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. As air temperature rises above the lower critical temperature, metabolic rate rises again as animals attempt to dump excess heat, increasing energetic and water costs.

The original proposal relates to the need to conserve heat, because colder ambient temperatures might select for animals with lower surface‐area‐to‐volume ratios, which declines as body size increases (Bergmann, 1847; Peters, 1983). However, this does not necessarily mean that an animal should be as large as possible in cold conditions because the absolute rate of heat loss increases with size, meaning greater energy requirements (McNab, 1971; Ergon et al., 2004). Greater energy requirements makes starvation more likely, and more time must be spent foraging for food, perhaps exposing the animal to its predators. Thus, resource limitation and predation risk can constrain body size despite thermoregulatory advantages of being large.

The physiological maintenance of a stable internal temperature by mammals and birds – the phenomenon termed homeothermy – is well known to be energetically expensive. The annual energy requirements of free-living mammals and birds are estimated to be 15–30 times higher than those of similar-size ectothermic vertebrates like lizards. Homeothermic mammals and birds maintain constant body temperatures, independent of air temperature, by intensifying metabolic heat production as their environment becomes colder and often by using metabolic energy to drive cooling as conditions become hotter.

Rates of both heat production and heat loss are higher in larger species than in smaller species, but basal metabolic rate (BMR) increases with mass more rapidly than minimal thermal conductance (Cmin), so larger endotherms are predicted to have a higher ratio of BMR/Cmin, to have a lower minimal temperature (Tlc), and to be better able to tolerate colder temperatures than smaller organisms. Thus, larger endotherms are expected to have an energetic advantage in cold environments but may face greater challenges dissipating metabolic heat in warm environments.

Across ecosystems globally, pyramid structure becomes consistently more bottom-heavy, and per capita production declines with increasing biomass.[2] These data reveal two ecosystem-level power law scaling relations: (i) predator biomass versus prey biomass, which indicates how the biomass pyramid changes shape, and (ii) community production versus community biomass, which indicates how per capita productivity changes at a given level in the pyramid.[2] We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾.[2]

A previous finding highlights remarkable regularity in how the ratio of predator-to-prey biomass changes across a gradient of prey biomass in both aquatic and terrestrial systems.[10] Predator biomass, y, was found to scale with the biomass of their prey, x, in a sub-linear fashion on double logarithmic scales.[10] The power-law exponent, k, has been found to be <1 and consistently close to ¾ across ecosystem types, implying biomass pyramids become systematically more bottom-heavy with increasing prey biomass.[10] These empirical patterns could be underpinned by systematic changes in total prey production available to predators – that is, because predator biomass and prey productivity are linearly related; if predator biomass is sub-linearly related to prey biomass, then prey productivity should also be sub-linearly related to prey biomass.[10]

Endothermy is energetically costly; endothermic vertebrates tend to require at least an order of magnitude more energy than ectotherms of the same size. Energetic constraints on abundance are evidenced by the decrease in population density with increasing body mass, since larger organisms have greater energetic needs. Overall, observations support the prediction that the abundance of endotherms is jointly limited by temperature and energy availability.

Empirical observations indicate that endothermic animals utilize energy for maintaining body heat rather than growth. Although endothermic animals have a metabolic rate and energy intake that is less dependent on external temperatures than ectotherms, they require more energy to sustain internal heat generation. Consequently, endothermic birds and mammals display higher metabolic rates and energy intakes than similarly sized ectothermic species.

This leads to pyramidal patterns of biomass across trophic levels with remarkably consistent biomass scaling between prey and predators and between herbivores and vegetation.[1] We find high spatial variation in the relationship between plant and herbivore biomass, with both positive and negative divergence in observed biomass from expectations based on primary productivity.[1] In conclusion, our study shows that across large parts of Norwegian rangelands, herbivore biomass is high in relation to primary productivity and large carnivore biomass is low in relation to primary productivity.[1]

The risk of starvation is higher in cold and seasonal environments and should favour larger animals with greater energy stores at high latitudes; larger animals may also be favoured at high latitudes if they consume larger prey or a greater variety of prey sizes (‘starvation risk hypothesis’). However, larger body size also increases absolute energetic requirements, which can be disadvantageous when prey biomass or primary productivity is low. Thus, changes in resource availability and thermal environment jointly shape the energetic costs and benefits of large body size.

Temperature–size (T–S) responses tend to be negative (e.g. smaller body size at maturity when reared under warmer conditions), which has been termed the temperature–size rule (TSR). At higher temperatures, ectotherms require more resources to fuel their enhanced activity rates. Although this increased demand may not constrain growth it could increase the risk that resources (e.g. oxygen or food) become limiting under resource‐demanding conditions. Therefore, negative T–S responses could have evolved to avoid resource limitation. In warmer, more energetically demanding environments, maintaining a large body size can increase the risk of resource limitation and associated energetic costs.

Climate warming creates energetic challenges for endothermic species by increasing metabolic and hydric costs of thermoregulation. During summer, moose spent an average of 67.8% of daylight hours bedded, and selected bed sites and home ranges that reduced risk of experiencing heat stress. For most of the day, shade could effectively mitigate the risk of experiencing heat stress up to 10°C, but at warmer temperatures (up to 20°C) wet soil was necessary to maintain homeostasis via conductive heat loss.

Heat stress induces a metabolic shift from anabolism to catabolism, prioritising immediate survival over long-term growth. During heat stress, energy that would typically be directed toward growth is instead diverted toward thermoregulatory processes such as increased respiratory rate and vasodilation. This metabolic shift results in poorer feed conversion efficiency, meaning that more feed is required to achieve the same weight gain, ultimately increasing production costs.

Biomass of herbivores increased in response to primary productivity where canid predators were rare, but showed muted responses to increasing productivity where canid predators were common.[8] As primary productivity increases, herbivore biomass is predicted to increase strongly in two-trophic link systems where carnivores are absent or rare, but will show a comparatively weak response in three link trophic systems where carnivores are common.[8]

Bergmann’s rule states that body size tends to decrease toward the equator, as small body size (which produces a higher surface-area-to-volume ratio) results in more effective heat exchange with the ambient environment and hence is advantageous in warm conditions. Conversely, large body size (lower surface-area-to-volume ratio) effectively reduces heat loss, thus is favorable in cold conditions. Larger bodies, however, incur higher absolute metabolic and energetic costs, especially outside the thermoneutral zone, so thermal benefits of large size must be balanced against increased energy requirements in low-resource environments.

Large mammals generate more heat than do small mammals, but the amount of heat produced per unit weight declines with increasing weight. The basic rate among eutherian mammals is about 70 kcal kg^0.75 daily; in other words, for every doubling of the body mass, the basal metabolic rate per unit of body tissue decreases by about 15%. When subjected to severe heat, some large mammals, like the camel and the hippopotamus, increase their body temperature. For a 500-kg camel, a 7°C change in body temperature corresponds to 2900 kcal of heat and a saving of 5 L of water that would be required to maintain thermal balance via evaporative cooling.

Bio-physical models showed that allowing body temperature to change in response to stressors liberated up to 24% of resting energy expenditure for other uses. Regardless of body mass and ambient temperature, the models predicted that these body-temperature responses reduced energetic costs of maintenance by an average of 4.8%, and up to 24% of resting metabolic rate.

Ecological communities around the world are richly varied, but a new study finds that many of these diverse communities follow an unexpected, yet consistent pattern: where prey are abundant, there are not proportionally more predators.[9] Instead, as prey biomass increases, the ratio of predator-to-prey biomass decreases.[9] The authors note a clear pattern of biomass scaling, with an exponent consistently near ¾, where the biomass of predators is threefold less than the biomass of prey.[9] Similar changes are also observed when comparing per capita productivity and biomass, implying that in the absence of predators, prey populations increase if food is available, but with an ever-diminishing tendency.[9]

Bergmann’s rule is the propensity for species-mean body size to decrease with increasing temperature. Temperature-dependent oxygen limitation has been hypothesized to help drive temperature–size relationships among ectotherms, including Bergmann’s rule, where organisms reduce body size under warm oxygen-limited conditions, thereby maintaining aerobic scope. In water, however, oxygen solubility is temperature dependent, and because water is viscous, the energetic costs of respiration and ventilation are higher than in air. Under high thermal load and reduced oxygen availability, larger body sizes can increase energetic costs of maintaining metabolism, particularly when resources are limited.

The energetic costs of maintaining high body temperatures render endotherms sensitive to pressures that increase foraging costs. In response, some mammals become more heterothermic to conserve energy. Nominally homeothermic mammals often lessen homeostatic control of thermoregulation when faced with energy limitations.

Mule deer density exhibited a positive, linear relationship with plant productivity (r² = 0.58), varying by a factor of 18 across the climate‐vegetation gradient.[11] This pattern resulted in a strong, positive association between plant productivity and mountain lion density (r² = 0.67).[11] Despite varying densities, the ratio of prey to predator remained constant across the climatic gradient (mean ± SE = 363 ± 29 mule deer/mountain lion), suggesting that the determinacy of the effect of primary productivity on consumer density was conserved across trophic levels.[11]

Intra-specifically, Bergmann’s rule states that the body size (and thus, surface-area-to-volume ratios) of conspecific endotherms is typically larger in cooler environments than in warmer environments. This negative correlation between size and ambient temperature is generally thought to reduce the costs of thermoregulation by slowing rates of heat loss in the cold, and increasing rates of heat loss in the warmth. The Thermal Advantage Hypothesis posits that cooler temperatures lead to increases in cumulative growth during development, thus increasing adult body size and decreasing the total costs of thermoregulation at maturity. Contrasting the Thermal Advantage Hypothesis, the Energy Efficiency Hypothesis posits that ambient temperature influences cumulative growth during development by establishing the amount of resources available for growth by first setting energy cost of thermoregulation. Higher thermal loads elevate energy expenditure, so under limited resource availability, the energetic cost of maintaining larger body size increases.

Resource availability is a major constraint on the overall success of many organisms. Resource scarcity can limit the total number of organisms in a habitat, and over time can also cause organisms to adapt by becoming smaller in body size. Resource availability thus becomes a modifying restraint on Bergmann's Rule. As food or prey biomass declines, the advantage of large body mass can be offset by the increased energetic cost of sustaining that mass in a low-resource environment, particularly when combined with high thermal stress.

To explain his generalization, Bergmann proposed that increasing body size would reduce heat loss. He reasoned that, since heat loss is proportional to surface area, metabolic output should be proportional to body mass to the 0.67 power. Increasing body size would therefore decrease the metabolic output per unit body weight. They conclude that indeed increasing body size will decrease the metabolic rate per unit surface area to achieve thermal equilibrium. Size acts as insulation, reducing the metabolic output required for thermoregulation.

For both groups, activity is always costly at high temperatures, because ambient temperature is above the lower critical temperature, and always costly for animals with small body sizes and experiencing low ambient temperatures because heat loss exceeds heat production.

An important finding is that the mechanism of evaporation demands a high caloric cost for the organism and entails significant physiological alterations, such as excessive water loss that alters osmotic stability. As a result, food must be available to cover the caloric and water costs and stabilize this balance. An option is high caloric density diets so that the individual can replenish energy losses with a small amount of food.

A quality food resource can be profitably exploited through an increased basal metabolic rate attained in terrestrial mammals by increased muscle mass, and in birds and bats by increased blood flow and mitochondrial density in pectoral muscles. The exploitation of an unreliable food resource requires a reduction of energy expenditure, which is facilitated by a reversal of these adjustments. High-quality resources support high levels of energy expenditure in endotherms.

Second, across communities, predator biomass density increases sublinearly with prey biomass density, a ‘power law’ which often is assumed to arise from donor control.[6] Second, across diverse ecosystems, herbivore biomass density increases as a sublinear function of primary productivity, and predator biomass density increases as a sublinear function of prey biomass density.[6]

This research area explores how body morphology, thermal environment, and physiological capacities interact to affect energy metabolism, thermoregulation, and ultimately productivity in domestic and wild large mammals. It addresses acclimation, metabolic cost of thermoregulation, adaptive behavioral responses, and measurement techniques such as infrared thermography for monitoring thermal status.

The EEH predicts stepwise trophic relationships among plants, herbivores, and predators along an increasing net primary productivity (NPP) gradient.[4] The EEH also suggests that herbivore biomass increases linearly with increasing NPP in unproductive ecosystems (<0.7 kg/m²/yr), but remains somewhat constant in the presence of predators in productive ecosystems.[4] We expect 1) carnivore densities to be resource limited and positively correlated with primary productivity and 2) herbivores mainly predator limited, such that herbivore density increases only slightly with increasing productivity.[4]

Bergmann's rule states that colder climates spawn bigger bodies because they help retain heat while smaller bodies help shed it. Animals in warmer regions tend to have smaller body sizes, which aids heat dissipation but also reflects constraints imposed by higher metabolic costs and often lower resource availability in these environments. Studies suggest that warming and changing productivity can lead to shrinking body sizes, consistent with increased energetic costs of large bodies under high thermal stress and limited food.

Daytime temperatures during the rest-phase allow species to maintain normothermic body temperatures with low energetic costs, and activity during the cooler night phase offsets thermal challenges. Allowing body temperature to track ambient temperature saves energy that would otherwise be required to maintain a body temperature elevated above cold ambient temperatures, the cost of which increases as ambient temperature decreases and the defended body temperature remains high. A greater ambient–body temperature differential increases the ability to dump heat to the environment and thereby reduces energy and water costs.

However, the cooling rate diminished with elevation and body size: highland lizards, with larger masses, have a higher thermal inertia for cooling, which allows them to maintain heat for more time and keep a high body temperature despite the lower thermal availability. Larger body size in cooler environments can thus reduce the energetic cost of thermoregulation. In warmer environments, where thermal load is high, this thermal inertia may become disadvantageous, as large bodies can overheat and require additional energetic expenditure to avoid thermal stress, particularly if resources are limited.

The key result that emerged from our 8-year study is that indirect effects of an entire vertebrate predator assemblage on plant productivity and seed predation were remarkably weak, despite strong consumer effects on both plant biomass and seed survival.[7] Predators had no significant indirect effects on primary production.[7] These results suggest that vertebrate predators do not fundamentally influence primary production or seed survival in our system.[7]

High temperatures and thermal stress may lead to a decline in energy reserves. Individuals with higher levels of thermal stress, especially larger-bodied individuals with higher energetic demands, showed poorer energetic reserves. The authors conclude that attaining greater thoracic mass may entail higher physiological costs under thermally stressful conditions in disturbed sites.

Our results are consistent with the hypothesis that suppression of an apex predator triggers a trophic cascade, but are at odds with the EEH’s prediction that the magnitude of trophic cascades should increase with primary productivity.[5] Our study demonstrates that temporal fluctuations in primary productivity can have effects on biomasses of plants and consumers which are in many ways analogous to those observed along spatial gradients of primary productivity.[5]

Hypothesis 6: Resource availability shows that there is a positive correlation between the size of individuals and the quantity of resource available. Large bodies facilitate the accumulation of reserves and have a slower metabolism. These characteristics give them better resistance to hunger. Thus, the largest mammals, and therefore with the slowest metabolism, have better resistance to famine than smaller ones. Resource availability is therefore also an important factor in the variability of size. When resources decline, the energetic advantages of large size can be outweighed by the difficulty of acquiring enough energy to maintain that mass, especially under conditions of high thermal stress.

The high rates of metabolism in mammals (and birds) mean that relatively large amounts of heat are produced as a by-product. As ambient temperature falls below the thermoneutral zone, the metabolic rate increases steadily, which means that the amount of metabolic heat produced also increases. When conditions become increasingly colder, the animal is likely to lose a greater amount of heat than it would in warmer temperatures, so the extra heat production can compensate for this increased loss. This elevation of metabolic rate is termed a thermogenic response and is one of the most important distinguishing features of mammals.

Our overarching hypothesis is, at large spatial (regional to continental) and temporal (centennial to millennial) scales, consumer dominance in temperate North America is primarily driven by the bottom-up effects of moisture availability on primary production, as well as the type, continuity, and structure of vegetation available for herbivores and fire.[13]

Bottom-up models predict that consumer biomass tracks plant quantity (e.g. productivity and standing biomass) and quality (nutrient content) and that ectotherm access to food increases with temperature.[3] Each of the focal trophic groups responded differently to these drivers: the biomass of sucking herbivores and omnivores increased with plant biomass; that of chewing herbivores tracked plant quality; and predator biomass did not depend on plant quality, plant quantity, or temperature.[3]

Projected increases of 1 and 2°C in ambient temperature result in an increase in overall thermal quality at both coastal and inland sites. Population differences in modeled standard metabolic rate estimates were driven by body size and not field-active body temperature, with inland snakes requiring 1.6 times more food annually than coastal snakes.

Biophysical models revealed that allowing body temperature to change after a stressor liberated up to 24% (mean = 5%) of resting energy expenditure for use toward coping. Thermal responses of individuals with relatively high body masses (> 222 g), however, were less nuanced: body temperatures of these individuals tended to increase after a stressor regardless of the current ambient temperature. Regardless of body mass and ambient temperature, how body temperatures responded to stressors across these animals reduced energetic costs of maintenance by on average 4.8%, and up to 24% of resting metabolic rate.

A mouse housed singly at 22 °C devotes approximately 42% of its energy expenditure to maintaining its body temperature, whereas the corresponding value in humans is approximately 0%. Small mammals housed below their thermoneutral zone expend a large fraction of their total energy budget on thermogenesis. In contrast, large mammals are better insulated and obtain most of their heat from metabolic processes as a by-product, so they devote a smaller fraction of their energy expenditure specifically to thermoregulation under moderate conditions.

A body mass of around 100 g in endotherms has been hypothesized to be a transition zone below which ambient temperature increasingly affects residual basal metabolic rate. As body size decreases, the surface-area-to-volume ratio increases, and with it the energetic cost of maintaining body temperature.