Faithful consensus methods for n-trees

A class of new consensus methods for n-trees (hierarchical clusterings) is proposed. These methods apply systematically to an arbitrary collection of given classifications of a fixed set of taxa, and produce a single consensus classification. They are motivated by the desire that the consensus classification retain as much information as possible from the given classifications, even in the case of only approximate agreement among them. A focus of the paper is the concept of faithfulness of consensus methods; this concept explicates the informal notion of adequate retention of information referred to above, and is proposed as a desirable requirement for consensus methods in general. The new methods are all faithful; they have the additional property that they take hierarchical level into account. Other general properties of consensus methods are investigated, especially with reference to their relation with faithfulness. The most important of these properties is neutrality; loosely speaking a consensus method is neutral if all nontrivial clusters are treated equally in the conditions on the given classifications required to guarantee the appearance of a cluster in the consensus. A central result of the paper is an analogue of the classical impossibility theorem of K. Arrow: with trivial exceptions it is impossible to have a consensus method that is simultaneously faithful and neutral. Thus two intuitively very appealing general properties of consensus methods are seen to be incompatible.     

Edge lengths of trees from sequence data

Frequently there is a need to determine lengths associated with each edge of a phylogenetic tree, as these are often used as an indication of relative time intervals. Where this tree has been constructed from sequence data of r characters for n taxa, using the maximum parsimony model, an edge length can be determined from the differences between the inferred sequences of the end vertices of that edge. These inferred sequences are often not uniquely defined; a range of possible sequences are possible at a given internal vertex. In this paper we introduce an efficient [O(r×n)] algorithm which calculates the range of lengths on any edge over all the minimal labelings and significantly reduces the number of potential cases to be considered to obtain an objective measure of edge length.     

Comparison of foliar water use efficiency among 17 provenances of Larix gmelinii in the Mao’ershan area

 研究环境变化下的树木水分利用效率对探讨森林生态系统碳水耦联关系及其对气候变化的响应和适应对策具有重要意义。落叶松(Larix gmelinii)为我国北方森林的建群种之一。将水热条件不同的17个种源落叶松种植在帽儿山森林生态系统研究站的同质园内30年后, 测定其针叶水分利用效率(WUE)及其相关因子。结果表明: WUE、净光合速率(P_n)、蒸腾速率(T_r)、气孔导度(G_s)、比叶面积(SLA)和叶片氮含量(N_L)均存在显著的种源差异(p < 0.05)。WUE和G_s呈显著指数相关关系, 当G_s < 0.2 时WUE随G_s的增大而明显增大, 而当G_s > 0.2时WUE趋于稳定。WUE和SLA及N_L分别呈线性负相关和正相关关系, 且随种源原地的干燥度指数(AI)的增大其相关性明显增强。WUE和种源原地年平均气温、平均年降水量及AI分别呈线性负相关、负相关和正相关关系, 并且相关系数依次增大; T_r则仅和种源原地年平均气温呈线性正相关关系, 而P_n和种源原地AI呈线性正相关关系。不同种源落叶松由于对种源原地环境条件的适应而存在针叶结构和生理特征的显著差异, 并因此引起针叶水分利用效率的差异。     

Evidences and magnitude of nighttime transpiration derived from <Emphasis Type="Italic">Populus euphratica</Emphasis> in the extreme arid region of China

Extensive research has found that nighttime transpiration (E _n) is positively correlated to the vapour pressure deficit (VPD), that suggested E _n was highest during the night under high temperatures and low humidity along with high soil water availability, typically for the riparian forest in the extreme arid region of China. This study used the heat ratio method to measure sap velocity (V _s) for mature and saplings Populus euphratica Oliv., and then E _n was conservatively calculated as total nocturnal sap flow (F _s, the product of V _s and sapwood area A _s) between 01:00 to 06:00. A gas exchange system was used to measure the leaf transpiration rate (T _r) and stomatal conductance (g _s) of saplings. For mature trees, nighttime V _s was extensive and logarithmic correlated to VPD (similar to daytime). For saplings, g _s and T _r was extensive in different months, and also a strong logarithmic relationship was found between V _s and VPD for both daytime and nighttime periods. Both of stem sap flow and leaf gas exchange suggusted the occurrence of E _n, whether mature or sapling trees. E _n contribution to daily transpiration (E _d) was high just as expected for P. euphratica, which was confirmed by proportional E _n to E _d (E _n/E _d) means taken in 2012 (24.99%) and 2013 (34.08%). Compared to mature trees, E _n/E _d of saplings in 2013 was lower with means of 12.06%, that supported further by the shorter duration times and less T _r,n (16.64%) and g _s,n (26.45%) of leaf, suggesting that E _n magnitude is associated to individual the tree size, that effect to stored water of individual trees, although this hypothesis requires further research.     

Coalescent histories for discordant gene trees and species trees

Given a gene tree and a species tree, a coalescent history is a list of the branches of the species tree on which coalescences in the gene tree take place. Each pair consisting of a gene tree topology and a species tree topology has some number of possible coalescent histories. Here we show that, for each n≥7, there exist a species tree topology S and a gene tree topology G≠S, both with n leaves, for which the number of coalescent histories exceeds the corresponding number of coalescent histories when the species tree topology is S and the gene tree topology is also S. This result has the interpretation that the gene tree topology G discordant with the species tree topology S can be produced by the evolutionary process in more ways than can the gene tree topology that matches the species tree topology, providing further insight into the surprising combinatorial properties of gene trees that arise from their joint consideration with species trees.     

On the optimality of the neighbor-joining algorithm

The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n ≤ 8. This requires the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. Our results include a demonstration that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the l ₂ radius for neighbor-joining for n = 5 and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree.     

Preconditioning 2D Integer Data for Fast Convex Hull Computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.     

Analysis of the bilayer phase transition temperatures of phosphatidylcholines with mixed chains

The analysis of the chain-length dependence of the chain-melting transition temperatures of bilayers composed of lipids with identical chains (Marsh, D. 1991. Biochim. Biophys. Acta. 1062: 1-6) is extended to include lipids with chains of unequal length. The bilayer transition temperatures of saturated asymmetrical phosphatidylcholines are interpreted by assuming that the transition enthalpy and transition entropy are linearly related to the absolute value of the difference in chain length between the sn-1 and sn-2 chains, with constant end contributions. Such an assumption is supported by calorimetric data on phosphatidylcholines of constant mean chainlength and varying chain asymmetry. In particular, a symmetrical linear dependence is observed on the chain asymmetry, Δn, which is centered around a value Δn° that corresponds to the conformational inequivalence of the sn-1 and sn-2 chains. The transition temperature then takes the form: T_t = T_t^∞(n - n_H - h′ | Δn + Δn° |)/(n - n_s - s′ | Δn + Δn°) where n_H, n_s are the end contributions, and h′, s′ are fractional deficits in the incremental transition enthalpy and entropy, respectively, arising from the overlapping regions of the longer chains. Optimization on the transition temperature data for the dependence on chain asymmetry of three series of phosphatidylcholines with constant mean chainlength, n, yields parameters that are capable of predicting the dependence of the transition temperatures on chain asymmetry for other mean chainlengths. The dependence of the transition temperature on mean chainlength for phosphatidylcholines in which the chain asymmetry is maintained constant, as well as the dependence on both mean chain length and chain asymmetry for phosphatidylcholines in which one of the two chains is maintained of constant length, are also described with high accuracy by using the same parameters.     

Yule-generated trees constrained by node imbalance

The Yule   process generates a class of binary trees which is fundamental to population genetic models and other applications in evolutionary biology. In this paper, we introduce a family of sub-classes of ranked trees, called Ω-trees, which are characterized by imbalance of internal nodes. The degree of imbalance is defined by an integer 0≤ω$0\le \omega$. For caterpillars  , the extreme case of unbalanced trees, ω=0$\omega =0$. Under models of neutral evolution, for instance the Yule model, trees with small ω are unlikely to occur by chance. Indeed, imbalance can be a signature of permanent selection pressure, such as observable in the genealogies of certain pathogens. From a mathematical point of view it is interesting to observe that the space of Ω-trees maintains several statistical invariants although it is drastically reduced in size compared to the space of unconstrained Yule trees. Using generating functions, we study here some basic combinatorial properties of Ω-trees. We focus on the distribution of the number of subtrees with two leaves. We show that expectation and variance of this distribution match those for unconstrained trees already for very small values of ω.     

Tear staining in pigs: a potential tool for welfare assessment on commercial farms

Tear staining or chromodacryorrhea refers to a dark stain below the inner corner of the eye, caused by porphyrin-pigmented secretion from the Harderian gland. It has been shown to be a consistent indicator of stress in rats and to correlate with social stress and a barren environment in pigs. The current study was, to our knowledge, the first to test it on commercial pig farms as a potential welfare indicator. The study was carried out on three commercial farms in Finland, in connection to a larger study on the effects of different types of manipulable objects on tail and ear biting and other behavioural parameters. Farm A was a fattening farm, on which 768 growing-finishing pigs were studied in 73 pens. Farm B had a fattening unit, in which 656 growing-finishing pigs were studied in 44 pens, and a farrowing unit, in which 29 sows and their litters totalling 303 piglets were studied in 29 pens. Farm C was a piglet-producing farm, on which 167 breeder gilts were studied in 24 pens. Data collection included individual-level scoring of tear staining; scoring of tail and ear damage in the growing-finishing pigs and breeder gilts; a novel object test for the piglets; and a novel person test for the growing-finishing pigs on Farm B and the breeder gilts on Farm C. On Farm A, tear staining was found to correlate with tail damage scores (n=768, r_s=0.14, P<0.001) and ear damage scores (n=768, r_s=0.16, P<0.001). In the growing-finishing pigs on Farm B, tear staining of the left eye correlated with tail damage (n=656, r_s=0.12, P<0.01) and that of the right eye correlated with ear damage (n=656, r_s=0.10, P<0.01). On Farm A, tear-staining sores were lower in the treatment with three different types of manipulable objects as compared with controls (mean scores 3.3 and 3.9, respectively, n=31, Fs₂₉=4.2, P<0.05). In the suckling piglets on Farm B, tear staining correlated with the latency to approach a novel object (n=29, r_p=0.41, P<0.05). Although correlations with tail and ear damage were low, it was concluded that tear staining has promising potential as a new, additional welfare indicator for commercial pig farming. Further research is needed on the mechanisms of tear staining.     

Quartet-based phylogenetic inference: improvements and limits

We analyze the performance of quartet methods in phylogenetic reconstruction. These methods first compute four-taxon trees (4-trees) and then use a combinatorial algorithm to infer a phylogeny that respects the inferred 4-trees as much as possible. Quartet puzzling (QP) is one of the few methods able to take weighting of the 4-trees, which is inferred by maximum likelihood, into account. QP seems to be widely used. We present weight optimization (WO), a new algorithm which is also based on weighted 4-trees. WO is faster and offers better theoretical guarantees than QP. Moreover, computer simulations indicate that the topological accuracy of WO is less dependent on the shape of the correct tree. However, although the performance of WO is better overall than that of QP, it is still less efficient than traditional phylogenetic reconstruction approaches based on pairwise evolutionary distances or maximum likelihood. This is likely related to long-branch attraction, a phenomenon to which quartet methods are very sensitive, and to inappropriate use of the initial results (weights) obtained by maximum likelihood for every quartet.     

rDNA units are highly polymorphic in Scutellospora castanea (Glomales,Zygomycetes)

The ribosomal DNA (rDNA) units in the glomalean zygomycete fungus Scutellospora castanea were analyzed. Dot-blot assays allowed an estimation of 75 copies per genome. After constructing a genomic library in a phage λEMBL3 vector, 13 rDNA clones were screened and explored. PCR experiments confirmed their nature and allowed homologous probes to be obtained. Restriction-fragment length polymorphism (RFLP) analysis and hybridizations with 18 s and 25 s probes allowed their grouping into nine families. The 18 s gene from these 13 clones was partially sequenced. The resulting 550 bases sequences were analyzed, and a phylogenetic tree was inferred. This revealed that two clones contain one highly divergent rDNA family (rUSc1) by comparison with other known 18 s sequences from the database. A phylogenetic tree was constructed with the entire 18 s sequences of rUSc1, rUSc3 and those of seven species representative of the glomalean fungi, Glomus, Entrophospora, Acaulospora, Scutellospora and Gigaspora. This tree confirmed that the rUSc1 sequence is the neighbor of 18 s sequences from Glomus (Glomineae), while rUSc3 remained in the group of the Gigaspora and Scutellospora (Gigasporineae). A specific primer, rUSc1-1, was generated from the ITS region of rUSc1, and used for PCR amplification from single spores, depicting the presence of rUSc1 in the genome of S. castanea at a lower frequency than other units.     

Exploring survival strategies of African Savanna trees by partial ordering techniques

The resilience of savanna ecosystems to climate and land-use changes is an important ecological and management question. The term ‘resilience’ is used to refer to the ability of a tree species to survive in a specific location, even under changing environmental conditions. In this study, vectors of functional traits of selected savanna tree species are studied by applying partial order algorithms to them. Some ecological interpretations are obtained and are compared to published research. One finding is the high rates of nitrogen fixation for the leaves of Acacia nigrescens. In opposition to this well-known fact, we discovered that Sclerocarya birrea has a bigger average leaf area than the other four tree species. Additionally, we found high carbonate values within the leaf from Colophospermum mopane, Combretum apiculatum, and Terminalis sericea. These results correspond to different ecological strategies for the tree species in question. It became obvious that geometric structures gained from partial ordering show a very good correspondence to ecological strategies of these tree species. Concepts of partial order theory may therefore be helpful in ecosystem research.     

广西猫儿山不同海拔常绿树种和落叶树种光合速率与氮的关系

分析广西猫儿山不同海拔常绿和落叶树种的光合作用-氮关系,探讨光合氮利用效率(PNUE)是否受到叶片习性和海拔的影响。落叶树种的PNUE都显著高于常绿树种,这与前者有较低的比叶重(LMA)和较高的单位叶重光合速率(Amass)、氮含量和气孔导度(gs)有密切关系。高海拔树种的PNUE显著低于中低海拔树种的PNUE,这与前者较高的LMA和较低的Amass和gs相关。PNUE和相关的叶片特征的主成分分析表明常绿-落叶树种和低海拔-中海拔-高海拔树种的分布是一个自然过渡的过程。此外,PNUE与土壤碳:氮比没有显著相关性,但与年均温正相关,这表明温度气候是调节PNUE沿海拔变化的主要环境因素。因此,这种叶片习性和温度气候调节的PNUE变化可能是调节猫儿山常绿树种沿海拔形成双峰分布的一种机制。     

Stability and Liquid-Liquid Phase Separation in Mixed Saturated Lipid Bilayers

The phase stability of a fluid lipid bilayer composed of a mixture of DC₁₈PC, (DSPC), and a shorter DC_ns PC, with n_s from 8 to 17, has been studied using a self-consistent field theory that explicitly includes molecular details and configurational properties of the lipid molecules. Phase separation between two liquid phases was found when there was a sufficient mismatch between the hydrophobic thicknesses of the two bilayers composed entirely of one component or the other. This occurs when n_s ≤ 12 and there is a sufficient concentration of the shorter lipid. The mixture separates into a thin bilayer depleted of DSPC and a thick bilayer enriched in DSPC. Even when there is no phase separation, as in the cases when there is either insufficient concentration of a sufficiently short lipid or any concentration of a lipid with n_s > 12, we observe that the effect of the shorter lipid is to increase the susceptibility of the system to fluctuations in the concentration. This is of interest, given that a common motif for the anchoring of proteins to the plasma membrane is via a myristoyl chain, that is, one with 14 carbons.     

四川柏木人工林林下植被生物量与林分结构的关系

森林结构与林下植被生物量的关系是森林持续经营与森林碳计量监测的科学基础,但一直缺乏必要的研究。以四川柏木(Cupressus funebris)人工林为研究对象,揭示林下植被生物量(Wu)、灌木生物量(Ws)和草本生物量(Wh)与林分结构的关系,并试图构建区域性林下植被生物量估测的混合模型。结果表明:(1)乔、灌、草群体共12个结构因子中,灌木群体的平均基径(Ds)、盖度(Cs)、高度(Hs)、体积(Vs)与林下植被生物量关系更紧密,在林下植被生物量模型构建中更有效;(2)多模型拟合与比较表明,柏木林Ws最佳估算模型为Ws=0.0005V1.0411s(R2a=0.762,P0.001,n=40),而Wu的最佳估算模型为ln Wu=0.0158Hs+0.0111Cs-0.5358(R2a=0.695,P0.001,n=40),但对于Wh未能获得较为理想的估算模型(R2a0.410,P0.01,n=40);(3)林分密度(Du)整合进入多元线性模型提高了林下植被生物量的估测精度,ln Wu=a+b Du+c Hs+d Cs(R2a=0.721,P0.001,n=40)。研究为区域性林下生物量估测模型构建提供了新论据。     

小麦和玉米叶片光合-蒸腾日变化耦合机理

植物叶片光合-蒸腾耦合是陆地生态系统碳-水耦合的基础.已有研究将叶片光合-蒸腾耦合笼统归因于气孔的共同控制作用,缺乏对其耦合机理的全面分析.选择华北地区大田作物冬小麦(C3)和夏玉米(C4)为研究对象,分别在小麦开花期和玉米拔节期选择典型晴天进行叶片光合蒸腾日变化观测(8:00-18:00).结果发现:1)光合速率(An)、蒸腾速率(Tr)以及光合有效辐射(PAR)、叶片表面温度(T)和气孔导度(gs)均表现出单峰日变化特征,峰值出现在正午前后;2)An-Tr具有极显著线性正相关关系(小麦和玉米的相关系数分别为0.75**和0.92**,回归直线斜率分别为1.99和3.62);3)PAR、T和gs与An和Tr有线性正相关关系;4)PAR-An与PAR-Tr、T-An与T-Tr、gs-An与gs-Tr的回归直线形态非常相似.分析认为:1)在光合-蒸腾耦合特征方面,C3作物小麦和C4作物玉米叶片光合-蒸腾都有明显的线性耦合关系,但两者的耦合关系特征存在明显差异,玉米的An-Tr线性回归斜率要明显大于小麦;2)在光合-蒸腾耦合机理方面,日变化中PAR、T和gs同时受太阳辐射调控与An、Tr发生趋向相同、形态相似且近似同步的变化,因此PAR-An与PAR-Tr、T-An与T-Tr、gs-An与gs-Tr具有形态相似的线性关系,这保证了在PAR、T和gs等调控因子发生较大变化的日变化过程中光合-蒸腾保持良好的线性耦合关系.     

Molecular evidence for the hybridity ofIlex × wandoensis and the phylogenetic study of KoreanIlex based on ITS sequence data

In this study, internal transcribed spacer (ITS) regions within the nuclear ribosomal DNA of KoreanIlex were analyzed in order to investigate any molecular evidence thatI. × wandoensis could serve as a putative hybrid betweenI. cornuta andI. integra. We also sought to clearly identify taxonomic relationships and problems caused by consecutive external morphological characters among taxa in the genus. We sequenced 20 clones fromI. × wandoensis and found these individuals displayed intra-genomic polymorphisms within ITS regions. The analysis of the clones clearly demonstrated the presence of discrete sequences from bothI. cornuta andI. integra, thereby confirmingI. × wandoensis is a species that was formed by crossingI. cornuta andI. integra. Lastly, the subgenusIlex, which contains the evergreen species, failed to form a monophyletic group in a strict consensus tree that was prepared based upon ITS regions.I. crenata var.microphylla in the subgenus KoreaIlex, which has presented taxonomic problems previously, formed an independent clade within the consensus tree, thereby showing distinction fromI. crenata.) Genetic discontinuity ofI. macropoda andI. Macropoda for.pseudo-macropoda individuals couldn't be confirmed.     

Age distribution of trees in stationary forest system

A statistical theory for the age distribution of spatially dominant trees in a stationary forest system is developed. The result depends whether or not mortality is spatially correlated, as well as whether or not the stand boundaries are pre-determined. In the case of spatially non-correlated mortality, the tree age distribution is an exponential with survival rate as the base. In the case of spatially correlated mortality within a stand with pre-determined boundaries, the age distribution within the stand is an exponential with natural base. For a small stand, the median life span of the stand is inversely proportional to the number of trees (n); the median life span in relation to stand closure time is inversely proportional to n ln(n). For a large stand, the stand life does not extend to the closure time.The behaviour of a forest system without fixed stand boundaries depends on the dimensionality of the system. In the case of a one-dimensional system, the longevity distribution is exponential, most of the trees however having the same longevity. Consequently, the probability density of tree age is constant. However, the probability mass of size of catastrophe destroying a particular tree is evenly distributed. This is due to trees being rapidly born on empty areas in the beginning of the life cycle, and clusters rapidly growing into larger ones close to the end of tree life.     

Genome-based phylogenetic analysis of Streptomyces and its relatives

MotivationStreptomyces is one of the best-studied genera of the order Actinomycetales due to its great importance in medical science, ecology and the biotechnology industry. A comprehensive, detailed and robust phylogeny of Streptomyces and its relatives is needed for understanding how this group emerged and maintained such a vast diversity throughout evolution and how soil-living mycelial forms (e.g., Streptomyces s. str.) are related to parasitic, unicellular pathogens (e.g., Mycobacterium tuberculosis) or marine species (e.g., Salinispora tropica). The most important application area of such a phylogenetic analysis will be in the comparative re-annotation of genome sequences and the reconstruction of Streptomyces metabolic networks for biotechnology.MethodsClassical 16S-rRNA-based phylogenetic reconstruction does not guarantee to produce well-resolved robust trees that reflect the overall relationship between bacterial species with widespread horizontal gene transfer. In our study we therefore combine three whole genome-based phylogenies with eight different, highly informative single-gene phylogenies to determine a new robust consensus tree of 45 Actinomycetales species with completely sequenced genomes.ResultsNone of the individual methods achieved a resolved phylogeny of Streptomyces and its relatives. Single-gene approaches failed to yield a detailed phylogeny; even though the single trees are in good agreement among each other, they show very low resolution of inner branches. The three whole genome-based methods improve resolution considerably. Only by combining the phylogenies from single gene-based and genome-based approaches we finally obtained a consensus tree with well-resolved branches for the entire set of Actinomycetales species. This phylogenetic information is stable and informative enough for application to the system-wide comparative modeling of bacterial physiology.