A brief history
Ever since the era of Charles Darwin biologists have been intrigued by how and why animals live where they do and what is it about their properties that makes them appear where they do, and appear in the species associations that they form. Hutchinson (1959) defined the concept of the niche. MacArthur et al. (1966), Roughgarden (1974) and many others explored aspects of how size and habitat may influence community structure. Norris (1967) and Bartlett and Gates (1967) were the first to calculate explicitly how climate affects animal heat and mass balance and the consequences for body temperature in outdoor environments. The climate space concept emerged from steady state heat and mass balance calculations and was used to explore how climates might constrain animal survival outdoors (Porter and Gates, 1969).
Those early animal models of the 1960s were limited by the lack of models for distributed heat generation internally, distributed evaporative water loss internally, and a first principles model of gut function. Batch reactor, plug flow and other models were already in existence in the chemical engineering literature (Bird et al., 1960) and it would take time for the biological community to rediscover them. Also missing were a first principles model of porous insulation for fur or feathers, an appendage model, and a general microclimate model that could use local macroclimate data to calculate the range of local microenvironments above and below ground. It became possible to estimate convection heat transfer properties knowing only the volume of an animal (Mitchell, 1976). Another useful development was the appearance of a countercurrent heat exchange model for appendages (Mitchell and Myers, 1968) and the measurement of heat transfer characteristics from animal appendage shapes (Wathen et al., 1971, 1974). It also became possible to deal with outdoor turbulence effects on convective heat transport (Kowalski and Mitchell, 1976). A general-purpose microclimate model emerged in the early 1970s (Beckman et al., 1971; Porter et al., 1973; Mitchell et al., 1975) that calculated above and below ground microclimates. The ability to deal with local environmental heterogeneity and calculate percent of thermally available habitat came later (Grant and Porter, 1992). Over time general-purpose conduction–radiation porous media models for fur appeared in the biological literature (Kowalski, 1978) and it became possible to refine and test them in a variety of habitats and on many species (Porter et al., 1994). The extension of the models to radial instead of Cartesian coordinates and the implementation of first principles fluid mechanics in the porous media (Stewart et al., 1993; Budaraju et al., 1994, 1997) added important new dimensions to the models, which could now calculate temperature and velocity profiles and therefore heat and mass transfer within the fur from basic principles. A test of the ectotherm and microclimate models to estimate a species’ survivorship, growth and reproduction at a continental scale appeared in the mid 1990s (Adolph and Porter, 1993, 1996).
Thanks to these developments and the ones reported in this paper, such as the temperature dependent behavior linked to the new thermoregulatory model, it is now possible to ask: “How does climate affect individual animals’ temperature dependent behavior and physiology and what role(s) does it play in population dynamics and community structure?” This paper attempts to address some of these questions.
We approach the problem from the perspective of a combination of heat and mass transfer engineering and specific aspects of morphology, physiology and temperature dependent behavior of individuals. We show how this interactive combination is essential to calculate preferred activity time that minimizes size specific heat/water stress.
Preferred activity time is a key link between individual energetics and population level variables of survivorship, growth and reproduction, since it impacts all three population variables. Both individual and population level effects may place constraints on community structure. At the individual level, climate at any given time and food type and quality affect the optimal body size that maximizes discretionary mass and energy, the resources needed for growth and reproduction. Climate also affects community structure by affecting individual survivorship directly (heat balance/metabolic costs) and indirectly (activity time overlap of predator and prey). Climate affects seasonal food availability, distribution of food in space and time, and the cost of foraging for that food at different times during a day. Survivorship is affected by temperature dependent behavior changes that allow animals to move to less costly microenvironments at any time. For small mammals, underground burrows or under snow tunnels provide temperatures that never stay below 0°C due to local heating effects of the animal’s metabolic heat production.
At the population level,climate plays a very important role in population numbers. Each species interacts in its own way with climate, affecting its abundance, and community structure. As Ives et al. (1999 p. 546) have pointed out
Our main result is that interspecific competition and species number have little influence on community-level variances; the variance in total community biomass depends only on how species respond to environmental fluctuations. This contrasts with arguments (Tilman and Downing, 1994; Lawton and Brown, 1993) that interspecific competition may decrease community-level variances by driving negative covariances between species abundances. We show that negative covariances are counteracted by increased species-level variances created by interspecific competition.
Consequently, assessing the effect of biodiversity on community variability should emphasize species-environment interactions and differences in species’ sensitivities to environmental fluctuations (for example, drought-tolerant species and phosphorus-limited species) (McNaughton, 1977, 1985; Frost et al., 1994). Competitive interactions are relatively unimportant except through their effects on mean abundances. We have focused on competitive communities, because much current experimental work has addressed competition among plants. Nonetheless, the same results can be shown to hold for more complex models with multiple trophic levels.
Exactly how climate variation, vegetation differences, animal morphology, and foraging behavior all interact to constrain multiple functional types’ existence as a community is still largely unknown. Very little is known about temperature dependent foraging in mammals, although this has been well studied in reptiles and insects. Quantitative consequences of functional morphology on encounter probability and food handling time also are relatively unexplored as yet in mammals.
Temporal climate variation in a locality creates the opportunity for multiple optimal body sizes over annual cycles. The spatial local variation in topography and vegetation creates multiple local climates. Thus temporal and spatial variation in climate creates opportunities for multiple functional types (sizes) to coexist as communities, because as we shall see below, different body sizes interact differently with climate. Qualitatively, this idea is not new. However with likely major shifts in global climates and the rapid global changes in land use, there is urgent need to move these qualitative ideas to a quantitative framework for protection of biodiversity, conservation biology, and a number of other applications. We focus in this paper on applications to mammals and birds.
An overview of this paper
The structure of the paper begins with an overview of how macroclimate drives microclimates, which in turn impact individual animal properties. We then show how key individual properties determine population level parameters that can be used to calculate population dynamics variables. We then illustrate how individual properties also impact on community structure, that in turn feed back to temperature dependent animal properties of individuals.
The initial overview provides a context for an analysis of the model components and their interactions in hierarchical contexts. We start with the model components from the core to the skin, then from the skin through the insulation to the environment. We demonstrate how these components collectively can define the metabolic cost to mammals ranging in size from mice to elephants. We show how the empirical mouse-to-elephant metabolic regression line for animals of different sizes changes depending upon the animal’s climate and posture.
Then we explore how changing mammal body size affects discretionary energy across all climates. Once the mammal model is explored, we repeat the process for the bird model. We demonstrate how we can estimate metabolic cost across bird sizes ranging from hummingbirds to ostriches. We show how postural changes and air temperature can alter metabolic cost estimates for birds.
Once sensitivity analyses are completed, we explore how temporal and spatial variation in global climate impact body size dependent discretionary energy assuming no food limitation and thereby place constraints on the potential combinations of body sizes (community structure) of mammals at the global scale.
Finally, we show how these models can be applied to estimate for the first time from basic principles the metabolic costs and food requirements of an endangered species of bird, the Orange-bellied Parrot of Tasmania and Australia. We show these results for body sizes ranging from hatchling to fully mature adult for a wide range of environmental conditions.
MATERIALS AND METHODS
(go to original paper for text and figures; topics and some sample text follow)
Survivorship (mortality) probability/hour
Growth and reproduction potential
Different sizes of animals
Model cross section
Inside the body
Heat generation models
Temperature regulation model
Temperature dependent feeding
Fur vs. feathers
Finite elements and flow through the fur
Modeling an individual
Internal body temperature profiles
Flow at very low wind
Scaling across mammal body sizes
Mouse to elephant metabolic rate
Mouse to elephant discretionary energy uptake
Diet effects on optimal body size
These results are reminiscent of Bergmann’s rule, an empirical observation that as climates get colder, animal sizes tend to get larger. Body size increases with decreasing temperature provide the greatest advantage at small size (Steudel et al., 1994). At larger body sizes, changes in fur insulation confer a greater advantage Steudel et al., 1994). Experimental data from different types of fur on a flat plate (Scholander et al., 1950) suggested this, but animals of larger size also have thicker boundary layers. A thicker boundary layer reduces convective heat loss and simultaneously enhances radiation temperature effects (Porter and Gates, 1969). Larger animals are taller, which means exposure to greater wind speeds higher above the ground. Higher wind speed reduces boundary layer thickness and may engender greater wind penetration of the fur. A first principles fur model can separate boundary layer effects due to size and wind from fur properties effects and provide better estimates of combined effects.
Assessment of consequences of Bergmann’s rule have pointed out that larger animals have the advantage of longer fasting ability under conditions of climate or food availability stress (Morrison, 1960). However, smaller animals have the advantage of lowering body temperature and seeking much more favorable microclimates, especially underground habits in severe cold. Careful transient modeling analyses of these two strategies in the animals’ microclimates would yield a testable hypothesis of the relative benefits of these different solutions to the same problem of dealing with cold.
Of course, survival in extreme temperature events is also important in affecting community structure. However, extreme temperature survival may be overrated in terms of its effects on community structure, at least for mammals. Temperature dependent behavior and selection of microhabitats by both small and large animals can greatly reduce cold or heat stress. For example, moving under or into trees and modifying the solar and infrared radiation and wind protection they provide can change equivalent local microenvironment temperatures by 20°C or more. Underground burrows or tunneling beneath the snow can provide habitats that typically do not drop below 0°C in winter when an animal is present, due to local heat from metabolism. Photoperiod-induced temperature dependent physiology, such as hibernation or estivation is another way that mammals can persist in habitats during periods of extreme heat or cold stress and thereby maintain community structure. Birds typically opt to migrate from extremely cold habitats in winter that they occupy in the summer. By exercising temperature dependent behavioral selection of microclimates through migration, the scale of their selection movements is simply larger due to the short time and lower costs of long distance bird transport.
Scaling across bird body size
Hummingbird to ostrich metabolic rates—Air temperature effect
Global communities-climatic constraints
Figure 16 shows temporal and spatial variation in optimal body size based on discretionary mass/energy for mammals for the months of January and July on a global scale. In January (winter) in the Northern Hemisphere, the optimal sizes are larger as one moves north. Large topographic features, such as the Rocky Mountains, are also predicted to have larger animals with their optima. In the Southern Hemisphere, where it is summer, topographic features do not stand out as strongly.
In July (winter) in the Southern Hemisphere there is somewhat of a “mirror image” effect on optimal body size. However, different topographic and latitudinal features create somewhat different patterns. In general, though, the model suggests that larger animals have the advantage. In the Northern Hemisphere at the same time smaller animals should have the advantage. Large topographic features like the Tibetan plateau with its cool weather in summer still show up fairly clearly as affecting optimal body size. For clarity, variation in vegetation type and food quality were not included in these graphs.
The criteria for optimization were maximum discretionary energy uptake for a given temperature at all possible body sizes. This figure was generated from the endotherm model driven by global weather data at half-degree intervals in latitude and longitude.
The map of optimal body size is different at different seasons of the year. This suggests that climate places important constraints on what functional types can coexist in a locality. Because the environment is constantly changing, it creates a constantly changing optimal body size in any locality. Changing environments create the opportunity for multiple functional types to coexist in the same area.
What is unknown at present is over what time intervals does natural selection integrate time and environmental conditions to “choose” body size? Figure 16 represents the beginnings of the effort to understand climatic constraints on community structure from basic principles. The vegetation on the landscape is certainly a very important variable that will modify the current version of the model. The spatial and temporal distribution of available food places important additional constraints on optimal body size. These constraints include encounter probabilities, handling time, food energy value and metabolic cost to get to the food. Three of these variables are related to body size and the “packaging” and “distribution” of food on the landscape. It is clear that this construct can also be applied to species of birds to study migratory patterns and other aspects of bird ecology.
It is important to note, as one reviewer did, that “evolution may select less for optima under average daily climate cycles and more for adaptations that increase survivorship during winnowing events. At any given time a population may consist of individuals with below or above optimal body sizes, should recent history include high mortality linked to extreme climate, with availability, or predation.” These important considerations have not been added to these models yet.
Conservation application: The Orange-bellied Parrot, Neophema chrysogaster
Ontogeny of metabolic costs
Surrogates for size in modeling metabolism
Body weight is a surrogate for body radius. Posture is a surrogate for body geometry. Empirical metabolism data collected since the time of Benedict in the 1930s have related metabolic heat production to body mass. However, mass is only one of the variables that drive metabolic heat production. A key variable is the radius of the trunk of the animal, which is in turn a function of the posture. Most of the analyses of metabolic scaling in the literature that we know ignore this important aspect. Furthermore, the role of a variety of environmental variables and different types of porous insulation in modifying metabolic demand have not been predictable because of the lack of reliable quantitative models.
However, our new animal models and the microclimate model that links them to macroclimate data have changed the outlook for understanding the quantitative relationships of these variables. Fortunately, there have been some careful experiments on endotherm heat loss in wind tunnels with solar radiation. They make it possible to test these models in much more realistic settings than metabolic chambers (Bakken, 1991; Bakken and Lee, 1992; Bakken et al., 1991; Hayes and Gessaman, 1980, 1982; Rogowitz and Gessaman, 1990; Walsberg, 1988a, b, c; Walsberg and Wolf, 1995).
Climate/body size effects on biodiversity
Body size affects discretionary mass and energy intake. Growth and reproduction potential affects fitness. As Figures 11 through 15 demonstrate, body size has important impacts through geometric form and radial dimensions on energy expenditure and intake. The surrogate for these primary variables is body weight (mass). We have pointed out here how air and radiant temperature and posture can make important modifications in energy cost in different environments. These energy costs are not linear with body size. Heat transfer mechanisms are not all linear with body size and neither are temperature regulation responses. Scaling of the gut is not linear with body size, either (Calder, 1984). The combinations of these nonlinear functions result in calculations that suggest discontinuous optimal body size with temperature. This is consistent with empirical data (Brown et al., 1993; Brown and Maurer, 1987; Brown and Nicoletto, 1991; Holling, 1992; Maurer et al., 1992; Peterson et al., 1998). However, there is an important reanalysis questioning these empirical results (Siemann and Brown, 1999). Our results of climate/body size/gut modeling suggest that whether or not animal sizes are clumped in nature may depend on the digestive efficiencies of foods consumed and the locations of those foods. High quality foods suggest greater clumping, low quality foods suggest very little in the way of body size clumping (Fig. 13a–d).
Body size effects on cost of foraging: temperature dependent foraging/activity time
Body size has multiple effects on cost of foraging. It affects heat and mass balance (Figs. 12, 13, 15, and 16). Body size affects cost of locomotion, which is constrained by the respiratory and mitochondrial systems of animals, as Taylor and his colleagues have so eloquently demonstrated (Mathieu et al., 1981; Taylor et al., 1982; Weibel et al., 1991). Their studies interface very nicely with recent work on animal scaling (Enquist et al., 1998; West et al., 1997, 1999).
The work presented here explains that changes in boundary conditions, such as environmental constraints on heat and mass exchange, alter fluxes and therefore alter internal scaling requirements that must adapt to changing needs. Thus, we suggest that temperature dependent behavior may be an important response to environmental change that tends to keep the organism as close as possible to optimal function as dictated by its internal and external anatomy, thereby maximizing fitness.
Body size determines whether a species can be fossorial or not, which affects diurnal microclimates and heat and mass balances. Body size affects likelihood of predation, which can be cast as a cost of foraging (Brown et al., 1994). Body size affects competition, which alters temperature-dependent activity time, which also affects cost of foraging.
Body size effects on total annual activity time
Body size effects on total annual activity time are mediated through heat and mass exchange with the environment. The onset of heat or cold stress appears to be an important constraint in limiting activity. That is, temperatures that force skin temperatures below 3°C or conditions where evaporative water loss must be elevated to protect organism integrity are bounds on activity time that impact animal fitness.
The boundary layer thickness in the air next to the animal surface constrains mass and heat transfer from an animal. Boundary layer thickness is a function of the friction between the animal surface and the air. The amount of friction depends on the dimension of the animal, fluid and animal speed relative to each other, and fluid properties of density, viscosity and thermal conductivity. On the one hand small animals have thin boundary layers and are more responsive to convective environments than to radiant heat exchange (Porter and Gates, 1969). On the other hand, large animals have thicker boundary layers and are more sensitive to the diurnal changes in infrared radiation and solar radiation fluxes in the environment. For large animals, absorption of radiant energy is a much greater challenge, since cooling by convective heat transfer is diminished because of the thicker insulating boundary layer around the larger animal.
Body size affects competitive success, hence temperature-dependent behavior including habitat utilization, which impacts on total annual activity time.
Vegetation/body size effects on biodiversity
Vegetation modifies microclimate conditions available to animals in predictable ways. Animal body size determines where animals spend their time in the wind patterns near the ground. Figure 16 is based on empirical climate data. Those empirical data reflect how vegetation may modify local microclimates. Vegetation also affects animal energetics either by direct shading of the animals or by providing cool surfaces that radiate back to animals. Thus, by directly and indirectly affecting the animal heat fluxes, vegetation impacts optimal body size and constrains functional types that might coexist in a community.
The distribution and quality of food in space and time changes in an annual cycle. Animal food encounter probabilities, and food handling time are consequences of vegetation structure and type. The calculations used in Figure 16 do not yet incorporate various possible distributions of food of various types in the environment. Diverse food distributions have not yet been explored using our models. Food encounter probabilities and handling times, which are a key part of food intake, are only beginning to be explored. The different food types, sizes and spacing also place important constraints on the range of body sizes of animals, which can efficiently utilize them.
Body size, cost of locomotion, and home range size are also interconnected. Home range size must be a function of body size, cost of locomotion, and the foraging thermal and vegetative environment. The minimum time and cost to forage for a particular type, distribution and size of food should be calculable for a broad range of body sizes and environments.
Feathers and plumage
When we watch the development of feathers through the ontogeny of a bird, it is apparent that the down structure is very much like the extremely dense fur of some mammals. Both types of fibers emerge from single openings in the skin as multiple fibers and then “fan out” in three dimensions as multiple fibers as they grow. In so doing they extend the layer of still air above the skin (and in the insulation) substantially. The second stage of plumage development with the eruption of feathers that tend to seal off air flow even further from the skin is unique in its efficiency of cross linking elements to hold complex units together and seal out air flow. The only fur that seems even closely comparable is that of the snowshoe hare that has fur tips that are flattened like tiny shovels (Porter, unpublished data). These structures probably assist in minimizing air and snow penetration into the coat.
The restriction of feather tracts to portions of a bird’s skin provide for flexibility in opening up skin areas to much more rapid heat transfer is also unique to birds. Some mammals like polar bears have inguinal regions that are highly vascularized and lightly furred. Polar bears sometimes apply them to the snow to dissipate heat, but mammals, unlike birds, have not evolved the ability to open large areas of nearly bare skin to dissipate or absorb heat.
1. Temporal and spatial variation in physical environments impose important constraints on functional types of animals that can coexist in biological communities. These constraints are further refined locally by food diversity representing different digestive qualities.
2. Morphology, physiology, and temperature-dependent activity in animals link individual energetics to population dynamics and community structure by specifying total annual activity time and mass/energy available for growth and reproduction.
3. Porous insulation in birds at rest can be modeled with current state-of-the-art fur models. Resting birds have feather positions that tend to seal off convective transport. This creates a conduction–radiation heat transfer environment. This is simpler to calculate than an environment where three heat transfer mechanisms are all important.
4. Posture plays an important role in metabolic heat loss. This is true mainly because posture affects the radial dimension of the animal, which is a key variable in the equation governing an animal’s total heat generation requirements. Posture is typically ignored in metabolic chamber metabolism studies. The model presented here allows the calculation of the upper and lower limits of metabolic expenditure for a wide variety of climatic conditions.
5. Animal geometry and posture, insulation properties, and environmental conditions influence “thermal conductance.” Thermal conductance is a term implying a passive transport of heat through a non-heat-generating medium. Thus, it is inappropriate for describing fluxes through flesh, where heat generation is occurring. It is also inappropriate in porous media that “act alive” by absorbing solar radiation in the insulation. Thermal conductance is affected by properties and boundary conditions that can have nonlinear effects on heat transport through the medium in question. It can be useful as a descriptive concept for heat source-free systems if all of the relevant boundary conditions and properties are specified.
6. The novel thermoregulatory model in conjunction with user specifications for diurnal/nocturnal/crepuscular activity allows for estimates of activity time that are in good agreement with published data.
7. Climate/body size/gut model calculations for different food types suggest that optimal body size (maximizing discretionary mass/energy) changes with different food types and their associated digestive efficiencies and the temperature. This suggests that vegetation diversity in a locality allows for specific multiple body sizes to coexist at the same point in time. As food quality declines from high digestive efficiencies of flesh/seeds to lower digestive efficiencies of grasses/leaves, optimal body size increases, lowest survival temperature rises, and the degree of clumping predicted for species in nature declines. Land use changes that tend toward monocultures would appear to dictate that fewer species would survive as vegetation diversity declines. Global warming trends would lead to smaller optimal body sizes with no change in vegetation. However vegetation changes associated with climate warming would specify larger or smaller body sizes depending on whether vegetation digestive qualities decrease or increase respectively.
8. Application of the microclimate and endotherm models to rare or endangered species requires relatively few, easily measured data to estimate food and water requirements, potential for activity time, growth, and reproduction for a wide variety of habits. This information will be useful as an aid for identification of potential reserves/transplantation sites and modification/management of existing habitats.
From the Symposium Evolutionary Origin of Feathers presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 6–10 January 1999, at Denver, Colorado.