Quantitative Genetics in the Age of Genomics

1. Quantitative Genetics in the Age of Genomics

2. Classical Quantitative Genetics • Quantitative genetics deals with the observed variation in a trait both within and between populations • Basic model (Fisher 1918): The phenotype (z) is the sum of (unseen) genetic (g) and environmental values (e) • z = g + e • The genetic value needs to be further decomposed into an additive part A passed for parent to offspring, separate from dominance (D) and epistatic effects (I) that are only fully passed along in clones • g = A + D + I • Var(g)/Var(z) is quantitative measure of nature vs. nurture • fraction of all trait variation due to genetic differences

3. Fisher’s great insight: Phenotypic covariances between relatives can estimate the variances of g, e, etc. • For example, in the simplest settings, • Cov(parent,offspring) = Var(A)/2 • Cov(Full sibs) = Var(A)/2 + Var(D)/4 • Cov(clones) = Var(g) = Var(A)+Var(D)+Var(I) • Random-effects model • Interest is in estimating variances • Thus, in classical quantitative genetics, a few statistical descriptors describe the underlying complex genetics • This leaves an uneasy feeling among most of my molecular colleagues. • Does the age of genomics usher in the death knell of Quantitative Genetics?

4. Approximate costs of genome projects • Arabidopsis Genome Project ... $500 million • Drosophila Genome Project ... $1 billion • Human Genome Project ... $10 billion • Working knowledge of multivariate statistics ... Priceless

5. Model systems

6. Euchloe guaymasensis

7. Neoclassical Quantitative Genetics • Use information from both an individual’s phenotype (z) and marker genotype (m) • z = u + Gm +g + e • Gm is genotypic value associated with the scored genotype (m ) • Obvious extensions: include Gm x e and Gm x g • Mixed model: can treat as the Gm as fixed effects; g and e as random • My molecular colleagues hope that Gm accounts for most of the variance in the trait • If true, then Var(g)/Var(z) trivial

8. Limitations on Gm • The importance of particular genotypes may be quite fleeting • can easily change as populations evolve and as the biotic and abiotic environments change • If epistasis and/or genotype-environment interactions are significant, any particular genotype may be a good, but not exceptional, predictor of phenotype • Quantitative genetics provides the machinery necessary for managing all this uncertainty in the face of some knowledge of important genotypes • e.g., proper accounting of correlations between relatives in the unmeasured genetic values (g)

9. The importance of even rather imperfect marker information • Suppose an F1 is segregating favorable alleles at n loci, and we inbred to fixation before selecting among pure lines • Pr (fixation favorable allele) = 1/2 • What are the required number of lines for Pr (at least one line fixed for n favorable alleles) = 0.9? • For n = 10: 2,360 lines • For n = 20: 2,400,000 lines • Suppose marker information increases the probability of fixation by 50% (to 0.75) • Required number of lines for Prob(at least one line fixed for n favorable alleles) = 0.9 • Forn = 10: 40 lines (60-fold reduction) • Forn = 20: 725 lines (3,300-fold reduction)

10. How do we obtain Gm? • Ideally, we screen a number of candidate loci • QTL (Quantitative trait locus) mapping • Uses molecular markers to follow which chromosome segments are common between individuals • This allows construction of a likelihood function, e.g.,

11. A typical QTL map from a likelihood analysis

12. Genomics and candidate loci • Typical QTL confidence interval 20-50 cM • The big question: how do we find suitable candidates? • The hope is that a genomic sequence will suggest candidates

13. Genomics tools to probe for candidates • Dense marker maps • Complete genome sequence • Expression data (microarrays) • Proteomics • Metablomics

14. The accelerating pace of genomics • Faster and cheaper sequencing • Rapid screening of thousands of loci via DNA chips • “Phylogenetic bootstrapping” from model systems to distant relatives

16. Prediction of Candidate Genes • Try homologous candidates from other species • Examine all Open Reading Frames (ORFs) within a QTL confidence interval • Expression array analysis of these ORFs • Lack of tissue-specific expression does not exclude a gene • Proteomics • Specific protein motifs may provide functional clues • Cracking the regulatory code (in silico genetics) • Analysis of networks and pathways

17. Searching for Natural Variation • This may be the area where genomics has the largest payoff • Source (natural and/or weakly domesticated) populations contain more variation than the current highly domesticated lines • Key is to first detect and localize importance variants, then introgress them into elite lines

18. Impact of other biotechnologies • Cloning, other reproductive technologies • Maintain elite lines as cell cultures? • Embryo transplation into elite maternal lines? • Transgenics • Important tool in both breeding and evolutionary biology • Complications: • Silencing of multiple copies in some species • Strong position effects • Currently restricted to major genes • Major genes can have deleterious effects on other characters • Importance of quantitative genetics for selecting for background polygenic modifiers

19. Useful Tools for Quantitative Genetic analysis • Four subfields of Quantitative Genetics • Plant breeding • Animal breeding (forest genetics) • Evolutionary Genetics • Human Genetics • Restricted communications between fields • Important tools often unknown outside a field

20. Tools from Plant Breeding • Special features dealt with by plant breeders • Diversity of mating systems (esp. selfing) • Sessile individuals • Issues • Creation and selection of inbred lines • Hybridization between lines • Genotype x Environment interactions • Competition • Plant breeding tools useful in other fields • Field-plot designs • G x E analysis models: AMMI and biplots • These designs are also excellent candidates for the analysis of microarray expression data • Covariance between inbred relatives • Line cross analysis

21. Animal Breeding • Special features • Complex pedigrees • Large half-sib (more rarely full-sib) families • Long life spans • Overlapping generations • Tree breeders face many of these same issues • Animal breeding tools useful in other fields • BLUP (best linear unbiased predictors) for genotypic values • REML (restricted maximum likelihood) for variance components • BLUP/REML allow for arbitrary pedigrees, very complex models • Maternal effects designs • Endosperm work of Shaw and Waser • Selection response in structured populations

22. Evolutionary Genetics • Issues • Estimating the nature and amount of selection • Population-genetic models of evolution • Tools • Estimation of the nature of natural selection on any specified character • Lande-Arnold fitness estimation; cubic splines • Using DNA sequences to detect selection on a locus • Example: teosinte-branched 1 • Coalescent theory • The genealogy of DNA sequences within a random sample • Analysis of finite-locus and non-Gaussian models of selection response • Barton and Turelli; Burger

23. Human Genetics • Issues • Very small family sizes • Lack of controlled mating designs • Tools of potential use • Sib-pair approaches for QTL mapping • QTL mapping in populations • Transmission-disequilibrium test (TDT) • Account for population structure • Linkage-disequilibrium mapping • Use historical recombinations to fine-map genes • Random-effects models for QTL mapping • BLUP/REML-type analysis over arbitrary pedigrees

24. A Bayesian Future? • 1970s saw the start of a shift in QG from methods-of moments approaches (i.e., estimators based on sample means and variance)to likelihood approaches that use the entire distribution of the data • Initial objections to having to specify a likelihood function, • L(u | data) • As these methods became computationally feasible, they started to supplant their method-of-moments counterparts. • Similarly, Bayesian approaches have become much more computationally feasible recently because of both advances in computational power and a greater appreciation of the power of resampling methods (MCMC and Gibbs samplers)

25. Posterior ( u | data ) = C* Likelihood ( u | data) * prior (u)

26. Why Bayesian? • Marginal posteriors • The effects of the uncertainty in estimating nuisance parameters (those not of interest) are fully accounted for. • Exact for small sample size • Powerful interative sampling methods (MCMC, Gibbs) allow Bayesian analysis to work on problems with a very large number of parameters and relative few actual data points (vectors)

27. Conclusions • Genomics will increase, not decrease, the importance of quantitative genetics • The machinery of classical quantitative genetics is easily modified (indeed, it is actually preadapted) to account for massive advances in genomics and other fields of biotechonology • Useful and powerful tools have been developed to address specific issues in the various subfields of quantitative genetics • Bayesian analysis will continue to increase in importance