On Some Stochastic Problems in Epidemiology under the Binomial Damage Model

The present paper discusses some probability problems in epidemiology in which a community is divided into two parts by means of the binomial damage model. The community size N is an integer-valued random v?ariable and p denotes the incidence rate of a certain disease such that conditional on N=n, the number B of infected individuals in the community follows a binomial distribution with parameters n and p. Let C denote the number of the susceptibles, where B + C = N. Probabilities are found of the events, such as, only half the community is hit by the disease, or there are n more susceptibles than are infected for n=0, 1, 2,…, or the susceptibles exceed the infected, or the susceptibles exceed (m-1) times the number of infected individuals for m = 2, 3,…, etc. These probabilities play an useful role when a public health official wishes to ascertain that only a given proportion 1/m of the community is infected with the disease. Only the cases when the community size N follows the geometric, negative binomial or FISHER'S logarithmic series distributions are considered with the mathematics being manageable.     

Effective number of breeding adults in Oregon spotted frogs (<Emphasis Type="Italic">Rana</Emphasis><Emphasis Type="Italic">pretiosa</Emphasis>): genetic estimates at two life stages

We used genetic methods to estimate the effective number of breeders (N _b) in a population of Rana pretiosa, an imperiled amphibian in western North America. Microsatellite data was gathered from large samples of adults, eggs, and juveniles collected in 2006. We wished to determine where in the life cycle the greatest reductions in N _b occur, and to compare genetic estimates of N _b to an egg mass count estimate of the number of breeding adults. We predicted that N _b estimated at the metamorph stage would be reduced by increased variance in family size due to egg mass mortality. Contrary to our prediction, estimates of N _b at the egg and metamorph stages were similar. Thus, we found no evidence of inflated variance in family size between the two stages. If our results for this population are typical for R. pretiosa, then increased variance in family size during the egg to metamorph stage may not be a strong factor in reducing the effective population sizes (N _e) relative to the census sizes (N) in this species.     

Importance of denitrifiers lacking the genes encoding the nitrous oxide reductase for N2O emissions from soil

Analyses of the complete genomes of sequenced denitrifying bacteria revealed that approximately 1/3 have a truncated denitrification pathway, lacking the nosZ gene encoding the nitrous oxide reductase. We investigated whether the number of denitrifiers lacking the genetic ability to synthesize the nitrous oxide reductase in soils is important for the proportion of N₂O emitted by denitrification. Serial dilutions of the denitrifying strain Agrobacterium tumefaciens C58 lacking the nosZ gene were inoculated into three different soils to modify the proportion of denitrifiers having the nitrous oxide reductase genes. The potential denitrification and N₂O emissions increased when the size of inoculated C58 population in the soils was in the same range as the indigenous nosZ community. However, in two of the three soils, the increase in potential denitrification in inoculated microcosms compared with the noninoculated microcosms was higher than the increase in N₂O emissions. This suggests that the indigenous denitrifier community was capable of acting as a sink for the N₂O produced by A. tumefaciens. The relative amount of N₂O emitted also increased in two soils with the number of inoculated C58 cells, establishing a direct causal link between the denitrifier community composition and potential N₂O emissions by manipulating the proportion of denitrifiers having the nosZ gene. However, the number of denitrifiers which do not possess a nitrous oxide reductase might not be as important for N₂O emissions in soils having a high N₂O uptake capacity compared with those with lower. In conclusion, we provide a proof of principle that the inability of some denitrifiers to synthesize the nitrous oxide reductase can influence the nature of the denitrification end products, indicating that the extent of the reduction of N₂O to N₂ by the denitrifying community can have a genetic basis.     

Incorporating functional dissimilarities into sample‐based rarefaction curves: from taxon resampling to functional resampling

Question: Indices of functional diversity have been seen as the key for integrating information on species richness with measures that focus on those components of community composition related to ecosystem functioning. For comparing species richness among habitats on an equal‐effort basis, so‐called sample‐based rarefaction curves may be used. Given a study area that is sampled for species presence and absence in N plots, sample‐based rarefaction generates the expected number of accumulated species as the number of sampled plots increases from 1 to N. Accordingly, the question for this study is: can we construct a ‘functional rarefaction curve’ that summarizes the expected functional dissimilarity between species when n plots are drawn at random from a larger pool of N plots? Methods: In this paper, we propose a parametric measure of functional diversity that is obtained by combining sample‐based rarefaction techniques that are usually applied to species richness with Rao's quadratic diversity. For a given set of N presence/absence plots, the resulting measure summarizes the expected functional dissimilarity at an increasingly larger cumulative number of plots n (n≤N). Results and Conclusions: Due to its parametric nature, the proposed measure is progressively more sensitive to rare species with increasing plot number, thus rendering this measure adequate for comparing the functional diversity of species assemblages that have been sampled with variable effort.     

The Discrete Distribution Used for the Log-rank Test Can Be Inaccurate

When the number of tumors is small, a significance level for the Cox-Mantel (log-rank) test Z is often computed using a discrete approximation to the permutation distribution. For j = 0,…, J let N_j(t) be the number of animals in group j alive and tumor-free at the start of time t. Make a 2 × (1+J) table for each time t of the number of animals R_j(t) with newly palpated tumor out of the total N_j(t) at risk. There are a total of say K tables, one for each distinct time t with observed death or newly palpated tumor. The usual discrete approximation to the permutation distribution of Z is defined by taking tables to be independent with fixed margins N_j(t) and ΣR_j(t) for all t. However, the N_j(t) are random variables for the actual permutation distribution of Z, resulting in dependence among the tables. Calculations for the exact permutation distribution are explained, and examples are given where the exact significance level differs substantially from the usual discrete approximation. The discrepancy arisis primarily because permutations with different Z-scores under the exact distribution can be equal for the discrete approximation, inflating the approximate P-value.     

Adult male–female social bond advertising: The primary function of coordinated singing intensity in a small ape

Adult male and female coordinated singing occur in diverse animal taxa. Adult male–female social bond advertising and strengthening have been proposed as two important functional hypotheses of coordinated singing. Here we studied these two functions in four groups of cao vit gibbon (Nomascus nasutus), a small ape that lives in polygynous family groups and adult members coordinated their sex-specific songs to produce complex duets or trios (three members sing together), using 6-year field behavioral data. In this study, we used the number of successful great call sequences per bout or per minute, and latency period from start of the adult male call to the first successful great call sequence to represent singing intensity. We used the proportion of proximity, behavioral synchronization, and grooming between adult male and female to represent bond strength. We used linear mixed-effects model to investigate the correlation between singing intensity and adult male–female social bond strength. We found a negative correlation between all three bond strength indicators and female latency period (N = 209), and a positive correlation between the number of successful great call sequences per bout (N = 253) and per minute (N = 254) and proximity. We used paired Wilcoxon signed-rank test to investigate if adult gibbons increase bond strength after singing. We found proximity (hourly level: N = 45; daily level: N = 54), behavioral synchronization (hourly level: N = 57; daily level: N = 49), and grooming (daily level: N = 34) in most of the groups did not increase significantly after singing in an hourly or daily level. Together, these results indicate that cao vit gibbon coordinated singing serves primarily in adult male–female social bond advertising and distinct singing intensity indicators advertise different information on adult male–female social bond strength.     

Sampling strategies for estimating brook trout effective population size

The influence of sampling strategy on estimates of effective population size (N _e ) from single-sample genetic methods has not been rigorously examined, though these methods are increasingly used. For headwater salmonids, spatially close kin association among age-0 individuals suggests that sampling strategy (number of individuals and location from which they are collected) will influence estimates of N _e through family representation effects. We collected age-0 brook trout by completely sampling three headwater habitat patches, and used microsatellite data and empirically parameterized simulations to test the effects of different combinations of sample size (S = 25, 50, 75, 100, 150, or 200) and number of equally-spaced sample starting locations (SL = 1, 2, 3, 4, or random) on estimates of mean family size and effective number of breeders (N _b ). Both S and SL had a strong influence on estimates of mean family size and [^(N)]_b , \hat{N}_{b} , however the strength of the effects varied among habitat patches that varied in family spatial distributions. The sampling strategy that resulted in an optimal balance between precise estimates of N _b and sampling effort regardless of family structure occurred with S = 75 and SL = 3. This strategy limited bias by ensuring samples contained individuals from a high proportion of available families while providing a large enough sample size for precise estimates. Because this sampling effort performed well for populations that vary in family structure, it should provide a generally applicable approach for genetic monitoring of iteroparous headwater stream fishes that have overlapping generations.     

On the classification of regular systems of inbreeding

Regular systems of inbreeding are defined as those with discrete, nonoverlapping generations and with the same number of individuals and mating pattern in every generation. Given the number of individuals in a generation, there are many possible regular mating systems. A notion of when two such mating systems are equivalent is introduced, and several necessary conditions are given for such an equivalence. The use of these conditions is illustrated for N = 2, 3, 4 and 5 individuals, and a complete enumeration has been found for these cases: the numbers of inequivalent mating systems are 1, 5, 57 and 858, respectively. The maximal eigenvalue of the matrix q that specifies the recursion relations satisfied by the probabilities of identity have also been found for these cases. For N = 3 and 4 (and 2 trivially), circular mating gives the slowest rate of approach to genetic uniformity of those systems that do evolve to uniformity, but for N = 5 there are two other mating systems that have a slower rate of convergence, and for N = 6 partial results show that there are many such examples.Deceased     

ESTIMATION OF PARAMETERS OF INBREEDING AND GENETIC DRIFT IN POPULATIONS WITH OVERLAPPING GENERATIONS

Many long‐lived plant and animal species have nondiscrete overlapping generations. Although numerous models have been developed to predict the effective sizes (N_e) of populations with overlapping generations, they are extremely difficult to apply to natural populations because of the large array of unknown and elusive life‐table parameters involved. Unfortunately, little work has been done to estimate the N_e of populations with overlapping generations from marker data, in sharp contrast to the situation of populations with discrete generations for which quite a few estimators are available. In this study, we propose an estimator (EPA, estimator by parentage assignments) of the current N_e of populations with overlapping generations, using the sex, age, and multilocus genotype information of a single sample of individuals taken at random from the population. Simulations show that EPA provides unbiased and accurate estimates of N_e under realistic sampling and genotyping effort. Additionally, it yields estimates of other interesting parameters such as generation interval, the variances and covariances of lifetime family size, effective number of breeders of each age class, and life‐table variables. Data from wild populations of baboons and hihi (stitchbird) were analyzed by EPA to demonstrate the use of the estimator in practical sampling and genotyping situations.     

INBREEDING AND VARIANCE EFFECTIVE SIZES FOR NONRANDOM MATING POPULATIONS

Following an inbreeding approach and assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, I have derived expressions for the inbreeding effective size, N_eI, for a finite diploid population with variable census sizes for three cases: monoecious populations with partial selfing; dioecious populations of equal numbers of males and females with partial sib mating; and unequal numbers of males and females with random mating. For the first two cases, recurrence equations for the inbreeding coefficient are also obtained, which allow inbreeding coefficients to be predicted exactly in both early and late generations. Following the variance of change in gene frequency approach, a general expression for variance effective size, N_eV, is obtained for a population with unequal numbers of male and female individuals, arbitrary family size distribution, and nonrandom mating. All the parameters involved are allowed to change over generations. For some special cases, the equation reduces to the simple expressions approximately as derived by previous authors. Comparisons are made between equations derived by the present study and those obtained by previous authors. Some of the published equations for N_eI and N_eV are shown to be incomplete or incorrect. Stochastic simulations are run to check the results where disagreements with others are involved.     

Sedimentation coefficients of DNA topoisomers: the helical wormlike chain

The sedimentation coefficient s_N of the DNA topoisomer with the linking number N is evaluated as a function of N and chain length on the basis of a (circular) twisted wormlike chain, i.e., a special case of the helical wormlike chain. Evaluation is carried out by an application of the Oseen–Burgers procedure of hydrodynamics to the cylinder model with the preaveraged Oseen tensor. The necessary mean reciprocal distance between two contour points is obtained by a Monte Carlo method. It is shown that s_N increases as |ΔN| is increased from 0 in the range of small |ΔN|, where ΔN = N ? N , with N the number of helix turns in the linear DNA chain in the undeformed state. It is found that there is semiquantitative agreement between the Monte Carlo values and the experimental data obtained by Wang for s_N.     

荒漠孑遗植物四合木对土壤古菌群落的影响

土壤是植物定居的场所,也是植物-微生物互作的重要界面。古菌是土壤微生物重要组份,在碳、氮、硫、铁等元素的生物地球化学循环和植物的生长发育、适应生境中发挥重要作用。植物定居对土壤古菌群落的影响研究鲜有开展,孑遗植物在研究植物-微生物-环境互作中具有独特的优势。采用扩增子高通量测序技术,研究以荒漠孑遗植物四合木为建群种或优势种的四合木-红砂-珍珠-针茅群落、四合木-针茅群落和四合木群落等三种荒漠植物群落类型中,四合木根区土壤和光板地土体土壤古菌群落特征,揭示四合木定居对土壤古菌物种数量、多样性、群落组成及功能的影响。结果表明,荒漠孑遗植物四合木定居不仅增加了根区土壤古菌的物种数量,提高了根区土壤古菌群落多样性,而且改变了土壤古菌群落组成,减少了奇古菌门Nitrososphaeraceae科未分类的属氨氧化古菌（unclassified_f_Nitrososphaeraceae）和暂定Nitrososphaera属氨氧化古菌（Candidatus Nitrososphaera）相对丰度,增加了Nitrososphaeraceae科暂定Nitrocosmicus属氨氧化古菌（Candidatus Nitrocosmicus）和广古菌门海洋古菌类群Ⅱ中未分类的属（norank_o_Marine_Group_II）相对丰度,广古菌门热原体纲未分类的属（unclassified_c__Thermoplasmata）相对丰度变化显著。植物群落演替对四合木根区土壤和光板地土体土壤古菌群落均无显著影响。Nitrososphaeraceae科氨氧化古菌是三种不同荒漠植物群落类型中土壤古菌的核心微生物组。四合木定居也显著改变土壤古菌群落的功能,减弱了高丰度功能,增强了低丰度功能,对有氧呼吸、核苷酸合成、氨基酸合成等途径影响显著。荒漠孑遗植物四合木定居改变了土壤古菌群落物种数量、多样性、组成、功能等特征。     

Density—body size allometry does not exist in a chironomid community on Myriophyllum

SUMMARY.

• 1 It has been proposed that population density is allometrically related to body size for a wide range of animal species. An interesting question is whether this applies to species within a specific community or trophic guild, thus constituting a ‘pattern’ of community structure.
• 2 Density-body size allometry can be translated into the relationship between population biomass (B) and population density (N). If the regression coefficient b in log B = a + b log N approximates 1, there is no allometric relation between density and body size.
• 3 Data from an epiphytic chironomid community show b～1, thus indicating that no density-body size allometry exists in this community.
• 4 Biomass is less equitably distributed than numbers among species in this and many other communities.
• 5 There is some difficulty in extending the logic of the density-body size allometry to many invertebrate communities, where body size is a strongly time-dependent, variable trait.

     

Metabarcoding as a tool for investigating arthropod diversity in Nepenthes pitcher plants

The biodiversity of tropical forests consists primarily of small organisms that are difficult to detect and characterize. Next‐generation sequencing (NGS) methods can facilitate analyses of these arthropod and microbial communities, leading to a better understanding of existing diversity and factors influencing community assembly. The pitchers of carnivorous pitcher plants often house surprisingly discrete communities and provide ideal systems for analysis using an NGS approach. The plants digest insects in order to access essential nutrients while growing in poor soils; however, the pitchers are also home to communities of living organisms, called inquilines. Certain arthropods appear to have coevolved with their pitcher plant hosts and are not found in other environments. We used Illumina amplicon sequencing of 18S rDNA to characterize the eukaryotes in three species of Nepenthes (Nepenthaceae) pitcher plants – N. gracilis, N. rafflesiana and N. ampullaria – in each of three different parks in Singapore. The data reveal an unexpected diversity of eukaryotes, significant differences in community diversity among host species, variation in host specificity of inquilines and the presence of gregarine parasites. Counts of whole inquiline arthropods from the first collection year were roughly correlated with scaled 18S sequence abundances, indicating that amplicon sequencing is an effective means of gauging community structure. We barcoded a subset of the dipteran larvae using COI primers, and the resulting phylogenetic tree is mostly congruent with that found using the 18S locus, with the exception of one of five morphospecies. For many 18S and COI sequences, the best BLASTn matches showed low sequence identity, illustrating the need for better databases of Southeast Asian dipterans. Finally, networks of core arthropods and their host species were used to investigate degree of host specificity across multiple hosts, and this revealed significant specialization of certain arthropod fauna.     

Managing genetic gain and diversity in clonal deployment of white spruce in New Brunswick,Canada

When selecting a clonal mixture for clonal forestry, a common practice is to specify a minimum acceptable genetic diversity for the mixture, and under that constraint, to maximize its genetic gain. Three selection methods—combined index selection (CIS), clonal mean selection (GMS), and family plus within-family clonal selection (FWFGS)—together with various restrictions on family contributions (family restrictions) were used to estimate gain at a given effective population size (N _e ) of clonal mixtures selected from a clonally replicated genetic test of white spruce. The designated target trait for improvement was individual tree volume at age 14 after planting. Regardless of selection method, all genetic gains were >30% at given N _e from five to 20, suggesting that implementing clonal forestry was a very effective deployment strategy. Genetic gain at a specified N _e could be enhanced by using appropriate selection methods: CIS was the most effective, followed by GMS and FWFGS. With an N _e of 15, CIS resulted in an average gain of 43.2%, which corresponded to an increase by 8.1% and 17.3% relative to GMS and FWFGS, respectively. Imposing family restriction increased gain at an N _e . Compared with the respective unrestricted selection, family restrictions increase genetic gain by 3.3%, 7.7%, and 54% for CIS, GMS, and FWFGS, respectively. The optimal family restriction level for each selection method varied with the specified N _e .     

The photosynthesis – leaf nitrogen relationship at ambient and elevated atmospheric carbon dioxide: a meta-analysis

Estimation of leaf photosynthetic rate (A) from leaf nitrogen content (N) is both conceptually and numerically important in models of plant, ecosystem, and biosphere responses to global change. The relationship between A and N has been studied extensively at ambient CO₂ but much less at elevated CO₂. This study was designed to (i) assess whether the A–N relationship was more similar for species within than between community and vegetation types, and (ii) examine how growth at elevated CO₂ affects the A–N relationship. Data were obtained for 39 C3 species grown at ambient CO₂ and 10 C3 species grown at ambient and elevated CO₂. A regression model was applied to each species as well as to species pooled within different community and vegetation types. Cluster analysis of the regression coefficients indicated that species measured at ambient CO₂ did not separate into distinct groups matching community or vegetation type. Instead, most community and vegetation types shared the same general parameter space for regression coefficients. Growth at elevated CO₂ increased photosynthetic nitrogen use efficiency for pines and deciduous trees. When species were pooled by vegetation type, the A–N relationship for deciduous trees expressed on a leaf-mass basis was not altered by elevated CO₂, while the intercept increased for pines. When regression coefficients were averaged to give mean responses for different vegetation types, elevated CO₂ increased the intercept and the slope for deciduous trees but increased only the intercept for pines. There were no statistical differences between the pines and deciduous trees for the effect of CO₂. Generalizations about the effect of elevated CO₂ on the A–N relationship, and differences between pines and deciduous trees will be enhanced as more data become available.     

Mechanistic studies on human N-acetylgalactosamine kinase

N-Acetylgalactosamine kinase (GALK2) is a small molecule kinase from the GHMP family which phosphorylates N-acetylgalactosamine at the expense of ATP. Recombinant GALK2 expressed in, and purified from, Escherichia coli was shown to be active with the following kinetic parameters: Michaelis constant for ATP, 14?±?3?μM; Michaelis constant for N-acetylgalactosamine, 40?±?14?μM; and turnover number, 1.0?±?0.1?s^?1. The combination of substrate inhibition by N-acetylgalactosamine and α-methylgalactopyranoside acting as an uncompetitive inhibitor with respect to ATP suggested that the enzyme has an ordered ternary complex mechanism in which ATP is the first substrate to bind. The effects of pH on the kinetic parameters provided evidence for ionizable residues playing a role in substrate binding and catalysis. These results are discussed in the context of the mechanisms of the GHMP kinases.     

The influence of variation in female fecundity on effective population size

Understanding the relationship between effective population size (N_e) and the number of adults in a population (N) is important for predicting genetic change in small populations. In general, N_e is expected to be close to N/2, i.e. in the range N/4-3N/4, provided that the powerful effect of population bottlenecks on reducing N_e is factored out (using the harmonic mean of N). However, some very low published estimates of N_e/N(< 0.1) raise the possibility that other factors acting to reduce N_e have been underestimated. Here one such factor, variation in female fecundity, is investigated. Its effect on N_e depends on the standardized variance in fecundity (per breeding season), a measure that is generally independent of mean fecundity. Empirical estimates of this standardized variance from 16 animal studies yielded an average value of 0.44, and a maximum value less than 1.5. To investigate the effect of such values, three kinds of fecundity variation were modelled: random (seasonal): individual; and age-related. Fixed individual differences among females reduce N_e the most. However, to reduce N_e to N/10, the resulting standardized variance must usually be 10 or more. Random differences need to be even larger to achieve the same reduction. One possible mechanism, the random loss of whole families, requires very high family mortality (90% or more). The third model, fecundity that increases linearly with age, is ineffective at causing a marked decrease in N_e. Given the finding that very unusual conditions are required to reduce N_e below N_e/10, low estimates of N_e/N need to be examined critically: the lowest published ratio, for a natural population of oysters, was found to be questionable because of possible immigration into the population by cultivated oysters.     

Adaptive characteristics of grassland community structure and leaf traits along an altitudinal gradient on a subtropical mountain in Chongqing,China

Community structure and leaf traits are important elements of terrestrial ecosystems. Changes of community structure and leaf traits are of particular use in the study of the influence of climate change on terrestrial ecosystems. Patterns of community structure (including species richness, above- and below-ground biomass) and leaf traits (including leaf mass per area (LMA), nitrogen content both on mass and area bases (N _mass and N _area), and foliar δ¹³C) from 19 grassland plots along an altitudinal transect at Hongchiba in Chongqing, China, were analyzed. Species richness along the altitudinal transect had a hump-shaped pattern. Above-ground biomass had a quadratic decrease along the altitudinal gradient whereas below-ground biomass had the opposite pattern. Change of above-ground biomass of various taxonomic groups with altitude was also studied. Poaceae showed strong negative relationships and Asteraceae showed a hump-shaped relationship with increase of altitude. Five common species of the grassland, Trifolium pratense, Geranium wilfordii, Aster tataricus, Leontopodium leontopodioides, and Spiraea prunifolia, were particularly studied for variation of leaf traits along the altitudinal gradient. Averaged for all species, LMA, N _area and foliar δ¹³C had positive correlations with altitude. N _mass did not change significantly as altitude increased. LMA and N _area showed significant positive relationships with foliar δ¹³C. The adaptive features of leaf traits among different species were not consistent. The study highlights specific adaptation patterns in relation to altitude for different plant species, provides further insights into adaptive trends of community structure and leaf traits in a specific ecological region filling a gap in the definition of global patterns, and adds to the understanding of how adaptive patterns of plants may respond to global climate change.