Model-based indicators
We fitted threshold AR(p ) models (p [1,3]) and found
that the best fitting model was AR(3) (Fig. 3). For female data, the
models’ fit were worse for p = 1 (ΔAIC = 1242) and p = 2
(ΔAIC = 14), similar to the male data (p = 1 (ΔAIC = 2630) andp = 2 (ΔAIC = 15)). The fit of the threshold AR(3) model was
statistically better than that of a simple AR(3) model for the female
(\(\chi_{3}^{2}+\chi_{4}^{2}=\) 51.63, P < 0.001)
and the male (\(\chi_{4}^{2}+\chi_{5}^{2}=\) 70.56, P< 0.001). AR(p ) models also showed that air temperature
explained an important part of the deviance in body temperatures,
especially during hibernation, when body temperature was highly
synchronous with air temperature (Appendix S1, Table S4). The fitted
model showed that there were alternative states between the activity and
the hibernation states, separated by unstable saddle points that
corresponded to flickering temperature causing a region of bistability
(Fig. 4). The potential landscape confirmed the occurrence of flickering
and of two minima (stable states) separated by a local maximum (unstable
equilibrium) (Fig. 4). The potential was lower and more narrow (lower
temperature range) for Te during normal activity
than for the hibernation temperature, and it showed a similar pattern
for the two studied dormice. Switches between hibernation and activity
occurred at different critical conditions of temperature, which was
indicative of hysteresis. In late spring, dormice awoke at higher air
temperatures than air temperature when they entered hibernation in late
autumn (Fig. 5).