最大信息熵原理与群体遗传平衡

建立了用最大信息熵原理推导群体遗传平衡定律的统一数学模型,并给出了模型的统一解,此解正是Hardy-Weinberg定律所给出的平衡群体的基因型频率,说明当群体信息熵达到最大时,群体基因型频率不再变化,即达到“平衡”。这证明了最大熵分布就是Hardy-Weinberg平衡分布。Hardy-Weinberg平衡定律与最大信息熵原理的内在一致性说明,杂交和随机交配是一个不可逆过程,使群体基因型信息熵增大,无序性增,是选择和近亲交配使群体的信息熵降低,有序性增加,育种过程实际就是调节群体信息熵的过程。过程信息熵的含义是表示一个概率分布的不确定性,最大熵原理意味着在一定的约束条件,选择具有最大不确定性的分布,从而其分布是最为随机的。最大熵原理在信息,工程,天文,地理,图像处理,模式识别等自然科学和社会科学领域都有广泛的成功应用,本文从群体遗传学角度证明了这一原理具有普遍适用性。熵是描述系统状态的函数,而最大熵原理则表明了系统发展变化的趋势,系统的最终状态必然是熵增加至最大值的状态,对于任何系统都是如此。因此,群体遗传系统的平衡定律可以统一用最大熵原理进行判定和描述;任意群体的基因型信息熵在随机交配世代传递时有不断增加的趋势;在一定约束条件下基因型信息熵达到最大值时,就称之为达到遗传平衡。本文将信息论原理应用于群体遗传学研究,揭示了基因信息熵的生物学意义,并表明可以用信息学和控制论的原理和方法来研究群体遗传学问题。     

两个基因座位的遗传平衡原理

由于许多教科书中关于连锁平衡的介绍,多是引用结论或是推导不太严谨,使学生在学习群体遗传学时对理解连锁平衡的原理感到困难。本文从遗传平衡的基本条件出发,通过较严谨的数学推导,介绍了两个基因座的连锁平衡条件、平衡过程等原理,供教师和学生在群体遗传学教学中参考。Abstract: Because linkage equilibrium is introduced by directly quoting the conclusions or imprecise mathematical reasoning in most of textbooks, many students are puzzled with the problem of linkage equilibrium when they learn population genetics. Based on the radical conditions of genetic equilibrium, the principle of linkage equilibrium condition and process, for two gene loci is introduced by precise mathematical reasoning. The article may provide reference to teachers and students in the teaching and learning of population genetics.     

关于最大信息熵原理与群体遗传平衡一致性的探讨

汪小龙等建立了用最大信息熵原理推导一个基因座上群体遗传平衡的统一数学模型,并给出了模型的最大值解,此解正是Hardy-Weinberg平衡定律所给出的基因型频率。这说明当群体基因型信息熵最大时,群体基因型频率不再变化,达到平衡状态,从而证明了最大信息熵原理与Hardy-Weinberg平衡定律具有一致性,同时指出这一结论可以推广至有迁移、突变、选择、遗传漂变、近亲交配的群体以及多个基因座情形。概括地说就是：最大信息熵原理与群体遗传平衡具有一致性。但是,他们仅仅证明了最大信息熵原理与一个基因座上Hardy-Weinberg平衡定律具有一致性,本文在这个范围内将其推广至多个基因座,且每一个基因座均为复等位基因情形。至于最大信息熵原理是否与其它的群体遗传平衡具有一致性,他们的结论仅仅是猜想,并未严格推导。事实上,要想将这种一致性推广到迁移、突变、随机漂变和近亲交配等群体,则不见得正确。      

Selection on Optimal Haploid Value Increases Genetic Gain and Preserves More Genetic Diversity Relative to Genomic Selection

Doubled haploids are routinely created and phenotypically selected in plant breeding programs to accelerate the breeding cycle. Genomic selection, which makes use of both phenotypes and genotypes, has been shown to further improve genetic gain through prediction of performance before or without phenotypic characterization of novel germplasm. Additional opportunities exist to combine genomic prediction methods with the creation of doubled haploids. Here we propose an extension to genomic selection, optimal haploid value (OHV) selection, which predicts the best doubled haploid that can be produced from a segregating plant. This method focuses selection on the haplotype and optimizes the breeding program toward its end goal of generating an elite fixed line. We rigorously tested OHV selection breeding programs, using computer simulation, and show that it results in up to 0.6 standard deviations more genetic gain than genomic selection. At the same time, OHV selection preserved a substantially greater amount of genetic diversity in the population than genomic selection, which is important to achieve long-term genetic gain in breeding populations.     

Access Point Selection Game with Mobile Users Using Correlated Equilibrium

One of the most important issues in wireless local area network (WLAN) systems with multiple access points (APs) is the AP selection problem. Game theory is a mathematical tool used to analyze the interactions in multiplayer systems and has been applied to various problems in wireless networks. Correlated equilibrium (CE) is one of the powerful game theory solution concepts, which is more general than the Nash equilibrium for analyzing the interactions in multiplayer mixed strategy games. A game-theoretic formulation of the AP selection problem with mobile users is presented using a novel scheme based on a regret-based learning procedure. Through convergence analysis, we show that the joint actions based on the proposed algorithm achieve CE. Simulation results illustrate that the proposed algorithm is effective in a realistic WLAN environment with user mobility and achieves maximum system throughput based on the game-theoretic formulation.     

Conformational Selection and Equilibrium Governs the Ability of Retinals to Bind Opsin

Despite extensive study, how retinal enters and exits the visual G protein-coupled receptor rhodopsin remains unclear. One clue may lie in two openings between transmembrane helix 1 (TM1) and TM7 and between TM5 and TM6 in the active receptor structure. Recently, retinal has been proposed to enter the inactive apoprotein opsin (ops) through these holes when the receptor transiently adopts the active opsin conformation (ops*). Here, we directly test this “transient activation” hypothesis using a fluorescence-based approach to measure rates of retinal binding to samples containing differing relative fractions of ops and ops*. In contrast to what the transient activation hypothesis model would predict, we found that binding for the inverse agonist, 11-cis-retinal (11CR), slowed when the sample contained more ops* (produced using M257Y, a constitutively activating mutation). Interestingly, the increased presence of ops* allowed for binding of the agonist, all-trans-retinal (ATR), whereas WT opsin showed no binding. Shifting the conformational equilibrium toward even more ops* using a G protein peptide mimic (either free in solution or fused to the receptor) accelerated the rate of ATR binding and slowed 11CR binding. An arrestin peptide mimic showed little effect on 11CR binding; however, it stabilized opsin·ATR complexes. The TM5/TM6 hole is apparently not involved in this conformational selection. Increasing its size by mutagenesis did not enable ATR binding but instead slowed 11CR binding, suggesting that it may play a role in trapping 11CR. In summary, our results indicate that conformational selection dictates stable retinal binding, which we propose involves ATR and 11CR binding to different states, the latter a previously unidentified, open-but-inactive conformation.     

Genetic Recombination and Clonal Selection in DROSOPHILA MERCATORUM

Discrete and continuous generation unisexual populations were established from parthenogenetic D. mercatorum females heterozygous for five visible loci and one electrophoretic locus, which marked all five major chromosome arms. In the first impaternate generation of the discrete generation population, all thirty-two possible recombinant genotypes for the five visible markers were displayed. However, 99% of these individuals were homozygous for all gene markers due to the predominant mode of parthenogenesis called nuclear duplication. Many of these homozygous individuals gave rise to isogenic clones that were compelled to compete with each other in subsequent generations. A detailed analysis of the genetic response of this clonal population showed strong evidence for selection involving epistatic interactions between linked and unlinked loci throughout the genome. The unit of selection is described as being determined as early as the zygotic stage of development.     

Selection and the Evolution of Genetic Life Cycles

The evolution of haploid and diploid phases of the life cycle is investigated theoretically, using a model where the relative length of haploid and diploid phases is under genetic control. The model assumes that selection occurs in both phases and that fitness in each phase is a function of the time spent in that phase. The equilibrium and stability conditions that allow for all-haploid, all-diploid, or polyphasic life cycles are considered for general survivorship functions. Types of stable life cycles possible depend on the form of the viability selection. If mortality rates are constant, either haploidy or diploidy is the only stable life cycle possible. Departures from constant mortality can give qualitatively different results. For example, when survivorship in each phase is a linear, decreasing function of the time spent in the phase, stable haploid, diploid or polyphasic life cycles are possible. The addition of genetic variation at a coevolving viability locus does not qualitatively affect the outcome with respect to the maintenance of polyphasic cycles but can lead to situations where more than one life cycle is concurrently stable. These results show that trade-offs between the advantages of being diploid and of being haploid may help explain the patterns of life cycles found in nature and that the type of selection may be critical to determining the results.     

动物遗传标记辅助选择研究及其应用

随着分子数量遗传学及其相关学科的发展,有关动物遗传标记辅助选择方面的研究也在不断深入,且已经在动物遗传改良中有了一些成功应用的示例。就如何综合利用表型、系谱和遗传标记信息进行育种值估计的统计学方法研究方面,目前已基本形成了较为完善的统计学方法。同时,在标记辅助选择相对效率及其影响因素,以及标记辅助选择实施方案的研究上也取得了不少喜人的成果。本文综述了动物遗传标记辅助选择研究的一些进展,并对标记辅助选择在动物遗传改良中应用的有关问题进行了讨论。 Abstract:With the development of molecular and quantitative genetics and its related subjects,it made a great progress on the research about animal genetic marker-assisted selection (MAS).There were also some successful examples on the application of MAS to animal genetic improvement.The statistical method which using phenotypic,pedigree and genetic marker information to predict individual breeding values has already been developed.Many achievements were obtained from the researches,which carried on MAS relative efficiency and its affecting factors and selection schemes.The present paper reviewed some progresses of MAS research and discussed some problems about MAS application to animal breeding.     

雄配子体选择的遗传分化效应及其在植物改良中的应用

在植物世代交替的生活史中,配子体是产生配子和具有单倍数染色体的植物体,并且有自己的遗传表达信息.在配子产生的过程中以及配子结合之前,适者生存的法则对配子发挥着选择作用,只有最适应外界环境条件的配子才能通过竞争性受精并产生合子.雄配子体选择是影响植物遗传分化、演变和遗传多样性的重要因素,被认为是生物进化的有力动力.此外,由于植物基因组中约有2/3的基因表达交错发生在配子体阶段和孢子体阶段,因此雄配子体选择的结果会影响到下一代孢子体的表现型.在育种实践中,利用雄配子体选择对植物进行遗传改良,具有提高选择机率和缩短育种年限等优点.本文主要概述雄配子体选择与孢子体表型的关刎系、遗传分化效应及其在植物遗传改良中的应用,以期为雄配子选择相关研究提供参考     

Social Selection and Indirect Genetic Effects in Structured populations

Social selection and indirect genetic effects (IGEs) are established concepts in both behavioural ecology and evolutionary genetics. While IGEs describe effects of an individual’s genotype on phenotypes of social partners (and may thus affect their fitness indirectly), the concept of social selection assumes that a given phenotype in one individual affects the fitness of other individuals directly. Although different frameworks, both have been used to investigate the evolution of social traits, such as cooperative behaviour. Despite their similarities (both concepts consider interactions among individuals), they differ in the type of interaction. It remains unclear whether the two concepts make the same predictions about evolutionary trajectories or not. To address this question, we investigate four possible scenarios of social interactions and compare the effects of IGEs and social selection for trait evolution in a multi-trait multi-member model. We show that the two mechanisms can yield similar evolutionary outcomes and that both can create selection pressure at the group level. However, the effect of IGEs can be stronger due to the possibility of feedback loops. Finally, we demonstrate that IGEs, but not social selection gradients, may lead to differences in the direction of evolutionary response between genotypes and phenotypes.     

黑河38号大豆品种的选育和遗传组成

利用遗传基础丰富的优良中间材料为亲本,配制杂交组合,选育出早熟、高产、适应性广的大豆新品种黑河38号,审定2年种植面积即达20万hm2。分析了黑河38号的遗传组成,核基因来源于十胜长叶、阿姆索等4份国外品种,盖家屯四粒荚、金元等5份农家品种以及1份育成品种和1份当地野生大豆,细胞质来源于克山白眉。     

Genetic Mapping and Genomic Selection Using Recombination Breakpoint Data

The correct models for quantitative trait locus mapping are the ones that simultaneously include all significant genetic effects. Such models are difficult to handle for high marker density. Improving statistical methods for high-dimensional data appears to have reached a plateau. Alternative approaches must be explored to break the bottleneck of genomic data analysis. The fact that all markers are located in a few chromosomes of the genome leads to linkage disequilibrium among markers. This suggests that dimension reduction can also be achieved through data manipulation. High-density markers are used to infer recombination breakpoints, which then facilitate construction of bins. The bins are treated as new synthetic markers. The number of bins is always a manageable number, on the order of a few thousand. Using the bin data of a recombinant inbred line population of rice, we demonstrated genetic mapping, using all bins in a simultaneous manner. To facilitate genomic selection, we developed a method to create user-defined (artificial) bins, in which breakpoints are allowed within bins. Using eight traits of rice, we showed that artificial bin data analysis often improves the predictability compared with natural bin data analysis. Of the eight traits, three showed high predictability, two had intermediate predictability, and two had low predictability. A binary trait with a known gene had predictability near perfect. Genetic mapping using bin data points to a new direction of genomic data analysis.     

Genetic Selection of Poliovirus 2Apro-Binding Peptides

The yeast two-hybrid system has been used to identify mammalian clones that interact with poliovirus 2A proteinase (2A^pro). Eight clones which encode previously unidentified human proteins were selected from a HeLa cell cDNA expression library. In addition, five clones encoding short peptides that interact with poliovirus 2A^pro were also identified. The lengths of these peptides range from 6 to 30 amino acids, but all of them contain the Leu-X-Thr-Z motif (X represents any amino acid; Z represents a hydrophobic residue). This sequence is invariably located just at the carboxy terminus of each peptide. This approach raises the possibility of designing substrate analogue inhibitors of 2A^pro. Thus, two nonhydrolyzable peptides containing the Leu-X-Thr-Z motif prevented cleavage of eukaryotic initiation factor 4G by poliovirus 2A^pro in vitro. A more general method for identifying peptides with antiproteinase activity is discussed.     

Genetic Diversity in the Interference Selection Limit

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, similar to models of quantitative genetics, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a “linkage block”). We exploit this insensitivity in a new “coarse-grained” coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations that create the same variance in fitness. This approximation generates accurate and efficient predictions for silent site variability when interference is common. However, these results suggest that there is reduced power to resolve individual selection pressures when interference is sufficiently widespread, since a broad range of parameters possess nearly identical patterns of silent site variability.     

Genetic Hitchhiking under Heterogeneous Spatial Selection Pressures

During adaptive evolutionary processes substantial heterogeneity in selective pressure might act across local habitats in sympatry. Examples are selection for drug resistance in malaria or herbicide resistance in weeds. In such setups standard population-genetic assumptions (homogeneous constant selection pressures, random mating etc.) are likely to be violated. To avoid misinferences on the strength and pattern of natural selection it is therefore necessary to adjust population-genetic theory to meet the specifics driving adaptive processes in particular organisms. We introduce a deterministic model in which selection acts heterogeneously on a population of haploid individuals across different patches over which the population randomly disperses every generation. A fixed proportion of individuals mates exclusively within patches, whereas the rest mates randomly across all patches. We study how the allele frequencies at neutral markers are affected by the spread of a beneficial mutation at a closely linked locus (genetic hitchhiking). We provide an analytical solution for the frequency change and the expected heterozygosity at the neutral locus after a single copy of a beneficial mutation became fixed. We furthermore provide approximations of these solutions which allow for more obvious interpretations. In addition, we validate the results by stochastic simulations. Our results show that the application of standard population-genetic theory is accurate as long as differences across selective environments are moderate. However, if selective differences are substantial, as for drug resistance in malaria, herbicide resistance in weeds, or insecticide resistance in agriculture, it is necessary to adapt available theory to the specifics of particular organisms.     

Equilibrium between Genetic Drift and Migration at Various Mutation Rates: Simulation Analysis

Rates of approach to equilibrium values of F _ST /R _ST at various mutation rates and using different mutation models (K-allele model KAM and stepwise model SMM) were analyzed numerically for the finite island model and the one-dimensional stepping stone models of migration, using simulation. In the island model of migration and the KAM mutation model, the rate of approach to the equilibrium F _ST value was appreciably higher and the equilibrium value was almost twofold lower at μ (mutation rate) = m (migration rate) than at μ ≪ m. In the one-dimensional stepping stone model of migration and the KAM model of mutation, the mutation rate significantly affected both the rate of approaching F _ST equilibrium and the equilibrium value. In both island and one-dimensional stepping stone models and SMM, R _ST was not influenced by various mutation rates. The rate of approach to the equilibrium values of both F _ST and R _ST was lower for the stepping stone model than to the island model. R _ST was rather resistant to deviations from the SMM mutation model. __________ Translated from Genetika, Vol. 41, No. 9, 2005, pp. 1283–1288. Original Russian Text Copyright ? 2005 by Efremov.