论Richards增长曲线

本文给出了Ｒｉｃｈａｒｄｓ增长曲线一个很好的解析表达式,它使得Ｌｏｇｉｓｔｉｃ增长曲线、Ｇｏｍｐｅｒｔｚ增长曲线与Ｒｉｃｈａｒｄｓ增长曲线之间的关系清晰了,提示了著名的Ｌｏｇｉｓｔｉｃ增长曲线与Ｇｏｍｐｅｒｔｚ增长曲线是Ｒｉｃｈａｒｄｓ增长曲线的特殊情形,而且还给出了Ｒｉｃｈａｒｄｓ增长曲线一些很好的特性。     

Gompertz曲线与logistic增长曲线之比较

本文给出了生物增长模型中常用的logistic曲线与Gompertz曲线之间的主要差异与相似处．     

The Ontogenetic Interpretation of the Growth Curve of Vertebral Organisms

The growth curve of vertebral organism can be resolved into four different phases according to four different states of ontogenesis.     

Analysis of experimental data with repeated measurements

Summary. Experimental data often consist of serial measurements on subjects after a treatment. Typical questions concerning such data are: (A) Do subjects really react to treatment or are the fluctuations just random? (B) What are the numerical characteristics of the response? (C) Is the response identical in all groups? Differences between the individuals in the dynamics of the reaction make it difficult to apply standard statistical procedures. This paper proposes to answer questions (A) and (B) at the individual level, then to give an answer to (C) on the basis of this information. This kind of analysis may be useful since it can separate subjects giving response from those that do not and can identify individual response patterns and compare treatments with respect to each numerical characteristic separately. To answer question (A), a permutation test is proposed and its power is evaluated by simulation.     

哺乳动物存活曲线类型的分析方法探讨

动物的存活曲线通常可分为3种类型：凸型（Ⅰ型或A型）、直线型（Ⅱ型或B型）和凹型（Ⅲ型或C型）。存活率曲线与存活曲线在概念上有一定的区别。存活率要经过对数转换（或者直接采用对数标尺）后才能得到存活曲线类型,从动物的存活率曲线上直接判读存活曲线类型可能会导致错误的结论。鉴于存活曲线分析研究中出现的问题,建议在进行物种存活曲线类型的分析时,务必先进行对数转换。     

Discrimination measures for survival outcomes: connection between the AUC and the predictiveness curve

Finding out biomarkers and building risk scores to predict the occurrence of survival outcomes is a major concern of clinical epidemiology, and so is the evaluation of prognostic models. In this paper, we are concerned with the estimation of the time-dependent AUC--area under the receiver-operating curve--which naturally extends standard AUC to the setting of survival outcomes and enables to evaluate the discriminative power of prognostic models. We establish a simple and useful relation between the predictiveness curve and the time-dependent AUC--AUC(t). This relation confirms that the predictiveness curve is the key concept for evaluating calibration and discrimination of prognostic models. It also highlights that accurate estimates of the conditional absolute risk function should yield accurate estimates for AUC(t). From this observation, we derive several estimators for AUC(t) relying on distinct estimators of the conditional absolute risk function. An empirical study was conducted to compare our estimators with the existing ones and assess the effect of model misspecification--when estimating the conditional absolute risk function--on the AUC(t) estimation. We further illustrate the methodology on the Mayo PBC and the VA lung cancer data sets.     

ADJUSTABILITY OF THE CIRCADIAN CLOCK IN THE COCKROACHES: A COMPARATIVE STUDY OF TWO CLOSELY,RELATED SPECIES,BLATTELLA GERMANICA AND BLATTELLA BISIGNATA

A single 2h light pulse (250 lux) was given at various times to phase shift the locomotor circadian rhythm of two species of closely related cockroaches, Blattella bisignata and Blatella germanica. The phase-response curve (PRC) of both species showed a similar pattern. Phase delays and advances were induced by light pulse during the early and late subjective night, respectively, while no clear phase shifting was elicited during the subjective day. However, the magnitude of the phase delay (1.89h ± 0.66h) and advance (0.69h ± 0.36h) of B. bisignata was significantly larger than that of B. germanica (0.78h ± 0.38h and 0.35h ± 0.18h, respectively). This result indicates the superior adjustability of the circadian clock in B. bisignata. The periodresponse curve (PdRC) was also constructed for both species. Although both species did not show great flexibility in circadian period changes, the phase shifts were significantly correlated with the period changes in the advance zone of B. bisignata (r = 0.72, P <. 1). This allowed the circadian clock of B. bisignata to display better entrainability since the phase advance adjustment was significantly more difficult than that of phase delay. The results indicate the overall adjustability of the circadian clock of B. germanica is inferior to that of B. bisignata. The significance of this finding is discussed from an ecological perspective. (Chronobiology International, 18(5), 767– 780, 2001)     

Speed stability in birds

Solutions for the speed stability problem in bird flight at low speed are developed. Speed stability is usually considered not to exist in flapping flight at speeds below the speed of the minimum power required, and in gliding flight below the speed for maximum range. Approaches thus far for solving the speed stability problem are relating to a 1-degree-of-freedom model of the bird where the speed is regarded as the only motion variable involved. However, a speed deviation is inherently associated with a deviation in the height. In this paper, an expanded treatment with an appropriate mathematical model is presented. The expanded treatment is based on a 2-degree-of-freedom model of the bird. Thus, it is possible to account for the speed and the height changes. With this expanded treatment, it can be shown that there is speed stability in the gliding flight of birds, whether the speed is below the speed for maximum range or above. This also holds for flapping flight with regard to speeds below the speed of the minimum power required. Further, it is shown that there can be speed instability if the bird acts as a controller to suppress height deviations. For this purpose, a model of the bird acting as a controller is presented.     

CIRCADIAN PHASE AND PERIOD RESPONSES TO LIGHT STIMULI IN TWO NOCTURNAL RODENTS

We report period response curves (τRC) for two nocturnal Murid species from India, Mus booduga and Mus platythrix. We further discuss the method of phase shift estimation in the presence of τ-changes, because such changes pose a serious methodological problem in the estimation of phase shifts. Although the τRC indicates that most of the phase shifts are associated with small changes in τ, the period changes across all the phases showed a significant positive correlation with the phase shifts. We conclude that τRCs are a reality even in nocturnal mammals, although their amplitude is less than what is usually found in diurnal mammals, and requires a larger data set to be distinguished from noise.     

Circadian phase and period responses to light stimuli in two nocturnal rodents

We report period response curves (τRC) for two nocturnal Murid species from India, Mus booduga and Mus platythrix. We further discuss the method of phase shift estimation in the presence of τ-changes, because such changes pose a serious methodological problem in the estimation of phase shifts. Although the τRC indicates that most of the phase shifts are associated with small changes in τ, the period changes across all the phases showed a significant positive correlation with the phase shifts. We conclude that τRCs are a reality even in nocturnal mammals, although their amplitude is less than what is usually found in diurnal mammals, and requires a larger data set to be distinguished from noise.     

星形胶质细胞的体外生长特性

目的研究纯化培养的星形胶质细胞的体外生长特性,作为进一步研究星形胶质细胞功能的依据。方法将纯化的星形胶质细胞分为6h、12h、18h、24h、30h、36h、42h、48h、54h、60h、72h、84h、96h、120h14个时间组,培养不同的时间后,采用细胞计数法绘制细胞生长曲线观察细胞的生长状况,用流式细胞学检测细胞周期各时相的变化并绘制增殖指数曲线,所得数据用SPSS软件进行统计学分析。结果①星形胶质细胞的生长曲线可明显的分为三个阶段:第一阶段为0至24h,在此时间内生长曲线平缓上升,其斜率为0.64。第二阶段为24h至84h,在此时间内生长曲线急剧上升,其斜率为2.69;此阶段中24h至48h时曲线最陡,斜率为3.94,细胞呈指数生长。第三阶段为84h至120h,在此时间内生长曲线走势平直,其斜率为-0.005。②星形胶质细胞的增殖指数在第一个细胞增殖周期内可以反映细胞的增殖状态,第一个细胞周期结束后,细胞的数量继续上升增殖指数却降低了。结论培养的星形胶质细胞的生长过程分为潜伏期、指数生长期和停滞期三个阶段,其潜伏期为0至24h,指数生长期为24h至48h,停滞期为84h以后。单纯用增殖指数等类似的指标作为细胞增殖状态的判断标准是有一定局限性的,一定要将这些指标与细胞数量结合起来分析。     

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.     

海南岛霸王岭不同热带森林类型的种-个体关系

 比较分析了海南岛霸王岭自然保护区核心区热带低山雨林、山地雨林、云雾林、山地矮林等4种热带森林类型中不同大小径级树木的物种—个体关系。结果表明：各种植被类型中物种数与个体数对数成线性关系是一种普遍现象,且不受调查树木的径木级影响。在相同个体数的条件下,累积物种数随海拔增高而逐渐减少,也即物种数由热带低山雨林、山地雨林、云雾林到热带山地矮林逐渐减少。对于各种植被类型的种—多度关系,单个体、双个体的物种有相当高的比例,其后一般依个体数的增加,而逐渐降低物种的出现频率,呈典型的倒J型曲线,而且这一比例随树木径级的增加而增加。     

实时荧光定量PCR技术综述

实时荧光定量PCR技术是在PCR技术基础上发展起来的一种高度灵敏的核酸定量技术。与传统PCR相比,实时定量PCR能够更加快速、灵敏,并有效地对核酸进行定量检测。     

Curve fitting of germination data using the Richards function

Abstract. The fitting of the generalized Richards function to germination data by using two nested iterative and least squares regression procedures to estimate the four parameters (all of which can be associated with features of biological growth) is demonstrated. The program also involves a procedure of parallel curve analysis which makes comparisons between two curves by examining the whole process represented by the curve and not just a point or portion thereof. Excellent agreement between observed and expected values was obtained by analyzing data which defined patterns of germination exhibiting a range of rates and final percentages. The program also calculates a number of derived quantities including maximum daily rate of germination and time to 50% of final germination.     

岩黄连光合与蒸腾特性及其对光照强度和CO_2浓度的响应

采用LI-6400便携式光合测定系统(Li-CorInc.,USA)对岩黄连叶片的气体交换进行了测定。结果表明(1)岩黄连叶片的光饱和点(LSP)为329.18μmol.m-2.s-1左右,光补偿点(LCP)为12.76μmol.m-2.s-1,最大净光合速率为2.96μmol.m-2.s-1,暗呼吸速率(Rd)为0.17μmol.m-2.s-1。光饱和点和光补偿点都比效低,表明岩黄连对光照的要求不高,属于阴生植物。(2)4月份,岩黄连Pn随CO2浓度升高而逐渐增大。当CO2浓度由50μmol.mol-1增加到600μmol.mol-1,Pn几乎呈直线上升,600~1000μmol.mol-1范围内逐渐缓和,到1000μmol.mol-1以后Pn变化平稳。由曲线估算CO2饱和点(CSP)大约在1000μmol.mol-1左右。CO2的补偿点为68.80μmol.mol-1。羧化效率为0.0308μmol.m-2.s-1。(3)岩黄连叶片水分利用率(WUE)随有效光辐射强度(PAR)的增强呈抛物线状变化,PAR在200μmol.m-2.s-1内呈直线上升,到200μmol.m-2.s-1时WUE达最大值,大于200μmol.m-2.s-1后WUE呈逐渐下降趋势。     

水稻细菌性条斑病时间增长最佳经验曲线拟合

通过人工和自然诱发试验,选择8种最常用经验曲线,采用Q〔O=∑(y－y）~2〕作为衡量配置曲线类型的优劣的指标．结果表明,描述水稻细菌性条斑病进展曲线以Logistic曲线为最佳．     

A Parametric ROC Model‐Based Approach for Evaluating the Predictiveness of Continuous Markers in Case–Control Studies

Summary The predictiveness curve shows the population distribution of risk endowed by a marker or risk prediction model. It provides a means for assessing the model's capacity for stratifying the population according to risk. Methods for making inference about the predictiveness curve have been developed using cross‐sectional or cohort data. Here we consider inference based on case–control studies, which are far more common in practice. We investigate the relationship between the ROC curve and the predictiveness curve. Insights about their relationship provide alternative ROC interpretations for the predictiveness curve and for a previously proposed summary index of it. Next the relationship motivates ROC based methods for estimating the predictiveness curve. An important advantage of these methods over previously proposed methods is that they are rank invariant. In addition they provide a way of combining information across populations that have similar ROC curves but varying prevalence of the outcome. We apply the methods to prostate‐specific antigen (PSA), a marker for predicting risk of prostate cancer.     

A mélange of curves – further dialogue about species–area relationships

Scheiner (2003) presented a classification of species–area curves into six types based on the pattern of sampling and how the data are combined to form the curves. Gray et al. (2004) contended that five of those types should be termed ‘species‐accumulation curves’, reserving ‘species–area curve’ for those based on island‐type data. Their proposition contradicts 70 years of usage and confounds curves that are area‐explicit with those that are area‐undefined. In exploring these issues, I highlight additional aspects of species–area and species‐accumulation curves, including the assumption of nesting in Type IV (island) curves, how to convert area‐unspecified curves into area curves, and the effects of the grain of the analysis on the properties of the curve. Further exploration, theoretical development, and dialogue are needed before we will understand all the biology that species–area curves summarize.