Use of Polytomous Logistic Model in Matched Case-Control Studies

Binary logistic model has been found useful for estimating odds ratio in case of dichotomous exposure variable under matched case-control retrospective design. We describe the use of polytomous logistic model for estimating odds ratios when the exposure of prime interests, relative to disease incidence, has more than two levels. An illustrative example is presented and discussed.     

一类生物系统平衡点的稳定性

本文利用Logistic模型和稳定性理论,建立了一类生物系统竞争和排斥的数学模型,并且讨论了模型平衡点稳定的条件。     

包容生态因子的广义Logistic模型

以Ｌｏｇｉｓｔｉｃ模型为代表的种群（ｘ）生长模型,仅依赖于时间（ｔ）,Ｘ＝ｆ（ｔ）,它是表达某一环境下生物过程的数学模型,其增长率参数（μ）为常数。本文发展了一种包含生态因子的广义Ｌｏｇｉｓｔｉｃ模型,Ｘ＝ｆ（Ｐ,ｔ）,ｐ表示生态因子,认为增长率是与生态因子有关的参数：μ＝μ０ｆ（ｐ）,该模型可以概括在不同环境下种群增长的重复试验,使用作物分期播种资料,建立了水稻干物质积累过程与生育阶段（时间）、播种期、太阳辐射、温度之间的关系,结果表明：该模型可以解释干物重变异的９６．９％。     

Sex allocation in the polydomous leaf-cutting ant <Emphasis Type="Italic">Acromyrmex</Emphasis><Emphasis Type="Italic">balzani</Emphasis>

Logistic regression analysis was used to analyse sex allocation in a population of the leaf-cutting ant Acromyrmex balzani occurring in a pasture in southern Brazil. The field sample consisted of 151 fungus-garden chambers (18 queenright and 133 queenless), belonging to 50 nests with three vertically stacked chambers per nest on average. Taking nest chamber as the unit of analysis, seven predictor variables were considered: sampling date, chamber depth, chamber volume, weight of fungus garden, presence of a queen, number of large workers, and number of small to medium workers. The population-level numerical proportion of females was 0.548 and the inferred proportional energetic investment in females 0.672. The former was not significantly different from 0.5 (P=0.168), but the latter was (P=0.0003). The proportional investment in females per fungus garden increased with the number of large workers present (P=0.0002) and decreased with the dry weight of the fungus garden (P=0.012). This implies that resource acquisition through foraging is likely to be a major proximate determinant of sex allocation. The negative correlation between female bias and fungus garden weight might be due to developing adult females requiring more food than males, but this hypothesis could not be confirmed by direct statistical evidence.     

Factors affecting secondary sex ratio in Iranian Holsteins

The objective of this study was to evaluate the factors affecting secondary sex ratio (SSR) in Iranian Holsteins. Data of 942,941 Holstein calving events from the Animal Breeding Center of Iran, recorded between January 1996 and December 2007, were used in the analysis. A multivariable logistic regression model was used to model the logit of the probability of a male calf being born. Male births accounted for 49.6% of the total observations. The ratio of males to females varied from 52.5:47.5 in calving year 1996-1999 (odds ratio (OR) = 1.18; P < 0.0001), to 48.5:51.5 in calving year 2004-2007. The greatest occurrence of male births was observed in spring (OR = 1.02; P < 0.0001), and the lowest incidence of male births was for summer or fall calvings. Also, the frequency of male births decreased from parity 1 to parity 4 and beyond (P < 0.0001; OR = 1.11). The greatest number of sires had the SSR equal to 0.5 with a minimum SSR of 32% while the maximum was 97%. Among cows that had a male birth, the chance of delivering a male calf again was 25.5% when cows had delivered a male once (OR = 1.14; P < 0.0001), and 12.7% if a male calf was delivered twice by a cow. This indicated that characteristics peculiar to the dam influence the sex of her offspring and suggests some degree of repeatability of calf sex within cows.     

云冷杉林建群种的种群优势度增长动态研究

 用有限空间种群增长的逻辑斯谛模型探讨了种群基面积增长规律,指出了云冷杉林建群种在不同状态下的基面积最大增长速度的径级范围,紫果云杉35—40cm,岷江冷杉50—55cm;在不同林分内,建群种具有不同的基面积最大增长期。     

贡嘎山暗针叶林不同林型的优势木生长动态

 根据贡嘎山16块样地的调查资料,运用逻辑斯谛模型探讨了暗针叶林不同林型优势木生长动态。建立了峨眉冷杉(Abies fabri)、麦吊杉(Picea brachytyla)和鳞皮冷杉(Abies squamata)的高、径和材积生长的逻辑斯谛模型。研究结果表明,3种林分优势木的高、径和材积的速生期和速生点都不相同,林线附近的峨眉冷杉高、径和材积的速生期最短,麦吊杉高和材积的速生期最长,鳞皮冷杉基径的速生期最长;林分优势木的生长动态和森林更新关系密切,各优势木的生长指标表明各自立地生态条件差异很大。     

A unified approach to the Richards-model family for use in growth analyses: Why we need only two model forms

This paper advances a unified approach to the modeling of sigmoid organismal growth. There are numerous studies on growth, and there have been several proposals and applications of candidate models. Still, a lack of interpretation of the parameter values persists and, consequently, differences in growth patterns have riddled this field. A candidate regression model as a tool should be able to assess and compare growth-curve shapes, systematically and precisely. The Richards models constitute a useful family of growth models that amongst a multitude of parameterizations, re-parameterizations and special cases, include familiar models such as the negative exponential, the logistic, the Bertalanffy and the Gompertz. We have reviewed and systemized this family of models. We demonstrate that two specific parameterizations (or re-parameterizations) of the Richards model are able to substitute, and thus to unify all other forms and models. This unified-Richards model (with its two forms) constitutes a powerful tool for an interpretation of important characteristics of observed growth patterns, namely, [I] maximum (relative) growth rate (i.e., slope at inflection), [II] age at maximum growth rate (i.e., time at inflection), [III] relative mass or length at maximum growth rate (i.e., relative value at an inflection), [IV] value at age zero (i.e., birth, hatching or germination), and [V] asymptotic value (i.e., adult weight or length). These five parameters can characterize uniquely any sigmoid-growth data. To date most studies only compare what is referred to as the “growth-rate constant” or simply “growth rate” (k). This parameter can be interpreted as neither relative nor actual growth rate, but only as a parameter that affects the slope at inflection. We fitted the unified-Richards and five other candidate models to six artificial data sets, generated from the same models, and made a comparison based on the corrected Akaike’s Information Criterion (AICc). The outcome may in part be the result of the random generation of data points. Still, in conclusion, the unified-Richards model performed consistently well for all data sets, despite the penalty imposed by the AICc.     

半数致死量LD50的百分偏差和渐近方差

毒性试验中的剂量与致死百分率平方根反正弦变换仍呈Ｓ形,且方差趋于同质, 半数致死量ＬＤ_(５０)可表示为 Ｌｏｇｉｓｔｉｃ模型参数的函数·因而,通过参数估计值的偏差和渐 过协方差矩阵,可推导出半数致死量ＬＤ_(５０)的百分偏差,渐近方差和ＬＤ_(５０)的置信区间．通 过 ２７个实例分析后建议,若 ＬＤ_(５０)的百分偏差超过 ５％,则 ＬＤ_(５０)估计值的误差较大     

取整对Logistic种群模型动态的影响

不考虑环境嗓音,Logistic取整模型的种群动态是非混沌的,只会出现稳态和周期;在1＜r＜3和0＜r＜1区间,取整模型较原始模型能较快收敛到定态或者灭绝;增大K不能消除取整效应;取整模型周期长度受初值、K值和r值的影响;取整是混沌控制的一条新途径,它可能是自然种群中很少能检测到混沌的重要原因之一．     

Logistic方程参数估计中的错误与修正

Logistic方程在种群生态学研究中被广泛应用,其积分式为N=k／（1＋e~（a-rt））,式中e~a=（k-N_0）／N_0。以往对该模型参数的各种估计方法,均将r,K和a作为三个相互独立的参数对待,而与e~a=（K-N_0）/N_0的假设相矛盾。由此估计出的参数K和a使实验初值N_0（t=0时的N值）发生偏离。笔者认为N_0是一个不带随机误差的常数,a值决定于K和N_0,而不是一个独立的参数,因而以往的参数估计方法是错误的,必须予以修正。本文提出了具体的修正方法,即用Marquardt方法或单纯形加速法求参数r和K,然后根据实验初值N_0求a,从而使Logistic微积分方程的共同参数r和K的估计一致。     

Successional colonization of temporary streams: An experimental approach using aquatic insects

The metacommunity concept studies the processes that structure communities on local and regional scales. This concept is useful to assess spatial variability. However, temporal patterns (e.g., ecological succession and colonization) are neglected in metacommunity studies, since such patterns require temporally extensive, and hard to execute studies. We used experimental habitats in temporary streams located within the Brazilian Cerrado to evaluate the importance of succession for the aquatic insect metacommunity. Five artificial habitats consisting of wrapped crushed rock were set transversally to the water flow in five streams. The habitats were sampled weekly to assess community composition, and replaced after sampling to identify new potential colonizers. We analyzed the accumulation of new colonizers after each week using a logistic model. We selected pairs of experimental habitats and estimated the Bray-Curtis dissimilarity index to assess the community composition trajectory during the experiment. We used the dissimilarity values in ANOVA tests, identifying the importance of time and space for the community. The number of new taxa stabilized in the third week, and we estimated a weekly increase of 1.61 new taxa in the community after stabilization. The overall pattern was a small change on community composition, but one stream had a higher weekly turnover. Our results showed a relevant influence of time in the initial communities of aquatic insects of temporary streams. However, we must observe the temporal pattern in a spatial context, once different streams have different successional history regarding number of taxa and community turnover. We highlight the importance of aerial dispersal and movement to seek oviposition sites as an important factor in determining colonization patterns.