Bias correction of bounded location error in binary data

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.     

Methods for fitting dominance/diversity curves

Abstract. Dominance/diversity curves, displaying the relative abundances of the species within a community, have often been constructed from field data. Several ecological and statistical models of dominance/diversity have been proposed, to explain the curves. Yet, rarely have curves of different models been fitted to field data. In this paper the appropriate parameters and methods of curve fitting for plant communities are described for the General Lognormal, Canonical Lognormal, Geometric, Broken Stick, Zipf and Zipf-Mandelbrot models. Distinction is made between fixed and optimised parameters, to clarify para-meterisation of the models. It is concluded that all should be fitted by minimising the deviance in a ranked-abundance plot. Statistical tests of goodness of fit are discussed. It is concluded that consistency of fit between replicate quadrats of a community provide the best test. Curves of all the models discussed are fitted to data from a species-rich Spanish hay meadow, and to data from a New Zealand intertidal algal community. The Spanish meadow data are best fitted by General Lognormal. The New Zealand algal data are best fitted by Geometric or General Lognormal. Goodness of fit for a sample is usually relatively good or poor for all models, since much of the deviance comes from steps in the curve which none of the models can fit closely.     

Can optimal resource allocation models explain why ectotherms grow larger in cold?

Basically all organisms can be classified as determinate growers if their growth stops or almost stops at maturation, or indeterminate growers if growth is still intense after maturation. Adult size for determinate growers is relatively well defined, whereas in indeterminate growers usually two measures are used: size at maturation and asymptotic size. The latter term is in fact not a direct measure but a parameter of a specific growth equation, most often Bertalanffy's growth curve. At a given food level, the growth rate in determinate growers depends under given food level on physiological constraints as well as on investments in repair and other mechanisms that improve future survival. The growth rate in indeterminate growers consists of two phases: juvenile and adult. The mechanisms determining the juvenile growth rate are similar to those in determinate growers, whereas allocation to reproduction (dependent on external mortality rate) seems to be the main factor limiting adult growth. Optimal resource allocation models can explain the temperature-size rule (stating that usually ectotherms grow slower in cold but attain larger size) if the exponents of functions describing the size-dependence of the resource acquisition and metabolic rates change with temperature or mortality increases with temperature. Emerging data support both assumptions. The results obtained with the aid of optimization models represent just a rule and not a law: it is possible to find the ranges of production parameters and mortality rates for which the temperature-size rule does not hold.     

Kitasatospora sp. MY5-36产ε-聚赖氨酸分批补料发酵动力学

以北里孢菌(Kitasatospora sp.)MY 5-36为供试菌株,对ε-聚赖氨酸分批补料发酵动力学模型进行研究。建立了该菌株发酵合成ε-聚赖氨酸的菌体生长、产物合成和总糖消耗的动力学模型,并通过Origin 8.1软件对模型参数进行非线性拟合。结果表明:菌体量和聚赖氨酸的产量分别为16.25和13.15 g/L,产物合成与菌体生长的关系为部分耦联型。经验证,预测值与实验值有良好的拟合性,拟合度分别为0.999、0.995和0.992,说明所构建模型能够较好地反映ε-聚赖氨酸分批补料发酵过程。     

A finite-state continuous-time approach for inferring regional migration and mortality rates from archival tagging and conventional tag-recovery experiments

Spatially structured population dynamics models are important management tools for harvested, highly mobile species and although conventional tag recovery experiments remain useful for estimation of various demographic parameters of these models, archival tagging experiments are becoming an important data source for analyzing migratory behavior of mobile marine species. We provide a likelihood-based approach for estimating the regional migration and mortality rate parameters intrinsic to these models that may use information obtained from conventional tag recovery and archival tagging experiments. Specifically, we assume that the regional location and survival of animals through time is a finite-state continuous-time stochastic process. The stochastic process is the basis of probability models for observations provided by the different types of tags. Results from application to simulated tagging experiments for western Atlantic bluefin tuna show that maximum likelihood estimators based on archival tagging observations and corresponding confidence intervals perform similar to conventional tagging observations for a given number of tag releases and releasing tags in each region can improve the behavior of maximum likelihood estimators regardless of tag type. We provide an example application with Atlantic bluefin tuna released with conventional tags in 1990-1992.     

Stepwise Kinetic Equilibrium Models of Quantitative Polymerase Chain Reaction

ABSTRACT: BACKGROUND: Numerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented. RESULTS: Two models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the literature. They also give better estimates of initial target concentration. Model 1 was found to be slightly more robust than model 2 giving better estimates of initial target concentration when estimation of parameters was done for qPCR curves with very different initial target concentration. Both models may be used to estimate the initial absolute concentration of target sequence when a standard curve is not available. CONCLUSIONS: It is argued that the kinetic approach to modeling and interpreting quantitative PCR data has the potential to give more precise estimates of the true initial target concentrations than other methods currently used for analysis of qPCR data. The two models presented here give a unified model of the qPCR process in that they explain the shape of the qPCR curve for a wide variety of initial target concentrations.     

The importance of incorporating age and sex when backcalculating length in bullhead Cottus gobio

The present study backcalculated body length for a data set of a bullhead Cottus gobio population located at different sampling sites in a river network. Model comparison between various growth models, which included successively new parameters, showed the effect and importance of taking sex, age and the location in the river network into account. The data sets obtained by backcalculation were fitted by the von Bertalanffy growth function, which revealed the effect of the backcalculation formula on the estimation of the von Bertalanffy growth parameters. Fitting results and parameter estimates showed again the importance of incorporating age and sex when backcalculating body length in the C. gobio population studied.     

Inferring the diameter of a biopolymer from its stretching response

We investigate the stretching response of a thick polymer model by means of extensive stochastic simulations. The computational results are synthesized in an analytic expression that characterizes how the force versus elongation curve depends on the polymer structural parameters: its thickness and granularity (spacing of the monomers). The expression is used to analyze experimental data for the stretching of various different types of biopolymers: polypeptides, polysaccharides, and nucleic acids. Besides recovering elastic parameters (such as the persistence length) that are consistent with those obtained from standard entropic models, the approach allows us to extract viable estimates for the polymers diameter and granularity. This shows that the basic structural polymer features have such a profound impact on the elastic behavior that they can be recovered with the sole input of stretching measurements.     

Survival analysis of three clones of Brachionus plicatilis (Rotifera)

Age-specific survival schedules of females from three genetically different clones of Brachionus plicatilis were analyzed at several environmental conditions in the laboratory.Lifespan showed the expected decrease with increasing temperature, but a general trend with salinity or genotype was not observed. Probability of death increased with age, as tested by polynomial regression analysis of the survival curve and using theoretical mortality distributions. Three two-parameter models (linear-exponential model, Weibull model, and Gompertz model) were fitted to the survival data. Fitting of these models to data was rather poor, but the Gompertz model and, to a lesser extent, the Weibull model fitted the data better than the linear-exponential model. Parameters obtained from the survival curve analyses were related to other demographic parameters. A significant relationship between the shape parameter of the Gompertz model and the cohort generation time was detected, suggesting, but not proving, an effect of reproductive effort on aging.     

Application of equilibrium and mass transfer models to dynamic removal of Cr(VI) ions by Chitin in packed column reactor

The dynamic removal of hexavalent chromium by chitin flakes was studied in a packed column reactor. The values of column parameters were predicted as a function of flow rate, bed depth, particle size and inlet metal ion concentration. On evaluating the breakthrough curves, sorption isotherms were obtained and modelled according to the Langmuir, the Redlich–Peterson and the Freundlich models. Kinetic and mass transfer aspects of the dynamic removal of Cr(VI) ions by chitin were investigated using several mathematical models. Column studies showed a good correlation between the experimental data and the calculated breakthrough curves obtained by the Adams–Bohart or the Wolborska models and the Clark model. The simulation of the whole breakthrough curve was effective with the Clark model, but the breakthrough was best predicted by Adams–Bohart, or related derived models.     

Development of mathematical models (Logistic, Gompertz and Richards models) describing the growth pattern of Pseudomonas putida (NICM 2174)

Bacterial growth curve, which is asymptotic after a certain period, is described using three different mathematical models, namely, Logistic model, Gompertz model and Richards model. The equations for these three models are fitted by evaluating the mathematical parameters involved in these models. This is done by applying the method of partial sums to the data in Table 1 containing the optical density values for different cell mass at different time intervals. The sum of square of residuals between the expected optical density values and the experimental values is calculated for each of these models. In the cases tested, the Logistic model was found to be the best fit for the growth curve of Pseudomonas putida (NICM 2174) and was found to be easy to use. These results fit the data very well at 5% level for more than 70% of the readings.     

木荷种源间光合作用参数分析

基于直角双曲线修正模型估算3个不同纬度的木荷种源(开平、太平和永丰种源)光补偿点、饱和点、最大净光合速率等参数,以便为评价不同木荷种源对环境的适应能力和优良种源选择等提供科学依据。结果表明:在3个不同纬度种源中,开平种源具有最高的净光合速率、最大净光合速率和较高的表观量子效率,且其生长速率最快;太平种源光饱和点最高,但其净光合速率、表观量子效率和最大净光合速率最低,其生长速率也最低;永丰种源具有较高的净光合速率、最大净光合速率和表观量子效率,其生长速率略高于太平种源。3个不同纬度木荷种源中,南部开平种源对当地环境具有较强的适应能力和生长潜力,具有较高的推广应用价值。     

Quantitative Assessment of LNAPL Retention in Soil Porous Media

The presence of hydrocarbon contaminants in the vadose zone is a serious hazard for environment quality. Moreover, there is an urgent need for accurate and reliable knowledge of the hydraulics of hydrocarbon contaminants in porous media to enhance efficiency of NAPLs remediation methods. The objective of this study was to quantitatively assess the hydraulic properties of different porous media with petroleum, kerosene, diesel fuel, and gasoline. The related retention curves were then experimentally obtained. Parameters of the soils retention curves were obtained based on van Genuchten (1980), Brooks-Corey (1964), and Campbell (1974) retention models. The accuracy of models was then assessed by some statistics. The results indicated that, in most cases, air entry value was significantly increased in a petroleum retention curve despite the fact that it was decreased for other NAPLs. The pore size distribution parameters (i.e., n, m, λ, and 1/b) of diesel fuel, kerosene, and gasoline did not change considerably compared to water retention curve. The Leverett (1941) scaling function was adopted to scale soil-fluid retention curves data in two-phase systems. The results indicated that, except for a silty clay medium and petroleum, the Leverett (1941) J-function could scale the LNAPL retention curves based on the water retention curve data.     

Genetic parameters of traits associated with the growth curve in Segureña sheep

This paper studies the genetic importance of growth curve parameters and their relevance as selection criteria in breeding programmes of Segureño sheep. Logistic and Verhulst growth functions were chosen for their best fit to BW/age in this breed; the first showed the best general fit and the second the best individual fit. Live weights of 41 330 individuals from the historical archives of the National Association of Segureña Sheep Breeders were used in the analysis. The progeny of 1464 rams and 27 048 ewes were used to study the genetic and phenotypic parameters of growth curve parameters and derived traits. Reproductive management in the population consists in controlled natural mating inside every herd, with a minimum of 15% of the females fertilized by artificial insemination with fresh semen; with the purpose being the herd genetic connections, all herd genealogies are screened with DNA markers. Estimates of growth curve parameters from birth to 80 days were obtained for each individual and each function by the non-linear regression procedure using IBM SPSS statistics (version 21) with the Levenberg–Marquart estimation method. (Co)variance components and genetic parameters were estimated by using the REML/Animal model methodology. The heritability of mature weight was estimated as 0.41±0.042 and 0.38±0.021 with the logistic and Verhulst models, respectively, and the heritability of other parameters ranged from 0.41 to 0.62 and 0.37 to 0.61, with the models, respectively. A negative genetic correlation between mature weight and rate of maturing was found.     

Accurate mathematical models to describe the lactation curve of Lacaune dairy sheep under intensive management

Although the intensive production system of Lacaune dairy sheep is the only profitable method for producers outside of the French Roquefort area, little is known about this type of systems. This study evaluated yield records of 3677 Lacaune sheep under intensive management between 2005 and 2010 in order to describe the lactation curve of this breed and to investigate the suitability of different mathematical functions for modeling this curve. A total of 7873 complete lactations during a 40-week lactation period corresponding to 201 281 pieces of weekly yield data were used. First, five mathematical functions were evaluated on the basis of the residual mean square, determination coefficient, Durbin Watson and Runs Test values. The two better models were found to be Pollott Additive and fractional polynomial (FP). In the second part of the study, the milk yield, peak of milk yield, day of peak and persistency of the lactations were calculated with Pollot Additive and FP models and compared with the real data. The results indicate that both models gave an extremely accurate fit to Lacaune lactation curves in order to predict milk yields (P = 0.871), with the FP model being the best choice to provide a good fit to an extensive amount of real data and applicable on farm without specific statistical software. On the other hand, the interpretation of the parameters of the Pollott Additive function helps to understand the biology of the udder of the Lacaune sheep. The characteristics of the Lacaune lactation curve and milk yield are affected by lactation number and length. The lactation curves obtained in the present study allow the early identification of ewes with low milk yield potential, which will help to optimize farm profitability.     

The dose-response relationships for myeloid leukemia and malignant lymphoma in BC3F1 mice

The present analysis of data on the induction of lymphoma and myeloid leukemia in BC3F1 mice has indicated some new and interesting aspects regarding the shapes of the dose-effect curves. The incidence data can be interpreted by radiobiological models of the induction process coupled with cell inactivation. In particular, for malignant lymphoma the dose-response curve after X rays can be described assuming a quadratic model corrected for cell inactivation, while the incidence data after fission neutrons are best fitted by a linear model which also allows for cell inactivation. Myeloid leukemia has also been induced in BC3F1 mice. The bell-shaped dose-response curves observed after irradiation with either X rays or neutrons are explained by assuming simultaneous initial transforming events and cell inactivation with the data for cell inactivation at higher doses being in agreement with data reported for other strains of mice. A value for relative biological effectiveness of 4 is obtained at the lowest neutron dose used. The value of the inactivation parameters can be compared with those of the cell inactivation probability per unit dose for the bone marrow hematopoietic stem cells, which are believed to be the target cells for these tumors.     

几种光合作用光响应典型模型的比较研究

光响应曲线是判定植物光合效率的重要方法,通过曲线可以获得植物光合特性的相关生理参数,但不同模型提取的光响应参数和指标存在差异。本文选择直角双曲线、非直角双曲线和两种指数曲线模型,分别对3个品系常绿杨光响应数据进行拟合,提取了各光响应曲线模型的主要特征参数,对比分析了各模型参数问的差异,并对光饱和点（LSP）的不同计算方法进行了讨论。最后用巨尾桉光响应数据对分析结果作了进一步验证。结果表明,直角和非直角双曲线模型拟合的最大净光合速率（P＇max）、表观量子效率（a）及暗呼吸速率（Rd）值高于指数模型拟合值,且直角双曲线拟合的各参数均比非直角双曲线拟合的各参数的值大,而两指数模型各参数拟合值基本一致;在LSP计算方法中,用光通量200μmol·m^-2·s^-1以下的点拟合的Pn-I直线与其它模型相结合得到光饱和点的方法不可靠,会使计算结果明显偏小,用接近最大总光合速率Pmax一定比例的方法估计LSP也存在较大偏差,而P＇max由于消除了Rd的影响,计算光饱和点时各模型的估计比例相对固定,是一个比较理想的LSP估计方法,初步得出直角、非直角及指数模型用P＇max来估计光饱和点时应选取的比例分别为（78±1）％、（82±1）％及（96±1）％。     

Estimation of non-linear growth models by linearization: a simulation study using a Gompertz function

A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.     

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. A simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rock lobsters to assess the possible seasonal effect on growth.     

Fitting growth curve models to longitudinal data with missing observations.

We discuss the analysis of growth curve data with missing or incomplete information. The approach is to fit subject-specific models and then to carry out an analysis in terms of the estimated parameters. This achieves reduction of data and eliminates the need for special considerations for subjects with missing data. Although there is no perfect substitute for complete data, our approach provides a way to handle missing data using a straightforward application of well-known statistical methodology.