Solar radiation alters heat balance and thermoregulation in a flying desert bee

Anthropogenic climate change is predicted to result in increases in average air temperatures of at least 1.5°C in the next 10 to 20 years (Diffenbaugh and Barnes, 2023; Kikstra et al., 2022). However, certain areas, such as the Sonoran Desert, are projected to also become drier (Weiss and Overpeck, 2005) and to experience increases in extreme heat events (Perkins and Alexander, 2013). As a result, desert vegetative landcover may shift in range, change phenology and/or decline in abundance (Bowers, 2007; Herrmann et al., 2016), altering the microclimatic landscape for animals. These climatic trends make it important to understand the thermal biology of insects such as pollinating desert bees, which are critical for the successful reproduction of many desert plants (Janeba, 2009; Simpson and Neff, 1987). Here, we assessed the impact of solar radiation on the thermal balance of Centris pallida, a solitary bee native to the Sonoran Desert. Centris pallida is a major pollinator of important Sonoran Desert plants including Parkinsonia microphylla, Olneya tesota, Prosopis velutina, Psorothamnus spinosus, Krameria bicolor and Larrea tridentata (Alcock et al., 1977; Rozen and Buchmann, 1990).

Solar radiation is a critical determinant of body temperature for terrestrial ectotherms, both vertebrate and invertebrate, many of whom shuttle between sun and shade to thermoregulate (Kearney et al., 2009; Ma et al., 2018; Seebacher and Franklin, 2005). Studies of solar radiation effects on flying insects have focused on the energy-saving benefits of solar radiation to heat balance, as it facilitates the warming of flight muscles in order to fly (Heinrich, 1986; Kovac et al., 2009, 2010; Stabentheiner and Kovac, 2023). But, solar radiation can be harmful instead of helpful in certain contexts. For example, direct solar radiation can impose a heat load 20 times the surface area-specific metabolic rate of mammals; however, the pelage of many mammals and birds acts as a heat shield, preventing much of this theoretical heat-loading (Maloney and Dawson, 1995; Tattersall et al., 2012; Walsberg and Wolf, 1995; Wolf and Walsberg, 1996). Physiological responses to solar radiation in nonflying mammals and birds include depressed metabolic rate, increased evaporative water loss rate (Cain et al., 2006; Wolf and Walsberg, 1996) and movement to cooler microclimates (Fuller et al., 2016). Given the well-known tendency of heat-stressed mammals and birds to shunt heat by increasing thermal conductance through mechanisms such as shunting blood flow to poorly insulated surfaces (Tattersall et al., 2012), it seems likely that this may occur in response to solar radiation in insects. We are unaware of studies that document such an effect, though there is evidence that butterflies modulate conductance between wings and body to vary heat transfer during solar basking (Kingsolver and Moffat, 1982). Hyperthermia is also a well-known response of freely moving vertebrate endotherms to high temperatures (Corbet and Huang, 2016; Sjöberg et al., 2023; Tattersall et al., 2012), and could also be a plausible consequence of solar radiation for flying insects. However, most large-bodied flying insects imperfectly regulate their thorax and, to a lesser extent, head temperatures as air temperature rises (Heinrich, 2013; Johnson et al., 2022, 2023).

In the context of climatic warming, it is important to examine the potential role of solar radiation in influencing the thermal balance of flying insects. For large-bodied insects flying at high temperatures, the additional heat gain due to solar radiation could be deadly, as has been shown for other freely moving animals (Athaíde et al., 2020; Corbet and Huang, 2016; Shi et al., 2015; Sjöberg et al., 2023). Flight metabolic rates decrease with air temperature in some flying insects that regulate thorax temperatures during flight, including honey bees (Borrell and Medeiros, 2004; Glass and Harrison, 2022; Roberts and Harrison, 1998, 1999) and C. pallida small morph males (Roberts et al., 1998), though C. caesalpiniae maintained constant flight metabolic rates (ml CO₂ h⁻¹) across air temperatures of 19 to 38°C (Johnson et al., 2022). Centris caesalpiniae large morph males strongly increased convective conductance (κ) at higher air temperatures, likely by shifting hemolymph from the well-insulated thorax to the relatively bare abdomen (Johnson et al., 2022). Similar responses have been documented in Bombus vosnesenskii queens, Hyles lineata, Manduca sexta, Sarcophoga subvicina, Sarcophoga carnaria and Melipona subnitida, but not Apis mellifera, B. vagans, Vespula spp. or Anax junius (Johnson et al., 2022). Increasing evaporative water loss is a major mechanism of thermoregulation in honey bees, but plays a minor role in thermoregulation at higher air temperatures for C. pallida small morph males and C. caesalpiniae large morph males (Johnson et al., 2022; Roberts et al., 1998). We hypothesize that solar radiation plays an important role in heating, and will increase the body temperatures of flying bees as it does for foraging bees (Stabentheiner and Kovac, 2023).

The objective of this study was to identify how male morphs and females of the same species respond to heat gain via solar radiation. Centris pallida males are dimorphic and have large variation in body sizes within each morph (Alcock et al., 1977). The C. pallida male morphs differ in coloration, with dorsal hair-like structures (setae) conferring possible thermal benefits (Barrett and O'Donnell, 2023). Large morph males are highly reflective in the near-infrared on the dorsal surface compared with small morph males, which reduces absorbed solar energy (Barrett and O'Donnell, 2023). Large morph males are mostly found on the hotter bare ground, engaged in competition with other large males or making patrol flights. Small morph males hover near palo verde well above ground or within shaded vegetation. Females are most often caught while foraging. Given the range of body sizes, we hypothesized that surface area to volume ratios would be a significant predictor of body temperature, thermoregulatory response and magnitude of thermoregulation. We predicted that surface area to volume ratios would be greatest in small morph males, intermediate in females and smallest in large morph males. We also predicted that all responses (body warming, as well as any thermoregulatory responses such as changes in metabolic heat production, thermal conductance and evaporative heat loss) would be greatest in small morph males, intermediate in females and smallest in large morph males. An alternative, or possible additional hypothesis, is that thermoregulatory responses are affected by differences in mating tactics between the male morphs and sex-specific differences between males and females. Because large male morphs are mostly found on the hotter bare ground, whereas smaller morphs are usually in cooler air well above ground or within shaded vegetation, and females are found in forward flight or foraging, it seems possible that large morph males have been selected to have more capacity (i.e. thermoregulatory mechanisms) to cope with radiant heating. Using flow-through respirometry in field conditions, we measured the routes of heat loss and gain of C. pallida bees exposed or not exposed to solar radiation. These field measures allowed us to calculate heat budgets, which quantify the relative importance of each avenue of heat exchange: i.e. do C. pallida primarily thermoregulate in response to solar radiation by reducing flight metabolic rate, increasing evaporative cooling, storing incident heat, increasing convective or radiative heat loss, or some combination of these? Heat budgets additionally provide the opportunity to accurately predict the body temperature of an animal in differing abiotic environments. To this end, we discuss how the effects of solar radiation will influence predictions of effects of climatic warming on the activity and survival of desert bees.

In April 2022, we studied an active mating and nesting aggregation of Centris pallida Fox 1899 males and females in the flood plains near the Salt River (GPS coordinates: 33.55, −111.56). Males are dimorphic and exhibit size-based mating strategies (Alcock et al., 1977; Barrett et al., 2021). We divided males into large and small categories based on mass and morphological features, following the same methods as Barrett et al. (2022). We selected fresh-looking bees with very little to no wing wear or ‘balding’ on the thorax for all measures conducted.

We used flow-through respirometry to measure the CO₂ and H₂O emissions of C. pallida bees during flight in the shade versus in full sun at ambient temperatures through the morning. Each individual was measured once, in either shade or sun. We set up the respirometry station on a table in the shade beneath a grove of palo verde trees (Parkinsonia microphylla) in the middle of the aggregation site to achieve shaded conditions. For measurements in the sun, we held a 500 ml cylindrical borosilicate chamber in which the bee flew in full sun, while keeping equipment in the shade. We set up the respirometry equipment in the same configuration as Johnson et al. (2022). Briefly, we used a SS-4 Sub-Sampler Pump (Sable Systems, Las Vegas, NV, USA) to pump air through a 1000 ml column of Drierite and a 1000 ml column of Drierite and Ascarite II at a rate of 1000 ml min⁻¹. The output of the columns flushed the 500 ml chamber, with the chamber output connected to the LI-7000 CO₂/H₂O Gas Analyzer (LI-COR, Lincoln, NE, USA). The reference cell was kept at zero via a scrubbing column. We recorded baseline measurements in an empty chamber for 1 min, introduced the animal to the chamber, and, after covering the chamber with a dark cotton cloth to block incoming light, allowed the chamber to flush for 3 min with the animal inside. We removed the cloth and encouraged flight by tilting the chamber to discourage landing. Centris pallida bees flew exceptionally well in the chamber with little need for stimulation such as shaking or tapping the chamber.

Following flight in the chamber, we recorded head, thorax and abdomen temperatures in addition to air temperature using a BAT-12 thermometer and hypodermic thermocouple (Physitemp, MT-29/5HT Needle Microprobe, time constant=0.025 s). Immediately after flight in the respirometry chamber, we opened the plug of the chamber, dumped the bee into a net over a Styrofoam board, and pierced the head, thorax and abdomen with a hypodermic thermocouple in a random order. Only measurements made within 5 s of cessation of flight were used, as longer time periods result in significant cooling (Stone and Willmer, 1989). We later calculated the tagma temperature elevation (the elevation of segment temperature over air temperature) by subtracting the tagma temperature from air temperature. We stored the bees in individual vials, placed on ice in an insulated cooler. We measured wet masses within 3 h of bee capture.

Heat budgets (which include metabolic heat production, evaporative heat loss, net longwave radiative flux and convective heat loss) were calculated as in Johnson et al. (2022) with the addition of heat gain from solar radiation for bees flying in the sun (Eqn 2). Briefly, we calculated metabolic heat production assuming carbohydrate as fuel, and evaporative heat loss using the rates of CO₂ and H₂O production measured in the field (Johnson et al., 2022). We calculated longwave radiative flux based on ambient temperature in the metabolic chamber, and the tagma body temperatures measured immediately following flight. We calculated convective heat loss by summing metabolic heat production, evaporative heat loss, longwave radiative flux, and heat gain from solar radiation. We calculated convective conductance (κ), a measure of the capacity to transfer heat via convection, by dividing convective heat loss by the bee surface area multiplied by the tagma-surface-area-weighted average temperature difference between the bee and the ambient air temperature.

We assigned a score from zero to five during respirometry measures to indicate the quality of hovering flight in the metabolic chamber. 0=no flight, 1=buzzing and crashing with little flight control, 2=unstable flight (<25% of the time) with frequent crashing (>10), 3=some hovering flight (∼50% of the time) with 3-6 crashes, 4=good hovering flight (∼75% of the time) with 1–3 crashes, 5=great hovering flight with one or fewer crashes.

Following wet mass measurements in the laboratory, we killed bees in a −20°C freezer and subsequently measured the surface area. We used a digital caliper (Vizbrite; accurate to 0.01 mm) to measure tagma surface areas assuming that the head is a cylinder, the thorax is a sphere, and the first to third terga are a cylinder, and the fourth to fifth terga are a cone (Johnson et al., 2022; Roberts and Harrison, 1999). We did not include antennae, wing or leg surface areas in the total body surface area calculation.

R_tagma will be constant and independent of air temperature (T_air) if heat moves from the thorax to the head or abdomen by mainly passive conduction. If heat is actively transferred from the thorax to the head or abdomen at high T_air, then R_tagma will increase with rising air temperature.

We tested data as to whether the assumptions of parametric statistics were met, log₁₀-transformed the data if necessary and ran statistical analyses in GraphPad Prism (version 8.0.0 for Windows; www.graphpad.com). We included and compared both male morphs and female C. pallida bees in all analyses. We used the ROUT method (with set Q equal to 1%) to identify outliers and only excluded data points if they corresponded with field notes indicating a problem with the quality of measurement (Motulsky and Brown, 2006). We included only bees that were flying in all respirometric analyses, as determined by a non-zero flight score. If means and slopes were presented, we included the 95% confidence limits. We determined two-tailed significance at α=0.05 for all analyses and chose the best general linear models (GLMs) based on Akaike's information criterion (AIC).

We tested for effects of air temperature on tagma temperatures of bees flying in the sun and shade. We used a GLM to test for two- and three-way interactions between location (sun or shade), morph (large morph male, small morph male or female) and air temperature, with tagma temperature as the dependent variable. We tested interactions via an ANOVA. We compared mean tagma temperatures in the sun and shade with an unpaired t-test.

We used a one-way ANOVA to compare R_h, R_abV_CO2, V_H2O, Q_M, Q_C, Q_R, Q_E and κ as dependent variables, with location (shade or sun) and bee type (large males, small males or females) as the independent variable. We used the Šídák multiple comparisons test, as each comparison (sun versus shade for each morph) was independent of each other (Abdi, 2007). We compared the scaling of log₁₀-transformed total body wet mass and V_CO2 using an ANCOVA. We tested for interactive effects of location, morph and air temperature for all dependent variables using a GLM.

Large morph males had the smallest surface area to volume ratios, followed by females and small morph males (ANOVA, F₂₁₂₅=4.06, P=0.020; Table S1). Bees measured in the sun versus shade did not differ in mass (ANOVA, F₁₁₃₉=3.49, P=0.64; Table S1). However, large morph males that we measured in the sun had higher surface area to volume ratios than in the shade. Small male and female surface area to volume ratio did not differ between the sun and shade (Table S1). Air temperatures were higher for bees measured in the sun (unpaired t-test: t₁₅₁=5.68, P<0.0001; Table S1). Higher air temperatures increased all tagma temperatures (Table S1).

Large males, small males and females differed in head temperature elevation across air temperatures (significant two-way morph×air temperature interaction; Table S2). The elevation of head temperature relative to air temperature (T_h−T_air) did not vary between shaded and sunny conditions (Table S2), but declined as air temperature rose, from approximately 15°C to 5°C as air temperature rose from 18°C to 37°C. Females had shallower slopes of T_h−T_air on air temperature than males (Fig. 1A, Table 1).

Thorax temperature elevation (T_th−T_air) was significantly increased by solar radiation and decreased as air temperature rose (Fig. 1B, Table 1). Thorax temperature elevation did not differ between male morphs and females, nor did it differ with varying surface area to volume ratios. Across all bee types (large males, small males and females), solar radiation increased thorax temperatures by 1.7°C at 30°C air temperature.

We found that solar radiation elevated abdominal temperatures (Table S1). Given the diverse trends, we analyzed the bee types separately. For females (Fig. 1C, Table 1), abdominal temperature elevation (T_ab−T_air) in the sun was 5°C higher than in the shade at 30°C air temperature; for large male morphs, the average abdominal temperature elevation caused by exposure to the sun was 3.4°C (Fig. 1D, Table 1); and for small morph males, average abdominal temperature elevation was 2.3°C (Fig. 1E, Table 1). On average, the abdominal temperature elevation of bees flying in the sun was 3°C greater than for bees flying in the shade.

Abdominal excess temperature ration (R_ab) varied complexly, with a significant three-way interaction between bee type, air temperature and location (Table S3). All potential two-way interactions were also significant (Table S3). Abdominal excess temperature ratio (R_ab) increased in the sun for all bee types, indicating that bees exposed to the sun likely shifted heat from the thorax to the abdomen (Table S3). Females flying in the respirometry chamber increased R_ab with air temperature in both the shade and sun (Fig. 2A,B, Table 1), and solar radiation increased the rate of R_ab increase with air temperature, suggesting that females shift more hemolymph from the thorax to the abdomen in response to solar radiation (ANOVA: F_1,35=15.05, P=0.0004). In contrast, in the sun, small morph males did not change R_ab with air temperature (Fig. 2B, Table 1). However, large males increased R_ab with air temperature in the sun, but not the shade (Fig. 2A,B, Table 1).

Both location (sun versus shade) and bee type affected mass-specific V_CO2, as did their interaction (Table S4). However, mass-specific V_CO2 was higher for bees flying in the sun relative to the shade (sun: 1.44, 95% CI [1.33, 1.54]; shade: 1.21, 95% CI [1.07, 1.35]; Table S4). In the shade, small morph males significantly decreased V_CO2 as air temperature rose (|t|=2.8, P=0.0059; Fig. 3A, Table 1), but air temperature did not affect V_CO2 in large morph males and females. In the sun, large morph males decreased V_CO2 as air temperature rose, but small morph males and females did not significantly vary V_CO2 with air temperature (Fig. 3B, Table 1).

We found a significant interaction between air temperature and location on V_H2O (Table S5). Pooled mean mass-specific V_H2O was higher for bees flying in the sun relative to those flying in the shade (sun: 0.53, 95%CI [0.22, 0.36]; shade: 0.29, 95% CI [0.22, 0.36]). Females and males had statistically similar slopes and intercepts of mass-specific V_H2O on air temperature in the shade (slope: F_2,65=0.42, P=0.66; intercept: F_2,67=1.57, P=0.22; Fig. 3C, Table 1), but V_H2O did not vary significantly as air temperatures rose (Table S5). Only females and small morph males flying in the sun showed significantly increased mass-specific V_H2O with air temperature (Fig. 3D, Table 1).

Mean metabolic heat production did not significantly differ between sunny and shaded locations for females and small males, whereas large males decreased metabolic production in the sun (Fig. 4A). Overall, convection strongly and significantly increased for all bees flying in sunny compared with shaded conditions (Fig. 4B), as did evaporative heat loss (Fig. 4D), though evaporation was a minor route of cooling in the heat budget. Females and large males additionally increased longwave radiative heat loss in the sun (Fig. 4C).

Convective conductance was significantly higher in the sun for females, large males and small males (Fig. 5A). Only small morph males showed increasing convective conductance with air temperature in the sun, but not in the shade (Fig. 5B).

Heat gain from solar radiation increased with rising air temperatures for both male morphs and for female bees (Fig. 6A–C, Table 2). Small morph males flying in the sun gained heat via solar radiation (in W g⁻¹) fastest, followed by females and large morph males. Metabolic heat production decreased with air temperature for only large morph males (Fig. 6B), with no significant difference between the mean metabolic heat production for males of both morphs and females (one-way ANOVA: F_2,59=0.88; Table S6). Evaporative cooling increased with air temperature for small males and females (Fig. 6A,C), with no significant difference in the rates of evaporative heat loss between small males and females (ANCOVA: F_1,31=0.58) or between the means of all bees (one-way ANOVA: F_2,59=1.35; Table S6). Longwave radiative heat loss increased for small males (Fig. 6C), with large males having the lowest mean radiative heat loss, followed by females and small males (one-way ANOVA: F_2,57=17.05, P<0.0001; Table S6). Convective cooling increased with air temperature for small males (Fig. 6C), and small males had higher mean convective cooling than large males and females (one-way ANOVA: F_2,60=3.51, P<0.005; Table S6).

We found that solar radiation was responsible for about half of the total heat gain to flying C. pallida bees (Fig. 6A–C), demonstrating a significant additional heat load during flight that has been previously unaccounted for in most studies of the thermal biology of large flying insects. Solar heating increased thorax temperatures depending on male morph and sex, and increased evaporative water loss rates. Perhaps not surprisingly, desert bees use very different mechanisms to regulate their body temperatures in response to solar radiation and/or higher air temperatures compared with the well-studied, non-flying desert vertebrates. Heat storage was minimal in flying C. pallida, and although evaporative cooling increased with solar radiation and at higher air temperatures, this was a small fraction of the heat budget. In some cases, metabolic heat production was suppressed, but overall, this was a minor adjustment to heat balance. Instead, to counteract the additional heat gain from the sun, flying C. pallida increased convective heat loss partly by increasing convective conductance (Figs 4B and 5A). The mechanism by which large morph males and females increased convective cooling was likely through the active transfer of heat from the thorax to the abdomen, a hypothesis supported by the increase in abdominal excess temperature ratio with air temperature in the sun (Fig. 2B). In contrast, the small morph males did not appear to actively transfer heat in the sun or shade (Fig. 2A,B), so the mechanism by which they increased convective conductance in response to solar heating or higher temperatures is unknown; however, this may include increasing flight speed.

We hypothesized that surface to volume ratios would strongly affect the responses of the different morphs/sexes to heating by solar radiation or higher air temperatures and found inconsistent support for this idea. As predicted by their high surface to volume ratios, small morph males were poor thermoregulators compared with large morph males, with slopes of thorax and head temperature on air temperature nearly double those of large morph males (Table S1). However, there was no evidence that solar heating induced stronger changes in body segment temperatures in small morph males compared with large morph males and females. Females, which are intermediate in body mass and surface to volume ratios, had body temperatures that were much more affected by solar heating than males. Females essentially suspended thermoregulation in the sun, with a slope of thorax and head temperatures on air temperature not significantly different from 1 (Table S1). These data suggest that thermoregulation is a high priority for males – who must be prepared to fly, fight and compete for matings – all while constrained to the hot microclimate from which females emerge. Females could be considerably less constrained in terms of microclimate usage, with the ability to leave a hot location in favor for a cooler one while foraging or nest digging, for example.

We hypothesized that large morph males might have the most capacity to cope with high temperatures and solar heat loads, as they spend significant time on or near the hot, sunny ground searching for females. Fitting with the predictions from this hypothesis, large morph males have the lowest coefficients of near infrared radiation absorption (Barrett et al., 2022). Large males were also the only group to lower metabolic heat production with air temperature, and did not increase evaporative heat loss at higher air temperatures (Figs 6B,D), which may allow them to remain in competition for females for a longer period in the heat without dangerous desiccation. The large morph males of a related Centris species also have the greatest thermal inertia and water stores (Johnson et al., 2023). Together these data strongly suggest that large morph males have specific adaptations to persist in the hunt for females on the hot, sunny desert ground.

Heat gain from solar radiation increased linearly with air temperature for all morphs and sexes (Fig. 6A–D), surpassing metabolic heat production later in the morning, at air temperatures above 27–30°C (Fig. 6A–C). The dorsal thoracic and abdominal coefficients of absorption differed based on male morph and sex (Barrett and O'Donnell, 2023). Small morph males had a high thoracic and abdominal coefficient of absorption (an emissivity 0.83 and 0.82, respectively), meaning that they absorbed more heat from solar radiation than large males (Barrett and O'Donnell, 2023). Large morph males, in contrast, had relatively lower coefficients of absorption, 0.76 for both the dorsal thorax and abdomen (Barrett and O'Donnell, 2023). Female thorax and abdomen coefficients of absorption were 0.80 and 0.75, respectively. Large males spend the majority of their activity period on the ground, fighting and digging for emerging, unmated females (Alcock et al., 1977), and would certainly benefit from reflecting as much heat gain from solar radiation as possible.

Hair-like structures called setae were responsible for the variation in coefficients of absorption for the male morphs and females (Barrett and O'Donnell, 2023). A recent study showed that desert bees are hairier and lighter in color than bees from other biomes, likely representing adaptation to high temperatures and low humidity (Ostwald et al., 2024). Dense hair on the thoraxes of flying facultative endotherms has been shown to help insulate the thorax and maintain high thorax temperatures in cool mornings, and a relatively bare abdomen allows for increased heat transfer from the abdomen to the environment in some species (Heinrich, 1976; Johnson et al., 2022). However, female C. pallida had more densely hairy abdomens than large or small morph males (Barrett and O'Donnell, 2023), yet females relied on the abdominal convector for heat transfer while flying in both shaded and sunny conditions (Fig. 2A,B). Clearly, a densely hairy abdomen does not necessarily preclude a large flying endotherm from dumping heat from the thorax to the abdomen at high air temperatures. One possible explanation is that reflection could be determined by hair length or branching, rather than density.

It is important to address that the mid-infrared spectrum (2.5–25 µm) also plays a large role in heating, particularly heat from the ground in desert conditions (Johnson et al., 2023; Krishna et al., 2021; Shi et al., 2015). We do not currently have values for the coefficient of absorption in this spectrum for C. pallida, so we used an assumed value of 0.96 (Stupski and Schilder, 2021). In the future, it will be important to quantify the coefficient of absorption in the mid-infrared spectrum to completely define the heat budget.

Solar heating more than doubled water loss rates compared with the shade (Fig. 3C,D). We did not observe defecation or extruded liquid on the proboscis of flying bees, so future work is needed to clarify the routes of water loss for C. pallida bees in flight. Cuticular permeabilities of C. pallida at rest are low compared with those measured during flight (Roberts et al., 1998), so water loss is likely to occur via the spiracles. Nonetheless, the increase in water loss rates associated with solar heating can potentially have strong effects on flight activity if water or nectar is in short supply. Activity times of desert Centris males are likely limited by desiccation, not overheating (Johnson et al., 2023), and our data suggest that an absence of shaded microclimates could further cut the activity window time for males by increasing water loss rates. The activity period of other desert vertebrates, such as lizards, is well known to also be constrained by the abiotic environment. For example, Sceloporus merriami is thermally constrained to a 2 h window in the morning and 1 h in the late afternoon (Grant and Dunham, 1988), and lizards found at higher elevations have a larger activity window than those at low elevations owing to lower temperatures, more rainfall and thus more nutritional availability (Grant and Dunham, 1990). The same may be true for C. pallida. It will be important to create an activity budget for desert Centris at different elevations with care to incorporate the heat and water balance costs of different types of flight and amount of time spent performing these different types of flight (i.e. forward flight in the field, hovering flight in the metabolic chamber, and foraging flight).

Convective cooling increased in the sun for all bees, and significantly increased with air temperature for small males (Figs 4B, 6C). It seems unlikely that small males were able to increase flight speeds in a 500 ml metabolic chamber; one possible mechanism to increase convection could be variable wingbeat frequency. Because convective cooling will be larger in magnitude in forward flight, the values we present here are likely conservative. Despite this, convective heat loss was the main avenue of cooling in the model presented here. Assuming that Centris have flight speeds similar to those of honey bees (∼7 m s⁻¹ in the field; Barron and Srinivasan, 2006), we can compare the speed of air entering the respirometry chamber with that of air passing over the body of the bee generated by forward flight in the field. Our respirometry flow rate was constant at 1 l min⁻¹ and the cross-sectional interior area of the respirometry chamber is approximately 78.54 cm². Thus, the approximate speed of air passing through the metabolic chamber was 0.0036 m s⁻¹. Chappell (1982) measured the effect of wind speed on thoracic conductance of carpenter bees, showing that it increased with the square root of wind speed. If Centris flies at the 7 m s⁻¹ speed observed in the field for honey bees, then Chappell's data suggest that in the field, convective conductances may be approximately double what we calculated here (Fig. 5A,B).

Mammals and birds mainly resort to panting and cuticular evaporative heat loss to keep cool (Fuller et al., 2016; Pessato et al., 2020; Schmidt-Nielsen, 1997), as do desert reptiles (Dawson and Templeton, 1963; DeNardo et al., 2004). Why not desert bees? Despite palo verde bloom availability during the activity period, C. pallida may still be water-limited, as nectar concentrations vary through the day, and earlier-foraging bees could potentially outcompete C. pallida. Low reliance on evaporative cooling across a wide range of air temperatures is a common occurrence for other desert-adapted bees (Chappell, 1984; Johnson et al., 2022, 2023; Willmer, 1986; Willmer and Stone, 1997). Similarly, desert grasshoppers show minimal evaporative heat loss across most air temperatures (Roxburgh et al., 1996). However, at extreme high air temperatures (>45°C), many insects exponentially increase evaporative cooling, either by panting in grasshoppers (Prange, 1996) or by regurgitation/tongue-lashing in bees (Chappell, 1984; Heinrich, 1976; Heinrich and Buchmann, 1986). It would seem that most desert insects ‘turn on’ evaporative cooling as a last resort at high air temperatures, but rely mainly on other thermoregulatory mechanisms as long as air temperatures remain below body temperatures, allowing cooling via convection. The most likely explanation is that the small body size and high surface to volume ratio of desert insects makes the use of evaporative water loss a dangerous thermoregulation strategy. An interesting exception to this apparent ‘rule’ is the honey bee worker. Increasing evaporative heat loss is an important part of thermoregulation and the heat budget at air temperatures above 33°C in honey bees, possibly because their large colonies and the social exchange of food, which increases the functional water stores of foragers (Ostwald et al., 2016).

For the first time, we show that solar radiation is a major heat source for large desert bees flying in sunny field conditions. Solar radiation substantially elevated body temperatures, evaporative water loss and convective heat loss. Future studies attempting to predict physiological responses of pollinators to warming will need to incorporate radiation effects into their models, as most pollinating bees are diurnal. Solar radiation also substantially increases water loss rates; this result suggests that hotter, drier conditions may provide significant limitations on bee activity, as desiccation can be the major abiotic limitation on flight durations (Johnson et al., 2023). Across all temperatures, increases in convective cooling were most important for thermoregulation in response to sun exposure. However, convection becomes increasingly limited as body temperature elevations above air temperature decline.

In the flying bees that have been studied, body temperatures approach air temperatures at the upper range of the air temperatures studied, suggesting that further increases in air temperatures, if combined with strong solar radiation, may push bees beyond the range at which convection can predominate for cooling, requiring strong, non-sustainable increases in evaporation for bee survival.

Many thanks to the multitude of people who made this work possible: Hannah Bercovici, Stephan Buchmann, Brooke Bothun, Michael Dillon, Dale DeNardo, Nicole DesJardins, Adrian Fisher, Jordan Glass, Lucille Johnson-Glazer, Victoria Morgan, Craig Perl, Grace Rauch and Yash Raka, as well as the insightful comments from two anonymous reviewers. The Results and Discussion in this paper are reproduced from the PhD thesis of M.G.J. (Arizona State University, 2023).