Most organisms restrict their specific activities and physiological and developmental processes to their optimal time of day to enhance their rates of survival and reproduction (DeCoursey, 2004, Saunders, 2002). The timing of many of these processes are regulated by circadian clocks with a period of ∼24 h. Phenomena induced by the circadian clock can be observed under constant conditions as clear free-running circadian rhythms with a periodicity that is slightly different from that of 24 h. These rhythms are entrained to the daily cycles of the environment because zeitgebers such as light and temperature induce a phase shift (phase advance or phase delay) of the circadian clock (DeCoursey, 2004, Pittendrigh, 1981a, Saunders, 2002).

Soil temperature cycles are important for the entrainment of the circadian clocks of underground organisms because light is not able to penetrate the soil (Miyazaki et al., 2011, Tanaka and Watari, 2003, Watari et al., 2006). However, owing to the low heat conductivity of soil, the amplitude of the temperature cycle (defined here as the difference between the maximum and minimum temperatures) decreases, and the phase of the temperature cycle is delayed with increasing soil depth (Bridges, 1997). If the circadian clock of underground organisms responds only to a particular phase in the temperature cycle, the biological event regulated by the clock occurs later with increasing soil depth, and its untimely occurrence could cause unfavorable outcomes. Therefore, organisms located deeper in the soil need to advance their circadian clocks relative to the phase of the temperature cycle (Tanaka and Watari, 2003).

The onion fly, Delia antiqua, pupates at a depth of 2–20 cm in the soil (Akita Agricultural Experiment Station, 1950, Inoue, 1967, Watari et al., 2006). This fly ecloses in the early morning to avoid soil surface temperatures of > 38 °C in the middle of sunny days (Tanaka and Watari, 2003, Tanaka and Watari, 2009). The timing of eclosion is controlled by the circadian clock (Watari, 2002a, Watari and Tanaka, 2014). Sensitivity to zeitgebers occurs only in the late pupal stage, and a lack of zeitgebers during this period causes arrhythmic eclosion (Watari, 2005, Watari and Tanaka, 2014). Therefore, in the soil, the temperature cycle seems to be the sole zeitgeber available to entrain the eclosion clock of D. antiqua (Tanaka and Watari, 2003, Watari, 2002b). To time eclosion, this fly can detect a temperature difference as small as 1 °C per day (Tanaka and Watari, 2003, Watari and Tanaka, 2014). Tanaka and Watari (2003) found that D. antiqua could compensate for the depth-dependent phase delay of soil temperature change by advancing its eclosion time as the temperature amplitude decreased. Therefore, the pupae can eclose early in the morning, irrespective of their depth. For example, eclosion in response to temperature cycles with an amplitude of 1–2 °C occurs 4–5 h earlier than that of those with an amplitude of 8 °C (Miyazaki et al., 2018, Tanaka and Watari, 2017, Watari and Tanaka, 2014). This “temperature-amplitude response” with respect to adult emergence has also been reported in the flesh fly Sarcophaga crassipalpis and in the cabbage moth, Mamestra brassicae, which both pupate underground (Miyazaki et al., 2011, Tanaka et al., 2013); in the Indian meal moth, Plodia interpunctella, which pupates within a food substrate such as grains (Kikukawa et al., 2013); and in the alfalfa leafcutting bee, Megachile rotundata, which pupates in various cavities (Bennett et al., 2018, Yocum et al., 2016).

The mechanism that regulates eclosion time in response to the temperature amplitude remains unknown. In D. antiqua, the timing of eclosion and the expression pattern of the circadian clock gene period depend in a similar manner on the amplitude of the temperature cycle (Miyazaki et al., 2016). This suggests that the mechanism that induces the temperature-amplitude response involves the circadian clock rather than further downstream physiological processes. In addition, it has been suggested that a large temperature amplitude acts as a strong zeitgeber and a small temperature amplitude acts as a weaker zeitgeber for this eclosion rhythm (Tanaka and Watari, 2017, Watari and Tanaka, 2010, Watari and Tanaka, 2014). The temperature-amplitude response of D. antiqua may be attributed to the dependence of the circadian phase shift on the temperature amplitude (Miyazaki et al., 2018).

The magnitude and direction of a phase shift of the circadian rhythm after applying a zeitgeber stimulus depend on the phase of the stimulus. Phase transition curves (PTCs) and phase response curves (PRCs) are constructed to represent the phase-dependent phase shifts obtained when single pulses of the zeitgeber systematically perturb various phases of a free-running rhythm (Johnson et al., 2004, Pittendrigh, 1981b, Saunders, 2002, Winfree, 2001). The strength of a zeitgeber pulse (e.g., the light intensity or duration of a light pulse and the amount of temperature change or duration of a temperature pulse) quantitatively affects the magnitude of the phase shift and can change the slope of the PTCs and the amplitude of the PRC (Francis and Sargent, 1979, Gooch et al., 2008, Pittendrigh, 1981b, Rensing and Ruoff, 2002, Saunders, 2002). PTCs and PRCs provide useful information regarding the entrainment of rhythm into an environmental cycle and the underlying mechanisms (Johnson et al., 2004, Pittendrigh, 1981b, Saunders, 2002, Winfree, 2001).

To clarify the physiological mechanisms that induce a temperature-amplitude response, we performed phase-resetting experiments for the circadian eclosion rhythm of D. antiqua using a single high- or low-temperature pulse with an amplitude of 1 °C or 4 °C. Based on these results, we constructed PTCs and PRCs. Furthermore, we discuss how the temperature-amplitude response of D. antiqua is established.