Genetics and Analysis of Quantitative Traits

by Lynch, Michael; Walsh, Bruce

• ISBN13: 9780878934812
• ISBN10: 0878934812
• Format: Hardcover
• Copyright: 1998-01-06
• Publisher: Sinauer Associates is an imprint of Oxford University Press

Summary

With the emerging recognition that the expression of most characters is influenced by multiple genes and multiple environmental factors, quantitative genetics has become the central paradigm for the analysis of phenotypic variation and evolution.

Genetics and Analysis of Quantitative Traits brings together the diverse array of theoretical and empirical applications of quantitative genetics under one cover, in a way that is both comprehensive and accessible to anyone with a rudimentary understanding of statistics and genetics. What was originally envisioned as a single text has now become two, with the focus of this first book being on the basic biology and methods of analysis of quantitative characters.

Three major features of Genetics and Analysis of Quantitative Traits distinguish it from earlier work. First, it reflects the explosive influx over the past few years of quantitative-genetic thinking into evolutionary biology. Second, in animal breeding, enormous strides have been made in the development of new techniques for estimating breeding values (for the purposes of identifying elite individuals in selection programs) and for estimating variance components from samples of complex pedigrees. In this text's last two chapters, the authors outline the basic principles of complex pedigree analysis, without getting bogged down in technical details. Third, Genetics and Analysis of Quantitative Traits provides a broad overview of the newly emerging array of techniques for quantitative-trait loci (QTL) analysis, currently one of the most active fields of quantitative-genetic research.

Genetics and Analysis of Quantitative Traits contains numerous fully-worked examples and illustrations of theoretical concepts, as well as over 2,000 references with indices by subject, author, and organism. In addition, the authors maintain a World Wide Web site featuring up-to-date lists of computer programs and on-line resources, and added information on various topics presented in the text.

Author Biography

Michael Lynch is Distinguished Professor of Biology at Indiana University.

Bruce Walsh is a Professor in the Department of Ecology and Evolutionary Biology at the University of Arizona.

Table of Contents

CONTENTS	i	(12)
PREFACE	xiii
I. FOUNDATIONS OF QUANTITATIVE GENETICS	1	(318)
1. AN OVERVIEW OF QUANTITATIVE GENETICS	3	(16)
The Adaptationist Approach to Phenotypic Evolution	3	(1)
Quantitative Genetics and Phenotypic Evolution	4	(3)
Historical Background	7	(6)
The Major Goals of Quantitative Genetics	13	(3)
The nature of quantitative-trait variation	13	(1)
The consequences of inbreeding and outcrossing	14	(1)
The constraints on the evolutionary process	15	(1)
The estimation of breeding values	15	(1)
The development of predictive models for evolutionary change	16	(1)
Mathematics in Biology	16	(3)
2. PROPERTIES OF DISTRIBUTIONS	19	(16)
Parameters of Univariate Distributions	19	(7)
The Normal Distribution	26	(6)
The truncated normal distribution	29	(3)
Confidence Intervals	32	(3)
3. COVARIANCE, REGRESSION, AND CORRELATION	35	(16)
Jointly Distributed Random Variables	35	(1)
Expectations of jointly distributed variables	36	(1)
Covariance	36	(3)
Useful identities for variances and covariances	38	(1)
Regression	39	(4)
Derivation of the least-squares linear regression	39	(2)
Properties of least-squares regressions	41	(2)
Correlation	43	(2)
A Taste of Quantitative-Genetic Theory	45	(6)
Directional selection differentials and the Robertson-Price identity	45	(2)
The correlation between genotypic and phenotypic values	47	(1)
Regression of offspring phenotype on parental phenotype	48	(3)
4. PROPERTIES OF SINGLE LOCI	51	(30)
Allele and Genotype Frequencies	52	(2)
The Transmission of Genetic Information	54	(7)
The Hardy-Weinberg principle	54	(2)
Sex-linked loci	56	(1)
Polyploidy	57	(3)
Age structure	60	(1)
Testing for Hardy-Weinberg Proportions	60	(1)
Characterizing the Influence of a Locus on the Phenotype	61	(2)
The Basis of Dominance	63	(2)
Fisher's Decomposition of the Genotypic Value	65	(4)
Partitioning the Genetic Variance	69	(2)
Additive Effects, Average Excesses, and Breeding Values	71	(3)
Extensions to Multiple Alleles and Nonrandom Mating	74	(7)
Average excess	74	(1)
Additive effects	75	(1)
Additive genetic variance	76	(5)
5. SOURCES OF GENETIC VARIATION FOR MULTILOCUS TRAITS	81	(26)
Epistasis	82	(3)
A General Least-Squares Model for Genetic Effects	85	(9)
Extension to haploids and polyploids	92	(2)
Linkage	94	(6)
Estimation of gametic phase disequilibrium	97	(3)
Effect of Disequilibrium on the Genetic Variance	100	(7)
The evidence	103	(4)
6. COMPONENTS OF ENVIRONMENTAL VARIATION	107	(24)
Extension of the Linear Model to Phenotypes	108	(3)
Special Environmental Effects	111	(12)
Within-individual variation	112	(4)
Developmental homeostasis and homozygosity	116	(5)
Repeatability	121	(2)
General Environmental Effects of Maternal Influence	123	(4)
Genotype x Environmental Interaction	127	(4)
7. RESEMBLANCE BETWEEN RELATIVES	131	(46)
Measures of Relatedness	132	(9)
Coefficients of identity	133	(2)
Coefficients of coancestry and inbreeding	135	(5)
The coefficient of fraternity	140	(1)
The Genetic Covariance Between Relatives	141	(5)
The Effects of Linkage and Gametic Phase Disequilibrium	146	(7)
Linkage	146	(4)
Gametic phase disequilibrium	150	(3)
Assortative Mating	153	(8)
Polyploidy	161	(1)
Environmental Sources of Covariance Between Relatives	162	(8)
The Heritability Concept	170	(7)
Evolvability	175	(2)
8. INTRODUCTION OF MATRIX ALGEBRA AND LINEAR MODELS	177	(28)
Multiple Regression	177	(5)
An application to multivariate selection	180	(2)
Elementary Matrix Algebra	182	(10)
Basic notation	182	(1)
Partitioned matrices	183	(1)
Addition and subtraction	183	(1)
Multiplication	184	(2)
Transposition	186	(1)
Inverses and solutions to systems of equations	187	(2)
Determinants and minors	189	(1)
Computing inverses	190	(2)
Expectations of Random Vectors and Matrices	192	(1)
Covariance Matrices of Transformed Vectors	193	(1)
The Multivariate Normal Distribution	194	(4)
Properties of the MVN	195	(3)
Overview of Linear Models	198	(7)
Ordinary least squares	200	(2)
Generalized least squares	202	(3)
9. ANALYSIS OF LINE CROSSES	205	(46)
Expectations for Line-cross Means	206	(7)
Estimation of Composite Effects	213	(9)
Hypothesis testing	215	(4)
Line crosses in Nicotiana rustica	219	(2)
Additional data	221	(1)
The Genetic Interpretation of Heterosis and Outbreeding Depression	222	(4)
Variance of Line-cross Derivatives	226	(5)
Biometrical Approaches to the Estimation of Gene Number	231	(13)
The Castle-Wright estimator	233	(5)
Effect of the leading factor	238	(3)
Extensions to haploids	241	(3)
Other Biometrical Approaches to Gene Number Estimation	244	(7)
The inbred-backcross technique	244	(2)
Genotype assay	246	(5)
10. INBREEDING DEPRESSION	251	(42)
The Genetic Basis of Inbreeding Depression	252	(7)
A more general model	256	(3)
Methodological Considerations	259	(10)
Single-generation analysis	260	(2)
Multigenerational analyses	262	(4)
Ritland's method	266	(1)
Epistasis and inbreeding depression	267	(1)
Variance in inbreeding depression	268	(1)
The Evidence	269	(5)
Purging Inbreeding Depression	274	(2)
Number of Lethal Equivalents	276	(7)
Results from vertebrates	278	(1)
Results from Drosophila	279	(2)
Results from plants	281	(2)
Partial Recessives vs. Overdominance	283	(10)
The (A+B)/A ratio	283	(1)
Estimating the average degree of dominance	284	(3)
Inferences from molecular markers	287	(6)
11. MATTERS OF SCALE	293	(26)
Transformations to Achieve Normality	293	(7)
Log-normal distributions and the log transform	294	(1)
Tests for normality	295	(5)
Stabilizing the Variance	300	(5)
Kleckowski's transformation	300	(1)
General variance stabilizing-transformations	301	(1)
The Roginskii-Yablokov effect	302	(3)
The Kluge-Kerfoot phenomenon	305	(1)
Allometry: the Scaling Implications of Body Size	305	(2)
Removing Interaction Effects	307	(2)
Developmental Maps, Canalization, and Genetic Assimilation	309	(10)
Estimating developmental maps	310	(4)
Selection and canalization	314	(2)
Genetic assimilation	316	(3)
II. QUANTITATIVE TRAIT LOCI	319	(216)
12. POLYGENES AND POLYGENIC MUTATION	321	(32)
The Genetic Basis of Quantitative-Genetic Variation	322	(6)
Major genes and isoalleles	322	(1)
The molecular nature of QTL variation	323	(5)
The Mutational Rate of Production of Quantitative Variation	328	(12)
Estimation from divergence experiments	330	(3)
Bristle numbers in Drosophila	333	(2)
Additional data	335	(5)
The Deleterious Effects of New Mutations	340	(13)
The Bateman-Mukai technique	341	(2)
Results from flies, plants, and bacteria	343	(5)
Analysis of natural populations	348	(3)
The persistence of new mutations	351	(2)
13. DETECTING MAJOR GENES	353	(26)
Elementary Tests	354	(5)
Departures from normality	354	(1)
Tests based on sibship variances	355	(2)
Major-gene indices (MGI)	357	(1)
Nonparametric line-cross tests	358	(1)
Mixture Models	359	(5)
The distribution under a mixture model	360	(1)
Parameter estimation	360	(1)
Hypothesis testing	361	(3)
Complex Segregation Analysis	364	(11)
Likelihood functions assuming a single major gene	366	(4)
Common-family effects	370	(1)
Polygenic background	371	(2)
Other extensions	373	(1)
Ascertainment bias	374	(1)
Estimating individual genotypes	374	(1)
Analysis of Discrete Characters	375	(4)
Single-locus penetrance model	376	(1)
Major gene plus a polygenic background	377	(2)
14. PRINCIPLES OF MARKER-BASED ANALYSIS	379	(52)
Classical Approaches	379	(11)
Chromosomal assays	380	(1)
Thoday's method	381	(4)
Genetics of Drosophila bristle number	385	(2)
Genetics of Drosophila speciation	387	(3)
Molecular Markers	390	(3)
Genetic Maps	393	(5)
Map distance vs. recombination frequencies	394	(3)
How many markers are needed?	397	(1)
Marker-trait Associations	398	(7)
Selective genotyping and progeny testing	401	(1)
Recombinant inbred lines (RILs)	401	(1)
Bulked segregant analysis	402	(2)
QTL mapping by marker changes in populations under selection	404	(1)
Marker-based Analysis Using Nearly Isogenic Lines (NILs)	405	(8)
Marker-based introgressions	407	(6)
Fine Mapping of Major Genes Using Population-level Disequilibrium	413	(5)
LD mapping in expanding populations	414	(4)
Candidate Loci	418	(7)
The transmission/disequilibrium test	419	(3)
Estimating effects of candidate loci	422	(2)
Templeton and Sing's method: Using the historical information in haplotypes	424	(1)
Cloning QTLs	425	(6)
Transposon tagging	426	(1)
Positional cloning and comparative mapping	426	(5)
15. MAPPING AND CHARACTERIZING QTLS: INBRED LINE CROSSES	431	(60)
Foundations of Line-Cross Mapping	431	(11)
Experimental designs	432	(1)
Conditional probabilities of QTL genotypes	433	(4)
Expected marker-class means	437	(2)
Marker variance and higher-order moments	439	(2)
Overall significance level with multiple tests	441	(1)
QTL Detection and Estimation Using Linear Models	442	(3)
QTL Detection and Estimation via Maximum Likelihood	445	(12)
Likelihood maps	446	(2)
Precision of ML estimates of QTL position	448	(2)
ML interval mapping	450	(3)
Approximating ML interval mapping by Haley-Knott regressions	453	(4)
Dealing with Multiple QTLs	457	(12)
Marker-difference regression	459	(4)
Interval mapping with marker cofactors	463	(4)
Detecting multiple linked QTLs using standard marker-trait regressions	467	(2)
Sample Size Required for QTL Detection	469	(8)
Power under selective genotyping	474	(1)
Power and repeatability of mapping experiments	474	(3)
Selected Applications	477	(14)
The nature of transgressive segregation	477	(1)
QTLs involved in reproductive isolation in Mimulus	478	(1)
QTLs involved in protein regulation	478	(1)
QTLs in the Illinois long-term selection maize lines	479	(2)
QTLs involved in the differences between maize and teosinte	481	(3)
QTLs for age-specific growth in mice	484	(1)
Summary of QTL mapping experiments	484	(7)
16. MAPPING AND CHARACTERIZING QTLS: OUTBRED POPULATIONS	491	(44)
Measures of Informativeness	492	(3)
Sib Analysis: Linear Models	495	(6)
A single half-sib family	496	(2)
Several half-sib families	498	(3)
Power of Nested ANOVA Designs	501	(4)
A single full-sib family	502	(2)
Several full-sib families	504	(1)
Sib Analysis: Maximum Likelihood	505	(5)
Constructing likelihood functions	507	(3)
Maximum Likelihood over General Pedigrees: Variance Components	510	(3)
Estimating QTL position	512	(1)
The Haseman-Elston Regression	513	(8)
Derivation of the Haseman-Elston regression	513	(3)
Estimating the number of marker genes ibd	516	(1)
Power and improvements	517	(1)
Interval mapping by a modified Haseman-Elston regression	518	(3)
Mapping Dichotomous Characters	521	(14)
Recurrent and relative risks of pairs of relatives	523	(2)
Affected sib-pair tests	525	(2)
Power of ASP tests and related issues	527	(2)
Genomic scanning	529	(1)
Exclusion mapping and information content mapping	530	(2)
Affected pedigree member tests	532	(3)
III. ESTIMATION PROCEDURES	535	(270)
17. PARENT-OFFSPRING REGRESSION	537	(16)
Estimation Procedures	538	(4)
Balanced data	538	(1)
Unequal family sizes	539	(3)
Standardization of data from the different sexes	542	(1)
Precision of Estimates	542	(1)
Optimum Experimental Designs	543	(5)
Assortative mating	547	(1)
Estimation of Heritability in Natural Populations	548	(2)
Linearity of the Parent-Offspring Regression	550	(3)
18. SIB ANALYSIS	553	(28)
Half-sib Analysis	554	(16)
One-way analysis of variance	556	(4)
Hypothesis testing	560	(1)
Sampling variance and standard errors	561	(1)
Confidence intervals	562	(1)
Negative estimates of heritability	563	(1)
Optimal experimental design	564	(2)
Unbalanced data	566	(3)
Resampling procedures	569	(1)
Full-sib Analysis	570	(11)
Nested analysis of variance	573	(1)
Hypothesis testing	574	(2)
Sampling error	576	(1)
Optimal design	577	(4)
19. TWINS AND CLONES	581	(16)
The Classical Approach	582	(5)
Heritability estimation	584	(3)
The Monozygotic-Twin Half-sib Method	587	(5)
Clonal Analysis	592	(5)
20. CROSS-CLASSIFIED DESIGNS	597	(32)
North Carolina Design II	598	(12)
The average degree of dominance	603	(2)
The Cockerham-Weir model	605	(5)
Diallels	610	(9)
Pooled reciprocals, no self crosses	611	(3)
Reciprocals, no self crosses	614	(4)
Complete diallels	618	(1)
Partial diallels	618	(1)
Hayman-Jinks analysis	619	(6)
North Carolina Design III and the Triple Test Cross	625	(2)
Some Closing Statistical Considerations	627	(2)
21. CORRELATIONS BETWEEN CHARACTERS	629	(28)
Theoretical Composition of the Genetic Covariance	630	(2)
Estimation of the Genetic Covariance	632	(5)
Pairwise comparison of relatives	632	(1)
Nested analysis of variance and covariance	633	(3)
Regression of family means	636	(1)
Components of Phenotypic Correlation	637	(2)
Phenotypic correlations as surrogate estimates of genetic correlations	639	(1)
Statistical Issues	639	(9)
Hypothesis tests	641	(1)
Standard errors	642	(2)
Bias due to selection	644	(4)
Applications	648	(1)
Genetic basis of population differentiation	648	(2)
The homogeneity of genetic covariance matrices among species	650	(3)
Evolutionary allometry	653	(2)
Evolution of life-history characters	655	(2)
22. GENOTYPE x ENVIRONMENT INTERACTION	657	(30)
Genetic Correlation Across Two Environments	660	(6)
Estimation procedures	663	(3)
Two-way Analysis of Variance	666	(6)
Relationship to Falconer's correlation across environments	671	(1)
Further Characterization of Interaction Effects	672	(6)
Joint-regression analysis	672	(6)
Testing for Cross-over Interaction	678	(2)
Concepts of Stability and Plasticity	680	(3)
Additional issues	682	(1)
The Quantitative Genetics of Genotype x Environment Interaction	683	(4)
23. MATERNAL EFFECTS	687	(28)
Components of Variance and Covariance	689	(7)
Cytoplasmic transmission	693	(2)
Postpollination reproductive traits in plants	695	(1)
Cross-fostering experiments	696	(7)
Body weight in mice	700	(3)
Eisen's Approach	703	(3)
Bondari's experiment	703	(3)
Falconer's Approach	706	(5)
Extension to Other Types of Relatives	711	(4)
24. SEX LINKAGE AND SEXUAL DIMORPHISM	715	(12)
Sex-linked Loci and Dosage Compensation	715	(3)
Sex-modified Expression of an Autosomal Locus	718	(1)
Gametic imprinting	718	(1)
Extension to Multiple Loci and the Covariance Between Relatives	719	(5)
Variation for Sexual Dimorphism	724	(3)
25. THRESHOLD CHARACTERS	727	(18)
Heritability on the Underlying Scale	730	(6)
Multiple Thresholds	736	(3)
Genetic Correlation Among Threshold Traits	739	(2)
Heritability on the Observed Scale	741	(4)
26. ESTIMATION OF BREEDING VALUES	745	(34)
The General Mixed Model	746	(2)
Estimating Fixed Factors and Predicting Random Effects	748	(7)
Estimability of fixed factors	753	(1)
Standard errors	754	(1)
Models for the Estimation of Breeding Values	755	(7)
The animal model	755	(3)
The gametic model	758	(1)
The reduced animal model	759	(3)
Simple Rules for Computing A and A(-1)	762	(5)
Allowing for mutation when computing A	766	(1)
Joint Estimation of Several Vectors of Random Effects	767	(12)
BLUP estimates of dominance values	767	(2)
Repeated records	769	(4)
Maternal effects	773	(1)
Multiple traits	774	(5)
27. VARIANCE-COMPONENT ESTIMATION WITH COMPLEX PEDIGREES	779	(26)
ML versus REML Estimates of Variance Components	780	(4)
A simple example of ML versus REML	781	(3)
ML Estimates of Variance Components in the General Mixed Model	784	(5)
Standard errors of ML estimates	788	(1)
Restricted Maximum Likelihood	789	(4)
Multivariate analysis	792	(1)
ML/REML estimation in populations under selection	792	(1)
Solving ML/REML Equations	793	(7)
Derivative-based methods	794	(3)
EM methods	797	(2)
Additional approaches	799	(1)
A Molecular-marker Based Method for Inferring Variance Components	800	(5)
IV. APPENDICES	805	(86)
A1. EXPECTATIONS, VARIANCES, AND COVARIANCES OF COMPOUND VARIABLES	807	(16)
The Delta Method	807	(6)
Expectations of complex variables	808	(2)
Variances of complex variables	810	(3)
Covariances of complex variables	813	(1)
Variance of Variances and Covariances	813	(4)
Expectations and Variances of Products	817	(1)
Expectations and Variances of Ratios	818	(5)
Sampling variance of regression and correlations coefficients	818	(1)
Sampling variance of a coefficient of variation	819	(4)
A2. PATH ANALYSIS	823	(12)
Univariate Analysis	823	(3)
Bivariate Analysis	826	(1)
Applications	826	(9)
Phenotypic correlation between parents and offspring	827	(2)
Correlations between characters	829	(2)
Growth analysis	831	(4)
A3. FURTHER TOPICS IN MATRIX ALGEBRA AND LINEAR MODELS	835	(18)
Generalized Inverses and Solutions to Singular Systems of Equations	835	(6)
Generalized inverses	836	(1)
Consistency and solutions to consistent systems	836	(3)
Estimability of fixed factors	839	(2)
The Square Root of a Matrix	841	(1)
Derivation of the GLS Estimators	842	(1)
Quadratic Forms and Sums of Squares	843	(5)
Moments of quadratic forms	843	(1)
The sample variance as a quadratic form	844	(2)
Sums of squares expressed as a quadratic form	846	(2)
Testing Hypotheses About Linear Models	848	(1)
Equivalent Linear Models	849	(2)
Derivatives of Vectors and Matrices	851	(2)
A4. MAXIMUM LIKELIHOOD ESTIMATION AND LIKELIHOOD-RATIO TESTS	853	(16)
Likelihood, Support, and Score Functions	853	(4)
Large-sample properties of MLEs	854	(1)
The Fisher information matrix	855	(2)
Likelihood-ratio tests	857	(4)
The G-test	859	(1)
Likelihood-ratio tests for the general linear model	860	(1)
Iterative Methods for Solving ML Equations	861	(8)
Newton-Raphson methods	861	(2)
Expectation-maximization methods	863	(1)
EM for mixture model likelihoods	863	(2)
EM modifications for QTL mapping	865	(4)
A5. COMPUTING THE POWER OF STATISTICAL TESTS	869	(22)
Power of Normally Distributed Test Statistics	870	(7)
One-sided tests	870	(2)
Two-sided tests	872	(2)
Applications: Parent-offspring regressions	874	(2)
Applications: QTL detection tests using doubly affected sib pairs	876	(1)
Power of F-ratio Tests	877	(14)
Central and noncentral X(2) distributions	878	(1)
Central and noncentral F distributions	879	(1)
Power of fixed-effects ANOVA designs	880	(3)
Application: Power of QTL mapping in half-sib families	883	(2)
Power of random-effects ANOVA designs	885	(2)
Application: Power of the half-sib design for variance estimation	887	(4)
LITERATURE CITED	891	(58)
AUTHOR INDEX	949	(12)
ORGANISM AND TRAIT INDEX	961	(10)
SUBJECT INDEX	971