Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

The genome sequencing of an albino Western lowland gorilla reveals inbreeding in the wild

BACKGROUND: The only known albino gorilla, named Snowflake, was a male wild born individual from Equatorial Guinea who lived at the Barcelona Zoo for almost 40 years. He was diagnosed with non-syndromic oculocutaneous albinism, i.e. white hair, light eyes, pink skin, photophobia and reduced visual acuity. Despite previous efforts to explain the genetic cause, this is still unknown. Here, we study the genetic cause of his albinism and making use of whole genome sequencing data we find a higher inbreeding coefficient compared to other gorillas.RESULTS: We successfully identified the causal genetic variant for Snowflake's albinism, a non-synonymous single nucleotide variant located in a transmembrane region of SLC45A2. This transporter is known to be involved in oculocutaneous albinism type 4 (OCA4) in humans. We provide experimental evidence that shows that this amino acid replacement alters the membrane spanning capability of this transmembrane region. Finally, we provide a comprehensive study of genome-wide patterns of autozygogosity revealing that Snowflake's parents were related, being this the first report of inbreeding in a wild born Western lowland gorilla.CONCLUSIONS: In this study we demonstrate how the use of whole genome sequencing can be extended to link genotype and phenotype in non-model organisms and it can be a powerful tool in conservation genetics (e.g., inbreeding and genetic diversity) with the expected decrease in sequencing cost.

Assessment of inbreeding depression in a Guzerat dairy herd: Effects of individual increase in inbreeding coefficients on production and reproduction

Influences of inbreeding on daily milk yield (DMY), age at first calving (AFC), and calving intervals (CI) were determined on a highly inbred zebu dairy subpopulation of the Guzerat breed. Variance components were estimated using animal models in single-trait analyses. Two approaches were employed to estimate inbreeding depression: using individual increase in inbreeding coefficients or using inbreeding coefficients as possible covariates included in the statistical models. The pedigree file included 9,915 animals, of which 9,055 were inbred, with an average inbreeding coefficient of 15.2%. The maximum inbreeding coefficient observed was 49.45%, and the average inbreeding for the females still in the herd during the analysis was 26.42%. Heritability estimates were 0.27 for DMY and 0.38 for AFC. The genetic variance ratio estimated with the random regression model for CI ranged around 0.10. Increased inbreeding caused poorer performance in DMY, AFC, and CI. However, some of the cows with the highest milk yield were among the highly inbred animals in this subpopulation. Individual increase in inbreeding used as a covariate in the statistical models accounted for inbreeding depression while avoiding overestimation that may result when fitting inbreeding coefficients.

Effect of inbreeding on growth and reproductive traits of Nellore cattle in Brazil

The objective of this study was to identify and quantify the influence of F (inbreeding coefficient) on weaning weight (WW), weight gain from weaning to 18 months of age (WG345), finishing visual score (precocity) at 18 months of age, muscling visual score at 18 months of age (MUS), hip height (HH), scrotal circumference at 18 months of age (SC), heifer probability of pregnancy at 14 months of age (PP14), and stayability (STAY) in Brazilian Nellore cattle. The complete pedigree included 417,552 animals born between 1984 and 2007 on 12 farms located in the states of Mato Grosso do Sul, Sao Paulo and Bahia. Following the observation of a statistically significant effect (P<0.05) of the covariates individual inbreeding coefficient (F) and maternal inbreeding coefficient, regression analysis of each trait, adjusted for all other effects, was performed as a function of the linear and quadratic effect of F and maternal F (when significant). Inbreeding negatively affected all traits studied (P<0.05), except for muscling. A quadratic effect of individual F on WW, WG345, HH and PP14, and a quadratic effect of maternal F on WG345 and HH were observed. Levels of inbreeding higher than 7-11% affected negatively growth and reproductive performance of Nellore cattle. Therefore, inbreeding should be avoided, except for purposes of genetic breeding whose main objective is the fixation of certain alleles in the population. (C) 2010 Elsevier B.V. All rights reserved.

Population structure and effects of inbreeding on milk yield and quality of Murrah buffaloes

To provide data for conservation, selection, and expansion programs of buffalo herds, this study evaluated the history of a population of Murrah buffaloes based on population structure and the effect of inbreeding on accumulated 305-d milk yield (MY), fat yield (FY), protein yield (PY), mozzarella production (MProd), and somatic cell score (SCS). The usefulness of including the individual inbreeding coefficient (F) or individual increase in inbreeding coefficient (Delta F) in the model to describe inbreeding depression was evaluated. Pedigree information from 8,054 animals born between 1976 and 2008 and 4,497 lactation records obtained from 12 herds were used. The realized effective population size was 40.10 +/- 1.27, and the mean F of the entire population was 2.14%. The ratio between the number of founders and ancestors demonstrated the existence of a bottleneck in the pedigree of this population, which may contribute to a reduction of genetic diversity. The effect of F on MY, FY, PY, MProd, and SCS was -1.005 kg, -0.299 kg, -0.246 kg, -1.201 kg, and -0.002 units, and the effect of Delta F transformed to equivalent F (%) for a mean of 2.57 equivalent generations was -4.287 kg, -0.581 kg, -0.383 kg, -2.001 kg, and -0.007 units, respectively. The inbreeding depression observed may have important economic repercussions for production systems. The Delta F can be considered the better of the two indicators of inbreeding depression due to its properties that prevent underestimation of this effect. A designed mating system to avoid inbreeding may be applied to this population to maintain genetic diversity.

Depression by inbreeding after four sucessive self-pollination squash generations

The strategy for breeding F-1 hybrid squash is to develop parental lines through self-pollination. However, it increases plant mean homozygosis, which is not the natural genetic state of a cross-pollinated species, and can cause inbreeding depression. The objective of this work was to evaluate this depression with sucessive generations of self-pollination (without selection) in Cucurbita moschata, cv. Piramoita. Populations were obtained from lines with one to four generations of self-pollination (obtained by the SSD method), from the original cv. Piramoita (population SO). Randomized blocks were used with five treatments (different generations of self-pollination -S-0 to S-4), six replicates and five plants per plot. Regression analysis was made by the Wright inbreeding coefficient (F) to measure the homozygosis level effect on vigor loss. There was a linear reduction of mean weight and fruit length, seed production (number and weight) per fruit with the increase of the homozygosis level; however inbreeding did not affect seed quality (weight of 100 seeds and germination).

Inbreeding and its effects on some productive and reproductive traits in a Murrah buffalo herd

Data concerning genealogy, milk yield, lactation length, caving interval and lac at first calving, obtained from Murrah buffaloes on a farm In São Paulo state, Brazil, were studied in order to determine the presence of inbreeding in the herd and to evaluate its effects as well as the effects of some environmental factors on productive and reproductive traits. The mean inbreeding coefficient estimated for 2414 animals, born from 1965 to 1995 was 2.94%. of these animals, 47% mere considered inbred with a mean inbreeding coefficient equal 6.25%. Milk production, lactation length, calving interval and age at first calving averaged 1493.3 +/- 60.7 kg, 271.0 +/- 37.3 days, 385.0 +/- 53.4 days and 33.05 +/- 6.05 months, respectively. Among all four traits, only lactation length was affected by inbreeding.

Pedigree analysis and inbreeding depression on growth traits in Brazilian Marchigiana and Bonsmara breeds

The study of population structure by pedigree analysis is useful to identify important circumstances that affect the genetic history of populations. The intensive use of a small number of superior individuals may reduce the genetic diversity of populations. This situation is very common for the beef cattle breeds. Therefore, the objectives of the present study were to analyze the pedigree and possible inbreeding depression on traits of economic interest in the Marchigiana and Bonsmara breeds and to test the inclusion of the individual inbreeding coefficient (F-i) or individual increases in inbreeding coefficient (Delta F-i) in the genetic evaluation model for the quantification of inbreeding depression. The complete pedigree file of the Marchigiana breed included 29,411 animals born between 1950 and 2003. For the Bonsmara breed, the pedigree file included 18,695 animals born between 1988 and 2006. Only animals with at least 2 equivalent generations of known pedigree were kept in the analyses of inbreeding effect on birth weight, weaning weight measured at about 205 d, and BW at 14 mo in the Marchigiana breed, and on birth weight, weaning weight, and scro-tal circumference measured at 12 mo in the Bonsmara breed. The degree of pedigree knowledge was greater for Marchigiana than for Bonsmara animals. The average generation interval was 7.02 and 3.19 for the Marchigiana and Bonsmara breed, respectively. The average inbreeding coefficient was 1.33% for Marchigiana and 0.26% for Bonsmara. The number of ancestors explaining 50% of the gene pool and effective population size computed via individual increase in coancestry were 13 and 97.79 for Marchigiana and 41 and 54.57 for Bonsmara, respectively. These estimates indicate reduction in genetic variability in both breeds. Inbreeding depression was observed for most of the growth traits. The model including Delta F-i can be considered more adequate to quantify inbreeding depression. The inclusion of F-i or Delta F-i in the genetic evaluation model may not result in better fit to the data. A genetic evaluation with simultaneous estimation of inbreeding depression can be performed in Marchigiana and Bonsmara breeds, providing additional information to producers and breeders.

Yield prediction and inbreeding of maize synthetics generated with lines and single crosses : classic probability

reduce costs and labor associated with predicting the genotypic mean (GM) of a synthetic variety (SV) of maize (Zea mays L.), breeders can develop SVs from L lines and s single crosses (SynL,SC) instead of L+2s lines (SynL). The objective of this work was to derive and study formulae for the inbreeding coefficient (IC) and GM of SynL,SC, SynL, and the SV derived from (L+2s)/2 single crosses (SynSC). All SVs were derived from the same L+2s unrelated lines whose IC is FL, and each parent of a SV was represented by m plants. An a priori probability equation for the IC was used. Important results were: 1) the largest and smallest GMs correspond to SynL and SynL,SC, respectively; 2) the GM predictors with the largest and intermediate precision are those for SynL and SynL,SC, respectively; 3) only when FL=1, or m is large, SynL and SynSC are the same population, but only with SynSC prediction costs and labor undergo the maximum decrease, although its prediction precision is the lowest. To determine the SV to be developed, breeders should also consider the availability of lines, single crosses, manpower and land area; besides budget, target farmers, target environments, etc.

Genetic diversity and population structure in Vicia faba L. landraces and wild related species assessed by nuclear SSRs

Research Article

Synergistic epistasis and alternative hypotheses.

Inbreeding generally results in deleterious shifts in mean fitness. If the fitness response to increasing inbreeding coefficient is non-linear, this suggests a contribution of epistasis to inbreeding depression. In a cross-breeding experiment, Salathe & Ebert (2003. J. Evol. Biol. 16: 976-985) tested and found the presence of this non-linearity in Daphnia magna. They argue that epistatic interactions cause this non-linearity. We argue here that their experimental protocol does not allow disentangling the effect of synergistic epistasis from two alternative hypotheses, namely hybrid vigour and statistical non-independence of data.

Low relatedness among cooperatively breeding workers of the greenhead ant Rhytidoponera metallica

The greenhead ant Rhytidoponera metallica has long been recognized as posing a potential challenge to kin selection theory because it has large queenless colonies where apparently many of the morphological workers are mated and reproducing. However this species has never been studied genetically and important elements of its breeding system and kin structure remain uncertain. We used microsatellite markers to measure the relatedness among nestmates unravel the fine-scale population genetic structure and infer the breeding system of R. metallica. The genetic relatedness among worker nestmates is very low but significantly greater than zero (r = 0.082 +/- 0.015) which demonstrates that nests contain many distantly related breeders. The inbreeding coefficient is very close to and not significantly different from zero indicating random mating and lack of microgeographic genetic differentiation. On average. closely located nests are not more similar genetically than distant nests which is surprising as new colonies form by budding and female dispersal is restricted. Lack of inbreeding and absence of population viscosity indicates high gene flow mediated by males. Overall the genetic pattern detected in R. metallica suggests that a high number of moderately related workers mate with unrelated males from distant nests. This breeding system results in the lowest relatedness among nestmates reported for social insect species where breeders and helpers are not morphologically differentiated. [References: 69]

The additive genetic variance after bottlenecks is affected by the number of loci involved in epistatic interactions.

We investigated the role of the number of loci coding for a neutral trait on the release of additive variance for this trait after population bottlenecks. Different bottleneck sizes and durations were tested for various matrices of genotypic values, with initial conditions covering the allele frequency space. We used three different types of matrices. First, we extended Cheverud and Routman's model by defining matrices of "pure" epistasis for three and four independent loci; second, we used genotypic values drawn randomly from uniform, normal, and exponential distributions; and third we used two models of simple metabolic pathways leading to physiological epistasis. For all these matrices of genotypic values except the dominant metabolic pathway, we find that, as the number of loci increases from two to three and four, an increase in the release of additive variance is occurring. The amount of additive variance released for a given set of genotypic values is a function of the inbreeding coefficient, independently of the size and duration of the bottleneck. The level of inbreeding necessary to achieve maximum release in additive variance increases with the number of loci. We find that additive-by-additive epistasis is the type of epistasis most easily converted into additive variance. For a wide range of models, our results show that epistasis, rather than dominance, plays a significant role in the increase of additive variance following bottlenecks.

Manipulating sex ratio to increase population growth: the example of the Lesser Kestrel

Small or decreasing populations call for emergency actions like, for example, captive breeding programs. Such programs aim at rapidly increasing population sizes in order to reduce the loss of genetic variability and to avoid possible Allee effects. The Lesser Kestrel Falco naumanni is one of the species that is currently supported in several captive breeding programs at various locations. Here, we model the demographic and genetic consequences of potential management strategies that are based on offspring sex ratio manipulation. Increased population growth could be achieved by manipulating female conditions and/or male attractiveness in the captive breeders and consequently shifting the offspring sex ratio towards more female offspring, which are then used for reintroduction. Fragmenting populations into wild-breeding and captive-breeding demes and manipulating population sex ratio both immediately increase the inbreeding coefficient in the next generation (i.e. decrease N-e) but may, in the long term, reduce the loss of genetic variability if population growth is restricted by the number of females. We use the Lesser Kestrel and the wealth of information that is available on this species to predict the long-term consequences of various kinds of sex-ratio manipulation. We find that, in our example and possibly in many other cases, a sex-ratio manipulation that seems realistic could have a beneficial effect on the captive breeding program. However, the possible long-term costs and benefits of such measures need to be carefully optimized.

Búsqueda de selección en el polimorfismo 677C>T (c.665C>T) del gen de la metilentetrahidrofolato reductasa (MTHFR) en una población Colombiana

Se realizó un estudio genético – poblacional en dos grupos etarios de población colombiana con la finalidad de evaluar las diferencias genéticas relacionadas con el polimorfismo MTHFR 677CT en busca de eventos genéticos que soporten la persistencia de este polimorfismo en la especie humana debido que este ha sido asociado con múltiples enfermedades. De esta manera se genotipificaron los individuos, se analizaron los genotipos, frecuencias alélicas y se realizaron diferentes pruebas genéticas-poblacionales. Contrario a lo observado en poblaciones Colombianas revisadas se identificó la ausencia del Equilibrio Hardy-Weinberg en el grupo de los niños y estructuras poblacionales entre los adultos lo que sugiere diferentes historias demográficas y culturales entre estos dos grupos poblacionales al tiempo, lo que soporta la hipótesis de un evento de selección sobre el polimorfismo en nuestra población. De igual manera nuestros datos fueron analizados junto con estudios previos a nivel nacional y mundial lo cual sustenta que el posible evento selectivo es debido a que el aporte de ácido fólico se ha incrementado durante las últimas dos décadas como consecuencia de las campañas de fortificación de las harinas y suplementación a las embarazadas con ácido fólico, por lo tanto aquí se propone un modelo de selección que se ajusta a los datos encontrados en este trabajo se establece una relación entre los patrones nutricionales de la especie humana a través de la historia que explica las diferencias en frecuencias de este polimorfismo a nivel espacial y temporal.