Computing the Distribution of a Tree Metric

The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for 20 years, an algorithm that is explicitly polynomial time has yet to be described for computing the distribution for trees around a given tree. In this paper, we derive a polynomial-time algorithm for this distribution. We show how the distribution can be approximated by a Poisson distribution determined by the proportion of leaves that lie in “cherries” of the given tree. We also describe how our results can be used to derive normalization constants that are required in a recently proposed maximum likelihood approach to supertree construction.     

Retention function of all segments of IUD usage: a compound distribution.

The distribution of the all segments of IUD use consists of two components: the distribution of the length of each segment and the distribution of the number of segments. In this article, a compound distribution of all segments of IUD, developed by the authors is described. The distribution assumes that each segment of IUD use is a mixed exponential distribution and the number of segments experienced by women is a truncated Poisson distribution. This distribution is useful in estimating the demographic impact of an IUD and IUD program.     

The distribution of structures in evolving protein populations

Proteins exhibit a nonuniform distribution of structures. A number of models have been advanced to explain this observation by considering the distribution of designabilities, that is, the fraction of all sequences that could successfully fold into any particular structure. It has been postulated that more designable structures should be more common, although the exact nature of this relationship has not been addressed. We find that the nonuniform distribution of protein structures found in nature can be explained by the interplay of evolution and population dynamics with the designability distribution. The relative frequency of different structures has a greater-than-linear dependence on designability, making the distribution of observed protein structures more uneven than the distribution of designabilities. The distribution of structures is also affected by additional factors such as the topology of the sequence space and the similarity of other structures.     

Convergence properties of the degree distribution of some growing network models

In this article we study a class of randomly grown graphs that includes some preferential attachment and uniform attachment models, as well as some evolving graph models that have been discussed previously in the literature. The degree distribution is assumed to form a Markov chain; this gives a particularly simple form for a stochastic recursion of the degree distribution. We show that for this class of models the empirical degree distribution tends almost surely and in norm to the expected degree distribution as the size of the graph grows to infinity and we provide a simple asymptotic expression for the expected degree distribution. Convergence of the empirical degree distribution has consequences for statistical analysis of network data in that it allows the full data to be summarized by the degree distribution of the nodes without losing the ability to obtain consistent estimates of parameters describing the network.     

Single-locus gametophytic incompatibility: the symmetric equilibrium is globally asymptotically stable

The deterministic dynamics of the classical single-locus multiple-allele model of gametophytic incompatibility is analyzed with the intention to prove the conjecture that the symmetric state (uniform distribution of genotypes) is the only polymorphic equilibrium and that this equilibrium is globally asymptotically stable in the interior of the frequency simplex. It is shown that the minimum allelic frequency increases strictly over the generations as long as a uniform allelic distribution is not realized. Hence, the minimum allelic frequency is a Ljapunov function for the invariant set of genotypic frequencies characterized by a uniform allelic distribution. Within this set, the uniform genotypic distribution is approached in an exponential fashion, which proves the assertion. An evolutionary optimization rule associated with the global convergence to the symmetric state is implied by the fact that at this state the overall amount of pollen elimination resulting from incompatible crosses is minimized.     

气候变暖情境下松材线虫在我国的适生区范围

基于历史气象数据(1971—2000),利用CLIMEX软件对松材线虫Bursaphelenchus xylophilus在我国的潜在适生区进行了预测,结果显示:松材线虫在我国的适生范围广、适生程度高,全国除黑龙江、吉林省无适生区外,其余各省市区均有适生区域,其中约2/3的适生区为高度适生区,覆盖整个南方地区,分布北界达内蒙古通辽地区,西至西藏的日喀则地区;进一步结合英国气候变化研究中心提供的气候变暖情境下未来气候模拟数据TYNSC2.0,利用CLIMEX软件预测出未来30年内(2010-2039)松材线虫在我国的潜在适生区,结果发现同历史气候条件下相比,未来30年内松材线虫在我国的适生分布区将呈现范围增加、适生程度增加、向北扩散的趋势,其中分布北界将到达吉林省西部,分布西界则与历史气候条件下预测结果相差无几。     

Detecting spatial aggregation from distance sampling: a probability distribution model of nearest neighbor distance

Spatial point pattern is an important tool for describing the spatial distribution of species in ecology. Negative binomial distribution (NBD) is widely used to model spatial aggregation. In this paper, we derive the probability distribution model of event-to-event nearest neighbor distance (distance from a focal individual to its n-th nearest individual). Compared with the probability distribution model of point-to-event nearest neighbor distance (distance from a randomly distributed sampling point to the n-th nearest individual), the new probability distribution model is more flexible. We propose that spatial aggregation can be detected by fitting this probability distribution model to event-to-event nearest neighbor distances. The performance is evaluated using both simulated and empirical spatial point patterns.     

Improved inference of mutation rates: I. An integral representation for the Luria-Delbrück distribution

The estimation of mutation rates is ordinarily performed using results based on the Luria-Delbrück distribution. There are certain difficulties associated with the use of this distribution in practice, some of which we address in this paper (others in the companion paper, Oprea and Kepler, Theor. Popul. Biol., 2001). The distribution is difficult to compute exactly, especially for large values of the random variable. To overcome this problem, we derive an integral representation of the Luria-Delbrück distribution that can be computed easily for large culture sizes. In addition, we introduce the usual assumption of very small probability of having a large proportion of mutants only after the generating function has been computed. Thus, we obtain information on the moments for the more general case. We examine the asymptotic behavior of this system. We find a scaling or "standardization" technique that reduces the family of distributions parameterized by three parameters (mutation rate, initial cell number, and final cell number) to a single distribution with no parameters, valid so long as the product of the mutation rate and the final culture is sufficiently large. We provide a pair of techniques for computing confidence intervals for the mutation rate. In the second paper of this series, we use the distribution derived here to find approximate distributions for the case where the cell cycle time is not well-described as an exponential random variable as is implicitly assumed by Luria-Delbrück distribution.     

THE DISTRIBUTION OF THE PIED STARLING,AND SOUTHERN AFRICAN BIOGEOGRAPHY

Craig, A. J. F. K. 1985. The distribution of the Pied Starling, and southern African biogeography. Ostrich 56:123-131.

The Pied Starling is restricted to South Africa, Lesotho and Swaziland, but within this region it occupies a variety of habitats. Its modern distribution is certainly influenced by its association with man. However, a comparison with other vertebrate species, and with patterns of plant distribution, suggests that its geographical distribution has been determined primarily by its evolutionary history. A hypothesis for the origin of this species leads to several predictions concerning biogeography in southern Africa.     

酵母基因组中ORF数目与长度的关系

根据NCBI数据库中基因注释序列及相关注释文件,统计了酿酒酵母基因组中不同长度的开阅读框架(Open ReadingFrame,ORF)的数目,分析了开阅读框架的数目随长度的分布关系,结果发现有明显的规律性。根据分布的特点用各种分布模型进行拟合比较,提出这类分布是Г(α,β)分布的假设。进一步根据Г(α,β)分布估算了酵母基因组蛋白质编码序列的数目为5870个。该结果对于基因注释具有一定的参考价值。     

Distribution of sphingosine kinase activity and mRNA in rodent brain

Sphingosine-1-phosphate (S1P) is a lipid mediator that exerts multiple cellular functions through activation of a subfamily of G-protein-coupled receptors. Although there is evidence that S1P plays a role in the developing and adult CNS, little is known about the ability of brain parenchyma to synthesize this lipid. We have therefore analyzed the brain distribution of the enzymatic activity of the S1P synthesizing enzyme, sphingosine kinase (SPHK) [EC:2.7.1.91], as well as mRNA distribution for one of the two isoforms of this enzyme, sphingosine kinase 2. SPHK activity, measured by the conversion of [(3)H]sphingosine to [(3)H]S1P, is highest in cerebellum, followed by cortex and brainstem. Lowest activities were found in striatum and hippocampus. Sensitivity to 0.1% Triton-X suggests that this activity is accounted for by SPHK2. RT-PCR and in situ hybridization studies show that mRNA for this isoform has a distribution similar to that of SPHK activity. In vivo and in vitro ischemia increase SPHK activity and SPHK2 mRNA levels. These results indicate that SPHK2 is the predominant S1P-synthesizing isoform in normal brain parenchyma. Its heterogeneous distribution, in particular laminar distribution in cortex, suggests a neuronal localization and a possible role in cortical and cerebellar functions, in normal as well as ischemic brain.     

A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite

This paper considers a generalized birth process {X^m(t), t > 0} and presents a new stochastic model for the number of eggs laid by a parasite on a host. Also, given an underlying distribution for the number of visits between parasites and a host, this distribution is generalized by the distribution of the number of eggs per visit laid on the host. If a certain number of eggs are already present on the host, a parasite such as a Japanese weevil, may avoid oviposition in subsequent visits (see JANARDAN (1980)) to the same host. A class of generalized distributions are presented to model such situations. The case of a single egg laying parasite and a Poisson distribution for the number of visits of the parasite to the same host yields a distribution of particular interest. In order to develop this model, certain lemmas are derived. Finally a characteristic property of this stochastic model is presented.     

林木分布格局多样性测度方法: 以阔叶红松林为例

林木分布格局是森林结构的重要组成部分, 直接影响森林生态系统的健康与稳定, 维持森林结构多样性被认为是保护生物多样性的最佳途径。本研究探讨了林木分布格局多样性的测度方法, 以期为揭示森林结构多样性提供理论依据。格局多样性研究的关键在于选择合适的生物多样性测度方法和具有分布属性的格局指数。本研究通过统计角尺度分布频率和Voronoi多边形边数分布频率, 运用Simpson指数分别计算角尺度多样性和Voronoi多边形边数分布多样性, 作为表达林木分布格局多样性指数的方法, 并以我国东北吉林蛟河的3个100 m × 100 m的阔叶红松(Pinus koreansis)林长期定位监测标准地为例, 分析了林木分布格局的多样性。结果表明: 无论是角尺度分布还是Voronoi多边形的边数分布都接近正态分布, 角尺度分布中随机分布林木的频数最多, 占55%以上; Voronoi多边形的类型多达10个以上, 50%以上的林木有5-6株最近相邻木。利用Simpson指数衡量林木格局多样性, 角尺度分布与Voronoi多边形的边数分布都显示出聚集分布的林分比随机分布林分的格局多样性高。研究还发现, 两种格局判定方法得出的Simpson指数值有所不同, 角尺度分布的多样性数值明显低于Voronoi多边形的边数分布的多样性数值, 主要原因是二者的等级数量不同。可见, 林木分布格局多样性研究应选择具有分布属性的格局指数, 但由于各指数反映的角度不同, 所以在分析比较不同林分格局多样性时应采用相同的分析方法。     

Quasi-stationary and ratio of expectations distributions: A comparative study

Many stochastic systems, including biological applications, use Markov chains in which there is a set of absorbing states. It is then needed to consider analogs of the stationary distribution of an irreducible chain. In this context, quasi-stationary distributions play a fundamental role to describe the long-term behavior of the system. The rationale for using quasi-stationary distribution is well established in the abundant existing literature. The aim of this study is to reformulate the ratio of means approach ( [Darroch and Seneta, 1965] and [Darroch and Seneta, 1967]) which provides a simple alternative. We have a two-fold objective. The first objective is viewing quasi-stationarity and ratio of expectations as two different approaches for understanding the dynamics of the system before absorption. At this point, we remark that the quasi-stationary distribution and a ratio of means distribution may give or not give similar information. In this way, we arrive to the second objective; namely, to investigate the possibility of using the ratio of expectations distribution as an approximation to the quasi-stationary distribution. This second objective is explored by comparing both distributions in some selected scenarios, which are mainly inspired in stochastic epidemic models. Previously, the rate of convergence to the quasi-stationary regime is taking into account in order to make meaningful the comparison.     

Back from a predicted climatic extinction of an island endemic: a future for the Corsican Nuthatch

The Corsican Nuthatch (Sitta whiteheadi) is red-listed as vulnerable to extinction by the IUCN because of its endemism, reduced population size, and recent decline. A further cause is the fragmentation and loss of its spatially-restricted favourite habitat, the Corsican pine (Pinus nigra laricio) forest. In this study, we aimed at estimating the potential impact of climate change on the distribution of the Corsican Nuthatch using species distribution models. Because this species has a strong trophic association with the Corsican and Maritime pines (P. nigra laricio and P. pinaster), we first modelled the current and future potential distribution of both pine species in order to use them as habitat variables when modelling the nuthatch distribution. However, the Corsican pine has suffered large distribution losses in the past centuries due to the development of anthropogenic activities, and is now restricted to mountainous woodland. As a consequence, its realized niche is likely significantly smaller than its fundamental niche, so that a projection of the current distribution under future climatic conditions would produce misleading results. To obtain a predicted pine distribution at closest to the geographic projection of the fundamental niche, we used available information on the current pine distribution associated to information on the persistence of isolated natural pine coppices. While common thresholds (maximizing the sum of sensitivity and specificity) predicted a potential large loss of the Corsican Nuthatch distribution by 2100, the use of more appropriate thresholds aiming at getting closer to the fundamental distribution of the Corsican pine predicted that 98% of the current presence points should remain potentially suitable for the nuthatch and its range could be 10% larger in the future. The habitat of the endemic Corsican Nuthatch is therefore more likely threatened by an increasing frequency and intensity of wildfires or anthropogenic activities than by climate change.     

Preliminary Report on the Distribution of <Emphasis Type="Italic">Callicebus oenanthe</Emphasis> on the Eastern Feet of the Andes

In 2007 we conducted a field study of almost 6 mo to determine the distribution of Callicebus oenanthe, formerly known as the Andean titi monkey. There previously has been no extensive study on the distribution and status by other fieldworkers. We visited a total of 96 localities within or around the presumed distribution of this rare primate species to determine the distribution of Callicebus oenanthe. We collected additional information on group size and threats to the species. Our expeditions revealed that the species is not endemic to the Alto Mayo Valley, as earlier authors suggested, but that its distribution extends into the Bajo Mayo and Huallaga Central. The study area is heavily deforested, and to date only one area was found where a viable population might live, although further research is needed to confirm this. The species lives in the southern part of its distribution in sympatry with another, undescribed species of Callicebus. We will continue the study to determine more precisely the distribution and conservation status of the Callicebus oenanthe, to determine if conservation measures are necessary for this species. This is the first activity of a long-term project for the conservation of Callicebus oenanthe initiated by La Vallée des Singes Primate park.     

A first principles derivation of animal group size distributions

Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.     

Robust reconstruction of the rate constant distribution using the phase function method

Many biological processes exhibit complex kinetic behavior that involves a nontrivial distribution of rate constants. Characterization of the rate constant distribution is often critical for mechanistic understandings of these processes. However, it is difficult to extract a rate constant distribution from data measured in the time domain. This is due to the numerical instability of the inverse Laplace transform, a long-standing mathematical challenge that has hampered data analysis in many disciplines. Here, we present a method that allows us to reconstruct the probability distribution of rate constants from decay data in the time domain, without fitting to specific trial functions or requiring any prior knowledge of the rate distribution. The robustness (numerical stability) of this reconstruction method is numerically illustrated by analyzing data with realistic noise and theoretically proved by the continuity of the transformations connecting the relevant function spaces. This development enhances our ability to characterize kinetics and dynamics of biological processes. We expect this method to be useful in a broad range of disciplines considering the prevalence of complex exponential decays in many experimental systems.     

Modelling the known and unknown plant biodiversity of the Amazon Basin

Aims The overall aim of this study is to provide the data needed for Amazonian conservation and the sustainable management of the region. To this end I model the hypothetical distribution of plant species richness across the Amazon Basin, the distribution of the proportion of this species richness that can be accounted for by described species, and hence the distribution of the biodiversity which remains unknown. Location Amazonia, Neotropics. Methods Species richness across the Amazon Basin is estimated by comparing the occurrences of 1584 species of Magnoliophyta whose taxonomy and geographical distributions are relatively well known. These data are used to collate checklists for squares of 1° latitude by 1° longitude. Comparison of the checklists allows estimation of the relative expected diversity in the vicinity of each degree square. Summing the distributions of the hypothetical real ranges gives the proportion of the biodiversity that can be accounted for by described species. Subtraction of the second distribution from the first gives a distribution of the contribution to the overall biodiversity that the model predicts, potentially, results from as yet undescribed species. Results Collections documented in recent botanical monographs show an extremely biased distribution with the best knowledge being found in a very few relatively well‐collected areas. At the degree square level, this model predicts that gamma biodiversity in the Amazon Basin is uniformly high across most of the basin. The model predicts that four large areas of the basin are particularly poorly known, and that they should contain large numbers of uncollected species. Main conclusions The model presented here highlights the difficulties of quantifying Amazonian plant diversity and its distribution. The low density of collections, and especially their extremely clumped distribution, undermines confidence in theories that seek to explain the apparent distribution of biodiversity. The model's prediction is substantially different from published predictions of the distribution of alpha diversity. Testing of this model in the areas identified as lacunae would require collecting programmes designed to collect fertile material of rare species. If the model's predictions are approximately accurate, the plant biodiversity of the Amazon Basin is considerably underestimated.