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．     

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。     

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.     

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.     

三次设计结合模矢法拟合Logistic曲线的研究

Ｌｏｇｉｓｔｉｃ曲线是种群动态的一个经典模型,针对传统拟合方法存在的缺陷和三次设计的优点,以及拟合过程是离差平方和最小──可看作是运筹学中无约束极值问题──的优化原则,本文提出新的方法－三次设计结合模大法的组合方法来拟合,结果表明该法能取长补短,拟合效果最佳,因此在一般非线性模型参数求解中具有普遍意义．     

重要值-面积曲线在热带亚热带森林中的应用

重要值—面积曲线不仅可以确定群落最小面积,并可绘出种群的相对稳定的重要值,表达出群落的最主要特征,因而,具有一定的理论意义和实用价值。 在种类复杂而偶见种又很多的森林群落中,如以传统的种—面积曲线确定的最小面积会很大,但实际上许多偶见种对群落性质的影响并不重要。如应用重要值—面积曲线获得的最小面积虽然相对较小,但它能满足群落学研究的需要。在寡种群落中,以种—面积曲线确定的最小面积会过小,不足以表达群落的主要特征,而重要值—面积曲线则可得到较大的,足以表达群落特征的最小面积。本文提出重要值数学公式,以及重复随机集合取样的数学公式为：以助于确定最小面积。     

光合作用对胞间和大气CO_2响应曲线的比较

利用Li-6400便携式光合作用系统测定华北平原冬小麦在温度为25℃和30℃、光合有效辐射为1500和2000 mmol·m~(-2)·s~(-1)条件下处于抽穗时期旗叶的CO_2响应曲线,研究植物光合作用对胞间CO_2响应(A/C_i)和对大气CO_2响应(A/C_a)的直角双曲线修正模型所给拟合结果的合理性.结果表明:由A/C_i和A/C_a修正模型所给的光合能力和CO_2补偿点几乎相同,但得到的光呼吸速率和初始羧化效率则完全不等;产生这种差异的原因是利用叶片气体交换测定的数据所计算的胞间CO_2浓度并不是植物叶片本身的胞间CO_2浓度;A/C_a修正模型比A/C_i修正模型更为合理是因为A/C_a所估算的光呼吸速率接近测量值.

Abstract：

By using Li-6400 portable photosynthesis system, the photosynthetic parameters of winter wheat (Triticum aestivum) during its heading stage in North China Plain were measured at air temperature 25℃ and 30℃ and at photosynthetically available radiation 1500 and 2000 mmol·m~(-2)·s~(-1). The measured data were fitted with the modified rectangular hyperbola models of the photosynthetic responses to flag leaf intercellular CO_2 concentration (A/C_i) and air CO_2 concentration (A/C_a), aimed to approach the reasonability of the fitted results obtained from the models. The photosynthetic capacity and CO_2 compensation point estimated by the modified A/C_i curve and A/C_a curve were nearly the same, but the photorespiration and initial earboxylation ef-ficiency estimated by them were completely different. The difference between the two modified curves came from the calculated but not the real intercellular CO_2 concentration. Modified A/C_a curve was more reasonable than the modified A/C_i curve, because the photorespiration rate esti-mated by the former was close to the measured value.     

Genetic architecture of growth curve parameters in chickens

Summary Genetic improvement in growth of poultry has traditionally proceeded via selection for body weight at a fixed age. Due to increased maintenance costs and reproductive problems of adult broiler breeders, the potential for genetic manipulation of the growth curve has been receiving increased interest. Research of both male and female progeny of a three-way diallel cross was used to investigate the inheritance of growth curve parameters. The Laird form of the Gompertz equation was used to determine growth curve parameters, and was suited to the juvenile growth data frequently collected from meat-type chickens. Growth rate exhibited significant heterosis due to both autosomes and the sex chromosomes. Age at inflection point also exhibited significant average heterosis, though only among females. Growth rate was also influenced by average line effects, as was age at inflection point. Maternal effects had no influence on growth curve parameters, while additive sex linkage was observed for growth rate. Phenotypic and genetic correlations were calculated among the growth curve parameters and suggest that specific breeding programs could alter the growth trajectory of the contemporary broiler chicken. Moderate heritabilities were observed for the growth curve parameters and support the hypothesis that the growth curve could be altered via genetic manipulation of early postnatal growth, especially during the first 14 days post-hatch.     

RNA-Z曲线及其在病毒基因识别中的应用

20世纪90年代中期提出的Z曲线方法从几何学的角度阐明了如何识别基因,并取得了非常好的实验结果．但它是完全基于DNA序列结构构建的,对于识别RNA病毒基因效果并不理想,本文提出的RNA—Z曲线方法则弥补了这一缺陷．     

马尾松-栎类天然混交林群落最小面积确定及方法比较

用种面积曲线和群落系数面积曲线的方法对宜昌梅子垭地区一种主要植物群落类型的最小面积进行了研究。结果表明,对所研究的植被类型,样地布置为 １０ｍ ×１０ｍ 及２０ｍ ×２０ｍ 可满足不同研究精度的要求。群落系统面积曲线和种面积曲线一样,比较直观。虽然取样调查时工作量稍大,但运用群落系数面积曲线的方法可更多地包含种类组成及群落结构随面积而变化的信息,所确定的最小面积也能够真实地反映整个群落种类组成及结构的特征。     

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.     

Synchronization by light of the circadian rhythm of motor activity in the crayfish

Abstract

We have studied the pattern for resetting the circadian rhythm in the spontaneous motor activity of the crayfish. Spontaneous motor activity was recorded continously at a constant temperature and under free running conditions in complete darkness. The effect of single light pulses applied at different circadian times, on the circadian rhythm of motor activity was measured in both transient stage and steady state. The results led us to construct a phase‐transition curve and phase‐response curve which were analyzed to obtain information about the oscillators which underlie the circadian rhythm of motor activity.     

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.     

大鼠听觉反应阈的测定

应用微电极技术测定了45只大鼠325根单一听神经纤维的特征频率及其阈值和调谐曲线。测得特征频率的最低值为0.58kHz,最高值为62.6kHz。敏感度最高的频带在20～50kHz,敏感度最高的阈值为6dB(SPL),其相应的频率为27.49kHz。由最低阈值连线延续到边侧的调谐曲线,便形成了大鼠整个的听反应阈曲线。该听反应阈曲线与行为测听所观察到的听力曲线近似。     

Theory for growth of plants derived from the nitrogen productivity concept

A theory is developed on the assumption that growth of plants is determined by the current amount of nitrogen in the plants. The nitrogen-growth relation is formalized in the nitrogen productivity concept (amount of biomass produced per amount of nitrogen in the biomass and per unit of time), which is essentially a constant for a given species under fixed environmental conditions. A number of results follow for increases in whole plant biomass: (A) The relative growth rate is a linear function of the internal nitrogen concentration. (B) The maximal relative growth rate uniquely determines the scaling of the time axis. (C) Exponential growth is consistent only with stable internal nitrogen concentration. Dose-response curves expressed in reduced variables (the ratio between a variable and the same variable for a plant growing under optimal conditions) are universal, so that all species and all environmental conditions yield the same curve. This is confirmed by experimental data. The shape (linear, exponential, etc.) of the nitrogen uptake curve is the only parameter differentiating these universal curves. The Mitscherlich curve or variations of it can be fitted very closely to the derived dose-response curves, except under exponential growth. A conclusion drawn from the analysis is that the results of nutrition experiments cannot be properly interpreted unless the variation with time of the amount of nitrogen in the plant is known. The theory can be extended to more complex situations, for example, time-varying environmental conditions.     

Growth rate of 21 captive-born,mother-raised cheetah cubs

This paper presents the growth rate of 21 clinically normal, mother-raised. captive cheetah cubs from birth through 45 days of age. The development of a growth curve for healthy, mother-raised cheetah cubs provides a diagnostic tool for individuals involved in cheetah propagation. Use of the curve may alert caretakers to problems early and thus help reduce the high neonatal mortality rate seen in captive-born cheetah cubs. The growth curve was constructed using 21 (11 males and 10 females) captiveborn cheetah cubs from six litters (offspring of three unrelated adult males and three unrelated adult females) born at the Columbus Zoo from September 1985 through December 1989. Each cub was weighed to the nearest gram the morning after birth and approximately the same time every consecutive morning for 45 days. The mean weight the morning after birth was 463 g (range 385–542 g). The average litter size was 3.5 (range 2–4, n = 6). The daily weight gain was 40–50 g/cub/day.     

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.     

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。