A model for the time–temperature–mortality relationship in the chill-susceptible beetle, Alphitobius diaperinus, exposed to fluctuating thermal regimes H. Colinet a,b,n , L. Lalouette b , D. Renault b a Earth and Life Institute ELI, Biodiversity Research Centre BDIV, Catholic University of Louvain, Croix du Sud 4-5, B-1348 Louvain-la-Neuve, Belgium b Universite´ de Rennes 1, UMR CNRS 6553 Ecobio, 263 Avenue du Ge´ne´ral Leclerc CS 74205, 35042 Rennes Cedex, France article info Article history: Received 27 May 2011 Accepted 15 July 2011 Available online 22 July 2011 Keywords: Temperature Thermal fluctuations Cold Insect Survival Recovery abstract Exposing insects to a fluctuating thermal regime (FTR) compared with constant low temperature (CLT) significantly reduces cold-induced mortality. The beneficial effects of FTR result from physiological repair during warming intervals. The duration and the temperature experienced during the recovery period are supposed to strongly impact the resulting cold survival; however, disentangling the effects of both recovery variables had not been broadly investigated. In this study, we investigate cold tolerance (lethal time, Lt 50 ) of the polyphagous beetle Alphitobius diaperinus. We examined adult survival under various CLTs (0, 5, 10 and 15 1C), and under 20 different FTR conditions, where the 0 1C exposure alternated with various recovery temperatures (Rt) (5, 10, 15 and 20 1C) combined with various recovery durations (Rds) (0.5, 1, 2, 3 and 4 h). Under CLTs, Lt 50 increased with temperature until no mortality occurred above the upper limit of cold injury zone (ULCIZ). Under FTRs, Lt 50 increased with both Rt and Rd. The magnitude of the survival gain was clearly boosted when Rt was above the ULCIZ (at 20 1C). Based on a data matrix of lethal times with multiple Rt  Rd combinations, a predictive model showed that cold survival increased exponentially with Rt and Rd. This model was subsequently validated with additional survival tests. We suggest that increasing recovery durations associated with optimal recovery temperatures eventually leads to a progressive chilling compensation. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Many arthropods, especially those from temperate and cold regions, may face periods of potentially harmful low tempera- tures during development or adult life (Denlinger and Lee, 2010). Environmental conditions are generally not static and diurnal thermal variations can have profound impacts on the life history traits of insects (MacMillan et al., 2005; Marshall and Sinclair, 2009; Fischer et al., 2011; Renault, 2011). Several studies demon- strated that exposing insects to fluctuating thermal regimes (FTRs) (i.e., cold-exposure interrupted by periodic short warming pulses) could significantly reduce adult mortality (Coulson and Bale, 1996; Nedvˇ ed et al., 1998; Hanc ˇ and Nedvˇ ed, 1999; Renault et al., 2004; Colinet et al., 2006; Koˇ sta ´l et al., 2007; Colinet and Hance, 2010; Renault, 2011; Terblanche et al., 2010). FTRs promote cold survival of insects despite the sudden thermal variations experienced by individuals. As the total duration at low temperature (i.e. overall dose of cold) is shorter under FTRs than under constant low temperature (CLT) (Hanc ˇ and Nedvˇ ed, 1999; Renault et al., 2004; Colinet et al., 2006), the beneficial effects of warming pulses results, at least in part, from a reduced amount of accumulated injuries under FTRs. However, this only partially explains the benefits of FTRs as the cold survival remains much higher under FTRs than CLTs, when subtracting the time spent at a high temperature (e.g. Hanc ˇ and Nedvˇ ed, 1999; Renault et al., 2004); the beneficial effects of warming pulses also provide a periodic opportunity to physiologically repair chilling injuries, which otherwise accumulate under CLTs (e.g. Colinet et al., 2007a, 2007b; Koˇ sta ´l et al., 2007; Lalouette et al., 2007). Survival of insects exposed to low temperature depends on combination of factors, such as the duration and temperature of exposure (e.g. Leather et al., 1993; Sømme, 1996; Bale, 2002; Chown and Terblanche, 2006). Cold-induced mortality is gener- ally determined by exposing insects to CLTs (Bale, 2002; Sømme, 1996). However, chill-susceptible species may exploit daily bouts at warm temperature to recover from chilling injuries. Several predictive models based on a degree-time concept have been proposed to describe the time–temperature–mortality relationship under CLTs (e.g. Turnock et al., 1983; Powell, 2003; 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.2011.07.004 n Corresponding author at: Earth and Life Institute ELI, Biodiversity Research Centre BDIV, Catholic University of Louvain, Croix du Sud 4-5, B-1348 Louvain-la- Neuve, Belgium. E-mail address: herve.colinet@uclouvain.be (H. Colinet). Journal of Thermal Biology 36 (2011) 403–408