Common-intersection hypothesis of development rate lines of ectotherms within a taxon revisited Olivier Bonato a,1 , Takaya Ikemoto b,1 , Peijian Shi c,1 , Feng Ge c,n , Yucheng Sun c , Haifeng Cao c a IRD—CBGP, Campus International de Baillarguet, 34988 Montferrier/Lez Cedex, France b Department of Microbiology, Teikyo University School of Medicine, Tokyo 173-8605, Japan c Institute of Zoology, Chinese Academy of Sciences, 1 Beichen West Road of Chaoyang District, Beijing 100101, China article info Article history: Received 1 June 2011 Accepted 25 July 2011 Available online 3 August 2011 Keywords: Effective temperature Linear model Aphididae Tetranychidae abstract The relationship between development rate of an ectotherm and temperature in experiments where insects or mites are reared under several constant temperatures, while non-linear over the entire range, can be approximately described by a line in the mid-temperature range. It was hypothesized that the development rate lines of ectotherms within a taxon such as a family would have a common intersection. Thus for a given temperature, the development time should be the same for all the species within any specified taxon. In the current study, the data on temperature-dependent development rates of species of the Aphididae and Tetranychidae families were used to test the validity of the common-intersection hypothesis. The hypothesis was supported with either dataset used. In addition, the current study tested the common-intersection hypothesis through mathematical analysis on the basis of two linear relationships (i.e., the linear relationship between temperature and development rate and that between the lower developmental threshold and the sum of effective temperatures). An attempt was made to combine the rate isomorphy hypothesis that all the lower developmental thresholds of different stages were assumed to be equal for a single species with the common-intersection hypothesis for related species within a taxon and hypothesize that if these two hypotheses hold, then for any developmental stages a common temperature of all stages should exist. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction The developmental rate of poikilothermic species is a non- linear function of constant temperature over the total range of no lethal temperatures and this relationship has been described by different models (Logan et al., 1976; Sharpe and DeMichele, 1977; Taylor, 1981; Wang et al., 1982; Schoolfield et al., 1981; Lactin et al., 1995; Bri  ere et al., 1999; Ikemoto, 2005, 2008; Shi et al., 2011). Although these models use different mathematical expres- sions they share a common characteristic, namely linearity of the relationship in the mid-temperature range (Campbell et al., 1974). Thus, a linear model is generally used to describe the tempera- ture-dependent development rates for the poikilothermic species over the mid-temperature range: r ¼ a þ bT ð1Þ where r represents the development rate, and T the temperature, while a and b are constants. The two thermal constants related to this linear model are the lower developmental threshold (t) and the sum of effective temperatures (k); t represents the critical temperature below which the development rate is equal to zero, and its estimate is  a/b; k represents the cumulative tempera- tures required for completing a developmental stage, and its estimate is 1/b. van Rijn et al. (1995) hypothesized that the lower developmental thresholds of the different stages of an insect or mite species are equal. Thus, Jaroˇ sı ´k et al. (2002, 2004) developed the rate isomorphy hypothesis (RIH, Fig. 1) using the published mean development rate data for insects and mites. Shi et al. (2010) found evidence supporting this hypothesis based on data on the developmental rate of egg and nymphal stages of Lygocoris lucorum Meyer-D ¨ ur. In addition Ikemoto (2003) pro- posed the common-intersection hypothesis (CIH), which states that the development times of the related members within a taxon (e.g., within a family) are equal at a given temperature. Therefore, the development rate lines of those species have a common intersection (Fig. 2) and the relationship between k and t could be written as k ¼ p þ qt ð2Þ where p and q are constants (see the Appendix for mathematical development). Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jtherbio Journal of Thermal Biology 0306-4565/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtherbio.2011.07.009 n Corresponding author. Tel.: þ86 10 6480 7123; fax: þ86 10 6480 7099. E-mail address: gef@ioz.ac.cn (F. Ge). 1 These three authors contributed equally to this work. Journal of Thermal Biology 36 (2011) 422–429