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The effect of time lags on the stability of the equilibrium state of a population growth equation


On the stability of the stationary state of a population growth equation with timelag


This is the intuition for why a linear differential equation makes sense as a benchmark for the population growth equation.




 The purpose of the present report is to study the population growth of a highly commercially exploited species, Hairtails, in its major distribution area in order to provide a ibasis for controlling the population dynamics and considering possible management measures.The specimens of the main population used for this study were collected in the northern East China Sea from May 1977 to June 1978, but some elder ones were the spawners in 1976 and 1979, and specimens of other populations were collected from 9... The purpose of the present report is to study the population growth of a highly commercially exploited species, Hairtails, in its major distribution area in order to provide a ibasis for controlling the population dynamics and considering possible management measures.The specimens of the main population used for this study were collected in the northern East China Sea from May 1977 to June 1978, but some elder ones were the spawners in 1976 and 1979, and specimens of other populations were collected from 9 fishing grounds located in the South China Sea and the southern East China Sea as well as the Bohai Sea and Huangbai Sea in. recent years.Based on the study of the age, the measurement of the body and its otolith transverse section, the relative growth of otolith and population growth pattern as well as the weightlength relationship of this fish, the problem of geographical differences in population growth ih the northern Bast China Sea and elsewhere is discussed. The results of our study are summarized as follows :1.The otolith and (body growth of this fish are 'closely related to the form of the power function curve, so that the otoliih can be used for (backcalculating the fish growth.2.The females fish grows slightly faster than the males, but the growth differences between the sexes are not significant statistically.3.Based on the bimodal distribution of first ring radius of otolith and body length of young fish, it may be concluded that the Hairtails generally consist of two or three groups such as spring and summer and autumn broods, but so far as concerns the main population, it may be devided into two groups by the size of the first ring radius, the earlierborn group .(spring and summer broed, r>0.72 mm) and lateborn group au tumn brood, r<0.72mm).4.The weightlength relationships of the main population (A+S) and its earlierborn group(S) and laterborn group (A) are expressed in equations 19  21.5. The growth pattern of this fish could be expressed in equations 1324.6.Growth in weight with age for this fish is determined also as a typically asbymetric sigmoid curve, the inflexion corresponding to maximum growth rate occurs at 3.26 age (3.17 for ealierborn group and 3.43 for laterborn group). It has been observed that the majority of individuals in 1 age group has attained sexual maturity and all the males and females 'become sexually mature in 2 years. The significance of the inflexion of the population growth equation by weight should be further netted because the size at instantaneous first capture providing the maximum yield generally lies at around this point.7.The increment and incremental rate of this fish in standard length and weight are described with dL/dt, d2L/dt2, dW/dt and d2W/dt2 curves respectively (F g. 2,4).8.The obvious growth difference in body length and weight between the earlier and laterborn group is found only in first two years, but not so obvious in growon parameters such as the limiting body length, weight and inflexion of growth curve for weight.9.The geographical difference in population growth is found obvious orey between the populations of subtropical waters (the South China Sea) and temperate waters.10.The Hairtails have a more rapid growth rate than the Large Yelloy Croaker or the Small Yellow Croaker, and its long breeding period as well as the predt tory and mixed feeding habit account for its great productivity. While the number of the other two species of croakers are greatly reduced as a result of heavy fishing pressure., they are still present in significant amount to be the main fish stock of the fishing ground and their growth rate is get higher than years ago. If the fishing of the, last two lowest age, group can be postponed one or two years later, its population productivity may possibly be increased greatly. Thus, it is very promosing to have a further development of this fishery. .  本文根据带鱼耳石横断面切片的显微观测和鱼体测量结果,着重分析物种数量分布中心海区的主体种群和不同季节出生群的生长特征,并对种群生长的地理差异以及年代差异与渔业资源的合理利用问题进行了探讨。  Rhesus, monkey (Macaco mulatta) at Nanwan Peninsula of Hainan Island were researched for five years by field observation from 1981 to 1985. By the end of 1984, the monkey population at the peninsula had reached 930 individuals. The average annual population growth rate was about 13% from 1965 to 1984. The relative equation between the growth rate and population density was described by y=0.0003x2 + 0.0857x+ 7.3534. The population growth equation can be written as exponential growth equation... Rhesus, monkey (Macaco mulatta) at Nanwan Peninsula of Hainan Island were researched for five years by field observation from 1981 to 1985. By the end of 1984, the monkey population at the peninsula had reached 930 individuals. The average annual population growth rate was about 13% from 1965 to 1984. The relative equation between the growth rate and population density was described by y=0.0003x2 + 0.0857x+ 7.3534. The population growth equation can be written as exponential growth equation Y = 0.1253e0.105x or Logistic growth equation N = 1850/1+e11.280.13x.The maximum carrying capacity at the peninsula is approximately 1850 individuals. The size of elastic core area of a group's activity was affected by the population density and the quality of vegetative cover.  自1981年以来,对海南岛南湾半岛猕猴进行了连续5年的调查研究。归纳1965年到1984年底的材料,该种群从100只发展到930只,其间种群的年均增长率为13％,种群增长率受着种群密度的制约,密度与增长率间存在着关系式y=0.0003x~2+0.0857x+0.3534。该种群生长曲线可表示为指数函数式y=0.1253e~(0.1046x)或为Logistic曲线N=1850/1+e~(11.280.13x)。该半岛猕猴最大容纳量为1850只。各猴群的弹性核域受猴群密度和植被质量的影响,绘出了它们之间的关系图。  Over population is a difficult problem facing mankind. The present papersuccessfully establishes a local population pattern by applying the population control theory and population growth equation. With the help of computer, an estimation of thefifteyeightyear population growth in Changnin County has been carried out. By comparing the figure obtained from the fourth national census of the county with the projectedpopulation in 1990, an absolute error is found to be only two persons, and... Over population is a difficult problem facing mankind. The present papersuccessfully establishes a local population pattern by applying the population control theory and population growth equation. With the help of computer, an estimation of thefifteyeightyear population growth in Changnin County has been carried out. By comparing the figure obtained from the fourth national census of the county with the projectedpopulation in 1990, an absolute error is found to be only two persons, and the rate of error is less than seven perucent. A scientific projection of the future population can provideastrong basis for the planning of the local economic and social development, the population program and the policy on population.  人口问题是人类面临的难题本义应用人口控制论及人口发展方程，成功地建立了区域人口模型。通过计算机对昌宁县的人口发展进行５８年预测．１９９０年人口预测值与全国第四次人口普查数相比，绝对误差仅２人，误差率不到百万分之七．科学地预测未来人口状况，能为区域经济和社会发展计划，人口规划和人口政策提供强有力的依据．   << 更多相关文摘 
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