Family-size distribution and Ewens'' equivalence theorem.

Segregation analysis of a data set containing nuclear families of more than one sibship size is considered, and two different formulations of the likelihood are examined. One is the "separate-multinomials" formulation, which treats each family size as representing a separate multinomial distribution; the other is the "grand-multinomial" formulation, which treats the entire data set as representing one distribution. It is shown that these two formulations are equivalent, if and only if the population distribution of family sizes is completely unknown. However, if anything is known about the family-size distribution, the grand-multinomial formulation, although more cumbersome, makes more complete use of the data; moreover, it enables the use of one-child families in a segregation analysis. The relationship of this work to Ewens' equivalence theorem concerning "unconditional" and "conditional" likelihoods is discussed. The findings are illustrated with a simple example, and their practical relevance to real-life segregation analysis is discussed.     

Distortion of the maternal segregation of the silent alleles of complement factor 4 in normal and diabetic families

54 normal Caucasian families and 169 families in whom at least one child had type I diabetes (IDDM) were genotyped for HLA-A, B, C, DR and for the complement factors Bf and C4. The paternal and maternal transmission of the different alleles and of haplotypes and complotypes in linkage desequilibrium have been analysed. No distortion of the paternal transmission has been observed in the offspring of the two series of families. On the contrary, a distortion of the maternal segregation of the silent alleles at the complement factor C4A and B locus was found: mothers transmitted C4AQ0 more often than expected to their male offspring (p less than 0.04 in normal families, p less than 0.001 in IDDM families) while they transmitted C4BQ0 in excess to their female offspring (p less than 0.01 and p less than 0.03 in normal and IDDM families, respectively).     

Mother-child HLA compatibility ratios in children of Amerinidian parents who share common haplotypes.

Among 166 children whose parents share the HLA-A, -B, and -C antigens of at least one haplotype, there is a superficial concordance between observed and expected proportions of children whose mothers would recognize no foreign antigen in them. However, this balance is composed of fewer (64%) homozygous offspring than expected and more (147%) than the expected number of genotypes identical to the mother's. A homozygous child would be expected to recognize his or her mother as foreign, unless the mother was also homozygous, but an HLA-identical child would not. Thus, the number of children who might be immunologically tolerant of their mothers was greater than expected. No one of the three loci included in designating haplotypes was individually responsible for the divergences in haplotype frequency.     

The mechanism of the mixed inheritance of chloroplast genes in Pelargonium

Summary The distributions are given of gene frequencies among embryos after G X W and W X G plastid crosses within and between eight Pelargonium cultivars and some of their inbred or hybrid derivatives.Two distinct segregation patterns are recognized. Homozygous type I female parents (Pr₁Pr₁) have a high frequency of progeny with only maternal alleles, are intermediate for biparental and low for paternal offspring. Heterozygous type II female plants (Pr₁Pr₂) have an equally high frequency of maternal and paternal offspring and a generally low biparental frequency. These correspond to L-shaped and U-shaped gene frequency distributions respectively in which the only modes are at 0 per cent (maternal embryos) and 100 per cent (paternal embryos), with no mode corresponding to the population mean and no sign of a Gaussian distribution.The extremely variable plastid gene frequencies are strongly influenced by the maternal nuclear genotype and by the plastid genotype in which the wild-type allele is always more successful than the mutant in strict comparisons.The relative frequencies of maternal and paternal zygotes, and the mean gene frequency among all the zygotes in a cross, are explicable in terms of the input frequencies of genes from the two parents, their degree of mixing, and by some form of selective replication of plastids. This selection is controlled by nuclear and plastid genotypes which may act in the same direction, to increase the frequency of either the maternal or the paternal alleles, or in opposition. But selection alone is inadequate to explain the shapes of the gene frequency distributions. Instead, a model is proposed in which the segregation or replication of plastids appears to have a strong random element, which results in random drift of gene frequencies within a heteroplasmic zygote or embryo.     

Detection of recombination events,haplotype reconstruction and imputation of sires using half-sib SNP genotypes

Background

Identifying recombination events and the chromosomal segments that constitute a gamete is useful for a number of applications in genomic analyses. In livestock, genotypic data are commonly available for half-sib families. We propose a straightforward but computationally efficient method to use single nucleotide polymorphism marker genotypes on half-sibs to reconstruct the recombination and segregation events that occurred during meiosis in a sire to form the haplotypes observed in its offspring. These meiosis events determine a block structure in paternal haplotypes of the progeny and this can be used to phase the genotypes of individuals in single half-sib families, to impute haplotypes of the sire if they are not genotyped or to impute the paternal strand of the offspring’s sequence based on sequence data of the sire.

Methods

The hsphase algorithm exploits information from opposing homozygotes among half-sibs to identify recombination events, and the chromosomal regions from the paternal and maternal strands of the sire (blocks) that were inherited by its progeny. This information is then used to impute the sire’s genotype, which, in turn, is used to phase the half-sib family. Accuracy (defined as R²) and performance of this approach were evaluated by using simulated and real datasets. Phasing results for the half-sibs were benchmarked to other commonly used phasing programs – AlphaPhase, BEAGLE and PedPhase 3.

Results

Using a simulated dataset with 20 markers per cM, and for a half-sib family size of 4 and 40, the accuracy of block detection, was 0.58 and 0.96, respectively. The accuracy of inferring sire genotypes was 0.75 and 1.00 and the accuracy of phasing was around 0.97, respectively. hsphase was more robust to genotyping errors than PedPhase 3, AlphaPhase and BEAGLE. Computationally, hsphase was much faster than AlphaPhase and BEAGLE.

Conclusions

In half-sib families of size 8 and above, hsphase can accurately detect block structure of paternal haplotypes, impute genotypes of ungenotyped sires and reconstruct haplotypes in progeny. The method is much faster and more accurate than other widely used population-based phasing programs. A program implementing the method is freely available as an R package (hsphase).     

An improvement on the maximum likelihood reconstruction of pedigrees from marker data

Many methods have been proposed to reconstruct the pedigree of a sample of individuals from their multilocus marker genotypes. These methods, like those in other fields of statistical inferences, may suffer from both type I (falsely related) and type II (falsely unrelated) errors. In sibship reconstruction, type I errors come from the spurious fusion of two or more small sibships into a single sibship, and type II errors originate from the spurious splitting of a large sibship into two or more small sibships. In this study I investigate the tendencies of both types of errors made by the likelihood methods in sibship reconstruction, using both analytical and simulation approaches. I propose an improvement on the likelihood methods to reduce sibship splitting, and thus type II errors by downscaling the number of inferred siblings sharing the same genotype at a locus. Simulations are then conducted to compare the accuracy of the original and improved likelihood methods in sibship reconstruction of a large sample of individuals in full-sib families of the same small size, the same large size and highly variable sizes, using a variable number of loci with a variable number of alleles per locus. The methods were also applied to the analysis of a salmon data set. I show that my scaling scheme prevents effectively the splitting of large sibships, and reduces type II errors greatly with little increase in type I errors. As a result, it improves the overall accuracy of sibship assignments, except when sibships are expected to be uniformly small or marker information is unrealistically scarce.     

Genetic analysis of HLA in the U.S. Schmiedenleut Hutterites.

The Hutterites are an Anabaptist population, highly inbred, with large family sizes and extensively documented pedigrees. As part of genetic-epidemiologic studies of the impact of HLA on fertility, HLA-A, -B, -C, -DR, and -DQ typing was performed on a total of 650 Schmiedenleut Hutterities in South Dakota. An extraordinary degree of homogeneity was found. HLA-A1, -A2, -A3, -A24, and -A26 accounted for 83%, HLA-B8, -B27, -B35, -B51, -Bw60, and -Bw62 for 75%, and HLA-DR1, -DR2, -DR3, and -DR4 for 66% of the antigens at the respective HLA-A, -B, and -DR loci. All Hutterites characterized for HLA were descendants of no more than 78 ancestors. However, family analysis identified only 45 unique HLA haplotypes thought to reflect the original gene pool. Eight haplotypes were particularly frequent, accounting for nearly 50% of all observed haplotypes; four of these were consistent with a European ancestry. Coefficients measuring linkage disequilibrium were computed from haplotypes identified by family analysis. Overall, HLA analysis portrayed the Schmiedenleut Hutterities as a homogeneous and unique population, with disequilibrium among particular alleles and a spectrum of common and uncommon European haplotypes.     

Fixation, Segregation and Linkage of Allozyme Loci in Inbred Families of the Pacific Oyster Crassostrea Gigas (Thunberg): Implications for the Causes of Inbreeding Depression

The effect that inbreeding has on the fixation and segregation of genes has rarely been confirmed by direct observation. Here, fixation, segregation, and linkage of allozymes is investigated in the progeny of self-fertilized hermaphrodites of the normally outcrossing Pacific oyster Crassostrea gigas. The estimate of fixation pooled over loci, individuals, and families, F = 0.462, is significantly lower than the expected value of 0.5. Log-likelihood ratios reveal significant heterogeneity in fixation among individuals, among families, and among loci. In addition, the grand pooled segregation ratio, 127:243:54, deviates significantly from 1:2:1, with a bias against homozygotes for alleles of lesser frequency in the natural population. Segregation ratios for 11 of 14 loci are significantly heterogeneous among families, and exact tests for segregation within families reveal 16 significant results out of 51 tests. Thus, fixation and segregation of allozyme markers in inbred oyster families deviates from the expectations of neutral inbreeding theory. Di-genic disequilibria are significant for four of 74 di-locus pairs revealing two linkage groups. Strong viability selection is apparently conditional on the genotype of the hermaphrodite-founders and is largely focused on these two linkage groups. These genetic effects are explained by interaction between cis-linked factors and polymorphic regulatory backgrounds.     

Rainbow trout offspring with different resistance to viral haemorrhagic septicaemia

To study immunological and immunogenetical parameters related to resistance against viral haemorrhagic septicaemia (VHS), attempts to make gynogenetic strains of rainbow trout selected for high and low resistance to VHS were initiated in 1988. The first gynogenetic generation of inbreeding resulted in the more resistant offspring E8 and the low resistance offspring K3; the K3 offspring having the same high mortality as the susceptible reference strain of outbred trout in infection trials. A second gynogenetic generation derived from the E8 strain resulted in some low resistance offspring, and two gynogenetic families in which all, or nearly all, fish survived challenge with VHS virus. In this study, an attempt to associate the distribution of different MHC class II genotypes with low and high resistance gynogenetic offspring was performed. Two different MHC haplotypes could be distinguished, and in both low and high resistance families all three genotypes were found, which could be explained by the fact that the mother fish carried the heterozygous genotype. Although no significant differences in MHC II genotypes were found between the high and low resistance offspring, a significantly different distribution of haplotypes in the low resistance offspring was observed, that could not be explained by a one- or two-locus model.     

HLA and mate choice in humans.

Evidence from studies in rodents suggests that mate selection is influenced by major-histocompatibility-complex haplotypes, with preferences for dissimilar partners. This study was initiated to determine whether avoidance of a mate with the same HLA haplotype as one's own might be occurring in the Hutterites, a North American reproductive isolate of European ancestry, notable for their large sibships, communal lifestyle, and limited number of five-locus HLA haplotypes (HLA-A, -B, -C, -DR, and -DQ). HLA haplotypes were known for 411 Hutterite couples. The number of couples expected to match for a haplotype was calculated in two ways: first, from population genotype frequencies, with account being taken of the nonrandom mating pattern with respect to colony lineages, and, second, from computer simulations using conservative founder assumptions and the exact genealogy of the 411 couples. We observed fewer matches for HLA haplotypes between spouses than expected (first method, P = .005; second method, P = .020-.067). Among couples who did match for a haplotype, the matched haplotype was inherited from the mother in 29 cases and from the father in 50 cases (P = .018). These results are consistent with the conclusion that Hutterite mate choice is influenced by HLA haplotypes, with an avoidance of spouses with haplotypes that are the same as one's own.     

Deleterious impact of feto-maternal MHC compatibility on the success of pregnancy in a macaque model

The impact of feto-maternal histocompatibility on reproduction has inspired long-lasting debates. However, after the review of numerous articles, the impact of HLA allele sharing within couples on fecundity remains questionable. We decided to explore the impact of major histocompatibility complex (MHC) feto-maternal compatibility on reproduction in a cynomolgus macaque facility composed of animals of Mauritian descent. The Mauritian-derived macaque population presents a very restricted MHC polymorphism (only seven founding haplotypes) due to a strong founding bottleneck effect. The MHC polymorphism was investigated in 237 trios (male, female and offspring) using 17 microsatellite markers distributed across the MHC. Haplotypes were confirmed by segregation analysis. We evaluated the relative frequencies of MHC-compatible and MHC-semi-compatible offspring with the mothers. Among the 237 trios, we selected 42 trios for which the identity of the father is certain and for which the theoretical probabilities of fully compatible and semi-compatible offspring were equal. We found 11 offspring fully compatible and 31 offspring semi-compatible with their respective mother. The observed proportions were clearly outside the interval of confidence of 99 % and therefore most probably resulted from a selection of the semi-compatible offspring during pregnancy. We concluded that MHC fully compatible cynomolgus macaque offspring have a selective survival disadvantage in comparison with offspring inheriting a paternal MHC haplotype differing from maternal haplotypes.     

Estimating quantitative genetic parameters using sibships reconstructed from marker data

Previous techniques for estimating quantitative genetic parameters, such as heritability in populations where exact relationships are unknown but are instead inferred from marker genotypes, have used data from individuals on a pairwise level only. At this level, families are weighted according to the number of pairs within which each family appears, hence by size rather than information content, and information from multiple relationships is lost. Estimates of parameters are therefore not the most efficient achievable. Here, Markov chain Monte Carlo techniques have been used to partition the population into complete sibships, including, if known, prior knowledge of the distribution of family sizes. These pedigrees have then been used with restricted maximum likelihood under an animal model to estimate quantitative genetic parameters. Simulations to compare the properties of parameter estimates with those of existing techniques indicate that the use of sibship reconstruction is superior to earlier methods, having lower mean square errors and showing nonsignificant downward bias. In addition, sibship reconstruction allows the estimation of population allele frequencies that account for the relationships within the sample, so prior knowledge of allele frequencies need not be assumed. Extensions to these techniques allow reconstruction of half sibships when some or all of the maternal genotypes are known.     

Ascertainment: An Overwiew of the Classical Segregation Analysis Model for Independent Sibships

Several different methodologies for parameter estimation under various ascertainment sampling schemes have been proposed in the past. In this article, some of the methodologies that have been proposed for independent sibships under the classical segregation analysis model are synthesized, and the general likelihoods derived for single, multiple and complete ascertainment. The issue of incorporating the sibship size distribution into the analysis is addressed, and the effect of conditioning the likelihood on the observed sibship sizes is discussed. It is shown that when the number of probands in a sibship is not specified, the corresponding likelihood can be used for a broader class of ascertainment schemes than is subsumed by the classical model.     

Operation of natural selection on human height

An association between fertility, sibship size, and mid-parental height was analyzed in an endemic rural population of Lahore, Punjab, Pakistan. The study was carried out on the population of Muridke, a town 27 km north of Lahore. Families were visited to record the heights of father and mother, total number of siblings born in each family, and sex of children. The data were analyzed for fertility and mean sibship size in relation to: maternal height (the data are based on 827 siblings consisting of 3337 total siblings born out of which 2870 were alive); paternal height (the data consist of a sample of 860 siblings containing 3420 total siblings out of which 3000 were alive); and mid-parental height (the data are comprised of 790 siblings composed of 3122 total siblings born of which 2693 were alive). The data were analyzed in 3 ways, i.e., fertility and mean sibship size in relation to maternal height, paternal height, and mid-parental height. The maternal heights were arranged into 6 classes. Mean maternal height in the sample if 152.59 +or- 4.48 cm, that of father 164.94 +or- 4.59 cm, and for mid-parental heights the mean is 159.65 +or- 6.00 cm. The highest mean number of total siblings born was not associated with the mean value class, 152-153, rather it was observed in the next higher class, 154-155. The lowest coefficient of variation was seen in the mean value class, though not the variance. If the average range classes, 3 + 4, are combined, this shows higher mean number of total siblings born than the remaining classes, and also the coefficient of variation is the lowest. For paternal heights, the mean value class, 164-165 shows less mean number of children than the next higher class, 166-167. When the average range classes, 4 + 5, are combined together, a higher mean number of total siblings is observed compared with the remaining classes. For mid-parental heights, in the mean value class, 158-159, mean number of total siblings born are more than the other classes. The analysis of the combined average range classes (3 + 4) shows higher mean sibship size compared with the remaining classes.     

Parentage and Sibship Inference From Multilocus Genotype Data Under Polygamy

Likelihood methods have been developed to partition individuals in a sample into sibling clusters using genetic marker data without parental information. Most of these methods assume either both sexes are monogamous to infer full sibships only or only one sex is polygamous to infer full sibships and paternal or maternal (but not both) half sibships. We extend our previous method to the more general case of both sexes being polygamous to infer full sibships, paternal half sibships, and maternal half sibships and to the case of a two-generation sample of individuals to infer parentage jointly with sibships. The extension not only expands enormously the scope of application of the method, but also increases its statistical power. The method is implemented for both diploid and haplodiploid species and for codominant and dominant markers, with mutations and genotyping errors accommodated. The performance and robustness of the method are evaluated by analyzing both simulated and empirical data sets. Our method is shown to be much more powerful than pairwise methods in both parentage and sibship assignments because of the more efficient use of marker information. It is little affected by inbreeding in parents and is moderately robust to nonrandom mating and linkage of markers. We also show that individually much less informative markers, such as SNPs or AFLPs, can reach the same power for parentage and sibship inferences as the highly informative marker simple sequence repeats (SSRs), as long as a sufficient number of loci are employed in the analysis.     

matesoft: a program for deducing parental genotypes and estimating mating system statistics in haplodiploid species

With the advent of sophisticated genetic markers, studies on mating systems and reproductive apportionment have become increasingly feasible. In particular, paternity analyses in haplodiploid species have gained in power as hemizygous paternal genotypes allow maternal and paternal genotypes to be directly inferred from offspring genotypes. The computer program matesoft offers both newly developed algorithms for inferring maternal and paternal genotypes, and integrated estimation and correction procedures for calculating mating frequency statistics. Standard data are offspring genotypes of male‐haplodiploid organisms, including social Hymenoptera.     

The affected sib-set method: revision based on the mixed model using a conditional probability approach]

One of the implicit assumptions of the single locus model, having been used so far in the analysis of linkage between the genetic marker locus and the disease predisposition locus, is the requirement of independent--from the rest of genotype--action of genotypes of the disease predisposition locus considered. In this communication, it is emphasized that the lack of this requirement makes problematical the theoretical substantiation of the affected sib-pair method in the linkage analysis. To remove this obstacle, explicit pointing out of independence of the action of the single locus genotypes on the rest of the genotype is necessary in formulating of the single locus model which, with due regard for this assumption, represents a special, perhaps, unique case of the gene action characterized by incomplete differential penetrances of the genotypes under conditions, when the genes of the rest of genotype involved to the disease, are fixed. In this connection, the mixed model of inheritance with the "major gene", proposed by Morton and MacLean (1974), is considered, on the basis of which the theoretical expectations of the proportions of the affected sib pairs, sharing the x = 2, 1, 0 haplotypes, identical by descent (IBD) in phenotypic matings with the h = 2, 1, 0 affected parents are derived. Based on the combinatorial analysis of IBD relationships in sib pairs and of the distribution of sibships of any size s greater than or equal to 2 by the numbers L = 2, 3, 4 haplotypes, inherited by s siblings, the empirical assessment of data on sibships of any size with r greater than or equal to 2 affected siblings is considered, which makes it possible to reduce the data observed on distribution of the numbers L in sibships, to that of the IBD relationships in the affected sib pairs. It is also pointed out that conditional probability approach, proposed by the author earlier, allows at the same time to obtain the empirical estimates of the recurrence risks, conditional both on phenotypes of siblings (r affected; s-r normal siblings), and on the number of L haplotypes inherited by sibships.     

Putative non-Mendelian transmission of retinoblastoma in males: a phenotypic segregation analysis of 150 pedigrees

In a previous genotypic study of eight families, we discribed paternal segregation distortion favoring the transmission of mutant alleles at the retinoblastoma gene locus (RB1). In the current study, we reviewed all published retinoblastoma pedigrees with defined ascertainment (n = 150), to determine whether the phenotypic segregation frequency at the RB1 locus is in general influenced by the sex of the transmitting parent. Segregation analysis under complete ascertainment revealed that 49.1% of the offspring of male transmitters were affected, while 44.3% of the offspring of female transmitters were affected. While this difference is not statistically significant, it is consistent with the previous findings. No significant sex distortion could be detected among the progeny of carrier fathers and mothers. In order to quantify the transmission ratio more precisely further prospective molecular genetic analysis is warranted. We propose a biological mechanism to account for a putative segregation distortion, namely that genetic recombination creates clones of spermatogonia that are homozygous for the mutant RB1 allele leading to a non-Mendelian ratio of sperm. This model can be experimentally tested using amplification of DNA from single sperm cells.     

Fitness consequences of parental compatibility in the frog Crinia georgiana

Theory suggests that multiple mating by females can evolve as a mechanism for acquiring compatible genes that promote offspring fitness. Genetic compatibility models predict that differences in fitness among offspring arise from interactions between male and female haplotypes. Using a cross-classified breeding design and in vitro fertilization, we raised families of maternal and paternal half-siblings of the frog Crinia georgiana, a species with a polyandrous breeding system and external fertilization. After controlling for variation in maternal provisioning, we found significant effects of interacting parental haplotypes on fertilization success, and nonadditive genetic effects on measures of offspring fitness such as embryo survival, and survival to, size at, and time to metamorphosis. Additive genetic variation due to males and females was negligible, and not statistically significant for any of the fitness traits measured. Combinations of parental haplotypes that resulted in high rates of fertilization produced offspring with higher embryo survival and rapid juvenile development. We suggest that a gamete recognition mechanism for selective fertilization by compatible sperm may promote offspring fitness in this system.     

POLDISP: a software package for indirect estimation of contemporary pollen dispersal

poldisp 1.0 is a free software package to estimate the distribution of pollen dispersal distances from mother–offspring diploid genotypic data. It requires the spatial coordinates and genotypes of a sample of seed plants and their respective maternal progenies, providing estimates of the average, variance and kurtosis of the pollen dispersal curve. poldisp also estimates the effective reproductive density of pollen donors and the correlation of paternity within and among maternal sibships. poldisp is useful for characterizing the spatial scale of pollen dispersal, for assessing the variation in male fertility and for investigating biological factors affecting correlated paternity in plants.