A Comparative Statistical Analysis of Genetic Distances. I - Estimation of Distances and of their Variances: Distribution of the Estimators

We present a Monte-Carlo simulation analysis of the statistical properties of absolute genetic distance and of Nei's minimum and standard genetic distances. The estimation of distances (bias) and of their variances is analysed as well as the distributions of distance and variance estimators, taking into account both gamete and locus samplings. Both of Nei's statistics are non-linear when distances are small and consequently the distributions of their estimators are extremely asymmetrical. It is difficult to find theoretical laws that fit such asymmetrical distributions. Absolute genetic distance is linear and its distributions are better fit by a normal distribution. When distances are medium or large, minimum distance and absolute distance distributions are close to a normal distribution, but those of the standard distance can never be considered as normal. For large distances the jack-knife estimator of the standard distance variance is bad; another standard distance estimator is suggested. Absolute distance, which has the best mathematical properties, is particularly interesting for small distances if the gamete sample size is large, even when the number of loci is small. When both distance and gamete sample size are small, this statistic is biased.     

Orientation factor in steady-state and time-resolved resonance energy transfer measurements.

Resonance energy transfer measurements provide a way to estimate distances between chromophores attached to different sites of macromolecules. There are two unknowns involved in resonance energy transfer measurements, the distance between two chromophores and their relative orientation. When static orientational disorder exists, the orientation factor, kappa 2, can vary from 0 to 4, leading to considerable uncertainty in estimation of distances. Fluorescence polarization anisotropy measurements can reduce the degree of uncertainty [Dale & Eisinger (1974) Biopolymers 13, 1573]. There may still be substantial error bounds for the average distance measurements. Time-resolved fluorescence measurements provide an "apparent" average distance and distance distribution containing contributions by both distance and orientation. The contribution of orientation to observed "apparent" average distance and distance distribution widths has been estimated for both simulated and real data. With a single unique distance as input in the simulation and with random but static orientation of donor and acceptor, the recovered average distance is very close to that of the input when the input distance is close to or larger than the F?rster distance. The recovered width of apparent distance distribution can be substantial and it changes as a function of F?rster distance to average distance ratio and as a function of F?rster distance. Similar conclusions apply to the case where there is a real distance distribution. Motional averaging of the orientation was simulated by the Monte Carlo method to estimate the contribution of orientation when chromophores have certain degrees of mobility.(ABSTRACT TRUNCATED AT 250 WORDS)     

Genome analysis with distance to the nearest dissimilar nucleotide

DNA may be represented by sequences of four symbols, but it is often useful to convert those symbols into real or complex numbers for further analysis. Several mapping schemes have been used in the past, but most of them seem to be unrelated to any intrinsic characteristic of DNA. The objective of this work was to study a mapping scheme that is directly related to DNA characteristics, and that could be useful in discriminating between different species.Recently, we have proposed a methodology based on the inter-nucleotide distance, which proved to contribute to the discrimination among species. In this paper, we introduce a new distance, the distance to the nearest dissimilar nucleotide, which is the distance of a nucleotide to first occurrence of a different nucleotide. This distance is related to the repetition structure of single nucleotides. Using the information resulting from the concatenation of the distance to the nearest dissimilar and the inter-nucleotide distance, we found that this new distance brings additional discriminative capabilities. This suggests that the distance to the nearest dissimilar nucleotide might contribute with useful information about the evolution of the species.     

The decay of parasite community similarity in ring‐billed gulls Larus delawarensis and other hosts

The similarity of parasite communities often decays with increasing geographic distance. Here, geographic distance decay is evaluated in parasite communities of 145 ring‐billed gulls from six localities in Quebec, Canada, among both individual gulls and gull populations. Spatial decay in similarity is compared to temporal decay, using host age differences as a distance measure. The similarity of parasite communities of individual gulls from localities spanning 300 km within Quebec is more strongly associated with host age differences than with geographic distance. Among gull populations in Quebec, only geographic distance is significantly related to parasite community similarity. The explanatory power of geographic distance is higher still when data from Quebec are combined with those from a study conducted 3000 km away, indicating an effect of spatial scale on geographic distance decay. The rate at which parasite community similarity decays with distance in gulls is compared with that of 17 other host species using data from published studies. Spatial scale explains two thirds of the variance in distance decay rates, and some of the remaining variance is explained by latitude. The rate of decay in parasite community similarity with distance is greater in larger scale studies and further away from the equator. Traits of host species traits such as vagility, body weight and trophic level have little or no effect on distance decay rates.     

Perceptual distance and the constancy of size and stereoscopic depth

The relationship between distance and size perception is unclear because of conflicting results of tests investigating the size-distance invariance hypothesis (SDIH), according to which perceived size is proportional to perceived distance. We propose that response bias with regard to measures of perceived distance is at the root of the conflict. Rather than employ the usual method of magnitude estimation, the bias-free two-alternative forced choice (2AFC) method was used to determine the precision (1/sigma) of discriminating depth at different distances. The results led us to define perceptual distance as a bias free power function of physical distance, with an exponent of approximately 0.5. Similar measures involving size differences among stimuli of equal angular size yield the same power function of distance. In addition, size discrimination is noisier than depth discrimination, suggesting that distance information is processed prior to angular size. Size constancy implies that the perceived size is proportional to perceptual distance. Moreover, given a constant relative disparity, depth constancy implies that perceived depth is proportional to the square of perceptual distance. However, the function relating the uncertainties of depth and of size discrimination to distance is the same. Hence, depth and size constancy may be accounted for by the same underlying law.     

Distance decay in an old‐growth neotropical forest

Abstract. Questions: Does distance decay exist in an old‐growth neotropical forest? Is this distance decay stronger than expected due to environmental heterogeneity alone? At what spatial scales are distance decay manifested? Location: La Selva Biological Station, Costa Rica, Central America. Methods: An index of distance decay is applied appropriate for small quadrats (the probability of encountering a conspecific tree) to a grid of 1170 0.01‐ha plots. A null model is provided that accounts for environmental heterogeneity. Results: Significant, but weak, distance decay is found. After correcting for known patterns of environmental heterogeneity, the distance decay almost disappears, except for fine spatial scales. Conclusions: These results are inconsistent with models that predict distance decay at all spatial scales. However, biological processes leading to distance decay may be more relevant and detectable at scales broader than this study. Research utilizing objectively‐located samples over much broader scales is necessary to evaluate the generality and magnitude of distance decay.     

Protein structure-structure alignment with discrete Fréchet distance

Matching two geometric objects in two-dimensional (2D) and three-dimensional (3D) spaces is a central problem in computer vision, pattern recognition, and protein structure prediction. In particular, the problem of aligning two polygonal chains under translation and rotation to minimize their distance has been studied using various distance measures. It is well known that the Hausdorff distance is useful for matching two point sets, and that the Fréchet distance is a superior measure for matching two polygonal chains. The discrete Fréchet distance closely approximates the (continuous) Fréchet distance, and is a natural measure for the geometric similarity of the folded 3D structures of biomolecules such as proteins. In this paper, we present new algorithms for matching two polygonal chains in two dimensions to minimize their discrete Fréchet distance under translation and rotation, and an effective heuristic for matching two polygonal chains in three dimensions. We also describe our empirical results on the application of the discrete Fréchet distance to protein structure-structure alignment.     

Statistical Measures of DNA Sequence Dissimilarity under Markov Chain Models of Base Composition

In molecular biology, the issue of quantifying the similarity between two biological sequences is very important. Past research has shown that word-based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like FASTA. Recently, under the independent model of base composition, Wu, Burke, and Davison (1997, Biometrics 53, 1431 1439) characterized a family of word-based dissimilarity measures that defined distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters (i.e., n-words) in the two sequences. Specifically, they introduced the use of Mahalanobis distance and standardized Euclidean distance into the study of DNA sequence dissimilarity. They showed that both distances had better sensitivity and selectivity than the commonly used Euclidean distance. The purpose of this article is to extend Mahalanobis and standardized Euclidean distances to Markov chain models of base composition. In addition, a new dissimilarity measure based on Kullback-Leibler discrepancy between frequencies of all n-words in the two sequences is introduced. Applications to real data demonstrate that Kullback-Leibler discrepancy gives a better performance than Euclidean distance. Moreover, under a Markov chain model of order kQ for base composition, where kQ is the estimated order based on the query sequence, standardized Euclidean distance performs very well. Under such a model, it performs as well as Mahalanobis distance and better than Kullback-Leibler discrepancy and Euclidean distance. Since standardized Euclidean distance is drastically faster to compute than Mahalanobis distance, in a usual workstation/PC computing environment, the use of standardized Euclidean distance under the Markov chain model of order kQ of base composition is generally recommended. However, if the user is very concerned with computational efficiency, then the use of Kullback-Leibler discrepancy, which can be computed as fast as Euclidean distance, is recommended. This can significantly enhance the current technology in comparing large datasets of DNA sequences.     

Molecular dynamics simulation using weak-coupling NOE distance restraining

Summary Application of the weak-coupling scheme to restrain the configurations of a molecular system to a set of NOE distance restraints is investigated using two test systems: (i) a 15-atom chain molecule with one distance restraint; and (ii) a protein molecule with hundreds of NOE distance restraints. Atom-atom distance restraining by the weak-coupling technique is possible, but this method does not produce as good results as the penalty function method normally used to maintain NOE distance restraints.Abbreviations NOE nuclear Overhauser effect - MD molecular dynamics - PDB protein data bank     

Breeding phenology determines evolutionary transitions in migratory behaviour in finches and allies

The breeding season of long‐distance migratory birds often starts later and is shorter than in resident or short‐distance species breeding at the same latitude, but the reason for this is unclear. Here we investigate the association between migration distance and breeding phenology in a group of passerine birds, the finches and their allies, using phylogenetic comparative methods. We confirm that migration distance is related to aspects of the species’ breeding phenology after controlling for the effect of potentially confounding variables. Directional phylogenetic analyses suggest that evolutionary transitions in migration distance are determined by the breeding phenology. A relatively long migration distance is more likely to evolve in birds with a late, short breeding season, whereas transitions to short distance migration are more likely to occur in lineages with an early, long breeding season. These results suggest that migration distance is constrained by breeding phenology and not vice versa. Thus, breeding phenology may be an important ultimate factor shaping the evolution of migratory strategies.     

The step-size distance in muscle contraction: properties and estimates

The step-size distance in muscle contraction is obtained using the step-size distance equation z = u/n, where z is the step-size distance, u is the actin filament velocity and n is the ATPase rate of splitting. In a previous study a step-size distance of about 17 Å at no load was determined for intact frog muscle. Some properties of the step-size distance equation are described. We have now made estimates of the step-size distance z for a variety of muscles using existing physiological and biochemical data in the literature. The estimates are listed in Tables 1 and 2. We find that the step-size distances are clustered in the range 13–17 Å for nearly all muscles.     

Isolation-by-distance in landscapes: considerations for landscape genetics

In landscape genetics, isolation-by-distance (IBD) is regarded as a baseline pattern that is obtained without additional effects of landscape elements on gene flow. However, the configuration of suitable habitat patches determines deme topology, which in turn should affect rates of gene flow. IBD patterns can be characterized either by monotonically increasing pairwise genetic differentiation (for example, F_ST) with increasing interdeme geographic distance (case-I pattern) or by monotonically increasing pairwise genetic differentiation up to a certain geographical distance beyond which no correlation is detectable anymore (case-IV pattern). We investigated if landscape configuration influenced the rate at which a case-IV pattern changed to a case-I pattern. We also determined at what interdeme distance the highest correlation was measured between genetic differentiation and geographic distance and whether this distance corresponded to the maximum migration distance. We set up a population genetic simulation study and assessed the development of IBD patterns for several habitat configurations and maximum migration distances. We show that the rate and likelihood of the transition of case-IV to case-I F_ST–distance relationships was strongly influenced by habitat configuration and maximum migration distance. We also found that the maximum correlation between genetic differentiation and geographic distance was not related to the maximum migration distance and was measured across all deme pairs in a case-I pattern and, for a case-IV pattern, at the distance where the F_ST–distance curve flattens out. We argue that in landscape genetics, separate analyses should be performed to either assess IBD or the landscape effects on gene flow.     

A Field Evaluation of Distance Measurement Error in Auditory Avian Point Count Surveys

ABSTRACT Detection distance is an important and common auxiliary variable measured during avian point count surveys. Distance data are used to determine the area sampled and to model the detection process using distance sampling theory. In densely forested habitats, visual detections of birds are rare, and most estimates of detection distance are based on auditory cues. Distance sampling theory assumes detection distances are measured accurately, but empirical validation of this assumption for auditory detections is lacking. We used a song playback system to simulate avian point counts with known distances in a forested habitat to determine the error structure of distance estimates based on auditory detections. We conducted field evaluations with 6 experienced observers both before and after distance estimation training. We conducted additional studies to determine the effect of height and speaker orientation (toward or away from observers) on distance estimation error. Distance estimation errors for all evaluations were substantial, although training reduced errors and bias in distance estimates by approximately 15%. Measurement errors showed a nonlinear relationship to distance. Our results suggest observers were not able to differentiate distances beyond 65 m. The height from which we played songs had no effect on distance estimation errors in this habitat. The orientation of the song source did have a large effect on distance estimation errors; observers generally doubled their distance estimates for songs played away from them compared with distance estimates for songs played directly toward them. These findings, which we based on realistic field conditions, suggest measures of uncertainty in distance estimates to auditory detections are substantially higher than assumed by most researchers. This means aural point count estimates of avian abundance based on distance methods deserve careful scrutiny because they are likely biased.     

Minimal folding pathways for coarse-grained biopolymer fragments

The minimal folding pathway or trajectory for a biopolymer can be defined as the transformation that minimizes the total distance traveled between a folded and an unfolded structure. This involves generalizing the usual Euclidean distance from points to one-dimensional objects such as a polymer. We apply this distance here to find minimal folding pathways for several candidate protein fragments, including the helix, the β-hairpin, and a nonplanar structure where chain noncrossing is important. Comparing the distances traveled with root mean-squared distance and mean root-squared distance, we show that chain noncrossing can have large effects on the kinetic proximity of apparently similar conformations. Structures that are aligned to the β-hairpin by minimizing mean root-squared distance, a quantity that closely approximates the true distance for long chains, show globally different orientation than structures aligned by minimizing root mean-squared distance.     

On the use of distance constraints in protein-protein docking computations

Protein-protein docking (PPD) is a computational process that predicts the structure of a complex of two interacting proteins from their unbound structures. The accuracy of PPD predictions is low, but can be greatly enhanced if experimentally determined distance data are available for incorporation into the prediction. However, the specific effects of distance constraints on PPD predictions are largely uncharacterized. In this study, we systematically simulated the effects of using distance constraints both on a new distance constraint-driven PPD approach, called DPPD, and also, by re-ranking, on a well-established grid-based global search approach. Our results for a PPD benchmark dataset of 84 protein complexes of known structures showed that near 100% docking success rates could be obtained when the number of distance constraints exceeded six, the degrees of freedom of the system, but the success rate was significantly reduced by long distance constraints, large binding-induced conformational changes, and large errors in the distance data. Our results also showed that, under most conditions simulated, even two or three distance constraints were sufficient to achieve a much better success rate than those using a sophisticated physicochemical function to re-rank the results of the global search. Our study provides guidelines for the practical incorporation of experimental distance data to aid PPD predictions.     

环境和扩散对草地群落构建的影响

植物群落构建机制是生态学研究的热点之一.长久以来这个难题并没有得到很好的解释,且争议较多.生态位理论或中性理论,或是二者的共同作用,这样的结论在不同的研究中都有印证.以黄土高原子午岭地区的草地群落为例,对3种不同的草地群落(5a的弃耕地、阴坡和阳坡的草地)进行了野外群落学调查,采用Mantel test和主轴邻距法(PCNM)分析方法,研究了空间地理距离和环境资源差异对于草本植物群落分布的影响,结果表明:地理距离和环境差异共同解释了群落组成相似性的79.3％,剔除环境因子的影响,地理距离解释了群落组成相似性的33.8％;而剔除地理距离的影响,环境因子解释了群落组成相似性的14.2％.无论是生态位理论还是中性理论,其在黄土高原草本群落构建过程中都有作用,但中性理论扮演了更为重要的角色.     

An Evaluation of Genetic Distances for Use with Microsatellite Loci

Mutations of alleles at microsatellite loci tend to result in alleles with repeat scores similar to those of the alleles from which they were derived. Therefore the difference in repeat score between alleles carries information about the amount of time that has passed since they shared a common ancestral allele. This information is ignored by genetic distances based on the infinite alleles model. Here we develop a genetic distance based on the stepwise mutation model that includes allelic repeat score. We adapt earlier treatments of the stepwise mutation model to show analytically that the expectation of this distance is a linear function of time. We then use computer simulations to evaluate the overall reliability of this distance and to compare it with allele sharing and Nei's distance. We find that no distance is uniformly superior for all purposes, but that for phylogenetic reconstruction of taxa that are sufficiently diverged, our new distance is preferable.     

Impact force and time analysis influenced by execution distance in a roundhouse kick to the head in taekwondo

The execution distance is a tactic factor that affects mechanical performance and execution technique in taekwondo. This study analyzes the roundhouse kick to the head by comparing the maximum impact force, execution time, and impact time in 3 distances according to the athletes' competition level. It also analyzes the relationship between impact force and weight in each group. It examines whether the execution distance affects the maximum impact force, execution time, and impact time, in each level group or 2 different competition levels. Participants were 27 male taekwondo players (13 medallists and 14 nonmedallists). The medallists executed the roundhouse kick to the head with greater impact force and in a shorter execution time than did the nonmedallists when they kicked from any distance different to their combat distance. However, the results showed that the execution distance is influential in the execution time and impact time in the nonmedallist group. It is considered appropriate to orientate the high-level competitors to train for offensive actions from any distance similar to the long execution distance because it offers equally effectiveness and a greater security against the opponent. Also, practitioners should focus their training to improve time performance because it is more affected by distance than impact force.     

Environment, dispersal and patterns of species similarity

Aim The aim of this paper is to evaluate the combined effects of geographical distance and environmental distance on patterns of species similarity (similarity in species composition between sites), and to identify factors affecting the rate of decay in species similarity with each type of distance. Location Israel. Methods Data on species composition of land snails and land birds were recorded in 27 sites of 1 × 1 km scattered across a rainfall gradient in Israel. Matrices of similarity in species composition between all pairs of sites were computed and analysed with respect to corresponding matrices of geographical distance and rainfall distance (defined as the difference in mean annual rainfall between sites, and used as a measure of environmental distance). Mantel tests were applied to determine the correlation between species similarity and each type of distance. Factors affecting the decay in species similarity were investigated by comparing different subsets of the data using randomization tests. Results Both rainfall distance and geographical distance had negative effects on species similarity. The effect of rainfall distance was statistically significant even after controlling for differences in geographical distance, and vice versa. The per‐unit effect of rainfall distance on species similarity decreased with increasing geographical distance, indicating that the two types of distances interacted in determining the similarity in species composition. Snails showed a higher rate of decay in species similarity with geographical distance than birds, and large snails showed a higher rate of decay than small snails, which are better passive dispersers. The per‐unit effects of both rainfall distance and geographical distance on species similarity were higher in the desert region than in the Mediterranean region. Analyses focusing on a grain size of 10 × 10 m showed a lower similarity in species composition and a lower rate of decay in species similarity with rainfall distance than analyses carried out at a grain size of 1 × 1 km. Main conclusions Patterns of similarity in species composition are influenced by the combined effects of environmental variation, the position of the area along environmental gradients, the dispersal properties of the component species, and the scale (both spatial extent and grain size) at which the patterns are examined.