基于样方数据的云南松林分生长模型研究——以云南省保山市杨柳白族彝族乡为例

以云南省保山市杨柳白族彝族乡实地调查的86块云南松样地数据,使用非线性拟合的方法拟合优选常用树木生长方程,建立了包括地位指数、密度指数、平均直径和蓄积量的生长模型。经验生长方程Schumacher的拟合度与其它方程相近,但模型中参数变异系数均比其余方程低,为地位指数、平均直径和蓄积量的最优方程。     

同龄纯林自然稀疏过程的经验模型研究

应用-3/2法则及广义Schumacher生长方程导出同龄纯林自然稀疏过程中密度随时间变化规律新模型,采用遗传算法对非线性模型参数进行最优估计.以山杨、云南松、杉木等树种同龄纯林自疏过程中密度随时间变化资料对新模型进行了验证,并与前人提出的主要森林自疏过程密度随时间变化规律模型进行了对比.结果表明,所提出的同龄纯林自疏规律模型能很好地拟合实际观测资料,具有良好的使用价值;新模型拟合效果较前人提出的自疏规律模型效果均更佳,说明新模型是一个描述同龄纯林自疏过程密度随时间变化规律的理想经验模型,可在森林自疏规律研究中应用.杉木林自疏过程密度变化规律的研究可为南方林区杉木林经营管理提供参考.     

免疫进化算法在建立地位指数曲线模型中的应用

选择Schumacher方程构建优势高和地位指数均能写成显式表达式的多形地位指数曲线模型,以同时兼顾优势高和地位指数的估测误差最小为目标函数,采用免疫进化算法求解参数．实例分析表明：该文建立的多形地位指数曲线模型能够客观地反映不同立地下优势高的生长规律,且误差小,应用方便．     

Richards方程的数学属性及其在兽类生长过程中的应用

通过对Richards方程数学属性的分析表明 ,该方程具有变动的拐点值 ,因而在描绘兽类多种多样的生长过程时具有良好的可塑性。依据其方程参数n取值的不同 ,Richards方程包含了Spillman ,Logistic,Gompertz以及Bertalanffy方程。为了评估Richards方程对兽类生长过程的拟合优度 ,作者引用 1 0组哺乳动物兽类生长数据 ,将它与一些经典的生长模型如Spillman ,Logistic,Gompertz以及Bertalanffy方程共同进行了拟合比较。结果表明 ,Richards方程具有良好的拟合优度 ,适于描绘多种多样的兽类生长模式。     

检测大肠杆菌群体生长动力学过程4种方法的比较

用浊度测定、菌落形成数计数（CFU）、流式细胞计数（FCT）,以及MTT还原测脱氢酶活力4种检测方法,测定了E．coliCVCC249群体的生长量,并通过Logistic模型、Sigmoid模型,以及正态分布方程拟合由上述生物量所表征的群体生长动力学过程曲线．结果表明,对浊度和流式检测数据,Logistic和Sigmoid方程可给出较好的拟合度,而对CFU法和脱氢酶活力检测法,仅有正态分布方程能呈现更好的拟合．通过应用有限时域向前差分的方法,消除不能增殖的休止细胞对浊度生长过程曲线的影响,以模拟菌群增殖的过程曲线．在此基础上,求得菌群生长的即时速度（advancingvelocity,Vad。）和即时速度的瞬变率,以此为据将E．coliCVCC249生长过程划分为线性增长期、指数增长期、指数减速期、线性减速期,以及衰亡期5个阶段．此外,对新的划分生长阶段的方法与经典方法的不同,以及R。（拟合决定系数）能否作为确定模型是否拟合的唯一判据,进行了讨论．     

中华乌塘鳢的生长、生长模型和生活史类型

采用胸鳍第三支鳍骨作为研究湛江沿海中华乌塘鳢的年龄鉴定材料。胸鳍第三支鳍骨（远侧部）的关径（R）与体长（L）的关系为L＝6.1145 51.1288R。用特殊von Bertalanffy生长方程、一般von Bertalanffy生长方程、逻辑斯谛生长方程、Gompertz生长方程和灰色动态生长模型等5种生长模型拟合了中华乌塘鳢的生长,根据各模型拟合残差平方和大小判断,灰色动态生长模型对中华乌塘鳢生长的拟合效果最好,其次是一般von Bertalanffy生长方程。根据r-选择和κ－选择的典型行征以及渐近体长（L∞）、渐近体重（W∞）、生长系数（κ）、初次生殖年龄（Tm）、最大年龄（Tmax）、瞬时自然死亡率（M）和性腺指数（GI）等7个生态学参数值,可以判断中华乌塘鳢偏向r-选择。应用单位补充量产量模型计算改变起捕年龄（Tc）和瞬时捕捞死亡率（F）的产量,分析产量变化曲线同样证实中华乌塘鳢生活史偏向r-选择。作为渔业管理对策,中华乌塘鳢的起捕年龄应定为2龄。     

生物种群动态微分方程模型参数估计方法

本文以数值分析和最优化技术的有机结合为基础,提出了一种新的对动态微分方程模型直接进行数据拟合和参数估计方法,并以Logistic微分方程、生物种间竞争关系微分方程以及一种复合形态的Logistic微分方程为例进行了数据拟合试验．结果表明,该方法对各种动态微分方程模型均能进行最优拟合分析并求解其参数．同时发现,以前有的作者〔1,2,3,4,5〕提出的方法所得到的参数估计值存在系统误差且误差较大．     

冷却猪肉中气单胞菌生长预测模型的建立和检验

为探讨冷却猪肉中气单胞菌的生长规律,将气单胞茵接种到经过80℃无菌水灭菌的冷却猪肉中,构建Gompertz和Baranyi初级模型来描述气单胞菌在不同温度下的生长状况。结果表明：修正的Gompertz模型对气单胞菌生长曲线的拟合效果优于Baranyi模型,R2均在0．97以上。应用平方根模型和Arrhenius模型对由修正的Gompertz模型得出的最大比生长速率进行拟合,所得平方根模型拟合效果略优于Arrhenius模型。实验所建二级模型能预测0-35℃贮藏条件下气单胞菌的生长。     

广义Logistic模型的拟合

给出了广义Logistic模型有显示解的存在定理及其参数的一种拟合方法,并以稻田捕食天敌种群数量变化进行实际拟合,从而验证该模型对于描述各种不同生物种群的动态有更广泛的适用性。     

杨树生长模型的选择

本文选用常用生长模型和4类灰色模型,分别对6个新品系杨树生长动态规律进行模拟;结果表明：在常用的生长模型中,Richards方程模拟效果最好,而不是通常认为的Logistic方程;在灰色模型中．以GM（1,1）模拟效果最好,也可作为杨树生长模型．     

A comparison of the Schumacher with other functions for describing growth in pigs

This study was undertaken to introduce the Schumacher equation and compare it with established functions for describing growth in pigs. The relationship between live weight (LW) and cumulative feed intake was also investigated. A database was constructed from three independent trials in which LW, age and intake were measured from birth to 937 days. Three growth functions were used for analysis of growth versus age: Gompertz, Schumacher and Weibull; and the Richards and monomolecular equations were used for analysis of cumulative feed intake versus LW. The growth functions have different points of inflexion. Liveweight at inflexion is W_f/e for the Gompertz, where W_f is the final weight, W_f/e² for the Schumacher, and W_f − (W_f − W₀) exp[−(n − 1)/n] for the Weibull, where W₀ is initial body weight and n is a shape parameter. Meta-analysis of the data using mixed model and nonlinear regression procedures was conducted to identify the most appropriate growth function. Functions were compared using F-tests or Bayesian Information Criteria, which give a value based on best fit and number of parameters in the model. The three equations were fitted to five individual pig growth profiles and to the composite data. Although the Weibull had a lower residual mean square, it did not significantly improve the fit compared to the simpler models and appears to be over-parameterised. The results suggest that model selection should be based on the type and amount of data available for analysis. Residuals plot showed that Schumacher and Weibull better predict the initial growth phase, however, all models showed largest magnitude of residuals towards the end of the growth profile. The monomolecular equation was most appropriate for describing LW against cumulative feed intake and may be used to formulate diets based on the efficiency of conversion of feed to LW at various stages of the animal's life span.     

A Study of Stand Growth Model for Pinus yunnanensis (Pinaceae) Based on Plots Data——A Case Study in Yangliu Township,Baoshan, Yunnan Province

Pinus yunnanensis is one of most important timber species in Yunnan Province, and widely distributed in southwest China. Studies on growth model have been reported, however, most of which focused on a specific part of growth model. To build detailed, easily used and accurate empirical stand growth model from the same dataset, a case study was conducted in Yangliu Township, Baoshan, Yunnan Province. A total of 86 sample plots data were collected using two stages sampling design. Several popular non-linear growth functions were fitted and compared, including Chapman-Richards, Mitscherlich, Schumacher, Gompertz, Logistic, Korf and Allometric function. Models of site index, density index, average diameter at breast height (DBH) and stock volume growth model were fitted respectively. The different models performed more or less similarly in terms of coefficients of determination and root mean square error (RMSE). However, empirical growth function “Schumacher” had lower coefficient of variation for all parameters than other models. Schumacher function was the most suitable one for site index, average DBH and stock volume growth model in all alternative functions.     

Growth and yield functions for irrigated plantations of Eucalyptus camaldulensis in the hot desert of India

Eucalyptus camaldulensis forms a major portion of irrigated plantations in the hot desert of India and for effective management of these plantations, growth and yield functions are necessary. This paper describes the development of height, diameter and volume growth functions based on the analysis of the data collected from the permanent sample plots laid out in the study area. The Chapman-Richards equation could be used for the prediction of diameter growth while the Schumacher model could be considered for predicting volume growth. Some base-age variant and invariant site-index models, already reported in the literature, were compared in terms of relative accuracy and it was found that the Payandeh and Wang model performed the best among the four models tried.     

Mathematical modeling of induced foreign protein production by recombinant bacteria

A new generalized mathematical model for recombinant bacteria which includes inducer effects on cell growth and foreign protein production is developed. The model equation set was applied to a host-vector system, Escherichi coli D1210 and plasmid pSD8. Batch experiments were designed and performed in shake flasks to verify the model. A parameter estimation method was developed and proven to be efficient. Although simple, the model can effectively describe the dynamics of the production of foreign protein in recombinant bacteria and can be used for optimization and control studies to maximize foreign protein production.     

Engelmann Spruce Site Index Models: A Comparison of Model Functions and Parameterizations

Engelmann spruce (Picea engelmannii Parry ex Engelm.) is a high-elevation species found in western Canada and western USA. As this species becomes increasingly targeted for harvesting, better height growth information is required for good management of this species. This project was initiated to fill this need. The objective of the project was threefold: develop a site index model for Engelmann spruce; compare the fits and modelling and application issues between three model formulations and four parameterizations; and more closely examine the grounded-Generalized Algebraic Difference Approach (g-GADA) model parameterization. The model fitting data consisted of 84 stem analyzed Engelmann spruce site trees sampled across the Engelmann Spruce – Subalpine Fir biogeoclimatic zone. The fitted models were based on the Chapman-Richards function, a modified Hossfeld IV function, and the Schumacher function. The model parameterizations that were tested are indicator variables, mixed-effects, GADA, and g-GADA. Model evaluation was based on the finite-sample corrected version of Akaike’s Information Criteria and the estimated variance. Model parameterization had more of an influence on the fit than did model formulation, with the indicator variable method providing the best fit, followed by the mixed-effects modelling (9% increase in the variance for the Chapman-Richards and Schumacher formulations over the indicator variable parameterization), g-GADA (optimal approach) (335% increase in the variance), and the GADA/g-GADA (with the GADA parameterization) (346% increase in the variance). Factors related to the application of the model must be considered when selecting the model for use as the best fitting methods have the most barriers in their application in terms of data and software requirements.     

昆虫杆状病毒流行病模拟模型及Java模拟软件

研究昆虫杆状病毒流行病模拟模型,对确定基因工程改造杆状病毒的主攻方向,明确病毒病田间流行的机制与关键因素,以及制定生物防治策略,均具有重要的理论与实践意义.本研究研制了用于昆虫杆状病毒流行病模拟的数学模型和Java模拟软件,该模型包括描述种群动态的一个微分方程组,描述气温变化、作物生长及病毒动态的若干模型等.模拟软件用...     

Analysis of logistic growth models

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.     

Determination of the shelf life of sliced cooked ham based on the growth of lactic acid bacteria in different steps of the chain

Aims: Development of a predictive model for the determination of the shelf life of modified atmosphere‐packed (MAP) cooked sliced ham in each step of the cold chain. Methods and Results: The growth of lactic acid bacteria (LAB), as well as the development of the total viable count and changes of sensory and pH value parameters in MAP cooked sliced ham, stored under different constant temperature conditions from 2 to 15°C was investigated. As a result of the measurements, the end of the shelf life could be considered as the time when LAB reach more than 7 log₁₀ CFU g^?1. Different primary and secondary models were tested and analysed to find the best way to calculate the shelf life. For primary modelling, the modified Gompertz Function and the modified Logistic Function were compared. There was no substantial difference between either model. The effect of temperature on the growth rate was modelled by using the Arrhenius and the Square root model, whereas the Arrhenius equation gave a better result. A combination of the primary and secondary model was used for shelf‐life prediction under dynamic conditions. This combination showed the best prediction of microbial counts using the modified Logistic model and the Arrhenius equation. Conclusions: With the developed model, it is possible to predict the shelf life of MAP cooked sliced ham based on the growth of LAB under different temperature conditions. Significance and Impact of the Study: The developed model can be used to calculate the remaining shelf life in different steps of the chain. Thus, it can deliver an important contribution to improve food quality by optimizing the storage management.     

New modified Square Root and Schoolfield models for predicting bacterial growth rate as a function of temperature

Summary A new modified Square Root model and two new modified Schoolfield models were evaluated for their ability to predict the growth rate ofYersinia enterocolitica as a function of temperature. The new Square Root model fits the data better than both the original Square Root model and the Zwietering Square Root model. Both new Schoolfield models, a six-and a four-parameter equation, fit the data better than the original Schoolfield model. The new four-parameter Schoolfield model was developed by removing the term describing low temperature inactivation from the new six-parameter Schoolfield model. Inclusion of the two extra parameters in the new six-parameter Schoolfield model (F=318) did not significantly improve the fit compared to the new fourparameter Schoolfield model (F=488).