Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values

Several theorems on estimation and verification of linear hypotheses in some Zyskind-Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ²V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ²V, where σ² is unknown scalar parameter, V is a known non-negative definite matrix such that R(X) ? R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind-Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y y₁ y₂ involves a vector y₁ of m missing values and a vector y₂ with (n — m) observed values. A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind-Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented. The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ²I) to ZM model. Estimation of vector y₁ (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ² (cf. th. 3.4) in actual ZMa model and in diagonal quasi-ZM model (ZMqd) are presented. Relation between y? ₁ and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.     

Age‐specific mortality analysis of the dry forest kissing bug,Rhodnius neglectus

Age‐specific mortality patterns can be very different across insects with different life histories. Some holometabolous insects (like mosquitoes, fruit flies) show a pattern where mortality rate decelerates at older ages, whereas other holometabolous insects (bruchid beetles) and hemimetabolous insects (cotton stainers, milkweed bugs, and kissing bugs) show an age‐specific mortality pattern that increases through all ages. Kissing bugs are strictly hematophagous and are vectors of Trypanosoma cruzi Chagas, the etiologic agent of Chagas disease. Here, we tested whether cohort data from the dry forest kissing bug, Rhodnius neglectus Lent (Hemiptera: Reduviidae), supports an increase of mortality rate that decelerates with age. We analyzed the age‐specific mortality pattern of a cohort of 250 individuals of R. neglectus. We used a suite of seven models with different degrees of complexity, to model age‐dependent forms of change in mortality rate increase in R. neglectus in the laboratory. We used the Akaike model selection criterion to choose between models that consider absence or presence of mortality deceleration. Five of the seven models (logistic, Gavrilovs, Gompertz, DeMoivre, and exponential) showed a statistically significant fit to the mortality rate. Weak late‐age mortality deceleration in R. neglectus was supported by the best fit (logistic model), and this result is consistent with predictions of the disposable soma theory of senescence.     

Improving Bayesian isotope mixing models: a response to Jackson et al. (2009)

We recently described a Bayesian framework for stable isotope mixing models and provided a software tool, MixSIR, for conducting such analyses (Ecol. Lett., 2008; 11 :470). Jackson et al. (Ecol. Lett., 2009; 12:E1) criticized the performance of our software based on tests using simulated data. However, their simulation data were flawed, rendering claims of erroneous behaviour inaccurate. A re‐evaluation of the MixSIR source code did, however, uncover two minor coding errors, which we have fixed. When data are correctly simulated according to eqns  (1)–(4) in Jackson et al. (2009) , MixSIR consistently and accurately estimated the proportional contribution of prey to a predator diet, and was surprisingly robust to additional unquantified error. Jackson et al. (2009) also suggested we use a Dirichlet prior on the source proportion parameters, which we agree with. Finally, Jackson et al. (2009) propose adding additional error parameters to our mixing model framework. We caution that such increases in model complexity should be evaluated based on data support.     

The role of a transient potassium current in a bursting neuron model

Presented here is a biophysical cell model which can exhibit low-frequency repetitive activity and bursting behavior. The model is developed from previous models (Av-Ron et al. 1991, 1993) for excitability, oscillations and bursting. A stepwise development of the present model shows the contribution of a transient potassium current (I _A ) to the overall dynamics. By changing a limited set of model parameters one can describe different firing patterns; oscillations with frequencies ranging from 2–200 Hz and a wide range of bursting behaviors in terms of the durations of bursting and quiescence, peak firing frequency and rate of change of the firing frequency.     

Multiscale model intercomparisons of CO2 and H2O exchange rates in a maturing southeastern US pine forest

We compared four existing process‐based stand‐level models of varying complexity (physiological principles in predicting growth, photosynthesis and evapotranspiration, biogeochemical cycles, and stand to ecosystem carbon and evapotranspiration simulator) and a new nested model with 4 years of eddy‐covariance‐measured water vapor (LE) and CO₂ (Fc) fluxes at a maturing loblolly pine forest. The nested model resolves the ‘fast’ CO₂ and H₂O exchange processes using canopy turbulence theories and radiative transfer principles whereas slowly evolving processes were resolved using standard carbon allocation methods modified to improve leaf phenology. This model captured most of the intraannual variations in leaf area index (LAI), net ecosystem exchange (NEE), and LE for this stand in which maximum LAI was not at a steady state. The model comparisons suggest strong linkages between carbon production and LAI variability, especially at seasonal time scales. This linkage necessitates the use of multilayer models to reproduce the seasonal dynamics of LAI, NEE, and LE. However, our findings suggest that increasing model complexity, often justified for resolving faster processes, does not necessarily translate into improved predictive skills at all time scales. Additionally, none of the models tested here adequately captured drought effects on water and CO₂ fluxes. Furthermore, the good performance of some models in capturing flux variability on interannual time scales appears to stem from erroneous LAI dynamics and from sensitivity to droughts that injects unrealistic flux variability at longer time scales.     

一种模型模拟结果的统计检验方法

模拟结果的准确性是衡量生态学模型是否成功的关键,但采用统计学方法判别模型模拟结果与观察值相符程度的报道较少。根据两个直线回归方程能否合并为一个方程的统计学检验方法,提出了通过检验观察值与模拟值直线回归方程和1∶1直线方程截距与斜率是否相同,进而在统计显著水平上判断生态学模型模拟值与观察值一致性的统计学检验方法。数据检验表明,此方法可以较好解决判断生态学模型模拟结果准确性的问题。     

Eggsac development rates and phenology of agrobiont linyphiid spiders in relation to temperature

Spider densities are often low after winter in annual crops, and crop management decimates spider populations several times per year. Population recovery rates and phenology depend on reproductive and development rates, which in turn are driven largely by temperature. We aimed to quantify the relationships between eggsac development rates and temperature in order to understand the relative value of different linyphiid species for the biological control of agricultural pests. Female adults of nine linyphiid species were collected from winter wheat in the UK over 3 years; Bathyphantes gracilis (Blackwall), Erigone atra (Blackwall), Erigone dentipalpis (Wider), Erigone promiscua O.P.‐Cambridge), Tenuiphantes tenuis (Blackwall) [formerly Lepthyphantes tenuis (Blackwall)], Meioneta rurestris (C.L. Koch), Oedothorax apicatus (Blackwall), Oedothorax fuscus (Blackwall), and Oedothorax retusus (Westring). These are agrobiont species that are dominant in agroecosystems. We tested how well development in the field can be predicted on the basis of laboratory experiments. We also built a simple phenology simulation model to test whether spider phenology in the field can be predicted by a general knowledge of the relationship between temperature and development rate. The relationships between temperature and development rates of eggsacs were not linear as described by a day‐degree model, but exponential as described by a biophysical model. Duration of the eggsac development period in the field was predicted accurately from laboratory experiments. We only found minor differences between development thresholds of eggsacs at constant temperatures compared with fluctuating temperatures. The phenology model predicted the phenology of L. tenuis and E. atra well, but the number of generations predicted for O. fuscus was not realised in the field. This suggests that development of this species may be affected by factors other than temperature. The methods used here could also be applied to other natural enemies, to determine whether their thermal biology is conducive to a role as biocontrol agents in disturbed agricultural systems.     

THEORY OF MAST REPRODUCTION IN PLANTS: STORAGE-SIZE DEPENDENT STRATEGY

The amount of available resource can be considered to restrict mast seeding behavior in plants, regardless of the cause of masting itself. The reproductive strategy of a plant that has stopped growing, but continues to maintain a constant size, is based on the allocation of assimilated resources between reproduction and storage. If both plant death and population growth rates are constant, the plant strategy is dependent only on its own storage size. Conditions for the evolution of mast reproduction were analyzed under both constant and varying environments, from the view point of storage-size dependent strategy, which is influenced by three parameters: the advantage coefficient of mast seeding, β; the cost coefficient of delayed seeding, γ; and the assimilation rate, P. The model indicated that: (1) mast seeding evolves only with a greater than linear increase in reproductive success with effort (β > 1) under both constant and varying environments; (2) in mast seeding, a critical storage size, S_c*, occurs, above which plants utilize all storage for reproduction; (3) in a constant environment, S_c* increases with increasing β and P and/or decreasing γ; (4) concomitant with (3), an intermasting period, τ, also increases with increasing β and decreasing 7, but is independent of P; (5) in a varying environment, S_c* and the average of τ increase with increasing variance of the assimilation rate, P; and (6) concomitant with (5), the intermasting period has a certain probability distribution. In addition, reproductive synchrony within the population and the relationship between mast seeding and species diversity are discussed.     

Chromosomes and the origins of apes and australopithecins

Comparison of molecular data suggests that the higher apes (Gorilla, Pan) and humankind (Homo) are closely related and that they diverged from the common ancestor through two speciation events situated very closely together in time. Examination of the chromosomal formulas of the living species reveals a paradox in the distribution of mutated chromosomes which can only be resolved by a model of trichotomic diversification. This new model of divergence from the common ancestor is characterized by the transition from (1) a monotypic phase to (2) a polytypic phase of three sub-species — pre-gorilla, pre-chimpanzee and preaustralopithecine. The quadruped ancestors ofAustralopithecus appear to have been one of the three components of the common ancestor. The question is whetherramidus is an australopithecine or a pre-australopithecine representative of the common ancestor. The new model of diversification of the common ancestor is resituated in the paleogeographic and paleoclimatic context which, through the north-south pattern of extension of aridity, provides a coherent scenario for the formation of extant species and subspecies of theGorilla andPan genera.     

Ecological Risk Assessment of DDT Accumulation in Aquatic Organisms of Taihu Lake,China

DDT (Dichlorophenyltrichloroethane) is a toxic, ubiquitous, and persistent bioaccumulative pollutant in the global environment. Although its use as an insecticide has been banned in China since 1983, residual DDT levels in the Taihu Lake are evident. Aimed at the protection of fish resources, three species of high-value fish in the Taihu Lake (Protosalanx hylocranius (Abbott), Salangichthys tangkahkeii (Wu), and Coilia nasus Temminck et Schlegel) were selected and an ecological risk assessment was used to estimate the DDT threats to fish populations. Based on a food web model, a bioaccumulation model was used to estimate the DDT concentration in zooplankton, benthos, and fish and the Monte Carlo (MC) simulation method was used to analyze the uncertainty in the bioaccumulation process. Then the chronic toxicity dose-response relationship of DDT on the Protosalanx hyalocranius (Abbott) population, estimated by ICE and ACE software, was used to calculate the mortality rates in different fish stages with the DDT concentrations. Last, the demographic modeling (Leslie matrix) was used to assess the ecological risk of DDT damage on the Protosalanx hyalocranius (Abbott) population. The results show that the estimated DDT concentrations in benthos and zooplankton were 0.14–16.56 μ g/kg, 2.15–99.30 μ g/kg, respectively. The fish DDT concentration results are a series of increasing curves and the maximal values reach 266, 101, and 211 μ g/kg for Protosalanx hylocranius (Abbott), Salangichthys tangkahkeii (Wu), and Coilia nasus Temminck et Schlegel, respectively. In the process of ecological risk quantization, a 4.06–7.25% reduction in the biomass of the Protosalanx hyalocranius (Abbott) population was estimated in 10,000 MC imulations and 4.21%, 4.89%, and 5.69% reductions were estimated in 75%, 50%, and 25% probability, respectively.     

A neural network model for estimating O2 absorption coefficient in shake-flasks

A comprehensive, simple, neural network model was constructed to replace the common semi-empirical mathematical models used for predicting individual O₂ absorption coefficients (K _L a) within Erlenmeyer and Hinton shake-flasks. Different factors that influence K _L a within shake-flasks, such as flask dimensions, working volumes, baffle-heights, and shaking speeds, were investigated and the experimental results employed to deduce the mathematical model for each type of shake-flask. Meanwhile, the K _L a values calculated from the mathematical models were used to derive a non-linear neural network estimator (NNE). The NNE for K _L a prediction was implemented to evaluate the O₂ absorption effect within the flasks and gave a promising result.     

Coccoid Helicobacter pylori Not Culturable In Vitro Reverts in Mice

An experimental rodent model was used to demonstrate the viability of the coccoid form of Helicobacter pylori. Concentrated suspensions were prepared for the two different morphologies: at 2 days incubation for the bacillary forms and at 20 days incubation for the “dormant” forms. The strains used for incubation were two fresh isolates from humans with duodenal ulceration, and two collection strains. Five hundred microliters of culture (OD₅₅₀ = 5 Mc Farland) of Helicobacter pylori with bacillary (2-5×10⁹ CFU/ml) and coccoid (0 CFU/ml) morphology were inoculated intragastrically in BALB/c mice. The gastric mucosa of the mice was colonized by Helicobacter pylori with the administration of fresh bacillary and coccoid cultures and not with the established cultures. Helicobacter pylori was isolated at 1 week after inoculation with the administration of fresh bacillary cultures, while fresh coccoid Helicobacter pylori was recovered in mice stomachs after 2 weeks of inoculation. After colonization, histopathologic changes occurred after 1 month from inoculation; all colonized mice showed a systemic antibody response to Helicobacter pylori. These results support the thesis of the viability of coccoid Helicobacter pylori non-culturable in vitro and confirm that concentrated bacterial suspensions are able to colonize and to produce gastric alterations in this suitable animal model.     

Model Construction and Model Examination on the Basis of Simulated Selection

By reason nonlinear relations founded between selection differential and realised selection response we have been made investigations about variants of the genetic-statistical model, which include this nonlinearity. The variations of the model would not only referred to the postulate pattern of the connection between phenotype, genotype and environment but also enclosed the postulate assumption about the distribution of the variates. In an investigated special case the linear model equation P = G ± e was held, however the distributions of P and G were defined over a limited range in one direction. For P we have defined a modified normal distribution and the distribution of the random vector (G, e) non normal regarded with cov (G, e) ≠ 0, By means of a solution set of an integral equation a density function of the random vector (P, G) has been received, in which the expectation of the selection response of the usual genetic-statistical model approximate is included as a special case. The genetical parameters has been derived, which result from changed model. However their representation was only possible partially as an integral function. A subsequent paper informs of the examination this mode! variants, which depend on a parameter of the nonlinearity c.     

Relationships between change in fire frequency and mortality due to spruce budworm outbreak in the southeastern Canadian boreal forest

Abstract. We present a simple empirical model that allows an estimation of mortality due to spruce budworm (Choristoneura fumiferana) outbreak in relation to fire frequency and site characteristics. The occurrence of a recent spruce budworm outbreak around Lake Duparquet (48° 30’N, 79° 20’W, ca. 300 m a.s.l.) in northwestern Québec permitted a reconstruction of the stand composition before the outbreak, and also of the mortality of Abies balsamea due to the outbreak. The basal area of A. balsamea increases with time since fire in all site types but with increasing values for (1) rock and shallow till, via (2) till and mesic clay up to (3) hydric clay. Mortality (measured as percentage loss of basal area due to the outbreak) increases with time since fire but did not vary with site type. The increasing abundance of A. balsamea with time since fire is mainly responsible for this increase in mortality. Mortality for a specific basal area is, however, lower for the more recently burned stands suggesting a significant residual effect of time since fire. A landscape model integrating mortality due to the outbreak for stands of different age is developed. Both absolute and relative losses of basal area increased with the length of the fire cycles. According to this model, changes in fire cycle could explain a large portion of the spatio-temporal variations observed in outbreak mortality in the southeastern boreal forest of Canada.     

A Mixed Model for Binary Data: The Modified X2-test

In this paper, a statistical model for clinical trials is presented for the special situation that a varying and unstructered number of binary responses is obtained from each subject. The assumptions of the model are the following: 1.) For each subject there is a (constant) individual Bernoulli parameter determining the distribution of the binary responses of this subject. 2.) The Bernoulli parameters associated with the subjects are realizations of independent random variables with distributions P_g in treatment group g(g = 1, 2, …, G). 3.) Given the value of the Bernoulli parameter, the observations are stochastically independent within each subject. Under these assumptions, a test statistic is derived to test the hypothesis H₀:E(P₁) = E(P₂) = … = E(P_G). It is proven and demonstrated by simulations, that the test statistic asymptotically (i.e. for a large number of subjects) follows the X²-distribution.     

THE EFFECTIVE SIZE OF A HIERARCHICALLY STRUCTURED POPULATION

A knowledge of the effective size of a population (N_e) is important in understanding its current and future evolutionary potential. Unfortunately, the effective size of a hierarchically structured population is not, in general, equal to the sum of its parts. In particular, the inbreeding structure has a major influence on N_e. Here I link N_e to Wright's hierarchical measures of inbreeding, F_IS and F_ST, for an island-structured population (or metapopulation) of size N_T. The influence of F_ST depends strongly on the degree to which island productivity is regulated. In the absence of local regulation (the interdemic model), interdemic genetic drift reduces N_e. When such drift is combined with local inbreeding under otherwise ideal conditions, the effects of F_IS and F_ST are identical: increasing inbreeding either within or between islands reduces N_e, with N_e = N_T/[(1 + F_IS)(1 + F_ST) ? 2F_ISF_ST]. However, if islands are all equally productive because of local density regulation (the traditional island model), then N_e = N_T/[(1 + F_IS)(1 –F_ST)] and the effect of F_ST is reversed. Under the interdemic model, random variation in the habitat quality (and hence productivity) of islands act to markedly decrease N_e. This variation has no effect under the island model because, by definition, all islands are equally productive. Even when no permanent island structure exists, spatial differences in habitat quality can significantly increase the overall variance in reproductive success of both males and females and hence lower N_e. Each of these basic results holds when other nonideal factors are added to the model. These factors, deviations from a 1:1 sex ratio, greater than Poisson variance in female reproductive success, and variation in male mating success due to polygynous mating systems, all act to lower N_e. The effects of male and female variance on N_e have important differences because only females affect island productivity. Finally, it is noted that to use these relationships, F_IS and F_ST must be estimated according to Wright's definition (and corrected to have a zero expectation under the null model). A commonly used partitioning (θ, θ_g) can be biased if either island size or the number of islands is small.     

Diagnosing and assessing uncertainties of terrestrial ecosystem models in a multimodel ensemble experiment: 1. Primary production

We conducted an ensemble modeling exercise using the Terrestrial Observation and Prediction System (TOPS) to evaluate sources of uncertainty in carbon flux estimates resulting from structural differences among ecosystem models. The experiment ran public‐domain versions of biome‐bgc, lpj, casa , and tops‐bgc over North America at 8 km resolution and for the period of 1982–2006. We developed the Hierarchical Framework for Diagnosing Ecosystem Models (HFDEM) to separate the simulated biogeochemistry into a cascade of three functional tiers and sequentially examine their characteristics in climate (temperature–precipitation) and other spaces. Analysis of the simulated annual gross primary production (GPP) in the climate domain indicates a general agreement among the models, all showing optimal GPP in regions where the relationship between annual average temperature (T, °C) and annual total precipitation (P, mm) is defined by P=50T+500. However, differences in simulated GPP are identified in magnitudes and distribution patterns. For forests, the GPP gradient along P=50T+500 ranges from ～50 g C yr^?1 m^?2 °C^?1 (casa ) to ～125 g C yr^?1 m^?2 °C^?1 (biome‐bgc ) in cold/temperate regions; for nonforests, the diversity among GPP distributions is even larger. Positive linear relationships are found between annual GPP and annual mean leaf area index (LAI) in all models. For biome‐bgc and lpj , such relationships lead to a positive feedback from LAI growth to GPP enhancement. Different approaches to constrain this feedback lead to different sensitivity of the models to disturbances such as fire, which contribute significantly to the diversity in GPP stated above. The ratios between independently simulated NPP and GPP are close to 50% on average; however, their distribution patterns vary significantly between models, reflecting the difficulties in estimating autotrophic respiration across various climate regimes. Although these results are drawn from our experiments with the tested model versions, the developed methodology has potential for other model exercises.     

A genome‐wide association study suggests several novel candidate genes for carcass traits in Chinese Simmental beef cattle

A genome‐wide association study (GWAS) was conducted for two carcass traits in Chinese Simmental beef cattle. The experimental population consisted of 1301 individuals genotyped with the Illumina BovineHD SNP BeadChip (770K). After quality control, 671 990 SNPs and 1217 individuals were retained for the GWAS. The phenotypic traits included carcass weight and bone weight, which were measured after the cattle were slaughtered at 16 to 18 months of age. Three statistical models—a fixed polygene model, a random polygene model and a composite interval mapping polygene model—were used for the GWAS. The genome‐wide significance threshold after Bonferroni correction was 7.44E‐08 (= 0.05/671 990). In this study, we detected eight and seven SNPs significantly associated with carcass weight and bone weight respectively. In total, 11 candidate genes were identified within or close to these significant SNPs. Of these, we found several novel candidate genes, including PBX1, GCNT4, ALDH1A2, LCORL and WDFY3, to be associated with carcass weight and bone weight in Chinese Simmental beef cattle, and their functional roles need to be verified in further studies.     

A Parameter-Elimination Method for Nonlinear Regression with Linear Parameters and Autocorrelated Errors

In this study, we are interested in the problem of estimating the parameters in a nonlinear regression model when the error terms are correlated. Throughout this work, we restrict ourselves to the special case when the error terms follow a pth order stationary autoregressive model (AR(p)). Following the idea of LAWTON and SYLVESTRE (1971) and GALLANT and GOEBEL (1976), a parameter-elimination method is proposed, which has the advantages that it is not sensitive to the initial values and convergence of the procedure may be more stable because of the reduced dimension of the problem. The parameter-elimination method is compared with the methods by GALLANT and GOEBEL (1976) and GLASBEY (1980) by Monte Carlo Simulation, and the results of applying the first two methods to the real data obtained from the Environmental Protection Administration of the Executive Yuan of the Republic of China are presented.