Logistic、崔-Lawson种群增长模型理论及实例拟合比较

本文求出了Logistic方程、崔-Lawson方程的速度、加速度方程。Logistic方程在加速度等于零时的增长拐点只能在K/2处,此时的最大增长速度为μ_LK/4;崔-Lawson方程在加速度等于零时的增长拐点在处,此时的最大增长速度为。通过b的变化,在描述种群增长规律时,崔-Lawson方程可优于Logistic方程。本文还用变步长坐标轮换法对两个方程进行实例拟合比较,Logistic方程还比较了Gause、Andrewartha、May、Pearl、Krebs、万昌秀、王莽莽等人的方法与结果。拟合结果表明,崔-Lawson方程最优;在拟合Logistic方程的各种方法中,本文方法较优。     

答疑——关于崔-Lawson单种群新模型

《生态学报》5卷3期发表了马钦彦君的《对崔-Lawson氏种群增长模型的探讨》。在学报上就学术问题进行争鸣,这是一个好现象。由于马君所探讨的问题,是针对我和一些合作者近几年发表在几个国际杂志和我国《生态学报》、《生态学杂志》(崔启武等,1982、1985;Cui Qiwu等,1982、1984、1985)上的有关种群增长的一个基础新数学模型(以下简称新模型)的,因此我必须作答。     

西双版纳不同斑块望天树种群的密度、结构和生物量

 根据5个不同斑块的野外调查数据,分析了残存分布在西双版纳的国家一级保护稀有树种望天树（Parashorea chinensis）的种群密度与数量、 年龄结构与生物量动态, 组建了不同生长发育阶段的望天树个体生长与年龄的回归模型、个体生物量模型及种群年龄结构模型, 编制了不同 斑块的望天树种群及整个种群的静态生命表、存活曲线和年龄结构图。结果表明,不同斑块的望天树种群因种群年龄及所受到的干扰方式的不 同,其种群密度和年龄结构差异很大,不同年龄阶段的死亡率也不同。面积最小的斑块缺乏成熟个体,并出现龄级结构缺省的现象。不同斑块 局部种群的生物量随林龄的变化近似于Logistic增长,但各斑块局部种群的最大生物量以及生物量随时间的动态变化有所不同。整个种群的年 龄结构为稳定增长型种群,1～60龄的种群个体的死亡率随林龄的增加而下降,60～150龄的个体死亡率随林龄的增加而上升,180 龄后种群呈 现生理衰退,个体出现死亡高峰。种群的生物量在180 龄前呈Logistic 增长,此后,生物量下降。部分斑块受到严重的人为干扰,已严重威胁 其局部种群的生存。     

松嫩平原朝鲜碱茅无性系种群构件生物量结构及相关模型分析

从构件水平对松嫩平原碱化草甸朝鲜碱茅无性系种群各功能构件的生物量结构,各功能构件生物量与丛径之间的关系,以及各功能构件生物量之间的关系均建立相应的模型进行了定量分析。结果表明,在孕穗和果后营养两个生育期,朝鲜碱茅无性系种群各功能构件生物量及所占总生物量的比率具有相同的规律;各功能构件生物量与丛径之间的定量关系在孕穗期以直线函数模型相关性最大,在果后营养期以幂函数模型相关性最大;各功能构件生物量之间的定量关系除光合构件与支持构件在孕穗期以直线函数模型相关性最大外,其他各构件生物量之间在两个生长期均以幂函数模型相关性最大。     

北京西部山区胡枝子种群研究: 个体和构件生物量

通过对北京西部山区胡枝子(Lespedeza bicolor Turcz.)种群个体和构件地上生物量进行系统研究。结果表明, 种群(总和)个体和各构件地上生物量积累与年龄的关系均可用方程式Y=axb表示。不同种群的植株个体和构件生物量有显著性不同(P<0.05), 在海拔910-1 100 m的山脊林缘的种群个体和构件地上生物量较其它种群大, 植株地上营养构件的生物量比率较小, 而繁殖构件生物量比率较大; 不适生境中的种群则反之。种群个体生长和各构件生物量动态与环境条件关系密切。构件生物量比率也随着年龄的增长而有所变化。叶生物量比率随年龄增加而减小; 枝构件生物量比率随年龄增加而增大; 繁殖构件的生物量比率随年龄增加先增后减。依据相关指数R2, 筛选各构件生物量估计的最优模型: 枝、枝叶生物量和地上生物量均为m(DW)= a(D2H1)b, 叶生物量和花果生物量均为m(DW)=a(D)b。     

北京西部山区胡枝子种群研究:个体和构件生物量

通过对北京西部山区胡枝子(Lespedeza bicolor Turcz.)种群个体和构件地上生物量进行系统研究。结果表明,种群(总和)个体和各构件地上生物量积累与年龄的关系均可用方程式Y=axb表示。不同种群的植株个体和构件生物量有显著性不同(P<0.05),在海拔910-1100m的山脊林缘的种群个体和构件地上生物量较其它种群大,植株地上营养构件的生物量比率较小,而繁殖构件生物量比率较大;不适生境中的种群则反之。种群个体生长和各构件生物量动态与环境条件关系密切。构件生物量比率也随着年龄的增长而有所变化。叶生物量比率随年龄增加而减小;枝构件生物量比率随年龄增加而增大;繁殖构件的生物量比率随年龄增加先增后减。依据相关指数R2,筛选各构件生物量估计的最优模型:枝、枝叶生物量和地上生物量均为m(DW)=a(D2H1)b,叶生物量和花果生物量均为m(DW)=a(D)b。     

格氏栲种群生态学研究 Ⅲ. 格氏栲种群优势度增长动态规律研究

采用有限空间种群增长的逻辑斯谛模型探讨格氏栲种群基面积增长规律。提出自适应通用模型ds/dt=rs(1-s^θ/k^φ).该模型包括Logistic模型、Smith模型、Gompertz模型、崔Lawson模型和Z-Logistic模型;运用改进单纯形对自适应通用模型进行优化,拟合结果比Logistic模型更符合格氏栲种群实际增长趋势,增长速度最大是在147年。     

珍稀濒危植物青钩栲种群数量特征研究

提出自适应种群增长新模型Ｓ＝ｅｘｐ（ａｌｎ＾２（１＋ｃｅ＾－ｒｔ）＋βｌｎ（１＋ｃｅ＾－ｅｔ）＋γ）,该模型包融了Ｌｏｇｉｓｔｉｃ模型、Ｓｍｉｔｈ模型、Ｇｏｍｐｅｒｔｚ模型、崔－Ｌａｗｓｏｎ模型、张－Ｌｏｇｉｓｔｉｃ模型和刘－Ｌｏｇｉｓｔｉｃ模型,运用遗传算法适应新模型进行参数估计,拟合青钩栲种群增长规律比其它种群增长模型更符合青钩栲群种的实际增长趋势,说明新模型具有一定的实用价值。     

格氏栲种群生态学研究Ⅲ.格氏栲种群优势度增长动态规律研究

采用有限空间种群增长的逻辑斯谛模型探讨格氏栲种群基面积增长规律．提出自适应通用模型ｄｓ／ｄｔ＝ｒｓ（１－ｓθ／ｋφ）．该模型包括Ｌｏｇｉｓｔｉｃ模型、Ｓｍｉｔｈ模型、Ｇｏｍｐｅｒｔｚ模型、崔Ｌａｗｓｏｎ模型和ＺＬｏｇｉｓｔｉｃ模型;运用改进单纯形对自适应通用模型进行优化,拟合结果比Ｌｏｇｉｓｔｉｃ模型更符合格氏栲种群实际增长趋势,增长速度最大是在１４７年．     

江西千烟洲不同恢复途径下白栎种群生物量

利用不同自变量和函数,建立白栎枝条和单株地上各器官的生物量模型,选择其中的最佳模型估算了千烟洲人工造林和自然封育两种恢复途径下白栎种群地上生物量及其年增长量,并利用地上生物量和地下生物量的线性关系,估算了白栎种群地下生物量及其年增长量.结果表明:模拟白栎枝条和单株地上各器官生物量的最佳函数均为幂函数,而最佳自变量分别为d²l和D²H.白栎种群各器官生物量和总生物量均为天然次生林大于人工湿地松林.次生林中白栎种群地上和地下生物量分别为3.592和1.723 t·hm^-2,其中树干生物量>枝生物量>叶生物量;湿地松林中白栎种群地上和地下生物量分别为0.666和0.462 t·hm^-2,其中树干生物量>叶生物量>枝生物量.2004—2006年,两种恢复途径下白栎种群地上、地下及总生物量的年增长量均逐年增加.其中地上生物量年增长量占总年增长量的比重呈逐年升高趋势,湿地松林中由54.35%增至62.20%,次生林中由67.27%增至68.94%.与次生林相比,湿地松林中白栎种群各器官生物量年增长量较小,但其相对增长速率较快.     

Simulation of rice biomass accumulation by an extended logistic model including influence of meteorological factors

The biomass (X) of a biological population, described by growth models, depends only on time (t), i.e., X = f(t). Some parameters in these models are frequently taken as constants, but they may vary with growth processes under different ecological conditions. An extended logistic model including changes in the influence of meteorological factors is developed to simulate biomass accumulation processes of rice sown on different dates. The model may be generally described as X = f (p, t), in which p stands for meteorological factors. The model can be used to generalize population growth processes in experiments carried out under different environments. It is shown that the model may account for 96.6% of the variance of rice biomass on the basis of sowing dates, developmental stage, solar radiation and temperature in the Yangtze River valley in China.     

Estimating the impact of oyster restoration scenarios on transient fish production

Oyster reef restoration projects are increasing in number both to enhance oyster density and to retain valuable ecosystem services provided by oyster reefs. Although some oyster restoration projects have demonstrated success by increasing density and biomass of transient fish, it still remains a challenge to quantify the effects of oyster restoration on transient fish communities. We developed a bioenergetics model to assess the impact of selected oyster reef restoration scenarios on associated transient fish species. We used the model to analyze the impact of changes in (1) oyster population carrying capacity; (2) oyster population growth rate; and (3) diet preference of transient fish on oyster reef development and associated transient fish species. Our model results indicate that resident fish biomass is directly affected by oyster restoration and oyster biomass, and oyster restoration can have cascading impacts on transient fish biomass. Furthermore, the results highlight the importance of a favorable oyster population growth rate during early restoration years, as it can lead to rapid increases in mean oyster biomass and biomass of transient fish species. The model also revealed that a transient fish's diet solely dependent on oyster reef‐derived prey could limit the biomass of transient fish species, emphasizing the importance of habitat connectivity in estuarine areas to enhance transient fish species biomass. Simple bioenergetics models can be developed to understand the dynamics of a system and make qualitative predictions of management and restoration scenarios.     

Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.     

A model for pellet size distributions in submerged mycelial cultures

Fungal liquid cultures differ from those of bacteria in that clumps, called pellets are formed. Diffusional limitations constrain growth to the surface of such clumps. Previous models for pellet growth have neglected the effect of clump size distributions on growth rates. The model derived by Edelstein (1981) can be used to approach this question, and to demonstrate that fragmentation can accelerate the overall biomass growth. Experimental observations reported in this paper are in agreement with one version of this model incorporating loss of part of the pellet population due to mechanical damage or washout.     

羊草种群密度与生长动态研究

 通过人为控制种群密度的栽培实验,从基株和构件水平上观察羊草无性系种群的生长动态,分析不同密度水平上羊草种群通过调节种群的生长、发育、增殖以及死亡过程来适应密度制约的途径。研究结果表明：1)羊草种群密度可在不同的构件水平间得到调节。当基株密度得到适当调节后便可减缓构件密度(无性系枝条、根茎芽等)的变化幅度和影响构件的发育进程。2)无性系枝条是羊草种群的主体,常在生长季后期出现大量增长,都处于生长旺盛的幼苗期,为翌年春季的返青积累能量和物质。3)单位面积总生物量随密度增加而提高,虽然尚未出现产量恒值现象,但存活枝条平均单株重(地上生物量)随密度增加呈下降趋势,这已反映出密度制约的作用。4)不同密度下羊草种群的生殖过程表现为：低密度时以无性繁殖为主,根茎芽的存活力较高;高密度时以有性繁殖为主,生殖分配值较大。     

A length-based hierarchical model of brown trout (Salmo trutta fario) growth and production

We present a hierarchical Bayesian model (HBM) to estimate the growth parameters, production, and production over biomass ratio (P/B) of resident brown trout (Salmo trutta fario) populations. The data which are required to run the model are removal sampling and air temperature data which are conveniently gathered by freshwater biologists. The model is the combination of eight submodels: abundance, weight, biomass, growth, growth rate, time of emergence, water temperature, and production. Abundance is modeled as a mixture of Gaussian cohorts; cohorts centers and standard deviations are related by a von Bertalanffy growth function; time of emergence and growth rate are functions of water temperature; water temperature is predicted from air temperature; biomass, production, and P/B are subsequently computed. We illustrate the capabilities of the model by investigating the growth and production of a brown trout population (Neste d'Oueil, Pyrénées, France) by using data collected in the field from 2005 to 2010.     

Food-dependent growth leads to overcompensation in stage-specific biomass when mortality increases: the influence of maturation versus reproduction regulation

We analyze a stage-structured biomass model for size-structured consumer-resource interactions. Maturation of juvenile consumers is modeled with a food-dependent function that consistently translates individual-level assumptions about growth in body size to the population level. Furthermore, the model accounts for stage-specific differences in resource use and mortality between juvenile and adult consumers. Without such differences, the model reduces to the Yodzis and Innes (1992) bioenergetics model, for which we show that model equilibria are characterized by a symmetry property that reproduction and maturation are equally limited by food density. As a consequence, biomass production rate exactly equals loss rate through maintenance and mortality in each consumer stage. Stage-specific differences break up this symmetry and turn specific stages into net producers and others into net losers of biomass. As a consequence, the population in equilibrium can be regulated in two distinct ways: either through total population reproduction or through total population maturation as limiting process. In the case of reproduction regulation, increases in mortality may lead to an increase of juvenile biomass. In the case of maturation regulation, increases in mortality may increase adult biomass. This overcompensation in biomass occurs with increases in both stage-independent and stage-specific mortality, even when the latter targets the stage exhibiting overcompensation.     

高寒典型草原主要物种的株高和盖度预测种群和群落地上生物量

为快速、准确、无破坏地测定草原地上生物量,在祁连山高寒典型草原植物生长旺季,观测了冬季和春秋季放牧地60个样方内各物种的株高、盖度等生长指标。以冬季牧地紫花针茅（Stipa purpurea）、醉马草（Achnatherum inebrians）、赖草（Leymus secalinus）、扁穗冰草（Agropyron cristatum）、二裂委陵菜（Potentilla bifurca）、银灰旋花（Convolvulus ammannii）6个主要物种的株高、盖度、株高和盖度的乘积为自变量,分别预测同物种、其他物种和群落地上生物量。用春秋季牧场的数据验证模型的精确性和稳定性。结果表明：主要物种的生长指标可预测其自身、其他物种和群落地上生物量。对自身种群,株高和盖度乘积的复合因子预测效果最好;4种禾草对其他物种、二裂委陵菜对菊科植物种群,株高、盖度单因子预测效果优于复合因子;6个主要物种单独或2-6个种结合均可预测群落地上生物量,但是以6个物种株高和盖度的乘积同时预测时决定系数最大,可解释群落地上生物量89.5%的变异,为高寒典型草原群落地上生物量最优预测模型。