An Algorithm for Temperature-Dependent Growth Rate Simulation

Abstract

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.

Estimative of Podisus nigrispinus (Dallas) (Heteroptera: Pentatomidae) development time with non linear models

“…Através de Modelos Não Lineares RESUMO -O objetivo deste estudo foi avaliar a precisão dos modelos não lineares de Davidson (1942Davidson ( , 1944, Stinner et al (1974), Sharpe & DeMichele (1977) PALAVRAS-CHAVE: Asopinae, controle biológico, Alabama argillacea, taxa de desenvolvimento, predador ABSTRACT -The objective of this study was to evaluate the precision of the non linear models of Davidson (1942Davidson ( , 1944, Stinner et al (1974), DeMichele (1977), and Lactin et al (1995) …”

“…The development of an organism is completed when the sum of their daily rate of development reaches value 1 (Curry & Feldman 1987). Therefore, the integral of the function of developmental rate along time (as the models of Davidson, 1942, 1944, Stinner et al 1974, Sharpe & DeMichele 1977, Lactin et al 1995 can be used to simulate the development of an organism submitted to changes in temperature. For this reason, descriptive non linear procedures have been used to analyse relationship between developmental rate of P. nigrispinus and temperature as described:…”

“…Davidson (1942Davidson ( , 1944 described developmental rate of insects as function of temperature through the use of logistic equations. Stinner et al (1974) described the effect of temperature on developmental rate as a modified sigmoid equation which results in a symmetrical curve at high temperatures. Sharpe & DeMichele (1977) formulated a complex biophysical model, later modified by Schoolfield et al (1981), which describes a non linear response of developmental rate of insects exposed to low and high temperatures as well as a linear response at intermediate temperatures.…”

“…For this reason, the purpose of this research was to determine which non linear model (Davidson, 1942, 1944, Stinner et al 1974, Sharpe & DeMichele 1977, Lactin et al 1995 can better describe the effect of temperature on P. nigrispinus development.…”

“…Several authors (Davidson 1942, 1944, Stinner et al 1974, Sharpe & DeMichele 1977, Lactin et al 1995 have formulated mathematical models to describe the relationship between developmental rate of insects and temperature. The knowledge of such relationships is important to determine seasonal occurrences of insect populations as strategies for integrated pest management (Marco et al 1997).…”