? **1 - .4 = .6**

b) What percent of the population possesses the dominant
allele (S)? ** 84% (everyone who
isn't ss possesses an S)**

5. The frequency of children homozygous for a recessive lethal allele is about 1/25,000. What proportion of the population are carriers of the lethal allele?

**
q = √.00004 = .0063
Carriers (heterozygotes) = 2(.0063)(.9937) = .013,
p = .9937
or 13 out of 1000 (314 out of 25000)**

6. Coat color in sheep is determined by a single gene. Allele B, for white wool, is dominant over allele b, for black wool. We have followed a population of sheep for two years. Below are the statistics we have compiled.

Black sheep 128

a) Determine the frequency of both alleles (B & b) in year 1.

128**/617 = .21 . . .
q = freq b = √.21
= .46 p = freq B = .54**

b) Determine the frequency of both alleles (B & b) in year 2.

**
176/858 = .21 . . . q = freq b = √.21
= .46 p = freq B = .54**

c) Is this population in Hardy-Weinberg equilibrium? Why or Why not?

**It
is in virtual H-W equilibrium, because there was no appreciable
change in frequencies from year 1 to year 2**

d) If the allelic frequencies for a particular gene in a population remain constant from year to year, what does this mean about the evolution of wool color in this population of sheep?

** It means
that there is no evolution taking place in that trait (at the moment)**

7. Some individuals inherit the ability to form methylmercaptan from
ingesting asparagus. To find out if you are one of these individuals,
simply eat a serving of asparagus and wait approximately 20 minutes
before urinating. You will be able to detect a very distinctive odor if
you have inherited the ability to form methylmercaptan. What percent of
the population would be homozygous recessive for this trait if it is
known that 30% are homozygous dominant?

** p = freq M = √.30
= .55
Homozygous recessive = .45 ^{2} = .20, so 20%
q = freq m = .45**

8. In a particular species of flower, C^{1} codes for red flowers, C^{2}
codes for white, with the heterozygous individuals being pink.

a. If the frequency of pink individuals in the population was .5163, would
you be able to estimate the frequencies of the individual alleles in the
population? Why or why not?

**No, because
the number of heterozygous individuals have two variables in the H-W equations
(p & q).**

b. If the frequency of red individuals in the population was .737, what would
the estimated frequency of pink and white individuals be in this same
population?

**
Freq C' is **
**√.737 = .86
Freq C" is = .14
So, freq of white = .14** (1 - [.737 +.02])

c. There is a pollinator of the flowers that prefers to visit white flowers 8
to 1 compared to red flowers, and visits red and pink flowers equally. Starting
from the frequencies in b. (above), and assuming all pollinated flowers
participate equally in generating the next generation, what would the
frequencies of the C^{1} and C^{2} alleles be in the next
generation?

**
# of alleles
Out of 1000 individuals:
next generation:
C' C"
737 red
737 x 1
1474
243
pink 243 x 1
243 243
20 white
20 x 8 = 160
320
1717 563
Total: 2280
freq C' = 1717/2280 = .753, freq C" = 563/2280 = .247**

9. Suppose the number of red, pink, and white individuals in another population of flowers was 566, 743, and 232 respectively. Could this population be said to be in H-W equilibrium?

Observed
**
C' C"
398 red
796
freq C' = 1585/3262 = .486
789 pink
789 789
freq C" = 1677/3262 = .514
444 white
**

**
Predicted C'C' frequency = .486 ^{2}**

Expected

.236 x 1631 = 385 red

.5 x 1631 = 815 pink

.264 x 1631 = 431 white

So**, compared
to the observed, the expected are kinda' close, but not so much that they could
be considered to be in H-W equilibrium.**