What happens to genes and alleles of genes in populations? If a new allele appears because of a...

• What happens to genes and alleles of genes in populations?• If a new allele appears because of a mutation, does it…• …immediately disappear?• …become a permanent part of the population?• Does it matter if the allele is beneficial or detrimental?• Does it matter if the population is large or small?• Does it matter if there are lots of alleles or only a few?• Does it matter if the genome is large or small?• Two mathematicians helped resolve these questions in the early

1900s• Godfrey Hardy and Wilhelm Weinberg• Developed a concept known now as Hardy-Weinberg Equilibrium

Population Genetics and Evolution

• Terminology• Population – a group of

interbreeding individuals• Gene pool – the collection

of genes and alleles in a population

• Each member of the population carries a portion of the gene pool

• H-W equilibrium models allele frequencies in a population under certain theoretical conditions

• Obviously, no real populations follow these assumptions


• Assume two alleles of a given gene, A1 and A2• There are three possible genotypes• A1A1, A2A2, A1A2

• The frequencies of those alleles are • f(A1) = p, f(A2) = q, with equal frequencies in males and

females• Assuming only the two alleles, p + q = 1

• q = 1 - p• Genotype frequencies can be computed as (p + q)2

• f(A1A1) = p2

• f(A1A2) = 2pq• f(A2A2) = q2

– With p2 + 2pq + q2 = 1


• Assume f(A1) = p = 0.6 and f(A2) = q = 0.4• The frequency of A1 in male gametes is 0.6

• Same for female gametes• The frequency of A2 in gametes is 0.4

– p2 + 2pq + q2 = 1– 0.62 + 2x0.6x0.4 + 0.42 = 1– 0.36 + 0.48 + 0.16 = 1

• Random mating produces genotype frequencies that are predictions of allele/genotype frequencies in the population

• Under H-W assumptions, the frequencies will remain constant over generations


• An example from this class• http://myweb.ttu.edu/daray/Genetics/

humantraits_BIOL3416_F15_112315.xlsx• Tongue rolling is a biallelic dominant trait

• RR, Rr = tongue roller• rr = non-tongue roller

• 237 people surveyed• 200 people in the survey can roll their tongue• Calculate the number of homozygotes from each

category and the number of heterozygotes• Calculate p and q


• An example from this class• Tongue rolling is a biallelic dominant trait• 237 people surveyed• 200 people in the survey can roll their tongue• Calculate the number of homozygotes from each category and the

number of heterozygotes• Calculate the p and q• Easiest way to start how many are homozygous recessive?

• 37 = # people with genotype rr• f(rr) = q2 = 37/237 = 0.156• q therefore = 0.395• p therefore = 1 – q = 0.605• p2 = f(RR) = 0.366• 2pq = f(Rr) = 0.478• Check your work

• p2 + 2pq + q2 = 0.366 + 0.478 + 0.156 = 1


• If two populations with unique allele frequencies are merged, a new equilibrium set of frequencies will result


• Note that each of the original populations has a distinct set of allele frequencies

• Taking a sample of the population and determining those frequencies in the sample can be used to identify the populations

• Ray et al. 2005 – Forensic Science International


• H-W equilibrium values can be determined for cases with more than two alleles

• Just add a factor• p + q + r = 1• p2 + 2pq + q2 + 2pr + r2 +2qr = 1• ABO blood type is the classic example


• H-W equilibrium is unattainable in natural populations• Natural selection, non-random

mating, migration, non-infinite population size, mutation, etc.

• We therefore expect H-W values to be at least slightly different from expected values

• Statistical tests such as the Χ2 test can be used to determine if observed frequencies are significantly different from what is predicted

• If so, the reason can be investigated• How do we measure selection?


• How do we measure selection?• Fitness = the ability of an organism to

survive and reproduce in an environment• Relative fitness (w) is determined when

we compare the fitness of some genotypes relative to others• Selection coefficient (s) = relative

fitness value for a given genotype• Genotypes with the highest

reproductive success w = 1• Genotypes with other fitness values

= 1 - s• Directional selection


• Directional selection• The phenotype associated with the

homozygous genotype has a higher relative fitness than others

• Acts to increase the frequency of the ‘better’ alleles

• Example – two codominant alleles of gene B• w(B1B1) = 1• w(B2B2) = 0.4 s = 0.6• w(B1B2) = 0.8 s = 0.2

• The relative success at reproduction are given by w in each case

• Imagine a population where B1 (p = 0.6) and B2 (q = 0.4)


• Directional selection• Example – two codominant alleles of gene B

• w(B1B1) = 1; w(B2B2) = 0.4; w(B1B2) = 0.8• Imagine a population where B1 (p = 0.6) and B2 (q = 0.4)• What happens after one generation of breeding?

• Note the change in freqencies


• Directional selection• If selection is strong enough and/or goes on for enough generations, the

favored allele will eventually become fixed in the population and the unfavored allele will go extinct


• Directional selection• Detrimental recessive alleles, even lethal ones can remain in populations

for long periods of time, hidden by the dominant alleles• Cystic fibrosis• PKU• Beta-thalassemia• Tay-Sachs disease• Blue diaper syndrome?

• https://en.wikipedia.org/wiki/Category:Autosomal_recessive_disorders


• Directional selection• Classic experiment by Cavener and Clegg• Four subpopulations derived from a single Drosophila population• Measured the frequency of two alleles over 50 generations

• Adh – detoxifies alcohol• AdhF – better at detoxifying alcohol

• Two subpopulations placed in alcohol-rich environment• Original frequency of AdhF = 0.38


• Balancing selection• The heterozygous genotype/phenotype has a

higher relative fitness than others• Results in a balanced polymorphism –

alternate allele frequencies are maintained• Classic example – sickle-cell trait• In regions where malaria is prevalant, having

one recessive sickle-cell allele confers an advantage


• Genetic drift• Chance fluctuations in allele frequencies that result from random

breeding/inheritance• Especially influential in small populations

• Original p=0.72, q = 0.28 p=0.77, q=0.23


• Genetic drift• Chance fluctuations in allele frequencies that result from random

breeding/inheritance• Especially influential in small populations

• Original p=0.72, q = 0.28 p=0.77, q=0.23• Post-apocalypse p=0.74, q=0.26 p=0.86, q=0.14


• December 8; 4:30 – 7:30; LH100 (here)• Rules:

– Bring ID– All mobile devices must be out of site during the exam

• Exam is cumulative– 20 questions each from Drs. Zhang and Rock– 40 questions from Dr. Ray

• Dr. Ray’s portion will cover– Slides associated with chapters 12, 13, 14, 15 and 22

• No review session this time. Sorry

Final Exam

What happens to genes and alleles of genes in populations? If a new allele appears because of a...

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