Skip to main content Accessibility help


  • R. E. Stinner (a1), A. P. Gutierrez (a2) and G. D. Butler (a3)


With the current advances in insect population modelling, the need for more accurate simulation of temperature-dependent growth rates has become vital. The day-degree concept, with its linear temperature–rate relationship, has not been adequate for simulation of field populations under highly variable temperature conditions. Similarly, several of the non-linear relationships proposed in the past (Janisch’s catenary, parabola) have also been inadequate. All of these relationships produce large errors at temperature extremes.

This paper presents a comparison of various functions which have been used for developmental time estimation and an algorithm for a sigmoid function which can be used in simulations having either a calendar or a physiological time base. Validation of the algorithm is presented for three insect species.



Hide All
Blunck, H. 1914. Die Entwicklung des Dytiscus marginalis L., vom Ei bis zur Imago. Z. wiss. Zool. 111: 76151.
Conway, G. R., Glass, N. R., and Wilcox, J. C.. 1970. Fitting nonlinear models to biological data by Marquardt's algorithm. Ecology 51: 503507.
Crozier, W. J. 1926. On curves of growth, especially in relation to temperature. J. gen. Physiol. 10: 5373.
Eubank, W. P. et al. 1973. The significance and thermodynamics of fluctuating versus statis thermal environment on Heliothis zea egg development rates. Environ. Ent. 2: 491496.
Janisch, E. 1925. Uber die Temperaturabhangigbeit biologischer Vorgange und ihre kurvenmassige Analyse. Arch. ges. Physiol. 209: 414436.
Krogh, A. 1914. On the influence of temperature on the rate of embryonic development. Z. allg. Physiol. 16: 163177.
Luckmann, W. H. 1963. Measurements of the incubation period of corn earworm eggs. J. econ. Ent. 56: 6062.
Marquardt, D. W. 1963. An algorithm for least-squares estimation of non-linear parameters. J. Soc. Lud. app. Math 11: 431441.
Marquardt, D. W. 1966. Least squares estimation of nonlinear parameters. IBM SHARE Library Distribution No. 309401, NLIN 2 August 1966.
Messenger, P. S. 1964. The influence of rhythmically fluctuating temperatures on the development and reproduction of the spotted alfalfa aphid, Therioaphis maculata. J. econ. Ent. 57: 7176.
Messenger, P. S. and Flitters, N. E.. 1958. Effect of constant temperature environments on the egg stage of three species of Hawaiian fruit flies. Ann. ent. Soc. Am. 51: 109119.
Messenger, P. S. and Flitters, N. E.. 1959. Effect of variable temperature environments on egg development of three species of fruit flies. Ann. ent. Soc. Am. 52: 191204.
Robertson, T. B. 1923. The chemical basis of growth and senescence. Lippincott, Philadelphia. 389 pp.
Sanderson, E. D. 1910. The relation of temperature to the growth of insects. J. econ. Ent. 3: 113140.


  • R. E. Stinner (a1), A. P. Gutierrez (a2) and G. D. Butler (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.