Population Genetics Exam 2

Natural selection can be summarized by four key points. List these four points:

1. Individuals of a species exhibit variations in phenotype 2. Many of these variations are heritable and passed on to offspring 3. Organisms tend to reproduce in an exponential fashion. More offspring are produced than can survive and reproduce. 4. Organisms with particular phenotypes will be more successful than others, allowing them to survive and reproduce at higher rates

A scientist measures the circumference of acorns in a population of oak trees and discovers that the mean circumference is 2cm. What would you expect the most common circumference(s) to be after 10 generations of stabilizing selection?

2cm

Calculate the effective population size for the following population given the number of individuals in each generation: Gen. 1 : 2 individuals Gen. 2 : 10 individuals Gen. 3 : 25 individuals Gen. 4 : 15 individuals

4/(1/2)+(1/10)+(1/25)+(1/15)

A survey of 10 000 births revealed 10 babies with an autosomal dominant disorder. Six of these individuals had affected parents, while the remaining 4 had unaffected parents. What is the mutation rate for this disorder?

4/20000 (1/5000 or 0.0002)

Calculate the absolute fitness for the following population: BB: 500 born, 475 lived to adulthood Bb: 1000 born, 800 lived to adulthood bb: 400 born, 225 lived to adulthood

475/300=0.95 800/1000=0.80 225/400=0.5625

What is a population bottleneck?

A drastic reduction in population size. Can be caused by natural disasters, human intervention (over fishing/hunting) etc.

Consider a gene with two alleles, A1 and A2. The frequency of the A1 allele is currently 0.9. In each generation the A1 allele mutates to the A2 allele at a rate of 1 x 10-5. What are the new frequencies of the A1 and A2 alleles in the next generation?

A1 = 0.899991 A2 = 0.100009

Define the term "migration-selection balance"?

An allele can be deleterious in one geographical region but not deleterious or less deleterious in a neighboring region Migrations from the latter continually replenish deleterious allele in the former region, where selection acts against it

The occurrence of large or small beak sizes among seed cracking birds in the absence of medium-sized beaks is an example of:

Disruptive selection

Define the term "fitness (w)" in terms of natural selection. How is this related to the "selection coefficient (s)"?

Fitness (w) measures the ability of an individual with a particular genotype to survive and reproduce The selection coefficient (s) measure the selective pressure against a genotype As such: s = 1-w

When a new population, derived from a small subset of individuals, has significantly less genetic diversity than the original population, it is said to be exhibiting a _________________.

Founder effect

Which of the following is the primary force that changes allele frequencies in small populations?

Genetic Drift

Refer to question 2, but this time answer what you would expect after 10 generations of disruptive selection

Greater than 2cl and less than 2cm

Refer to question 2, but this time answer what you would expect after 10 generations of directional selection

Greater than 2cm or less than 2cm

Consider a gene with two alleles, p and q. Also consider two populations, one with 500 individuals and one with 35 individuals. In each population, the initial heterozygosity is the same (2pq = 0.5). Calculate the expected heterozygosity for both populations after 20 generations.

Ht = (1 - (1/2N))t H0 Population 1: N = 500 individuals H20 = (1- (1/1000))20 x 0.5 = (1 - 0.001)20 x 0.5 = 0.99920 x 0.5 = 0.98 x 0.5 = 0.49 Population 2: N = 35 individuals H20 = (1- (1/70))20 x 0.5 = (1 - 0.01428)20 x 0.5 = 0.9857220 x 0.5 = 0.75 x 0.5 = 0.375

What is meant by the term "effective population size"

In natural populations, the number of adults in a population may be greater than the number that actually contribute to the next generation The effective population size (Ne) is the size of a theoretical population that would lose heterozygosity at the same rate as the actual

The fitnesses of 3 genotypes are: wAA = 0.9, wAa = 1.0, waa = 0.7. If the population starts at the allelic frequency of A = 0.5, what is the value of A in the next generation?

Let A = p and a = q p' = p2wAA + pqwAa / p2wAA + 2pqwAa + q2waa = 0.52 x 0.9 + 0.5 x 0.5 x 1 / 0.52 x 0.9 + 2 x 0.5 x 0.5 x 1 + 0.52 x 0.7 = 0.225 + 0.25 / 0.225 + 0.5 + 0.175 = 0.475 / 0.9 = 0.5278

Define the term "gene flow"

Movement of alleles between populations

Suppose that a given gene undergoes a mutation to its dominant allele such that two out of 100,000 offspring exhibit the new mutant phenotype. Assuming that these offspring are heterozygous, what is the mutation rate for the gene?

Mutation rate = 2/200 000 = 1 in 100 000

Achondroplasia is a dominant trait that causes a characteristic form of dwarfism, with the homozygous dominant genotype lethal before birth. In a survey of 50,000 births, five infants with achondroplasia were identified. Three of the affected infants had affected parents, while two had normal parents. Calculate the mutation rate for achondroplasia

Mutation rate = new mutations / total alleles = 2 / 100 000 = 1 in 50 000

Which of the following is the primary force that changes allele frequencies in large populations?

Natural Selection

Calculate the effective population size for a breeding population of 60 adult males and 40 adult females

Ne = (4xNFxNM)/(NF+NM) = (4 x 40 x 60) / (40 + 60) = 9600 / 100 = 96

A population contains 110 individuals, however only 10 are male and 100 are female. What is the effective population size of this population?

Ne = 4NmNf / (Nm+Nf ) Ne = 4 x 10 x 100 / (10+100) Ne = 36.36

Define the term "population bottleneck"

Sudden reduction in the size of a population, such that genes from only a few individuals are used for repopulation

The total number of individuals in a population (all males + all females)

The breeding population. The size of a population that would lose heterozygosity at the same rate as the actual population

When considering a situation where mutation is acting on alleles of a gene we can measure the equilibrium frequency of the allele designated q using the following formula. q = μ/μ + ν Briefly explain what exactly is meant by the equilibrium value of q?

The point where the increase in q from forward mutation is offset by the reduction in q from reverse mutation - q stays the same

What is meant by the term absolute population size (N)?

The total number of individuals in a population (all males + all females)

In 1950 one breading pair of Canadian Isle Royale grey wolves crossed an ice bridge to an island. There were no other wolves on the island when they arrived. Shortly after they arrived the ice-bridge melted, such that they were the only two wolves on the island. This pair went on to establish a population of grey wolves on the island, producing 3 litters each containing 4 pups. These 12 pups went on to produce 35 offspring and these 35 offspring went on to produce 50 offspring. However, a study of the next (5th) generation showed that only 10 pups survived to adulthood to reproduce. a. What is the effective population size across the five generations of this study? b. Given what you know about population genetics theory, what reasons could account for the rapid decline in surviving wolf pups in the 5th generation (assume that food and resources were plentiful and no external forces such as natural disasters or hunting occurred)

a. Ne = t / å1/N = 5 / (1/2) + (1/12) + (1/35) + (1/50) + (1/10) = 5 / 0.5 + 0.83 + 0.028 + 0.02 + 0.1 = 5 / 0.7319 = 6.83 b. To start with, the population is affected by the founder effect. Since only two individuals were present to start the population, the gene pool was incredibly limited. Furthermore, any offspring resulting from the second generation are inbred. As such, the reproductive failure seen in the 5th generation is likely due to inbreeding depression. Overall inbreeding depression is associated with reduced fitness and lower survival rates. Inbreeding depression often results from increased homozygosity for deleterious alleles - if either of the founders had recessive deleterious alleles there is a greater chance that the resulting generations of inbred offspring would be homozygous for these alleles and would therefore display these harmful traits.

A wildflower native to California, the dwarf lupin (Lupinus nanus) normally bears blue flowers. Occasionally, plants with pink flowers are observed in wild populations. Flower color is controlled at a single locus, with the pink allele completely recessive to the blue allele. Harding (1970) censused several lupin populations in the California Coast Ranges. In one population of lupins at Spanish Flat, California, he found 25 pink flowers and 3291 blue flowers, for a total of 3316 flowers a) Calculate the expected allele frequencies and genotype frequencies if the population were in Hardy-Weinberg equilibrium. b) Harding studied the fertility of lupins by counting number of seed pods produced per plant in a subsample of the Spanish Flat population. He found that the relative fitness of blue flowers, regardless of genotype was the same (w = 1). However, pink flowers had a reduced relative fitness (w = 0.677). Using the above determine allele frequencies, calculate the effects of natural selection on allele frequencies after one generation.

a.Let Blue = B and Pink = b Let B = p and b = q Therefore: Pink (bb) = 25 / 3316 = 0.0075 Therefore q2 = 0.0075 Therefore: q = sqrtq2 = sqrt0.0075 = 0.0868 p = 1 - q = 1 - 0.0868 = 0.9132 BB = p2 = 0.91322 = 0.834 Bb = 2pq = 2 x 0.9132 x 0.0868 = 0.1585 b.wBB = 1 / wBb = 1 / wbb = 0.677 p' = p2wBB + pqwBb / p2wBB + 2pqwBb + q2wbb = 0.91322 x 1 + 0.9132 x 0.0868 x 1 / 0.91322 x 1 + 0.9132 x 0.0868 x 1 + 0.08682 x 0.677 = 0.834 + 0.07925 / 0.834 + 0.1585 + 0.0051 = 0.91325 / 0.9976 = 0.9154 q' = 1 - p' = 1 - 0.9154 = 0.0846 b.wBB = 1 / wBb = 1 / wbb = 0.677 p' = p2wBB + pqwBb / p2wBB + 2pqwBb + q2wbb = 0.91322 x 1 + 0.9132 x 0.0868 x 1 / 0.91322 x 1 + 0.9132 x 0.0868 x 1 + 0.08682 x 0.677 = 0.834 + 0.07925 / 0.834 + 0.1585 + 0.0051 = 0.91325 / 0.9976 = 0.9154 q' = 1 - p' = 1 - 0.9154 = 0.0846

Consider a gene with two alleles A and a. The forward and reverse mutation rates for these alleles are 1 x 10-5 and 0.3 x 10-5 per generation respectively. The frequency of A = 0.9 and the frequency of a = 0.1. a. Calculate Δq for this population b. Based on this Δq results, what will be the frequencies of A and a in the next generation? c. What is the equilibrium frequency of q?

a.Δq = up - vq = (1 x 10-5 x 0.9) - (0.3 x 10-5 x 0.1) = 8.7 x 10-6 b.qt = qt-1 + Δq = 0.1 + 8.7 x 10-6 = 0.1000087 pt = 1 - qt = 1 - 0.1000087 = 0.8999913 c.Equilibrium q = u / u + v = 1 x 10-5 / 1 x 10-5 + 0.3 x 10-5 = 0.769

Five hundred years ago an earthquake caused the separation of a piece of the mainland such than an island population was formed. However, migration can still occur between the mainland and the island. Consider a single locus with the alleles A and a. The frequency of the A allele on the mainland is 0.7 and while the frequency of A the island is 0.4. What would be the new frequency of A on the island if 5% of parents for the next generation were migrants from the mainland?

pi' = (1 - m)pi + mpm = (1 - 0.05) x 0.4 + 0.05 x 0.7 = 0.38 + 0.035 = 0.415

Consider two populations, one on the mainland (m), one on an island (i). Migration can still occur between the mainland and the island. When considering a single locus with two alleles, p and q, what would be the new frequency of p on the island (pi') if pm = 0.6, pi = 0.4 and 10% of the parents for next generation are migrants from the mainland?

pi' = 0.42

For an irreversible mutation with a forward mutation rate of μ = 5 x 10-6, calculate the expected frequency of p after 10, 100 and 1000 generations, assuming the starting frequency of p = 1.

pt = p0 (1-u)t p10 = 1 x (1 - 5x10-6)10 = 0.99995 p100 = 1 x (1 - 5x10-6)100 = 0.9995 p1000 = 1 x (1 - 5x10-6)1000 = 0.995

When considering how mutation affects allele frequencies, we can encounter scenarios where there is both forward and reverse mutation. What formula can be used to calculate the new frequency of the allele designated p in the next generation when both forward and reverse mutation are in play?

pt = pt (1 - μ) + qtν

Calculate the relative fitness for the following population: BB: 500 born, 475 lived to adulthood Bb: 1000 born, 800 lived to adulthood bb: 400 born, 225 lived to adulthood

wBB= 1 wBb= .80/.95 = .842 Wbb= .5625/.95 = .592

What three conditions must be met in order to measure the mutation rate of a dominant mutation based on phenotype frequency?

· Mutation must produce a distinct phenotype - different to any phenotype produced by a recessive mutations · The mutation must be completely penetrant · Phenotype cannot be caused by any environmental effects, chemicals or toxins etc.