一种自适应的种群增长模型及参数估计

通过对种群增长的非线性制约机制的数学形态分析,提出了一种新的种群增长数学模型ｄｘ／ｄｔ＝ｒｘ（１－（ｘ／ｘｍ）＾ｓ）其解析解为：ｘ（ｔ）＝ｘｍ／（１＋（ｘ＾ｓｍ／ｘ＾ｓ０－１）ｅ＾－ｒｓｔ）＾１／ｓ该模型当非线性密度制约指数ｓ〈１,ｓ＝１,ｓ〉１及ｓ→∞时分别对尖于ＳｍｉｔｈＬｏｇｉｓｔｉｃ,崔－Ｌａｗｓｏｎ及指数增长模型,具有自适应性,本文还提出了一种种群增长模型对数估计的搜索寻优方法,只要给出     

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．     

干旱胁迫对黄瓜PSⅡ颗粒铁组分Mossbauer谱的影响

黄瓜（Ｇｃｕｍｉｓ ｓａｔｉｖｕｓ Ｌ）叶片ＰＳⅡ颗粒的Ｍｏｓｓｂａｕｅｒ谱呈现４套双峰,依它们的化学位移相四敬矩劈塑数值,分别属于氧化态Ｃｙｔ－ｂ５５９,还原态Ｃｙｌ－ｂ５５９、Ｆｅ＾３＋－Ｑ画物和Ｆｅ＾２＋－Ｑ复合物。干埋胁迫旱影响ＱＡ／ＱＢ中铁（Ｆｅ）参与电子传递的速率,使ＰＳⅡ颗粒的ｏｓｓｂａｕｅｔ谱中Ｆｅ＾２＋的吸收双峰消失,即还原态Ｇ７ｙｔ－Ｂ５５９转变为氧化态Ｃｙｔ－ｂ５５９Ｆｅ＾２     

松嫩平原退化盐渍草地生态特性研究

松嫩平原退化盐渍草地生态特性研究侯彦林（北京农业大学博士后站土地资源系,１０００９４）ＥｃｏｌｏｇｉｃａｌＣｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆＤｅｇｒａｄｅｄＳａｌｉｎｅＧｒａｓｓｌａｎｄｉｎＳｏｎｇｎｅｎＰｌａｉｎ￥ＨｏｕＹａｎｌｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＬａｎｄＲｅｓｏｕｒｃｅＳｃｉｅｎｃｅｓ,ＢｅｉｊｉｎｇＡｇｒｉｃｕｌｔｕｒａｌＵｎｉｖｅｒｓｉｔｙ,１０００９４）．ＣｈｉｎｅｓｅＪｏｕｒｎａｌｏｆＥｃｏｌｏｇｙ,１９９３,１２（１）：１１－１４．ＴｈｅｒｅｓｅａｒｃｈｅｓｓｈｏｗｔｈａｔｔｈｅｓａｌｉｎｅｇｒａｓｓｌａｎｄｉｎＳｏｎｇｎｅｎＰｌａｉｎｈａｓｂｅｅｎｇｅｎｅｒａｌｌｙａｎｄｒａｐｉｄｌｙｄｅｇｒａｄｅｄｂｙｈｅａｖｙｇｒａｚｉｎｇ．Ｉｎｔｈｅｐｒｏｃｅｓｓｏｆｇｒａｓｓｌａｎｄｄｅｇｒａｄａｔｉｏｎ,ｓｏｉｌｄｅｔｅｒｉｏｒａｔｉｏｎｉｓｓｏｍｅｗｈａｔｓｌｏｗｅｒｃｏｍ－ｐａｒｅｄｗｉｔｈｖｅｇｅｔａｔｉｏｎｄｅｇｒａｄａｔｉｏｎ,ｗｈｉｃｈｄｅｔｅｒｍｉｎｅｓｔｈｅｆａｃｔｔｈａｔａｎｉｍａｌｈｕｓｂａｎｄｒｙｉｓｔｈｅｃｈｉｅｆｗａｙｏｆｅｘｐｌｏｉｔｉｎｇｓｏｄａ－ａｌｉｎｅ     

柞蚕林生物生产力和干物质转化研究

柞蚕林生物生产力和干物质转化研究温达志,杨思河（中国科学院华南植物研究所,广州５１０６５０）（中国科学院沈阳应用生态研究所,１１００１５）姜波（辽宁省蚕业科学研究所,凤城１１８１０１）ＢｉｏｐｒｏｄｕｃｔｉｖｉｔｙａｎｄＤｒｙＭａｔｔｅｒＴｒａｎｓｆｅｒｏｆＴｕｓｓａｈ－ＦｅｅｄｉｎｇＯａｋＦｏｒｅｓｔ￥ＷｅｎＤａｚｈｉ（ＳｏｕｔｈＣｈｉｎａＩｎｓｔｉ－ｔｕｔｅｏｆＢｏｔａｎｙ,ＡｃａｄｅｍｉａＳｉｎｉｃａ,Ｇｕａｎｇｚｈｏｕ５１０６５０）,ＹａｎｇＳｉｈｅ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＥｃｏｌｏｇｙ,Ａ－ｃａｄｅｍｉａＳｉｎｉｃａ,Ｓｈｅｎｙａｎｇ１１００１５）,ＪｉａｎｇＢｏ（ＩｎｓｔｉｔｕｔｅｏｆＳｅｒｉｃｕｌｔｕｒａｌＳｃｉｅｎｃｅ,Ｆｅｎｇｃｈｅｎｇ,ＬｉａｏｎｉｎｇＰｒｏｖｉｎｃｅ１１３１００）．ＣｈｉｎｅｓｅＪｏｕｒｎａｌｏｆＥｃｏｌｏｇｙ,１９９３,１２（１）：５－１０．ＴｈｅｐｒｅｓｅｎｔｓｔｕｄｙｄｅａｌｓｗｉｔｈｔｈｅｂｉｏｐｒｏｄｕｃｔｉｖｉｔｙａｎｄｄｒｙｍａｔｔｅｒｔｒａｎｓｆｅｒｏｆＣｈｉｎｅｓｅＴｕｓｓａｈ－ｆｅｅｄｉｎｇｏａｋｆｏｒｅｓｔｉｎｈｉｌｌｙａｒｅａｏｆｅ     

带扩散的Logistic单种群模型及其最优收获

在一些合理的假设条件下,就空间分布非均匀的Ｌｏｇｉｓｔｉｃ型收获模型 得到了与空间分布均匀的Ｌｏｇｉｓｔｉｃ型收获模型［１,２,３］完全平行的结论,其中包括种群持续生存和灭绝时收获努力量 Ｅ（ｘ）须满足的充要条件、种群持续生存时趋于正平衡状态的速度估计、种群灭绝时其密度趋于０的速度估计以及在种群持续生存条件下的最优收获努力量 Ｅ、最优平衡解 ｐ（ｘ）和最大收获量 ｈ＊     

不同纬度来源的野生大豆拟种群动态参数及其生态适应意义

对５个不同纬度来源的野生大豆（Ｇｌｙｃｉｎｅｓｏｊａ）、栽培大豆（Ｇｌｙｃｉｎｅｍａｓ）和半野生大豆进行同地移栽和分期播种实验表明,１年生野生大豆的拟种群的３类组元动态均符合Ｌｏｇｉｓｔｉｃ增长规律,参数ｒ与纬度呈正相关,参数Ｋ受环境饰变影响．拟种群动态拟合参数ｒ与个体的生殖力呈正相关,证实植物拟种群动态具有重要的生态适应意义．     

温度和食料对斜纹夜蛾种群的影响

用正弦模型Ｖ（Ｔ）＝Ａ＋Ｂｓｉｎ（Ｃ０＋Ｃ１ｅ＾Ｃ３Ｔ＋Ｃ２ｅ＾－Ｃ３Ｔ）拟合了斜纹夜蛾（Ｓｐｏｄｏｐｔｅｒａ ｌｉｔｕｒａ）发育与温度的关系,并用直接最优法估算了斜纹夜蛾不同发育阶段的温度阈值和所需热量。根据不同温度下的实验种群生命表资料,拟合了斜纹夜蛾不同发育阶段的存活率与温度关系的模型,卵、低龄幼虫、高龄幼虫、蛹的理论最适温度分别为２６．７、２４．７、２４．９、２５．８℃。本文研究了甘蓝、     

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％。     

Watkinson时滞差分方程模型的全局渐近稳定性

考虑差分方程ｘｎ＋１＝λｘｎ／（１＋ａｘｎ－ｋ）＾ｐ＋ｂλｘｎ－ｍ,ｎ＝０,１,２,…,其中ａ,ｂ,ｐ＞０,λ＞１,ｋ,ｍ∈｛０,１,２,…｝,当ｋ＝ｍ＝０时,Ｗａｔｋｉｎｓｏｎ用此方程来描述热带地区季蜀黍属作物的生长规律,当Ｐ＝１时,此方程就是著名的含多个滞量的Ｌｏｇｉｓｔｉｃ微分方程的离散模拟,本文主要目的是研究该方程唯一正平衡解的全局渐近稳定性。     

油松植物种群自疏规律模型的研究

根据植物生长的密度理论和有关生物学假设,推导出一种新的植物各自疏规律模型,即Ｎ＝ｅｘｐ（ａｌｎ＾２Ｂ＋ｂｌｎＢ＋ｃ）,这里Ｎ和Ｂ分别为种群密度和植物种群平均重量或平均胸高断面积,ａ,ｂ,ｃ为参数。将该模型应用于油松种群密度变化规律研究中,证明该模型能很好地拟合实际的观测资料,并且具有表达式简单等特点,因而,该模型是油松植物种群自疏规律的有效描述。     

基于线性混合效应的红松人工林枝条生物量模型

基于黑龙江省孟家岗林场60株红松解析木3643个枝条生物量的实测数据,利用全部子回归技术建立了枝条生物量模型(枝、叶和枝总生物量模型),最终选择lnw=k₁+k₂lnL_b+k₃lnD_b为枝条生物量最优基础模型.利用SAS 9.3统计软件的PROC MIXED模块建立枝条生物量混合模型,并采用AIC、BIC、对数似然值和似然比等统计指标评价不同模型的拟合效果.结果表明: 红松解析木的叶和枝总生物量混合模型以k₁、k₂、k₃作为随机效应参数的拟合效果最好,而枝生物量混合模型以k₁、k₂作为随机效应参数的拟合效果最好.最后将枝条生物量最优基础模型与最优混合模型进行模型检验.混合模型各项指标优于基础模型,能有效地提高模型的预估精度,并且通过方差协方差结构校正随机参数来反映树木之间的差异.     

Probability of fixation under weak selection: a branching process unifying approach

We link two-allele population models by Haldane and Fisher with Kimura's diffusion approximations of the Wright-Fisher model, by considering continuous-state branching (CB) processes which are either independent (model I) or conditioned to have constant sum (model II). Recent works by the author allow us to further include logistic density-dependence (model III), which is ubiquitous in ecology. In all models, each allele (mutant or resident) is then characterized by a triple demographic trait: intrinsic growth rate r, reproduction variance sigma and competition sensitivity c. Generally, the fixation probability u of the mutant depends on its initial proportion p, the total initial population size z, and the six demographic traits. Under weak selection, we can linearize u in all models thanks to the same master formula u = p + p(1 - p)[g(r)s(r) + g(sigma)s(sigma) + g(c)s(c)] + o(s(r),s(sigma),s(c), where s(r) = r' - r, s(sigma) = sigma-sigma' and s(c) = c - c' are selection coefficients, and g(r), g(sigma), g(c) are invasibility coefficients (' refers to the mutant traits), which are positive and do not depend on p. In particular, increased reproduction variance is always deleterious. We prove that in all three models g(sigma) = 1/sigma and g(r) = z/sigma for small initial population sizes z. In model II, g(r) = z/sigma for all z, and we display invasion isoclines of the 'mean vs variance' type. A slight departure from the isocline is shown to be more beneficial to alleles with low sigma than with high r. In model III, g(c) increases with z like ln(z)/c, and g(r)(z) converges to a finite limit L > K/sigma, where K = r/c is the carrying capacity. For r > 0 the growth invasibility is above z/sigma when z < K, and below z/sigma when z > K, showing that classical models I and II underestimate the fixation probabilities in growing populations, and overestimate them in declining populations.     

Prediction Equation for Lower Limbs Lean Soft Tissue in Circumpubertal Boys Using Anthropometry and Biological Maturation

Lean soft tissue (LST), a surrogate of skeletal muscle mass, is largely limited to appendicular body regions. Simple and accurate methods to estimate lower limbs LST are often used in attempts to partition out the influence of body size on performance outputs. The aim of the current study was to develop and cross-validate a new model to predict lower limbs LST in boys aged 10–13 years, using dual-energy X-ray absorptiometry (DXA) as the reference method. Total body and segmental (lower limbs) composition were assessed with a Hologic Explorer-W QDR DXA scanner in a cross-sectional sample of 75 Portuguese boys (144.8±6.4 cm; 40.2±9.0 kg). Skinfolds were measured at the anterior and posterior mid-thigh, and medial calf. Circumferences were measured at the proximal, mid and distal thigh. Leg length was estimated as stature minus sitting height. Current stature expressed as a percentage of attained predicted mature stature (PMS) was used as an estimate of biological maturity status. Backward proportional allometric models were used to identify the model with the best statistical fit: ln (lower limbs LST)  = 0.838× ln (body mass) +0.476× ln (leg length) – 0.135× ln (mid-thigh circumference) – 0.053× ln (anterior mid-thigh skinfold) – 0.098× ln (medial calf skinfold) – 2.680+0.010× (percentage of attained PMS) (R = 0.95). The obtained equation was cross-validated using the predicted residuals sum of squares statistics (PRESS) method (R ² _PRESS = 0.90). Deming repression analysis between predicted and current lower limbs LST showed a standard error of estimation of 0.52 kg (95% limits of agreement: 0.77 to −1.27 kg). The new model accurately predicts lower limbs LST in circumpubertal boys.     

The bioenergetics of the southern catfish (Silurus meridionalis Chen): growth rate as a function of ration level, body weight, and temperature

A feeding-growth experiment was conducted in the laboratory on 114 young southern catfish ( Silurus meridionalis Chen) with initial weights of 8.71–127.9g at 15, 20, 25 and 30°C. The experiment consisted of eight weight-temperature groups, with five ration levels ranging from starvation to satiation in each group. A multiple regression equation fitted to the experimental data was developed to describe the relation between specific growth rate (SGR) and the three factors, ration level (RL), body weight ( W ) and temperature ( T ): SGR = 0.471 + 0.172ln W −0.0443 T +0.0682 T ln(RL + l). This predicts that with increasing temperature the specific growth rate decreases at lower ration levels and increases at higher ration levels. The equation, SGR = a + b ln(RL + l), may be considered as the basic growth model where a is the maintenance metabolism exponent and b is the conversion exponent of the net energy; body weight and temperature influence the two parameters. With this relationship the two antagonistic effects of temperature on growth can be understood, increasing temperature imposes a negative effect on growth due to increment in energy cost for maintenance metabolism, and a positive effect due to higher efficiency of transforming food energy into net energy; the positive effect will increase at higher ration levels. This could also explain why at a restricted ration level relationships between growth and temperature are different in different species.     

Age and growth of Atlantic bluefin tuna, Thunnus thynnus (Osteichthyes: Thunnidae), in the Mediterranean Sea

The objective of the study was to describe the biometry of Mediterranean bluefin tuna, Thunnus thynnus, the biology of which is not yet well understood. A total of 504 specimens was collected from 1998 to 2005 in the central part of the Mediterranean basin. They were sexed and measured; fork lengths (FL) ranged from 51.0 to 255.0 cm while body weights (W) ranged from 2.6 to 247.0 kg. The first spiniform ray (spine) of the first dorsal fin was removed and cross‐sectioned near the condyle base in order to count annuli for age estimation. The regression coefficient (b) of the female FL–W relationship was significantly higher than that of the male, and both sexes displayed a negatively allometric growth (b < 3); male regression equation: ln W = ?2.942 + 2.730 ln FL; female regression equation: ln W = ?3.660 + 2.878 ln FL. Based on counts of the translucent zones in the sections of the first ray of the first dorsal fin, estimated ages ranged from 1 to 15 years for males and 1 to 14 years for females. The correlation between the spine ray (R) and FL fit the allometric model best; the R–FL regression equations of the two sexes did not differ significantly and the overall equation was: ln FL = 3.721 + 0.851 ln R. Due to the R–FL allometric correlation, estimates of fork lengths at previous ages, FL_i, were back‐calculated with a body proportional hypothesis. Von Bertalanffy growth equations were derived from both observed and back‐calculated FLs‐at‐age, which did not differ significantly. Moreover, no significant difference was found between the growth equations of the two sexes; the overall equation was FL_t = 373.08 [1?e^{?0.07(t + 1.76)}]. Weight‐at‐age values were derived from the von Bertalanffy predicted FLs‐at‐age by the FL–W correlation equations for males and females. The paper represents the first comprehensive study on the biometry, including age and growth, of bluefin tuna captured in the Mediterranean Sea.     

Mathematical Model of Biological Order State or Syndrome in Traditional Chinese Medicine: Based on Electromagnetic Radiation within the Human Body

In this study, based on the resonator model and exciplex model of electromagnetic radiation within the human body, mathematical model of biological order state, also referred to as syndrome in traditional Chinese medicine, was established and expressed as: “ \textSy = n/ln(6I + 1) {\text{Sy}} = \nu /\ln (6I + 1) ”. This model provides the theoretical foundation for experimental research addressing the order state of living system, especially the quantitative research syndrome in traditional Chinese medicine.     

The relative gonadal index: an alternative index for quantification of reproductive condition

Gonadal indices (i.e. GSI = gonadal wt/body wt X 100) commonly are used to quantify reproductive condition in fishes. These indices may be inappropriate with specimens of different sizes, however, for gonadal growth often is allometric. A new gonadal index (relative gonadal index, RGI) was developed to quantify the reproductive condition of animals independent of body size. The RGI is based on the underlying model W = alpha i X S beta i, where W is gonadal weight, S is body size (less gonadal weight if body weight is used), and alpha i and beta i are parameters to be estimated for gonadal developmental stage i. Assuming that a multiplicative lognormal error is appropriate, parameter estimates for alpha i and beta i were obtained by linear least squares regression for the log-transformed model ln(W) = beta i X ln(S) + ln(alpha i), where, in this form, beta i is the slope and ln(alpha i) is the intercept. Only if estimates of beta i do not differ significantly among ovarian developmental stages, as in our case, can a pooled estimate of beta be used to obtain the relative gonadal index, RGI = alpha i = W/S beta. Applicability of the RGI was tested using ovaries of three ecologically distinct fish species. The RGI was found to be more appropriate than the gonosomatic index for all three species.     

Estimation of Growth Rate from the Mitotic Index

The growth rate of a eukaryotic population dividing at a constant rate can be estimated from the equation, t_m/g ln 2 = ln (1 + R), in which t_m is the time required for mitosis, g is the generation time, and R is the fraction of cells undergoing mitosis. Values for t_m and R can be determined by direct microscope examination of the population. The validity of the derived equation has been checked with an exponentially growing culture of a prokaryote, Escherichia coli, in which chloramphenicol was administered to inhibit protein synthesis. Cells having enough protein completed the division process whereas the rest of the population was inhibited. From the plot of the growth curve before and after administration of chloramphenicol, t_m and R were estimated. The calculated and actual growth rates were almost identical.     

Dynamics of age- and size-structured populations in fluctuating environments: Applications of stochastic matrix models to natural populations

Recent developments of the theory of stochastic matrix modeling have made it possible to estimate general properties of age- and size-structured populations in fluctuating environments. However, applications of the theory to natural populations are still few. The empirical studies which have used stochastic matrix models are reviewed here to examine whether predictions made by the theory can be generally found in wild populations. The organisms studied include terrestrial grasses and herbs, a seaweed, a fish, a reptile, a deer and some marine invertebrates. In all the studies, the stochastic population growth rate (ln λ _s ) was no greater than the deterministic population growth rate determined using average vital rates, suggesting that the model based only on average vital rates may overestimate growth rates of populations in fluctuating environments. Factors affecting ln λ _s include the magnitude of variation in vital rates, probability distribution of random environments, fluctuation in different types of vital rates, covariances between vital rates, and autocorrelation between successive environments. However, comprehensive rules were hardly found through the comparisons of the empirical studies. Based on shortcomings of previous studies, I address some important subjects which should be examined in future studies.