powerpoint slides for chapter 16: variation and population genetics section 16.2: how can population...

PowerPoint Slides for Chapter 16:Variation and Population Genetics

Section 16.2: How can population genetic information be used to predict evolution?

Integrating Concepts in Biology

by A. Malcolm Campbell, Laurie J. Heyer, & Christopher Paradise

Biology Learning Objectives• Explain how the Hardy-Weinberg equilibrium

works and how it relates to information in populations.

• Evaluate the application of Hardy-Weinberg equilibrium equation to information and evolution.

• Understand how application of Hardy-Weinberg equation can be used to determine if a population is evolving.

Section 16.2: How can population genetic information be used to predict evolution?

Figure 16.9

Observed genotype frequencies of the MN genetic locus in Philippine populations

From Arcellana et al., 2011, Figure 2.

Figure 16.9

More north to more south

Figure 16.9

Is there a latitudinal gradient? Do more northern populations have higher frequencies of certain genotypes?

Figure 16.9

Using genotype frequencies to determine allele frequencies: • Frequency of MM = 0.73• Frequency of MN = 0.12• Frequency of NN = 0.15

Figure 16.9

Using genotype frequencies to determine allele frequencies: • The frequency of M allele

(denoted p) is fMM + fMN/2 = 0.73 + 0.12/2 = 0.79.

• The frequency of N allele (denoted q) is fNN + fMN/2 = 0.15 + 0.12/2 = 0.21.

Figures 16.9 and 10

• The frequency of M allele (denoted p) is fMM + fMN/2 = 0.73 + 0.12/2 = 0.79.

• The frequency of N allele (denoted q) is fNN + fMN/2 = 0.15 + 0.12/2 = 0.21.

From Arcellana et al., 2011, Figure 2 & 3.

Figure 16.10

More north to more south

Figure 16.10

Is there a latitudinal gradient? Do more northern populations have higher frequencies of certain genotypes?

Table 16.2

Possible combinations of mating pairs in a population where 3 genotypes exist at one

genetic locus with two alleles

Table 16.2

All offspring of MM parents (MM x MM mating) result in MM offspring.

Table 16.2

When a MM male mates with a MN female, for instance, 50% of their offspring are predicted to be MM and 50% are predicted to be MN.

Table 16.2

When two heterozygotes mate they are predicted to produce offspring of all 3 genotypes in the percentages given above.

Table 16.2

Table 16.3

Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents

• To determine the probability of obtaining a target genotype, figure out all possible pairings that produce that genotype.

Table 16.3

• Here, MM x MM matings will ONLY produce MM offspring (1 in column 3)

• Probability of two MM individuals mating is fMM x fMM

Table 16.3

• Here, MM x MM matings will ONLY produce MM offspring (1 in column 3)

• Probability of two MM individuals mating is fMM x fMM

• Probability of the mating (4) times probability that offspring will be target (3) is in column 5.

Table 16.3

• MM x MN matings will produce MM offspring half the time (1/2 in column 3)

• Probability of a MM x MN mating is fMM x fMN

Table 16.3

• Similarly, MN x MM matings will produce MM offspring half the time (1/2 in column 3)

• Probability of a MN x MM mating is fMN x fMM

Table 16.3

• Finally, MN x MN matings will produce MM offspring 25% of the time (1/4 in column 3)

• Probability of a MN x MN mating is fMN x fMN

Table 16.3

• Add all cells in column 5 to get equation in column 6• Repeat process for MN and NN offspring:

Table 16.3

• Add all cells in column 5 to get equation in column 6

Table 16.3

• Add all cells in column 5 to get equation in column 6

Table 16.3

BME 16.2: How can you predict the Hardy-Weinberg equilibrium?

• To find the probability that a particular mating will produce the target offspring genotype, as shown in column 3, you multiply the probability that the mother and father each donate the necessary alleles.

• Use the multiplication rule and addition rule

• The multiplication rule: the probability of events A and B both occurring is the probability that A occurs multiplied by the probability that B occurs, provided that A and B are independent.

• Used to determine probability of each pairing in column 4• Used to determine probability that a mating will occur and that

• The addition rule: the probability of event A or event B occurring is the probability that A occurs plus the probability that B occurs, provided that A and B are mutually exclusive.

• Used to determine total probability of a target offspring genotype. • The matings that can produce the target genotype are mutually

exclusive: probability of MM offspring = probability of MM from MM x MM or MM x MN or MN x MM or MN x MN.

genotypeobserved frequency

HW equilibrium frequencies

MM 0.74 0.632025MN 0.11 0.32595NN 0.15 0.042025total 1 1

genotypeHW equilibrium

frequenciespredicted next

generationMM 0.632025 0.632025MN 0.32595 0.32595NN 0.042025 0.042025total 1 1

VALIDATION

CALCULATION

BME 16.2: Hardy-Weinberg.xlsx

Where do these appear in Table 16.3?

MM 0.74 0.632025MN 0.11 0.32595NN 0.15 0.042025total 1 1

VALIDATION

CALCULATION

Column 6 from Table 16.3

MM 0.74 0.632025MN 0.11 0.32595NN 0.15 0.042025total 1 1

VALIDATION

CALCULATION

What is significance if these do not change from generation to generation?

MM 0.74 0.632025MN 0.11 0.32595NN 0.15 0.042025total 1 1

VALIDATION

CALCULATION

Population moves quickly to Hardy-Weinberg equilibrium

Population is NOT in Hardy-Weinberg equilibrium

MM 0.25 0.25MN 0.5 0.5NN 0.25 0.25total 1 1

VALIDATION

CALCULATION

Population stays in Hardy-Weinberg equilibrium

Population is in Hardy-Weinberg equilibrium

MM 0.1 0.25MN 0.8 0.5NN 0.1 0.25total 1 1

VALIDATION

CALCULATION

Population moves quickly to Hardy-Weinberg equilibrium

Population is NOT in Hardy-Weinberg equilibrium

MM 0.04 0.04MN 0.32 0.32NN 0.64 0.64total 1 1

VALIDATION

CALCULATION

Population stays in Hardy-Weinberg equilibrium

Population is in Hardy-Weinberg equilibrium

BME 16.2: How can you predict the Hardy-Weinberg equilibrium? Using allele

frequencies to calculate H-W equilibrium• Allele frequencies should tell us a lot about the next generation’s

genotype frequencies. • Let the proportion of M alleles = p • Let the proportion of N alleles = q,

frequencies to calculate H-W equilibrium• Allele frequencies should tell us a lot about the next generation’s

genotype frequencies. • Let the proportion of M alleles = p • Let the proportion of N alleles = q, • You might predict that any randomly selected offspring would be

MM with probability p2, MN with probability 2pq, and NN with probability q2.

Bio-Math Exploration Integrating Question7. Recall the relationship between allele frequencies and genotype frequencies: p = fMM + fMN/2 and q = fNN + fMN/2. Use these formulas and algebraic manipulation to calculate p2, 2pq, and q2.

frequencies to calculate H-W equilibriumBio-Math Exploration Integrating Question7. Recall the relationship between allele frequencies and genotype frequencies: p = fMM + fMN/2 and q = fNN + fMN/2. Use these formulas and algebraic manipulation to calculate p2, 2pq, and q2. • p2 = fMM

2 + fMM x fMN + ¼ x fMN2 (probability of MM in the offspring

generation from Table 16.3)• 2pq = fMM x fMN + 2 fMM x fNN + fMN

2/2 + fMN x fNN, from Table 16.3

• q2 = ¼ x fMN2 + fMN x fNN + fNN

2, also from Table 16.3

frequencies to calculate H-W equilibriumTherefore, once you know the allele frequencies p and q in a population, the Hardy-Weinberg frequencies are very easy to calculate. p2 = fMM

2 + fMM x fMN + ¼ x fMN2 (probability of MM in the offspring

generation from Table 16.3)2pq = fMM x fMN + 2 fMM x fNN + fMN

2/2 + fMN x fNN, from Table 16.3q2 = ¼ x fMN

2 + fMN x fNN + fNN2

, also from Table 16.3

Hardy-Weinberg frequencies are given by the terms in the expansion of (p + q)2 = p2 + 2pq + q2. Verify this alternative way to calculate Hardy-Weinberg genotype frequencies in “hardy-weinberg.xlsx.”

allele allele freq genotype

M 0.2 MM 0.04N 0.8 MN 0.32

NN 0.64Total 1 1

genotype

predicted next

generationMM 0.04 0.04MN 0.32 0.32NN 0.64 0.64

Total 1 1

VALIDATION

CALCULATION

p2 + 2pq + q2 = 1

p + q = 1

Using allele frequencies to calculate H-W equilibrium

frequencies to calculate H-W equilibrium

Now you know how to predict long-run genotype frequencies, assuming random mating, a large population, no genetic drift, and no

gene flow, and you know how to use these predictions to identify populations undergoing evolution.

Figure 16.11

Observed and HW genotype frequencies of the MN genetic locus in Philippine populations

Observed genotype frequencies from Figure 16.9 and the predicted genotype frequencies are represented by two shades of the same color

From Arcellana et al., 2011, Figure 2 and calculated from data in Figures 2 and 3.

Figure 16.11

If bars of a similar color are different heights, the population is judged to NOT be in Hardy-Weinberg equilibrium.

Figure 16.11

• The population is judged to NOT be in Hardy-Weinberg equilibrium.

• Isabela composed of high proportion of a particular ethnic group, with high localized migration from nearby towns.

• Towns had similar frequencies of M and N alleles.

• Isolation and inbreeding in small populations can lead to populations not in HW equilibrium.

Figure 16.11

If bars of a similar color are the same or similar height, then the population is judged to be in Hardy-Weinberg equilibrium.

Figure 16.11

judged to be in HW equilibrium.

Figure 16.11

judged to NOT be in HW equilibrium.

Figure 16.11

NO north to south trend

powerpoint slides for chapter 16: variation and population genetics section 16.2: how can population...

observed genotype frequencies

allele frequencies

mn genetic locus

population genetic information

northern populations

population geneticssection

latitudinal gradient

philippine populationsis

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