The distribution of fitness effects among beneficial mutations in Fisher's geometric model of adaptation

Recent models of adaptation at the DNA sequence level assume that the fitness effects of new mutations show certain statistical properties. In particular, these models assume that the distribution of fitness effects among new mutations is in the domain of attraction of the so-called Gumbel-type extreme value distribution. This assumption has not, however, been justified on any biological or theoretical grounds. In this note, I study random mutation in one of the simplest models of mutation and adaptation-Fisher's geometric model. I show that random mutation in this model yields a distribution of mutational effects that belongs to the Gumbel type. I also show that the distribution of fitness effects among rare beneficial mutations in Fisher's model is asymptotically exponential. I confirm these analytic findings with exact computer simulations. These results provide some support for the use of Gumbel-type extreme value theory in studies of adaptation and point to a surprising connection between recent phenotypic- and sequence-based models of adaptation: in both, the distribution of fitness effects among rare beneficial mutations is approximately exponential.     

A semiparametric estimation procedure of dependence parameters in multivariate families of distributions

This paper investigates the properties of a semiparametric methodfor estimating the dependence parameters in a family of multivariatedistributions. The proposed estimator, obtained as a solutionof a pseudo-likelihood equation, is shown to be consistent,asymptotically normal and fully efficient at independence. Anatural estimator of its asymptotic variance is proved to beconsistent. Comparisons are made with alternative semiparametricestimators in the special case of Clayton's model for associationin bivariate data.     

枣园中枣瘿蚊和草间小黑蛛的空间分布格局及空间依赖性

利用地统计学原理和方法,对枣园中枣瘿蚊及其天敌草间小黑蛛种群的空间结构和空间相关性进行了研究.结果表明,6月8日、8月27日、10月19日枣树主要生育期阶段,枣瘿蚊种群的半变异函数模型为球形.在林间基本上呈聚集分布,其样点空间依赖性距离分别为26.3、7.8和22.0 m,其空间依赖性程度分别为88.05%、85.77%和87.58%.草间小黑蛛种群的半变异函数也为球形,呈聚集分布,空间依赖距离分别为28.3、22.5和22.2 m,且在该取样尺度下,总变异中分别有90.09%、87.96%和85.72%是由空间依赖性产生的.两者空间依赖关系说明草间小黑蛛对枣瘿蚊有较强的追随作用.     

Properties of adaptive walks on uncorrelated landscapes under strong selection and weak mutation

We examine properties of adaptive walks on uncorrelated (i.e. random) fitness landscapes starting from moderately fit genotypes under strong selection weak mutation. As an extension of Orr's model for a single step in an adaptive walk under these conditions, we show that the fitness rank of the dominant genotype in a population after the fixation of a beneficial mutation is, on average, (i+6)/4, where i is the fitness rank of the starting genotype. This accounts for the change in rank due to acquiring a new set of single-mutation neighbors after fixing a new allele through natural selection. Under this scenario, adaptive walks can be modeled as a simple Markov chain on the space of possible fitness ranks with an absorbing state at i = 1, from which no beneficial mutations are accessible. We find that these walks are typically short and are often completed in a single step when starting from a moderately fit genotype. As in Orr's original model, these results are insensitive to both the distribution of fitness effects and most biological details of the system under consideration.     

Beneficial fitness effects are not exponential for two viruses

The distribution of fitness effects for beneficial mutations is of paramount importance in determining the outcome of adaptation. It is generally assumed that fitness effects of beneficial mutations follow an exponential distribution, for example, in theoretical treatments of quantitative genetics, clonal interference, experimental evolution, and the adaptation of DNA sequences. This assumption has been justified by the statistical theory of extreme values, because the fitnesses conferred by beneficial mutations should represent samples from the extreme right tail of the fitness distribution. Yet in extreme value theory, there are three different limiting forms for right tails of distributions, and the exponential describes only those of distributions in the Gumbel domain of attraction. Using beneficial mutations from two viruses, we show for the first time that the Gumbel domain can be rejected in favor of a distribution with a right-truncated tail, thus providing evidence for an upper bound on fitness effects. Our data also violate the common assumption that small-effect beneficial mutations greatly outnumber those of large effect, as they are consistent with a uniform distribution of beneficial effects.     

Distance dependence and salt sensitivity of pairwise, coulombic interactions in a protein

Histidine pK(a) values were measured in charge-reversal (K78E, K97E, K127E, and K97E/K127E) and charge-neutralization (E10A, E101A, and R35A) mutants of staphylococcal nuclease (SNase) by (1)H-NMR spectroscopy. Energies of interaction between pairs of charges (DeltaG(ij)) were obtained from the shifts in pK(a) values relative to wild-type values. The data describe the distance dependence and salt sensitivity of pairwise coulombic interactions. Calculations with a continuum electrostatics method captured the experimental DeltaG(ij) when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The DeltaG(ij) when r(ij) < or = 10 A were exaggerated slightly in the calculations. Coulomb's law with a dielectric constant near 80 and a Debye-Hückel term to account for screening by the ionic strength reproduced the salt sensitivity and distance dependence of DeltaG(ij) as well as the structure-based method. In their interactions with each other, surface charges behave as if immersed in water; the Debye length describes realistically the distance where interactions become negligible at a given ionic strength. On average, charges separated by distances (r(ij)) approximately 5 A interacted with DeltaG(ij) approximately 0.6 kcal/mole in 0.01 M KCl, but DeltaG(ij) decayed to < or =0.10 kcal/mole when r(ij) = 20 A. In 0.10 M KCl, DeltaG(ij) approximately 0.10 kcal/mole when r(ij) = 10 A. In 1.5 M KCl, only short-range interactions with r(ij) < or = 5 A persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 A are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects.     

Spatial analysis of structural and tree‐ring related parameters in a timberline forest in the Italian Alps

Abstract. We investigated the variability in spatial pattern of some structural, dendrochronological and dendroclimatological features of a mixed Larix decidua‐Pinus cembra forest at the timberline in the eastern Italian Alps at fine geographical and temporal scales. Forest structure variables such as stem diameter, tree height, age and tree‐ring related parameters (yearly growth index, mean sensitivity, first order autocorrelation and some dendroclimatic variables) have been compared at various scale levels. We observed that most of the variables show positive autocorrelated structures due to both forest dynamics and fine‐scale driving forces, probably related to microrelief. Spatial structure of yearly indexed radial growth appears sensitive to extreme climatic events. Secondary succession after past disturbances drives the forest towards a structure governed by a gap regeneration dynamics that seems to ensure the different requirements of the two main tree species present. Small spatial scale studies of forest structures, especially if integrated to dendro‐ecological data, seem an efficient tool to assess the disturbance regime and species sensitivity to environmental change.     

High affinity extremes in combinatorial libraries and repertoires

By generating a large diversity of molecules, the immune system selects antibodies that bind antigens. Sharing the same approach, combinatorial biotechnologies use a large library of compounds to screen for molecules of high affinity to a given target. Understanding the properties of the best binders in the pool aids the design of the library. In particular, how does the maximum affinity increase with the size of the library or repertoire? We consider two alternative models to examine the properties of extreme affinities. In the first model, affinities are distributed lognormally, while in the second, affinities are determined by the number of matches to a target sequence. The second model more explicitly models nucleic acids (DNA or RNA) and proteins such as antibodies. Using extreme value theory we show that the logarithm of the mean of the highest affinity in a combinatorial library grows linearly with the square root of the log of the library size. When there is an upper bound to affinity, this “absolute maximum” is also approached approximately linearly with root log library size, reaching the upper limit abruptly. The design of libraries may benefit from considering how this plateau is reached as the library size is increased.     

Brownian models and coalescent structures

Brownian motions on coalescent structures have a biological relevance, either as an approximation of the stepwise mutation model for microsatellites, or as a model of spatial evolution considering the locations of individuals at successive generations. We discuss estimation procedures for the dispersal parameter of a Brownian motion defined on coalescent trees. First, we consider the mean square distance unbiased estimator and compute its variance. In a second approach, we introduce a phylogenetic estimator. Given the UPGMA topology, the likelihood of the parameter is computed thanks to a new dynamical programming method. By a proper correction, an unbiased estimator is derived from the pseudomaximum of the likelihood. The last approach consists of computing the likelihood by a Markov chain Monte Carlo sampling method. In the one-dimensional Brownian motion, this method seems less reliable than pseudomaximum-likelihood.     

Information and discrimination in pairwise contact potentials

We examine the information-theoretic characteristics of statistical potentials that describe pairwise long-range contacts between amino acid residues in proteins. In our work, we seek to map out an efficient information-based strategy to detect and optimally utilize the structural information latent in empirical data, to make contact potentials, and other statistically derived folding potentials, more effective tools in protein structure prediction. Foremost, we establish fundamental connections between basic information-theoretic quantities (including the ubiquitous Z-score) and contact "energies" or scores used routinely in protein structure prediction, and demonstrate that the informatic quantity that mediates fold discrimination is the total divergence. We find that pairwise contacts between residues bear a moderate amount of fold information, and if optimized, can assist in the discrimination of native conformations from large ensembles of native-like decoys. Using an extensive battery of threading tests, we demonstrate that parameters that affect the information content of contact potentials (e.g., choice of atoms to define residue location and the cut-off distance between pairs) have a significant influence in their performance in fold recognition. We conclude that potentials that have been optimized for mutual information and that have high number of score events per sequence-structure alignment are superior in identifying the correct fold. We derive the quantity "information product" that embodies these two critical factors. We demonstrate that the information product, which does not require explicit threading to compute, is as effective as the Z-score, which requires expensive decoy threading to evaluate. This new objective function may be able to speed up the multidimensional parameter search for better statistical potentials. Lastly, by demonstrating the functional equivalence of quasi-chemically approximated "energies" to fundamental informatic quantities, we make statistical potentials less dependent on theoretically tenuous biophysical formalisms and more amenable to direct bioinformatic optimization.     

白马鸡繁殖早期栖息地选择和空间分布

2003年1-6月和2004年4-6月考察了分布于四川省稻城县著杰寺周围的白马鸡(Crossoptiloncrossop-tilon)种群,分析繁殖早期白马鸡繁殖对的栖息地选择和空间分布特征。雌雄个体配对前,对整个研究区域进行系统取样并测量若干环境变量的参数。配对后,利用随机样线调查繁殖对出现的位置和数量。有繁殖对出现的栅格定义为探测栅格,反之为非探测栅格。水源距离、灌木盖度、灌木高度和草本高度等变量在探测和非探测栅格间差异显著。将显著差异变量及这些变量间的一级互作经单变量逻辑斯蒂回归进行筛选,以保留变量为自变量进行向前筛选的逐步逻辑斯蒂回归,最后选择具有最小AICC值的回归等式为最佳的回归模型。模型表明繁殖对的栖息地选择与水源距离负相关,与灌木盖度正相关。2004年进行了重复调查,获得实际的探测和非探测栅格与模型预测值之间无显著差异。计算繁殖对在0°(东-西),45°(东北-西南),90°(南-北)和135°(西北-东南)4个方向上的变异函数。结果表明:繁殖对的方向性变异函数可用球状模型来拟合,拟合曲线和实验曲线间的拟合程度达到显著水平,繁殖对呈明显的各向异性聚集分布[动物学报51(3):383-392,2005]。