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 effect of different levels of inbreeding on self-incompatibility and inbreeding depression in pineapple

A high level of heterozygosity in domesticated pineapple is one of the main obstacles hindering the efficient development of new varieties. Selfing has been proposed as a strategy to minimise this heterozygosity through the development of parentals with a greater level of homozygosity. Selfing and a range of lesser levels of inbreeding were evaluated for their effects on seed production and inbreeding depression in the early growth of seedlings. Selfing produced few seeds, and very few viable seedlings. The paternal backcross and several half-sib combinations exhibited minimal effects on seed development or early growth and in some cases were similar to the outcross. Sibcrosses were generally unsuccessful. The highest inbreeding coefficient that was not associated with severe inbreeding depression was approximately 0.25. The effect of inbreeding depression and the level of homozygosity on several quantitative traits including those related to fruit quality within the inbred populations, is now being assessed.

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.

Effect of family relatedness on characteristics of estimated IBD probabilities in relation to precision of QTL estimates

Background: A random QTL effects model uses a function of probabilities that two alleles in the same or in different animals at a particular genomic position are identical by descent (IBD). Estimates of such IBD probabilities and therefore, modeling and estimating QTL variances, depend on marker polymorphism, strength of linkage and linkage disequilibrium of markers and QTL, and the relatedness of animals in the pedigree. The effect of relatedness of animals in a pedigree on IBD probabilities and their characteristics was examined in a simulation study. Results: The study based on nine multi-generational family structures, similar to a pedigree structure of a real dairy population, distinguished by an increased level of inbreeding from zero to 28 % across the studied population. Highest inbreeding level in the pedigree, connected with highest relatedness, was accompanied by highest IBD probabilities of two alleles at the same locus, and by lower relative variation coefficients. Profiles of correlation coefficients of IBD probabilities along the marked chromosomal segment with those at the true QTL position were steepest when the inbreeding coefficient in the pedigree was highest. Precision of estimated QTL location increased with increasing inbreeding and pedigree relatedness. A method to assess the optimum level of inbreeding for QTL detection is proposed, depending on population parameters. Conclusions: An increased overall relationship in a QTL mapping design has positive effects on precision of QTL position estimates. But the relationship of inbreeding level and the capacity for QTL detection depending on the recombination rate of QTL and adjacent informative marker is not linear. © 2010 Freyer et al., licensee BioMed Central Ltd.

Investigation of population genetic structure and mating system in the ant Pheidole pallidula

The origin of eusociality in haplo-diploid organisms such as Hymenoptera has been mostly explained by kin selection. However, several studies have uncovered decreased relatedness values within colonies, resulting primarily from multiple queen matings (polyandry) and/or from the presence of more than one functional queen (polygyny). Here, we report on the use of microsatellite data for the investigation of sociogenetic parameters, such as relatedness, and levels of polygyny and polyandry, in the ant Pheidole pallidula. We demonstrate, through analysis of mother-offspring combinations and the use of direct sperm typing, that each queen is inseminated by a single male. The inbreeding coefficient within colonies and the levels of relatedness between the queens and their mate are not significantly different from zero, indicating that matings occur between unrelated individuals. Analyses of worker genotypes demonstrate that 38% of the colonies are polygynous with 2-4 functional queens, and suggest the existence of reproductive skew, i.e. unequal respective contribution of queens to reproduction. Finally, our analyses indicate that colonies are genetically differentiated and form a population exhibiting significant isolation-by-distance, suggesting that some colonies originate through budding.

Morphological and molecular characters reveal differentiation in a Neotropical social bee, Melipona beecheii (Apidae : Meliponini)

Morphometrics and DNA microsatellites were used to analyse the genetic structure of populations of the stingless bee M. beecheii from two extremes of its geographic range. The results showed that populations from Costa Rica and Yucatan exhibit substantial phenotypic and molecular differentiation. Bees from Yucatan were smaller and paler than those from Costa Rica. The value of multilocus F-ST = 0.280 (P <0.001) confirmed that there were significant molecular genetic differences between the two populations. Populations showed significant deviation from Hardy Weinberg equilibrium and the values of FIS (the inbreeding coefficient) were positive for Costa Rica = 0.416 and the Yucatan Peninsula = 0.193, indicating a lack of heterozygotes in both populations possibly due to inbreeding. The DNA sequence of 678 bp of the mitochondrial gene COI differed between populations by 1.2%. The results of this study should be considered in conservation programmes, particularly with regard to the movement of colonies between regions.

Estudo da variabilidade genética de marcadores moleculares ligados ao gene da MGP e sua aplicação para paternidades em Sparus aurata

Dissertação de Mestrado, Biologia Marinha, Especialização em Biotecnologia Marinha, Faculdade de Ciências do Mar e do Ambiente, Universidade do Algarve, 2008

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.  

An approximate Bayesian computation approach to overcome biases that arise when using amplified fragment length polymorphism markers to study population structure

There is great interest in using amplified fragment length polymorphism (AFLP) markers because they are inexpensive and easy to produce. It is, therefore, possible to generate a large number of markers that have a wide coverage of species genotnes. Several statistical methods have been proposed to study the genetic structure using AFLP's but they assume Hardy-Weinberg equilibrium and do not estimate the inbreeding coefficient, F-IS. A Bayesian method has been proposed by Holsinger and colleagues that relaxes these simplifying assumptions but we have identified two sources of bias that can influence estimates based on these markers: (i) the use of a uniform prior on ancestral allele frequencies and (ii) the ascertainment bias of AFLP markers. We present a new Bayesian method that avoids these biases by using an implementation based on the approximate Bayesian computation (ABC) algorithm. This new method estimates population-specific F-IS and F-ST values and offers users the possibility of taking into account the criteria for selecting the markers that are used in the analyses. The software is available at our web site (http://www-leca.uif-grenoble.fi-/logiciels.htm). Finally, we provide advice on how to avoid the effects of ascertainment bias.