Name: Answer Key

BIOL 464/GEN 535 Population GeneticsFall 2011

Test # 2, 11/2/2011

Please answer all questions unless otherwise specified. Show as much of your work as you can, including which formulas you use (even if actual calculations are done with software). Use the back of the page and additional sheets as necessary.

1. Indicate the correct relationship between the terms or parameters in the table, all else being equal. (15 points)

Term 1 ≤ or ≥ or =

Term 2

1 Genetic drift in large populations ≤ Genetic drift in small populations2 HT ≥ Average HS

3 Census population size ≥ Effective population size4 Number of alleles prior to bottleneck ≥ Number of alleles after bottleneck5 FST with high gene flow between populations ≤ FST with low gene flow between populations6 Variance in allele frequencies among

completely isolated populations undergoing genetic drift

≥ Variance in allele frequencies within completely isolated populations undergoing genetic drift

7 FST among populations with very small effective population sizes

≥ FST among populations with very large effective population sizes

8 Average allele frequency among many isolated subpopulations before genetic drift

= Average allele frequency among many isolated subpopulations after genetic drift

9 Genetic match probability with genotyping error included

≥ Genetic match probability without considering genotyping error

10 Genetic match probability with population structure included

≥ Genetic match probability without considering population structure

11 FRT ≤ FST

12 Match probability for 10 loci with 2 alleles with equal population frequencies

≥ Match probability for 2 loci with 10 alleles with equal population frequencies

13 Time to coalescence for first coalescent event for a locus with six alleles

≤ Time to coalescence for fifth coalescent event for a locus with six alleles

14 Average time to fixation of a favored allele in a large population

≥ Average time to fixation of a favored allele in a small population

15 Number of possible rooted trees for a group of taxa

≥ Number of possible unrooted trees for a group of taxa

2. The following phylogeny and Structure bar plot was derived from 96 microsatellite genotypes for 69 dog breeds (Parker et al. 2004)

Parker et al. 2004. Genetic Structure of the Purebred Domestic Dog. Science 304: 1160-1164.

A. Based on the phylogenetic tree above, mark the following statements True or False (5 points)

1. The Akita is more closely related to the Siberian Husky than to the Afghan Hound. T F False2. The Akita is more closely related to the Chow Chow than to the Shiba Inu. T F True3. The Akita is more closely related to the Shiba Inu than to the Chinese Shar-Pei. T F True4. The Basenji is more closely related to the Siberian Husky than to the Saluki. T F False5. The Basenji is more closely related to the Saluki than to the Akita. T F True

B. Based on the figures on the previous page, propose a reasonable hypothesis for the origin and evolution of the Alaskan Malamute (marked with circle). (5 points)

Based on the phylogenetic tree, it is reasonable to assume that the Alaskan Malamute is derived from the Gray wolf. However, the results of the Structure analysis suggest that there has been recent admixture between the modern gray wolf and another Malamute ancestor that is more closely-related to domesticated dog breeds. Therefore, the Malamute breed probably results from recent hybridization, either through directed breeding efforts or through secondary contact between feral dogs and wolves.

C. Why do you think the phylogenetic analysis failed to resolve the relationships among most of the highly domesticated breeds? (5 points)

Domesticated dog breeds are probably highly similar across most of their genomes due to their rather recent evolution from a common ancestor as well as the very specific breeding targets that drove the crossing efforts, targeting relatively small portions of the dog genomes. Therefore, the most discriminant markers may not have been used in this phylogenetic analysis, which was based on noncoding microsatellites. More importantly, modern breeds are the result of extensive cross-hybridization among different lineages, which is difficult to recreate with a simple, bifurcating tree such as that which results from a Neighbor-Joining analysis.

D. What additional analyses would you perform with this same set of genetic data to evaluate substructure and relationships among the breeds? (5 points)

The first, and probably most important analysis, is to determine if Structure will detect further subdivision in this dataset using k>2 a priori groups. The most likely number of groups could be determined from the likelihood ratios derived from the mean posterior probabilities of each run, or by the delta-k method of Evanno et al. 2005. After this initial run, subsequent runs of structure should be performed on each of the groups identified in the full dataset. This procedure should be continued until k=1 is the best-supported grouping for each subgroup. This would provide a much more fine-grained view of the relationships among the groups, and in principle should be able to accommodate admixture among the breeds.

Many student answered this question by stating that they would perform some form of AMOVA on the breeds. This approach is likely to be inferior to the phylogenetic approaches because it wouldn’t readily recapitulate the hierarchical relationships among the breeds, and it would still be subject to the same limitations that are listed above for the phylogenetic analysis.

Answers that suggested some form of additional data gathering received partial credit. This almost always helps enhance resolution.

Locus Fish Genotype Blackwater Creek (native) Allele Frequencies

Tygart Lake (stocked) Allele Frequencies

1 121 121 0.68 0.68 0.24 0.242 135 139 0.59 0.32 0.07 0.093 148 154 0.69 0.31 0.21 0.06

3. A Fish and Game warden detains a fisherman suspected of catching trout illegally in Blackwater Creek, where fishing is prohibited. The fisherman claims to have caught the fish legally in a recreational lake that is routinely stocked. The warden, having taken BIOL 464, decides to resolve the issue with microsatellites. Based on the following profile, calculate an appropriate likelihood ratio. Be sure to state the two hypotheses that you are comparing, and present a proper interpretation of the results. (15 points)

See the Excel sheet for the calculations.

Hypothesis 1: The fish comes from the Blackwater Creek population.Hypothesis 2: The fish comes from Tygart Lake (or some other location stocked from the same ponds)

Equations for determining the probability of observing a genotype in a given population:2lilk pP ljlilk ppP 2

m

kkPP

1

P(G|H1)= (0.68)2(2)(0.59)(0.32)(2)(0.69)(0.31) = 0.0747P(G|H1)= (0.24)2(2)(0.07)(0.09)(2)(0.21)(0.06) = 1.83x10-5

L( H1 , H2|G)= LR=P(G|H1 )P (G|H2 )

= 0 . 07471. 83 x10−5 =4084 . 1

It approximately 4084 times more likely that the fish came from Blackwater Creek than from Tygart Lake. Therefore, it appears that the angler should be fined for illegally catching protected fish.

4. Blackwater Creek in problem 3 has a highly degraded trout population due to historical overfishing and habitat degradation. The current population size is estimated to be 50. Only two alleles are detected for Locus 3, as shown in the table.

a. What is the probability that allele 148 will eventually become fixed in this population due to genetic drift? (5 points)

This is simply the allele frequency: 0.690)( qqu

b. What is the mean expected time to fixation for allele 148 in the Blackwater Creek population? (10 points)

You can either use the diffusion approximation for this, or you can do the simulations in Populus, as we did in the lab.Diffusion approximation:

T ( p )=−4 N (1− p ) ln (1− p)

p=

−4(50 )(1−0 . 69) ln (1−0. 69 )0 .69

=105.24

It will take approximately 105 generations for this allele to reach fixation.

c. What are the key assumptions of this calculation? What would cause underestimation of the time to fixation? What could cause overestimation? (5 points)

The primary assumption is that census population size is a reasonable approximation of the drift effective population size. This essentially means that Hardy-Weinberg conditions are met currently (i.e., random mating, no immigration, no selection, equal sex ratio), and that there haven’t been gigantic fluctuations in population size historically.

5. The following table contains data from locus 3 for 7 trout populations. a. Assuming equal population sizes, estimate the proportion of genetic variation that is due to

differentiation among populations. (10 points)

See excel sheet for the calculations.HS=0.41GST=0.023

Approximately 2.3% of the total genetic variation is due to differentiation among subpopulations

b. What can you infer about the degree of connectedness and genetic exchange among these populations? (5 points)

The low amount of differentiation among populations suggests that there is a high degree of connectivity historically. This may not be reflective of current amounts of genetic exchange, because there may not currently be an equilibrium between genetic drift and mutation, a prerequisite for drawing inferences about connectedness from population structure estimates.

c. Based on this calculation, would you revise your conclusions in problem 4? Why? (5 points)

Problem 4 should certainly be revisited because the drift calculation assumes that the creek is isolated from other sources of genetic material. Fixation might be much slower than what we predicted based on an effective population size of 50.

HT = 0.42

)(11

m

iSiS H

mH STST HHD

T

STST H

DG

Population HSi

Blackwater Creek 0.47Poplar Creek 0.29Cheat River 0.40Monongahela River 0.48New River 0.45Gauley River 0.47Shavers Fork 0.31

Short Answer. Graduate students answer any 3. Undergraduates answer any 2. Please aim for no more than a paragraph (less than 150 words) per answer. (Grads: 10 points each; Undergrads: 15 points each)

6. Explain how genetic drift plays a central role in Wright’s Shifting Balance theory.

Wright’s shifting balance theory posits that populations are divided into isolated demes that can become differentiated through random genetic drift at the many loci that make up the genome. These multi-locus genotypes will therefore vary extensively and somewhat randomly, thereby sampling a varied fitness landscape. Selection will tend to push demes up local adaptive peaks, while drift can allow demes to move off of local peaks, cross fitness valleys, and subsequently reach other adaptive slopes. Selection will then push the deme to a new peak. Low levels of gene exchange among demes will enable occasional bouts of mass selection, when multilocus genotypes on particularly high adaptive peaks will sweep through the entire population, enabling directional evolution of the entire population.

7. A. How does genetic drift affect the efficiency of selection in small populations? Genetic drift has a two-fold effect on the efficiency of selection. On the one hand, alleles with higher marginal fitness can be pushed to selection much more quickly in small populations than in large ones. However, if 4NeS<1, drift plays a predominant role and alleles with lower marginal fitness can become fixed by chance alone, thereby controverting the effects of directional selection within a population.

B. How does the level of dominance affect this relationship?

The level of dominance will somewhat accentuate the effects of genetic drift by protecting alleles from selection in heterozygotes, in cases where the allele with higher marginal fitness is also dominant. In cases where the allele with lower marginal fitness is dominant, fixation should occur more quickly.

8. What is the difference between cladistic and phenetic approaches to phylogenetic analysis? What are the advantages and disadvantages of each?

Cladistic approaches are essentially distance-based approaches to phylogenetic analysis that rely upon construction of bifurcating trees that hierarchically group taxa that are progressively less closely related. The advantages of this approach are that it is objective, typically relies upon a readily-understood quantitative model and is generally computationally tractable.

Phenetic approaches typically have an underlying evolutionary model to represent the inheritance of characters from common ancestors. Different tree topologies are compared based on the number of required character state changes to arrive at the final state of the operational taxonomic units. The principle of parsimony drives most methods, with the assumption being that the scenario requiring the smallest number of steps is the most likely one. Phenetic approaches are favored by many because they have an underlying evolutionary model and therefore explicitly represent a biological hypothesis. Evolutionary changes can be readily mapped onto phenetic trees, and evolutionary hypotheses can be directly generated and assessed. A disadvantage is that the methods are generally more computationally intensive than cladistics approaches, and they are perceived to be subjective by some practitioners.

9. Compare and contrast coalescent and phylogenetic approaches to the study of evolution. How does one depend on the other?

These approaches are highly related in that they both try to reconstruct ancestral relationships based on extant taxa based on inference about common ancestors. Phylogenetic approaches reconstruct nodes of a phylogenetic tree that represent putative ancestral states, and they typically rely upon multiple character states. Coalescent trees typically refer to a specific molecule or entity, and they attempt to reconstruct demographic events that lead back in time to the coalescence of different forms of that molecule or entity (usually alleles). In many ways coalescent approaches are more flexible than phylogenetic approaches because they have explicit underlying population models with parameters depicting historical demographic events. Phylogenetic approaches assume coalescence of the measured character states are concordant with the evolutionary events represented in the phylogeny of the taxa. This is not always the case, such as when gene trees do not match species trees due to incomplete lineage sorting, essentially when coalescence occurs following population subdivision leading to the evolution of the two taxa.

10. List at least three possible types of errors in paternity analysis, and explain how each of these can these be overcome.

1. Genotyping Error causes false exclusion of the true father. This can be overcome by using likelihood-based approaches that account for genotyping error by allowing some degree of mismatch between paternal and offspring genotypes.

2. No males are compatible with the offspring. This could be caused by gene flow from unsampled males. This can be circumvented by sampling more males until the true father is found.

3. Cryptic gene flow. Compatible males are identified within the sampled population, but the true father is an unsampled male that happened to produce a gamete that is compatible with the genotypes of the sampled males. This can be minimized by adding genetic power and sampling more males.

4. Multiple males are compatible. This can be circumvented by using more genetic markers and/or by incorporating priors into the likelihood calculation that account for differential probability of paternity (e.g., in the case of plants, fecundity and proximity are good predictors of paternity)

11. What does the following equation mean, what are its underlying assumptions, and what are some alternatives to this approach?

ST

ST

FFNm

41

This equation relates the effective population size and the migration rate to the degree of population differentiation. One underlying assumption is that there is an equilibrium between mutation and genetic drift, such that genetic differentiation is primarily an inverse function of degree of connectedness. Another assumption is that mutation is negligible and can be safely ignored. Finally, the simplified form of this equation assumes that the migration rate is relatively low, such that the m2 and 2m terms can be disgregarded.

The approach is potentially flawed, primarily because the equilibrium assumption and island models often do not hold in real populations. An alternative is to measure gene flow between populations directly, either using parentage analysis techniques or some form of mark-recapture experiment. It also may be possible to examine contemporary movement using population assignment techniques.