#### Thermal Tolerances and Metabolic Rate

We assessed thermal tolerance and metabolic rate for each grasshopper as described below. Between 8 and 25 individuals were measured for each population (mean *n* = 13, median *n* = 12). We first measured preferred body temperatures (PBT) using a thermal gradient constructed on an aluminium sheet (0·125″ × 24″ × 48″). We placed one end in an ice bath and the other on a hotplate (Springate & Thomas 2005), which created a temperature gradient spanning *c*. 5–50 °C. Grasshoppers were placed within the 5-cm-wide lanes created by corrugated plastic dividers that ran the long way across the thermal gradient. A clear acrylic lid was then placed above the gradient with holes for circulation and thermocouple measurements, and the grasshoppers were allowed to acclimate for 30 min. We then used an Extech type K thermocouple to monitor the thermal gradient and record the temperatures associated with the position of grasshoppers every 10 min over a 50-min period (following Forsman 2000; Springate & Thomas 2005). During the acclimation period, the grasshopper moved throughout the thermal gradient before reducing activity. Most grasshoppers spent the duration of the observation period resting in one position.

The relationship between metabolic rate and temperature for each population was measured using stop flow respirometry as follows. Grasshoppers were placed into 60-mL syringes and stored in dark incubators at 20, 30 and 40 °C. Grasshoppers were allowed to acclimate for 1 h, and then, the syringes were flushed with CO_{2} and H_{2}O free air for 1 min at a flow rate of 100 mL min^{−1}. Water was removed with Drierite and CO_{2} was removed with soda lime using a syringe scrubber. The syringes were then sealed at a volume of 50 mL using a Luer Loc and placed in a dark chamber. After one hour, a 35-mL volume of air was injected from each syringe into a Foxbox Gas Analysis System (Sable Systems) for analysis of CO_{2} and O_{2} concentrations. Rates of CO_{2} and O_{2} consumption were calculated using the relationships in Lighton (2008). Closed respirometry techniques analogous to ours have frequently been used to measure the temperature dependence of metabolic rates, but we note the rate estimates can be effected by grasshopper activity (Irlich *et al*. 2009).

Following metabolic rate measurements, we measured both critical thermal minima and critical thermal maxima, CT_{min} and CT_{max}, which were defined as the lower and upper temperatures at which the grasshoppers were no longer able to right themselves. For these measurements, grasshoppers were placed individually into 50-mL centrifuge tubes, which were slowly (~0·2 °C min^{−1}) cooled or heated in a water bath. Given that warming rates may influence estimates of critical thermal limits, we chose an intermediate rate (Chown *et al*. 2009). We waited an hour after the cooling to commence warming. We measured body mass (g), body and femur length (mm), and width (mm).

#### Biophysical Model

We introduce our biophysical model as an overview of how phenotypes and environmental conditions interact to determine body temperatures. We use an energy budget to describe the flow of energy between the grasshopper and the environment: *Q*_{s} *= Q*_{t} *+* *Q*_{c} *+* *Q*_{cond}. Here, *Q*_{s} is the total input of heat due to solar radiation. *Q*_{t} describes the flux of thermal radiative heat due to both incoming thermal radiation (ground and sky) and that emitted by the grasshopper. *Q*_{c} is flux of heat between the grasshopper and the surrounding fluid (air) via convection. *Q*_{cond} is the flux of heat between the grasshopper's body and the solid surfaces with which the grasshopper's body is in contact via conduction. We omit evaporative heat loss as it should be negligible for the grasshopper (Anderson, Tracy & Abramsky 1979).

The solar radiative heat flux is estimated as the sum of direct (*Q*_{s,dir}), diffuse (*Q*_{s,dif}) and reflected (*Q*_{s,ref}) components (Kingsolver 1983):

- (eqn 1)

Each component is calculated as the product of the solar absorptivity of the grasshopper [we assume *α* = 0·7, (Anderson, Tracy & Abramsky 1979)], the horizontal flux of solar radiation (*H*_{s,dir}, *H*_{s,dif} and *H*_{s,ttl} for the direct, diffuse and total fluxes, respectively) and the silhouette area of the grasshopper exposed to solar radiation (*A*_{s,dir}, *A*_{s,dif} and *A*_{s,ttl} for the direct, diffuse and total surface areas, respectively). The direct radiation is adjusted for the zenith angle (*z*, degrees), which is the angle of the sun away from vertical.

We calculate the surface area by approximating the body of a female grasshopper as a rotational ellipsoid (Samietz, Salser & Dingle 2005). The major axis is equal to the grasshopper's length. We calculate the semi-minor axis (half of the grasshopper's width) as *a *= (0·365 + 0·241*1000 *L*)/1000 using a regression from Lactin & Johnson (1998). If , surface area can be calculated as follows:

- (eqn 2)

The ratio of silhouette area to surface of a grasshopper is a linear function of zenith angle: *A*_{s}/*A *=* *0·19–0·00173*z*. Thus, *A*_{s,dir}* = A*_{s,ref}* = *(0·19–0·00173*z*)*A*. We partitioned the observed total radiation (*H*_{s,ttl}) into diffuse (*H*_{s,dif}) and direct (*H*_{s,dir}) components using the polynomial function of a clearness index, *k*_{t}, developed by Erbs, Klein & Duffie (1982).

We estimate thermal radiative flux as the sum of radiation from the sky and ground. We assume that one half of the grasshopper's body is subject to atmospheric radiation and the other half is subject to thermal radiation from the ground surface. Thermal radiation is calculated using the Stefan–Boltzmann law, which states that radiative flux is proportional to the forth power of the absolute temperature of a body. Here, *T*_{b} is the absolute body temperature, *T*_{g} is the absolute ground surface temperature and *T*_{sky} is the equivalent black body sky temperature [0·0552*(*T*_{a}+273)^{1·5}, (Swinbank 1963)]. The Stefan–Boltzmann constant (*σ)* characterizes the proportionality of this relationship. The thermal emissivity (*Є*) accounts for incomplete absorption or emission of thermal radiation, but in this case, we assume that both the grasshopper and ground are perfect black bodies (*Є *= 1). We account for the thermal radiative heat-transfer surface area (*A*_{t} *= A*). The relationship is thus:

- (eqn 3)

Convective heat flux is estimated as the product of the convective heat-transfer coefficient in turbulent air (*h*_{cs}), the grasshopper's surface area exposed to convective heat flux (*A*_{c} *= A*) and the temperature difference between the grasshopper's body temperature (*T*_{b}) and air temperature (*T*_{a}):

- (eqn 4)

We calculate *h*_{cs} from the convective heat-transfer coefficient as *h*_{cs} = *h*_{c}(−0·007*z*/*L *+ 1·71) where *z *= 0·001 m is the height above the ground. We use an empirically derived relationship for grasshoppers to estimate the heat-transfer coefficient, *h*_{c} (Wm^{−2}C^{−1}) (Lactin & Johnson 1998): *h*_{c} = Nu**K*_{f}/*L* where the thermal conductivity of fluid, *K*_{f} = 0·024 + 0·00007(*T*_{a} + 273)Wm^{−1}K^{−1}.

We use an empirical relationship from Anderson, Tracy & Abramsky (1979) to estimate the Nusselt number, *N*_{u}, as *N*_{u}* = *0·41 Re^{0·5} where Re is the Reynolds number. Re = *u L/v*, where *u* is windspeed (m s^{−1}) and *v* is the kinematic viscosity of air (m^{2} s^{−1}) (*v *=* *15·68 × 10^{−6} at 300 K).

The rate of conduction is a function of the body area in contact with the substrate and the temperature differential between the body and the surface:

- (eqn 5)

where *h*_{cut} is the thermal conductivity of the grasshopper cuticle (approximated as 0·15 W m^{−1} K^{−1}; value for hornets; Galushko *et al*. 2005); *A*_{cond} is the surface area of the grasshopper in contact with the substrate; and *T* is the cuticle thickness (approximated as 6 × 10^{−5 }m; Galushko *et al*. 2005). We only model conductance through the cuticle as we assume that the interior of the grasshopper is well mixed.

#### Weather Data

We recorded (shaded) air and soil temperatures (Pace PT907 30k ohm thermistor, ±0·15 °C), radiation (Pace SRS-100 Silicon Photodiode, 400–1100 nm, ±5% accuracy) and windspeed (anemometer, 0·9–78 m s^{−1} range, ±5% accuracy) averaged over 3-min intervals at our four focal sites using a Pace XR5 datalogger (Pace Scientific, Mooresville, NC, USA). We used these weather data to estimate grasshopper body temperatures, metabolic rates and the potential for activity at 3-min intervals. These estimates were then averaged between sunrise and sunset across July for each site.

We additionally monitored the body temperatures of grasshopper physical models placed on the ground in representative vegetation. We constructed the physical models by placing thermistors into the thorax and abdomen of previously frozen grasshoppers, which were then dried and coated with clear epoxy. We monitored the temperatures of live and dead grasshoppers (by inserting a thin, type k thermocouple) along with our physical model in a variety of weather conditions to confirm that our physical model provides an accurate estimate of grasshopper body temperatures. We used the grab-and-stab method with a Type K thermocouple to detect the effect of behavioural thermoregulation on the relationship between ambient and air temperature.