# Ecological responses of squamate reptiles to nocturnal warming

Alexis Rutschmann, Constant Perry, Jean-François Le Galliard, Andréaz Dupoué, Olivier Lourdais, Michaël Guillon, George Brusch, Julien Cote,

Murielle Richard, Jean Clobert, et al.

► To cite this version:

Alexis Rutschmann, Constant Perry, Jean-François Le Galliard, Andréaz Dupoué, Olivier Lourdais, et al.. Ecological responses of squamate reptiles to nocturnal warming. Biological Reviews, 2024, 99 (2), pp.598-621. 10.1111/brv.13037. hal-04330903

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1 Ecological responses of squamate reptiles to nocturnal warming

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3 Alexis Rutschmann¹,*, Constant Perry¹, Jean-François Le Galliard²,³, Andréaz

4 Dupoué⁴, Olivier Lourdais⁵,⁶, Michaël Guillon⁵,⁷, George Brusch IV⁸, Julien

5 Cote⁹, Murielle Richard¹, Jean Clobert¹ and Donal B. Miles¹⁰

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7 ¹Station d'Ecologie Théorique et Expérimentale de Moulis, CNRS UAR2029, 02 route du CNRS, 09200 Moulis, France

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9 ²Sorbonne Université, CNRS, UMR 7618, IRD, INRAE, Institut d'écologie et des sciences de l'environnement (iEES Paris), Tours 44-45, 4 Place Jussieu, 75005 Paris, France

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11 ³Département de Biologie, Ecole Normale Supérieure, PSL Research University, CNRS, UMS
12 3194, Centre de Recherche en écologie expérimentale et Prédictive (CEREEP-Ecotron
13 IleDeFrance), 78 rue du château, 77140 Saint-Pierre-Lès-Nemours, France

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14 ⁴Ifremer, Univ Brest, CNRS, IRD, UMR 6539, LEMAR, 1625 Rte de Sainte-Anne, 29280 Plouzané, France

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16 ⁵Centre d'Etudes Biologiques de Chizé, CNRS UMR 7372 - Université de La Rochelle, 405 Route de Prissé la Charrière, 79630 Villiers-en-Bois, France

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18 ⁶School of Life Sciences, Arizona State University, Life Sciences Center Building, 427E Tyler Mall, Tempe, AZ 85281, USA

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20 ⁷Cistude Nature, Chemin du Moulinat - 33185 Le Haillan, France

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21 ⁸Department of Biological Sciences, California State University San Marcos, 333 S. Twin Oaks Valley Rd., San Marcos, California 92096, USA

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23 ⁹Laboratoire Evolution et Diversité Biologique (EDB), UMR5174, Université Toulouse 3 Paul Sabatier, CNRS, IRD, 118 Rte de Narbonne, 31077, Toulouse, France

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¹⁰Department of Biological Sciences, 131 Life Science Building, Ohio University, Athens,

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Ohio 45701, USA

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*Author for correspondence (E-mail: alexis.rutschmann@gmail.com; Tel.: +33 5 61 04 03

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60).

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ABSTRACT

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Nocturnal temperatures are increasing at a pace exceeding diurnal temperatures in most parts of the world. The role of warmer nocturnal temperatures in animal ecology has received scant attention and most studies focus on diurnal or daily descriptors of thermal environments' temporal trends. Yet, available evidence from plant and insect studies suggests that organisms can exhibit contrasting physiological responses to diurnal and nocturnal warming. Limiting studies to diurnal trends can thus result in incomplete and misleading interpretations of the ability of species to cope with global warming. Although they are expected to be impacted by warmer nocturnal temperatures, insufficient data are available regarding the night-time ecology of vertebrate ectotherms. Here, we illustrate the complex effects of nocturnal warming on squamate reptiles, a keystone group of vertebrate ectotherms. Our review includes discussion of diurnal and nocturnal ectotherms, but we mainly focus on diurnal species for which nocturnal warming affects a period dedicated to physiological recovery, and thus may perturb activity patterns and energy balance. We first summarise the physical consequences of nocturnal warming on habitats used by squamate reptiles. Second, we describe how such changes can alter the energy balance of diurnal species. We illustrate this with empirical data from the asp viper (*Vipera aspis*) and common wall lizard (*Podarcis muralis*), two diurnal species found throughout western Europe. Third, we make use of a mechanistic approach based on an energy-balance model to draw general conclusions about
the effects of nocturnal temperatures. Fourth, we examine how warmer nights may affect squamates over their lifetime, with potential consequences on individual fitness and population dynamics. We review quantitative evidence for such lifetime effects using recent data derived from a range of studies on the European common lizard (Zootoca vivipara).

Finally, we consider the broader eco-evolutionary ramifications of nocturnal warming and highlight several research questions that require future attention. Our work emphasises the importance of considering the joint influence of diurnal and nocturnal warming on the responses of vertebrate ectotherms to climate warming.

*Key words:* ectotherms, energy-balance model, global warming, minimum temperature, squamates, thermal performance curve.

# CONTENTS

## I. Introduction

## II. Nocturnal warming and the thermal microhabitats of squamates

(1) The asymmetry in warming between diurnal and nocturnal air temperatures

(2) Nocturnal warming and microhabitats exploited by squamates: the value of legacy data

## III. Impact of nocturnal warming: short-term effects on the cost-to-benefit balance?

(1) Increased performance and new opportunities for activity for diurnal ectotherms

(2) Limits to nocturnal activity for diurnal ectotherms

(3) Summer heatwave and nocturnal warming: a case study in a diurnal snake

## IV. Balance between costs and benefits: a modelling approach

(1) Model development

(2) Modelled scenarios: nocturnal temperature and thermoregulation pattern

(3) Results and conclusions
(4) Empirical analysis of energy balance in the European common lizard

V. Chronic effects of nocturnal warming

(1) Warmer nights entail delayed costs in diurnal species

(2) Can diurnal ectotherms mitigate the impacts of chronic nocturnal warming?

(3) Quantitative insights from the European common lizard

VI. Nocturnal warming: open questions and future research

(1) Are the effects of warmer nights similar for diurnal and nocturnal species?

(2) Are the effects of warmer nights similar in tropical, arid and temperate areas?

(3) Will warmer nocturnal temperatures shift life-history strategies?

(4) Will warmer nights alter interactions between squamates and other species?

(5) Will interactions between warmer nights and other climatic factors alter squamate
ecology?

VII. Conclusions

VIII. Acknowledgments

IX. Author contributions

X. References

XI. Supporting information

**I. INTRODUCTION**

Over the past century, mean air temperatures have been increasing across most regions of the
globe, threatening numerous species and ecosystems (Pörtner *et al.*, 2022). Yet, in many parts
of the world, climate warming appears to be an asymmetrical process driven by a more rapid
increase of nocturnal ($T_N$) than diurnal air temperatures ($T_D$) (Dai, Trenberth & Karl, 1999;
Sun *et al.*, 2000; Vose, Easterling & Gleason, 2005; Alexander *et al.*, 2006). Despite this,
most studies evaluating the impact of global warming either consider temperature increments
to be constant over a 24-h cycle or focus solely on diurnal patterns (e.g. maximum daily temperature), with nocturnal warming often considered an inconsequential aspect of climate change (Speights et al., 2018). Ignoring nocturnal warming is however of particular concern because the available data show that organisms can exhibit different, and sometimes opposing, eco-physiological responses to T~D~ and T~N~ (Xia et al., 2009; Zhao et al., 2014; Freixa et al., 2017; Speights & Barton, 2019). Thus, studies that focus only on diurnal warming may provide a somewhat simplified and incomplete assessment of the vulnerability and capacity of organisms to cope with climate change (Vickerman & Sunderland, 1975; Peng et al., 2013; Zhao et al., 2014; Speights, Harmon & Barton, 2017; Ma, Ma & Pincebourde, 2021).

Plant ecologists have been at the forefront of investigations of the impacts of nocturnal warming on functional traits and ecological interactions of organisms. For example, in an early study, Alward, Detling & Milchunas (1999) demonstrated that warmer T~N~ altered the composition of plant communities of the north-eastern Colorado steppes, with a decrease of the dominant C~4~ grass species in favour of exotic and native C~3~ forbs. Warmer T~NS~ were later shown to influence vegetation productivity (Peng et al., 2013; Mu et al., 2015), growth (Clark, Clark & Oberbauer, 2010; Xia et al., 2018) and phenology (Wang, Luo & Shafeeque, 2019). Mechanistic responses by plants to warmer T~N~ are complex and operate at different levels (Sadok & Krishna Jagadish, 2020). Leaf morphology and physiology appear to play a crucial role, with warmer T~NS~ leading to a reduction in leaf quality and earlier senescence, which results in higher respiration rates at night and a decline in photosynthesis-dependent processes. Ultimately, these modifications can have cascading effects on plant growth, seed production and fitness (García et al., 2015; Lesjak & Calderini, 2017). Recently, entomologists have begun to investigate the effects of the diel patterns of climate change. Studies focusing on insect species have revealed heterogeneous and complex responses (i.e.
neutral, positive and/or negative) to warmer $T_{NS}$, ranging from individual physiology to community dynamics (Whitney-Johnson, Thompson & Hon, 2005; Warren & Chick, 2013; Ma, Hoffmann & Ma, 2015; Barton, 2017; Speights et al., 2017; Bai et al., 2019).

The susceptibility of insects to warmer $T_{NS}$ is not surprising: ectotherms rely on external heat sources to regulate their body temperature and to maintain it within a range of temperatures that optimises performance (Angilletta et al., 2002; Seebacher & Franklin, 2005; Clusella-Trullas, Blackburn & Chown, 2011). The temperature dependence of physiological performance in ectotherms is classically conceptualised as a thermal performance curve (TPC; Fig. 1). The curve describes the response of a focal performance trait [e.g. activity, metabolic rate (MR), individual growth rate, locomotion, digestion, population growth rates] to changes in body temperature. Most TPCs are assumed to follow a left-skewed bell-shaped curve: the performance increases steadily from the critical thermal minimum ($CT_{min}$) up to a peak value attained at the optimal body temperature ($T_{opt}$). Above $T_{opt}$, performance usually exhibits a sharp decline towards the critical thermal maximum ($CT_{max}$). The range between $CT_{min}$ and $CT_{max}$ therefore defines an organism's critical thermal range for nocturnal and diurnal activities. Given the rapid decline of performance above $T_{opt}$, ectotherms are highly sensitive to increases in maximum environmental temperatures as these temperatures are likely to push an organism's body temperature beyond $T_{opt}$ and towards $CT_{max}$ (Deutsch et al., 2008; Buckley, Tewksbury & Deutsch, 2013; Rohr & Palmer, 2013; Burraco et al., 2020; Clusella-Trullas et al., 2021). Yet patterns of activity can also be influenced by minimum temperatures: daily or seasonal increase in $T_N$ can push organism body temperatures towards higher values, away from their $CT_{min}$ and therefore to within an adequate thermal range for activity. An increase in minimum temperatures can, for example, facilitate the colonisation of new habitats by offering new opportunities for foraging and hunting or by increasing intrinsic physiological rates (e.g. digestion, metabolic rates) (Battisti
et al., 2005). Another potential consequence is the alteration of an individual's resting thermal range: warmer minimum temperatures may trigger an increase in resting physiological rates (e.g. resting MR, cellular damage reparation rates) that could increase energy consumption (Speights et al., 2017; Ma et al., 2020).

Because research on the impact of nocturnal warming is at an early stage, our goal here is threefold. We first discuss the potential responses of vertebrate ectotherms to warmer nights. Next, we use published data, legacy data and analytical models to illustrate such responses. Finally, we propose avenues for future research studying the impact of nocturnal warming on organisms. To do so, we present a comprehensive assessment of the consequences of warmer nights on an emblematic group of vertebrate ectotherms, the order Squamata. This order includes three keystone groups (amphisbaenians, lizards and snakes) and represents the largest group of non-avian reptiles (11,549 species; Uetz et al., 2023). Squamates occur in most biomes of the globe and exhibit a wide diversity of morphological, physiological, behavioural and ecological strategies (Meiri, 2018). The sensitivity of squamates to increasing maximum air temperature is well documented (Thomas et al., 2004; Araújo & Rahbek, 2006; Dupoué et al., 2022; Stark et al., 2023; Zhang et al., 2023) and one study forecasts that climate warming will lead to the extinction of almost 40% of these species by 2080 (Sinervo et al., 2010). Yet little is known about the impact (positive or negative) of warmer minimum air temperatures (i.e. T<sub>N</sub>) on this extinction rate. The well-studied group of squamates thus provides an opportunity to clarify the impacts of nocturnal warming on ectothermic vertebrates (Taylor et al., 2020), and we anticipate the general conclusions drawn from our work are likely to be applicable to other taxonomic groups. Although our review discusses such impacts on both diurnal and nocturnal ectotherms (see Sections IV.2 and VI.1), we mainly focus on diurnal squamates. For diurnal species, nocturnal warming affects a period dedicated to physiological recovery, and may perturb activity patterns and energy
balance in a complex manner (Fig. 2). By contrast, warmer $T_N$ affects the primary activity period of nocturnal species and it is possible that nocturnal reptiles mainly benefit from increasing physiological performance and foraging opportunities, although there are fewer data to confirm this hypothesis.

We first discuss the physical basis of nocturnal warming and the implications of warmer nights on habitats used by squamates. Here, we emphasise the importance of legacy data to understand better the microhabitat dynamics of nocturnal warming. Second, we focus on the immediate effects of warmer nights on an individual's physiology and behaviour. In particular, we illustrate how warmer nights may change the activity window of many diurnal species while also entailing a concomitant increase in metabolic expenditure. Third, we explore the immediate energetic costs and benefits of warmer nights for a range of behavioural and foraging strategies used by ectothermic predators by extending the energy balance model of Huey & Kingsolver (2019). Fourth, we expand our discussion beyond short-term effects and consider the potential chronic implications of nocturnal warming on the physiology, life history, and population ecology of squamates. We illustrate this by synthesising extensive quantitative evidence from studies of the European common lizard (*Zootoca vivipara*) in our laboratories. Finally, we highlight the eco-evolutionary ramifications of nocturnal warming by proposing future avenues of research and emphasise the importance of considering the multifaceted aspects of climate change when studying nocturnal warming.

## II. NOCTURNAL WARMING AND THE THERMAL MICROHABITATS OF SQUAMATES

### (1) The asymmetry in warming between diurnal and nocturnal air temperatures

Between 1950 and 2004, $T_{NS}$ increased at a rate exceeding 1.4 times the observed change in maximum $T_D$ on average across the world (0.204 versus 0.141 °C per decade) (Karl *et al*.,
1993; Easterling *et al.*, 1997; Dai *et al.*, 1999; Vose *et al.*, 2005; Thorne *et al.*, 2016). This trend was observed over most regions of the globe (Alexander *et al.*, 2006), but is much stronger in the northern hemisphere (e.g. North America, Europe, China, Himalaya region) and Australia than in the rest of the world (e.g. India, New Zealand, parts of Africa) (Davy *et al.*, 2017; Sun *et al.*, 2018). The physical mechanisms involved in this pattern are still debated and seem to be multi-factorial. The most likely explanations include the thickening of global cloud cover (Easterling *et al.*, 1997; Dai *et al.*, 1999; Cox *et al.*, 2020), increased soil moisture and its positive effect on diurnal plant transpiration (Dai *et al.*, 1999), changes in land use due to rapid urbanisation (Small, Sloan & Nychka, 2001; Zhou *et al.*, 2009), and variation in global atmospheric circulation (Vose *et al.*, 2005) and in the planetary boundary layer thickness (Davy *et al.*, 2017). Regardless of the underlying physical reasons for the asymmetry in diel warming, this trend is expected to continue in the future. For example, the percentage of unusually warm nights recorded each year is expected to rise by 20–40% by 2100 under realistic greenhouse gas emissions scenarios (Karl *et al.*, 2008; Sillmann *et al.*, 2013).

Consequences of warmer nights are not limited to changes in air temperatures above ground. Changes in ground temperatures related to nocturnal warming have been well documented (Wu *et al.*, 2012, Shi *et al.*, 2021) and could modify the microclimatic conditions of ground shelters used by ectotherms. During the day, the organic layer of the soil (first 5 cm) intercepts solar energy that radiates to lower soil horizons (subsoil). At night, the top ground layer cools down faster than deeper ones, because of contact with cooler air temperatures. A fraction of the thermal energy accumulated in the subsoil is transferred back towards the surface, warming the top layer of the ground (Shi *et al.*, 2021). As atmospheric $T_N$ increases due to global warming, the cooling effect from the air is reduced, without a radical change in the restoration of heat energy coming from deeper layers, which causes a
disproportionate augmentation of temperature in the top soil layers. To illustrate this, field experiments using large infrared heaters suspended above the ground generated asymmetric warming patterns between daytime and night (Wu et al., 2012). Minimum temperatures recorded 10 cm above the ground significantly increased from 0.65 °C to 1.33 °C (0.68 °C difference) through nocturnal warming, but were not affected by daytime warming treatments. In parallel, minimum ground temperatures significantly increased from 4.05 °C to 5.34 °C (1.29 °C difference) through the nocturnal warming treatment but, again, remained unaffected by experimental diurnal warming. Nocturnal warming at the soil surface was found to shorten significantly the development of eggs and nymphs in three grasshopper species, leading to an advance in adult emergence time by 2–6 days depending on species (Wu et al., 2012).

(2) Nocturnal warming and microhabitats exploited by squamates: the value of legacy data

Squamates can be found in myriad microhabitats. They notably rely on burrows, substrate elements, canopy leaves, rock cracks, holes in trees or water to regulate their body temperature, lay their eggs, evade predators or stressful thermal conditions during their activity periods, and shelter during periods of rest and inactivity (Huey et al., 1989; Goldenberg et al., 2021; Mohanty et al., 2022; Nordberg & McKnight, 2023). For ectotherms, appropriate selection of nesting, retreat and resting sites is key as such sites offer a variety of thermoregulatory opportunities that influence many physiological rates (e.g. developmental, metabolic and digestive rates). Alternatively, this choice may have deleterious consequences and reduce an individual's fitness if the retreat-site temperature is inappropriate (e.g. too deep or too shallow) (Huey et al., 1989; Kearney, 2002; Lelièvre et al., 2010; Bentley et al., 2020; Chukwuka, Monks & Cree, 2020). As a consequence, the thermal quality of the habitat cannot simply be reduced to air temperature, but should rather be
described by the mosaic of operative environmental temperatures ($T_e$, the temperature of an object with no heat capacity and resulting from both radiation and convective heat transfer) present in the environment (Bakken & Gates, 1975; Kearney, Isaac & Porter, 2014; Ma *et al.*, 2021).

Unfortunately, there are insufficient published data to provide an exhaustive description of the impact of nocturnal warming on all relevant microhabitats exploited by squamate species (e.g. ground substrates, leaf litter, boulders, rock cavities, tree trunks, branches or canopy). However, some inferences can be made from legacy data re-analysed under the prism of nocturnality (Huey, Miles & Pianka, 2021b). As an example, we analysed $T_{es}$ originally recorded at Saguaro National Park (SNP, Arizona, USA; D.B. Miles, unpublished data) to estimate the diurnal thermal quality of the habitat exploited by the ornate tree lizard (*Urosaurus ornatus*) (see online Supporting Information, Appendix S1). This diurnal lizard species is arboreal and occupies mesquite (*Prosopis velutina*) and paloverde (*Parkinsonia aculeata*) trees. Analysis of the data shows that both the minimum $T_{NS}$ and maximum $T_{DS}$ increased over the 2001–2022 period. However, the minimum $T_{NS}$ increased faster, as indicated by the significant interaction between time (in years) and temperature parameter detected in our linear model ($F_{1,63} = 111.1, P<0.005$; see Table S1 in Appendix S1) (Fig. 3). For comparison, between 2001 and 2022, minimum $T_N$ have increased by 9.4 °C while $T_{DS}$ have increased by 5.6 °C. For *U. ornatus*, mid-late spring coincides with a critical period of reproduction: females have already mated and a clutch of eggs is developing *in utero*. Rising temperatures during this period not only have the potential to influence the phenotypic traits of hatchlings but can also impact the post-gestation state of females. We encourage re-analysis of similar historical data (Huey *et al.*, 1989; Kearney, 2002; Sabo, 2003; Lelièvre *et al.*, 2010; Gunderson *et al.*, 2019) to investigate the nocturnal thermal characteristics of other substrates and environments.
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### III. IMPACT OF NOCTURNAL WARMING: SHORT-TERM EFFECTS ON THE COST-TO-BENEFIT BALANCE?

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#### (1) Increased performance and new opportunities for activity for diurnal ectotherms

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At first sight, warmer nights appear beneficial for diurnal ectotherms. Based on the shape of the thermal performance curve (Fig. 1), diurnal ectotherms are expected to benefit from a passive increase in performance as warmer $T_N$ creates a thermal environment (air or substrate) characterised by prolonged exposure to temperatures above $CT_{min}$ (and closer to $T_{opt}$). For temperature-sensitive traits, such as metabolism, gut passage rate or development time, small increments in temperature can be sufficient to lead to a significant performance advantage.

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For example, an increase of approximately 1 °C in air temperature could potentially result in an 8.9% increase in metabolic expenditure of ectotherms in temperate regions (Dillon, Wang & Huey, 2010). To illustrate this passive temperature effect, we collected MR data from 65 male wall lizards (*Podarcis muralis*) at four body temperatures (30, 25, 20 and 15 °C), during both their active (day) and inactive (night) phases (see Appendix S2 for methodology). We therefore compared the resting metabolic rate (RMR) measured over the active phase with the standard metabolic rate (SMR) measured over the inactive phase, as defined in Andrews & Pough (1985). We observed lower MRs at night (i.e. SMR), regardless of air temperature (Fig. 4). We also found a positive relationship between body temperature and both RMR and SMR. The slope of this relationship was steeper for RMR (i.e. during the day) than for SMR (i.e. during the night) (see Table S2 in Appendix S2). Interestingly, we observed that despite individuals being at rest, SMR at warm $T_{NS}$ could exceed RMR recorded during the day at colder $T_{DS}$. Further, the variance in SMR was significantly smaller than the variance in RMR at each temperature (Levene's test for homogeneity of variance; $F_{7,1594} = 221.4, P<0.005$).

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Together, these observations confirm that, in diurnal ectotherms, increasing $T_N$ over the resting period leads to a passive increase in physiological rates. The results also highlight a

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potential inability to buffer the effect of temperature on metabolic rate physiologically or
behaviourally during a nocturnal period of inactivity, even where MRs are high (e.g. mean
SMR at 30 °C exceeds mean RMR at 20 °C; Fig. 4).

Another possible response of diurnal species to increased T<sub>NS</sub> is to extend their daily
foraging activity window at dusk, dawn, and eventually over part of the night (Sperry, Ward
& Weatherhead, 2013; Lara Resendiz, 2019; Levy et al., 2019) (Fig. 2A). Such increased
activity has been well documented in insects. For example, warmer T<sub>NS</sub> enhanced the
opportunity for dispersal outbreaks in the pine processionary moth (*Thaumetopoea
pityocampa*) in USA and Canada (Battisti et al., 2005), facilitated elevational shifts in a
North American ant species (*Aphaenogaster rudis*) (Warren & Chick, 2013), increased
nocturnal foraging activity in different species of soil-dwelling ants (McMunn & Pepi, 2022),
and augmented nocturnal hunting activity in the American nursery web spider (*Pisaurina
mira*) (Barton & Schmitz, 2018) and the harlequin ladybird (*Harmonia axyridis*) (Speights &
Barton, 2019). In squamates, similar patterns have been observed in ratsnakes (*Pantherophis
spp.*) (Sperry et al., 2013) and rock rattlesnakes (*Crotalus lepidus*) (Mata-Silva et al., 2018),
both diurnal species that extend their foraging activity into the night when T<sub>NS</sub> are favourable.
Note however that, in a globally warming environment, the benefits of extension of activity
into part of the night may be counterbalanced by a reduction in midday activity due to T<sub>D</sub>
exceeding CT<sub>max</sub> (Vickers, Manicom & Schwarzkopf, 2011).

Together with increased foraging activity, higher physiological rates could translate into
an increase in the daily opportunities for conversion or storage of energy, which may improve
body growth, shorten the gestation period, and ultimately increase individual fitness (Ma et
al., 2020). Such positive effects of warmer nights have been documented in insects (reviewed
in Ma et al., 2020), where warmer T<sub>N</sub> can reduce the development time of eggs (Wu et al.,
2012; Zhao et al., 2014; Speights & Barton, 2019) or larvae (Whitney-Johnson et al., 2005;
Wu *et al.*, 2012; Kingsolver, Higgins & Augustine, 2015). Similar results have been found for squamates, with warmer $T_{NS}$ accelerating gestation and embryonic development in lizards (Clarke & Zani, 2012; Brusch IV *et al.*, 2023) and geckos (Moore, Penniket & Cree, 2020).

Warmer nights also increased hatchling size (Clarke & Zani, 2012), adult body condition (Moore *et al.*, 2020) and juvenile growth rates (Dupoué *et al.*, 2017b; Rutschmann *et al.*, 2021) in different squamate species.

## (2) Limits to nocturnal activity for diurnal ectotherms

A key question is whether diurnal squamates always benefit from a warmer nocturnal environment, whether by switching from strict diurnal to cathemeral or nocturnal activity, or via an increase in their metabolic and physiological rates. Although physiological traits such as metabolic, gut passage, or assimilation rates should be faster with small increases in $T_N$ (Dillon *et al.*, 2010), this increase in $T_N$ might not be sufficient to initiate locomotor, foraging or hunting activities. First, even if the thermal environment becomes optimal, foraging activity at night could remain constrained by factors independent of temperature, such as higher risks of predation (Berger & Gotthard, 2008; Amadi *et al.*, 2021), or a requirement for light for visual detection of prey (Brown & Shine, 2006; Sperry *et al.*, 2013; Mukherjee & Mohan, 2022). An individual's intrinsic circadian cycle may also inhibit nocturnal activity if it is relatively inflexible (Bradshaw & Holzapfel, 2009; Tougeron & Abram, 2017; Shemesh, Cohen & Bloch, 2007; Coomans *et al.*, 2015; Krzeptowski & Hess, 2018).

Second, differences in the TPCs for different physiological traits are expected under the 'multiple performances–multiple optima' hypothesis (Huey, 1982; Clark, Sandblom & Jutfelt, 2013). Therefore, although they could increase metabolic activity, nocturnal thermal conditions may remain well below the preferred body temperature ($T_{pref}$) for other traits such as locomotion. $T_{NS}$ are indeed frequently lower than the thermoregulatory requirements of a species to initiate activity [i.e. voluntary minimum temperature ($VT_{min}$), often estimated as
the 25th percentile of $T_{\text{pref}}$, or as the lowest recorded active body temperature when lizards first emerge from a refuge] (Kubisch et al., 2016; Taylor et al., 2020). For example, Kubisch et al. (2016) found $VT_{\text{min}}$ to vary from 24.6 to 31.3 °C in three lizard species from Patagonia. Similarly, Diele-Vegas et al. (2018) found $VT_{\text{min}}$ to vary between 19.9 and 32.9 °C among 27 different species of South American lizards. In both studies, the lower limit for voluntary foraging activity was quite high (ca. 25 °C for diurnal lizard species), hence limiting opportunities for these species to engage in foraging activities despite warm nocturnal conditions. Whether warmer nocturnal thermal conditions are sufficient to increase performance levels of all traits necessary for activity therefore will rely on an individual's thermoregulation capacities and requirements (Kearney, Shine & Porter, 2009; Vickers et al., 2011). Among diurnal thermoregulators, species predominantly use heat from the sun to reach a body temperature within the range that favours performance (Angilletta, 2009; Kearney et al., 2009). In the absence of solar radiation, the potential for thermoregulation is restricted to heat conduction from substrates that emit heat accumulated during the day and thus requires the use of a behavioural thermoregulation strategy based on thigmothermy rather than heliothermy (Huey et al., 1989; Kearney & Predavec, 2000; Nordberg & Schwarzkopf, 2019). Despite numerous studies showing that nocturnal species are capable of exploiting such thermal opportunities (Kearney & Predavec, 2000; Vidan et al., 2017), little is known about this ability in diurnal thermoregulators (see Section VI.1).

Third, the use of a favourable nocturnal thermal environment can also be constrained by diurnal activity patterns and thermoregulation preferences. For example, one field study showed that exploitation of warmer artificial shelters differed between two sympatric colubrid snakes (*Hierophis viridiflavus* and *Zamenis longissimus*). Such artificial shelters improved nocturnal digestion rates significantly for *H. viridiflavus* (by up to 25%) compared to *Z. longissimus* (4.4% increase) (Lelièvre et al., 2010). This pattern could be explained by
differences in diurnal thermal preferences between these species: *H. viridiflavus* is considered
to be thermophilic, with higher preferred body temperatures (27.5–31.1 °C) relative to *Z.
longissimus*. As such, *H. viridiflavus* favoured the warmer artificial refuges over natural ones
during the daytime. This preferential diurnal use of artificial structures also allowed this
species to benefit from warmer nocturnal conditions and therefore to increase its RMR and
nocturnal digestion rate. By contrast, *Z. longissimus* favoured cooler environments (21.5–
25.5 °C) and did not exploit the artificial shelters during the daytime, hence missing an
opportunity to exploit a warmer nocturnal thermal habitat.

Overall, although occasional nocturnal activity (de Mesquita, Passos & Rodrigues, 2012) or prolonged switches to nocturnal and cathemeral patterns have been reported for squamates (Seifan et al., 2010; Sperry et al., 2013; Mata-Silva et al., 2018; Lara Resendiz, 2019; Mukherjee & Mohan, 2022), there remains a need for further studies of nocturnal thermoregulation strategies of squamates and their relationship with daytime thermoregulation.

(3) Summer heatwave and nocturnal warming: a case study in a diurnal snake

To address further the impact of warm nocturnal conditions on resting body temperature and
nocturnal thermoregulation, we analysed unpublished body temperature data for the asp viper
(*Vipera aspis*) and T<sub>e</sub> data from a viper biomimetic model, both collected by M. Guillon and
O. Lourdais during the 2003 European mega-heatwave (Garcia-Herrera *et al.*, 2010; Russo,
Sillmann & Fischer, 2015) (see Appendix S3 for details). The asp viper is a typical diurnal
and heliothermic snake species. Mean ± SD T<sub>pref</sub> for non-reproductive individuals is 30.6 ±
4.2 °C (Lorioux, Lisse & Lourdais, 2013). At night, vipers' shelter in underground refuges to
avoid predation.

During the study, seventeen hot days (maximum air temperature in the shade 30–35 °C)
and eleven very hot days (>35 °C) were identified by the French national meteorological
agency (Météo France) classification (Fig. 5). Daily maximum surface temperature in the enclosure (mean ± SE; 40.48 ± 9.27 °C) significantly influenced the minimum temperature in the refuge in the following night (19.98 ± 2.57 °C; ANOVA, $\beta$ = 0.24 ± 0.02, $F_{1,64}$ = 87.61, P<0.005; Table S3 in Appendix S3), likely due to ground thermal inertia (Rosen & Lowe, 1994). Despite extremely high operative temperatures during the daytime (Fig. 5), vipers were able to thermoregulate efficiently during the daytime: individuals avoided overheating and maintained a mean diurnal maximum body temperature of 31.8 ± 2.7 °C, which is very close to their $T_{pref}$. At night, body temperature followed closely the thermal conditions recorded in the shelters (Figs 5 and 6). Mean nocturnal body temperatures (recorded between 22:00 and 08:00) were influenced both by previous day type ($F_{2,60}$ = 256.95, P<0.005) and minimum shelter temperature during that night ($\beta$ = 0.62 ± 0.06, $F_{1,60}$ = 127.92, P<0.005; the interaction term was not significant ($F_{2,60}$ = 1.28, P = 0.28; Table S4 in Appendix S3).

Nocturnal body temperatures were higher during nights following very hot days and hot days compared to those following normal days (mean ± SE = 25.37 ± 1.14 °C and 22.42 ± 1.43 °C versus 19.34 ± 1.51 °C, respectively). During the night, temperatures within a burrow are often warmer than temperatures at the surface (Fig. 5), allowing vipers within their overnight refuge to maintain nocturnal body temperatures sometimes exceeding the body temperature recorded for actively thermoregulating vipers during the day. This pattern was particularly pronounced during the peak of the heatwave from 1 to 12 August (Fig. 5).

Together, these observations confirm, for this heliothermic diurnal species, a 'passive' influence of nocturnal refuge conditions on body temperature. While individuals remained in their shelter we did not detect any foraging attempts (as shown by the synchrony between nocturnal body temperature and shelter temperature despite warm surface temperatures) (mean 25.97 ± 10.76 °C). Shelter use by this diurnal species may allow them to avoid predation or may result from an intrinsic circadian rhythm. It is also likely that shelter-use
behaviours limit water loss and are thus important in hydroregulation, as demonstrated experimentally by Dezetter, Le Gallliard & Lourdais (2022). However, the likely increase in SMR during the warmest nights could potentially affect energy balance and lead to a loss of body condition (Zhao *et al.*, 2014; Speights *et al.*, 2017). Further, any negative impacts on body reserves during non-reproductive years in capital breeding species such as the asp viper could influence reproductive success in the following year (Lourdais *et al.*, 2002; Lourdais *et al.*, 2003; see Section VI.3).

## IV. BALANCE BETWEEN COSTS AND BENEFITS: A MODELLING APPROACH

That ectotherms might be constrained in their capacity to forage at night despite warmer nocturnal conditions, themselves associated with higher SMRs, raises a second question: do warmer nights entail energetic costs that cannot be compensated by diurnal feeding activity? To answer this question and to explore the energetic costs and benefits of warmer $T_{NS}$, we extended the energy-balance model of Huey & Kingsolver (2019) (see Appendix S4). Their original model quantifies the daily net energy gain ($NEG_d$) of an active, thermoconforming ectothermic predator at different environmental temperatures. Their model assumes that the net energy budget depends on energetic input from food intake and assimilation, and output from energy expenditure. By extending this model we partition an active phase [i.e. diurnal phase with positive attack rates (AR) and metabolic rates (MR)] from a resting phase (i.e. nocturnal phase with zero AR but positive MR) and disentangle the effects of warmer $T_D$ and $T_N$. Note that whereas Huey & Kingsolver (2019) assumed a Type I functional response where food intake increases linearly with food density, we assume a more realistic Type II functional response (Englund *et al.*, 2011) where food intake increases with resource density at low prey availability (in proportion to AR) but saturates at high prey availability (in proportion to handling and ingestion time and satiation; see Fig. S1 in Appendix S4). Also
note that we chose default parameters to match the thermal biology of an “average” species,
but our qualitative predictions should hold for different parameterisations.

## (1) Model development

We provide here a brief description of our model and refer readers to Appendix S4 for a full description and the R code. The NEG<sub>d</sub> (i.e. the energy derived from food consumption and assimilation) includes a positive input from a temperature (T)- and resource (R)-dependent functional response (FR<sub>R,T</sub>) and a negative output (MR<sub>T</sub>) from energy expenditure associated with basal metabolism and body maintenance. Energy input is scaled by the conversion efficiency during food assimilation α set to 69% and assumed to be independent of temperature in all simulations (Levy et al., 2017). Energy output is implemented as a temperature-dependent MR (the energy expended per unit time):

$$ \text{NEG}_{R,T} = \alpha * \text{FR}_{R,T} - \text{MR}_{T} \quad (1) $$

The Type II functional response (FR<sub>R,T</sub>) is given by:

$$ \text{FR}_{R,T} = \frac{\text{AR}_{T} * \text{R}}{1 + \text{AR}_{T} * \text{R} / \text{IR}_{T}} \quad (2) $$

where R denotes the resource density (arbitrarily fixed to R = 2 in all examples), AR<sub>T</sub> is the temperature-dependent attack rate, and IR<sub>T</sub> is the temperature-dependent ingestion rate. The body temperature dependence of the AR and IR were both modelled using Arrhenius-like equations as recommended by Englund *et al.* (2011). We scaled all parameters of AR and IR (see equations S6 and S7 in Appendix S4) to have a unimodal relationship with body temperature and a maximum of 1 at an optimal body temperature [T<sub>opt</sub>; here, T<sub>opt</sub> = 30 °C, which is within the range of optimal temperatures for locomotion and food consumption in lizards (Clusella-Trullas & Chown, 2014)], and used empirical data from the meta-analysis of Englund *et al.* (2011) to derive parameters for these equations (see Fig. S2 in Appendix S4). We first set a default metabolic rate with a basal value of 1 at 20 °C (DMR<sub>20</sub>) and assumed that it would increase exponentially with the inverse of body temperature (in °K) according to
equation S10. Note that in our simulations, $DMR_{20}$ was then set to 1, 5, 10 or 15% of the maximum energy intake at 20 °C (Andrews & Pough, 1985). At each time-step, the air temperature $T$ was estimated using an asymmetric 24-h periodic function that provides a good description of diel cycles in above-ground air temperature (Parton & Logan, 1981) (see Fig. S3 in Appendix S4). Because our focus was on nocturnal warming, we kept maximum diurnal temperatures ($T_{D, max}$) constant (40 °C) across all simulations, while varying minimum nocturnal temperatures ($T_{N, min}$) from 0 to 30 °C (Fig. S3).

We computed the net energy gain for each hour ($NEG_h$), summing these over the 24-h cycle to obtain $NEG_d$. All simulations and statistical analyses were performed with R statistical software (version 3.3.2, R Development Core Team, 2023).

## (2) Modelled scenarios: nocturnal temperature and thermoregulation pattern

To validate our model, we first (Scenario 0, see Appendix S4) simulated a perfect thermoconformer (i.e. an animal that spends no time or metabolic energy on behavioural thermoregulation). Unlike other scenarios, Scenario 0 was set in an environment with variations in $T_{D, max}$ and in resource density, but no variations in $T_{N, min}$. As in Huey & Kingsolver (2019), this model highlighted that reduced resource levels in warmer diurnal environments trigger a 'metabolic meltdown', i.e. declining energy intake paired with increased energetic expenditure and a reduced activity opportunity due to warmer diurnal maximum temperatures in the middle of the day.

We then compared five alternative scenarios to investigate the impacts of warmer nights (i.e. $T_{N, min}$) on species with different thermoregulation strategies and foraging styles (Table 1). In Scenario 1, we assumed a thermoconforming ectotherm with 24 h foraging activity. This allowed us to investigate effects of minimum $T_N$ in the absence of time partitioning of activity and of any behavioural control of body temperature. In Scenario 2, we extended the model to the case of a thermoconforming ectotherm with an activity cycle based on
photoperiod. This organism was active during the day (07:00 to 20:00) and inactive over the
night (21:00 to 06:00). To make this tractable without explicitly modelling kinematics of
handling, gut passage time and assimilation of food (Levy et al., 2017), we assumed that
foraging behaviour (i.e. AR) was only possible between 07:00 and 20:00 (AR, IR & MR all
>0); IR and MR were calculated all over the full 24-h period (AR = 0 while IR & MR >0). In
Scenario 3, we applied the model to a perfectly thermoregulating ectotherm (i.e. a species
that maintains body temperature within a range of temperatures optimal for performance) for
which the activity window was possible over the 24-h daily cycle but limited by
environmental temperatures. This scenario thus represents an ectothermic predator able to
extend its foraging activity into the night when environmental temperatures are suitable.
Here, we assumed that AR was limited by a lower (18 °C) and upper threshold (40 °C)
corresponding to typical values of VTmin and VTmax for foraging in many terrestrial lizards
[see Rozen-Rechels et al. (2020) for an example]. Moreover, as the organism was able to
thermoregulate, we assumed that it could maintain a body temperature of 30 °C matching the
Topt for foraging whenever environmental temperatures exceeded Opt. Scenario 4 illustrates
the case of a perfect thermoregulator with an activity window delimited by both temperature
and photoperiod. As in Scenario 2, AR was limited by daylight, while IR and MR were
dependent only on body temperature. As in Scenario 3, this scenario assumes body
temperature during daytime was 30 °C whenever environmental temperatures exceeded 30°C
(i.e. efficient behavioural thermoregulation). The final scenario (Scenario 5) describes a
nocturnal thermoregulator, with a foraging activity window strictly delimited to the night
(20:00 to 07:00). For this scenario, AR was positive at night and depended on body
temperature, while IR and MR depend only on body temperature. We assume the species is
capable of selecting retreat sites to maintain a diurnal body temperature close to 30 °C (Tpref)
whenever diurnal environmental temperatures exceeded 30 °C (Kearney & Predavec, 2000;
524

Tan & Schwanz, 2015; Chukwuka *et al.*, 2021). At night, foraging activity is delimited by VT<sub>min</sub> and VT<sub>max</sub>, which are fixed at 15 °C and 35 °C because those values are typically lower in nocturnal than diurnal ectotherm species.

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526

527

For all scenarios (with the exception of Scenario 0), we evaluated the response of NEG<sub>d</sub> to varying minimum T<sub>NS</sub> ranging from 0 to 30 °C. We also evaluated varying resting metabolic expenditure by using DMR<sub>20</sub> values of 0.01, 0.05, 0.1, and 0.15 (Andrews & Pough, 1985) to allow us to characterise the effects of nocturnal warming on species with increasing resting metabolic rates.

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(3) Results and conclusions

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536

537

538

539

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The model highlights that the consequences of nocturnal warming for an organism’s daily energy budget depend on a species’ thermoregulatory behaviour and activity patterns. First, the model shows that, for diurnal species, for a given foraging activity window and regardless of the thermal ecology of the species (Scenarios 1–4), a higher DMR<sub>20</sub> (lower lines in blue and green on Fig. 7) involves a lower net energy gain. In natural conditions, this difference could be compensated by increased food intake provided that sufficient resources are available in the environment and until the required amount of energy exceeds the satiation point in the case of a Type II functional response (Huey & Kingsolver, 2019).

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Second, in all scenarios the model has an optimal T<sub>N</sub> (T<sub>N,Ypt</sub>) for the NEG<sub>d</sub> (Fig. 7, circles). Below this optimum, an increase of T<sub>N</sub> increases NEG<sub>d</sub>. Above it, NEG<sub>d</sub> decreases and, in some cases, even becomes negative (Scenario 2). Thus, whenever T<sub>N</sub> exceeds the T<sub>N,Ypt</sub>, the concomitant increase in MR is not compensated by the AR, resulting in an energetic debt. Note that for higher DMR<sub>20</sub> (and more restricted activity patterns), T<sub>N,Ypt</sub> is lower. To compensate for this, we expect foraging effort to increase in ectotherms with higher energy demands when T<sub>N</sub> is higher in the absence of specific constraints on nocturnal foraging activity (i.e. Scenarios 2 & 4; see Section III.2). Such a change in foraging effort driven by

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543

544

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546

547

548
549 nocturnal warming could have important consequences on food-web dynamics (see Section VI.4) as already demonstrated by several studies on insects (Barton & Schmitz, 2018; Ma *et al.*, 2020). It is also possible that changes of DMR *via* metabolic plasticity (Norin, Malte & Clark, 2016; Sun *et al.*, 2022) would help individuals to acclimatise to warmer $T_N$. Similarly, 551 inter-individual variation in DMR may facilitate adaptation to higher $T_N$ by lowering DMR in 552 the population through natural selection. 553

554 Third, comparing different activity patterns and thermoregulation strategies, we found that 555 species limited only by temperature in their activity (Scenarios 1 and 3) generally performed 556 better than species also limited by daylight (Scenarios 2 and 4), even when $T_{Ns}$ were high. 557 This confirms the idea that ectotherms with flexible daily activity patterns should benefit (up 558 to a certain point) from warmer $T_N$, whereas strictly diurnal species are likely to be more 559 constrained. Furthermore, compared to thermoconformers (Scenarios 1 and 2), the ability of 560 thermoregulators (Scenarios 3 and 4) to optimise their body temperature over a larger part of 561 the daytime provides a buffer against the negative energetic impacts of warmer nights beyond 562 the $T_{N, opt}$ for $NEG_d$ (i.e. slopes are less negative beyond $T_{N, opt}$). This is not surprising as 563 efficient thermoregulators can maintain a higher foraging rate despite diurnal environmental 564 temperatures exceeding $T_{opt}$, and can therefore reduce the cost of a higher metabolism during 565 the warmest part of the day. 566

567 Finally, nocturnal species (Scenario 5) show the greatest relative energetic benefit from 568 warmer nights, as illustrated by the largest amplitude of $NEG_d$ gained at warmer nocturnal 569 temperatures compared to diurnal species (Fig. 7). From low to intermediate minimum 570 temperatures, $NEG_d$ benefits exponentially from increased ARs with increasing temperatures. 571 Once minimum $T_N$ reaches $VT_{min}$, the increase in $NEG_d$ plateaus until it reaches $T_{N, opt}$. There 572 are two possible explanations for this pattern. First, foraging activity (AR) may be maximal 573 and therefore there is no further opportunity to increase energetic income. Second, with
increasing minimum $T_N$ thermal conditions will exceed $VT_{max}$ over a larger part of the night, reducing AR and energetic income. Above $T_{N, opt}$, minimum temperature exceeds $VT_{max}$ for the majority of the night and foraging is highly restricted, resulting in a drop in $NEG_d$. Also note that for the highest $DMR_{20}$, $NEG_d$ is only positive over a short range of temperature in nocturnal species. This result may be related to our parameterisation of the model where we decided not to modify the AR functions for the nocturnal species. Instead, several studies have reported higher efficiency of locomotion at low temperatures in nocturnal squamates, which would translate to a higher AR at low temperatures (Autumn *et al.*, 1999; Hare *et al.*, 2007) (see Fig. S15 in Appendix S4). Similarly, a higher MR efficiency at low temperatures is a common assumption for such species (Autumn *et al.*, 1999; Kearney & Porter, 2004).
Adjusting these two characteristics could reduce $T_{N, opt}$ and thereby increase the benefit of warmer nights for nocturnal species (see Scenario 5 in Appendix S4 for an illustration).
Whether warmer nights will benefit all nocturnal species yet remains to be confirmed.
Nocturnal ectotherms are rarely active over the entire night and temperatures below $VT_{min}$ also represent thermal refugia for these species (Kearney & Porter, 2004). A reduction in the time dedicated to rest and recovery thus could entail negative fitness effects in nocturnal ectotherms too (see Section VI.1).

Altogether, our model confirms that approaches based only on instantaneous TPCs will provide an incomplete picture, by failing to consider the temporal dynamics and trade-offs of different performances involved in maintenance, foraging, digestion and energy balance.
Energetic intake and expenditure must be integrated over the entire day, and potentially over an individual's lifetime to measure the actual cost-benefit balance of warmer nights. This point has been made previously in other recent studies using TPCs to make predictions about the temperature dependence of fitness traits (Kingsolver & Woods, 2016; Sinclair *et al.*, 2016).
(4) Empirical analysis of energy balance in the European common lizard

Testing our model’s predictions would require empirical data on food intake and energy balance in ectotherms at different T<sub>NS</sub> with different activity and foraging patterns, as well as different thermoregulation strategies. Suitable unpublished information about food intake and energy balance was recorded by Brusch IV *et al.* (2023) in an experiment designed to quantify the effects of T<sub>N</sub>, T<sub>D</sub> and water availability on the costs of reproduction and reproductive success in European common lizards (see Appendix S5 for details). Female common lizards use mixed income and capital breeding strategies and feed during reproduction to fuel their energy investment during mating, vitellogenesis (i.e. yolk formation) and gestation (Bleu *et al.*, 2013; Brusch IV *et al.*, 2023). In this experiment, body mass of females increased during gestation (+1.8 g during 40–60 days) due to an increase in somatic mass at the beginning of gestation and to egg growth at the end of gestation, mostly from water uptake. In addition, there was a temporal pattern in mass change with a rapid increase in body mass during the first two-thirds of gestation followed by a plateau in the last third of gestation (Brusch IV *et al.*, 2023). The average weekly mass gain of gravid females correlated positively with their weekly food intake with a food mass to body mass conversion rate of 0.31 (linear regression, F<sub>1,631</sub>=311.6, P < 0.001, β ± SE = 0.31 ± 0.02). The best repeated measures model describing the weekly food mass to body mass conversion revealed a positive interaction term between T<sub>D</sub> and time (F<sub>1,498</sub>=12.2, P < 0.005; Table S5 in Appendix S5) but a negative effect of T<sub>N</sub> (F<sub>1,128</sub> = 4.05, P = 0.046, β ± SE = -0.55 ± 0.02), thus confirming our models’ predictions of potential negative effects of night-time warming on energy balance. In addition, it was found that females had lower post-parturition body condition in hot- than in cold-night conditions (see Brusch IV *et al.*, 2023). Together, these results indicate asymmetric effects of nocturnal and daytime warming on the energy budget
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of a strictly diurnal species, unable to extend its activity and foraging into the night (see also

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Section VI.3).

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# V. CHRONIC EFFECTS OF NOCTURNAL WARMING

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## (1) Warmer nights entail delayed costs in diurnal species

627

In an experimental study, Zhao *et al.* (2014) demonstrated that nocturnal warming

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significantly enhanced the development rate of English grain aphid (*Sitobion avenae*)

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nymphs. However, chronic exposure to warmer $T_{NS}$ also resulted in a dramatic reduction in

630

the survival and reproductive performance of adults, leading to a 30% decrease in population

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growth rate. These results highlight the importance of considering the lifetime and chronic

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consequences of warmer nights. To explore this in more detail, we first review different

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mechanisms by which warmer nights could entail long-term fitness costs, before illustrating

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these costs using the common lizard as a model species.

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First, warmer nocturnal environments are known to affect sleep quality and therefore to

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compromise rest and recovery (Tougeron & Abram, 2017) (Fig. 2). During the sleep phase,

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metabolism usually decreases, providing an opportunity to repair cellular or tissue damage

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(Didomenico, Bugaisky & Lindquist, 1982) and to modulate immune responses, cognition

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(e.g. memory consolidation) and waste clearance (e.g. reactive oxygen species, ROS)

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(Sharma & Kavuru, 2010). For young individuals (e.g. neonates) sleep is also important for

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brain maturation and neuromuscular development in reptiles (Libourel & Herrel, 2016). In

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insects, warmer nights affect the central oscillator complex (i.e. a transcription-translation

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feedback loop of five genes regulating circadian rhythms) (Saunders *et al.*, 2002; Beck, 2012)

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and perturb the internal clock (Dunlap, 1999). In both cases, the end result is

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desynchronisation of the photo- and thermoperiod, forcing an active state when individuals

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are typically asleep (Kayser, Yue & Sehgal, 2014).
Examples of costs related to sleep disturbance for vertebrate ectotherms are rare in the literature. Yet, an indirect demonstration of such costs comes from studies of warming effects on the resistance of amphibians to environmental stressors such as heavy metal pollution (Hallman & Brooks, 2015) or pathogenic contamination (Neely et al., 2020). In both cases, experimental reduction of $T_{NS}$ (hence, a better resting environment) significantly increased the survival potential of individuals to the stressor, especially for cold-adapted species. In other words, the higher the quantity of resources mobilised to cope with a nocturnal heat stress and the lower the resting quality, the fewer resources remained to cope with the contaminant.

Another long-term cost of warmer nights may be the accumulation of metabolic by-products resulting from nocturnal activity. In squamates, the maintenance of active metabolic rates below $T_{opt}$ (i.e. typical scenario during warmer nights; Fig. 1) can be particularly challenging. Physiological activity at suboptimal temperatures (i.e. below the thermal performance optimum) may induce stronger oxidative stress *via* sustained mitochondrial activities and associated ROS production, while also impeding antioxidant defences and lowering repair capabilities [see Ritchie & Friesen (2022) for a review]. Eventually, chronic exposure to warmer conditions at night and the resulting oxidative stress may affect individual life-history trajectories by trading off higher investments in immediate physiological activities (and in the management of their by-products) against longevity and/or lifetime reproductive success (Monaghan, Metcalfe & Torres, 2009; Speakman *et al.*, 2015).
Among the cellular mechanisms involved in such a response, oxidative stress can favour telomere erosion (i.e. the protective DNA sequences capping the end of chromosomes), accelerate aging rates and hasten senescence (Reichert, Stier & Stier, 2017; Chatelain, Drobniak & Szulkin, 2020; Burraco *et al.*, 2022). To illustrate this, a recent conceptual model (i.e. the ‘aging loop hypothesis’) was developed from empirical evidence on the European
common lizard (Dupoué *et al.*, 2022). This mechanistic model investigated the effects of increasing temperatures, physiological stress and population dynamics and posited that warmer conditions during resting phases can accelerate the pace of life of a diurnal ectotherm, with deleterious effects accumulating across generations through biomarkers such as telomeric DNA, leading eventually to population collapse.

Several other short-term benefits associated with increased metabolic activity (e.g. faster growth rate, higher gut-passage rates, earlier onset of reproduction) may require trade-offs in energy allocation between maintenance, growth or reproduction and survival, ultimately imposing long-term costs that reduce an individual's fitness (see Section VI.3) (Metcalfe, Monaghan & Metcalfe, 2001; Bestion *et al.*, 2015; Dupoué *et al.*, 2017b). It is thus clear that it will only be possible to understand the impacts of nocturnal warming by integrating its effects over the entire life of an individual, rather than by focusing only on short-term positive effects (Zhao *et al.*, 2014; Rutschmann *et al.*, 2021).

## (2) Can diurnal ectotherms mitigate the impacts of chronic nocturnal warming?

Without further empirical studies, it is difficult to evaluate to what extent long-term effects of warmer $T_N$ will impact ectotherms in natural conditions, or whether some species have the capacity to mitigate at least some of the chronic costs associated with nocturnal warming, and thus maintain high fitness (Battisti *et al.*, 2005; Clarke & Zani, 2012; Moore *et al.*, 2020).
One potential way to mitigate energetic costs associated with warmer nocturnal environments lies in the capacity of squamates to select cooler refugia when usual resting environments are too warm. Yet limited data are available regarding the ability of diurnal thermoregulators to extend their thermoregulatory behaviour overnight. A common assumption is that such capacities are limited, because $T_{NS}$ are uniformly low among thermal refugia, i.e. natural selection operating on nocturnal thermoregulation (which depends on the spatial thermal heterogeneity of retreat sites) is likely to be weak for diurnal species (Huey *et al.*, 2021a).
Recent studies have reported previously undocumented nocturnal basking activity for tropical crocodilians and turtles (McKnight et al., 2023; Nordberg & McKnight, 2023). While individuals normally rest in water at night, occurrences of terrestrial nocturnal basking were recorded in nights with high water surface temperatures. One hypothesis is that air temperatures offer a cool thermal refuge from waters exceeding T<sub>pref</sub> (e.g. > 30 °C). Such nocturnal basking behaviour was however seen in only 13 of the 29 freshwater turtle species studied by McKnight et al. (2023), highlighting heterogeneity in the ability of diurnal species to alter their nocturnal behaviour in a context of warming nights.

Further, because warmer nocturnal environments come with some immediate benefits (e.g. digestion, growth), it is difficult to confirm whether organisms seek cooler resting temperatures *via* thermoregulation behaviour and thus forfeit such benefits to avoid potential long-term fitness costs. Most studies focusing on the responses of individuals to immediate benefits *versus* long-term costs suggest that animals favour short-term over long-term consequences (Drent & Daan, 1980; Metcalfe et al., 2001; Stephens & Anderson, 2001; Stephens, Kerr & Ferna, 2004; Stevens & Stephens, 2010).

Another possible route for diurnal ectotherms to cope with warmer T_N is through plasticity of their diurnal behaviour or physiology (Sun et al., 2022) so as to limit the negative effects of exposure to warmer T_N. Studies on the European common lizard found correlations among several physiological traits and warmer nocturnal environments, implying that plasticity may serve as a buffer to nocturnal warming (see Section V.3 for detailed examples). It is also possible that, despite costs associated with foraging and exploring a nocturnal environment (e.g. predation risk, absence of light, adjustments to internal clock), individuals could adopt an energetically conservative hunting behaviour at night such as ‘sit-and-wait’ or ‘sit-and-pursue’ strategies rather than active foraging–hunting (Kruse, Toft & Suncerland, 2008; Schmitz & Barton, 2014), although this requires empirical investigation.
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(3) Quantitative insights from the European common lizard

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To illustrate the chronic effects of warming nights, we gathered published data collected by

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our laboratories on the European common lizard (see Fig. 8). This species has a broad

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geographic distribution, extending across Europe and Asia, and evolved in cold mesic

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environments. The common lizard has been a key model squamate species used to understand

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the responses of vertebrate ectotherms to global warming (Chamaille-Jammes et al., 2006;

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Bestion et al., 2015; Massot et al., 2017; Rozen-Rechels et al., 2020; Horreo & Fitze, 2022).

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As expected, experimental and comparative studies have highlighted positive effects of

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warmer nights. Notably, lizards exposed to warmer $T_N$ showed increased growth rates and a

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shorter gestation time. For example, a 40 day-long experimental exposure to warmer nights

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(+5 °C) increased mean body growth rate in yearling individuals by almost 20%

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(Rutschmann et al., 2021). Furthermore, both experimental and comparative studies reported

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positive effects on female reproductive phenology, with warmer nights (+5 °C) accelerating

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gestation time by almost 30% (Brusch IV et al., 2023). Other studies identified potential costs

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of warmer $T_N$. First, energy allocation to rapid growth involves a trade-off with energy

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reserves (i.e. energy storage). For example, yearling lizards exposed to warmer $T_N$ during 38

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days displayed higher growth rates, but also lower body condition and lower levels of fat

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reserves (i.e. tail volume) than yearlings in the control treatment (Rutschmann et al., 2021).

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Similarly, in females, earlier parturition in a warmer nocturnal treatment was associated with

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a smaller litter size (~5 *versus* 6 juveniles per litter) (Brusch IV et al., 2023, Dupoué et al., in

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preparation), lower litter mass (~33% reduction in mass per juvenile) and lower *postpartum*

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body condition (Brusch IV et al., 2023). In both cases, it appears that significant quantities of

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energy had to be mobilised to compensate for the accelerated pace of life, potentially

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reducing the amount of energy available for other critical maintenance functions, such as

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immunity (e.g. ectoparasite infestations; Rutschmann et al., 2021). Contrary to our previous
747 predictions regarding enhanced generation of ROS from elevated metabolic rates, warmer $T_N$
748 did not result in higher levels of oxidative stress (no significant effect on oxygen metabolites
749 and non-enzymatic antioxidant capacity; Fig. 8) (Dupoué *et al.*, 2020; Rutschmann *et al.*,
750 2021). It remains difficult to conclude whether the absence of an oxidative stress response
751 reflects an actual absence of stress, whether individuals managed to mitigate this acute stress,
752 or whether the markers analysed were not appropriate to characterise the oxidative stress
753 related to increased resting metabolic activity and/or sleep deprivation (Zhang *et al.*, 2023).
754 In fact, in a comparative study across 10 populations, telomere length (an integrative measure
755 of cellular aging) was found to decrease at higher $T_N$ (no effect of $T_D$ was detected),
756 confirming that common lizards are physiologically challenged in warmer nocturnal
757 environments (Dupoué *et al.*, 2017b). This finding also confirms that $T_N$-related stresses can
758 have chronic effects. This conclusion was strengthened by a non-linear correlation between
759 $T_N$ and the extinction risk of a population: collapsing populations experienced warmer
760 minimum $T_N$ (Dupoué *et al.*, 2017b).

761 Other indirect arguments supporting a detrimental impact of warmer nights come from the
762 many relationships found between $T_N$ and physiological and behavioural traits of common
763 lizards. There was a negative relationship between minimum $T_N$ and baseline corticosterone
764 levels (a glucocorticoid-type hormone involved in energy regulation, immune reactions and
765 stress responses) of adult and yearling females (Dupoué *et al.*, 2018), with warmer nights
766 correlated with lower baseline corticosterone levels. The authors suggested that high $T_N$ may
767 exacerbate chronic stress such that individuals regularly exposed to increased $T_N$
768 downregulate corticosterone secretion to reduce activity levels, mitigate maintenance costs,
769 and ultimately conserve energy and water. Other physiological parameters such as osmolality
770 changes (Brusch IV *et al.*, 2023), evaporative water loss (Dupoué *et al.*, 2017c), heating rates
771 (Rutschmann *et al.*, 2020), prey consumption rate (Brusch IV *et al.*, 2023) or changes in
772 dorsal colouration (Rutschmann *et al.*, 2021) were all correlated with $T_N$ consistently with
773 buffering of the impact of warmer nights (Fig. 8). Note however that no behavioural
774 adjustment *via* thermoregulation preferences has been detected so far for the common lizard
775 (Rutschmann *et al.*, 2021; Rozen-Rechels *et al.*, 2021). Rather, unpublished results show an
776 opposite pattern: male common lizards favoured relatively warm nocturnal body temperatures
777 when exposed to a temperature gradient (10–50 °C) in thermal preference laboratory tests
778 (mean ± SE: diurnal $T_{pref}$ = 29.9 ± 2.35 °C; nocturnal $T_{pref}$ = 26.7 ± 3.3 °C; C. Perry & J. Cote,
779 unpublished observations).

780

**VI. NOCTURNAL WARMING: OPEN QUESTIONS AND FUTURE RESEARCH**

781 Above we considered both immediate and long-term costs and benefits of nocturnal warming.
782 It may also have wider eco-evolutionary ramifications and many other questions remain
783 unaddressed. Below we consider five questions that could be explored in future research.

784
(1) Are the effects of warmer nights similar for diurnal and nocturnal species?

785 The diel activity pattern describes when a species is most active during the day-night cycle
786 (i.e. diurnal, nocturnal or crepuscular), or whether it exhibits activity during both day and
787 night (i.e. cathemeral species) or whether it shows flexibility between different activity
788 strategies. It is thought that the ancestral state in reptiles was strict nocturnality. Yet,
789 diurnality is now the dominant pattern for many lizard species (around 70%) with
790 heterogeneous frequencies among clades (Kearney & Predavec, 2000; Gamble et al., 2015;
791 Vidan et al., 2017; Slavenko et al., 2022). In snakes, ancestral clades are mostly nocturnal,
792 with the exception of derived species within the family Colubridae, which are mainly diurnal
793 (Gibbons & Semlitsch, 1987; Anderson & Wiens, 2017). In general, crepuscular or
794 cathemeral species are rarer in reptiles (i.e. 254 species identified in a recent review of the
795 literature; Cox & Gaston, 2023), and examples of intra-specific flexibility in daily activity
796 patterns are scarce (Abom et al., 2012; Degregorio et al., 2014; Vidan et al., 2017). Reasons
for this lack of flexibility include sensory constraints, the role of predation or resource
availability, and adaptations to nocturnal life, including more efficient performance at low
than high temperatures, especially for locomotion (Autumn *et al.*, 1999; Llewelyn, Shine &
Webb, 2005; Ibargüengoytía *et al.*, 2007; Anderson & Wiens, 2017; Dayananda, Jeffree &
Webb, 2020). Thus, most species might be constrained by their strict diurnal or nocturnal
lifestyles, with only a minority able to adjust their activity to warmer nocturnal climates
(McCain & King, 2014).

In nocturnal species, which can be good thermoregulators (Kearney & Predavec, 2000;
Nordberg & Schwarzkopf, 2019; Chukwuka *et al.*, 2021), metabolism, physiological
performance, locomotor activity and prey capture are generally constrained by low T<sub>N</sub>
(Autumn *et al.*, 1999; Kruse *et al.*, 2008; Hare *et al.*, 2010). As long as they do not exceed
CT<sub>max</sub> (Sunday *et al.*, 2014; Garcia-Robledo *et al.*, 2018), warmer T<sub>NS</sub> should therefore
favour these species by extending their opportunities for activity and foraging (Kearney &
Porter, 2004; Scenario 5 in Fig. 7). For example, Kearney & Porter (2004) estimated that
food consumption dedicated to maintenance in the Australian nocturnal gecko *Heteronotia
binoei* would differ by 6.3 g per night between the coldest (2.2 g) and warmest (8.5 g) part of
the species distribution. On warmer nights, the encounter rate necessary to fulfil such
requirements was calculated to be relatively low (0.03 g/h), because the activity window is
large. On colder nights, due to activity restrictions, this encounter rate was estimated to be
almost six times higher (0.17 g/h). This example illustrates how warmer nights can increase
activity opportunities and facilitate resource acquisition in nocturnal reptiles.

However, just as for diurnal species, an extension of activity into longer periods of the
night does not necessarily translate into fitness benefits in all nocturnal species. First, greater
opportunities for nocturnal activity can be limited by an increased risk of encountering
predators. Apart from nocturnal predators (which could also see their activity period
enlarged), diurnal predators could show a switch towards nocturnal activity and act as new agents of selection. Second, as seen in *H. binoei* higher MRs during warmer nights need to be balanced by higher resource acquisition. If prey activity does not match nocturnal predators' increase in activity, encounter rates could decrease and nocturnal predators could face metabolic meltdown (Huey & Kingsolver, 2019). Finally, for nocturnal species subject to increasing $T_N$, the time spent at low temperatures ($T_e<VT_{min}$) will be restricted to shorter portions of the late night. Over the day, temperatures are often high enough to allow thermoregulation and physiological activity, even within diurnal refuges (Kearney & Predavec, 2000; Croak *et al.*, 2012; Chukwuka *et al.*, 2020). Thus, the time window available for metabolic recovery may be limited and could shrink further in a context of nocturnal warming, leading to long-term negative effects.

The long-term effects of nocturnal warming on nocturnal species are however difficult to predict without further data. We suggest that a formal framework for comparing different modes of activity should take into account differences in exposure to nocturnal warming (i.e. modes are not evenly distributed across the globe) and in thermal sensitivity (especially using the formalism of TPCs). We also suggest that future research focuses on nocturnal thermoregulatory abilities and nocturnal heating and cooling rates of diurnal species (Lelièvre *et al.*, 2010). The analysis of species with flexible diel activity patterns, such as some snakes and lizards, or comparisons of closely related taxa that display a diversity of diel activity patterns (e.g. Gekkonidae or Scincidae) could represent a promising research perspective.

## (2) Are the effects of warmer nights similar in tropical, arid and temperate areas?

One major difference between climate zones is the magnitude of temperature variation at annual, seasonal and diel scales (Janzen, 1967). Temperate-zone climates are highly seasonal, with a pronounced difference in daily maximum and minimum temperatures during the activity seasons of squamate reptiles (spring and summer). Daily temperature variation can be
higher in mediterranean, arid and semi-arid environments where the difference between daily maximum and minimum T_c during summer often exceeds 30 °C. By contrast, tropical environments, notably tropical forests, tend to exhibit low annual mean thermal oscillations, even at high elevations (e.g. Janzen, 1967). As a consequence, the majority of tropical squamate species tend to be thermal specialists (stenothermic) [see Van Berkum (1986) and de Souza Terra, Ortega & Ferreira (2018) for tropical savannas] because of the low seasonality in temperature and the relative homogeneity of their thermal environment (Tewksbury, Huey & Deutsch, 2008; Huey et al., 2009). By contrast, high heterogeneity in the thermal landscape across temperate or arid habitats has favoured the evolution of hibernology, which allows squamates to regulate their body temperature over a wide thermal tolerance range. It is therefore likely that the effect of warmer nights on squamate reptiles will vary across biomes because of differences in exposure and behavioural sensitivity to nocturnal warming.

It is crucial also to consider physiological adaptations to climatic zones. So far, we have mainly focused our attention on species inhabiting temperate zones. Cold-adapted squamates are often strictly diurnal and have higher SMRs than warm-adapted species (Lourdais et al., 2013; Dupoué, Brischoux & Lourdais, 2017a; Sun et al., 2022), which may be particularly disadvantageous in the context of a passive resting temperature increase induced by nocturnal warming. On the other hand, tropical squamates often show lower CTmax and narrower TPCs (Garcia-Robledo et al., 2018) than squamates from temperate climate zones. Because nights are already warm in tropical environments, an increase in T_N should not impact the low-temperature region of the TPC, but could affect its upper region, moving individuals closer to their CTmax. One consequence of this is that the effects of warmer nights could vary across biomes: being chronic and long-term in some areas (e.g. temperature zone), whereas acute and immediate in others (e.g. tropics).
Finally, rising $T_{Ds}$ may depress the activity of squamates during the hottest part of the day, leading to a larger number of hours of restricted activity (Vickers *et al.*, 2011), and this may differ among tropical, temperate and arid areas (Deutsch *et al.*, 2008; Tewksbury *et al.*, 2008; Huey, Losos & Moritz, 2010). The expected result is a switch of activity towards early morning and early evening, which may be facilitated by warmer $T_N$. However, as previously discussed, it is not certain that this reduction in diurnal activity and consequent lost feeding opportunities can be offset by increased nocturnal activity. We encourage future research to compare the responses of species from different climatic zones to assess whether warming nights have similar impacts across the globe.

### (3) Will warmer nocturnal temperatures shift life-history strategies?

Because of seasonal variation, fluctuations in prey density or predation risk, reptiles face constraints on their ability to acquire, store and spend energy (Sinervo & Licht, 1991; Bleu *et al.*, 2013; Arnall *et al.*, 2019), and there will be multiple trade-offs in energy allocation among maintenance, growth, reproduction and survival. Such trade-offs among life-history traits are known to vary with individual characteristics, but also with local conditions (Ernande *et al.*, 2004; Sgrò & Hoffmann, 2004; Rutschmann *et al.*, 2016). Through its contrasting influence on different physiological and behavioural processes (Clark *et al.*, 2013), nocturnal warming may also affect these life-history trade-offs (e.g. levy their intensity or shift their relative importance). For example, nocturnal warming alters energy allocation rules in juvenile common lizards, with individuals exposed to warmer $T_{Ns}$ being more likely to invest in immediate growth rather than long-term reserves (Rutschmann *et al.*, 2021). How this could influence winter survival and next-season reproduction is yet to be explored (Bestion *et al.*, 2015). In the same species, $T_N$ also influenced energy allocation in adult females (Brusch IV *et al.*, 2023), with colder $T_N$ resulting in lower litter mass and
longer gestation. Interestingly, warmer days had the opposite effect, highlighting the contrasting impacts of $T_D$ and $T_N$ (Speights & Barton, 2019).

Another illustration of life-history shifts driven by warmer $T_N$ comes from the nocturnal *Woodworthia* 'Otago/Southland' gecko species from southern New Zealand. This species classically reproduces biennially, with embryos retained *in utero* over winter (Cree & Guillette, 1995). However, experimental exposure to warmer $T_N$ during late summer was shown to advance the parturition season to the autumn, leading to changes in female life history (e.g. doubling reproductive rate) and population dynamics (Moore *et al.*, 2020).

Further work is needed to explore the long-term implications of nocturnal warming on life-history trade-offs and strategies of energy investment.

## (4) Will warmer nights alter interactions between squamates and other species?

Squamates are keystone species in their ecosystems and are engaged in numerous predator–prey relationships. Thus, by affecting the ecology of ectotherms, warmer $T_N$ may also perturb the trophic networks in which they are embedded. Further, because the thermal preferences and TPCs of prey and predator species do not usually overlap (Bennett *et al.*, 2018), it is unlikely that all elements of a trophic network will respond uniformly to warmer nights.

Thus, one might expect the destabilisation of prey–predator systems or the emergence of new ones, leading to a potential reorganisation of trophic communities. For example, extension of the activity window in insects has been shown to increase the top-down effects of insects on plants (see review by Ma *et al.*, 2020). Similarly, bottom-up effects have been documented to be altered through modified nectar production in plants (Mu *et al.*, 2015) or through altered nutrient allocation within plants (Jing *et al.*, 2016). Community-level studies specifically focusing on vertebrate ectotherms are still rare but it has already been shown that shifts from diurnal towards cathemeral/nocturnal activity during periods of warmer temperatures (i.e.
920

summer or heatwaves) can result in diet and microhabitat-use changes (Sperry *et al.*, 2013; Mata-Silva *et al.*, 2018; Lara Resendiz, 2019).

921

922

Further, ectothermic vertebrates are frequently involved in mutualistic associations with
symbionts and microbiota crucial for digestion or nutrient acquisition (Shigenobu, Watanabe
& Hattori, 2000). The microbiome also plays essential roles in behaviour, immunity, and life
history (Macke *et al.*, 2016). Whether effects of nocturnal warming on an individual's
microbiota differ from effects of diurnal warming (Bestion *et al.*, 2017; Moeller *et al.*, 2020)
is difficult to determine. However, the dynamics of the microbiome is shaped both by the
thermal tolerance capacities of the symbionts and by the temperature-dependent immune
responses of the individual hosts (Ferguson, Heinrichs & Sinclair, 2016; Goessling &
Mendonça, 2016; Abram & Dixon, 2017). By affecting the body temperature or the
thermoregulatory behaviour of the host, warmer nights therefore have the potential to affect
microbiome dynamics and ultimately to impact the fitness of the ectotherm (Burke *et al.*,
2010; Higashi, Barton & Oliver, 2020).

923

924

925

926

927

928

929

930

931

932

933

934

(5) Will interactions between warmer nights and other climatic factors alter squamate
ecology?

935

936

Global change is undoubtedly multi-factorial and, among other parameters, warmer *T*<sub>NS</sub> are
likely to be accompanied by changing precipitation and snow regimes (Yang *et al.*, 2016;
Dai, Zhao & Chen, 2018), water temperatures (Nordberg & McKnight, 2023), heatwave
intensity and frequency (Meehl & Tebaldi, 2004; Sanderson, Hemming & Betts, 2011;
Murali *et al.*, 2023), or habitat quality and diversity (Hoekstra *et al.*, 2005). Nocturnal
warming is likely to reduce the quality of rest periods for diurnal species and their ability to
recover from diurnal stressors. Thus, it could exacerbate the already detrimental effects of
other diurnal environmental changes. For example, warmer *T*<sub>NS</sub> have been found to reduce
the longevity and fecundity of English grain aphids when combined with warm *T*<sub>DS</sub> (Zhao *et

937

938

939

940

941

942

943

944
al., 2014). Warmer nocturnal temperatures were also reported to exacerbate the detrimental effects of metallic pollutants on amphibian species (Hallman & Brooks, 2015) and to interact with light pollution to alter the food-chain dynamics of aphids and ladybirds (Miller et al., 2017). Further research investigating interactions between distinct components of global change and nocturnal warming could provide a more complete picture of how ectotherms will respond to future modifications of their environment.

## VII. CONCLUSIONS

(1) Nocturnal warming is an understudied aspect of global warming. Using diurnal squamates as a model taxon, we demonstrated that impacts of warmer nights can be very different from those of $T_D$ increases.

(2) Because they affect the coldest hours of the diel cycle, usually dedicated to rest in diurnal species, warmer $T_{NS}$ have the potential to alter the time budget dedicated to the different activity phases of diurnal ectotherms. Whether warmer nights are beneficial or detrimental will ultimately depend on the balance between energy acquisition and expenditure.

(3) Because warmer nights allow an increase in performance, they may have positive effects as long as they also allow species to (i) acquire sufficient energy to meet their increased metabolism, and (ii) rest sufficiently to recover and eliminate metabolic stressors produced by elevated metabolic activity. If individuals cannot fulfil these conditions, warmer nights could be deleterious.

(4) Because $T_{NS}$ are far from upper $CT_{max}$, any effects of increasing $T_N$ are not as immediate as effects of warmer maximum $T_D$. Instead, warmer nights may impose chronic costs accumulating over an individual's lifetime and leading to a reduction in lifetime fitness. Whether such negative effects can be compensated by behavioural or physiological adjustments is yet to be evaluated for most ectothermic species.
969 (5) Many important questions remain unanswered, including whether there are differences
970 among species with different behavioural strategies, differences between climate zones and
971 effects on ecological interactions between squamates and their prey, predators and
972 microbiome. New research programs and new protocols will be necessary to explore
973 nocturnal warming as a key element of global warming. While legacy data can be re-analysed
974 to answer some of these questions, others will require novel explorations of the night-time
975 behaviour, physiology and population ecology of reptiles.

## VIII. ACKNOWLEDGMENTS

977 The authors are greatly indebted to F. Aubret, E. Bestion, P. Blaimont, E. Gangloff, M. Gifford, S. Meylan, C. Parmesan, D. Rozen-Rechels and A. Santure for inspiring discussions.
978 A.R. was supported by a French "Make Our Planet Great Again award" to C. Parmesan
979 (project CCISS, number ANR-17-MPGA-0007). D.B.M. acknowledges support from NSF
980 (DEB-1950636). J.F.IG and G.B. acknowledge funding support provided by the "Agence
981 Nationale de la Recherche" under the "Aquatherm" project (ANR-17-CE02-0013). J.Co. was
982 supported by the European Research Council (ERC) under the European Union's Horizon
983 2020 research and innovation programme (grant agreement No 81777). O.L. and M.G.
984 acknowledge support from the "Conseil Régional de Nouvelle-Aquitaine" under the
985 "Aquastress" project (2018-1R20214 to OL) and from the Climate Sentinels Program 2016-
986 2021 funded by the European Regional Development Fund, the region Nouvelle Aquitaine,
987 and the departement of Gironde and Pyrénées-Atlantiques (coordinator: Cistude Nature). We
988 are grateful to Dr D. Cox, Associate Editor Alison Cooper and an anonymous reviewer for
989 their insightful comments on an earlier version.

## IX. AUTHOR CONTRIBUTIONS

992 A.R. drafted the manuscript, performed the literature review and supervised the project. C.P.
993 helped with the literature review, carried out the experiment for Section III.1 and analysed
data together with A.R. J.F.IG. designed the model and scenarios for Sections IV.1–3 and
performed computation together with A.R., analysed data (collected by G.B.) and drafted
Sections IV.4 and VI.1. A.D. performed the statistical analyses for Section V.3 and drafted
that section. M.G. collected data for Section III.3 under the supervision of O.L. who analysed
data and drafted that section. M.R., J.Co. and J.Cl. helped discuss the results and provided
critical feedback on the manuscript. D.B.M. collected data for Section II.3, analysed the data
and drafted that section, helped with the literature review and drafted Sections VI.2 and VI.3.
A.R., A.D., J.Cl. and D.B.M. conceived the original idea of the project. All authors
contributed to the final version.

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1620 **XI. SUPPORTING INFORMATION**

1621 Additional supporting information may be found online in the Supporting Information section

1622 at the end of the article.

1623 **Appendix S1.** Saguaro National Park legacy operative environmental temperature data.

1624 **Appendix S2.** Diurnal and nocturnal metabolic rates of *Podarcis muralis*.

1625 **Appendix S3.** Summer heatwave and nocturnal warming: a case study in a diurnal snake.

1626 **Appendix S4.** Bioenergetic modelling of energy balance.

1627 **Appendix S5.** Empirical analysis of energy balance.

1628
1629

1630

FIGURE CAPTIONS

1631

1632

1633

1634

1635

1636

1637

1638

1639

1640

1641

**Fig. 1.** Impact of warmer days and nights on individual performance. In ectotherms the temperature dependence of biological processes is conceptualised as a thermal performance curve (TPC). The curve describes the response of performance traits to changes in body temperature. Because of the left-skewed bell shape of the TPC, it is assumed that increasing temperatures near or at the critical thermal maximum (CTmax) have a large and negative instantaneous impact on performance (orange arrow). On the other hand, a similar increase in temperature at or near the critical thermal minimum (CTmin) is presumed to have a positive, but smaller, instantaneous impact on performance (blue arrow). In addition, warmer minimum temperatures during the night can push body temperature away from CTmin and towards the optimal body temperature (Topt), hence allowing higher levels of performance.

Modified from Speights *et al.* (2017).

1642

1643

1644

1645

1646

1647

1648

1649

1650

1651

1652

1653

**Fig. 2.** Impact of warmer nocturnal temperatures on the nocturnal activity and energy budget of squamate reptiles. Warmer nocturnal temperatures are expected to modify opportunities for activity (A); as nocturnal temperatures increase, operative temperatures (y-axis) are likely to exceed the minimum voluntary temperature (VTmin) (horizontal broken line) later at night and earlier in the morning (black arrows), offering increased opportunities for foraging or physiological activity. The gain in potential activity time is represented by the yellow shaded area. This extension of activity occurs at the detriment of resting time (blue area), potentially affecting the quality of physiological recovery. From an energy budget perspective (B), compared to a cold night (pale green or pale orange), warmer nights (dark green or dark orange) may offset the balance between energy income (green lines) and metabolic expenses (orange lines). Activity extension can offer opportunities for foraging or assimilation over a
larger part of the day, hence increasing the energetic intake (green shaded area). On the other hand, warmer nocturnal activity can also increase nocturnal metabolic and physiological activity, therefore raising energetic expenses over the night (orange shaded area). The overall energetic costs and benefits of warmer nocturnal temperatures will depend on the balance between these two processes.

**Fig. 3.** Temporal pattern of diurnal and nocturnal operative temperatures recorded in mid-late spring on mesquite trees exploited by the diurnal ornate tree lizard (*Urosaurus ornatus*), in the desert of Saguaro National Park (Arizona, USA). Dots represents average minimum (blue) or average maximum (yellow) temperature recorded each year. Vertical bars represent standard deviation from the mean.

**Fig. 4.** Diurnal and nocturnal metabolic rates of 65 male wall lizards (*Podarcis muralis*) at four different temperatures. Resting metabolic rate (RMR) was measured three times for each individual at each temperature, at rest (no locomotor activity and in a post-prandial physiological state) during the active (diurnal) phase of the diel cycle (measurements took place between 10:00 and 16:00). Standard metabolic rate (SMR) was also measured three times for each individual at each temperature, during the inactive (nocturnal) phase of the diel cycle (measurements took place between 22:00 and 04:00). From bottom to top, horizontal lines represent the 25th percentile (Q1), the median and the 75th percentile (Q3) of each group. Vertical lines represent the minimum (Q1 – interquartile range) and maximum (Q3 + interquartile range) values. Dots represents outliers. See Appendix S2 for further details.

**Fig. 5.** Mean daily variation in body temperature in six asp vipers (*Vipera aspis*) (solid blue line) shows a close match with minimum shelter temperatures measured using biomimetic
models (*N* = 3; solid black line) over the course of the night. Mean surface temperatures (*N* = 3 biomimetic models; solid yellow line) often exceeded the preferred body temperature of *V. aspis* (mean ± SD *T*<sub>pref</sub> = 30.63 ± 4.22, dashed black line; Lorioux *et al.*, 2013), highlighting the ability of this species to thermoregulate efficiently during the day while being more thermally passive in their shelter over the night. Periods of heatwaves (as defined by Météo France) are shaded in light grey (hot; *T*<sub>max</sub> 30–35 °C) and dark grey (extremely hot; *T*<sub>max</sub> > 35 °C). Note that this classification was made at a regional level, leading to some mismatches with our data set.

1687

Fig. 6. Relationship between nocturnal minimum environmental temperature recorded in a shelter and mean asp viper (*Vipera aspis*) nocturnal body temperature. Nocturnal temperatures were recorded from 22:00 to 08:00. Data are plotted separately for three different categories of day according to Météo France classification: normal (maximum air temperature in the shade < 30 °C; blue), hot (30–35 °C; yellow), and very hot (> 35 °C; red).

Solid lines represent the estimated slope and shaded regions the 95% confidence intervals.

The black dashed line is y = x.

1695

Fig. 7. Daily net energy gain (NEG<sub>d</sub>) predicted by our energy budget model for different thermoregulation behaviours (thermoconformer *versus* thermoregulator), ecological behaviours (diurnal *versus* nocturnal) and default metabolic rates at 20 °C (DMR<sub>20</sub>). For each increment of daily minimum nocturnal temperature tested (0–30 °C), a daily temperature cycle was created (see Fig. S3). NEG was then calculated hourly for each temperature cycle, before being integrated over 24 h to obtain one NEG<sub>d</sub> value for each minimum nocturnal temperature. Scenario 1 represents a thermoconforming ectotherm with no time constraints on activity. Scenario 2 represents a thermoconforming ectotherm with strictly diurnal
1704 foraging activity. Scenario 3 represents a thermoregulator (preferred temperature $T_{\text{pref}} = 30$ °C) with a 24 h active phase bounded by voluntary thermal limits (18 – 40 °C). Scenario 4
1705 represents a perfect thermoregulator ($T_{\text{pref}} = 30$ °C), bounded by voluntary thermal limits and
1706 with a strict diurnal activity phase. Scenario 5 represents a perfect thermoregulator ($T_{\text{pref}} = 30$
1707 °C) with a nocturnal activity phase, bounded by voluntary thermal limits (15 – 35 °C). The
1708 different colours represent curves for different $DMR_{20}$ values. $DMR_{20}$ is expressed as a
1709 percentage of the daily maximum energy intake, and can be interpreted as a proxy for animal
1710 size, with larger animals having a lower metabolic rate. Circles show the optimum minimum
1711 nocturnal temperature ($T_{\text{N, opt}}$) and represent a tipping point between positive and negative
1712 effects of nocturnal temperature on daily net energy gain. Pictograms indicate the ecological
1713 and thermoregulatory characteristics of the simulated ectotherms.
1714

1715

1716 **Fig. 8.** Plot of effect sizes (Cohen's *d*) for the effects of warmer nocturnal temperatures ($T_N$)
1717 on phenotypic traits of the common lizard (*Zootoca vivipara*). Correlative studies are shown
1718 in orange and experimental studies in grey. Stars indicate significance level (***, *P* < 0.001;
1719 **, *P* < 0.01; *, *P* < 0.05). Cohen's *d* and associated 95% confidence intervals were estimated
1720 using the *t_to_d* function in R (*effectsize* package; Ben-Shachar *et al.*, 2020) for all traits
1721 other than the heating rates variables, for which non-linear mixed effect models were used
1722 (*lme.dscore* function in *EMAtools* R package; Kleiman, 2022) and confidence intervals could
1723 not be calculated. BC, body condition; CORT, corticosterone; LM, litter mass; LS, litter size;
1724 OXY, oxygen metabolites; ROM, non-enzymatic antioxidant capacity; SVL, snout-vent
1725 length; TL, telomere length; $T_{\text{pref}}$, preferred body temperature. 'Levels' indicates measures
1726 from comparative studies. 'Change' indicates measures implying an experimental design
1727 where levels were compared before and after treatments. List of publications: a. Dupoué *et al.*
1728 (2017b); b. Dupoué *et al.* (in preparation); c. Brusch IV *et al.* (2023); d. Rutschmann *et al.*
1729 (2021); e. Dupoué et al. (2018); f. Rutschmann et al. (2020); g. Dupoué et al. (2017c); h.

1730 Dupoué et al. (2020); i. Rozen-Rechels et al. (2021).

1731
1732

1733

<caption>Figure 1</caption>

1734

<figure><img src="image_2.png" /></figure>
1735

1736

<caption>**Figure 2**</caption>

1737

<figure><img src="image_3.png" /></figure>

1738

**Energetics**

<figure><img src="image_4.png" /></figure>
1739

1740

1741

<figure><img src="image_5.png" /><figcaption>**Figure 3**</figcaption></figure>

1742
1743

1744

<figure><img src="image_6.png" /><figcaption>1745 **Figure 4**</figcaption></figure>

1746
1747

1748

<figure><img src="image_7.png" /><figcaption>**Figure 5**</figcaption></figure>

1749
1750

1751

<figure><img src="image_8.png" /><figcaption>**Figure 6**</figcaption></figure>

1752
<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>1757 **Figure 8**</figcaption></figure>
PrePrint Version
1760

1761 Table 1. Summary of the scenarios tested using our energy balance model. AR, attack rate;

1762 IR, ingestion rate; MR, metabolic rate. All rates (AR, IR and MR) were dependent on

1763 temperature. Depending on the scenario, AR was either positive throughout the 24 h diel cycle, only diurnal (positive from 07:00 to 20:00), only nocturnal (positive from 20:00 to

1764 07:00) or constrained by a temperature window (e.g. positive when $T \ge 18$ °C and $T \le 40$ °C).

1765 See Section IV.2 and Appendix S4 for detailed description of each scenario.

1767

<table><thead><tr><th>Scenario</th><th>Thermoregulation strategy</th><th>Temperature variation</th><th>AR</th><th>IR and MR</th></tr></thead><tbody><tr><td>0</td><td>Thermoconforming</td><td>$T_{D,max}$</td><td>24 h</td><td>24 h</td></tr><tr><td>1</td><td>Thermoconforming</td><td>$T_{N,min}$</td><td>24 h</td><td>24 h</td></tr><tr><td>2</td><td>Thermoconforming</td><td>$T_{N,min}$</td><td>Diurnal</td><td>24 h</td></tr><tr><td>3</td><td>Thermoregulating</td><td>$T_{N,min}$</td><td>24 h &amp; $T \in [18$ °C – $40$ °C]</td><td>24 h</td></tr><tr><td>4</td><td>Thermoregulating</td><td>$T_{N,min}$</td><td>Diurnal &amp; $T \in [18$ °C – $40$ °C]</td><td>24 h</td></tr><tr><td>5</td><td>Thermoregulating</td><td>$T_{N,min}$</td><td>Nocturnal &amp; $T \in [15$ °C – $35$ °C]</td><td>24 h</td></tr></tbody></table>

1768

1769
1770

1771

ECOLOGICAL RESPONSES OF SQUAMATE REPTILES TO NOCTURNAL

1772

WARMING - Supporting Information

1773

1774

CONTENTS

1775

Appendix S1. Saguaro National Park legacy operative environmental temperature data

1776

(1) Study system

1777

(2) Statistical analyses

1778

1779

Appendix S2. Diurnal and nocturnal metabolic rates of *Podarcis muralis*

1780

(1) Study species

1781

(2) Experimental design

1782

(3) Measurement of metabolic rates

1783

(4) Statistical analyses

1784

1785

Appendix S3. Summer heatwave and nocturnal warming: a case study in a diurnal snake

1786

(1) Thermoregulation under semi-natural conditions

1787

(2) Statistical analyses

1788

1789

Appendix S4. Bioenergetic modelling of energy balance

1790

(1) List of abbreviations

1791

(2) Context

1792

(a) Net energy gain model

1793

(b) Functional response

1794

(c) Attack and intake rates

1795

(d) Metabolic rate

1796

(e) Daily temperature cycles

1797

(f) Daily energy acquisition and expenses

1798

(3) R Code of the bioenergetic model

1799

(a) Libraries

1800

(b) Parameters and default values

1801

(c) Basic functions

1802

(i) Arrhenius equation for MR

1803

(ii) Functional response (Type II)

1804

(iii) Temperature dependence of functional response parameters

1805

(iv) Temperature cycle function

1806

(v) Testing the influence of nocturnal temperature and DMR<sub>20</sub>

1807

(4) Scenarios

1808

(a) Scenario 0. Model validation

1809

(b) Scenario 1. Thermoconformer with 24-h foraging activity

1810

(c) Scenario 2. Thermoconformer with diurnal foraging activity

1811

(d) Scenario 3. Thermoregulator with 24-h foraging activity

1812

(e) Scenario 4. Thermoregulator with diurnal foraging activity

1813

(f) Scenario 5. Thermoregulator with nocturnal foraging activity

1814

(g) Effects of efficient AR at low temperature

1815

1816

Appendix S5. Empirical analysis of energy balance
# Appendix S1. Saguaro National Park legacy operative environmental temperature data

1817

1818

1819

1820

## (1) Study system

1821

1822

1823

1824

1825

1826

1827

1828

D.B. Miles measured operative environmental temperatures ($T_e$s) at Saguaro National Park (SNP, Arizona, USA). $T_e$s represent the body temperature of an inactive ectotherm in a given microhabitat and were originally recorded to estimate the thermal quality of the habitat exploited by the diurnal ornate tree lizard (Urosaurus ornatus). At SNP, these lizards are arboreal and occupy mesquite (Prosopis velutina) and paloverde (Parkinsonia aculeata) trees. In mid-late spring (~25 May – 15 June) 2001, 2002, 2015, 2020 and 2022, 2–4 biomimetic lizard-shaped models made of polyvinyl chloride (PVC) were placed on the same trees used by lizards for a period of 5–15 days. The sensors within these models were programmed to record $T_e$ every 5 min over a 24-h period.

1829

## (2) Statistical analyses

1830

1831

1832

1833

1834

1835

1836

Each year, and for each biomimetic logger, we extracted the minimum and maximum temperatures recorded each day. We then calculated the mean daily minimum and mean daily maximum $T_e$ among loggers to obtain a single value for each day. We used a linear model to investigate whether $T_e$ changed significantly over the study period. In the model, we also included an interaction term between time of day (i.e. minimum or maximum temperature) and year (as a continuous factor). The interaction term was statistically significant: minimum $T_e$ increased faster than maximum $T_e$ in SNP over the period 2001–2022 (see Table S1).

1837

1838

<table><caption>**Table S1.** Results of ANOVA linear model relating mean daily operative environmental temperature ($T_e$) to study year, time of the day (i.e. minimum or maximum $T_e$) and their interaction term.</caption><thead><tr><td>Explanatory variables</td><td>Df</td><td>Mean Sq.</td><td>F value</td><td>P</td></tr></thead><tbody><tr><td>Year</td><td>1</td><td>51.9</td><td>4.18</td><td>0.04</td></tr><tr><td>Time of day</td><td>1</td><td>18464.9</td><td>1488.78</td><td>&lt;0.005</td></tr><tr><td>Year × Time of day</td><td>1</td><td>111.1</td><td>8.89</td><td>&lt;0.005</td></tr><tr><td>Residuals</td><td>63</td><td>12.4</td><td>—</td><td>—</td></tr></tbody></table>

1839

1840

1841

1842

Although we were interested in the trend in temperature changes, note that the difference over the study period was 5.56 °C for maximum $T_e$ and 9.37 °C for minimum $T_e$. The absolute change in minimum and maximum $T_e$ over the period 2001–2022 was estimated as the difference between the median values obtained for the minimum and maximum $T_e$ recorded in 2022 and 2001.
PrePrint Version
1844

1845

1846

1847

1848

# Appendix S2. Diurnal and nocturnal metabolic rates of *Podarcis muralis*

## (1) Study species

1849

1850

1851

1852

1853

1854

1855

1856

1857

1858

1859

1860

1861

1862

1863

1864

1865

1866

1867

The wall lizard (*Podarcis muralis*; Laurenti 1768) is a small heliothermic and strictly diurnal squamate widespread in Central Europe. Males (N = 65) were captured by C. Perry and A. Rutschmann between April 8 and 17 2022 using the lasso method (Blomberg & Shine, 2006) at three sites, all located within a 10 km radius of the Station d'Ecologie Théorique et Expérimentale (SETE, Moulis, France 42°57'26.8" N, 1°05'08.3" E; 436 m ASL). Immediately after capture, we measured body mass (mean ± S.D.: 7.17 ± 0.81 g) and snout-vent length (SVL = 69.09 ± 2.69 mm). Lizards were transported to temperature-controlled environment chambers located in the SETE where they were marked using a cautery pen with a unique identification number on their ventral scales (Vervust & Van Damme, 2009). For logistic reasons, lizards were acclimated in pairs in plastic enclosures (56 × 39 × 28 cm). Each enclosure contained a thin layer of wood straw as a substrate, a water supply, paving stones used as thermoregulation platforms (15 × 15 × 6 cm) and two plastic refuges for sheltering. Every second day, lizards were fed *ad libitum* with mealworms (*Tenebrio* sp. larvae) and crickets (*Acheta domestica*). Water was provided *ad libitum*. Terraria were misted with a water sprayer every second day in the morning (08:00). An ultraviolet lamp provided light for 12 h per day (07:00–19:00). Each tank was heated with an incandescent heat lamp (42 W) for 6 h per day at 1 h intervals. This provided a diurnal thermal gradient ranging from 24 to 36 °C, a range that includes the preferred body temperature (*T*<sub>pref</sub>) for thermoregulation in this species (*T*<sub>pref</sub> = 32.9 °C) (Bodensteiner *et al.*, 2021). During the night, the lamp was switched off, with nocturnal air temperature (*T*<sub>N</sub>) controlled at 17 °C in the environmental chambers.

1868

## (2) Experimental design

1869

1870

1871

1872

1873

Forty-five days after capture, we measured both diurnal and nocturnal metabolic rate (MR). For each individual, six measurements were made at each of four different body temperatures (15, 20, 25, 30 °C), which includes the range of body temperatures over which MR increases exponentially (C. Perry, personal observations). Following Andrews & Pough (1985), for each body temperature resting MR (RMR) was measured three times during the active phase of the day (10:00–16:00), while standard
1874 MR (SMR) was measured three times during the resting phase of the day (22:00–04:00). Prior to the
1875 experiment, lizards were randomly assigned to a group of 5–7 individuals (10 groups in total) and
1876 each group was randomly assigned to one of the four temperatures. Both diurnal and nocturnal MR
1877 were measured for the given temperature, and three groups were tested, within a single 24-h diel
1878 cycle. Before being tested again at a different randomly chosen temperature, lizards were allowed to
1879 rest for at least 24 h. The experiment lasted 13 days and nights in total.

1880 **(3) Measurement of metabolic rates**

1881 Thirty minutes prior to MR measurements, lizards were individually placed in a black canvas sock (10
1882 cm × 4 cm), within one of the eight 75 ml opaque plastic metabolic chambers of an incubator
1883 (Aqualytic Incubator TC 140 G, Germany). After this acclimation period, chambers were closed for
1884 three sessions of 15 min each to measure oxygen consumption (PreSens© OXT-4 SMA system)
1885 (Warkentin et al., 2007). Between each session, chambers were opened for 15 min to allow
1886 replacement of oxygen. One of the eight metabolic chambers, which was always the same, remained
1887 empty to serve as a control. Individual MRs were then obtained as the slope (b) of the oxygen
1888 consumption curve as a function of time. To calibrate MR (Warkentin et al., 2007), each b value was
1889 corrected by the average slope (bcontrol) recorded within the control chamber at each temperature
1890 (Andrews & Pough, 1985). Then, MR was estimated as:

$$
MR = \frac{(V_{\text{chamber}} - V_{\text{id}}) * \%O_2 * (\beta - \beta_{\text{control}})}{100} \quad (S1)
$$

1891 where V<sub>chamber</sub> is chamber volume, V<sub>id</sub> is individual volume (approximated as individual mass), and
1892 %O<sub>2</sub> is the initial proportion of oxygen in the chamber. RMR and SMR were further adjusted by
1893 individual mass following Brown *et al.* (2004) to give mass-specific metabolic rates:

$$
MR_m = \frac{MR}{Mass^\alpha} \tag{S2}
$$
with $\alpha$ estimated as the slope coefficient of the linear regression between mass and metabolic rate
(0.74 for RMR and 0.91 for SMR).

1896 **(4) Statistical analyses**

1897 All statistical comparisons were performed in R software version 4.2.3. We used a linear mixed-
1898 effects model to test whether the reaction norm (i.e. temperature dependence of MR) varied
1899 significantly between day (RMR) and night (SMR) measurements. In the model, we also included an
1900 interaction term between the time of the day (i.e. SMR versus RMR) and temperature. We included
1901 individual as a random effect to control for repeated measures. The interaction term was significant,
1902 with RMR increasing faster with temperature than SMR.

1903 **Table S2.** Results of ANOVA linear model relating metabolic rate to the time of the day [i.e. whether
1904 standard metabolic rate (night) or resting metabolic rate (day) was measured], temperature and
1905 their interaction term.

<table><thead><tr><th>Explanatory variables</th><th>Numerator DF</th><th>Denominator DF</th><th>F value</th><th>P</th></tr></thead><tbody><tr><td>(Intercept)</td><td>1</td><td>1534</td><td>812.6</td><td><strong>&lt;0.005</strong></td></tr><tr><td>Time of day</td><td>1</td><td>1534</td><td>1418.6</td><td><strong>&lt;0.005</strong></td></tr><tr><td>Temperature</td><td>1</td><td>1534</td><td>1678.4</td><td><strong>&lt;0.005</strong></td></tr><tr><td>Interaction (Temperature × Time of day)</td><td>1</td><td>1534</td><td>482.7</td><td><strong>&lt;0.005</strong></td></tr></tbody></table>

1906

1907 We also analysed the variance between temperatures in each metabolic rate group using the
1908 *leveneTest* function in R (Fox, 2016). The variance in MR was significantly different between SMR and
1909 RMR across all temperatures (*F*<sub>7,1594</sub>= 221.4, *P* <0.005). A graphical representation of the data (see
1910 Fig. 4 in the main article) confirms that variance increased with temperature, especially for RMR.

1911
# Appendix S3. Summer heatwave and nocturnal warming: a case study in a diurnal snake

## (1) Thermoregulation under semi-natural conditions

To examine the influence of weather conditions on thermoregulation, in late spring 2003 six non-pregnant adult female asp vipers (Vipera aspis) of similar mass and size (mean ± SD SVL = 49.5 ± 4.5 cm; body mass = 88.8 ± 25.6 g) were captured in the wild in western France by M. Guillon and O. Lourdais. Vipers were housed in an 80 m² outdoor enclosure at the CEBC-CNRS study site in France (46°8'48"N; 0°25'31"E), located in the geographic range of V. aspis. The enclosure provided a mosaic of diverse vegetation, basking sites, shade, rocky shelters, and underground refuges, that mimicked the natural habitat of this species. We implanted temperature loggers (Ibutton @Maxim dallas) into the body cavity following a previously described protocol (Lourdais et al., 2013). Body temperature ($T_b$) was measured every hour of the 24-h diel cycle, from July 1 to September 4. Simultaneously, we measured $T_e$ every hour in six biomimetic models (copper tubes filled with water) designed to match the biophysical properties (shape, size and reflective properties) of the study species. We placed the models into two contrasting microhabitats: on the ground in the open ($N$ = 3) and in underground shelter ($N$ = 3) to record the range of $T_e$. Each day was classified as very hot (>35 °C), hot (maximum air temperature in the shade 30-35 °C), or normal (<30 °C) according to the French national meteorological agency (Météo France) classification for the study area (Laadi et al., 2012). Because behavioural activity occurs only during the day in this species, we distinguished between the daytime activity period (from 09:00 to 21:00) and the nocturnal resting period (22:00 to 08:00).

## (2) Statistical analyses

All statistical comparisons were performed in R software version 4.2.3. For each hour, we averaged data collected for body temperatures ($N$ = 6 individuals) and microhabitat $T_e$ ($N$ = 3 replicates per category). We used a linear model to examine the relationship between minimal nocturnal environmental temperature in the shelter ($T_{N shelter}$) and maximal environmental temperatures ($T_D$ open) recorded in the open during the previous day (see Table S3).

<table><caption>**Table S3.** Results of a linear model relating daily nocturnal shelter environmental minimum temperature ($T_{N shelter}$) to the maximum environmental temperature in the open ($T_D$ open) during the previous day.</caption><thead><tr><td>Explanatory variables</td><td>df</td><td>Sum Sq</td><td>Mean Sq</td><td>F value</td><td>P</td></tr></thead></table>
<table><tr><td>T<sub>D open</sub></td><td>1</td><td>310.89</td><td>310.89</td><td>87.61</td><td><strong>&lt; 0.005</strong></td></tr><tr><td>residuals</td><td>64</td><td>227.1</td><td>3.54</td><td></td><td></td></tr></table>

1942

We used a second linear model to examine variation in mean nocturnal body temperature ($T_{b night}$) (i.e. averaged across the period 22:00–8:00) with conditions in the previous day. The model included the previous day type as a factor (i.e. very hot, hot or normal), $T_{N shelter}$ as a covariate and their interaction term (see Table S4).

**Table S4.** Results of ANOVA linear model relating mean nocturnal body temperature to the previous day type (normal, hot, very hot), the nocturnal shelter minimum temperature ($T_{N shelter}$), and their interaction term.

1950

<table><thead><tr><th>Explanatory variable</th><th>df</th><th>Sum Sq</th><th>Mean Sq</th><th>F value</th><th>P</th></tr></thead><tbody><tr><td>Previous day type</td><td>2</td><td>350.8</td><td>175.41</td><td>256.95</td><td><strong>&lt; 0.005</strong></td></tr><tr><td><i>T</i><sub>N shelter</sub></td><td>1</td><td>97.83</td><td>87.33</td><td>127.92</td><td><strong>&lt; 0.005</strong></td></tr><tr><td>Interaction (Previous day type × <i>T</i><sub>N shelter</sub>)</td><td>2</td><td>1.76</td><td>0.88</td><td>1.28</td><td>0.28</td></tr><tr><td>Residuals</td><td>60</td><td>40.96</td><td>0.68</td><td></td><td></td></tr></tbody></table>

1951

1952

1953
1954

# Appendix S4. Bioenergetic modelling of energy balance

1955

1956

## (1) List of abbreviations

<table><tr><td>α</td><td>Conversion efficiency of food to energy parameter</td></tr><tr><td>AR<sub>T</sub></td><td>Temperature-dependent food attack rate</td></tr><tr><td>b<sub>AR</sub>/b<sub>IR</sub></td><td>Linear parameter for attack rate and intake rate</td></tr><tr><td>DMR<sub>20</sub></td><td>Default metabolic rate at 20 °C</td></tr><tr><td>E<sub>α</sub></td><td>Activation energy parameter</td></tr><tr><td>FR<sub>R,T</sub></td><td>Functional response (the energy derived from food consumption and assimilation)</td></tr><tr><td>h</td><td>Handling time</td></tr><tr><td>IR<sub>T</sub></td><td>Temperature-dependent food ingestion rate</td></tr><tr><td>k<sub>b</sub></td><td>Boltzmann constant</td></tr><tr><td>K<sub>AR</sub>/K<sub>IR</sub></td><td>Scaling parameter for attack rate / intake rate</td></tr><tr><td>MR<sub>T</sub></td><td>Temperature-dependent metabolic rate (energy expenditure)</td></tr><tr><td>NEG<sub>d</sub></td><td>Daily net energy gain</td></tr><tr><td>NEG<sub>h</sub></td><td>Hourly net energy gain</td></tr><tr><td>NEG<sub>R,T</sub></td><td>Temperature- and resource-dependent instantaneous net energy gain</td></tr><tr><td>R</td><td>Resource (food) density</td></tr><tr><td>q<sub>AR</sub>/q<sub>IR</sub></td><td>Quadratic parameter for attack rate and intake rate</td></tr><tr><td>T</td><td>Temperature</td></tr><tr><td>T<sub>A</sub></td><td>Arrhenius temperature</td></tr><tr><td>T<sub>D</sub></td><td>Diurnal air temperature</td></tr><tr><td>T<sub>e</sub></td><td>Operative environmental temperature</td></tr><tr><td>T<sub>N</sub></td><td>Nocturnal air temperature</td></tr><tr><td>T<sub>N opt</sub></td><td>Optimal nocturnal air temperature</td></tr><tr><td>T<sub>opt</sub></td><td>Optimal body temperature</td></tr><tr><td>T<sub>pref</sub></td><td>Preferred body temperature</td></tr><tr><td>TPC</td><td>thermal preference curve</td></tr><tr><td>VT<sub>min</sub></td><td>Voluntary minimum temperature</td></tr><tr><td>VT<sub>max</sub></td><td>Voluntary maximum temperature</td></tr></table>

1957

## (2) Context

1958

### (a) Net energy gain model

1959

1960

1961

1962

1963

We extended the energy balance model of Huey & Kingsolver (2019) to characterise the net energy intake of an ectothermic predator at different nocturnal environmental temperatures ($T_{NS}$). The model assumes that net energy gain (NEG) depends on a positive input (from food consumption and assimilation) and a negative output (from energy expenditure associated with basal metabolism and body maintenance).

$$ NEG_{R,T} = FR_{R,T} * \alpha - MR_{T} \qquad (S3) $$

1964

1965

Where NEG and the functional response FR depend on resource density ($R$) and temperature ($T$) and the metabolic rate MR depends on temperature alone. The conversion efficiency of food to
1966 energy (a) was set to 69% in all simulations (Levy et al., 2017) and assumed to be independent of
1967 temperature.

1968 (b)

<figure><img src="image_11.png" /></figure>

1974 functional response (as used in Huey & Kingsolver, 2019) with a Type II functional response (as used
1975 in our model).

1976 Rather than assuming a Type I functional response as in Huey & Kingsolver (2019) where food intake
1977 increases linearly with prey density up to a saturation point, we used a Type II functional response
1978 that assumes a decelerating intake rate with food density (Fig. S1). In the Type II functional
1979 response, intake rate depends on both attack rate (AR; the rate at which prey is encountered and
1980 attacked) and an ingestion rate (IR; the rate at which prey is ingested). Varying AR conveniently
1981 allowed us to separate a diurnal (AR >0) and nocturnal (AR = 0) phase for food acquisition (i.e.
1982 foraging). The Type II functional response is given by equation S4:

$$
\text{FR}_{\text{R,T}} = \frac{\text{AR}_{\text{T}} * \text{R}}{1 + \text{AR}_{\text{T}} * \frac{\text{R}}{\text{IR}_{\text{T}}}} \quad (\text{S4})
$$

1983 where food intake depends on food density R (arbitrarily set to R = 2 in all cases), attack rate AR
1984 (which determines food intake at low food density) and ingestion rate IR. IR was replaced in our
1985 equations by the handling time (h; inversely proportional to IR) which represents the time spent
1986 handling, eating and digesting prey and therefore determines food intake at high food density:
1987

$$
\text{FR}_{\text{R,T}} = \frac{\text{AR}_{\text{T}} * \text{R}}{1 + \text{AR}_{\text{T}} * h_{\text{T}} * \text{R}} \quad (\text{S5})
$$

1993 The temperature dependence of AR and IR were modelled using Arrhenius-like equations (see
1994 Englund et al., 2011).

1995 (c) Attack and intake rates
1996 We scaled all parameters of the AR and IR equations to have a unimodal relationship with
1997 body temperature and a maximum of 1 at an optimal body temperature $T_{opt}$ (here, scaled

1998 such that $T_{opt} = 30$ °C). $AR_T$ and $IR_T$ were estimated as follows:

$$AR_T = K_{AR} * \exp(b_{AR} * T_A + (q_{AR} * T_A)^2) \quad (S6)$$

$$IR_T = K_{IR} * \exp(b_{IR} * T_A + (q_{IR} * T_A)^2) \quad (S7)$$

1999 where $K_{AR}$ and $K_{IR}$ are scaling parameters, $b$ and $q$ are the linear and quadratic parameters of the
2000 equation, and $T_A$ is Arrhenius temperature. $K_{AR}$ and $K_{IR}$ (1.679$^{-220}$ and 2.957$^{-103}$ respectively)

2001 were calculated as:

$$K_{AR} = \frac{1}{\max AR} \quad \text{and} \quad K_{IR} = \frac{1}{\max IR} \quad (S8)$$

2002 Arrhenius temperatures ($T_A$) were calculated using the Boltzmann constant ($k_B = 8.617 * 10^{-05}$

2003 $eV.K^{-1}$) and body temperature ($T$) in degrees Kelvin (293.5 °K or 20 °C) following:

$$T_A = \frac{-1}{k_B * T} \quad (S9)$$

2004

<figure><img src="image_12.png" /></figure>

2005

2006

<caption>Fig. S2. Estimation of parameters $b$ and $q$ for attack rate AR (A) and ingestion rate IR (B). Data are modified from Englund et al. (2011) to match an optimal temperature for AR and IR of 30°C.</caption>

2009

2010

2011 Finally, the parameters $b$ and $q$ were estimated using empirical data presented by Englund et al.

2012 (2011) for diverse ectotherms (Fig. S2). We obtained parameters $b$ (i.e. linear slope) and $q$ (i.e.

2013 quadratic slope) by fitting a non-linear model to the log-transformed raw data of this meta-analysis

2014 ($I_m$ function in R; Fig. S2). Note that for both AR and IR, body temperature data from Englund et al.

2015 (2011) were shifted from $T_{opt}$ of 25 °C to higher values (by adding 5 °C to every body temperature
recorded) in order to match the $T_{opt}$ of 30 °C used in our model. This adjustment corresponds with the thermal characteristics of a 'standard' lizard and allowed better visualization of $T_N$ effects.

2018

### (d) Metabolic rate

The temperature-dependent metabolic rate (MR$_T$) represents the energy output of the model. It was set to a standard value at 20 °C (293.15 °K) and assumed to increase exponentially with the inverse of body temperature (in °K) according to the following equation:

$$MR_T = DMR_{20} * \exp \left( E_a * \frac{T - T_0}{k_b * T * T_0} \right) \quad (S10)$$

where DMR$_{20}$ is the default metabolic rate for a maximum energy intake of 1 at 20 °C; $E_a$ (electron-volt, eV) is the activation energy parameter (set at 0.64 according to Fussmann et al., 2014), T is body temperature (in °K) and $T_0$ is the reference temperature (293.15 °K). In our simulations, DMR$_{20}$ was set to 1, 5, 10 or 15% of the maximum energy intake at 20 °C to explore the impact of changes in $T_N$ on different organism types (i.e. larger organisms are expected to have a lower mass-specific MR than smaller ones or species with a fast life history are assumed to have a higher mass-specific MR than species with a slow life history).

### (e) Daily temperature cycles

Air temperature was modelled using an asymmetric 24-h periodic function that was built to match the shape of diurnal cycles recorded during the 2003 heatwave study described in Section III.3 of main article. Mathematical equations describing this cycle were adapted from the Parton–Logan function (Parton & Logan, 1981; McMunn & Pepi, 2022) and use a combination of linear and sine-like functions to simulate a realistic temperature cycle during a sunny day (Fig. S3). From sunrise at 07:00, the temperature increases linearly from its minimum until it reaches mean daily temperature at 10:00. From there until sunset (20:00), it follows a sine-like function, reaching the diurnal peak temperature at 14:00 (40 °C), before decreasing. Overnight (21:00 to 07:00), the air temperature decreases linearly to reach a minimal value at sunrise. Because our focus was on nocturnal warming, we held maximum diurnal temperature constant across simulations (40 °C), while minimum nocturnal temperature was varied from 0 to 30 °C (Fig. S3). See Section 3.c.iv below for R code.
<figure><img src="image_13.png" /><figcaption>Fig. S3. Daily temperature cycles used in our model based on the Parton–Logan function (Parton & Logan, 1981; McMunn & Pepi, 2022). The model uses a combination of linear and sine-like functions to simulate a realistic temperature cycle during a sunny day. Atmospheric temperatures increase linearly from 07:00 to reach mean daily temperature at 10:00, after which it follows a sine-like function, reaching a peak day temperature of 40 °C at 14:00 and then decreasing until 20:00. Overnight (20:00 to 07:00), atmospheric temperature decreases linearly to reach once again a minimum value at 07:00.</figcaption></figure>

(f) Daily energy acquisition and expenses

For each hour of the day, we characterised air temperature using the asymmetric 24-h periodic function described above. We used these air temperatures to calculate hourly AR, IR and MR (see below for R code) and then calculated hourly net energy gain (NEG<sub>h</sub>). The daily net energy gain (NEG<sub>d</sub>) was estimated as the sum of NEG<sub>h</sub> values:

$$NEG_d = \sum_{i=1}^{24} NEG_h \qquad (S11)$$
2059 We computed NEG<sub>d</sub> for different scenarios of thermoregulation behaviours (see Section IV.2 in the main article), for different minimal nocturnal temperatures (T<sub>N,min</sub>) and for different values of default metabolic rate (DMR<sub>20</sub>).

2062 **(3) R code of the bioenergetic model**

2063 **(a) Libraries**

2064 library(dplyr)
2065 library(ggplot2)
2066 library(gridExtra)
2067 library(lattice)
2068 library(plotly)

2069 **(b) Parameters and default values**

2070 alpha <- 0.69 # Conversion efficiency
2071 b_a <- -26.37628 # Linear slope for AR
2072 b_a_N <- -19.94401 # Linear slope for AR (nocturnal species)
2073 b_i <- -12.37742 # Linear slope for IR
2074 c <- 8 # Sinusoidal period parameter
2075 Ea <- 0.64 # Energy activation rate for metabolic expenditure
2076 HA_max <- 20 # Maximal time for activity (Scenario 2 & 4)
2077 HA_min <- 7 # Minimal time for activity (Scenario 2 & 4)
2078 Hmax <- 20 # Time of sunset
2079 Hmin <- 7 # Time of sunrise
2080 k_a <- 1.679279e-220 # Standardizing parameter for AR
2081 k_a_N <- 1.382221e-167 # Standardizing parameter for AR (Nocturnal sp.)
2082 k_b <- 8.6173303e-05 # Boltzmann's constant (eV.K-1)
2083 k_i <- 2.957385e-103 # Standardizing parameter for intake rate
2084 M_met <- 0.1 # Default metabolic expenditure at 20°C (set to 10% of maximum intake with default parameters)
2085
2086 pi <- 3.14159265359 # Quadratic slope for AR
2087 q_a <- -0.3436951 # Quadratic slope for AR (Nocturnal species)
2088 q_A_N <- -0.2588205 # Quadratic slope for AR (Nocturnal species)
2089 q_i <- -0.1622324 # Quadratic slope for IR
2090 R <- 2 # Resource rate
2091 Tpref <- 30 # Preferred body temperature; Default value
2092 Tref <- 20 # Standard temperature for metabolic expenditure
2093 VTmax_D <- 40 # Voluntary thermal limit (upper)
2094 VTmin_D <- 18 # Voluntary thermal limit (lower)
2095 VTmax_N <- 30 # Voluntary thermal limit (upper)
2096 VTmin_N <- 15 # Voluntary thermal limit (lower)

2097 **(c) Basic functions**

2098 **(i) Arrhenius equation for MR**

2099 Returns MR according to environmental temperature.

2100 **Parameters**

2101 t # Temperature (in °C)

2102 k0 # Normalizing parameter (k_a or k_i)
2103 Ea # Energy activation rate for metabolic expenditure
2104 Tref # Standard temperature for metabolic expenditure

2105 Function
2106 Arrhenius_function=function(t,k0,Ea,Tref){
2107 T=t+273.15 # Convert °C to °K
2108 T0=Tref+273.15 # Convert standard temperature in °K
2109 k0*exp(Ea*(T-T0)/(k_b*T*T0)) # Standard Arrhenius equation with
2110 } # a normalizing temperature

2111 (ii) Functional response (Type II):

2112 Parameters
2113 r # Resource density
2114 a # Attack rate
2115 h # Handling rate (inverse of Intake rate)

2116 Function
2117 FR_function=function(r,a,h){a*r/(1+a*h*r)}

2118 (iii) Temperature dependence of functional response parameters:

2119 Parameters
2120 t # Temperature (in °C)
2121 k0 # Normalizing parameter (k_a or k_i)
2122 b # Linear slope for AR and IR
2123 q # Quadratic slope for AR and IR

2124 Function
2125 Temperature_function=function(t,k0,b,q){
2126 T=t+273.15 # Convert °C in °K
2127 Arrhenius_Temp=-1/(k_b*T) # Convert °K in Arrhenius temperature
2128 k0*exp(b*Arrhenius_Temp+q*Arrhenius_Temp^2))

2129 (iv) Temperature cycle function

2130 Parameters
2131 hour # Hour of the day
2132 Tmin # Minimum temperature of the day (Varying from 0 to 30°)
2133 Tmax # Maximum temperature of the day (40°C)
2134 Hmin # Time of sunrise (07h00)
2135 Hmax # Time of sunset (20h00)
2136 c # Sinusoidal period parameter (8)

2137 Function
2138 Temperature_cycle <- function(hour, Tmin,Tmax,c,Hmin,Hmax){
2139 Tr <- (Tmax-Tmin)/2 # Temperature range
2140 Tm <- (Tmin+Tmax)/2 # Mean temperature
2141 Tcx <- (Tr*sin(2*pi/24*(Hmax-c)))+Tm # Hmax temperature
2142 Tcn <- Tmin # Hmin temperature
2143 Hourx <- c+12-6 # Warmest hour of the day
2144 Hm <- (Hourx+Hmin)/2 # Hour for mean temperature
2145 coefn <- (Tcn-Tcx)/((24+Hmin)-Hmax) # Slope coef. for the
2146 # nocturnal linear function
2147 coefd <- ((Tr*sin(2*pi/24*(Hm-c))+Tm)-Tcn)/(Hm-Hmin) # Slope coef. for the
2148 # diurnal linear function
2149 ifelse(hour<=Hmin, (Tcx + coefn*((24-Hmax)+hour)),
2150
2151 ifelse (hour <= Hm, (Tcn+coefd*(hour-Hmin)),
2152 ifelse (hour >= Hmax, (Tcx+ coefn*(hour-Hmax)),
2153 (Tr*sin(2*pi/24*(hour-c))+Tm))))}

2154 Example plot

2155 Example of daily temperature cycle with a $T_{N,min}$ of 0, 15 and 30 °C at 07:00 and a $T_{max}$ of
2156 40 °C at 14:00. Days start at 07:00 and end at 20:00. R code is provided for $T_{N,min} = 0$ °C.

2157 x_range=c(0,24)
2158 y_range=c(0,40)
2159 x_lab=c("Time of day (hours from midnight)")
2160 y_lab=c("Temperature (°C)")
2161 curve(Temperature_cycle(x,0,40,8,7,20),
2162 xlim=x_range,
2163 ylim=y_range,
2164 xlab=x_lab,
2165 ylab=y_lab,
2166 col="blue",
2167 axes=FALSE)
2168 axis(side=1, at = seq(0,24,2))
2169 axis(side=2, at = seq(0,40,10))

2170 (v) Testing the influence of nocturnal temperature and DMR<sub>20</sub>

2171 In all scenarios, we evaluated the response of the NEG<sub>d</sub> to varying minimum T<sub>N</sub> ranging
2172 from 0 °C to 30 °C. We also modified the value of DMR<sub>20</sub> = 0.01, 0.05, 0.1, and 0.15
2173 (Andrews & Pough, 1985) to explore the effects of nocturnal thermal conditions on species
2174 with low, moderate or high resting metabolic rates. For the sake of simplicity, we provide
2175 below the code for one level of DMR<sub>20</sub> (= 0.1). To explore other parameter combinations,
2176 users can modify values for <i>M met</i>. Results for the different DMR<sub>20</sub> values are provided in Fig.
2177 7 of the main article.

2178 (4) Scenarios

2179 (a) Scenario 0. Model validation

2180 Scenario 0 was designed to validate our model by confirming results from Huey & Kingsolver (2019).
2181 We modelled a thermoconforming ectotherm (i.e. an animal that spends no time or metabolic
2182 energy on the regulation of body temperature) in an environment with variation in resource density
2183 (varying from 1 to 10) and maximum TD (10–50 °C). Minimum T<sub>N</sub> was fixed to 5 °C and DMR<sub>20</sub> to 0.1.
2184 As in Huey & Kingsolver (2019), the model highlights that reduced resource levels in warmer
2185 environments trigger a ‘metabolic meltdown’ (i.e. declining energy intake paired with increased
2186 energetic expenditure and a reduced activity opportunity due to warmer diurnal maximum
2187 temperatures in the middle of the day) (Fig. S4). Details of the energy balance function are provided
2188 in Scenario 1. Only parameterisation for T<sub>N,min</sub>, T<sub>D,max</sub>, DMR<sub>20</sub> and R changed.

2189
<figure><img src="image_14.png" /></figure>

2190

2191 **Fig. S4.** Daily net energy gain rate (NEG<sub>d</sub>) at different maximum diurnal temperatures (T<sub>D,max</sub>) and resource density (R). Minimum T<sub>N</sub> (T<sub>N,min</sub>) is fixed to 5°C. DMR<sub>20</sub> is fixed to 0.1. Yellow colours represent high values of NEG<sub>d</sub>. Red colours represent low values of NEG<sub>d</sub>.

2194 (b) Scenario 1. *Thermoconformer* with 24-h foraging activity

2195 In Scenario 1, we modelled a thermoconforming ectotherm with an activity window of 24 h.
2196 This allowed us to investigate effects of minimum T<sub>N</sub>, in the absence of time partitioning of
2197 activity and behavioural control of body temperature.

2198 Attack rate

2199 AR is positive over the entire 24-h cycle and depends only on environmental temperature.

2200 AR is calculated hourly with the *Attack_function_TC1_H* function, and is then integrated
2201 over the entire day using the *Attack_function_TC1_24* function.

2202 Parameters

2203 x # Hour of the day
2204 Tmin # Minimum temperature of the day (e.g., Varying from 0 to 30°C)
2205 Tmax # Maximum temperature of the day (e.g., 40°C)
2206 Hmin # Time of sunrise (e.g., 07:00)
2207 Hmax # Time of sunset (e.g., 20:00)
2208 c # Sinusoidal parameter (e.g., 8)
2209 k_a # Normalizing parameter for AR
2210 b_a # Linear slope for AR: -26.37628
2211 q_a # Quadratic slope for AR: -0.3436951
2212 Hourly attack rate:
2213 Attack_function_TC1_H=function(x,Tmin,Tmax,c,Hmin,Hmax){
2214 Temperature_function(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax),k_a,b_a,q_a)}

2215 Daily attack rate:
2216 Attack_function_TC1_24= Vectorize(function(Tmin,Tmax,c,Hmin,Hmax){
2217 integrate(function(x)
2218 Attack_function_TC1_H(x,Tmin,Tmax,c,Hmin,Hmax), 0, 24)$value/24})

2219 Ingestion rate

2220 IR is positive over the entire 24-h cycle and depends only on environmental temperature. IR
2221 is calculated hourly with the *Ingestion_function_TC1_H* function, and is then integrated
2222 over the entire day using the *Ingestion_function_TC1_24* function.

2223 Parameters
2224 k_i # Normalizing parameter for IR
2225 b_i # Linear slope for IR
2226 q_i # Quadratic slope for IR

2227 Hourly intake rate:
2228 Ingestion_function_TC1_H=function(x,Tmin,Tmax,c,Hmin,Hmax){
2229 Temperature_function(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax),k_i,b_i,q_i)}

2230 Daily mean intake rate:
2231 Ingestion_function_TC1_24= Vectorize(function(Tmin,Tmax,c,Hmin,Hmax){
2232 integrate(function(x)
2233 Ingestion_function_TC1_H(x,Tmin,Tmax,c,Hmin,Hmax), 0, 24)$value/24})

2234 Metabolic expenditure

2235 MR is positive over the entire 24-h cycle and depends only on environmental temperature.
2236 MR is calculated hourly with the *Metabolism_function_TC1_H* function, and is then
2237 integrated over the entire day using the *Metabolism_function_TC1_24* function.

2238 M_met # Default metabolic expenditure at 20°C
2239 Tref # Standard temperature for metabolic expenditure
2240 Ea # Energy activation rate for metabolic expenditure

2241 Hourly MR
2242 Metabolism_function_TC1_H=function(x,Tmin,Tmax,c,Hmin,Hmax,M_met,Tref){
2243 Arrhenius_function(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax),M_met,Ea,Tref)}

2244 Daily MR
2245 Metabolism_function_TC1_24= Vectorize(function(Tmin,Tmax,c,Hmin,Hmax,M_met,Tref){
2246 integrate(function(x)
2247 Metabolism_function_TC1_H(x,Tmin,Tmax,c,Hmin,Hmax,M_met,Tref),0, 24)$value})
2248 Energy balance

2249 NEG<sub>d</sub> is calculated using the difference between daily energy acquisition and expenditure. It
2250 therefore includes the calculation of daily mean FR, which uses daily mean AR and daily
2251 mean IR.

2252 Parameters

2253 alpha # Resource conversion efficiency
2254 ar_max # Maximum attack rate
2255 hr_max # Maximum handling time rate

2256 Daily MR

2257 Energy_balance_TC1_24=
2258 function(r,Tmin,Tmax,c,Hmin,Hmax,alpha,ar_max,hr_max,M_met,Tref){
2259 24*FR_function(R,
2260 ar_max*Attack_function_TC1_24(Tmin,Tmax,c,Hmin,Hmax),
2261 hr_max/Ingestion_function_TC1_24(Tmin,Tmax,c,Hmin,Hmax))*alpha -
2262 Metabolism_function_TC1_24(Tmin,Tmax,c,Hmin,Hmax,M_met,Tref)}

2263 Plot: energetic inputs (FR) and outputs (MR) over a 24-hour cycle

2264 x_range <- c(0,24)
2265 y_range <- c(0,0.5)
2266 curve(Metabolism_function_TC1_H(x,10,35,8,7,20,0.1,20), col="red",
2267 xlab="Time of day (hours from midnight)",
2268 ylab="Mean FR or MR",
2269 xlim=x_range, ylim=y_range)
2270 curve(FR_function(2,1*Attack_function_TC1_H(x,10,35,8,7,20),
2271 1/Ingestion_function_TC1_H(x,10,35,8,7,20))*0.69, add=TRUE, col="blue")
2272 curve(Metabolism_function_TC1_H(x,20,35,8,7,20,0.1,20), col="red", add=TRUE, lty=2)
2273 curve(FR_function(2,1*Attack_function_TC1_H(x,20,35,8,7,20),
2274 1/Ingestion_function_TC1_H(x,20,35,8,7,20))*0.69, add=TRUE, col="blue", lty=2)
2275 text(2,0.5, label="Scenario 1", cex=0.9)

2276
<figure><img src="image_15.png" /><figcaption>Fig. S5. Metabolic rate (MR) (in red) and function rate (FR) (in blue) are represented for Scenario 1 for a minimum $T_N$ of 10 °C (solid lines) or 20 °C (broken lines) for each hour.</figcaption></figure>

2280 Plot: Energy balance vs $T_N$

2281 # Plot NEG<sub>d</sub> over a range of nocturnal temperature (i.e., 0 to 30°C)

2282 x_range=c(0,30)

2283 y_range=c(-5,12)

2284 x_lab=c("Minimum nocturnal temperature (°C)")

2285 y_lab=c("Daily net energy gain")

2286 curve(Energy_balance_TC1_24(r=2,

Tmin=x,Tmax=35,c=8,Hmin=7,Hmax=20,

alpha=0.69,ar_max=1,hr_max=1,

M_met=0.1,Tref=20)),

2291 xlim=x_range,ylim=y_range,xlab=x_lab,ylab=y_lab,col='blue')

2292 abline(0,0,lty=3)

2293 legend(-1,12.5,legend="Scenario 1",bty="n")

2295 # Add optimal nocturnal temperature for NEG

2296 Sc1_0.1

<- (Energy_balance_TC1_24(r=2,

Tmin=seq(0,30),Tmax=35,c=8,Hmin=7,Hmax=20,

alpha=0.69,ar_max=1,hr_max=1,

M_met=0.1,Tref=20))

2300 Sc1_0.1 <- cbind(seq(0,30,1),Sc1_0.1)

2301 colnames(Sc1_0.1) <- c("Tmin","NEG")

2302 Sc1_0.1.x <- Sc1_0.1[which(Sc1_0.1[, 'NEG'] == max(Sc1_0.1[, 'NEG'])),1]

2303 Sc1_0.1.y <- Sc1_0.1[which(Sc1_0.1[, 'NEG'] == max(Sc1_0.1[, 'NEG'])),2]

2304 points(Sc1_0.1.x,Sc1_0.1.y,col='blue',pch=16,cex=1.2)
<figure><img src="image_16.png" /><figcaption>**Fig. S6.** Daily net energy gain ($NEG_d$) for Scenario 1 at different minimum nocturnal temperatures ($T_{N,min}$) and with a default metabolic rate ($DMR_{20}$) of 0.1. The circle represents the tipping point between positive and negative effects of nocturnal temperature increase on $NEG_d$.</figcaption></figure>

### (c) Scenario 2. Thermoconformer with diurnal foraging activity

In Scenario 2, we extended the model to represent a thermoconforming ectotherm, with an activity cycle based on photoperiod: the organism was active during the day and inactive at night. To make this tractable without explicitly modelling the kinematics of gut passage time and food assimilation (Levy et al., 2017), we assumed that foraging behaviour (i.e. AR) was only possible between 07:00 and 20:00 (AR, IR & MR all >0), while IR and MR were calculated for the entire 24-h cycle (AR = 0 while IR & MR >0).

#### Attack rate

HA_min # Minimum hour for activity (AR>0)

HA_max # Maximum hour for activity (AR<0)

Attack_function_TC2_H=function(x,Tmin,Tmax,c,Hmin,Hmax,HA_min,HA_max){

ifelse(x<HA_min,0,

ifelse(x>HA_max,0,

Temperature_function(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax),k_a,b_a,q_a)))}

Attack_function_TC2_24= Vectorize(function(Tmin,Tmax,c,Hmin,Hmax,HA_min,HA_max){

integrate(function(x)
2327 Attack_function_TC2_H(x, Tmin, Tmax, c, Hmin, Hmax, HA_min, HA_max), 0,
2328 24)$value/24})

2329 Intake rate

2330 Ingestion_function_TC2_H = function(x, Tmin, Tmax, c, Hmin, Hmax) {
2331 Temperature_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), k_i, b_i, q_i))

2332

2333 Ingestion_function_TC2_24 = Vectorize(function(Tmin, Tmax, c, Hmin, Hmax) {

2334 integrate(function(x)

2335 Ingestion_function_TC2_H(x, Tmin, Tmax, c, Hmin, Hmax), 0, 24)$value/24})

2336 Metabolic expenditure

2337 Metabolism_function_TC2_H = function(x, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {
2338 Arrhenius_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), M_met, Ea, Tref))

2339

2340 Metabolism_function_TC2_24 = Vectorize(function(Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {

2341 integrate(function(x)

2342 Metabolism_function_TC2_H(x, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref), 0, 24)$value}

2343 Energy balance

2344 Energy_balance_TC2_24 =
2345 function(r, Tmin, Tmax, c, Hmin, Hmax, HA_min, HA_max, alpha, ar_max, hr_max, M_met, Tref) {
2346 24*FR_function(r,

2347

2348 a = ar_max * (Attack_function_TC2_24(Tmin, Tmax, c, Hmin, Hmax, HA_min, HA_max)),
2349 h = hr_max / Ingestion_function_TC2_24(Tmin, Tmax, c, Hmin, Hmax)) * alpha -
2350 Metabolism_function_TC2_24(Tmin, Tmax, c, Hmin, Hmax, M_met, Tref))

2351

<figure><img src="image_17.png" /><figcaption>Plot: energetic inputs (FR) and outputs (MR) over the day</figcaption></figure>

2352 Fig. S7. Metabolic rate (MR) (in red) and function rate (FR) (in blue) are represented for Scenario 2
2353 for a minimum T_N of 10 °C (solid lines) or 20 °C (broken lines) for each hour.
2354

<figure><img src="image_18.png" /><figcaption>Plot: Energy balance vs $T_{N,min}$</figcaption></figure>

2355

2356

2357

2358

2359

<caption>**Fig. S8.** Daily net energy gain ($NEG_d$) for Scenario 2 at different minimum nocturnal temperatures ($T_{N,min}$) and with a default metabolic rate ($DMR_{20}$) of 0.1. The circle represents the tipping point between positive and negative effects of nocturnal temperature increase on $NEG_d$.</caption>

### (d) Scenario 3. Thermoregulator with 24-h foraging activity

2360

2361

2362

2363

2364

2365

2366

2367

2368

2369

In Scenario 3, we modelled a perfectly thermoregulating ectotherm (i.e. an animal that maintains body temperature within a range of optimal temperatures for performance) for which the activity window was limited only by environmental temperature. This scenario represents the case of an ectothermic predator able to extend its foraging activity over part of the night when $T_{Ns}$ are suitable. Here, we assumed that AR is limited by a lower (18 °C) and upper (40 °C) threshold corresponding to typical minimum ($VT_{min}$) and maximum ($VT_{max}$) voluntary temperatures for foraging in terrestrial lizards (Rozen-Rechels et al., 2020). Moreover, because the organism is able to thermoregulate, we assumed that individuals could maintain a body temperature of 30 °C matching $T_{opt}$ for foraging whenever environmental temperatures were within the thermal range 18–40 °C.

2370

### Attack rate

2371

Tpref # Preferred temperature for activity

2372

VTmin_D # Minimum temperature for activity

2373

VTmax_D # Maximum temperature for activity

2374

2375

2376

2377

2378

Attack_function_TR1_H =function(x,Tpref,Tmin,Tmax,c,Hmin,Hmax,VTmin_D,VTmax_D){
ifelse(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax)<VTmin_D,0,
ifelse(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax)>VTmax_D,0,
ifelse(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax)<Tpref,
2379
2379 Temperature_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), k_a, b_a, q_a),
2380 Temperature_function(Tpref, k_a, b_a, q_a)))}
2381
2382 Attack_function_TR1_24= Vectorize(function(Tpref, Tmin, Tmax, c, Hmin,
2383 Hmax, VTmin_D, VTmax_D){
2384 integrate(function(x)
2385 Attack_function_TR1_H(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, VTmin_D, VTmax_D),
2386 0, 24)$value/24})
2387
2388 Intake rate
2389 Ingestion_function_TR1_H= function(x, Tpref, Tmin, Tmax, c, Hmin, Hmax) {
2390 ifelse(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax) < Tpref,
2391 Temperature_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), k_i, b_i, q_i),
2392 Temperature_function(Tpref, k_i, b_i, q_i)))
2393
2394 Ingestion_function_TR1_24= Vectorize(function(Tpref, Tmin, Tmax, c, Hmin, Hmax) {
2395 integrate(function(x)
2396 Ingestion_function_TR1_H(x, Tpref, Tmin, Tmax, c, Hmin, Hmax), 0, 24)$value/24})
2397
2398 Metabolic expenditure
2399 Metabolism_function_TR1_H= function(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {
2400 ifelse(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax) < Tpref,
2401 Arrhenius_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), M_met, Ea, Tref),
2402 Arrhenius_function(Tpref, M_met, Ea, Tref)))
2403
2404 Metabolism_function_TR1_24=
2405 Vectorize(function(Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {
2406 integrate(function(x)
2407 Metabolism_function_TR1_H(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref),
2408 0, 24)$value})
2409
2410 Energy balance
2411 Energy_balance_TR1_24=
2412 function(r, Tpref, Tmin, Tmax, c, alpha, ar_max, hr_max, Hmin, Hmax, VTmin_D, VTmax_D, HA_min, H
2413 A_max, M_met, Tref) {
2414 24*FR_function(r,
2415
2416 a=ar_max*(Attack_function_TR1_24(Tpref, Tmin, Tmax, c, Hmin, Hmax, VTmin_D, VTmax_D)),
2417 h=(hr_max/Ingestion_function_TR1_24(Tpref, Tmin, Tmax, c, Hmin, Hmax)))*
2418 alpha - Metabolism_function_TR1_24(Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref)})
2419

<figure><img src="image_19.png" /><figcaption>Plot: energetic inputs (FR) and outputs (MR) over the day</figcaption></figure>

2420

2421

2422

<caption>Fig. S9. Metabolic rate (MR) (in red) and function rate (FR) (in blue) are represented for Scenario 3 for a minimum $T_N$ of 10 °C (solid lines) or 20 °C (broken lines) for each hour.</caption>

2423

<figure><img src="image_20.png" /><figcaption>Plot: Energy balance vs $T_{min}$</figcaption></figure>

2424
2425 **Fig. S10.** Daily net energy gain ($NEG_d$) for Scenario 3 at different minimum nocturnal temperatures ($T_{N,min}$) and with a default metabolic rate ($DMR_{20}$) of 0.1. The circle represents the tipping point between positive and negative effects of nocturnal temperature increase on $NEG_d$.

2428 (e) **Scenario 4. Thermoregulator with diurnal foraging activity**

2429 Scenario 4 modelled a perfect thermoregulator with an activity window strictly delimited by photoperiod. As in Scenario 2, AR is limited by daylight, while IR and MR were dependent only on body temperature. In this scenario, body temperature during daytime was set to 30 °C whenever environmental temperatures exceeded the 30 °C threshold (i.e. efficient behavioural thermoregulation).

2434 **Attack rate**

2435 Attack_function_TR2_H = function(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, HA_min, HA_max) {
2436     ifelse(x < HA_min, 0,
2437     ifelse(x > HA_max, 0,
2438     ifelse(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax) < Tpref,
2439         Temperature_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), k_a, b_a, q_a),
2440         Temperature_function(Tpref, k_a, b_a, q_a)))))
2442
2443 Attack_function_TR2_24 =
2444     Vectorize(function(Tpref, Tmin, Tmax, c, Hmin, Hmax, HA_min, HA_max){integrate(function(x
2445         Attack_function_TR2_H(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, HA_min, HA_max), 0,
2446     24)$value/24
2448     })
2449
**Intake Rate**

2450 Ingestion_function_TR2_H = function(x, Tpref, Tmin, Tmax, c, Hmin, Hmax) {
2451     ifelse(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax) < Tpref,
2452         Temperature_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), k_i, b_i, q_i),
2453         Temperature_function(Tpref, k_i, b_i, q_i))}
2455
2456 Ingestion_function_TR2_24 = Vectorize(function(Tpref, Tmin, Tmax, c, Hmin, Hmax) {
2457     integrate(function(x) Ingestion_function_TR2_H(x, Tpref, Tmin, Tmax, c, Hmin, Hmax),
2458         0, 24)$value/24})
2459
**Metabolic rate**

2460 Metabolism_function_TR2_H = function(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {
2461     ifelse(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax) < Tpref,
2462         Arrhenius_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), M_met, Ea, Tref),
2463         Arrhenius_function(Tpref, M_met, Ea, Tref))}
2465
2466 Metabolism_function_TR2_24 =
2467     Vectorize(function(Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {
2468     integrate(function(x)
2469         Metabolism_function_TR2_H(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref),
2470         0, 24)$value})
2471 Energy balance
2472 Energy_balance_TR2_24=
2473
2474 function(r,Tpref,Tmin,Tmax,c,alpha,ar_max,hr_max,Hmin,Hmax,HA_min,HA_max,M_met,Tref)
2475 f){
2476 24*FR_function(r,
2477
2478 a=ar_max*(Attack_function_TR2_24(Tpref,Tmin,Tmax,c,Hmin,Hmax,HA_min,HA_max)),
2479 h=hr_max/Ingestion_function_TR2_24(Tpref,Tmin,Tmax,c,Hmin,Hmax))*
2480 alpha -
2481 Metabolism_function_TR2_24(Tpref,Tmin,Tmax,c,Hmin,Hmax,M_met,Tref)}

2482 Plot: energetic inputs (FR) and outputs (MR) over the day

<figure><img src="image_21.png" /></figure>

2483

2484 Fig. S11. Metabolic rate (MR) (in red) and function rate (FR) (in blue) are represented for Scenario 4 for a minimum T<sub>N</sub> of 10 °C (solid lines) or 20 °C (broken lines) for each hour.
2485
2486

<figure><img src="image_22.png" /><figcaption>Plot: Energy balance vs Tmin</figcaption></figure>

2487

2488

<caption>**Fig. S12.** Daily net energy gain ($NEG_d$) for Scenario 4 at different minimum nocturnal temperatures ($T_{N,min}$) and with a default metabolic rate ($DMR_{20}$) of 0.1. The circle represents the tipping point between positive and negative effects of nocturnal temperature increase on $NEG_d$.</caption>

2489

2490

2491

(f) Scenario 5. Thermoregulator with nocturnal foraging activity

2492

2493

2494

2495

2496

2497

2498

2499

2500

Scenario 5 illustrates the case of a nocturnal thermoregulator with a foraging activity window delimited by photoperiod. Here, *AR* is positive only at night (20:00 to 07:00) and depends on body temperature. *IR* and *MR* depend only on body temperature. We assume that the nocturnal thermoregulator selects refugia to maintain a diurnal body temperature close to 30 °C ($T_{pref}$), whenever diurnal environmental temperatures exceeded 30 °C [i.e. efficient behavioural thermoregulation; see Chukwuka *et al.* (2021) for an example], i.e. is a perfect thermoregulator. At night, foraging activity is delimited by the voluntary thermal limits for activity ($VT_{min}$ and $VT_{max}$) arbitrarily fixed at 15 °C and 35 °C. Outside this range, individuals do not forage.

2501

Attack rate

2502

2503

2504

2505

2506

2507

2508

2509

2510

Attack_function_N=function(x,VTmin,VTmax,Tmin,Tmax,c,Hmin,Hmax){
ifelse(x<Hmin | x>Hmax,
       ifelse(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax) >= VTmin &
                Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax) <= VTmax,
                Temperature_function(Temperature_cycle(x,Tmin,Tmax,c,Hmin,Hmax),
                                     k_a, b_a, q_a),
                0),
       0)}
2511 Attack_function_N_24= Vectorize(function(VTmin,VTmax,Tmin,Tmax,c,Hmin,Hmax) {
2512 integrate(function(x) Attack_function_N(x,VTmin,VTmax,Tmin,Tmax,c,Hmin,Hmax),
2513 0,24)$value/24})

2514 Intake Rate

2515 Ingestion_function_N= function(x, Tpref, Tmin, Tmax, c, Hmin, Hmax) {
2516 ifelse(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax) <= Tpref,
2517
2518 Temperature_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), k_i, b_i, q_i),
2519 Temperature_function(Tpref, k_i, b_i, q_i)))
2520
2521 Ingestion_function_N_24= Vectorize(function(Tpref, Tmin, Tmax, c, Hmin, Hmax) {
2522 integrate(function(x) Ingestion_function_N(x, Tpref, Tmin, Tmax, c, Hmin, Hmax),
2523 0, 24)$value/24})

2524 Metabolic rate

2525 Metabolism_function_N= function(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {
2526 ifelse(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax) < Tpref,
2527
2528 Arrhenius_function(Temperature_cycle(x, Tmin, Tmax, c, Hmin, Hmax), M_met, Ea, Tref),
2529 Arrhenius_function(Tpref, M_met, Ea, Tref)))
2530
2531 Metabolism_function_N_24=
2532 Vectorize(function(Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref) {
2533 integrate(function(x)
2534 Metabolism_function_N(x, Tpref, Tmin, Tmax, c, Hmin, Hmax, M_met, Tref),
2535 0, 24)$value})

2536 Energy balance

2537 Energy_balance_N_24=
2538
2539 function(r,VTmin,VTmax,Tpref,Tmin,Tmax,c, alpha,ar_max,hr_max,Hmin,Hmax,M_met,Tref)
2540 {
2541 24*FR_function(r,
2542 a=ar_max*(Attack_function_N_24(VTmin,VTmax,Tmin,Tmax,c,Hmin,Hmax)),
2543 h=hr_max/Ingestion_function_N_24(Tpref,Tmin,Tmax,c,Hmin,Hmax))*
2544 alpha - Metabolism_function_N_24(Tpref,Tmin,Tmax,c,Hmin,Hmax,M_met,Tref)}
2545

<figure><img src="image_23.png" /><figcaption>Plot: energetic inputs (FR) and outputs (MR) over the day</figcaption></figure>

2546

2547

2548

<caption>**Fig. S13.** Metabolic rate (MR) (in red) and function rate (FR) (in blue) are represented for Scenario 5 for a minimum $T_N$ of 10 °C (solid lines) or 20 °C (broken lines) for each hour.</caption>