Assessment of relationships between pigs based on pedigree and genomic information

Relationships play a very important role in studies on quantitative genetics. In traditional breeding, pedigree records are used to establish relationships between animals; while this kind of relationship actually represents one kind of relatedness, it cannot distinguish individual specificity, capture the variation between individuals or determine the actual genetic superiority of an animal. However, with the popularization of high-throughput genotypes, assessments of relationships among animals based on genomic information could be a better option. In this study, we compared the relationships between animals based on pedigree and genomic information from two pig breeding herds with different genetic backgrounds and a simulated dataset. Two different methods were implemented to calculate genomic relationship coefficients and genomic kinship coefficients, respectively. Our results show that, for the same kind of relative, the average genomic relationship coefficients (G matrix) were very close to the pedigree relationship coefficients (A matrix), and on average, the corresponding values were halved in genomic kinship coefficients (K matrix). However, the genomic relationship yielded a larger variation than the pedigree relationship, and the latter was similar to that expected for one relative with no or little variation. Two genomic relationship coefficients were highly correlated, for farm1, farm2 and simulated data, and the correlations for the parent-offspring, full-sib and half-sib were 0.95, 0.90 and 0.85; 0.93, 0.96 and 0.89; and 0.52, 0.85 and 0.77, respectively. When the inbreeding coefficient was measured, the genomic information also yielded a higher inbreeding coefficient and a larger variation than that yielded by the pedigree information. For the two genetically divergent Large White populations, the pedigree relationship coefficients between the individuals were 0, and 62 310 and 175 271 animal pairs in the G matrix and K matrix were greater than 0. Our results demonstrated that genomic information outperformed the pedigree information; it can more accurately reflect the relationships and capture the variation that is not detected by pedigree. This information is very helpful in the estimation of genomic breeding values or gene mapping. In addition, genomic information is useful for pedigree correction. Further, our findings also indicate that genomic information can establish the genetic connection between different groups with different genetic background. In addition, it can be used to provide a more accurate measurement of the inbreeding of an animal, which is very important for the assessment of a population structure and breeding plan. However, the approaches for measuring genomic relationships need further investigation.     

Effect of lipid membranes on the apparent pK of the local anesthetic tetracaine spin label and titration studies

Electrometric titrations and spin label data demonstrate changes in the experimentally determined apparent pK of an ionizable drug in the presence of membranes. This effect is attributed to the difference in partition coefficients for the charged and uncharged forms of the drug. Investigation of the binding of a local anesthetic, tetracaine, to egg phosphatidylcholine membranes indicates that the drug apparent pK decreases in the presence of membranes, the decrease being a function of membrane concentration. The agreement between titration and spin label studies is very good and could be simulated by calculating membrane-bound and free populations of charged and uncharged tetracaine from the independently-measured partition coefficients for the two forms.     

Comparing the van Oosterhout and Chybicki‐Burczyk methods of estimating null allele frequencies for inbred populations

In spite of the usefulness of codominant markers in population genetics, the existence of null alleles raises challenging estimation issues in natural populations that are characterized by positive inbreeding coefficients (F > 0). Disregarding the possibility of F > 0 in a population will generally lead to overestimates of null allele frequencies. Conversely, estimates of inbreeding coefficients (F) may be strongly biased upwards (excess homozygotes), in the presence of nontrivial frequencies of null alleles. An algorithm has been presented for the estimation of null allele frequencies in inbred populations (van Oosterhout method), using external estimates of the F‐statistics. The goal of this study is to introduce a modification of this method and to provide a formal comparison with an alternative likelihood‐based method (Chybicki‐Burczyk). Using simulated data, we illustrate the strengths and limitations of these competing methods. Under most circumstances, the likelihood method is preferable, but for highly inbred organisms, a modified van Oosterhout method offers some advantages.     

Genetic evaluation methods for populations with dominance and inbreeding

Summary The effect of inbreeding on mean and genetic covariance matrix for a quantitative trait in a population with additive and dominance effects is shown. This genetic covariance matrix is a function of five relationship matrices and five genetic parameters describing the population. Elements of the relationship matrices are functions of Gillois (1964) identity coefficients for the four genes at a locus in two individuals. The equivalence of the path coefficient method (Jacquard 1966) and the tabular method (Smith and Mäki-Tanila 1990) to compute the covariance matrix of additive and dominance effects in a population with inbreeding is shown. The tabular method is modified to compute relationship matrices rather than the covariance matrix, which is trait dependent. Finally, approximate and exact Best Linear Unbiased Predictions (BLUP) of additive and dominance effects are compared using simulated data with inbreeding but no directional selection. The trait simulated was affected by 64 unlinked biallelic loci with equal effect and complete dominance. Simulated average inbreeding levels ranged from zero in generation one to 0.35 in generation five. The approximate method only accounted for the effect of inbreeding on mean and additive genetic covariance matrix, whereas the exact accounted for all of the changes in mean and genetic covariance matrix due to inbreeding. Approximate BLUP, which is computable for large populations where exact BLUP is not feasible, yielded unbiased predictions of additive and dominance effects in each generation with only slightly reduced accuracies relative to exact BLUP.     

A cautionary note on elasticity analyses in a ternary plot using randomly generated population matrices

Matrix population models are one of the most common mathematical models in ecology, which describe the dynamics of stage-structured populations and provide us many population statistics. One of the statistics, elasticity onto population growth rate, is frequently used and represents the degree of the relative impact of life history parameters to the population growth rate. Due to the utility of elasticities for cross-taxonomic comparisons, Silvertown and his coauthors have published multiple papers and reported the relationship between elasticities and life forms (or life history) in multiple plant species, using a triangle map (called “ternary plot”). To understand why their elasticities are located in specific regions of the ternary plot, we constructed four archetypes of population matrices, from which we simulated 24,000 randomly generated population matrices and obtained the consequent elasticities. We found a large discrepancy when comparing our results to those in Silvertown et al.'s study (Conserv Biol 10:591–597, 1996): for our simulated matrices where rapid transitions were not allowed (e.g., trees), the elasticity distribution resulted in a line across the ternary plot. We provided the mathematical proof for this result, and found that its slope depends on matrix dimension. We also used 1230 matrices from the COMPADRE Plant Matrix Database and calculated the elasticities. Our simulated results were validated with field data from COMPADRE: two straight lines appeared in the ternary plot. Furthermore, we answered several addressed questions, such as, “Is there any special elasticity distribution in matrices with high population growth rates?” and “Why are the elasticities of natural populations concentrated in the upper half of the ternary plot?”.     

Simple deterministic identity-by-descent coefficients and estimation of QTL allelic effects in full and half sibs

Accurate and rapid methods for the detection of quantitative trait loci (QTLs) and evaluation of consequent allelic effects are required to implement marker-assisted selection in outbred populations. In this study, we present a simple deterministic method for estimating identity-by-descent (IBD) coefficients in full- and half-sib families that can be used for the detection of QTLs via a variance-component approach. In a simulated dataset, IBD coefficients among sibs estimated by the simple deterministic and Markov chain Monte Carlo (MCMC) methods with three or four alleles at each marker locus exhibited a correlation of greater than 0.99. This high correlation was also found in QTL analyses of data from an outbred pig population. Variance component analysis used both the simple deterministic and MCMC methods to estimate IBD coefficients. Both procedures detected a QTL at the same position and gave similar test statistics and heritabilities. The MCMC method, however, required much longer computation than the simple method. The conversion of estimated QTL genotypic effects into allelic effects for use in marker-assisted selection is also demonstrated.     

Stochastic flowering phenology in Dactylis glomerata populations described by Markov chain modelling

Understanding the relationship between flowering patterns and pollen dispersal is important in climate change modelling, pollen forecasting, forestry and agriculture. Enhanced understanding of this connection can be gained through detailed spatial and temporal flowering observations on a population level, combined with modelling simulating the dynamics. Species with large distribution ranges, long flowering seasons, high pollen production and naturally large populations can be used to illustrate these dynamics. Revealing and simulating species-specific demographic and stochastic elements in the flowering process will likely be important in determining when pollen release is likely to happen in flowering plants. Spatial and temporal dynamics of eight populations of Dactylis glomerata were collected over the course of two years to determine high-resolution demographic elements. Stochastic elements were accounted for using Markov chain approaches in order to evaluate tiller-specific contribution to overall population dynamics. Tiller-specific developmental dynamics were evaluated using three different RV matrix correlation coefficients. We found that the demographic patterns in population development were the same for all populations with key phenological events differing only by a few days over the course of the seasons. Many tillers transitioned very quickly from non-flowering to full flowering, a process that can be replicated with Markov chain modelling. Our novel approach demonstrates the identification and quantification of stochastic elements in the flowering process of D. glomerata, an element likely to be found in many flowering plants. The stochastic modelling approach can be used to develop detailed pollen release models for Dactylis, other grass species and probably other flowering plants.

     

Effect of lipid membranes on the apparent pK of the local anesthetic tetracaine. Spin label and titration studies

Electrometric titrations and spin label data demonstrate changes in the experimentally determined apparent pK of an ionizable drug in the presence of membranes. This effect is attributed to the difference in partition coefficients for the charged and uncharged forms of the drug. Investigation of the binding of a local anesthetic, tetracaine, to egg phosphatidylcholine membranes indicates that the drug apparent pK decreases in the presence of membranes, the decrease being a function of membrane concentration. The agreement between titration and spin label studies is very good and could be simulated by calculating membrane-bound and free populations of charged and uncharged tetracaine from the independently-measured partition coefficients for the two forms.     

Inexpensive Computation of the Inverse of the Genomic Relationship Matrix in Populations with Small Effective Population Size

Many computations with SNP data including genomic evaluation, parameter estimation, and genome-wide association studies use an inverse of the genomic relationship matrix. The cost of a regular inversion is cubic and is prohibitively expensive for large matrices. Recent studies in cattle demonstrated that the inverse can be computed in almost linear time by recursion on any subset of ∼10,000 individuals. The purpose of this study is to present a theory of why such a recursion works and its implication for other populations. Assume that, because of a small effective population size, the additive information in a genotyped population has a small dimensionality, even with a very large number of SNP markers. That dimensionality is visible as a limited number of effective SNP effects, independent chromosome segments, or the rank of the genomic relationship matrix. Decompose a population arbitrarily into core and noncore individuals, with the number of core individuals equal to that dimensionality. Then, breeding values of noncore individuals can be derived by recursions on breeding values of core individuals, with coefficients of the recursion computed from the genomic relationship matrix. A resulting algorithm for the inversion called “algorithm for proven and young” (APY) has a linear computing and memory cost for noncore animals. Noninfinitesimal genetic architecture can be accommodated through a trait-specific genomic relationship matrix, possibly derived from Bayesian regressions. For populations with small effective population size, the inverse of the genomic relationship matrix can be computed inexpensively for a very large number of genotyped individuals.     

From inclusive fitness to fixation probability in homogeneous structured populations

The methods of inclusive fitness provide a powerful analysis of the action of selection on social behaviour. The key component of this analysis is the concept of relatedness R. In infinite populations, a standard method of calculating relatedness coefficients is through coefficients of consanguinity using the notion of genetic identity by descent. In this paper, we show that this approach can also be made to work in finite populations and we assume here that the population has a homogeneous structure, such as an island model. We demonstrate that, under the assumption that genetic effects are small and additive, the resulting formulation of inclusive fitness is equivalent to other significant measures of selection in finite populations, including the change in average allele frequency and fixation probability. The results are illustrated for a model of the evolution of cooperation in a finite island population.     

Relationship between Recrystallization Rate of Ice Crystals in Sugar Solutions and Water Mobility in Freeze-Concentrated Matrix

To better understand the relation between recrystallization rate and water mobility in freeze-concentrated matrix, isothermal ice recrystallization rates in several sugar aqueous solutions and self-diffusion coefficients of water component in corresponding freeze-concentrated matrix were measured. The sugars used were fructose, glucose, maltose, and sucrose. The sugar concentrations and temperature were varied so that ice contents for all samples were almost equal. Neither recrystallization rates nor diffusion coefficients depended uniformly on temperature. The recrystallization rates increased with increasing the diffusion coefficients, and a direct relationship was found between recrystallization rate and diffusion coefficient. This indicated that self-diffusion coefficient of water component in freeze-concentrated matrix is a useful parameter for predicting and controlling recrystallization rate in sugar solutions relevant to frozen desserts.     

The joint allele frequency spectrum of multiple populations: a coalescent theory approach

The allele frequency spectrum is a series of statistics that describe genetic polymorphism, and is commonly used for inferring population genetic parameters and detecting natural selection. Population genetic theory on the allele frequency spectrum for a single population has been well studied using both coalescent theory and diffusion equations. Recently, the theory was extended to the joint allele frequency spectrum (JAFS) for three populations using diffusion equations and was shown to be very useful in inferring human demographic history. In this paper, I show that the JAFS can be analytically derived with coalescent theory for a basic model of two isolated populations and then extended to multiple populations and various complex scenarios, such as those involving population growth and bottleneck, migration, and positive selection. Simulation study is used to demonstrate the accuracy and applicability of the theoretical model. The coalescent theory-based approach for the JAFS can characterize the demographic history with comprehensive statistical models as the diffusion approach does, and in addition gains several novel advantages: the computational complexity of calculating the JAFS with coalescent theory is reduced, and thus it is feasible to analytically obtain the JAFS for multiple populations; the hitchhiking effect can be efficiently modeled in coalescent theory, enabling the development of methodologies for detecting selection via multi-population polymorphism data. As an alternative to the diffusion approximation approach, the coalescent theory for the JAFS also provides a foundation for population genetic inference with the advent of large-scale genomic polymorphism data.     

Interpopulation variation in mating system and late-stage inbreeding depression in Magnolia stellata

Inbreeding has the potential to cause evolutionary changes in populations, although these changes are likely to drive populations to extinction through inbreeding depression and reductions in genetic diversity. We investigated the mating system and late-stage inbreeding depression (δ) in 10 populations of Magnolia stellata using nine microsatellite markers and evaluated the effects of population size and the degree of population isolation through inbreeding and inbreeding depression on the persistence of populations. The outcrossing rates were very similar (~0.7) among populations, but the correlations of paternity, fractions of biparental inbreeding and inbreeding coefficients at the seed stage ( F _S) varied among populations, suggesting that the level of outcrossing was similar among populations, while the quality of it was not. A significant negative correlation was detected between F _S and population size. The average value of δ was 0.709, and the values in six of the 10 populations were significant. The values of δ differed among populations, although clear relationships with population size and the degree of population isolation were not detected. However, in one population, which was very small and located in the edge of the species' range, we obtained a very low value of δ (–0.096), which may be indicative of purging or the fixation of deleterious alleles. Existing M. stellata populations that are small (and thus might be expected to have higher frequencies of inbreeding) and have large values of δ may be in danger of declining, even if the populations are located within the central region of the species' range.     

内蒙古典型草原作物系数的动态模拟与确定

作物系数是计算作物需水量必不可少的参数。利用2008年野外水分试验和4个气象站近26年的土壤水分和气象等常规观测资料, 以相关分析和回归分析等统计学方法为基础, 根据水量平衡原理计算了内蒙古典型草原区的作物系数, 分析了其在生长期和不同站点间的变化规律; 建立了典型草原标准作物系数与返青后年日数和大于0 ℃积温的模拟方程, 相关指数在0.94以上。在分析湿润指数、叶面积指数和盖度与作物系数关系的基础上, 提出标准作物系数的气候修正方法和胁迫条件下作物系数的修正方法。同时, 与修正后的联合国粮农组织(FAO)推荐值比较后得出, 生长季标准作物系数的平均值为0.60, 最大值为1.02; 不同生长阶段作物系数的典型值分别为: 初始生长期0.40, 生长中期0.93, 生长后期0.80, 相应的阈值范围为0.35-0.45、0.85-1.00和0.70-0.90。通过旬蒸散量的模拟计算值与蒸渗仪实测结果的比较, 平均相对误差在20%-24%之间, 生长旺盛期大多低于10%, 从而初步证明该文提出的方法在内蒙古典型草原区有较好的适用性。     

芯片数据标准化方法比较研究

在基因芯片实验中,基因表达水平之间的相关性在推断基因间相互关系时起到非常重要的作用.未经标准化处理的芯片数据基因之间往往都呈现出很强的相关性,这些高相关性一部分是由基因表达水平变化引起的,而另外一部分是由系统偏差引起的.对芯片数据进行标准化处理的目的之一是消除系统偏差引起的高相关性,同时保留由真正生物学原因引起的基因表达水平高相关性.虽然目前对标准化方法已经有了不少比较研究,但还较少有人研究标准化方法对基因之间相关系数的影响,以及哪种方法最有利于恢复基因之间的相关性结构.通过对基因表达水平数据的模拟,具体比较了几种常用标准化方法的效果,从而给出最有利于恢复基因之间相关性结构的那种标准化方法.     

A fast and reliable computational method for estimating population genetic parameters

The estimation of ancestral and current effective population sizes in expanding populations is a fundamental problem in population genetics. Recently it has become possible to scan entire genomes of several individuals within a population. These genomic data sets can be used to estimate basic population parameters such as the effective population size and population growth rate. Full-data-likelihood methods potentially offer a powerful statistical framework for inferring population genetic parameters. However, for large data sets, computationally intensive methods based upon full-likelihood estimates may encounter difficulties. First, the computational method may be prohibitively slow or difficult to implement for large data. Second, estimation bias may markedly affect the accuracy and reliability of parameter estimates, as suggested from past work on coalescent methods. To address these problems, a fast and computationally efficient least-squares method for estimating population parameters from genomic data is presented here. Instead of modeling genomic data using a full likelihood, this new approach uses an analogous function, in which the full data are replaced with a vector of summary statistics. Furthermore, these least-squares estimators may show significantly less estimation bias for growth rate and genetic diversity than a corresponding maximum-likelihood estimator for the same coalescent process. The least-squares statistics also scale up to genome-sized data sets with many nucleotides and loci. These results demonstrate that least-squares statistics will likely prove useful for nonlinear parameter estimation when the underlying population genomic processes have complex evolutionary dynamics involving interactions between mutation, selection, demography, and recombination.     

A note on simulating null distributions for G matrix comparisons

Genetic variances and covariances, summarized in G matrices, are key determinants of the course of adaptive evolution. Consequently, understanding how G matrices vary among populations is critical to answering a variety of questions in evolutionary biology. A method has recently been proposed for generating null distributions of statistics pertaining to differences in G matrices among populations. The general approach facilitated by this method is likely to prove to be very important in studies of the evolution of G . We have identified an issue in the method that will cause it to create null distributions of differences in G matrices that are likely to be far too narrow. The issue arises from the fact that the method as currently used generates null distributions of statistics pertaining to differences in G matrices across populations by simulating breeding value vectors based on G matrices estimated from data, randomizing these vectors across populations, and then calculating null values of statistics from G matrices that are calculated directly from the variances and covariances among randomized vectors. This calculation treats breeding values as quantities that are directly measurable, instead of predicted from G matrices that are themselves estimated from patterns of covariance among kin. The existing method thus neglects a major source of uncertainty in G matrices, which renders it anti‐conservative. We first suggest a correction to the method. We then apply the original and modified methods to a very simple instructive scenario. Finally, we demonstrate the use of both methods in the analysis of a real data set.     

Impact of biparental mating on correlation coefficients in bread wheat

Summary Phenotypic and genotypic correlation coefficients and path-coefficients were studied in the biparental (BIPs) and F₃ self progenies of the two wheat crosses. A comparison of correlation coefficients in the BIPs and the F₃'s revealed that as many as twelve new significant correlations were noticed in case of the BIPs in cross I although some of them occurred in the undesirable direction. On the other hand, only three new correlations were observed in the BIPs of cross II, although as many as fifteen correlations were not significant. Results suggested that intermating in the F₂ was effective in breaking the linkages. Path-coefficient analysis further revealed that the direct effect of tillers/ plant on grain yield was important and remained unchanged in both populations of cross I. In cross II, the direct effect of tillers/plants on grain yield was also high and it increased in the BIPs. Intermating seemed to have influenced considerably both the direct and indirect effects.     

Study of the variability and evolution of Orobanche cumana populations infesting sunflower in different European countries

 The parasitic plant Orobanche cumana Wallr. has become a limiting factor for sunflower crops in infested countries. Over the past few years the progression of this parasitic plant, its introduction into new countries, and the development of new and more virulent races have all been observed. Consequently, the survey and understanding of broomrape population evolution is now crucial for the establishment of efficient breeding programmes. With this in prospect, the genetic variability of O. cumana populations from infested European countries, Bulgaria, Romania, Turkey and Spain, was studied using RAPD markers. Eight populations with a total of 180 plants were analysed. Twenty three primers were used to obtain 133 reproducible bands which led to a binary matrix. This matrix was subjected to various complementary analyses including pairwise distances computed with the Nei and Li coefficient, AMOVA, Nei’s genetic diversity statistics, and an estimation of gene flow among populations with the infinite-island formula. The results gave consistent conclusions whatever the method used for data treatment. We show that this parasitic plant is probably self-pollinated, that there is little intra-population variability, and very little gene exchange appears to occur between different geographic regions. Populations were well structured and organized into two distinct groups (one group corresponding to the East European countries, Bulgaria, Romania and Turkey, and the other group corresponding to Spanish populations) and could have a monophyletic origin. These results are discussed in relation to the applied uses of RAPD markers in the determination of true O. cumana races instead of populations. Received: 20 December 1997 / Accepted: 4 February 1998     

Quantifying gene flow from spatial genetic structure data in a metapopulation of Chamaecrista fasciculata (Leguminosae)

Abstract An extensive allozyme survey was conducted within a natural "meta" population of the native North American annual legume, Chamaecrista fasciculata (Leguminosae) to quantify genetic structure at different spatial scales. Gene flow was then estimated by a recently developed indirect method based on a continuous population model, using pairwise kinship coefficients between individuals. The indirect estimates of gene flow, quantified in terms of neighborhood size, with an average value on the order of 150 individuals, were concordant among different spatial scales (subpopulation, population, metapopulation). This gene-flow value lies within the range of direct estimates previously documented from observations of pollen and seed dispersal for the same metapopulation. Monte Carlo simulations using the direct measures of gene flow as parameters further demonstrated that the observed spatial pattern of allozyme variation was congruent with a model of isolation by distance. Combining previously published estimates of pollen dispersal distances with kinship coefficients from this study, we quantified biparental inbreeding relative to either a single subpopulation or the whole metapopulation. At the level of a neighborhood, little biparental inbreeding was observed and most departure from Hardy-Weinberg genotypic proportions was explained by self-fertilization, whereas both selfing and biparental inbreeding contributed to nonrandom mating at the metapopulation level. Gene flow was also estimated from indirect methods based on a discontinuous population structure model. We discuss these results with respect to the effect of a patchy population structure on estimation of gene flow.