Influence of selection on the probability of fixation at a locus with multiple alleles.

BACKGROUND: Genes exist in a population in a variety of forms (alleles), as a consequence of multiple mutation events that have arisen over the course of time. In this work we consider a locus that is subject to either multiplicative or additive selection, and has n alleles, where n can take the values 2, 3, 4, … . We focus on determining the probability of fixation of each of the n alleles. For n = 2 alleles, analytical results, that are 'exact', under the diffusion approximation, can be found for the fixation probability. However generally there are no equally exact results for n ≥ 3 alleles. In the absence of such exact results, we proceed by finding results for the fixation probability, under the diffusion approximation, as a power series in scaled strengths of selection such as R i , j = 2 N e ( s i - s j ) , where N e is the effective population size, while s i and s j are the selection coefficients associated with alleles i and j, respectively. RESULTS: We determined the fixation probability when all terms up to second order in the R i , j are kept. The truncation of the power series requires that the R i , j cannot be indefinitely large. For magnitudes of the R i , j up to a value of approximately 1, numerical evidence suggests that the results work well. Additionally, results given for the particular case of n = 3 alleles illustrate a general feature that holds for n ≥ 3 alleles, that the fixation probability of a particular allele depends on that allele's initial frequency, but generally, this fixation probability also depends on the initial frequencies of other alleles at the locus, as well as their selective effects. CONCLUSIONS: We have analytically exposed the leading way the probability of fixation, at a locus with multiple alleles, is affected by selection. This result may offer important insights into CDCV traits that have extreme phenotypic variance due to numerous, low-penetrance susceptibility alleles.

Lethal mutations with fluctuating heterozygous effect: the lethal force of effective dominance.

The theory of population genetics leads to the expectation that in very large populations the frequencies of recessive lethal mutations are close to the square root of the mutation rate, corresponding to mutation-selection balance. There are numerous examples where the frequencies of such alleles are orders of magnitude larger than this result. In this work we theoretically investigate the role of temporal fluctuations in the heterozygous effect (h) for lethal mutations in very large populations. For fluctuations of h, around a mean value of [Formula: see text], we find a biased outcome that is described by an effective dominance coefficient, heff, that is generally less than the mean dominance coefficient, i.e., [Formula: see text]. In the case where the mean dominance coefficient is zero, the effective dominance coefficient is negative: heff < 0, corresponding to the lethal allele behaving as though overdominant and having an elevated mean frequency. This case plausibly explains mean allele frequencies that are an order of magnitude larger than the equilibrium frequency of a recessive allele with a constant dominance coefficient. Our analysis may be relevant to explaining lethal disorders with anomalously high frequencies, such as cystic fibrosis and Tay-Sachs, and may open the door to further investigations into the statistics of fluctuations of the heterozygous effect.

The association of hypertension with renin-angiotensin system gene polymorphisms in the Lebanese population.

AIM: The study objective was to examine the association of hypertension in the Lebanese population with three renin-angiotensin system gene polymorphisms (RAS): angiotensin-converting enzyme (ACE), angiotensinogen (AGT) and angiotensin-receptor type 1 (AT1R). METHODS: A total of 270 subjects (124 hypertensive vs 146 normotensive) were genotyped for ACE insertion (I)/deletion (D), AGT (M235T), and AT(1)R (A1166C) gene polymorphisms by polymerase chain reaction and restriction fragment length polymorphism. RESULTS: The studied genes showed no deviation from Hardy-Weinberg equilibrium. No association could be reported with the ACE I/D polymorphism, although the D allele frequency was high (77%) in patients. AGT TT genotype prevalence was found to be lower in hypertensive versus normotensive subjects (p<0.0001). AT(1)R CC and AC genotypes were significantly more frequent in hypertensive than normotensive subjects (p<0.0001). CONCLUSION: The first conducted study on the RAS gene polymorphisms in Lebanese hypertensive patients demonstrated a possible association of the AGT T and AT(1)R C alleles with hypertension.

The geographic distribution of the ACE II genotype: a novel finding.

Angiotensin converting enzyme (ACE) gene polymorphism insertion (I) or deletion (D) has been widely studied in different populations, and linked to various functional effects and associated with common diseases. The purpose of the present study was to investigate the relationship between the ACE I/D frequency in different populations and geographic location; ACE I/D allele frequency in the Lebanese population and ACE II genotype contribution to the geographic trend were also identified. Five hundred and seventy healthy volunteers were recruited from the Lebanese population. Genomic DNA was extracted from buccal cells, and amplified by polymerase chain reaction; products were then identified by gel electrophoresis. The frequencies of the different ACE I/D genotypes were determined and tested for Hardy-Weinberg equilibrium (HWE). To assess the relationship between ACE I/D frequency and geographic location, and to identify how the Lebanese population contributes to the geographic trend in ACE I/D frequencies, Eurasian population samples and Asians were incorporated in the analyses from the literature. The frequency of the I allele in the Lebanese population was 27% and the corresponding II genotype was at a frequency of 7.37% (in HWE; P=0.979). The ACE I allele and genotype frequencies show an association with longitude, with frequencies increasing eastwards and westwards from the Middle East.

Heterozygosity, inbreeding and neonatal traits in Soay sheep on St Kilda.

We investigated whether birth weight and neonatal survival, a period within which 24% of all mortalities occur, were correlated with levels of inbreeding in St Kilda Soay sheep, using pedigree inbreeding coefficients and four marker-based estimators of inbreeding. None of the inbreeding estimators, either of the offspring, or of their mothers, explained significant variation in a lamb's birth weight or probability of surviving the neonatal period, suggesting low inbreeding depression for these traits. We evaluated the correlation between the marker-based measures of inbreeding and inbreeding coefficients obtained from the Soay pedigree, where paternal links were inferred using the same panel of microsatellite markers. Even when using a relatively complete portion of the pedigree, in which all individuals had known maternal and paternal grandparents, the correlation was found to be weak (r = -0.207, where mean f = 0.0168). These results add support to the recent prediction that when the mean and variance in inbreeding are low in a population, heterozygosity-fitness correlations can be very weak or even undetectable. The pursuit of more detailed pedigrees offers the best prospect for identifying inbreeding depression within this study population.

Maternal genetic effects set the potential for evolution in a free-living vertebrate population.

Heritable maternal effects have important consequences for the evolutionary dynamics of phenotypic traits under selection, but have only rarely been tested for or quantified in evolutionary studies. Here we estimate maternal effects on early-life traits in a feral population of Soay sheep (Ovis aries) from St Kilda, Scotland. We then partition the maternal effects into genetic and environmental components to obtain the first direct estimates of maternal genetic effects in a free-living population, and furthermore test for covariance between direct and maternal genetic effects. Using an animal model approach, direct heritabilities (h2) were low but maternal genetic effects (m2) represented a relatively large proportion of the total phenotypic variance for each trait (birth weight m2=0.119, birth date m2=0.197, natal litter size m2=0.211). A negative correlation between direct and maternal genetic effects was estimated for each trait, but was only statistically significant for natal litter size (ram= -0.714). Total heritabilities (incorporating variance from heritable maternal effects and the direct-maternal genetic covariance) were significant for birth weight and birth date but not for natal litter size. Inadequately specified models greatly overestimated additive genetic variance and hence direct h2 (by a factor of up to 6.45 in the case of birth date). We conclude that failure to model heritable maternal variance can result in over- or under-estimation of the potential for traits to respond to selection, and advocate an increased effort to explicitly measure maternal genetic effects in evolutionary studies.

An analysis of consanguinity and social structure within the UK Asian population using microsatellite data.

We analysed microsatellite genotypes sampled from the Pakistani and Indian communities in Nottingham, UK, to investigate the genetic consequences of substructuring mediated by traditional marriage customs. The application of a recently developed likelihood approach identified significant levels of population substructure within the Pakistani community as a whole, as well as within the finer divisions of castes and biradheri. In addition, high levels of cryptic or unacknowledged consanguinity were detected within subgroups of this community, including biradheri. The Indian sample showed no significant evidence of either substructure or consanguinity. We demonstrate that estimates of disease gene frequencies can be inaccurate unless they are made jointly with estimates of population substructure and consanguinity ((theta congruent to FST) and C). The magnitude of these estimates also highlights the importance of accounting for the finer scale of social structuring when making decisions regarding the risk of recessive disorders in offspring.

Population genetic structure of the lettuce root aphid, Pemphigus bursarius (L.), in relation to geographic distance, gene flow and host plant usage.

Microsatellite markers were used to examine the population structure of Pemphigus bursarius, a cyclically parthenogenetic aphid. Substantial allele frequency differences were observed between populations on the primary host plant (collected shortly after sexual reproduction) separated by distances as low as 14 km. This suggested that migratory movements occur over relatively short distances in this species. However, the degree of allele frequency divergence between populations was not correlated with their geographical separation, indicating that isolation by distance was not the sole cause of spatial genetic structuring. Significant excesses of homozygotes were observed in several populations. Substantial allele frequency differences were also found between aphids on the primary host and those sampled from a secondary host plant after several parthenogenetic generations at the same location in two successive years. This could have been due to the existence of obligately parthenogenetic lineages living on the secondary host or genetically divergent populations confined to different secondary host plant species but sharing a common primary host.

The effect of reproductive compensation on recessive disorders within consanguineous human populations.

We investigate the effects of consanguinity and population substructure on genetic health using the UK Asian population as an example. We review and expand upon previous treatments dealing with the deleterious effects of consanguinity on recessive disorders and consider how other factors, such as population substructure, may be of equal importance. For illustration, we quantify the relative risks of recessive lethal disorders by presenting some simple calculations that demonstrate the effect 'reproductive compensation' has on the maintenance of recessive alleles. The results show how reproductive compensation can effectively counteract the purging of deleterious alleles within consanguineous populations. Whereas inbreeding does not elevate the equilibrium frequency of affected individuals, reproductive compensation does. We suggest this effect must be built into interpretations of the incidence of genetic disease within populations such as the UK Asians. Information of this nature will benefit health care workers who inform such communities.