An evaluation of a biophysical model for predicting avian thermoregulation in the heat

For diurnal endotherms inhabiting hot environments, rapid anthropogenic global heating is exacerbating the challenges of maintaining energy and water balance (Parmesan, 2006; Urban et al., 2016). During hot conditions, endotherms maintain body temperature (T_b) below lethal limits via physiological and behavioural processes (Dawson, 1964, 1954; McKechnie et al., 2021a). Increasingly intense heat waves exert direct pressure on water budgets (Albright et al., 2017; Riddell et al., 2019), occasionally exceeding the physiological ability of endotherms to avoid lethal dehydration and/or hyperthermia (Albright et al., 2017; McKechnie et al., 2021b; McKechnie and Wolf, 2010; Ratnayake et al., 2019), as illustrated by a number of recent heat-related mass mortality events (Holt and Boersma, 2022; McKechnie et al., 2021b; Quintana et al., 2022; Sloane et al., 2022). Additionally, the increased duration and frequency of sustained hot weather places indirect pressure on endotherms through missed-opportunity costs arising from trade-offs between thermoregulation and activities such as foraging (Cunningham et al., 2021). Among birds, functional links between hotter conditions and fitness costs are becoming increasingly apparent for a handful of well-studied species (e.g. Carroll et al., 2015; du Plessis et al., 2012; Edwards et al., 2015; Kemp et al., 2020; Sharpe et al., 2019; van de Ven et al., 2019) but remain unexplored for most species.

Physiological thermoregulatory responses (e.g. evaporative cooling) to changing environmental conditions have been studied by extrapolating empirical laboratory data to the field via regression models (e.g. McKechnie and Wolf, 2010). Such approaches are limited by challenges of translating results from simple laboratory thermal environments to complex natural ones, and because the accuracy and applicability of the model is a direct function of the amount of data and range of conditions studied. Alternatively, thermoregulatory responses can be predicted using biophysical models that integrate functional traits of organisms and their environment via heat exchange models to predict T_b, metabolic rates and water loss in response to complex and often variable natural conditions (Porter and Gates, 1969; Porter et al., 1973; Tracy, 1976). Heat exchange and water exchange are tightly coupled and can be defined mathematically based on universal physical and biological principles (Porter and Gates, 1969) and used to predict species' environmental responses given their functional traits (Kearney et al., 2021). Biophysical models have been used to understand the role of thermoregulation in buffering species from increasingly extreme conditions associated with climate change (Kearney et al., 2009, 2013; Kearney and Porter, 2017; Malishev et al., 2017; Mathewson et al., 2016), and to evaluate the cost of increased cooling requirements (Riddell et al., 2021, 2019). Additionally, biophysical models have been shown to predict metabolic rate better than allometric models in white-footed sportive lemurs (Lepilemur leucopus; Stalenberg, 2019). However, empirical data are needed to test and parameterise these models to appropriately capture species-specific behavioural and physiological responses, particularly under environmental conditions on the upper edge of the thermoneutral zone. Once tested, these models can be used to predict species’ responses under any given combination of environmental conditions, or to explore the thermoregulatory responses available to organisms within the constraints of thermodynamics.

Although biophysical models have a long history (Briscoe et al., 2023), they have often been challenging to apply because of limited documentation, closed-source code and convoluted pipelines for integrating data on traits and environments. The recently developed NicheMapR biophysical modelling package is an open-source program which aims to provide ecologists with an accessible and flexible suite of tools for analysing, visualising and predicting energy and mass budgets of species, including endotherms. The package is based on the original work of Porter and his colleagues for modelling heat balance across taxa by solving steady-state heat budgets (Kearney and Porter, 2017; McCullough and Porter, 1971; Porter et al., 1973). The release of the NicheMapR endotherm model (Kearney et al., 2021) resolves previous accessibility issues and provides new opportunities to understand and predict responses of birds and mammals to their environments. The model operates under user-specified microclimate conditions and is based on species' morphological and physiological functional traits. Appropriate functional trait data are therefore essential, and can either be obtained directly or inferred from species that are phylogenetically closely related and/or ecologically similar (e.g. Kearney et al., 2016).

Here, we evaluated the endotherm model of NicheMapR for predicting evaporative water loss (EWL), resting metabolic rate (RMR) and T_b for three southern African arid-zone birds, southern yellow-billed hornbill (Tockus leucomelas), southern pied babbler (Turdoides bicolor) and southern fiscal (Lanius collaris). These species differ in patterns of behavioural thermoregulation, foraging mode and use of cool microsites in their arid savanna habitats. Biologically important daily maximum air temperature (T_air) thresholds exist in the 30–40°C range, above which sublethal fitness costs related to body mass maintenance and breeding success have been documented for all three species (Cunningham et al., 2013; du Plessis et al., 2012; van de Ven et al., 2019). Moreover, physiological adjustments, including changes in thermal conductance, T_b and EWL, begin to occur within this range of T_air values, and upper critical limits of thermoneutrality are often within this same range (McKechnie et al., 2021a). We thus focused on (1) evaluating NicheMapR's ability to adequately predict thermal responses of birds by comparing the accuracy of the respective model outputs with empirically collected thermal physiology data at T_air values between 30 and 40°C and under very hot conditions when T_air>T_b, and (2) evaluating the sensitivity of the model to parameter changes and assessing whether accurate predictions can still be obtained with limited empirical data and biophysical modelling knowledge. We used a combination of measurements from museum specimens (e.g. plumage depth, body length) and published physiological information on thermal responses (e.g. heat tolerance limit, basal metabolic rate) to parameterise biophysical models for these three species. The model was set up to represent simulated metabolic chamber conditions, which were then tested against empirical EWL, RMR and T_b data collected under laboratory conditions.

All three species are widespread and common in the southern Kalahari Desert. The area experiences hot summers and cool, dry winters with a mean annual rainfall of ∼221 mm and average daily summer maximum T_air of ∼33–37°C (Fick and Hijmans, 2017). The southern Kalahari region is experiencing rapid warming, making it particularly vulnerable to the negative effects of climate change. For instance, the Kgalagadi Transfrontier Park spanning South Africa and Botswana has experienced warming of 0.039±0.007°C year⁻¹ (mean±s.e.m.) and annual mean maximum temperatures have increased by 1.95°C since 1960 (Moise and Hudson, 2008; van Wilgen et al., 2016).

Southern yellow-billed hornbills [‘hornbills’, Tockus leucomelas) (Lichtenstein 1842)] and southern pied babblers [‘babblers’, Turdoides bicolor (Jardine 1831)] forage predominantly on the ground, with hornbills occasionally hawking flying insects and gleaning in trees (Kemp, 1995). In contrast, southern fiscals (‘fiscals’, Lanius collaris Linnaeus 1766) hunt for their prey by perching predominantly on exposed posts or branches and pouncing on invertebrates and small vertebrates (Dean, 2005). Data on interactions between metabolic heat production, evaporative heat loss and the consequent patterns of T_b at moderate to high T_air are available for these three species (Czenze et al., 2020; van Jaarsveld et al., 2021). Data were collected using standardised respirometry methods involving exposure to stepped series of progressively higher T_air at very low chamber humidities (Czenze et al., 2020). We collected additional data for hornbills (n=10) at T_air=10–25°C during summer (October–November 2020), near the south-eastern edge of the Kalahari Desert (Radnor Farm, 26°6′23″S, 22°52′54″E) in South Africa. We used a flow-through respirometry system as described by van Jaarsveld et al. (2021) to measure oxygen consumption, carbon dioxide production and EWL at T_air values between 10 and 25°C. Birds were fasted for 24 h and individually placed in a ∼17 l airtight chamber positioned inside a ∼195 l modified chest freezer used as a temperature control unit. In brief, atmospheric air from an oil-free compressor was filtered through a membrane dryer (Champion^®CMD3 air dryer and filter, Champion Pneumatic, Quincy, IL, USA) to remove any water vapour present. The filtered atmospheric air was regulated using a mass flow controller (0-30 SLPM, Alicat Scientific Inc., Tuscon, AZ, USA), entering the chamber through an inlet fitted near the top of the chamber. Birds were exposed to each T_air value (T_air=10, 15, 20, 25°C) for ∼1.5 h during daytime runs where flow rates were regulated at 6–11 l min⁻¹ (usually ∼7 l min⁻¹) depending on the bird's behaviour and chamber humidity (<1 kPa). All experimental protocols were approved by the University of Pretoria Animal Ethics committee (protocol NAS058/2020), the Animal Research and Scientific Ethics Committee of the South African National Biodiversity Institute (protocol P18-12) and the Northwest Parks Board (permit 26026).

We obtained measurements from museum specimens at Ditsong Museum of Natural History, Pretoria, South Africa (n=10 per species, comprising 5 adult males and 5 adult females) following the methods described by Kearney et al. (2016). Specifically, we measured the depth of plumage at multiple locations (∼20) on the dorsal and ventral sides (∼10 per side) from the top of the shoulder to the base of the tail, as well as the length of feathers (∼3 per side) for all three species. These measurements were collected using a standard measuring tape, measuring rod and string. Shape estimates for each species were derived by measuring relative dimensions (length from the beak to the base of the body, width and depth at the shoulder).

To model EWL, RMR and T_b under standard metabolic chamber conditions (i.e. operative temperature equivalent to T_air), we used the endotherm model (function endoR_devel) of the NicheMapR biophysical modelling package (version 3.1) in the R programming environment (version 1.2.5033, http://www.R-project.org/) using the RStudio (version 3.2.3, https://posit.co/products/open-source/rstudio/) interface. The model setup has been described in detail elsewhere (Kearney et al., 2021) but, in brief, consists of a suite of subroutines to solve coupled heat and water budgets given a set of physiological and morphological traits that can be configured to match species-specific behavioural thermoregulatory sequences under specific environmental conditions for every hour of the day. The model computes the RMR and EWL necessary to maintain T_b given conductive, convective, radiative and evaporative heat exchange with the surrounding environment by calling a set of routines from a Fortran library using the endoR_devel interface in R (Kearney et al., 2021). The endoR_devel function allows the user to code behaviour and thermoregulatory responses configured for a species from the default version in R (Kearney et al., 2021). As described below, we adjusted the endoR_devel code to represent the general behavioural and physiological requirements of a bird, which was then used as the baseline model for all three species. The species-specific input biophysical traits (e.g. body dimensions, Table 1) and physiological responses (e.g. respiratory rate, Table 1) were then used to parameterise the general bird model for each species (Tables S1 and S2). Thereafter, we compared the outputs from the default endoR_devel code with the outputs from the aforementioned adjusted endoR_devel code (online appendix available from GitHub: https://github.com/ShannonConradie1/NicheMapR-endoR_devel_edited.git). See Supplementary Materials and Methods.

Our main objective was to examine model performance and establish whether predicted relationships between environmental temperature and thermoregulatory responses were consistent with observed thermal physiology. We predicted EWL, RMR and T_b for hornbills, babblers and fiscals at rest under standard metabolic chamber conditions [i.e. incremental increases in T_air (0–55°C), low relative humidity (5%) and wind speed (0.01 m s⁻²), no solar heat gain (Lustick, 1969)] and compared the model output with thermal physiology data collected here and previously (Czenze et al., 2020; van Jaarsveld et al., 2021). Model performance was determined based on the agreement between model outputs and thermal physiological data, where we considered good agreement if 95% of model output values across T_air fell within the range of observed values. The default model parameterisation has been described by Kearney et al. (2021) but, in brief, begins with physiological settings anticipated under cold conditions and simultaneously solves for metabolic heat production, and skin and feather/fur temperature that balance the heat budget for a specified core T_b. If predicted metabolic heat production is lower than the specified minimum (e.g. basal metabolic rate for a resting individual), a series of species-specific behaviours and physiological responses are invoked such as altering posture, increasing flesh thermal conductivity, panting and allowing core T_b to rise. The main adjustments we made to the base endoR_devel model involved allowing for ptiloerection of feathers at T_air values below the thermoneutral zone, where feather depth begins at feather length and is progressively sleeked to normal as T_air increases (Fig. S1). Here, we also adjusted the sequence of behavioural responses to start with an endotherm in a heat-loss minimising posture, with ptiloerect feathers and proceed to heat-loss maximising responses as skin temperatures increase (full code available from GitHub: https://github.com/ShannonConradie1/NicheMapR-endoR_devel_edited.git): (1) flatten feathers to normal position, (2) change posture (uncurl), (3) increase conductivity of flesh, and (4) simultaneously increase T_b and EWL.

This sequence contrasts that of the default model parameterisation, which initiates a stepwise sequence of behavioural responses (Fig. S1). Allowing changes in T_b and EWL to occur simultaneously resulted in a more gradual increase in T_b, accounting for interactions between EWL, RMR and T_b. We modelled thermoregulation for each of the three bird species following the aforementioned sequence of responses, and only changed input parameters relating to morphology (measured), target core and maximum T_b, respiratory rate and skin wetness (inferred from empirical data) to species-specific values (see Tables S1 and S2 for full parameter descriptions).

We ran a sensitivity analysis for the hornbill model only, because the empirical dataset for this species spans a wide range of diurnal T_air values (T_air=10–50°C) likely to be experienced by the species, whereas the other two species' datasets are only for T_air>30°C. We used the hornbill model to evaluate whether accurate predictions of avian thermoregulation can still be obtained with limited species-specific empirical data and biophysical modelling knowledge. We quantified the sensitivity of the hornbill model to input variables by adjusting morphological and physiological values to determine their effect on the predicted EWL, RMR and T_b inflection points (i.e. T_air above which each variable dramatically increased) and slopes (i.e. relationship between T_air and each variable, for T_air above the respective inflection points). Additionally, we determined the hornbill model's sensitivity to low (100 W m⁻²) and high (900 W m⁻²) short-wave solar radiation by changing the QSOL input parameter in NicheMapR, assuming all other variables remain the same. We fitted a piecewise linear regression model (SiZer package; https://CRAN.R-project.org/package=SiZer) to model outputs (EWL, RMR and T_b) in order to identify changes in predicted inflection points and segmented general linear models (lme4 package; Bates et al., 2015) to identify changes in the predicted relationship between EWL, RMR, T_b and T_air in hornbills (i.e. slopes). Specifically, sensitivity of the predicted relationship between EWL, T_b and T_air to input parameters was assessed because of the importance of variation in these parameters in predicting species’ vulnerability to lethal dehydration and hyperthermia (Albright et al., 2017; Conradie et al., 2020). Cohen's d values (effsize package; https://CRAN.R-project.org/package=effsize) were used to assess the effect sizes of the change in the response variable (i.e. EWL, RMR and T_b) for over- and under-estimating biophysical input variables (Cohen, 1992, 1977). Here, deviations in predictions were scaled using the residual variation in the empirical dataset. These analyses were conducted under the simulated metabolic chamber conditions described above, minimising the effects of environment and bird behaviour. All user-specified variables were held constant except for the one being evaluated, which was varied within biologically realistic values based on observed among-individual variation and known maximum and minimum values for hornbills (van de Ven, 2017; van de Ven et al., 2020; van Jaarsveld et al., 2021).

Species-specific NicheMapR models, with our adjusted sequence of behavioural responses (e.g. flattened feathers to normal position, increase T_b and EWL in parallel but independently, etc.), accurately predicted EWL, metabolic rate and T_b in all three study species at T_air between 30 and 52°C (Fig. 1), with predictions greatly improved compared with those under the default NicheMapR model parameterisation (i.e. stepwise sequence of behavioural responses; Fig. S2). The greatest discrepancy between the species-specific NicheMapR predicted and observed values was an overestimation of hornbill and babbler EWL at T_air=35°C (EWL: hornbills: predicted=0.95 g h⁻¹, observed=0.31–0.73 g h⁻¹; babblers: predicted=0.53 g h⁻¹, observed=0.27–0.52 g h⁻¹). At T_air>40°C, however, model predictions fell well within the range of empirically observed values. T_b predictions were also slightly above the mean observed values for hornbills (observed−predicted=0.13–0.8°C), but within the upper limit of observations. In contrast, the default model T_b predictions all fell outside the limit of observations for T_air=30–50°C, and overestimated T_b by ∼2°C (Fig. S2).

The hornbill biophysical model accurately predicted EWL and T_b, with correlation coefficients between observed and predicted values of 0.86 and 0.97 for T_air above the respective predicted inflection points (Fig. 2). The model-predicted inflections in EWL and T_b at T_air=38.3°C and T_air=30.3°C, respectively, both fell within 95% confidence intervals (CI) for observed values (EWL 95% CI: T_air=38.2–41.1°C, R²=0.86 and T_b 95% CI: T_air=28.3–35.0°C, R²=0.97; Fig. 2).

The NicheMapR endotherm model was most sensitive to changes in water budget parameters, particularly base and maximum skin wetness (i.e. area of skin that can act as a free-water surface), respiratory rate and the increments by which the panting multiplier (i.e. effect of panting on basal metabolic rate) increased (Fig. 3, Table 1; Fig. S2). Underestimation or overestimation of biophysical traits that produced the greatest effect on predicted EWL had negligible effects on predicted T_b and vice versa. For example, underestimating maximum skin wetness had the greatest effect on EWL (Cohen's d=0.61), but negligible effect on T_b (Cohen's d=0.03; Fig. 3). In contrast, underestimation of respiratory rate had the greatest effect on T_b (Cohen's d=0.5), and a negligible effect on EWL (Cohen's d=0.1; Fig. 3). Under standard, near black-body, metabolic chamber conditions, the model was least sensitive to morphometric data, with variables such as feather length exerting negligible influence (Cohen's d<0.2; Table 1). However, species-specific estimates of size and shape had small effects on EWL and T_b predictions (Cohen's d≈0.2–0.4; Table 1). Including low solar radiation (100 W m⁻²) had negligible effects on the overall predicted EWL and T_b (EWL: Cohen's d=0.11; T_b: Cohen's d=0.07; Table S2). However, under high solar radiation (900 W m⁻²), these effect sizes increased for the overall predictions of EWL and T_b to large and medium, respectively (EWL: Cohen's d=0.94; T_b: Cohen's d=0.78; Table S2). The model remained sensitive to changes in water budget variables under high solar radiation, and the sensitivity of the model to morphometric data increased, with feather length, plumage depth and feather reflectivity having the greatest overall effect sizes (Figs S2 and S3, Table S2).

This study demonstrates that the NicheMapR endotherm model, when parameterised appropriately, can be used to accurately predict thermoregulatory responses of birds to hot conditions. In three arid-zone species, the predicted species-specific patterns of evaporative heat dissipation, metabolic heat production and T_b were very similar to those observed under laboratory conditions. This strong correspondence between predicted and observed values spans the range of T_air over which consequential behavioural and physiological thresholds occur in most species investigated to date (T_air=30–40°C) and extends up to T_air≈10°C above normothermic T_b. In contrast, the default NicheMapR endotherm thermoregulatory sequence overestimated T_b by ∼2°C within this critical range of T_air (30–40°C), highlighting the importance of appropriately customising thermoregulatory responses for the modelled taxa.

Evaporative heat dissipation is the only physiological mechanism whereby birds can avoid lethal hyperthermia when environmental temperature exceeds normothermic T_b (reviewed by McKechnie et al., 2021a,b) and the NicheMapR endotherm model accurately predicted rates of EWL for all three species. The only noteworthy differences between predicted and observed values occurred at T_air=35°C, where EWL was overestimated by 51% in hornbills and 24% in babblers. Our analysis suggests that these differences will not meaningfully reduce the overall predictive power of the models, for two reasons. First, in both hornbills and babblers, the observed−predicted differences in EWL at T_air=35°C are equivalent to <0.25% of body mass and are probably too small to significantly affect predictions of variables such as time to dehydration during extreme heat events, with predicted values closely matching observed values at all T_air>40°C. Second, inflection points and slopes of EWL were accurately predicted (Fig. 2) and the predicted T_b and RMR values all fell well within the range of observed values, as did the predicted T_air at which each species reached their known maximum T_b (McKechnie et al., 2021a; van Jaarsveld et al., 2021).

Parameterising NicheMapR endotherm models as we have done here improves the accuracy of predictions for the effects of high environmental temperatures on energy and water balance compared with previous applications of this approach to species in hot, arid environments (e.g. Kearney et al., 2016). One obvious improvement compared with previous models concerns predicted T_b within the T_air=30–40°C range, as well as when T_air>T_b. For example, in a study of budgerigars by Kearney et al. (2016), predicted T_b differed substantially from actual values in the 30–40°C range, with the model underestimating T_b at T_air=30°C by ∼2°C and overestimating the T_air at which T_b reaches 40°C by 3–4°C (fig. A1.1 and 2B of Kearney et al., 2016). Accurate predictions of T_b are critical for predicting patterns of behavioural thermoregulation, such as the environmental temperatures at which endotherms retreat to shaded microsites or the onset of panting, which can lead to large reductions in foraging efficiency (van de Ven et al., 2019).

The hornbill model sensitivity analysis revealed model outputs were most sensitive to changes in water budget variables (e.g. respiratory rates and skin wetness), with the strongest effects (Cohen's d>0.5) on biologically realistic input values for these parameters under conditions of low solar radiation (≤100 W m²). Overestimating or underestimating morphological input variables has small or negligible effects on the EWL, T_b and RMR predictions provided the values are within the natural range experienced by the species. Our findings are consistent with those of Peterman and Gade (2017), who found respiratory rate to be the most important parameter in their biophysical modelling approach affecting energy balance in salamanders (Plethodon jordani).

In contrast, under conditions of high solar radiation (900 W m⁻²), model water budget outputs become increasingly sensitive to changes in morphological variables (especially feather properties). Several authors have reported that fur depth and solar reflectivity were the most important parameters affecting model predictions of metabolic rate and T_b in mammals (Mathewson et al., 2020; Moyer-Horner et al., 2015; Ratnayake, 2018). Thus, pelage and feather properties are likely to be more important for biophysical models under environmental conditions where solar heat gain plays a crucial role, unlike the standard black-body chamber conditions presented here (Wolf et al., 2000; Wolf and Walsberg, 2000).

One limitation of this study is that it focused on birds experiencing low metabolic chamber humidities. These conditions are likely to be representative of hot summer days in the southern African arid zone but, in more mesic, humid environments, evaporative cooling efficiency is likely to be lower (Gerson et al., 2014; Weathers, 1997). Although relatively few studies have empirically quantified the relationships between humidity and thermoregulation at T_air approaching or exceeding T_b under metabolic chamber conditions (Gerson et al., 2014; Powers, 1992; van Dyk et al., 2019), NicheMapR accounts for the effects of ambient humidity. Specifically, the model increases rates of EWL, RMR and T_b more rapidly at higher humidities, with maximum T_b reached at lower T_air compared with drier conditions. We are unaware of avian studies that have used empirical data to validate the predictions of biophysical models over a range of humidities (but see Briscoe et al., 2021), although the physical principles are well understood; such validations are a prerequisite to applying a biophysical modelling approach to species occupying humid environments.

A second limitation of the present study is that it involved laboratory conditions under which T_air≈environmental temperature (T_e) rather than natural thermal environments in which heat exchange involves more complex combinations of radiative, forced convective and conductive fluxes (Bakken, 1976; Robinson et al., 1976). Our sensitivity analysis, for instance, is based on conditions birds experience in metabolic chambers, including predominantly free convection and limited radiative flux. Under natural conditions, additional avenues of heat transfer may influence the sequence of physiological responses (Wolf et al., 2000) and the sensitivity of the model to specific input variables. NicheMapR has a microclimate subroutine that can be used to predict the fine-scale thermal landscape experienced by a species (Kearney and Porter, 2017), which in turn can be linked to the model used here to predict heat and water exchange in individuals experiencing natural thermal environments and including behavioural thermoregulation. For example, Mathewson et al. (2020) demonstrated that a similar biophysical modelling approach can predict vervet monkey T_b within 0.5°C of actual values measured in free-living animals for specific behaviour categories (e.g. huddled, inactive, uncurled, etc.). Integrated with models or empirical data on behaviour, biophysical modelling approaches can provide predictions that account for time–activity budgets and animals' movements through landscapes (Malishev et al., 2017).

Our model did not account for excess heat loss via appendages such as the beak or when holding the wings open. Heat loss via beaks has been shown to be an important contributor to avian thermoregulation, particularly in species with disproportionately large beaks relative to body size, such as toucans and hornbills (Tattersall et al., 2009; van de Ven et al., 2016). Vasodilation in a highly vascularised beak, such as those of hornbills or toucans, can cause beak surface temperature to increase, reducing the need for evaporative heat dissipation (Tattersall, 2016; van de Ven et al., 2016). However, the capacity for non-evaporative heat dissipation via the beak is most effective when T_air<T_b, with the T_b–T_air gradient declining to zero at T_b=T_air (van de Ven et al., 2016). Our predictions for heat loss under high T_air, specifically when T_air ≥T_b, are thus unlikely to be altered by heat loss via the beak.

Biophysical model predictions can provide a mechanistic understanding of species’ sensitivity to climate change, accounting for physiological tolerance and the environment (Briscoe et al., 2023). Accurate predictions of species' energy and water flux under hot conditions, in addition to improving our understanding of their ecology and evolution, provide the basis for modelling exposure to several categories of risk associated with climate change. Models of the risks of lethal dehydration or lethal hyperthermia have, in the past, been based on either species-specific empirical data (Albright et al., 2017; Conradie et al., 2019; Conradie et al., 2020; Wolf, 2000) or allometrically predicted values (McKechnie and Wolf, 2010). The former method is restricted to species for which suitable physiological data exist, whereas the latter approach fails to capture interspecific and intraspecific variation in traits such as the primary avenue of evaporative heat dissipation, which can result in overestimation or underestimation of exposure to potentially lethal conditions (McKechnie et al., 2021a). Biophysical approaches have the potential to overcome these limitations and accurately predict exposure to acute, lethal risks in species for which thermal physiology and behavioural data are limited, but exist for ecologically similar species and/or can be allometrically predicted. Moreover, key functional traits may be phylogenetically conserved (e.g. whether the primary avenue for evaporation is respiratory or cutaneous; McKechnie et al., 2021a), increasing the potential to make inferences for data-deficient taxa. Our sensitivity analysis also provides insight into which functional traits (i.e. respiratory rate and skin wetness) should be prioritised in empirical studies.

Additionally, the model can be used in a hypothetico-deductive approach to understand thermal adaptation or the underlying mechanisms of a system. For example, mismatches between model predictions and observations can potentially provide insight into physiological adaptations. The model can also be used to test hypotheses about thermal constraints on species’ occurrence, based on universal physical principles and functional trait data. However, although the model is widely applicable and general taxon-non-specific values can often be used, caution is sometimes needed in extrapolating data from the literature to unstudied species. For example, red-billed queleas (Quelea quelea) have recently been shown to tolerate extreme hyperthermia with maximum T_b averaging 48.0°C (Freeman et al., 2020), values ∼3°C higher than the maximum T_b of most small passerines. The exceptionally high ceiling to T_b of this species underscores the importance of empirical evidence in ground-truthing model predictions.

Quantifying thermoregulatory responses of endotherms to more complex thermal environments in the lab is difficult and time consuming and likely produces species-specific results (Wolf et al., 2000; Wolf and Walsberg, 1996). Our study shows that biophysical models can capture the complex physiological responses of birds to thermal extremes, increasing confidence in the ability of such models to infer thermoregulatory performance in endotherms under the more complex conditions found in nature. In principle, biophysical models permit rapid assessment of species and population responses to a rapidly changing climate without the challenge of collecting and extrapolating respirometry data to free-ranging species. However, users still need a general understanding of the underlying physical principles, and how these processes are implemented in biophysical models, to generate appropriate predictions (Briscoe et al., 2023). Biophysical models are not meant to replace empirical data but, as they provide insight into the underlying mechanisms of a system, should be used to complement and interpret empirical data and focus data collection. For instance, the NicheMapR endotherm model or other similar models for threatened or data-deficient species can provide a credible basis for evaluating physiological constraints and risks associated with climate change or human alteration of thermal landscapes, information that is often vital for conservation and evaluation of potential management interventions.

The authors thank the Mathews family for allowing us to conduct research at Radnor Farm. We thank two anonymous reviewers whose comments improved the quality of the manuscript. This work is based on research supported by the National Research Foundation of South Africa and the University of Pretoria.