Numerical classification of enterococci

The taxonomic analysis of enterococci by a mathematical method has revealed that these organisms are subdivided, according to their properties, into three taxons; of these, two taxons correspond to the species known as Streptococcus faecalis and Streptococcus faecium, while the third taxon, sharply different from the rest, comprises mobile enterococci which can be probably regarded as a separate species and differentiated from the other two species by a number of characteristics.     

Modeling DNA shuffling.

In vitro evolution is a new, important laboratory method to evolve molecules with desired properties. It has been used in a variety of biological studies and drug development. In this paper, we study one important mutagenesis method used in in vitro evolution experiments called DNA shuffling. We construct a mathematical model for DNA shuffling and study the properties of molecules after DNA shuffling experiments based on this model. The model for DNA shuffling consists of two parts. First we apply the Lander-Waterman model for physical mapping by fingerprinting random clones to model the distribution of regions that can be reassembled through DNA shuffling. Then we present a model for recombination between different DNA species with different mutations. We compare our theoretical results with experimental data. Finally we propose novel applications of the theoretical results to the optimal design of DNA shuffling experiments and to physical mapping using DNA shuffling.     

Emerging niche clustering results from both competition and predation

Understanding species coexistence has been a central question in ecology for decades, and the notion that competing species need to differ in their ecological niche for stable coexistence has dominated. Recent theoretical and empirical work suggests differently. Species can also escape competitive exclusion by being similar, leading to clusters of species with similar traits. This theory has so far only been explored under competition. By combining mathematical and numerical analyses, we reveal that competition and predation are equally capable to promote clusters of similar species in prey–predator communities, their relative importance being modulated by resource availability. We further show that predation has a stabilizing effect on clustering patterns, making the clusters more diverse. Our results merge different ecological theories and bring new light to the emergent neutrality theory by adding the perspective of trophic interactions. These results open new perspectives to the study of trait distributions in ecological interaction networks.     

Spectrally decomposed dark-to-light transitions in a PSI-deficient mutant of Synechocystis sp. PCC 6803

Cyanobacterial thylakoid membranes are known to host photosynthetic and respiratory complexes. This hampers a straight forward interpretation of the highly dynamic fluorescence originating from photosynthetic units. The present study focuses on dark-to-light transitions in whole cells of a PSI-deficient mutant of the cyanobacterium Synechocystis sp. PCC 6803. The time-dependent cellular fluorescence spectrum has been measured, while having previously exposed the cells to different conditions that affect respiratory activity. The analysis method used allows the detected signal to be decomposed in a few components that are then assigned to functional emitting species. Additionally, we have worked out a minimal mathematical model consisting of sensible postulated species to interpret the recorded data. We conclude that the following two functional complexes play a major role: a phycobilisome antenna complex coupled to a PSII dimer with either two or no closed reaction centers. Crucially, we present evidence for an additional species capable of strongly quenching fluorescence, whose formation requires the presence of oxygen.     

Evidence for lottery recruitment in Mediterranean old fields

Abstract. The hypothesis of lottery establishment ( Sale 1977 ) explains coexistence of species with similar niches through processes of stochastic recruitment. This initial idea forms the basis for a variety of mathematical models, but has not been tested empirically. This study is a field investigation of lottery establishment for plants with a seed bank, using Canonical Correspondence Analysis to compare the compositions of the vegetation and the seed bank according to different hypotheses on the mechanisms of establishment. This method was used for a data set from old fields from southern France. The weighted lottery (i.e. a random draw from the seed pool, weighted by the frequencies of each species) appeared as the best suited hypothesis to explain the high degree of similarity between the vegetation and the seed bank and the relative spatial distributions of the species. Several mechanisms are probably interacting, depending on the life histories of the species. Modelling and experimental approaches are needed to further test the hypothesis of lottery recruitment.     

Uptake of cadmium and zinc by the alga Chlorella vulgaris: II. Multi-ion situation

Many microorganisms are capable of sequestering and concentrating heavy metals from their aqueous environment. While much research has beep carried out on the uptake of single species of metal ions, little attention seems to have been given to the study of multimetal ion systems. A mathematical model has previously been developed to describe the uptake of individual metal species by a microorganism. The model proposes two sequential processes: an initial rapid uptake due to cellular surface adsorption and a subsequent slow uptake due to membrane transport of the metal into the cells. This article extends the treatment by considering the uptake of two metal species together, cadmium and zinc, under different experimental conditions. The results are discussed in terms of possible mechanistic interactions.     

多种病原物混合侵染的昆虫流行病模型

两种或两种以上的病原物同时侵染昆虫寄主时,病原物之间的相互作用表现为偏利、偏害、中性及竞争等类型,寄生群体的病症可呈多种形式．根据单种病菌的重叠侵染原理,建立了多种病原物混合侵染时以温度、病原接种量、虫龄及湿度为因子的昆虫流行病模型．由模型可计算寄生群体中不同病原物的致病比率,及寄主群体的总发病率,给出了模型的参数求解算法,以及病原物相互作用类型的判定准则．这类模型可用于多种病原物混合侵染的昆虫流行病预测,也可作为多种病原物混合施用防治害虫的最优化模型．     

Primate cognition: putting two and two together

The human mind has the capacity for abstract numerical representations that cut across different sensory modalities. New research with monkeys shows that this mathematical achievement is not unique to our species.     

Numerical simulation for heat transfer in tissues during thermal therapy

In this paper, a mathematical model describing the process of heat transfer in biological tissues for different coordinate system during thermal therapy by electromagnetic radiation is studied. The boundary value problem governing this process has been solved using Galerkin’s method taking B-polynomial as basis function. The system of ordinary differential equation in unknown time variable, thus obtained, is solved by homotopy perturbation method. The effect of thermal conductivity, antenna power constant, surface temperature, and blood perfusion rate on temperature for different coordinates are discussed. It has been observed that the process is faster in spherical symmetric coordinates in comparison to axisymmetric coordinate and faster in axisymmetric in comparison to Cartesian coordinate.     

The partitioning of diversity: showing Theseus a way out of the labyrinth

A methodology for partitioning of biodiversity into α, β and γ components has long been debated, resulting in different mathematical frameworks. Recently, use of the Rao quadratic entropy index has been advocated since it allows comparison of various facets of diversity (e.g. taxonomic, phylogenetic and functional) within the same mathematical framework. However, if not well implemented, the Rao index can easily yield biologically meaningless results and lead into a mathematical labyrinth. As a practical guideline for ecologists, we present a critical synthesis of diverging implementations of the index in the recent literature and a new extension of the index for measuring β‐diversity. First, we detail correct computation of the index that needs to be applied in order not to obtain negative β‐diversity values, which are ecologically unacceptable, and elucidate the main approaches to calculate the Rao quadratic entropy at different spatial scales. Then, we emphasize that, similar to other entropy measures, the Rao index often produces lower‐than‐expected β‐diversity values. To solve this, we extend a correction based on equivalent numbers, as proposed by Jost (2007), to the Rao index. We further show that this correction can be applied to additive partitioning of diversity and not only its multiplicative form. These developments around the Rao index open up an exciting avenue to develop an estimator of turnover diversity across different environmental and temporal scales, allowing meaningful comparisons of partitioning across species, phylogenetic and functional diversities within the same mathematical framework. We also propose a set of R functions, based on existing developments, which perform different key computations to apply this framework in biodiversity science.     

定量地层对比常用方法的比较和适用性分析

定量地层学以生物地层学原理为核心,将地层学信息定量化,运用数学模型进行地层对比,作为传统地层学对比的重要补充。传统的生物地层学根据经验选取标准化石来建立生物地层序列,但同时也丢失了大量的化石信息。定量地层学则能够利用所有的化石信息,在传统生物地层学的基础上得到更高分辨率的地层对比结果。现阶段定量地层对比常用的方法主要有图形对比法、约束最优化法和单元组合法三种,但对于这三种方法各自适应的数据情况方面,目前成果较少。本文对这三种方法的原理进行了简要的介绍和分析,并建立数据模型,从标准化石的可对比性、数据集的物种总数、剖面间共有物种和单延限分子的比例四个方面对三种方法的适用条件进行了讨论。其中图形对比法更适用于单延限分子较少、标准化石可对比性强的数据集。单元组合法对数据集中物种间相互关系的复杂程度较为敏感,共有物种较多的数据集有更好的对比结果,但数据集中物种总数的增加会对其产生一定的负面影响,需要依靠进一步的人工调整。约束最优化法则对数据集各方面的优化均有响应,对物种总数较大的数据集有较好的对比结果,且剖面间共有物种占比越大,对比结果越理想。     

Detection of punctuated equilibrium from molecular phylogenies

Abstract The theory of ‘punctuated equilibrium’ hypothesises that most morphological change in species takes place in rapid bursts triggered by speciation. Eldregde and Gould postulated the theory in 1972, as an alternative to the idea that morphological change slowly accumulates in the course of time, a then common belief they dubbed ‘phyletic gradualism’. Ever since its introduction the theory of punctuated equilibrium has been the subject of speculation rather than empirical validation. Here I present a method to detect punctuated evolution without reference to fossil data, based on the phenotypes of extant species and on their relatedness as revealed by molecular phylogeny. The method involves a general mathematical model describing morphological differentiation of two species over time. The two parameters in the model, the rates of punctual (cladogenetic) and gradual (anagenetic) change, are estimated from plots of morphological diversification against time since divergence of extant species.     

具体长结构的鱼类种群的数学模型及其应用

本文报道了一个新的鱼类种群的数学模型,它是一阶变系数线性偏微分方程。该模型可用于预测某一水域中某种鱼类种群不同体长的鱼的数量随时间变化的情况。       

Measuring biodiversity to explain community assembly: a unified approach

One of the oldest challenges in ecology is to understand the processes that underpin the composition of communities. Historically, an obvious way in which to describe community compositions has been diversity in terms of the number and abundances of species. However, the failure to reject contradictory models has led to communities now being characterized by trait and phylogenetic diversities. Our objective here is to demonstrate how species, trait and phylogenetic diversity can be combined together from large to local spatial scales to reveal the historical, deterministic and stochastic processes that impact the compositions of local communities. Research in this area has recently been advanced by the development of mathematical measures that incorporate trait dissimilarities and phylogenetic relatedness between species. However, measures of trait diversity have been developed independently of phylogenetic measures and conversely most of the phylogenetic diversity measures have been developed independently of trait diversity measures. This has led to semantic confusions particularly when classical ecological and evolutionary approaches are integrated so closely together. Consequently, we propose a unified semantic framework and demonstrate the importance of the links among species, phylogenetic and trait diversity indices. Furthermore, species, trait and phylogenetic diversity indices differ in the ways they can be used across different spatial scales. The connections between large‐scale, regional and local processes allow the consideration of historical factors in addition to local ecological deterministic or stochastic processes. Phylogenetic and trait diversity have been used in large‐scale analyses to determine how historical and/or environmental factors affect both the formation of species assemblages and patterns in species richness across latitude or elevation gradients. Both phylogenetic and trait diversity have been used at different spatial scales to identify the relative impacts of ecological deterministic processes such as environmental filtering and limiting similarity from alternative processes such as random speciation and extinction, random dispersal and ecological drift. Measures of phylogenetic diversity combine phenotypic and genetic diversity and have the potential to reveal both the ecological and historical factors that impact local communities. Consequently, we demonstrate that, when used in a comparative way, species, trait and phylogenetic structures have the potential to reveal essential details that might act simultaneously in the assembly of species communities. We highlight potential directions for future research. These might include how variation in trait and phylogenetic diversity alters with spatial distances, the role of trait and phylogenetic diversity in global‐scale gradients, the connections between traits and phylogeny, the importance of trait rarity and independent evolutionary history in community assembly, the loss of trait and phylogenetic diversity due to human impacts, and the mathematical developments of biodiversity indices including within‐species variations.     

Modeling species distributions by breaking the assumption of self-similarity

Species distributions are commonly measured as the number of sites, or geographic grid cells occupied. These data may then be used to model species distributions and to examine patterns in both intraspecific and interspecific distributions. Harte et al. (1999) used a model based on a bisection rule and assuming self-similarity in species distributions to do so. However, this approach has also been criticized for several reasons. Here we show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The outcomes of models based on these two assumptions (self-similar and power-scaling) have not previously been compared. Based on Harte's bisection method and an occupancy probability transition model under these two assumptions (self-similar and power-scaling), we compared the scaling pattern of occupancy (also known as the area-of-occupancy) and the spatial distribution of species. The two assumptions of species distribution lead to a relatively similar interspecific occupancy frequency distribution pattern, although the spatial distribution of individual species and the scaling pattern of occupancy differ significantly. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales.     

A quantitative estimation of degree of purity of preparations of subcellular structures

A method of mathematical treatment of the results of the analysis of enzymic activity of fractions has been suggested, allowing a quantitative estimation of both the degree of purity of fractions and the yield. Using this method the preparation of mitochondria, microsomes and lysosomes have been characterized. The method may also be used to elucidate the localization of some, not strictly organelle-specific enzymes of different subcellular structures.     

Maintenance of forest species diversity and latitudinal gradient

The species diversity of trees maintained in tropical rain forests is much higher than in temperate, boreal, or seasonally dry tropical forests. Many hypotheses have been proposed for higher diversity in tropical rain forests, including: (i) higher specialization of resource use, (ii) different mode of disturbance, (iii) smaller opportunity for competition on oligotrophic soil, (iv) higher productivity, (v) more active specific herbivores and pathogens, (vi) evolutionary/ecological history. In this paper we report mathematical models for tree-by-tree replacement. First the analysis of random drift model shows that the effect of gap size to species diversity is not very strong. Second we study phenological segregation model, which has the following assumptions: Basic mechanism for many species to coexist in the community is assumed given by the storage effect of lottery model, as species differ in seasonality in peak fruit production and in the subsequent period of high regeneration ability. Gaps formed during unfavorable season accumulate and become available for regeneration in the beginning of the growing season. The resulting synchronization of regeneration opportunity jeopardizes the coexistence of many similar species in seasonal environments. Analysis of a mathematical model shows: (1) the existence of unfavorable season can greatly reduce the diversity of coexisting species. (2) Diversity in the equilibrium community can be high when niche width of each species is broad and resource use is strongly overlapped. (3) Equilibrium community may include several distinct groups of species differing in phenology of regeneration. Effect of unequal niche width and frequency dependent regeneration are also examined.     

Reverse Engineering of Gene Regulatory Networks: A Comparative Study

Reverse engineering of gene regulatory networks has been an intensively studied topic in bioinformatics since it constitutes an intermediate step from explorative to causative gene expression analysis. Many methods have been proposed through recent years leading to a wide range of mathematical approaches. In practice, different mathematical approaches will generate different resulting network structures, thus, it is very important for users to assess the performance of these algorithms. We have conducted a comparative study with six different reverse engineering methods, including relevance networks, neural networks, and Bayesian networks. Our approach consists of the generation of defined benchmark data, the analysis of these data with the different methods, and the assessment of algorithmic performances by statistical analyses. Performance was judged by network size and noise levels. The results of the comparative study highlight the neural network approach as best performing method among those under study.