Probability models and statistical methods in genetics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Wiley
1971
|
| Series: | Wiley series in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 592 S. graph. Darst. |
| ISBN: | 0471234907 |
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| adam_text | Contents
Special Notation and Symbols
Chapter 1. Basic Terms and Definitions in Genetics 1
1. Introduction, 1. — 2. Chromosomes and genes, 1. — 3. Genotype
and phenotype, 4. Dominance and recessiveness, 4. — 4. Autosomal
linkage, 6. Crossing over, 6 — 5. Sex linked inheritance, 8.
PART I. POPULATION GENETICS. PROBABILITY MODELS
Chapter 2. Probability Models. General Concepts and Definitions 13
1. Models, 13 — 2. Sample space, random events, probability, 14 —
3. Compound events, 18 — 4. Addition law of probabilities, 22 —
5. Probability distribution of events, 23 — 6. Conditional probability
and multiplication law, 24 — 7. Independent events, 25 — 8. Some
applications of the probability theory of compound events, 26 —
9. Product of sample space. Joint probability of compound events, 28
— 10. Joint probability distribution, 29 — 11. Marginal probability
distributions, 31 — 12. Conditional distributions. Independence, 32 —
13. Genotype and phenotype distributions with respect to two linked
loci, 33 — 14. Continuous sample space, 35.
Chapter 3. Genotypes and Phenotypes in Experimental Populations 39
1. Simple combinatorial problems, 39 — V 2. Generating functions, 42
— 3. The number of genotypes and phenotypes, 44 — 4. Evaluation
of phenotypic ratios in intercrosses and backcrosses, using generating
function, 46 — 5. Independence, dependence and interaction, 48 —
6. Epistasis, 52.
ix
X CONTENTS
Chapter 4. Equilibrium Laws in Panmictic Populations 57
1. Concept of gene frequency, 57 — 2. Random mating, 59 — V 3.
Matrix theory of random mating, 61 — T 4. Gamete and genotype
distributions in the #th generation under random mating, 65 — 5. Ap¬
plication of matrix algebra in evaluation of the genotype distribution
in the nth generation for two linked loci, 66 — 6. Gene frequencies in
the wth generation, 70 — 7. Theorem on genetic equilibrium in a
randomly mating population, 71 — 8. Equilibrium for X linked genes,
75.
Chapter 5. Random Variables and Their Distributions 83
1. Definition of a random variable, 83 — 2. Probability distribution
and cumulative distribution function of a random variable, 85 —
3. Continuous random variable. Density function, 88 — 4. Truncated
distributions, 89 — 5. Joint and marginal distributions in a two
dimensional sample space, 91 — 6. Conditional distributions. Inde¬
pendence of random variables, 95 — 7. Distribution of the sum of
random variables, 97.
Chapter 6. Moments of Random Variables 102
1. Expected values, 102 — 2. Definitions of moments, 106 — 3. Vari¬
ance, 107 — 4. Covariance, 109 — 5. Variance of linear functions of
two or more random variables, 112 — 6. Phenotypic and genotypic
values of metrical characters, 113 — 7. Additive genetic variance, 114
— y 8. Dominance genetic variance, 116 — 9. Mixtures of two (or
more) populations, 117.
Chapter 7. Genotype Distributions for Relatives in Randomly Mating
Populations 122
1. Introduction, 122 — 2. Bayes theorem. A posteriori proba¬
bility, 123 — V 3. Generalized forms of Bayes theorem, 125 —
4. Mating types and their offspring. Single autosomal locus with
multiple alleles, 126 — 5. Joint parent child distribution, 128 —
6. Conditional distributions of child genotypes when the parent s
genotype is given, and vice versa, 133 — 7. Joint grandparent grand¬
child genotype distribution, 136 — 8. Ancestral correlation, 138 —
9. Joint parent child genotype distribution and their correlation for
CONTENTS Xi
X Iinked genes, 141 — 10. Joint genotype distribution of grand¬
parent and grandchild when the genes are X linked, 142 — 11. Joint
full sib distributions and their genotypic correlation coefficient, 144 —
12. Interpretation of joint distribution of relatives in large popula¬
tions, 149— 13. Snyder s ratios, 149.
Chapter 8. Some Standard Distributions and Their Properties 155
1. Introduction, 155 — 2. The normal distribution, 156 — 3. The
standard normal distribution, 157 — 4. Table of percentage points for
normal distribution, 157 — 5. Some distributions related to the
normal, 162 — 6. Bernoulli trials, 166 — 7. The binomial distribu¬
tion, 167 — 8. Proportions of segregating and nonsegregating families
for a simple recessive trait, 169 — 9. Distribution of proportions, 173 —
10. The geometric and negative binomial distributions, 174 — 11. The
multinomial distribution, 176 — 12. The Poisson distribution, 178 —
13. Population and sample. Sampling from infinite and finite popula¬
tions, 179 — 14. The distribution of the sample, 182 — 15. Sampling
distributions, 184 — 16. Some exact sampling distributions from
normal population, 184 — 17. Large sample theory. The central limit
theorem, 186 — 18. Normal approximation to the binomial distribu¬
tion, 188 — 19. The approximate ^ distribution for a function of
multinomial variables, 189 — 20. Approximate mean and variance of
a function of random variables, 190.
Chapter 9. Inbreeding and Nonrandom Mating 196
1. Inbreeding. Identities of genes, 196 — 2. Coefficient of inbreeding
of an individual. Malecot s definition, 200 — 3. Consanguinity of two
individuals. Malecot s coefficient of parentage, 200 — 4. Relations be¬
tween F and p, 201 — 5. Wright s formula for evaluation of an in¬
breeding coefficient in an irregular pedigree, 206 — 6. The X linked
genes, 212 — 7. The structure of a population subject to inbreeding.
Wright s definitions of the coefficients of inbreeding and relation¬
ship, 213 — 8. Genotypic mean and variance in a population with
inbreeding, 216 — 9. Gene frequency of rare recessive traits evaluated
from consanguineous marriages, 218 — 10. Regular breeding sys¬
tems, 219 — 11. Mixture of selfing and random mating in a population,
225 — 12. Inbreeding in randomly mating population of finite size,
227 — 13. Inbreeding in a population divided into isolates. Wahlund s
principle, 228 — 14. General remarks on different definitions and
applicability of the inbreeding coefficient, 229 — 15. Assortative
Xii CONTENTS
mating, 231 — 16. Approach to homozygosity by successive back
crosses, 234.
Chapter 10. Natural Selection and Mutation 240
1. Mechanisms of selection, 240 — 2. Fitnesses of genotypes, 241 —
3. A single autosomal locus with multiple alleles. Changes in gene
frequencies due to selection, 244 — 4. Randomly mating population
under selection, 247 — 5. The rate of increase of the mean fitness per
generation. Fundamental theorem of natural selection, 248 — f 6. Sta¬
ble and unstable equilibria, 251 — 7. Single locus with two alleles,
257 — 8. Randomly mating population. Variable fitnesses depending
on gene frequencies, 259 — 9. Different fitnesses in the two sexes, 260 —
10. Selection at the X linked locus, 261 — fll. Selection at two
autosomal loci. Randomly mating population, 265 — 12. Selection
and inbreeding, 269 — 13. Distribution of mutants in a population,
272 —14. Changes in gene frequencies due to mutation, 272—15. The
probability of extinction of a mutant gene, 274 — 16. Joint effects of
mutation and selection, 275.
PART H. EXPERIMENTAL GENETICS. ESTIMATION OF
GENETIC PARAMETERS AND TESTING GENETIC HYPOTHESES
Chapter 11. Estimation of Genetic Parameters. General Theory 285
1. General problem of estimation, 285 — 2. Properties of a good
estimator, 287 — 3. The maximum likelihood method of estimation.
One parameter, 290 — 4. Asymptotic properties of maximum likeli¬
hood estimators, 295 — 5. Functions of the ML estimators, 298 —
6. Confidence intervals, 299 — 7. Scores and amount of information,
302 — y8. Estimation of several parameters by the method of maxi¬
mum likelihood, 305 — y 9. Confidence regions, 308 — 10. Planning
of experiments. Required sample size, 309.
Chapter 12. Estimation of Parameters Associated with Multinomial
Distributions 314
1. Introduction, 314 — 2. Maximum likelihood estimators of multi¬
nomial parameters, 314 — 3. The ML estimator of a function of multi¬
nomial proportions. Single parameter, 315 — 4. Estimation of gene
CONTENTS Xiii
frequencies in randomly mating natural populations. General remarks,
317 — 5. ML estimators of gene frequencies from the numbers of
genotypes or phenotypes observed in a simple random sample from a
population, 318 — 6. Simple random sample from a truncated
population, 321 — 7. Sampling from one generation when in¬
formation about parental genotypes is available, 321 — 8. Sampling
from two generations, 322 — 9. Sampling from a population of related
pairs, 323 — 10. Maximum likelihood scores for samples of mother
child pairs, 324 — 11. Combination of data, 328 — V 12. ML estima¬
tors of functions of multinomial proportions. Several parameters, 332 —
T 13. Estimation of admixtures in a hybrid population, 334 —
14. Minimum chi square estimators, 338.
Chapter 13. Testing Genetic Hypotheses 345
1. Genetic and statistical hypotheses, 345 — 2. Statistical test, 346 —
3. The power of the test, 348 — 4. Construction of a significance test
for a parametric hypothesis, 353 — 5. Chi square tests of significance
useful in genetics. General remarks, 354 — 6. Approximate significance
tests about parameters. Large sample theory, 355 — 7. Tests of good¬
ness of fit, 357 — 8. Tests of independence (or tests for association), 360
— 9. Test for association and the sample correlation coefficient for A
2x2 contingency table, 362 — 10. Tests of homogeneity (or for
heterogeneity). General concepts, 365 — f 11, A general method of
homogeneity testing based on large sample theory, 366 — 12. Tests
for heterogeneity about multinomial parameters specified by H^n), 370
— 13. Tests for heterogeneity when multinomial proportions are
functions of some parameters not specified by H^n). Equilibrium and
heterogeneity, 371 — y 14. Evaluation of the power of the test. Dis¬
crimination between two simple hypotheses, 376 — 15. Sample size
when a and ft are specified, 380 — T 16. Sequential tests, 380.
Chapter 14. Human Blood Groups 391
1. Introduction, 391 — 2. Serology of blood groups, 391 — 3. In¬
heritance of blood antigens, 392 — 4. Genetics of the A^A^fiO blood
group system and its association with the H and Se loci, 393 — 5. Esti¬
mation of gene frequencies in blood group systems. General remarks,
395 — 6. Bernstein s method of estimating the ABO gene frequencies,
396 — 7.The maximum likelihood estimators of the ABO gene frequen¬
cies, 398 — 8. Gene counting estimators of the ABO gene frequencies,
400 —• 9. Efficiency of Bernstein s estimators, 402 — 10. Estimation of
Xiv CONTENTS
the gene frequencies in the A^A^BO blood system, 402 — 11. The Lewis
blood group system, 403— 12. The P blood group system, 405— 13.
TheMNSshlood group system, 405 —14. Estimation of gene frequencies
in the MNSs blood system, using anti M, anti N, and anti S reagents,
406 — 15. The Rhesus blood group system, 411 — 16. The Lutheran
blood group system and its linkage with the secretor locus, 413 —17. The
X linked blood group system, 414 — 18. Other blood group systems,
414 — 19. Blood groups and diseases, 414 — 20. Selection at the
ABO and the MNSs loci, 415.
Chapter 15. Autosomal Linkage in Experimental Populations 421
1. Introduction, 421 — 2. Orthogonal functions of random variables,
421, — 3. Detection of linkage from double backcrosses, 423 — 4. De¬
tection of linkage from intercrosses, 425 — 5. Detection of linkage
from triple backcrosses, 427 — 6. Estimation of the strength of linkage,
428 — 7. Disturbance factors in linkage, 431 — 8. Double crossing
over, 431 — 9. Interference and the coefficient of coincidence, 432 —
10. Arrangement of loci on a chromosome, 433 — 11. Estimation of
the coefficient of coincidence from three point testcross, 433 —
12. Chromosome mapping, 435.
Chapter 16. Statistically Equivalent Models of Inheritance 439
1. Identical phenotype distributions under different modes of inherit¬
ance, 439 — 2. Incomplete penetrance and expressivity, 440 —•
3. Several loci with additive phenotypic effects versus single locus.
Equivalent models, 442 — 4. A discriminatory design for models with
additive phenotypic effects, 449 — 5. Differential viability, 451 —
6. Simple versus double (or multiple) recessive. Indistinguishable
Snyder s ratios, 453.
Chapter 17. Segregation Ratios in Families. Simple Modes of
Inheritance 458
1. Random sampling and family records, 458 — 2. Rare and common
genetic traits, 459 — 3. Segregating and nonsegregating families.
Ascertainment, 461 — 4. Ascertainment through the affected children.
Terminology and definitions, 463 — 5. The distribution of affected
children in high risk segregating families, 466 — 6. Maximum likeli¬
hood estimator of the segregation parameter Q under multiple ascertain
CONTENTS XV
ment (0 it 1), with known it. Fixed numbers of ascertained
families, 468 — 7. Maximum likelihood estimator of 6 under complete
ascertainment (jr = 1), 472 — 8. Evaluation of scores, amounts of infor¬
mation, and heterogeneity tests, 474 — 9. Approximate Weinberg s sib
method, 479 — 10. An approximate method of Li and Mantel for esti¬
mating d, 481 —11. Efficiencies of the approximate estimators ds and ds,
482 — 12. Maximum likelihood estimator of 6 under single ascertain¬
ment (it ^ 0), 484—13. Weinberg s proband method, 486—14. Test
of goodness of fit under single ascertainment, 486 — 15. The ascertain¬
ment probability, it, and its estimation, 487 — 16. The number of
families under risk, 490 — 17. Ascertainment through the parents.
Recessive trait, 492 — 18. Difficulties in analysis of family data, 492.
Y Chapter 18. Complex Segregation Analysis 497
1. More advanced models for analyzing family data. Advantages and
difficulties, 497 — 2. A general model for complex segregation analy¬
sis. Random sampling of parents, 498 — 3. Models for complex
segregation analysis. Selection through the children, 501 — 4. Likeli¬
hood equations and information matrix, 502 — 5. Testing hypotheses,
504 — 6. Estimation of gene frequencies from family data. Separation
of nonsegregating and segregating families, 506 — 7. Interaction of
loci. Double autosomal recessive, 509 — 8. Complex segregation
analysis for multiple classification, 513 — 9. Estimation of gene
frequencies and recombination fraction of two linked loci, using family
data, 515.
Chapter 19. Histocompatibility Testing 521
1. Immunogenetic mechanism of histocompatibility, 521 — 2. Histo¬
compatibility models. General assumptions, 522 — 3. Some terminology
in tissue transplantation, 523 — 4. Immunological unresponsiveness
and tolerance, 525 — 5. Types of designs for histocompatibility testing
in laboratory animals, 526 — 6. Estimation of the number of histo¬
compatibility loci in laboratory animals. Single, one way (D R)
grafting designs, 526 — 7. Required sample size, 530 — 8. Grafting
among relatives, 531 — 9. Reciprocal grafting designs (Dt ^ D2), 532
— 10. Double grafting designs (£ i R « £ .,), 535—11. Strength
of immune response to transplantation antigens. The H loci in mice, 537
— 12. Some arbitrary measure of strength of histocompatibility alleles
(antigens), 539 — 13. A model including strong, weak, and mixed loci
XVI CONTENTS
for one way single grafting designs, 540 — V 14. A model including
strong and weak loci for the double grafting design P^ Fa — Pt2, 543
—15. Histocompatibility systems in man. The HL A system, 546
— 16. Histocompatibility models in randomly mating populations,
547 — 17. General remarks, 548.
Appendix I Elements of Matrix Algebra 555
Appendix II Minima and Maxima of Functions. Taylor s
Expansions 569
Index 577
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| id | DE-604.BV000936735 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:21:31Z |
| institution | BVB |
| isbn | 0471234907 |
| language | English |
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| record_format | marc |
| series2 | Wiley series in probability and mathematical statistics |
| spelling | Elandt-Johnson, Regina C. Verfasser aut Probability models and statistical methods in genetics Regina C. Elandt-Johnson New York Wiley 1971 XVIII, 592 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Génétique - Méthodes statistiques Biometry Genetics Genetics Statistical methods Models, Biological Genetik (DE-588)4071711-2 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s Genetik (DE-588)4071711-2 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000573148&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elandt-Johnson, Regina C. Probability models and statistical methods in genetics Génétique - Méthodes statistiques Biometry Genetics Genetics Statistical methods Models, Biological Genetik (DE-588)4071711-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4071711-2 (DE-588)4064324-4 (DE-588)4056995-0 |
| title | Probability models and statistical methods in genetics |
| title_auth | Probability models and statistical methods in genetics |
| title_exact_search | Probability models and statistical methods in genetics |
| title_full | Probability models and statistical methods in genetics Regina C. Elandt-Johnson |
| title_fullStr | Probability models and statistical methods in genetics Regina C. Elandt-Johnson |
| title_full_unstemmed | Probability models and statistical methods in genetics Regina C. Elandt-Johnson |
| title_short | Probability models and statistical methods in genetics |
| title_sort | probability models and statistical methods in genetics |
| topic | Génétique - Méthodes statistiques Biometry Genetics Genetics Statistical methods Models, Biological Genetik (DE-588)4071711-2 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Génétique - Méthodes statistiques Biometry Genetics Genetics Statistical methods Models, Biological Genetik Wahrscheinlichkeitsrechnung Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000573148&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT elandtjohnsonreginac probabilitymodelsandstatisticalmethodsingenetics |