A new linearized formula for the law of total effective temperature and the evaluation of line-fitting methods with both variables subject to error

被引:268
作者
Ikemoto, T
Takai, K
机构
[1] St Marianna Univ, Sch Med, Dept Immunol & Med Zool, Miyamae Ku, Kawasaki, Kanagawa 2168511, Japan
[2] Teikyo Univ, Sch Med, Dept Microbiol, Itabashi Ku, Tokyo 1730003, Japan
关键词
temperature-dependent development; linear-fitting; errors-in-variables models; reduced major axis; geometric mean functional relationship;
D O I
10.1603/0046-225X-29.4.671
中图分类号
Q96 [昆虫学];
学科分类号
摘要
In the quantitative analysis of experimental data regarding temperature-dependent development, the so-called law of total effective temperature is sometimes expressed in the linearized equation 1:1/D = - (t/k) + (1/k) T. D indicates the duration of development; T, temperature; t, the estimated developmental zero temperature; and k, the effective cumulative temperature. The method of fitting usually involves the regression of y = 1/D on x = T. Although the degree of fitting of equation 1 to data within optimum temperature ranges is fairly satisfactory, we have in the current study addressed three problems regarding the use of equation 1 and methods of fitting involving the regression of y on x. First, we found that the detection of optimum temperature ranges is frequently difficult with equation 1. Second, in applying the method of regression of y on x with equation 1, the weights of the data points are disproportionate between those in the upper and lower parts of the line and they are not homogeneous along the temperature axis. The lower the temperature, the more disproportionate weight is burdened and the less weight is loaded. Third, in most of the data, errors in the x-variable are ignored. The second and third problems would in most cases res result in a reduction in the slope of the line, a smaller t, and a larger k. Therefore, we proposed a new linearized formula: (DT) = k + tD. We further propose the use of the reduced major axis, obtained as the solution of the functional model among bivariate errors-in-variables models, in the method of fitting to data. We demonstrated that the majority of the problems raised above could be unraveled under this new approach based on statistical analysis.
引用
收藏
页码:671 / 682
页数:12
相关论文
共 66 条
[1]  
ANDERSON TW, 1956, 3RD P BERK S MATH ST, V5, P111
[2]   THERMAL RESPONSE AND REVERSIBILITY OF DIAPAUSE IN THE EGGS OF LOCUSTA-MIGRATORIA [J].
ANDO, Y .
PHYSIOLOGICAL ENTOMOLOGY, 1993, 18 (01) :1-6
[3]  
[Anonymous], 1998, Applied regression analysis, DOI 10.1002/9781118625590
[4]  
[Anonymous], 1979, The Advanced Theory of Statistics
[5]   PROPERTIES OF THE GEOMETRIC MEAN FUNCTIONAL-RELATIONSHIP [J].
BARKER, F ;
SOH, YC ;
EVANS, RJ .
BIOMETRICS, 1988, 44 (01) :279-281
[6]   ARE THERE 2 REGRESSIONS [J].
BERKSON, J .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1950, 45 (250) :164-180
[7]  
Bodenheimer F. S., 1926, Zeitschrift fuer Angewandte Entomologie, V12, P91
[8]   Comparison of temperature-dependent growth models with the development of Lobesia botrana (Lepidoptera: Tortricidae) [J].
Briere, JF ;
Pracros, P .
ENVIRONMENTAL ENTOMOLOGY, 1998, 27 (01) :94-101
[9]   A novel rate model of temperature-dependent development for arthropods [J].
Briere, JF ;
Pracros, P ;
Le Roux, AY ;
Pierre, JS .
ENVIRONMENTAL ENTOMOLOGY, 1999, 28 (01) :22-29
[10]   TEMPERATURE REQUIREMENTS OF SOME APHIDS AND THEIR PARASITES [J].
CAMPBELL, A ;
FRAZER, BD ;
GILBERT, N ;
GUTIERREZ, AP ;
MACKAUER, M .
JOURNAL OF APPLIED ECOLOGY, 1974, 11 (02) :431-438