Estimating the age of alleles by use of intraallelic variability.

A method is presented for estimating the age of an allele by use of its frequency and the extent of variation among different copies. The method uses the joint distribution of the number of copies in a population sample and the coalescence times of the intraallelic gene genealogy conditioned on the number of copies. The linear birth-death process is used to approximate the dynamics of a rare allele in a finite population. A maximum-likelihood estimate of the age of the allele is obtained by Monte Carlo integration over the coalescence times. The method is applied to two alleles at the cystic fibrosis (CFTR) locus, deltaF508 and G542X, for which intraallelic variability at three intronic microsatellite loci has been examined. Our results indicate that G542X is somewhat older than deltaF508. Although absolute estimates depend on the mutation rates at the microsatellite loci, our results support the hypothesis that deltaF508 arose < 500 generations (approximately 10,000 years) ago.     

Reversibility and the age of an allele. I. Moran's infinitely many neutral alleles model

A population of constant size is subjected to mutation, such that each mutant is of a new allelic type. For the particular population model studied in this paper, the age of an allele, whose present frequency is known, is a random variable with distribution independent of the frequencies of other alleles. As a consequence of reversibility of the population process, the age of an allele, from the past to the present, has the same distribution as its time to extinction, from the present into the future. This verifies, and re-interprets, certain diffusion approximations found by Kimura and Ohta [Genetics 75, 199–212 (1973)] and Maruyama [Genet. Res. Cambridge 23, 137–143 (1974)].     

Competition at the Mouse t Complex: Rare Alleles Are Inherently Favored

We investigate the competition between alleles at a segregation distorter locus. The focus is on the invasion prospects of rare mutant distorter alleles in a population in which a wildtype and a resident distorter allele are present. The parameters are chosen to reflect the situation at the t complex of the house mouse, one of the best-studied examples of segregation distortion. By analyzing the invasion chances of rare alleles, we provide an analytical justification of earlier simulation results. We show that a new distorter allele can successfully invade even if it is inferior both at the gamete and at the individual level. In fact, newly arising distorter alleles have an inherent rareness advantage if their negative fitness consequences are restricted to homozygous condition. Likewise, rare mutant wildtype alleles may often invade even if their viability or fertility is reduced. As a consequence, the competition between alleles at a segregation distorter locus should lead to a high degree of polymorphism. We discuss the implications of this conclusion for the t complex of the house mouse and for the evolutionary stability of “honest” Mendelian segregation.     

A vectorized method of importance sampling with applications to models of mutation and migration

An importance-sampling method is presented for computing the likelihood of the configuration of population genetic data under general assumptions about population history and transitions among states. The configuration of the data is the number of chromosomes sampled that are in each of a finite set of states. Transitions among states are governed by a Markov chain with transition probabilities dependent on one or more parameters. The method assumes that the joint distribution of coalescence times of the underlying gene genealogy is independent of the genetic state of each lineage. Given a set of coalescence times, the probability that a pair of lineages is chosen to coalesce in each replicate is proportional to the contribution that the coalescence event makes to the probability of the data. This method can be applied to gene genealogies generated by the neutral coalescent process and to genealogies generated by other processes, such as a linear birth-death process which provides a good approximation to the dynamics of low-frequency alleles. Two applications are described. In the first, the fit of allele frequencies at two microsatellite loci sampled in a Sardinian population to the one-step mutation model is tested. The one-step model is rejected for one locus but not for the other. The second application is to low-frequency alleles in a geographically subdivided population. The geographic location is the allelic state, and the alleles are assumed to be sufficiently rare that their dynamics can be approximated by a linear birth-death process in which the birth and death rates are independent of geographic location. The analysis of eight low-frequency allozyme alleles found in the glaucous-winged gull, Larus glaucescens, illustrates how geographically restricted dispersal can be detected.     

The average frequency of private alleles in a partially isolated population

An analytic model is developed to explore the relationship between gene flow, selection, and genetic drift. We assume that a single copy of a mutant allele appears in a finite, partially isolated population and allow for the effects of immigration, genic selection, and mutation on the frequency of the mutant. Our concern is with the distribution of the mutant's frequency before it either is lost from the population or emigrates. Before either of these events, the allele will be a “private allele” and would be found in only one of several populations in a larger collection. Slatkin [(1985) Evolution 39, 53–65] found several simple properties of private alleles in his simulations. We use the method developed by Karlin and Tavaré [(1980) Genet. Res. 37, 33–46; (1981a), Theor. Pop. Biol. 19, 187–214; (1981b) Theor. Pop. Biol. 19, 215–229] for a model similar to ours to obtain a diffusion equation with a “killing term” and obtain the mean and variance of the mutant's frequency and its expected frequency in samples of a specified size. There is only fair agreement between the analytic results from this model and those from Slatkin's (loc. cit.) simulations. The rescaling method used to obtain the results indicates that if emigration is relatively frequent, the distribution of rare alleles is governed largely by the balance between genetic drift and emigration, with selection, mutation, and immigration playing a lesser role.     

The plasminogen polymorphism in South African Negro populations: genetics and anthropogenetics

Summary Genetic polymorphism of human plasminogen (PLG) was investigated in 1252 unrelated individuals from eight South African Bantu-speaking Negro tribes. PLG phenotypes were determined by isoelectric focusing (pH 3.5–9.5 and 5–8 gradients) of neuraminidase-treated samples and subsequent detection by caseinolytic overlay or immunoblotting with specific antibody. No significant difference in the distribution of PLG alleles among the eight ethnic groups was observed. The combined allele frequencies of the common alleles in South African Negroes were 0.6977 for PLG*A, 0.2736 for PLG*B. In addition, six rare alleles were seen: PLG*A3, *A1, *M2, *B1, *B2, *B3. The rare variant PLG*B2 was proven to segregate by autosomal Mendelian inheritance in a family. The combined frequency for the rare alleles was 0.0287. The distribution of phenotypes in the total population sample was found to be in Hardy-Weinberg equilibrium. A striking difference in PLG allele distribution between Negroes from South Africa and published Negroid frequencies from North America could be observed. This difference was also seen in comparison with Mongoloid populations; in contrast, PLG frequencies for South African Negroes were similar or almost identical to known Caucasoid distributions.     

Five genetic loci involved in the synthesis of acidic exopolysaccharides are closely linked in the genome of Rhizobium sp strain NGR234

Summary R-prime plasmids were constructed from a derivative of Rhizobium strain NGR234 (ANU280) and were shown to contain overlapping genomic DNA segments involved in biosynthesis of exopolysaccharides (EPS). The R-primes originally constructed carried the mutant allele from Tn5-induced EPS-deficient (Exo^–) mutant ANU2811. This plasmid-located mutant allele was dominant to the corresponding wild-type allele as merodiploid strains were Exo^–. Exo⁺ revertants occurred at a low rate (1×10^-7) and these were shown to result from double reciprocal recombination events, which led to the isolation of R-prime plasmids carrying functional wild-type exo alleles. R-prime plasmids that carry overlapping segments of DNA from parental strain ANU280 complemented 28 of the 30 group 2 Exo^– mutants of strain ANU280. Complementation of these Exo^– mutants also restored their symbiotic abilities of effective nodulation. Subsequent in vivo recombination between the wild-type alleles located on the R-prime and the corresponding mutated allele on the genome, was used to generate a new family of R-primes, which carried mutations in the exo genes. The 30 group 2 Exo^– mutants were classified into 7 distinct genetic groups based upon complementation and physical mapping data. Five of the seven exo loci were gentically linked and located on a 15-kb region of DNA. Mutations at two loci were dominant only when the mutations were R-prime plasmid-located while a mutation at a second locus was cis-dominant to two other exo loci. At least five genes involved in the synthesis of acidic exopolysaccharide synthesis have been identified.     

Statistical genetic considerations for maintaining germ plasm collections

One objective of the regeneration of genetic populations is to maintain at least one copy of each allele present in the original population. Genetic diversity within populations depends on the number and frequency of alleles across all loci. The objectives of this study on outbreeding crops are: (1) to use probability models to determine optimal sample sizes for the regeneration for a number of alleles at independent loci; and (2) to examine theoretical considerations in choosing core subsets of a collection. If we assume that k-1 alleles occur at an identical low frequency of p₀ and that the k^th allele occurs at a frequency of 1-[(k-1)p₀], for loci with two, three, or four alleles, each with a p₀ of 0.05, 89–110 additional individuals are required if at least one allele at each of 10 loci is to be retained with a 90% probability; if 100 loci are involved, 134–155 individuals are required. For two, three, or four alleles, when p₀ is 0.03 at each of 10 loci, the sample size required to include at least one of the alleles from each class in each locus is 150–186 individuals; if 100 loci are involved, 75 additional individuals are required. Sample sizes of 160–210 plants are required to capture alleles at frequencies of 0.05 or higher in each of 150 loci, with a 90–95% probability. For rare alleles widespread throughout the collection, most alleles with frequencies of 0.03 and 0.05 per locus will be included in a core subset of 25–100 accessions.     

Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations

Summary By making use of pedigree information and information on marker-genotypes of the parent and F-1 individuals crossed to form an F-2 population, it is possible to carry out a linkage analysis between marker loci and loci affecting quantitative traits in a cross between segregating parent populations that are at fixation for alternative alleles at the QTL, but share the same alleles at the marker loci. For two-allele systems, depending on marker allele frequencies in the parent populations, 2–4 times as many F-2 offspring will have to be raised and scored for markers and quantitative traits in order to provide power equivalent to that obtained in a cross between fully inbred lines. Major savings in number of F-2 offspring raised can be achieved by scoring each parent pair for a large number of markers in each chromosomal region and scoring F-1 and F-2 offspring only for those markers for which the parents were homozygous for alternative alleles. For multiple allele systems, particularly when dealing with hypervariable loci, only 10%–20% additional F-2 offspring will have to be raised and scored to provide power equivalent to that obtained in a cross between inbred lines. When a resource population contains novel favorable alleles at quantitative trait loci that are not present (or rare) in a commercial population, analyses of this sort will enable the loci of interest to be identified, mapped and manipulated effectively in breeding programs.Contribution no. 2124-E, 1987 series from The Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel     

Polymorphism of Trinucleotide Repeats at Loci FRAXA and FRAXE in the Population of Tomsk

Polymorphism of CGG and GCC trinucleotide repeats, whose expansions at the FRAXA and FRAXE loci have been identified as causative mutations in two forms of mental retardation, was studied in Slavic population of Tomsk. At the FRAXA locus a total of 31 allelic variants ranging from 8 to 56 copies of CGG repeat with two modal classes of 28–29 and 18–20 repeat units (with the frequencies of 24.6 and 11.5% respectively) were revealed. Compared to other populations, this locus was characterized by unusually high frequency of intermediate alleles with the sizes of more than 40 CGG repeat units (12.4%). Since intermediate repeats of the FRAXAlocus were more prone to instability than normal alleles, it was suggested that Slavic population of Siberia had higher risk of the development of FMR1 dynamic mutations, giving rise to the Martin–Bell syndrome. The FRAXE allele frequency distribution was demonstrated to be normal with 18 allelic variants ranging from 9 to 27 GCC repeat units. In the population of Tomsk this locus had higher than in other populations frequency (26.7%) of short (less than 15 repeat units in size) alleles. In addition, in the Tomsk population both loci were characterized by high level of heterozygosity and low frequencies of modal allele classes. These results can be explained by the high level of outbreeding typical of the population of Siberia.     

A “new” genetic polymorphism of a human serum protein: inter-alpha-trypsin-inhibitor

Summary A new genetic polymorphism of a human serum glycoprotein, the inter--trypsin-inhibitor (ITI), has been demonstrated by population and family studies. Sera were examined after neuraminidase treatment by isoelectric focusing on agarose gels followed by immunoblotting or by immunfixation with specific ITI-antiserum. Using this method, three common ITI phenotypes 1, 1–2 and 2, as well as two further rare ITI types 1–3 and 2–3 were disclosed. Genetically, these phenotypes are controlled by three allelic genes that determine a total of six phenotypes. These alleles are designated ITI^*1, ITI^*2 and ITI^*3. The homozygous form of the third allele ITI^*3 has not been found, as yet. The frequencies of ITI were examined in two population samples from Southern Germany (n=248) and from Tyrol, Austria (n=124). The gene frequencies of the common alleles ITI^*1 and ITI^*2 were 0.575 and 0.417, respectively, in Southern Germany, and 0.577 and 0.423, respectively, in Tyrol, Austria. The third allele ITI^*3 was found only in the sample from Southern Germany, thus far, and was calculated to be 0.008.     

On three methods for estimating mutation rates indirectly.

Methods for estimating a mutation rate mu has been proposed by Kimura and Ohta; Nei; and Rothman and Adams. It is shown here that all three methods are best applied to rare alleles and that they are all based upon the assumption that all alleles ultimately become extinct. If there is a neutral allele in a growing population, there is conditioning on ultimate extinction, which implies that the underlying stochastic process can be approximated by a branching process for which the mean number of offspring is less than 1. The low numerical values of t0, the mean time to extinction of a line descended from a single mutant, found in two simulation studies, can be attributed to two features. First, the data on which these studies were based came from a fairly rapidly growing population. In such a population, we would expect that extinction, if it does occur, takes place quickly. A second factor is that the effective population size is somewhat lower than the actual number of adults. Population subdivision and migration does not seem to play a significant role. Conservative high and low estimates of mutation rates are computed, and an estimate is obtained for the standard deviation of the estimate of mu. These allow a rough estimate of a 95% confidence interval, which contains estimates of mu found by Neel and Rothman.     

The Hill-Robertson effect and the evolution of recombination

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.     

Sequential activation and loss of the pre-B cell Thy-1 gene in T-cell x pre-B cell somatic hybrids

In somatic cell hybrids between the pseudodiploid Thy-1^– Abelson-leukemia-virus-induced pre-B cell lymphoma RAW 253.1 and the Thy-1⁺ T-cell lymphoma, AKR1 (Thy-1⁺), all cells express the Thy-1 allele of the T-cell parent but most hybrid cells do not express the Thy-1 allele of the pre-B cell lymphoma parent. The Thy-1 allele of the pre-B cell parent, however, is spontaneously activated in a minor proportion of hybrid cells. By sorting for cells expressing the Thy-1 allele of the pre-B cell parent, derivative clones in which 100% of cells express both parental Thy-1 alleles can be isolated. Revertants with a phenotype identical with that of the original hybrid cell line can be isolated from these derivatives by sorting for nonexpression of the Thy-1 allele of the pre-B cell parent. These first-generation revertant cell lines have lost one copy of the Thy-1 gene derived from the pre-B cell lymphoma parent. By a further cycle of sorting, derivatives in which 100% of cells express both parental Thy-1 alleles can again be obtained. Second-generation revertants isolated by sorting these Thy-1⁺ hybrid cells for nonexpression of the Thy-1 allele of the pre-B cell parent no longer contain a normal copy of the pre-B cell Thy-1 allele and this surface antigen is no longer expressed by any cells in the population. These results are consistent with a mechanism that sequentially activates each copy of the Thy-1 gene derived from the pre-B cell lymphoma parent. Hybrids between the class D Thy-1 ^– mutant, AKR1(Thy-1^–d), in which the 5 region of the Thy-1 structural gene has been deleted, and RAW 253.1 cannot be activated to express either Thy-1 allele. This result indicates that a sequence upstream of exon 2 of the active Thy-1 allele is critical for the initial activation event.     

Fission Models of Population Variability

Most models in population genetics are models of allele frequency, making implicit or explicit assumptions of equilibrium or constant population size. In recent papers, we have attempted to develop more appropriate models for the analysis of rare variant data in South American Indian tribes; these are branching process models for the total number of replicates of a variant allele. The spatial distribution of a variant may convey information about its history and characteristics, and this paper extends previous models to take this factor into consideration. A model of fission into subdivisions is superimposed on the previous branching process, and variation between subdivisions is considered. The case where fission is nonrandom and the locations of like alleles are initially positively associated, as would happen were a tribal cluster or village to split on familial lines, is also analyzed. The statistics developed are applied to Yanomama Indian data on rare genetic variants. Due to insufficient time depth, no definitive new inferences can be drawn, but the analysis shows that this model provides results consistent with previous conclusions, and demonstrates the general type of question that may be answered by the approach taken here. In particular, striking confirmation of a higher-than-average growth rate, and hence smaller-than-previously-estimated age, is obtained for the Yan2 serum albumen variant.     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N _e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988     

Fixation probability with multiple alleles and projected average allelic effect on selection

The first-order effect of selection on the probability of fixation of an allele, with respect to an intensity of selection s>0 in a diploid population of fixed finite size N, undergoing discrete, non-overlapping generations, is shown to be given by the sum of the average effects of that allele on the coefficient of selection in the current generation and all future generations, given the population state in the current generation. This projected average allelic effect is a weighted sum of average allelic effects in allozygous and autozygous offspring in the initial generation, with weights given in terms of expected coalescence times, under neutrality, for the lineages of two or three gametes chosen at random in the same generation. This is shown in the framework of multiple alleles at one locus, with genotypic values determining either viability or fertility differences, and with either multinomial or exchangeable reproduction schemes. In the limit of weak selection in a large population such that Ns tends to zero, the initial average allelic effects in allozygous offspring and autozygous offspring have the same weight on the fixation probability only in the domain of application of the Kingman coalescent. With frequency-dependent selection in a linear-game-theoretic context with two phenotypes determined by additive gene action, the first-order effect on the fixation probability is a combination of two effects of frequency-independent selection, one in a haploid population, the other in a diploid population. In the domain of application of the Kingman coalescent as the population size goes to infinity and Ns to zero, the first effect is three times more important than the second effect. This explains the one-third law of evolutionary dynamics in this domain, and shows how this law can be extended beyond this domain.     

Phenotypes of lethal alleles of the recessive temperature sensitive paralytic mutantstambh A ofDrosophila melanogaster suggest its neurogenic function

The mutantstambhA ¹ (2–56.8) ofDrosophila melanogaster was identified as a reversible temperature sensitive adult and larval paralytic. We have (i) isolated and analysed phenotypes of one new homozygous viable paralytic allele and two recessive unconditional embryonic lethal alleles ofstmA and (ii) studied the interaction of the viable paralytic alleles with ts paralytic mutantsnap ^ts1 (2–55.2) andpara ^ts1 (1–53.9). The homozygous viable paralytic allelesstmA ² andstmA ¹ are semi dominant neomorphs. The lethal allelesstmA ¹² andstmA ⁷ appear to be amorphs. Unhatched embryos expressing lethalstmA alleles showed hypotrophy of the anterior dorsal cuticle overlying the brain with a concomitant hypertrophy of the anterior dorsal neurogenic region (the brain). The ventral cuticle was poorly differentiated, and the ventral nerve chord showed mild hypertrophy and poor organisation. The epidermal cells in 12–13 h old embryos did not show the normal palisade layer arrangement. These phenotypes are similar to mutant phenotypes of the neurogenic class of genes whose wild type functions are necessary for intercellular communication. The allelesstmA ¹ andstmA ² do not appear to interact with the paralytic mutantsnap ^ts1 orpara ^ts1 in double mutant combinations. On the basis of our results it is proposed thatstmA may belong to the neurogenic class of genes.     

Survival probabilities for some multitype branching processes in genetics

Consider a positively regular, slightly supercritical branching process with K types. An approximation to the probability of survival of a line descended from a single individual of type i has recently been derived by Hoppe. If K is large, however, this approximation may not be easy to compute. A further approximation that is easily computable is given. The result is used to estimate probabilities of survival of an allele A that is originally present in one male or one female in a large, random mating, age-structured population. Both autosomal and sex-linked loci are considered. Another application of the approximation is also discussed.Journal paper no. J-13183 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa, project 2588     

Polymorphisms of the apolipoprotein B and E genes and their relationship to plasma lipid variables in healthy Chinese men

In this study we have analysed the apolipoprotein (Apo) E polymorphism and polymorphisms of the ApoB gene, including the ApoB/Xba I and ApoB/4311 diallelic polymorphisms and a hypervariable region (HVR) situated in the 3 region of the gene (ApoB/3HVR), in a sample of healthy male subjects from Taiyuan (northern People's Republic of China). In comparison to Caucasian populations, in the Chinese sample, the Xba I2 allele (presence of cutting site; frequency 6.1%; and 95% confidence interval, 3.3–8.9) and the long HVR alleles (9.4%; 6.0–12.8) were rare, whereas the ApoB/4311 (Ser) allele (70.8%; 65.4–76.2) and the 34-repeat allele of the HVR (HVR34; 62.4%; 56.8–68.0) were frequent. In subjects having none, one, or two HVR34 alleles, the mean levels of plasma triglycerides were 2.32±1.44 (SD), 1.45+0.74, and 1.75±1.07 g/l, respectively (P < 0.007). Similar trends were observed for very low density lipoprotein (VLDL) cholesterol, LpE:B, and LpCIII:B. The frequencies of the ApoE alleles were similar to those reported in other populations of Asian origin; E2 (7.4%; 4.2–10.6), E3 (84.4%; 80.2–88.6), and E4 (8.2%; 5.0–11.4). Individuals carrying the E2 allele had a lower mean level of ApoB than E33 individuals: 0.87±0.16 and 1.00±0.22 g/l, respectively (P < 0.007). Individuals carrying the E4 allele had higher levels of ApoE than E33 individuals: 0.140±0.084 and 0.094±0.052 g/l, respectively (P < 0.004); similar trends were observed for VLDL cholesterol, triglycerides, LpE:B, and LpCIII:B. The ApoB/ HVR34 and ApoE/E4 polymorphisms accounted for 10% to 15% of the variability of the plasma levels of VLDL cholesterol, ApoE, triglycerides, LpE:B, and LpCIII:B. Several lipid variables appeared to be favourably affected by specific forms of ApoB and ApoE that are particularly frequent in this Chinese population.