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Chapter 2 Genotype Frequencies
2.1 Mendel's model of particulate genetics
Mendel's breeding experiments. Independent assortment of alleles. Independent
segregation of loci. Some common genetic terminology.
2.2 Hardy-Weinberg Expected Genotype Frequencies
Hardy-Weinberg and its assumptions. Each assumption is a population genetic process.
Hardy-Weinberg is a null model. Hardy-Weinberg in haplo-diploid systems.
Interact Box 2.1 Genotype frequencies.
2.3 Why does Hardy-Weinberg work?
A simple proof of Hardy-Weinberg. Hardy-Weinberg with more than 2 alleles.
2.4 Applications of Hardy-Weinberg
Apply Hardy-Weinberg to estimate the frequency of an observed genotype in a forensic
DNA typing case. The χ2 test to gauge if observed and expected differ more than
expected by chance. Assume Hardy-Weinberg to compare two genetic models.

Problem 2.1 The expected genotype frequency for a DNA profile
Box 2.1 DNA Profiling
Interact Box 2.2 χ2 test
Problem 2.2 Proving allele frequencies are obtained from expected genotype frequencies
Problem 2.3 Inheritance for corn kernel phenotypes

2.5 The Fixation Index and Heterozygosity
The fixation index (F) measures deviation from Hardy-Weinberg expected
heterozygote frequencies. Examples of mating systems and F in wild populations.
Observed and expected heterozygosity.

Interact Box 2.3 Assortative mating and genotype frequencies
Box 2.2 Protein locus or allozyme genotyping

2.6 Mating among relatives
Consanguineous mating alters genotype frequencies but not allele frequencies. Mating
among relatives and the probability that two alleles are identical by descent. Inbreeding depression and its possible causes. The many meanings of inbreeding.

2.7 Gametic Disequilibrium
Estimating gametic disequilibrium with D. Approach to gametic equilibrium over time
Causes of gametic disequilibrium.

Interact Box 2.4 Decay of gametic disequilibrium and a χ2 test
Interact Box 2.5 Gametic disequilibrium under both recombination and natural selection
Interact Box 2.6 Estimating genotypic disequilibrium

Chapter 3 Genetic Drift and Effective Population Size
3.1 The effects of sampling lead to genetic drift
Biological populations are finite. A simple sampling experiment with microfuge tube
"populations." Wright-Fisher model of sampling. Sampling error and genetic drift in
biological populations.
Interact Box 3.1 Genetic drift
3.2 Models of genetic drift
An introduction to the binomial and Markov chains. The diffusion approximation of
genetic drift.

Problem 3.1 Applying the binomial formula
Math Box 3.1 Variance of a Binomial Variable
Interact Box 3.2 Genetic drift simulated with a Markov chain model
Problem 3.2 Constructing a transition probability matrix

3.3 Effective population size
Defining genetic populations. Census and effective population size. Example of
bottleneck and harmonic mean to demonstrate effective population size versus census
size. Effective population size due to unequal sex ratio and variation in family size.

Problem 3.3 Estimating Ne from information about N

3.4 Parallelism between drift and inbreeding
Autozygosity due to sampling in a finite gamete population. The relationship between
the fixation index (F) and heterozygosity (H). Decline in heterozygosity over time due to
genetic drift. Heterozygosity in island and mainland populations.

Interact Box 3.3 Heterozygosity and inbreeding over time in finite populations

3.5 Estimating effective population size
Variance and inbreeding effective population size. Breeding effective population size in
continuous populations. Effective population sizes for different genomes.

Problem 3.4 Estimating Ne from observed heterozygosity over time

3.6 Gene genealogies and the coalescent model
Modeling the branching of lineages to predict the time to the most recent common
ancestor.

Math Box 3.2 Approximating the probability of a coalescent event with the exponential distribution

Interact Box 3.4 Build your own coalescent genealogies

3.6 Effective population size in the coalescent model
The coalescent model effective population size. Coalescent genealogies and population
bottlenecks. Coalescent genealogies in growing and shrinking populations.

Interact Box 3.5 Simulating gene genealogies in populations with different effective sizes
Interact Box 3.6 Coalescent Genealogies in Populations with Changing Size

Chapter 4 Population Structure and Gene Flow
4.1 Genetic populations
Genetic versus geographic organization of populations. Isolation by distance and
divergence of populations. Gene flow and migration. Direct and indirect measures of
gene flow.

Method Box 4.1 Are allele frequencies random or clumped in two dimensions?

4.2 Direct measures of gene flow
Genetic marker based parentage analysis.

Problem Box 4.1 Calculate the probability of a random haplotype match and the
exclusion probability
Interact Box 4.1 Average exclusion probability for a locus

4.3 Fixation indices to measure the pattern of population subdivision
Extending the fixation index to measure the pattern of population structure through FIS, FST and FIT.

Problem Box 4.2 Compute FIS, FST and FIT.
Method Box 4.2 Estimating fixation indices.

4.4 Population subdivision and the Wahlund effect
Genetic variation can be present as heterozygosity within a panmictic population or as
differences in allele frequency among diverged subpopulations.

Interact Box 4.2 Simulating the Wahlund effect
Problem Box 4.3 Account for population structure in a DNA profile match probability

4.5 Models of population structure
Continent-island, two island and infinite island models. Stepping stone and
metapopulation population models. General expectations and conclusions from the
different migration models.

Interact Box 4.3 Continent-island model of gene flow
Interact Box 4.4 Two island model of gene flow
Math Box 4.1 The expected value of FST in the infinite island model
Problem Box 4.4 Expected levels of FST for Y-chromosome and organelle loci
Interact Box 4.5 Finite island model of gene flow

4.6 The impact of population structure on genealogical branching
Bugs in many boxes. Event times with population subdivision. Sample configurations.
Mean and variance of waiting time in a two demes.

Interact Box 4.6 Coalescent events in two demes
Math Box 4.2 Solving two equations with two unknowns for average coalescence times

Chapter 5 Mutation
5.1 The source of all genetic variation
Types of mutations and rates of mutation. How can a low probability event like mutation
account for genetic variation? The spectrum of fitness for mutations.

5.2 The fate of a new mutation
The chance a neutral or beneficial is lost due to Mendelian segregation. Mutations fixed by natural selection. Frequency of a mutant allele in a finite population. Accumulation of deleterious mutations by Muller's ratchet without recombination.

Interact Box 5.1 Frequency of neutral mutations in a finite population
Interact Box 5.2 Muller's ratchet

5.3 Mutation models
The infinite alleles, k alleles and stepwise mutation models. Understanding the
implications of mutation models using the standard genetic distance and RST. The infinite sites and finite sites mutation models for DNA sequences.

Interact Box 5.3 RST and FST as examples of the consequences of different mutation
models

5.4 The influence of mutation on allele frequency and autozygosity
Irreversible and bi-directional mutation models. The parallels between the processes of mutation and gene flow. Expected autozygosity at equilibrium under mutation and
genetic drift. Expected heterozygosity and the biological interpretation of θ.

Math Box 5.1 Equilibrium allele frequency with two-way mutation
Interact Box 5.4 Simulating irreversible and bi-directional mutation

5.5 The coalescent model with mutation
Adding the process of mutation to coalescence. Longer genealogical branches
experience more mutations. Genealogies under the infinite alleles and infinite sites
models of mutation.

Interact Box 5.5 Build your own coalescent genealogies with mutation

Chapter 6 Fundamentals of Natural Selection
6.1 Natural Selection
Translating Darwin's ideas into a model. Natural selection as differential population
growth. Natural selection with clonal reproduction. Natural selection with sexual
reproduction and its assumptions.

Problem Box 6.1 Relative fitness of human immunodeficiency virus (HIV) genotypes
Math Box 6.1 The change in allele frequency each generation under natural selection

6.2 General results for natural selection on a diallelic locus
Selection against a recessive phenotype. Selection against a dominant phenotype. The
general effects of dominance. Heterozygote disadvantage and advantage. The strength
of natural selection.
Math Box 6.2 Equilibrium allele frequency with overdominance

6.3 How natural selection works to increase average fitness
Natural selection acts to increase mean fitness. The fundamental theorem of natural
selection.

Problem Box 6.2 Mean fitness and change in allele frequency
Interact Box 6.1 Natural selection on one locus with two alleles

Chapter 7 Further Models of Natural Selection
7.1 Viability selection with three alleles or two loci
Mean fitness surfaces. Natural selection on one locus with three alleles. Natural
selection on two diallelic loci.
Problem Box 7.1 Marginal fitness and Δp for the Hb C allele.
Interact Box 7.1 Natural selection on one locus with three or more alleles

7.2 Alternative models of natural selection
Moving beyond the assumptions of fitness as constant viability in an infinitely growing
population. Natural selection via different levels of fecundity. Natural selection with frequency-dependent fitness. Natural selection with density-dependent fitness.

Math Box 7.1 The change in allele frequency with frequency dependent selection
Interact Box 7.2 Frequency-dependent natural selection
Interact Box 7.3 Density-dependent natural selection

7.3 Combining natural selection with other processes
Natural selection and genetic drift acting simultaneously. The balance between natural selection and mutation.

Interact Box 7.4 The balance of natural selection and genetic drift at a diallelic locus
Interact Box 7.5 Natural selection and mutation

7.4 Natural selection in genealogical branching models
The problem modeling natural selection in genealogical branching models. Directional
selection and the ancestral selection graph. Genealogies and balancing selection.

Problem Box 7.2 Resolving possible selection events on an ancestral selection graph
Interact Box 7.6 Coalescent genealogies with directional selection
Chapter 8 Molecular Evolution

8.1 Neutral theory
The neutral theory and its predictions for levels of polymorphism and rates of
divergence. Nearly neutral theory.
Interact Box 8.1 The relative strengths of genetic drift and natural selection

8.2 Measures of divergence and polymorphism
Measuring divergence of DNA sequences. Nucleotide substitution models correct
divergence estimates for saturation. DNA polymorphism measured by number of
segregating sites and nucleotide diversity.

Box 8.1 DNA sequencing
Interact Box 8.2 Estimating π and θ from DNA sequence data

8.3 DNA sequence divergence and the molecular clock
The molecular clock hypothesis for DNA divergence. Dating divergence events with a
molecular clock.
Problem Box 8.1 Estimating divergence times with the molecular clock

8.4 Testing the molecular clock hypothesis and explanations for rate variation in molecular
evolution
Rate heterogeneity in the molecular clock. The Poisson process model of the molecular
clock. Ancestral polymorphism and the molecular clock. Relative rate tests of the
molecular clock. Possible causes of rate heterogeneity.

Math Box 8.1 The dispersion index with ancestral polymorphism and divergence

8.5 Testing the neutral theory null model of DNA sequence evolution
The Hudson-Kreitman-Aguadé (HKA) test. The McDonald-Kreitman (MK) test.
Tajima's D statistic. Mismatch distributions.

Problem Box 8.2 Computing Tajima's D from DNA sequence data
Interact Box 8.3 The mismatch distribution for neutral genealogies in stable,
growing or shrinking populations

8.6 Molecular evolution of loci that are not independent
Gametic disequilibrium between neutral and selected sites influences polymorphism.
Genetic hitch-hiking and selective sweeps from positive selection. Genetic hitch-hiking due to background or balancing selection. Linkage and rates of divergence

8.7 Recombination in genealogical branching models
Adding the process of recombination to coalescence. The impact of recombination on
polymorphism.

Problem Box 8.3 The impact of recombination events on a genealogy
Interact Box 8.4 Coalescent genealogies with recombination

Chapter 9 Quantitative trait variation and evolution
9.1 Quantitative traits
Components of phenotypic variation. Components of genotypic variation (VG).
Inheritance of additive (VA), dominance (VD) and epistasis (VI) components of genotypic variation. Genotype by environment interaction (VGxE). Additional sources of phenotypic variation.

Problem Box 9.1 Phenotypic distribution produced by Mendelian inheritance of three
diallelic loci
Math Box 9.1 Summing two variances

9.2 Evolutionary change in quantitative traits.
Heritability and the breeder's equation. Changes in quantitative trait mean and variance due to natural selection. Estimating heritability by parent-offspring regression. Response to selection on correlated traits. Long-term response to selection. Neutral evolution of quantitative traits.

Interact Box 9.1 Estimating heritability with parent-offspring regression
Interact Box 9.2 Response to natural selection on two correlated traits
Interact Box 9.3 Response to selection and the number of loci that cause quantitative trait variation
Interact Box 9.4 Effective population size and genotypic variation in a neutral
quantitative trait

9.3 Quantitative trait loci (QTL)
QTL mapping with single marker loci. QTL mapping with multiple marker loci.
Limitations of QTL mapping studies. Biological significance of QTL mapping.

Problem Box 9.2 Compute the effect and dominance coefficient of a QTL
Problem Box 9.3 Derive the expected marker class means for a backcross mating design
Interact Box 9.5 Effect sizes and response to selection at quantitative trait loci (QTL)

Chapter 10 The Mendelian basis of quantitative trait variation
10.1 The connection between particulate inheritance and quantitative trait variation. The scale of genotypic values.

Problem Box 10.1 Compute values on the genotypic scale of measurement for IGF1 in
dogs

10.2 Mean genotypic value in a population.

10.3 Average effect of an allele.

Math Box 10.1 The average effect of the A1 allele
Problem Box 10.2 Compute average effects for IGF1 in dogs

10.4 Breeding value and Dominance deviation.

Interact Box 10.1 Average effects, breeding values and dominance deviations

10.5 Components of total genotypic variance.

Interact Box 10.2 Components of total genotypic variance VG
Math Box 10.2 Deriving the total genotypic variance VG

10.6 Genotypic resemblance between relatives.

Chapter 11 Synthetic topics
11.1 Historical controversies in population genetics
The classical and balance hypotheses. How to explain levels of allozyme polymorphism. Genetic load. The selectionist - neutralist debates.

11.2 Shifting balance theory
Sewall Wright's classic model of natural selection, genetic drift, gene flow and mutation on an adaptive landscape.

Appendix
Statistical uncertainty
Quantities in population genetics are estimated with error. Parameters and parameter
estimates. Introduction to variance, standard deviation and standard error.

Problem A.1: Estimating the variance
Interact Box A.1: The central limit theorem

Literature cited
Index