DISCUSSION
We show that criticality occurs in the hibernation dynamics of dormice. Around fold bifurcation points, a tiny change in ambient temperature pushes body temperature across boundaries of alternative states (from a euthermic temperature to a hibernation temperature) through large transitions. These critical transitions are characterized by flickering and punctuated changes in body temperature. Flickering is a type of complex dynamics that occur when a system rapidly moves back and forth to the vicinity of an alternative state preceding the upcoming critical transition (Scheffer et al. 2009; Dakos et al. 2013). In our study, flickering of body temperature started far from bifurcation points and it increased when the system approached these points. Thus, flickering anticipated critical transitions in hibernating dormice, as it likely does for dormice from the core of the range distribution and for other hibernating mammals, when looking at the dynamics of body temperatures (Hut et al. 2002; e.g. Talaei et al. 2011; Hoelzl et al. 2015). In humans, flickering may also anticipate physiological responses, such as epileptic seizures and narcolepsy (Scheffer 2009; Yang et al. 2016). Together with flickering, other indicators of EWS anticipated the approaching of critical transitions in hibernation dynamics. Previous studies suggest that, contrary to critical slowing down, flickering is associated with an increase in both variance and lag-1 autocorrelation, as we found in our study (Wang et al. 2012; Dakos et al. 2013). Nevertheless, the rest of indicators were less informative and even erratic: for instance, CH did not anticipate bifurcation, while DDJ metrics were very noisy. As Dakos et al. (2012) pointed out when developing the indicators, the performance of any indicator, as well as the interpretations based on them, is likely depending on the features and dynamics of the biological system studied.
Hibernation dynamics of dormice also have hysteresis, which shows the tendency of body temperature to remain on the same attractor until attaining a critical threshold value of air temperature, with the particularity that bifurcations occurred at different air temperatures for each of the two cyclic transitions. These cyclic transitions resemble the dynamics of wake-sleep and microsleeps occurring for circadian cycles in mammals (Yang et al. 2016). Since hibernation is driven by seasonal climate, its dynamics follow cycles that are locked into phase (Scheffer 2009). This type of complex cyclic dynamics occur between coupled oscillators and commonly occurs in nature (e.g. heart beating, reproductive events, and predator-prey fluctuations). Epileptic seizures mentioned above occur by the phase locking of firing in neural cells (Scheffer et al. 2009). In our study, locking of forced hibernation by forcing winter occurs with 1:1 rhythm, which means that little climate forcing is enough for locking (Scheffer 2009). Phase locking occurs for global climatic indexes such as NAO and ENSO, which are known to be coupled with a number of local seasonal ecological processes.
Statistical indicators of EWS quantify critical transitions and resilience for very different ecological systems (Scheffer et al.2015), and we show that these generic indicators can be also applied to other dynamical systems sharing their fundamental properties, such as physiological hibernation. Other physiologically critical transitions during hibernation dynamics may occur and may be anticipated, such as lipid structure and enzyme function of mitochondrial membranes from liver, kidney, brown fat, and heart tissues. High-dimensional physiological systems, such as blood cells with functional heterogeneity or neurons involved in sleep-wake cycles, also show critical transitions that can be predicted before bifurcation (Mojtahedi et al. 2016). The same dynamics occur for homeostatic changes in hormone regulation, immune responses, gene expression and asthma incidence (Krotov et al. 2014; Trefois et al. 2015). Our capacity to anticipate pathological changes and loss of resilience, e.g. due to opposite physiological commitment to that intended in normal conditions, is crucial for human health (Scheffer et al. 2018). Interestingly, hibernation dynamics and human health converge due to the increased scientific interest in the benefits of dormancy for humans in coping with different stresses, e.g. the potential of a hibernating state in astronauts for deep space travel (Lovegrove et al. 2014). Similarly, EWS can be used to detect changes in the non-linear dynamics of body temperature and the resilience of hibernating mammals due to increasing climatic stress. Physiological variables can perform better to anticipate non-linear dynamics than noisier ecological variables (Perretti & Munch 2012; Benedetti-Cecchi et al. 2015), and the former may be a good bio-indicator of ecological changes and temporal variability in resilience. Given the potential consequences that hibernation dynamics may have on population fluctuations and extinction, there is a growing concern about the impacts of climate warming on hibernating species (Inouye et al. 2000).
The influence of climate may be greater for species such as edible dormice in our Mediterranean study area. Here, heat and drought waves are associated and their frequency is increasing (Diffenbaugh et al. 2007; Vautard et al. 2007), which is affecting cold‐temperate forests, the preferred habitat of dormice (Peñuelas & Boada 2003). The potential impact on hibernating mammals in many regions is likely related to a loss of suitable habitat, mediated by climate variability, and not to a direct impact on hibernation dynamics. This is because hibernation is a very effective resilient physiological mechanism to cope with climatic stress (Lebl et al. 2011; Boutin & Lane 2014; Mitchell et al. 2018). Animals can adjust hibernation to maximize fitness, because it influences life-history traits such as recruitment by age and the onset of reproduction (Bieberet al. 2018). The evolution of hibernation has selected for a very plastic trait. The duration of hibernation may change with seasonal climate variability and with the availability of resources. For instance, rising temperatures cause earlier emergence from hibernation in the yellow-bellied marmot (Marmota flaviventris ), which has led to a longer growing season and larger body masses before entering hibernation (Ozgul et al. 2010). The demographic consequences included higher adult survival and a sharp increase in population growth rate. Hibernation in dormice shows large differences between populations depending on local climate, and harsher and longer winter means longer hibernation times, e.g. up to 11 months (Hoelzl et al. 2015). Interestingly, life history strategies of dormice are very plastic depending on those local climatic conditions, since as long as the duration of hibernation increases, adult survival is higher and fertility is lower (Pilastro et al. 2003; Ruf et al. 2006; Lebl et al. 2011). Hysteresis, such as that shown by the studied Mediterranean edible dormice, may also increase resilience by avoiding the termination of hibernation earlier than the optimal time, which may occur in regions where temperatures are sharply rising, especially during winter (Mitchell et al. 2018). Experimental studies looking at how environmental stress affects hibernation dynamics (e.g. Siutz et al. 2018) are promising to assess the changes in leading indicators of critical transitions. Exploring how criticality and tipping points appear in different hibernating animals with different evolutionary life histories and with varying ecological features may also shed light on how resilience of physiological systems cope with environmental stress.