powerpoint slides for chapter 16: variation and population genetics section 16.2: how can population...
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PowerPoint Slides for Chapter 16:Variation and Population Genetics
Section 16.2: How can population genetic information be used to predict evolution?
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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
Observed genotype frequencies of the MN genetic locus in Philippine populations
More north to more south
From Arcellana et al., 2011, Figure 2.
Figure 16.9
Observed genotype frequencies of the MN genetic locus in Philippine populations
Is there a latitudinal gradient? Do more northern populations have higher frequencies of certain genotypes?
From Arcellana et al., 2011, Figure 2.
Figure 16.9
Observed genotype frequencies of the MN genetic locus in Philippine populations
Using genotype frequencies to determine allele frequencies: • Frequency of MM = 0.73• Frequency of MN = 0.12• Frequency of NN = 0.15
From Arcellana et al., 2011, Figure 2.
Figure 16.9
Observed genotype frequencies of the MN genetic locus in Philippine populations
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.
From Arcellana et al., 2011, Figure 2.
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.
Observed genotype frequencies of the MN genetic locus in Philippine populations
From Arcellana et al., 2011, Figure 2 & 3.
Figure 16.10
Observed genotype frequencies of the MN genetic locus in Philippine populations
From Arcellana et al., 2011, Figure 3.
Figure 16.10
Observed genotype frequencies of the MN genetic locus in Philippine populations
More north to more south
From Arcellana et al., 2011, Figure 3.
Figure 16.10
Observed genotype frequencies of the MN genetic locus in Philippine populations
Is there a latitudinal gradient? Do more northern populations have higher frequencies of certain genotypes?
From Arcellana et al., 2011, Figure 3.
Table 16.2
Possible combinations of mating pairs in a population where 3 genotypes exist at one
genetic locus with two alleles
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.2
Possible combinations of mating pairs in a population where 3 genotypes exist at one
genetic locus with two alleles
All offspring of MM parents (MM x MM mating) result in MM offspring.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.2
Possible combinations of mating pairs in a population where 3 genotypes exist at one
genetic locus with two alleles
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.2
Possible combinations of mating pairs in a population where 3 genotypes exist at one
genetic locus with two alleles
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.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.2
Possible combinations of mating pairs in a population where 3 genotypes exist at one
genetic locus with two alleles
When two heterozygotes mate they are predicted to produce offspring of all 3 genotypes in the percentages given above.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.2
Possible combinations of mating pairs in a population where 3 genotypes exist at one
genetic locus with two alleles
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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.
• Here, MM x MM matings will ONLY produce MM offspring (1 in column 3)
• Probability of two MM individuals mating is fMM x fMM
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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.
• 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.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.3
Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents
• 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
• Probability of the mating (4) times probability that offspring will be target (3) is in column 5.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.3
Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents
• 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
• Probability of the mating (4) times probability that offspring will be target (3) is in column 5.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.3
Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents
• 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
• Probability of the mating (4) times probability that offspring will be target (3) is in column 5.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.3
Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents
• Add all cells in column 5 to get equation in column 6• Repeat process for MN and NN offspring:
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.3
Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents
• Add all cells in column 5 to get equation in column 6
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.3
Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents
• Add all cells in column 5 to get equation in column 6
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
Table 16.3
Ways to get MM, MN, and NN offspring from matings of MM, MN, and NN parents
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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
Table 16.3 Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
BME 16.2: How can you predict the Hardy-Weinberg equilibrium?
• 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
it will produce target offspring (column 4 x column 3 = column 5)Table 16.3 Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
BME 16.2: How can you predict the Hardy-Weinberg equilibrium?
• 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.
Table 16.3 Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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?
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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
Column 6 from Table 16.3
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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
What is significance if these do not change from generation to generation?
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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
Population moves quickly to Hardy-Weinberg equilibrium
Population is NOT in Hardy-Weinberg equilibrium
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
genotypeobserved frequency
HW equilibrium frequencies
MM 0.25 0.25MN 0.5 0.5NN 0.25 0.25total 1 1
genotypeHW equilibrium
frequenciespredicted next
generationMM 0.25 0.25MN 0.5 0.5NN 0.25 0.25total 1 1
VALIDATION
CALCULATION
BME 16.2: Hardy-Weinberg.xlsx
Population stays in Hardy-Weinberg equilibrium
Population is in Hardy-Weinberg equilibrium
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
genotypeobserved frequency
HW equilibrium frequencies
MM 0.1 0.25MN 0.8 0.5NN 0.1 0.25total 1 1
genotypeHW equilibrium
frequenciespredicted next
generationMM 0.25 0.25MN 0.5 0.5NN 0.25 0.25total 1 1
VALIDATION
CALCULATION
BME 16.2: Hardy-Weinberg.xlsx
Population moves quickly to Hardy-Weinberg equilibrium
Population is NOT in Hardy-Weinberg equilibrium
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
genotypeobserved frequency
HW equilibrium frequencies
MM 0.04 0.04MN 0.32 0.32NN 0.64 0.64total 1 1
genotypeHW equilibrium
frequenciespredicted next
generationMM 0.04 0.04MN 0.32 0.32NN 0.64 0.64total 1 1
VALIDATION
CALCULATION
BME 16.2: Hardy-Weinberg.xlsx
Population stays in Hardy-Weinberg equilibrium
Population is in Hardy-Weinberg equilibrium
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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,
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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, • 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.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
BME 16.2: How can you predict the Hardy-Weinberg equilibrium? Using allele
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
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
BME 16.2: How can you predict the Hardy-Weinberg equilibrium? Using allele
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.”
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
allele allele freq genotype
HW equilibrium frequencies
M 0.2 MM 0.04N 0.8 MN 0.32
NN 0.64Total 1 1
genotype
HW equilibrium frequencies
predicted next
generationMM 0.04 0.04MN 0.32 0.32NN 0.64 0.64
Total 1 1
VALIDATION
CALCULATION
BME 16.2: How can you predict the Hardy-Weinberg equilibrium?
p2 + 2pq + q2 = 1
p + q = 1
Using allele frequencies to calculate H-W equilibrium
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
BME 16.2: How can you predict the Hardy-Weinberg equilibrium? Using allele
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.
Copyright © 2015 by AM Campbell, LJ Heyer, CJ Paradise. All rights reserved.
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
Observed and HW genotype frequencies of the MN genetic locus in Philippine populations
If bars of a similar color are different heights, the population is judged to NOT be in Hardy-Weinberg equilibrium.
Figure 16.11
Observed and HW genotype frequencies of the MN genetic locus in Philippine populations
• 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
Observed and HW genotype frequencies of the MN genetic locus in Philippine populations
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
Observed and HW genotype frequencies of the MN genetic locus in Philippine populations
judged to be in HW equilibrium.
Figure 16.11
Observed and HW genotype frequencies of the MN genetic locus in Philippine populations
judged to NOT be in HW equilibrium.
Figure 16.11
Observed and HW genotype frequencies of the MN genetic locus in Philippine populations
NO north to south trend