{"title":"[用Verhulst和Gompertz模型逼近尾草履虫动力学的时间序列:非传统方法]。","authors":"L V Nedorezov","doi":"","DOIUrl":null,"url":null,"abstract":"<p><p>For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a \"fine\" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.</p>","PeriodicalId":8942,"journal":{"name":"Biofizika","volume":"60 3","pages":"564-73"},"PeriodicalIF":0.0000,"publicationDate":"2015-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"[Approximation of Time Series of Paramecia caudatum Dynamics by Verhulst and Gompertz Models: Non-traditional Approach].\",\"authors\":\"L V Nedorezov\",\"doi\":\"\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a \\\"fine\\\" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.</p>\",\"PeriodicalId\":8942,\"journal\":{\"name\":\"Biofizika\",\"volume\":\"60 3\",\"pages\":\"564-73\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Biofizika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Biofizika","FirstCategoryId":"1085","ListUrlMain":"","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
为了近似一些著名的尾草履虫种群动态的时间序列(G. F. Gause, The Struggle For Existence, 1934),使用了Verhulst和Gompertz模型。用两种不同的方法对每个模型的参数进行估计:使用最小二乘法(全局拟合)和非传统方法(极值点方法)。对所得结果进行了比较,并与G. F.高斯所代表的结果进行了比较。理论(模型)轨迹与实验时间序列的偏差使用各种非参数统计检验进行检验。结果表明,最小二乘法估计的结果并不总是满足“精细”模型的要求。但在某些情况下,对最小二乘法估计稍加修改,可以使实验数据集得到令人满意的近似表示。
[Approximation of Time Series of Paramecia caudatum Dynamics by Verhulst and Gompertz Models: Non-traditional Approach].
For approximation of some well-known time series of Paramecia caudatun population dynamics (G. F. Gause, The Struggle for Existence, 1934) Verhulst and Gompertz models were used. The parameters were estimated for each of the models in two different ways: with the least squares method (global fitting) and non-traditional approach (a method of extreme points). The results obtained were compared and also with those represented by G. F. Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the least square method-estimations lead to the results which not always meet the requirements imposed for a "fine" model. But in some cases a small modification of the least square method-estimations is possible allowing for satisfactory representations of experimental data set for approximation.