Figure 1.
Rate of energy use as a function of ambient temperature (Ta) in mammalian species: interpretive framework and examples.
(A) The conventional metabolic rate-Ta relation in individual homeotherms [1]–[2]. Within the thermoneutral zone (TNZ), the animal’s metabolic rate, termed its RMR, is low and independent of Ta. The lower and upper limits of the TNZ are the lower (TLC) and upper (TUC) critical temperatures. Thermoregulation in the TNZ is achieved by autonomic modulation of body insulation: low near TUC but high near TLC. At Ta<TLC, body insulation is approximately constant, and accordingly the rate of metabolic heat production required for thermoregulation increases as Ta falls. The absolute value of the slope of this increase is conductance (C). Based on a first-order model, extrapolation is expected to intersect the abscissa at Ta equal to body temperature (Tb). (B-I) Metabolic rate-Ta relations in eight mammal species. Each symbol represents one individual at one Ta. Vertical dashed lines identify TLC and TUC where statistically defined. Horizontal dashed line identifies resting metabolic rate (RMR). Species and sources are: B, Pteronotus davyi [32]; C, Acrobates pygmaeus [33]; D, Peromyscus eremicus (Nevada) [34]; E, Desmodus rotundus [35]; F, Blarina brevicauda [36]; G, Peromyscus californicus (parasiticus) [34]; H, Sylvilagus audubonii (winter) [37]; I, Vulpes macrotis (winter) [38].
Figure 2.
Rate of energy use as a function of ambient temperature (Ta) in six North American cities.
Each plot covers 365 days, with each symbol representing one day. The rate of heat production each day is expressed per utility account (i.e., per separately billed house or other living unit), and Ta is the daily average (Table S1) for the same day. Taverage annual is the average Ta for all days included in the annual dataset. Lines between individual city Ta axes and the Taverage annual axis connect equal temperatures. Vertical and horizontal dashed lines are as in Fig. 1A. C is the absolute value of the slope at Ta<TLC (see Fig. 1A).
Table 1.
Statistical results for the six cities, listed (left to right) from highest to lowest average annual temperature.
Figure 3.
Meta-analysis of metabolic cost of thermoregulation in naked men: metabolic rate per person as a function of ambient temperature (Ta).
Men wore skimpy shorts and in some cases shoes (to peddle an ergometer). Values at Ta<−3°C were excluded from the regression analysis because subjects were notably uncomfortable under such cold conditions. Original papers presented metabolic rates as percentages of basal or resting metabolic rates, i.e., 100 = basal or resting rate, 200 = twice basal or resting, etc. Linear least-squares regression was carried out in this scaling domain: Metabolic rate as percentage of basal or resting = −9.812 (Ta − 37) (r2 = 0.98). For this plot, a 178-cm-tall, 70-kg subject (body surface area = 1.8 m2) [39] with resting metabolic rate = 1 met (50 kcal m−2 h−1 = 58 W m−2) [20] is assumed. A basal or resting metabolic rate of 104 W is thus assumed: Metabolic rate (W/individual) = −10.27 (Ta − 37). Citations: Erikson et al. 1956 [16]; Scholander et al.1957 [17]; Scholander et al.1958 [18]; Wilkerson et al. 1972 [19].
Figure 4.
Per capita energy demands of human thermoregulation by endogenous and exogenous heat production.
(A) Meta-analysis of all pertinent data available on thermoregulation in naked people from Fig. 3. (B) Metabolism-Ta curves for clothed people (equations and derivation in Table S2). Only a narrow thermoneutral zone (TNZ) is shown in each plot because a person would not elect to stay in the specified clothing at highly elevated Ta. Dot is a direct measurement on a man in winter sports clothing [16]. (C) The rate of addition of heat to the interior of Jack London’s Yukon cabin required to maintain an interior temperature of 20°C (Table S3): W/individual = −74.4 (Ta – 20°C). A cabin heated with hand-cut wood and devoid of electricity has no TNZ because the fire would be allowed to go out at high outside Ta. (D) Data from Fig. 2 for Ames, IA, a city with median properties, assuming 2.6 people per household [40]. Regression below thermoneutrality: W/individual = 2863 – 105Ta.