Simulating genealogies of selected alleles in a population of variable size

An importance-sampling method is presented that allows the simulation of the history of a selected allele in a population of variable size. A sample path describing the number of copies of an allele that arose as a single mutant is generated by simulating backwards from the current frequency until the allele is lost. The mathematical expectation of a quantity or statistic is then estimated by taking averages over replicate simulations, weighting each replicate by the ratio of its probabilities under the Markov chains for the forward and backwards processes. This method was used to find the average age of a selected allele in an exponentially growing population. In terms of the effect on average allele age, selection in favour of an allele is not equivalent to exponential growth. To generate gene genealogies of a sample of copies of a selected allele, the neutral coalescent model is simulated for the subpopulation containing only the selected allele. From the resulting intra-allelic genealogy, it is possible to calculate the likelihood of the selection intensity as a function of the observed level of variability at marker loci closely linked to the selected allele. This method was used to estimate the intensity of selection affecting the delta 32 allele at the CCR5 locus in Europeans and a mutant at the MLH1 locus associated with colorectal cancer in the Finnish population.     

How old is the most recent ancestor of two copies of an allele?

An important clue to the evolutionary history of an allele is the structure of the neighboring region of the genome, which we term the genomic background of the allele. Consider two copies of the allele. How similar we expect their genomic background to be is strongly influenced by the age of their most recent common ancestor (MRCA). We apply diffusion theory, first used by Motoo Kimura as a tool for predicting the changes in allele frequencies over time and developed by him in many articles in this journal, to prove a variety of new results on the age of the MRCA under the simplest demographic assumptions. In particular, we show that the expected age of the MRCA of two copies of an allele with population frequency f is just 2Nf generations, where N is the effective population size. Our results are a first step in running exact coalescent simulations, where we also simulate the history of the population frequency of an allele.     

PGI*3(Israel), a new,unstable allele in the phosphoglucose isomerase system

Summary Phosphoglucose isomerase (PGI) and 16 other biochemical genetic markers were studied in an Israeli-Arab family previously described for hereditary deficiency of adenylate kinase (AK) and glucose 6-phosphate dehydrogenase (G6PD). In this inbred family a rare PGI*3 allele was observed in 11 of 32 members tested, indicating an autosomal codominant inberitance. The electrophoretic mobility of this allele is similar to that of the PGI*3 allele found in Indian populations, but unlike the Indian allele, it has a very low specific activity and heat stability. This PGI*3 allele, designated PGI*3 (Israel), seems to be a different unstable mutation and along with AK and G6PD deficiencies seems to be associated with severe anaemia.     

Association of a missense mutation in the bovine leptin gene with carcass fat content and leptin mRNA levels

Previously, we have shown that alleles of the BM1500 microsatellite, located 3.6 kb downstream of the leptin gene in cattle, were associated with carcass fat measures in a population of 154 unrelated beef bulls. Subsequently, a cytosine (C) to thymine (T) transition that encoded an amino acid change of an arginine to a cysteine was identified in exon 2 of the leptin gene. A PCR-RFLP was designed and allele frequencies in four beef breeds were correlated with levels of carcass fat. The T allele was associated with fatter carcasses and the C allele with leaner carcasses. The frequencies of the SNP alleles among breeds indicated that British breeds have a higher frequency of the T allele whereas the continental breeds have a higher occurrence of the C allele. A ribonuclease protection assay was developed to quantify leptin mRNA in a separate group of animals selected by genotype. Animals homozygous for thymine expressed higher levels of leptin mRNA. This may suggest that the T allele, which adds an extra cysteine to the protein, imparts a partial loss of biological function and hence could be the causative mutation.     

Fixation of advantageous alleles in partially self-fertilizing populations. The effect of different selection modes

The expected fixation probability of an advantageous allele was examined in a partially self-fertilizing hermaphroditic plant species using the diffusion approximation. The selective advantage of the advantageous allele was assumed to be increased viability, increased fecundity, or an increase in male fitness. The mode of selection, as well as the selfing rate, the population size, and the dominance of the advantageous allele, affect the fixation probability of the allele. In general it was found that increases in selfing rate decrease the fixation probability under male sexual selection, increase fixation probability under fecundity selection, and increase when recessive and decrease when dominant under viability selection. In some cases the highest fixation probability of advantageous alleles under fecundity or under male sexual selection occurred at an intermediary selfing rate. The expected mean fixation times of the advantageous allele were also examined using the diffusion approximation.     

A PCR-based marker for a locus conferring the aroma in Myanmar rice (Oryza sativa L.)

Aromatic rice is an important commodity for international trade, which has encouraged the interest of rice breeders to identify the genetic control of rice aroma. The recessive Os2AP gene, which is located on chromosome 8, has been reported to be associated with rice aroma. The 8-bp deletion in exon 7 is an aromatic allele that is present in most aromatic accessions, including the most popular aromatic rice varieties, Jasmine and Basmati. However, other mutations associated with aroma have been detected, but the other mutations are less frequent. In this study, we report an aromatic allele, a 3-bp insertion in exon 13 of Os2AP, as a major allele found in aromatic rice varieties from Myanmar. The insertion is in frame and causes an additional tyrosine (Y) in the amino acid sequence. However, the mutation does not affect the expression of the Os2AP gene. A functional marker for detecting this allele was developed and tested in an aroma-segregating F(2) population. The aroma phenotypes and genotypes showed perfect co-segregation of this population. The marker was also used for screening a collection of aromatic rice varieties collected from different geographical sites of Myanmar. Twice as many aromatic Myanmar rice varieties containing the 3-bp insertion allele were found as the varieties containing the 8-bp deletion allele, which suggested that the 3-bp insertion allele originated in regions of Myanmar.     

Efficient allelic replacement in rice by gene editing: A case study of the NRT1.1B gene

Precise replacement of an existing allele in commercial cultivars with an elite allele is a major goal in crop breeding. A single nucleotide polymorphism in the NRT1.1 B gene between japonica and indica rice is responsible for the improved nitrogen use efficiency in indica rice. Herein, we precisely replaced the japonica NRT1.1 B allele with the indica allele, in just one generation, using CRISPR/Cas9 gene-editing technology.No additional selective pressure was needed to enrich the precise replacement events. This work demonstrates the feasibility of replacing any genes with elite alleles within one generation, greatly expanding our ability to improve agriculturally important traits.     

The occurrence of the alpha G-Philadelphia-globin allele on a double-locus chromosome.

Hb G-Philadelphia, an alpha-globin allele, is expressed as either 20%, 30%, or 40% of the total hemoglobin. Restriction analyses published thus far have shown that among persons with 30% and 40% hemoglobin (Hb) G the alpha G allele is seen only in a single-locus haplotype. We now report the identification of a second haplotype in which the alpha G allele is found in tandem with an alpha A allele. This haplotype has been found present in DNA from the members of one family in which Hb G is expressed as 20% of the total hemoglobin, determined by both cellulose acetate electrophoresis and high-performance liquid chromatography (HPLC). Synthesis was balanced in all individuals. The identification of a variant alpha-globin allele in two distinct haplotypes presents the possibility of independent mutation. However, an alternative explanation cannot be ruled out; namely, that the original allele may have become distributed among the two haplotypes by unequal crossing-over.     

DNA polymorphisms of the apolipoprotein B and A-I/C-III genes are associated with variations of serum low density lipoprotein cholesterol level in childhood.

A number of restriction fragment length polymorphisms (RFLPs) of the apolipoprotein B (apoB) and apolipoprotein A-I/C-III(apoA-I/C-III) genes have been found to be associated with serum lipoprotein levels in many adult populations. In order to examine whether these genetic polymorphisms influence serum lipoprotein levels in childhood and adolescence, we determined the apoB XbaI and apoA-I/C-III SstI genotypes and serum lipoprotein concentrations in 307 healthy Finns aged 9 to 21 years. In the age groups of 9, 12, and 15 years, subjects homozygous for the X2 allele (the XbaI site present) of the apoB gene had mean serum low-density lipoprotein (LDL) cholesterol levels (3.69, 3.43, and 3.15 mmol/l, respectively) that were 12-20% higher than those in subjects homozygous for the absence of this allele (3.08, 3.02, and 2.80 mmol/l, respectively). This association was more significant in males than in females. At the age of 9 to 18 years, subjects carrying the S2 allele (SstI site present) of the apoA-I/C-III gene complex had an approximately 6-15% higher mean serum LDL-cholesterol level than those homozygous for its absence. The combined genotype X2+S2+ (the simultaneous presence of the X2 allele and the S2 allele) was associated with an even more marked elevation of serum LDL-cholesterol level than either allele alone. As an example, the serum LDL cholesterol concentration was 20% higher in 9-year-old subjects with at least one X2 and one S2 allele than in those without either allele (3.55 vs. 2.97 mmol/l, P less than 0.005). The S2 allele was found to be significantly more frequent in eastern than in western Finland, whereas no significant areal differences were seen in the occurrence of the X2 allele. In conclusion, genetic variations of the apoB and apoA-I/C-III gene loci influence serum lipoprotein concentrations already in childhood.     

Rearrangement at the 5'' end of amplified c-myc in human COLO 320 cells is associated with abnormal transcription.

The proto-oncogene c-myc is amplified in sublines of human COLO 320 cells carrying either homogeneously staining chromosomal regions or double minutes. COLO 320 cells carrying homogeneously staining chromosomal regions have 15 to 20 copies of an apparently normal c-myc allele and 1 to 2 copies of an abnormal c-myc allele lacking exon 1 and express high levels of a normal c-myc mRNA 2.5 kilobases in size. COLO 320 cells carrying double minutes have about 25 copies each of the normal allele and the abnormal allele but express preferentially an abnormal c-myc mRNA 2.2 kilobases in size. Nucleotide sequence analyses revealed that the break point of rearrangement resulting in the loss of exon 1 in the abnormal allele lies within a region frequently rearranged in human and murine B-cell tumors.     

Pollen transfer dynamics and the evolution of gametophytic self-incompatibility

Recent studies of mating system evolution have attempted to include aspects of pollination biology in analysis of both theoretical models and experimental systems. In light of this growing trend, we propose a simple population genetic model for the evolution of gametophytic self-incompatibility, incorporating parameters for pollen discounting and pollen export/capture. In this model, we consider several cases that span the spectrum for dominance of the mutant self-incompatibility allele and for the degree of incompatibility conferred by the allele. We confirm earlier results that inbreeding depression is required for successful invasion of the self-incompatibility allele and we demonstrate that, unless pollen discounting is very low, the level of inbreeding depression must be very high for an allele conferring self-incompatibility to become established. Finally, we show that the dominance of the mutant allele has a greater impact on the fate of a newly arisen self-incompatibility allele than the strength of the incompatibility conferred by the allele. In particular, the more recessive the self-incompatibility expression in heterozygote stigmas and the weaker the response induced, the easier it is for a self-incompatibility allele to invade.     

Generation of novel conditional and hypomorphic alleles of the Smad2 gene

Smad2 is an intracellular mediator of the transforming growth factor beta signaling (TGFbeta) pathway. It has been previously shown that, in the mouse, ablation of functional Smad2 results in embryonic lethality due to gastrulation defects. To circumvent the early lethality and study the spatially and temporally specific functions of Smad2, we utilized the Cre-loxP system to generate a Smad2 conditional allele. Here we show that a conditional allele, Smad2(flox), was generated. In this allele, exons 9 and 10 are flanked by loxP sites and the gene is functionally wildtype. Cre-mediated recombination results in a deletion allele which phenocopies our previously reported Smad2(DeltaC) null mutation. To generate this conditional allele, we first made a targeted mutation which introduced a floxed neo cassette into intron 10. This allele (Smad2(3loxP)) functions hypomorphically when placed opposite a null allele, and unlike the other published Smad2 hypomorphic allele, can be maintained in the homozygous state.     

Analyses of the age of genes and the first arrival times in a finite population

The age of a mutant gene is studied using the infinite allele model in which every mutant is new and selectively neutral. Based on a time reversal theory of Markov processes, we develop a method of mathematical analysis that is considerably simpler for calculating the various statistics of the age than previous methods. Formulas for the mean and variance and for the distribution of age are presented together with some examples of relevance to cases in natural populations.—Theoretical studies of the first arrival time of an allele to a specified frequency, given an initially monomorphic condition of the locus, are presented. It is shown that, beginning with an allele that has frequency p = 1 or an allele with frequency p = 1/2N, there is an initial lag phase in which there is virtually no chance of an allele with a specified intermediate frequency appearing in the population. The distribution of the first arrival time is also presented. The distribution shows several characteristics that are not immediately obvious from a consideration of only the mean and variance of first arrival time. Especially noteworthy is the existence of a very long tail to the distribution. We have also studied the distribution of the age of an allele in the population. Again, the distribution of this measure is shown to be more informative for several questions than are the mean and variance alone.     

Placental enzyme polymorphisms in Canadian populations.

Phenotype distributions and allele frequencies of adenylate kinase and esterase D were determined for four Canadian populations. In two population samples from south-western Ontario, allele frequencies at both loci were similar to those of European populations. In two northern, indigenous populations, the allele AK2 was not detected. There was variation at the EsD locus with EsD2 having a frequency of 0.176 in an Indian population, and 0.156 in an Eskimo population.     

SNP allele frequency estimation in DNA pools and variance components analysis

The estimation of single nucleotide polymorphism (SNP) allele frequency in pooled DNA samples has been proposed as a cost-effective approach to whole genome association studies. However, the key issue is the allele frequency window in which a genotyping method operates and provides a statistically reliable answer. We assessed the homogeneous mass extend assay and estimated the variance associated with each experimental stage. We report that a relationship between estimated allele frequency and variance might exist, suggesting that high statistical power can be retained at low, as well as high, allele frequencies. Assuming this relationship, the formation of subpools consisting of 100 samples retains an effective sample size greater than 70% of the true sample size, with a savings of 11-fold the cost of an individual genotyping study, regardless of allele frequency.     

Genetic confirmation of facioscapulohumeral muscular dystrophy in a case with complex D4Z4 rearrangments

Facioscapulohumeral muscular dystrophy (FSHD) is caused by contraction of the D4Z4 repeat on chromosome 4q. Genetic confirmation of the clinical diagnosis of FSHD is complicated by the presence of a homologous repeat on chromosome 10q and the frequent repeat exchanges between both chromosomes. Here, we describe the genetic evaluation of an FSHD patient with a complex D4Z4 allele constitution in which the potentially pathogenic allele seemingly resides on chromosome 10, despite FSHD being exclusively linked to chromosome 4. Complementary allele typing and segregation analysis confirmed the clinical diagnosis of FSHD by revealing the chromosome 4 origin of the pathogenic allele in the presence of two exchanged repeat arrays, one on chromosome 4 and one on chromosome 10, an allele constitution that cannot be identified by conventional DNA diagnosis.     

Is drift ‘directional’? Unequal breeding sex ratio revisited

Unequal breeding sex ratio can significantly reduce effective population size, allowing a rare neutral allele to jump to a high frequency through genetic drift. However, this one-way alteration to allele frequency appears inconsistent with the concept that drift is non-directional. Based on binomial sampling distribution, this study developed a method to directly and exhaustively measure drift by calculating the mean deviation of change in allele frequency, then applied it to cases of unequal breeding sex ratio. The result shows that, under those cases, (1) the mean deviation can always be divided into two halves that are equal in size but opposite in direction; (2) each half consists of one or several categories represented by various allele proportions in the rare sex; (3) this proportion is another factor that determines the outcome of drift, in addition to effective population size and allele frequency; (4) drift is non-directional on a global scale, but whether an allele will drift up or down can be predicted based on the above factors. This method enables us to dissect every component of the expected change in allele frequency caused by drift and to find out the combined effect of population size, allele frequency and allele proportion in the rarer sex under neutrality but unequal breeding sex ratio.     

Genetic analysis and molecular mapping of a pale flower allele at the W4 locus in soybean.

In soybean (Glycine max (L.) Merr.), the w4-mutable line that harbors the w4-m allele was identified in 1983. It was proposed that this line contained an autonomous transposable element at the W4 locus, which is a major locus controlling the biosynthesis of anthocyanin. The w4-m allele can revert to the W4 allele that produces the wild-type phenotype, or sometimes to other alleles that produce intermediate phenotypes. Mutant plants that produce pale flowers were identified among the progeny of a single germinal revertant event from the w4-mutable line. Through genetic analysis, we established that the pale-flower mutation was conditioned by a new allele (w4-p) at the W4 locus. The w4-p allele is dominant to the w4 allele but recessive to the W4 allele, and the w1 allele has an epistatic effect on the w4-p allele. The pale-mutant line (w4-pw4-p) was designated as Genetic Type Collection number T369. An F2 mapping population derived from the cross of Minsoy (W4W4) x T369 (w4-pw4-p) was used to map the W4/w4-p locus, using simple sequence repeat (SSR) markers. The W4 locus was located at one end of molecular linkage group D2, 2.3 cM from the SSR marker Satt386 and close to the nearby telomere.