Size, shape, and the thermal niche of endotherms

Abstract

A key challenge in ecology is to define species' niches on the basis of functional traits. Size and shape are important determinants of a species' niche but their causal role is often difficult to interpret. For endotherms, size and shape define the thermal niche through their interaction with core temperature, insulation, and environmental conditions, determining the thermoneutral zone (TNZ) where energy and water costs are minimized. Laboratory measures of metabolic rate used to describe TNZs cannot be generalized to infer the capacity for terrestrial animals to find their TNZ in complex natural environments. Here, we derive an analytical model of the thermal niche of an ellipsoid furred endotherm that accurately predicts field and laboratory data. We use the model to illustrate the relative importance of size and shape on the location of the TNZ under different environmental conditions. The interaction between body shape and posture strongly influences the location of the TNZ and the expected scaling of metabolic rate with size at constant temperature. We demonstrate that the latter relationship has a slope of approximately (1/2) rather than the commonly expected surface area/volume scaling of (2/3). We show how such functional traits models can be integrated with spatial environmental datasets to calculate null expectations for body size clines from a thermal perspective, aiding mechanistic interpretation of empirical clines such as Bergmann's Rule. The combination of spatially explicit data with biophysical models of heat exchange provides a powerful means for studying the thermal niches of endotherms across climatic gradients.

Fig. 1.

Observed metabolic rates as a function chamber temperature in laboratory studies of the weasel and the woodrat by Brown and Lasiewski (20) together with predicted values based on an analytical biophysical model of convective and radiant heat exchange in a furred ellipsoid with distributed heat generation using the parameters in Table 1. Light gray arrows indicate the location of the LCT and hence the beginning of the TNZ.

Fig. 2.

The simulated effect of variation in posture (A) and wind speed (B) on the TNZ of a 150-g weasel. In postural analyses, shape was allowed to vary according to changes in the ratios of the semimajor axes a and b of between 1.5 and 5.5, assuming an oblate spheroid with fur of depth 5.3 mm, holding wind speed constant at 0.7 mm/s. For wind speed analyses, wind speed was varied by orders of magnitude from 0.5 mm/s to 5 m/s, holding shape constant at a 2.5 ratio between the semimajor axes a and b. Light gray arrows indicate the location of the LCT and hence the beginning of the TNZ.

Fig. 3.

The effect of size, shape (sphere vs. ellipsoid with a:b = c 5:1), and pelage on the metabolic rate at constant air temperature, 20 °C, under low wind speed as found in metabolic chambers (0.001 m/s) (A) and high wind speed (10 m/s) (B). Calculations are based on the ellipsoid model as described. Also indicated on each graph are the mouse–elephant empirical relationship for BMR and the expected relationship for a copper sphere. Where predicted metabolic rate goes below the mouse–elephant curve, animals would be above their LCT and may have to lose considerable heat through evaporation or enhanced blood flow to specialized appendages (e.g., elephant ears) to maintain constant core. Note that the slope of the relationship between metabolic rate and body mass is considerably lower than expected from simple considerations of surface area/volume unless the organism is of uniform temperature, as is the case for copper sphere.

Fig. 4.

Metabolic rate relative to basal as a function of air temperature for a variety of mammals as measured in environmental chambers by Scholander et al. (24) (A) and as predicted by our analytical ellipsoid model of heat exchange in a furred endotherm (B) (see also Fig. S2). Parameter values are presented in Table 1.

Fig. 5.

Simulated lower critical air temperature (beginning of the TNZ) for different size endotherms as a function of posture and wind speed. Results are presented for animals with and without fur. Notice that smaller animals have much stronger response to lower wind speeds than larger animals because of their thinner boundary layer thickness and hence stronger coupling to air temperature effects.

Fig. 6.

Analysis of a Bergmann's cline in the Australian brush-tail possum (Trichosurus vulpecula) using the furred ellipsoid model (see Table 1 for parameter values). (A) The observed Bergmann's cline (from ref. 37) compared with the expected cline that would maximize time spent within the TNZ. (B) Latitudinal change in the predicted time within the TNZ for three different body sizes.