GNM 3201
Darwin and Mendel
STUDY GUIDE: WILSON AND BOSSERT, RATES OF CHANGE & STATISTICS
Change
1. If you start at your house and drive south 10 miles, how has your distance from home
changed? That is, what is d, where d = distance from home? d = 10 miles
2. If you have $500 in your checking account on Monday, and on Thursday you have $85, what is
$? What would $ be if on Thursday you had $5000?
$ = -415
or $ = 4500
3. If your employer automatically deposits $2000 in your bank account every four weeks, what is
the $/t for your bank account per week? Assume you don't withdraw or add any other $$.
$/t = 500/week
4. If you drive 10 miles in fifteen minutes, what is your d/t in miles per hour?
d/t = 40mph
5. If you have a cat which gives birth to 6 kittens, and then you accept two more kittens from a
neighbor, what is the change in the number of Felis domesticus in your house, (n)?
n = +8
6. How many kittens would you have to give away to make n = 0?
8
Growth Rates
7. What is the rate of change d$/dt in the value of $1000 invested at 4% annual interest (assume
continuous compounding of the interest)? What interest rate would give d$/dt = 0?
d$/dt = 40/yr
0%
8. What is the value of that investment after 2.5 years? Hint: use the ex key on your calculator.
$2.5 = $1000(e0.04 * 2.5) = 1105.17
Statistics
9. What is the mean of (20, 25, 35, 50)
32.5
10. What is the standard deviation for the same data?
13.2 or 11.5
GNM 3201
Darwin and Mendel
STUDY GUIDE: WILSON AND BOSSERT, POPULATION GENETICS
PROBLEMS
My son and I used to play a game that used dice that had different numbers of sides. They
included 4, 6, 8, 12 and 20-sided shapes. All were numbered from 1 to the total number of sides.
If you roll one die with four sides and one with eight sides, what is the chance of getting a pair of
threes?
p x q is the probability
probability of getting 3 on a 4-sided die = 1/4
probability of getting 3 on an 8-sided die = 1/8
so 1/4 x 1/8 = 1/32 is the chance of a pair of 3’s
The wrinkled (a) gene occurs at a frequency of 0.55 in a population. What is the frequency of the
round (A) gene, if no other forms are present?
ANSWER:
Frequency of round = 1 - 0.55 = 0.45
A certain recessive gene (a) occurs at a frequency of 0.05 in the population. What is the
frequency of the other, dominant form of the gene (A) and what are the expected frequencies of
the diploid genotypes (AA, Aa, aa)?
ANSWER:
Frequency of A = 1 - 0.1 = 0.95
Frequency of AA = (0.95) x (0.95) = 0.9025
Frequency of aa = 2 x (0.95) x (0.05) = 0.095
Frequency of aa = (0.05) x (0.05) = 0.0025
Consider again the round (A) and wrinkled (a) genes. If the frequency of the melanic gene (M)
in a moth population is 0.7, what are the frequencies of the three forms (MM, Mm, mm)?
ANSWER:
Frequency of M = 0.7
Frequency of m = 1 - 0.7 = 0.3
Frequency of MM = (0.7) x (0.7) = 0.49
Frequency of Mm = 2 x (0.7) x (0.3) = 0.42
Frequency of mm = (0.3) x (0.3) = 0.09
If 36% of the individuals in a moth population exhibit the recessive trait, speckled white
coloration, what is the frequency of the gene m, for the trait?
ANSWER:
GNM 3201
Darwin and Mendel
Assuming the population is in Hardy-Weinberg equilibrium, 36% represents q , the square
of the frequency of the recessive (a). So:
q = square root of 0.36 = 0.6
If we have a population consisting entirely of 40 AA and 60 aa individuals, what are the
frequencies of the genes A and a?
ANSWER:
Frequency of A = 80/200 = 0.4
Frequency of a = 120/200 = 0.6
If we had 150 MM individuals in a population and 50 mm individuals, and if they mated at
random, what would be the frequencies of MM, Mm and mm individuals in the offspring?
ANSWER:
Frequency of M = 300/400 = 0.75
Frequency of m = 100/400 =0.25
Frequency of the genotypes:
MM = 0.75 x 0.75 = .5625
Mm = 2 x 0.75 x 0.25 = 0.375
Mm = 0.25 x 0.25 = 0.0625
Mutational equilibrium (page 44). What is the equilibrium frequency of gene a2 if the mutation
rate () from a1 to a2 is 5 x 10-5 and the mutation rate () from a2 to a1 is 5 x 10-6?
The equilibrium frequency is the ratio of the mutation rate from a1 to a2 (5 x 10-5) divided by the
sum of the two mutation rates. This is .00005/(.00005+.000005) = 0.91
Gene flow (see pages 46-47): What is the amount of change in a generation of the frequency (q)
of an allele where the frequency in one population (q) is 0.3 and in another population (q) is
0.8, if population  gets 0.1 of its individuals in each generation from population 
q  -m(q – q) = -0.1(0.3-0.8) = -0.1(-0.5) = 0.05
Selection in one generation (page 50): Calculate the selection coefficients for the following
case. Is selection happening? What type? Yes, disruptive selection is happening (against
heterozygotes)
Genotypes
AA
Aa
aa
Number before selection
2300
1000
1700
After selection in same
generation
Survival Rate
Relative Fitness
Selection Coefficient
1700
0.74
1.00
0.00
300
0.30
0.41
0.59
1000
0.59
0.80
0.20
GNM 3201
Darwin and Mendel
Selection between one generation and the next generation (page 52): Calculate the selection
coefficients for the following case. Is selection happening? What type?
Genotypes
Number in
first
generation
(before
selection)
Number
expected in
next
generation
based on the
H-W formula
Number in
second
generation
(after
selection)
Corrected
Rate of
Increase
Relative
fitness
Selection
coefficient
AA
Aa
aa
Total
gene frequencies of A and
a in Gen. 1
4000
3000
3000
10000
9000/20000
= 0.55
0.55 x
0.55 x
10000 =
3025
2 x 0.55
x 0.45 x
10000 =
4950
0.45 x
0.45 x
10000 =
2025
10000
4400
2600
3000
10000
1.45
0.53
1.48
0.98
0.35
1.00
0.02
0.65
0.00
6000/20000
= 0.45
Yes, disruptive selection is happening (the selection is against heterozygotes).
Elimination of recessives (page 53): Consider a recessive gene that is lethal when homozygous,
but harmless if the dominant gene is present. Suppose we start out with the frequency of that
gene in a population equal to 0.3. What will the frequency be after 10 generations if only natural
selection affects it?
The selection coefficient is 1 against the recessive homozygote, so we can apply the formula on
page 53 [6] to get frequency after ten generations = 0.3/(1+10(0.3)) = 0.3/4 = 0.075
Mutation and selection (page 61): Consider a recessive gene that is lethal when homozygous,
but harmless if the dominant gene is present. If the mutation rate from the dominant to the
recessive is 0.0005, what will be the equilibrium frequency of the recessive allele, if no other
factors act on the gene frequencies?
Since the selection coefficient is 1, the equilibrium frequency is the square root of 0.0005/1 =
square root of 0.0005 = 0.022
GNM 3201
Darwin and Mendel