Balancing heat, water and nutrients under environmental change: a thermodynamic niche framework


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  1. Models of the regulatory behaviour of organisms are fundamental to a strong physiologically-based understanding of species' responses to global environmental change. Biophysical models of heat and water exchange in organisms (biophysical ecology) and nutritionally-explicit models for understanding feeding behaviour and its fitness consequences (the Geometric Framework of nutrition, GF) are providing such an underpinning. However, temperature, water and nutrition interact in fundamental ways in influencing the responses of the organism to their environment, and a priority is to develop an integrated approach for conceptualising and measuring these interactions.
  2. Ideally, such an approach would be based on a thermodynamically-formalized energy and mass budgeting approach that is sparsely parameterised and sufficiently general to apply across a range of situations and organisms. Here we illustrate how mass-balance aspects of Dynamic Energy Budget theory can be applied to obtain first-principles estimates of fluxes of O2, CO2, H2O and nitrogenous waste.
  3. Then, using an herbivorous lizard (Egernia cunninghami) as a case study, we demonstrate how these estimates can be integrated with heat/water exchange models and environmental data to provide a holistic understanding of how foraging strategy, food availability, habitat and weather interact with heat, water and nutrient/energy budgets across the life-cycle.
  4. The analysis shows the potential importance of the water balance in affecting the energy budgets of ‘ dry skinned’ ectotherms, especially early in ontogeny, and highlights a significant gap in our knowledge of the physiological and behavioural traits that affect water balance when compared with our knowledge of thermal traits.
  5. In general, the modelling approach we describe can provide the thermodynamically-constrained stage on which other evolutionary and ecological interactions play out; the ‘thermodynamic niche’. This in turn provides a solid foundation from which to tackle key questions about organismal responses to environmental change.


Conservation physiology is emerging as a vital approach for understanding how organisms are responding to global environmental changes and for forecasting how they will respond in the future (Wikelski & Cooke 2006; Seebacher & Franklin 2012). A key feature of conservation physiology as a discipline is that it focuses on mechanistic processes mediating physiological responses to environmental change. Primary among these are the regulatory behaviours that balance the thermal, hydric and nutritional states of the organism. The distribution and abundance of organisms reflects, in part, the extent that they can defend some degree of homoeostasis in these state variables under environmental changes. Our understanding of the efficacy of, and constraints on, such regulatory behaviour is therefore critical to predicting impacts of global environmental changes such as climate change (Williams et al. 2008).

Often, the regulation of temperature, water and nutrients is considered separately. There are strong connections and interactions between these state variables, however, and consequently, an animal's regulatory behaviour must often represent homoeostatic compromises. Moreover, nutrition itself is often considered in a univariate sense (e.g. energy only), but, in a multinutrient space, there can be important homoeostatic compromises both in terms of ingestive behaviour and body composition, with ensuing consequences for fitness (Simpson & Raubenheimer 2012).

Raubenheimer, Simpson & Tait (2012) recently emphasized the strong similarities between conservation physiology and nutritional ecology as disciplines. Both disciplines aim to understand how organisms balance compromises in their regulatory responses to environmental change, viewed in the context of evolutionary fitness. Raubenheimer, Simpson & Tait (2012) further suggested that an integrative framework developed within nutritional ecology, the Geometric Framework for nutrition (GF), could be extended to areas within conservation physiology. This framework takes individual nutrient regulation responses to changed environmental conditions as the focus, but explicitly considers the consequences across multiple levels of biological organization (populations, communities and associated biotic interactions) and across multiple time-scales (learning, phenotypic plasticity, epigenetics and adaptation) (see fig. 2 in Simpson et al. 2010). Such a framework produces an understanding of the regulatory behaviour of organisms in a manner that is nutritionally (i.e. physiologically), organismally and ecologically explicit (sensu Raubenheimer, Simpson & Mayntz 2009).

The connections between thermal, hydric and nutritional regulation represent a ripe area for integrating further aspects of conservation physiology within the Geometric Framework. The explicit interactions and compromises among nutrients, water and temperature, and their impacts on fitness, are rarely considered jointly, perhaps because such models could be extremely parameter rich and of low generality when based on species-specific, empirically determined functions. However, the unification of these interactions in a thermodynamic framework can reduce the potential complexity of such models while simultaneously increasing their generality. For example, Kearney et al. (2010) provided an overview of how the thermodynamic principles applied in biophysical ecology and metabolic theory can be integrated to provide a thermodynamically grounded model of the niche. They showed how dynamic energy budget (DEB) theory provides a parameter sparse framework to connect behaviour with temperature, water and nutrient homoeostasis, and to determine the implications of different behavioural ‘strategies’ (for growth, development, reproduction, senescence, etc.). This modelling approach, which we here describe as capturing the ‘thermodynamic niche’, provides a powerful foundation for building a physiologically grounded understanding of the topic of this special issue of Functional Ecology – how species will respond to global environmental changes.

In this article, we extend the ideas outlined previously by providing a deeper analysis of how the mass aspects of DEB theory can be applied jointly with biophysical models of heat and water exchange. In particular, we show how such a model can be used to consider the consequences of foraging behaviour for heat, water and nutrient balance, using the conceptual framework of the GF. Such a modelling framework opens up exciting possibilities in the development of dynamic, spatially explicit models of organisms interacting in climatic and nutritional environments (Simpson et al. 2010). We illustrate the approach using the example of an herbivorous, rock-dwelling lizard from Australia, the Cunningham's Skink Egernia cunninghami. Our goal is to show how this ‘thermodynamic niche’ modelling approach can be used to enrich our understanding of the regulatory responses of organisms to environmental change and how these affect their continued persistence.

Heat, water and time budgets, and their connection to metabolism

The field of biophysical ecology (Porter & Gates 1969; Porter et al. 1973; Gates 1980; Campbell & Norman 1998) applies thermodynamic principles to organisms to predict their body temperature and water balance. Such models are increasingly being applied together with spatial environmental data to make physiologically grounded predictions of species responses to environmental change (Kearney & Porter 2009).

Biophysical models are derived from the physics of heat/mass exchange through the processes of radiation, conduction, convection and evaporation (Fig. 1). In the case of the Cunningham's skink, for example, the body temperature Tb can be predicted from knowledge of a set of functional traits that include the surface areas of its body exposed to convective and conductive heat exchange, the silhouette area to solar radiation, solar reflectivity, infrared emissivity, volume, density and specific heat capacity (Table 1), together with the environmental factors of air temperature, wind speed, solar and infrared radiation levels and substrate temperature experienced by the organism. A calculation of steady-state body temperature on this basis is referred to as the ‘operative’ environmental temperature Te. The biggest challenge in making such calculations, however, lies in determining what environments are actually experienced, which depends in part on the microclimatic conditions available in the lizard's habitat, as well as the way the lizard behaves in that habitat. Throughout this article, we use the software package NicheMapR (M.R. Kearney and W.P. Porter, in prep.), which provides an integration of DEB theory with the biophysical modelling facilities of the programs described by Beckman, Mitchell & Porter (1973), Porter et al. (1973), Porter & Mitchell (2006) and Kearney (2012).

Table 1. Animal heat/water budget model parameters
εbody, skin longwave infrared emissivity1·0Assumed
αbody, skin solar absorptivity0·857Fraser (1985)
ρbody, flesh densitykg m−31000Assumed
kbody, flesh thermal conductivityW m−1 °C−10·5Assumed
Cbody, flesh-specific heat capacityJ kg−1 K−14185Assumed
Fbody,sky, configuration factor body to sky0·4Porter et al. (1973)
Fbody,sub, configuration factor body to substrate0·4Porter et al. (1973)
A, lizard surface areacm210·4713 inline image where Ww is wet weight in gPorter et al. (1973)
Asil, silhouette area normal to the suncm23·798 inline image where Ww is wet weight in gPorter et al. (1973)
Fsub, fraction of surface area contacting the substrate0·1Assumed
Fwet, fraction of surface area that is wet0·01Assumed
inline image, oxygen extraction efficiency0·2Perry (1992)
FH,X, fraction water in food0·82Shine (1971)
FH,P, fraction water in faeces0·73Shine (1971)
Δresp, temperature difference between expired and inspired air°C0·1Assumed
Figure 1.

Coupled heat/mass balance equations for an organism (modified from Porter & Tracy 1983). The terms in red represent the heat balance and, in a biophysical model, are calculated using the physical equations for heat exchange. The terms in brown and blue, within the shaded grey area, represent connections between the mass balances (food/water/gas exchange/excretion) and the heat balance, and are normally based on empirically determined relationships. However, dynamic energy budget theory provides a mechanistic link between these metabolic processes and the heat/mass balance.

The first challenge of understanding available microclimates can be tackled by combining weather station data with microclimate models. For the case of the Cunningham's skink, for example, we can drive the microclimate model (described in Porter et al. 1969) of NicheMapR with historical continent-wide 0·05° grids of daily minimum and maximum temperature, vapour pressure, rainfall and daily solar radiation available through the Australian Water Availability Project (AWAP, Raupach et al. 2011) (Fig. 2). The microclimate model calculates the clear sky solar radiation from first principles, and we can account for cloud cover effects on solar (and infrared) radiation exposure through the AWAP daily solar estimates (i.e. observed daily solar over calculated clear sky solar). In the absence of interpolated daily wind speed data, we use gridded long-term average wind speed (obtained from ANUCLIM, Houlder et al. 2000). Using the thermal properties of a rock type commonly used by the Cunningham's skink (granite) (Table 2), we can apply the microclimate model to obtain estimates of surface temperature and temperatures in crevices at different depths within the granite, including the effects of rain (producing a wet rock surface) and vapour pressure on the heat budget of the substrate. In sum, these microclimate calculations provide highly realistic (see Fig. 3) hourly estimates of the microclimatic conditions above and below ground available to the Cunningham's skink over a 20-year period from 1990 to 2009.

Table 2. Microclimate model parameters
δsub, roughness height of the substratem0·00268Default
εsub, substrate longwave infrared emissivity0·96
αsub, substrate solar absorptivity0·82M.R. Kearney, unpublished (natural granite rock)
ρsub, substrate densitykg m−32560Cho, Kwon & Choi (2009)
ksub, substrate thermal conductivityW m−1 °C−12·79Cho, Kwon & Choi (2009)
csub, substrate-specific heat capacityJ kg−1 K−1790
Figure 2.

Interpolated environmental data for the year 1998, an El Niño year, at Weetangera near Canberra, Australia from 0·05° resolution continent-wide surfaces. The daily minimum and maximum air temperatures (a), integrated solar radiation (b), rainfall (c) and vapour pressure (d) are extracted from the Australian Water Availability Project database (Raupach et al. 2011), while monthly estimates of pasture biomass (e) and growth (f) are from the Aussie Grass database (Carter et al. 2000).

Figure 3.

Predicted and observed environmental and body temperatures for the Cunningham's skink Egernia cunninghami at Weetangera, near Canberra, Australia. The predictions were made using the software package NicheMapR (M.R. Kearney and W.P. Porter, in prep.) and include predictions of granite surface temperature, temperature in a 20-cm deep crevice and core body temperature of an adult lizard foraging according to the parameters in Tables 1-3. Observed data come from Shine (1971).

The second challenge, of predicting the behaviour of the Cunningham's skink, is where the core biology enters the problem. From a heat-only perspective, we need to know the activity period of the lizard (nocturnal, diurnal and crepuscular), at what body temperatures it will voluntarily leave its rock crevice and bask or forage, and what its preferred temperature is (Table 3). Moreover, we can use the critical thermal limits to predict at what depth in the granite the lizard will need to go to avoid temperature stress. Examples of such calculations for summer, spring and winter in 1998 for Weetangera, a site near Canberra where the species has been studied extensively (Barwick 1965; Shine 1971) are compared in Fig. 3 compared with empirical observations at the same site in 1971.

Table 3. Animal behaviour parameters
CTmin, critical thermal minimum°C4·7Spellerberg (1972)
CTmax, critical thermal maximum°C41·9Spellerberg (1972)
inline image, minimum temperature for leaving crevice°C14·0Fraser (1985)
inline image, minimum basking temperature°C14·0Fraser (1985)
inline image, minimum foraging temperature°C28·6Fraser (1985)
inline image, maximum foraging temperature°C35·4Fraser (1985)
Tpref, preferred temperature°C35·1Fraser (1985)
inline image, fractional stomach-fill triggering foraging0·75Assumed
inline image, fractional body water preventing emergence0·65 or 0·95Assumed

The metabolism of the organism affects the heat/water budget in two ways: heat and water produced by metabolic processes and heat and water lost through respiration. For a lizard, metabolism has a negligible impact on the heat budget, but it is of great importance to the water budget. The metabolic contributions to the heat/mass budget are typically estimated empirically from data for a given species or taxonomic group. For example, the ‘Niche Mapper’ system, when applied to lizards (e.g. Kearney & Porter 2004), has used the allometric equation of Bennett and Dawson inline image to predict metabolic heat production inline image given the wet body mass Ww and the body temperature estimate Tb. This can then be converted to O2 consumption rate to estimate mass flow through the lungs and hence the respiratory water exchange. It also uses fixed yields of water from metabolism given the proportion of the food assimilated that is protein, carbohydrate and lipid. Ideally, however, one would derive these from the metabolism from first principles, and this can be achieved with DEB theory, which we illustrate next.

Dynamic energy budget theory: mass and energy aspects

Despite its name, DEB theory explicitly considers fluxes of both energy and mass through an organism (Fig. 4). Mass fluxes are denoted by the symbol inline image (mass/time), while energy fluxes (referred to as ‘powers’) are denoted by the symbol inline image (energy/time), and one can easily switch between a mass or an energy frame of reference using the couplers μ (energy/mass) and η (mass/energy). Under the DEB theory framework, the rates of food intake inline image and energy assimilation inline image are explicitly related to food density through a functional response curve f = X/(X + XK), where X is the food density (J ha−1) and XK is the half-saturation constant (J ha−1). Development, growth and reproduction are predicted dynamically according to the κ-rule whereby a fixed (throughout ontogeny) fraction κ of the energy/matter mobilized from the ‘reserve’ (see below) inline image flows to growth inline image and to somatic maintenance inline image (and heat production inline image in the case of endotherms), the rest inline image to maintain inline image the level of maturity EH, and, with the remainder, inline image, either increasing the maturity level or, once maturity is reached, to reproduction (Fig. 4).

Figure 4.

Overview of standard DEB model of metabolism, showing processes (ellipses), state variables (boxes), energy fluxes inline image and ‘mineral’/heat fluxes (red arrows).

Mass balances must be made not just in terms of grams of compounds (food, biomass and faeces), but in terms of chemical elements. The strategy under DEB theory is to model the mass balance of the organism as a number of compartments, each of which does not change in chemical composition through time – the ‘strong homoeostasis’ assumption. A key feature of DEB theory is the qualitative distinction of these mass compartments as either ‘structure’, V, or ‘reserve’, E (including the reproduction buffer ER). The structure is the ‘permanent’ biomass and requires energy and matter for its maintenance (protein turnover and the maintenance of concentration gradients and ionic potentials) in direct proportion to structural volume. Both the structure and reserve may consist of, for example, fat, carbohydrate and proteins distributed throughout the body. As reserve is used and replenished, it does not require maintenance. The DEB approach is to define as many reserve and structure compartments as is necessary to meet the assumption of strong homoeostasis. These stoichiometrically fixed, abstracted compartments can then be quantified using the concept of the ‘C-mole’, which gives the numbers of hydrogen, oxygen and nitrogen atoms relative to carbon atoms. Thus, the C-mole expression for glucose (C6H12O6) is CH2O, and one mole of glucose equals 6 C-mol of glucose.

In the ‘standard DEB model’, only one structure V and one reserve E are used and isomorphy of the reserve/structure interface is assumed. These components, together with the ‘food’ X and the ‘products’ P (e.g. faeces), are called ‘organics’, and their composition in C-moles is summarized by the matrix

display math

The example matrix of nO above is based on the compositions and enthalpies of key macromolecules such as proteins, carbohydrates and lipids (Kooijman 2010). The composition of the ‘minerals’, carbon dioxide C, oxygen O, water H and the nitrogenous waste product N, respectively, is summarized by the matrix

display math

Note that the nitrogenous waste product may vary, with the example matrix showing the formula for uric acid for the case of a lizard.

Then, the conservation law for mass means that the mass fluxes inline image of the minerals and organics must balance, that is

display math

or, in matrix form, inline image.

The organic fluxes inline image relate to the energy fluxes associated with three ‘powers’: assimilation inline image, growth inline image and ‘dissipation’ inline image as

display math

because each of these three processes can be represented by a single macrochemical reaction equation with constant coefficients (Kooijman 2010, p. 139). Heat production is also weighted sum of these three powers. In the aforementioned formula, the dissipation term inline image is the sum of somatic maintenance inline image, maturation inline image, maturity maintenance inline image and reproduction overheads inline image where κR is the efficiency of yolk production from reserve. In addition, μE is the chemical potential of reserve (J mol−1), ηXA is the coefficient coupling the flux of food dry mass to assimilated energy flux (mol J−1), ηVG couples the mass of structure to the growth energy flux, and ηPA, ηPD and ηPG couple mass flux of product (faeces) to the assimilation, dissipation and growth energy fluxes, respectively.

In this way, the DEB theory provides a mechanistic underpinning to indirect calorimetry and predicts the respiration rate (O2 consumption and CO2 production), metabolic water and nitrogenous waste. Respiration and urination quotients, and entropy production, can also be derived from this (see Kooijman 2010; Chapter 4, for further details). It thus makes the scheme depicted in Fig. 1 maximally mechanistic by providing the heat and water production from metabolism, as well as the respiratory gas fluxes that are needed for calculating respiratory water loss. It also quantifies nutrient fluxes in terms of the quality and quantity of food eaten and faeces and other products produced, therefore providing a powerful link to nutritional ecology.

Estimating DEB parameters and mass exchange for the Cunningham's skink

Dynamic energy budget model parameters cannot be measured directly because they relate to the abstract-state variables of reserve, structure and maturity. However, because of the one-to-many relationship between DEB parameters and observable outcomes of the energy budget, such as wet mass, physical length and growth rate, the parameters can be estimated in an inverse fashion from a wide range of empirical observations using an approach called the ‘covariation method’ (Lika, Kearney & Kooijman 2011; Lika et al. 2011). We fitted the DEB parameters for E. cunninghami using observations of its length and weight at birth, maturity and asymptotic size, together with temperature-specific observations on time to birth, maturity and death, and reproductive frequency (Table 4a) (see Kearney 2012 for more details on DEB model parameter estimation from this kind of data). The associated Matlab scripts used to estimate the parameters can be found at The DEB parameter estimates for E. cunninghami are presented in Table 4b. From these, we can predict the trajectory of growth (Fig. 5a), differentiation and reproduction under any combinations of food level and body temperature, as well as the associated metabolic mass fluxes of O2 (Fig. 5b,c), CO2, H2O, uric acid, food intake and faeces production.

Table 4. (a) Observed and predicted values from the DEB ‘covariation’ parameter estimation procedure for Egernia cunninghami and (b) resulting DEB parameter estimates (rates corrected to 20 °C), and additional DEB parameters either independently observed or assumed to have default values
(a) Observed and predicted data
DataObs.Pred.UnitsData source
ab, age at birth10593·7days (28·5 °C)Table 2, Chapple (2003)
ap, age at puberty16121628days (20·7 °C)Barwick (1965)
lb, length at birth7·06·6cmBarwick (1965)
lp, length at puberty19·018·1cmBarwick (1965)
l, maximum length21·623·6cmBarwick (1965)
Wb, mass at birth1·791·9g, dryBarwick (1965)
Wp, mass at puberty49·340·4g, dryBarwick (1965)
W, maximum mass83·388·8g, dryBarwick (1965)
R, max reproduction rate5·87·8# year−1 (20·7 °C)Barwick (1965)
(b) DEB parameters
  1. DEB, dynamic energy budget; SVL, snout-vent length.

  2. The shape coefficient is for SVL. The temperatures for the observations of ab, ap and R were obtained using NicheMapR to simulate hourly body temperatures and associated Arrhenius temperature correction factors for the locations and periods for which the observations were made and determining the body temperature corresponding to the mean value of the temperature correction factor across all hourly temperatures.

z, zoom factor (relative volumetric length)5·027Estimated
δM, shape correction factor0·2131Estimated
v, energy conductance0·02735cm day−1Estimated
κ, allocation fraction to soma0·5667Estimated
[pM], somatic maintenance28·28J cm−3 day−1Estimated
[EG], cost of structure7523J cm−3Estimated
inline image, maturity at birth1·576 × 104JEstimated
inline image, maturity at puberty3·323 × 105JEstimated
κX, digestion efficiency0·85Shine (1971)
κR, reproduction efficiency0·95Default
inline image, maximum specific stomach energy1116J cm−3Barwick (1965)
inline image, maximum specific food intake13 290J cm−2Wilson (1964) and Shine (1971)
XK, half-saturation constant365J ha−1Assumed
dV, density of structure0·3g cm−3Shine (1971)
WV, molecular weight of structure23·9g C-mol−1Default
μX, chemical potential of food525 000J C-mol−1Default
μE, chemical potential of reserve585 000J C-mol−1Default
μV, chemical potential of structure500 000J C-mol−1Default
μP, chemical potential of faeces480 000J C-mol−1Default
κXP, fraction of food energy into faeces0·1Default
TA, Arrhenius temperature7716KWilson (1964) and Pollock (1989)
TL, lower bound for TA280KMatched to critical thermal minimum
TH, upper bound for TA312KMatched to critical thermal maximum
TAL, value of TA below lower bound50 000KKearney (2012)
TAH, value of TA above upper bound90 000KKearney (2012)
Figure 5.

Dynamic energy budget (DEB) theory predictions and observed data on growth and oxygen consumption rate for the Cunningham's skink Egernia cunninghami. All DEB theory predictions are represented by the dashed grey line and are based on the parameter estimation procedure summarized in Table 4. For growth data, observations (black squares) come from Pollock (1989). For respiration data (b, c), the black solid line comes from the allometric equation estimated by Pollock (1989), while the black dots come from Wilson (1964) for a mean mass of 261 g. The allometric equations in b–c are fits to DEB predictions (top equations) and those observed by Wilson (1964) (bottom equations).

As a worked example of how the mass balance can be calculated, consider a hatchling Cunningham's skink that has the state variables V = 2·63 cm3, [E] = 9172 J cm−3 and EH = 15 760 J. This lizard would have a dry mass of

display math

where dV is the density of structure (g cm−3), wE is the molar weight of reserve (g mol−1), and μE is the chemical potential of reserve (J C-mol−1). Assuming 78% water for juveniles (Shine 1971), the wet mass is inline image.

As described previously, the mass balance is inline image thus, to get the ‘mineral fluxes’ of carbon dioxide, water, oxygen and nitrogenous waste inline image for this 7·1 g newborn we need

display math

We then need to obtain

display math

The mass/energy coupler relating the mass of food ingested to the energy assimilated, ηXA = (κXμx)−1 = (0·85 × 525 000)−1 = 2·24 × 10−6 C-mol J−1, where μx is the chemical potential of food and κX is the digestive efficiency (Table 4). The mass/energy coupler relating the mass of structure produced to energy allocated to growth, ηVG = dV(WV[EG])−1 = 0·22 × (23·9 × 7523)−1 = 1·22 × 10−6 C-mol J−1, where WV is the molecular weight of structure. The mass/energy coupler relating the mass of faeces produced to energy allocated to assimilation, ηPA = κXP(μPκX)−1 = 0·1 × (480 000 × 0·85)−1 = 2·45 × 10−7 C-mol J−1, where κXP is the fraction of energy from food that appears in the faeces and μP is the chemical potential of faeces (Table 4). In this case, because the ‘product’ is faeces, ηPD and ηPG = 0.

Next, we need the assimilation, dissipation and growth powers, which we will calculate here for the case of the preferred activity Tpref of 35·1 °C and ad libitum food (i.e. f = 1 and adjusting the rate parameters according to the Arrhenius parameters in Table 4). The assimilation power inline image. The energy flowing out of the reserve that is available for use by the newborn for maintenance, growth and differentiation, that is the mobilization rate,

display math

Part of this energy flow is being dissipated through somatic and maturity maintenance, as well as through the increase in maturity (differentiation), that is inline image where inline image, inline image and inline image. Thus, inline image. Finally, the remaining energy flowing out of the reserve goes to growth, inline image.

Thus, inline image

display math

or 0·090 g of dry food eaten, 0·034 g of total dry mass grown (reserve plus structure) and 0·010 g of dry faces produced per day. We can then complete the calculation for the ‘mineral’ fluxes,

display math

or 67·0 mL CO2 day−1, 0·029 g H2O day−1, −85·0 mL O2 day−1 and 0·012 g uric acid day−1.

Estimating the water budget from energy and heat budgets

The total water budget for an organism, as depicted in Fig. 1, is the mass of water ingested in the food or through drinking inline image plus the metabolic water produced inline image less the water lost in the urine inline image, faeces inline image and through evaporation (respiratory inline image and cutaneous inline image). In the previous section, we showed how DEB theory can be used to compute the mass balance of a hatchling Cunningham's skink in terms of its dry food intake and faeces production, the resultant change in dry mass (reserve and structure), the O2 consumption rate and the production of CO2, metabolic water and uric acid. Thus, with the additional knowledge of the water content of the food, faeces and urine, the permeability of the skin to water (Table 1) and the evaporative power of the environment, we can compute all aspects of the water budget.

The respiratory and cutaneous water loss rates are, respectively, inline image and inline image, where inline image is the volume of oxygen consumed per time, inline image is the oxygen extraction efficiency, RH is the relative humidity, hD is the mass transfer coefficient, Askin is the skin surface area, Fwet is the fraction of the skin area that acts as a free water surface across which mass exchange occurs, and ρH is the density of water vapour at saturation, indicated for the temperature of the body, air or skin. The mass transfer coefficient can be calculated using the Colburn analogy to relate the heat transfer coefficients for both free and forced convection to mass transfer (Tracy 1976; Bird, Stewart & Lightfoot 2002). Two key parameters for determining evaporative water loss are therefore inline image and Fwet. Unfortunately, neither of these parameters is commonly measured for reptiles, and they are unknown for the Cunningham's skink. Here, we assume an O2 extraction efficiency of 0·2, as was measured for a number of reptiles at a Tb of 35 °C (Perry 1992). The parameter Fwet can be obtained from data on cutaneous water loss (see appendix D in Kearney & Porter 2004). We used a figure of Fwet = 0·01 (i.e. 1% of the skin surface area is ‘wet’) for the Cunningham's skink, which produced estimates of total evaporative water loss typical for semi-arid to mesic habitat lizards (Mautz 1982).

Using the newborn Cunningham's skink again as an example, in 35·1 °C air at 30% rh with a wind speed of 0·1 m s−1, JH,RESP = 0·244 g day−1 and JH,CUT = 1·042 g day−1. Assuming a food water content of 82%, a faecal water content of 73% (Shine 1971), and no water loss through the production of uric acid, the water balance or net water stored, would be inline image, and thus, the lizard would have to drink 0·874 mL of water per day to maintain a positive water balance in this environment.

From the previous two sections, it should be apparent that the water budget is intimately related to the energy budget, not only via the direct physiochemical connections quantified by DEB theory, as just described, but also through behavioural choices of what foods to eat, how much food is eaten, whether to seek drinking water and under what environmental conditions the animal forages. We next consider how the Geometric Framework of nutrition can be used to understand how animals might alter their foraging behaviour to deal with trade-offs in balancing water and energy budgets in different environments.

The geometric framework of nutrition and the interpretation of energy and water budgets

The Geometric Framework for nutrition (GF) is an approach based on state space geometry for modelling the nutritional interactions between organisms and their environments. It is a conceptual tool for interpreting patterns in the relationship between food composition, nutrient consumption, nutrient allocation and fitness components in multivariate nutritional space. Each axis in the state space represents a food component that is functionally relevant to the animal (Raubenheimer & Simpson 2009). This could include various nutritional components of the dry mass of food, such as protein, carbohydrate and salt, but may also include water (Raubenheimer & Gäde 1994). Under the GF, foods are represented as open-ended trajectories termed ‘nutritional rails’, which radiate from the origin through the hypervolume at angles defined by the balance they contain of the defining components (see Fig. 6). As the animal eats, it ingests the food components in the same balance as they exist in the food and can thus be modelled as ‘moving’ along the nutritional rail at a rate determined by the rate of ingestion and density of nutrients in the food. By selecting different foods and regulating the rate at which each is eaten, animals can thus navigate through nutritional space, inhabiting those areas that confer fitness advantages and avoiding others. The area of maximal advantage is termed the ‘intake target’. This is not a static area, but moves and changes shape as the animal encounters differential demands for nutrients (e.g. with ontogeny, activity levels, environmental conditions, health and reproductive status). The intake target relates to the ‘growth target’ as the optimal amounts of each nutrient ingested that are invested as biomass in the form of somatic growth, storage and reproductive investment. Growth, as just defined, may exceed the nutrient target if the animal is forced to feed on a diet that is unbalanced and therefore requires over-ingestion of the nonlimiting nutrient(s). The foraging challenge for the animal is thus to track its moving intake target and, to the extent that it is constrained by ecological or other factors, realized nutrition-derived fitness benefits are inversely proportional to the distance it achieves from the target.

Figure 6.

Simulated consequences on the water budget of intake along different ‘nutritional rails’ in a two-dimensional space of water and dry food for hatchling and adult Cunningham's skinks Egernia cunninghami. The dark contour lines represent the water balance, with zero representing balanced hydration (they are slated because water balance is a function of food intake). The light grey rails radiating from the origin represent diets differing in water content from 0% to 95%. The red bars show an intake ‘rule of compromise’ representing a non-negative water balance and sufficient dry matter intake to pay for all metabolic processes, assuming dry food is balanced in nutrient composition. Dry matter intake above the red line would result in increasing excretion costs or levels of obesity. Water intake moving to the right along the red line would represent excessive water ingestion. The red dotted line represents a case of over-ingestion of food along the 90% water rail to balance the water budget.

A key part of the GF is in partitioning each ingested nutrient I into that which is retained R and that which is dissociated D, and further partitioning these components into a functional classification of that which is wasted w and that which is utilized u (Raubenheimer & Simpson 1994, 1995). Thus, the energy/mass budget is conceived, for each nutrient, as is I = R(u) R(w) D(u) D(w). Examples where food intake is retained and utilized include somatic growth, reproduction and storage, while retained but wasted food may include excess nonlimiting nutrients, water or toxins. Food that is dissociated but utilized may contribute to somatic maintenance costs – for example milk production and silk production – while food that is dissociated but wasted may involve excess nutrients that are excreted. Over-consumption of water is unlikely to incur high fitness costs as excess water is easily voided from the body. Animals could potentially over-ingest food, however, to reach their target water intake, thereby incurring any fitness costs associated with the extra weight gain.

In the case of the Cunningham's skink, we can use the graphical methods of the GF to represent its dry matter and free water nutrient space, with nutritional rails representing foods with different percentages of water (Fig. 6). We can then simulate the water and dry biomass balances of lizards foraging in different climatic environments (e.g. air temperature, humidity and wind speed) and overlay the consequences for lizard's water balance. In these analyses, we have assumed air, body and radiant temperatures of 30 °C, a wind speed of 0·1 m s−1 and two humidities (50% and 80%). We have considered situations where the lizard both under- and over-eats dry matter, with the red lines representing the range of free water intakes at the target dry matter intake (for all maintenance growth and development) that produces a non-negative water balance. This red line therefore represents a ‘rule of compromise’ (Raubenheimer & Simpson 1993) whereby a non-negative water balance is achieved and sufficient dry matter intake to pay for all metabolic processes (growth, maintenance, differentiation and reproduction), assuming dry food is balanced in nutrient composition. This rule of compromise assumes (infinitely) high costs to exceeding dry food needs and that there are no costs to over-ingesting water (but see Köhler, Raubenheimer & Nicolson 2012); with different costs for ingesting excess water or dry food, the slope and curvature of the line will change (Simpson et al. 2004).

In general, these analyses show that the Cunningham's skink must eat foods of relatively high water content to balance its water budget and achieve its food requirements, even in humid air where 80–82·5% water in food is needed. Adult animals are less vulnerable to entering negative water balance than are juveniles, as expected because of their lower surface area-to-volume ratio, although the differences are relatively minor in the environments considered; for example, a hatchling would have to feed along the food rail representing 92·5% water content at 50% relative humidity (Fig. 6b), while an adult could maintain a positive water balance in the same environment on food that is 90% water (Fig. 6d). At this humidity, a hatchling on food rail representing 85% water would have to increase its food intake by about 15% to balance its water budget (red dotted arrow in Fig. 6b).

Putting it all together: The heat, water and energy budget of the Cunningham's skink during an El Niño year

The analyses in the previous section considered the steady-state energy and water budget in a static environment where no behavioural homoeostatic options were available. In nature, Cunningham's skinks are exposed to substantial environmental fluctuations in weather, and in the availability of food and water across space and time, which they can exploit, to an extent, through behaviour to maintain homoeostasis. They may also engage in degrees of ‘allostasis’ by allowing their energy and water reserves, and their body temperature, to fluctuate within certain limits – that is to tolerate some ‘allostatic load’ (Raubenheimer, Simpson & Tait 2012). The integration of the biophysical models of heat and water exchange with DEB theory-based models of the energy and mass budget provides a powerful means to understand how species respond to the rich complexity of environmental conditions in nature.

To illustrate this, we have simulated the heat, water and energy budgets of a hatchling (7 g) and an adult (250 g) during 1998, an El Niño year, at the Weetangera site. Our calculations of the thermal constraints on foraging are described previously and driven by the daily data on air temperature, solar radiation and vapour pressure in Fig. 2. While Cunningham's skinks of all ages prefer insects over plant matter as food, in the field adults and juveniles alike have diets consisting of 75–100% plant matter (Pollock 1989). An advantage of considering an herbivorous lizard is that it is possible to quantify its food availability from gridded information on pasture growth available through the ‘Aussie Grass’ model (Carter et al. 2000). This data set includes monthly estimates of historical standing dry matter as well as growth (e.g. Fig. 2e,f). We have assumed a diet of clover throughout ontogeny, with the values for water and energy content taken from Shine (1971), and that clover biomass is represented in the ‘Aussie Grass’ model estimates of pasture.

From a behavioural point of view, we assumed that the lizards have three foraging states: retreating in a rock crevice R, basking just outside of the crevice B and foraging F. The possible transitions between these foraging states, and the conditions under which we assumed they will occur, are summarized in Table 5 and are based on our own observations of this species in the field and those of others (Shine 1971; Wilson & Lee 1974; Fraser 1985). Basking is always considered as an intermediate state between foraging and retreating, that is inline image. Basking and foraging were only allowed when the sun was up (zenith angle Z < 90°, as computed by the microclimate model of NicheMapR) and while the relative hydration state inline image was less than a threshold value inline image. When in the retreat, evaporative water loss was assumed to be minimal (relative humidity 99% and wind speed 0·01 m s−1) and the lizard was assumed to choose any depth between 20 and 200 cm such that they minimized exposure to temperatures below the critical thermal minimum CTmin = 4·6 °C and above the voluntary thermal maximum inline image (crevices used by these lizards that are shallower than 20 cm are typically still exposed to ambient humidity and significant air flow). We assumed that the lizards would emerge to bask if their body temperature in the crevice Te,R was greater than a threshold inline image (i.e. they were warm enough to move and transition from retreating to basking), that their basking temperature Te,B was greater than the lowest temperature at which the species has been observed to bask inline image = 14·0 °C (Fraser 1985) but not higher than inline image and that they would be warmer if basking than if they were in their retreat. The latter was conditional on whether the relative food energy level in the stomach eS, that is the satiation level, was less than a threshold value inline image that initiates foraging. If this was true, the B → F transition could occur, contingent on whether the potential foraging temperature Te,F was between the foraging temperature thresholds inline image. Foraging ceased, and the animal returned to the basking state, when any of the following occurred: the stomach was full, the body temperature was outside the foraging thresholds, and the desiccation threshold was reached or the sun went down. The animals were assumed to seek shade (0–100%) when basking and foraging.

Table 5. Behavioural state changes between retreating R, basking B and foraging F, and the conditions under which they were assumed to occur
TransitionConditions invoking the transition
  1. Z refers to the zenith angle of the sun. Te refers to the potential body temperature (or ‘operative’ temperature), depending on what the animal is doing (e.g. for retreating Te,R), whereas T refers to a body temperature threshold (e.g. minimum threshold for basking, inline image). See the main text and Table 3 for the symbology and further explanation.

R → B inline image
B → R inline image
B → F inline image
F → B inline image

We have considered three scenarios in terms of the water budget for both the hatchling and the adult: unlimited water (as would be the case, for example, when living alongside a stream), and limited water with feeding restricted when body water content reached thresholds, inline image, of either 0·95 or 0·65, that is 5% or 35% desiccated (few lizards tolerate desiccation above 35%, Munsey 1972; Heatwole & Veron 1977; Leclair 1978; Mautz 1982). Under the limited water scenarios, drinking (full rehydration) was permitted whenever rainfall was >5 mm and the animal was above its critical thermal minimum, on the assumption that this much rain would produce pools of water on the rocky outcrop and in the retreat sites.

We interpolated the monthly AWAP pasture data to a daily time step and applied a functional response to feeding such that the rate at which the stomach fills is

display math

where Es is the stomach energy content (J), (F = 1) means that the lizard is in the foraging state, inline image is the maximum specific food assimilation rate (J cm−3 h−1), f = X/(X + XK) where X is the food density (J/ha) and XK is the half-saturation constant (J ha−1), and inline image is the maximum specific food intake rate (J cm−2 h−1). We assumed food had a gross food energy content equivalent to clover 21·525 kJ g−1 (Shine 1971). While basking or retreating, food in the stomach decreased as inline image. We assumed that the maximum stomach volume was 13·4% of the total body volume (Barwick 1965), producing a maximum structural volume-specific energy content inline image. If the stomach is full, inline image, and the time spent basking equals inline image until foraging is resumed. Mean maximum feeding occurs if f = 1, meaning that inline image. As foraging only commences when inline image, the time spent foraging inline image until basking is resumed. As adult E. cunninghami can typically fill their guts within an hour of feeding (Shine 1971; Wilson & Lee 1974), and we are working with an hourly time step, we assumed a value of inline image = 13 290 J cm−2 such that tf for an adult at a foraging temperature of 35 °C is 0·9 h. Our calculations are conservative in that we used value of XK that was 10% of the maximum pasture density predicted at the study site since 1960. The water content of the food was assumed to be zero when pasture biomass growth rates were zero, but otherwise, it was assumed to be that of clover (82%).

Figure 7 shows the implications of these scenarios for the activity budget. Under the unlimited water scenario, the hatchling and the adult had similar annual basking periods (2813 and 2805 h, respectively), but the hatchling had to forage twice as frequently as the adult (150 vs. 74 h, respectively) because of her relatively faster gut passage rate and relatively lower stomach volume. If there is a substantial predation risk to foraging (Adolph & Porter 1993), this alone would increase the mortality rate of the hatchlings. Under the limited water scenarios, a desiccation tolerance limit of 5% substantially curtailed the basking period of the hatchling relative to the adult (1110 and 1456 h, respectively) with similarly severe impacts on their foraging period (49 and 54 h, respectively). Increasing the desiccation tolerance threshold from 5% to 35% desiccation allowed partial recovery of the basking period for the hatchling and for the adult (1404 and 2212 h, respectively), and also increased their foraging time (94 and 65 h, respectively).

Figure 7.

Annual basking (grey squares) and foraging (black squares) periods simulated using NicheMapR for hatchling and adult Cunningham's skinks at Weetangera, Canberra, for the year 1998 under different scenarios of water limitation. In the unlimited water scenario, the lizards are assumed to have access to permanent water, for example a nearby stream. In the limited water scenario (a, b), water only comes in through the food unless >5-mm rainfalls in a day, upon which the animal fully rehydrates. In the limited water scenario, foraging stopped when body water content dropped by either 5% (c, d) or 35% (e, f) of the fully hydrated state. In all scenarios, lizards cease activity if their guts are >75% full.

The body condition of both the hatchling and the adult was negatively affected by these constraints on basking and foraging time budgets under the limited water scenarios (Fig. 8). Moreover, the hatchling experienced negative growth (i.e. shrinkage) (Fig. 9a) and the adult failed to accumulate energy in her reproductive buffer (Fig. 9c) when the desiccation threshold was set to 5%. When desiccation tolerance was increased to 35%, the partial recovery of foraging time substantially increased the growth rate of the hatchling and prevented any shrinkage (Fig. 9b). For the adult, the same increase in desiccation tolerance produced an almost full recovery in terms of the accrual of reproductive energy (Fig. 9c). However, an increased behavioural threshold for desiccation tolerance had significant consequences for the risk of lethal desiccation because water loss continued when the animals retreated (via faecal water loss only, because of the high humidity assumed in the crevice) and rehydration occurred only when it next rained (5 mm or greater). If 40% desiccation was considered as the lethal threshold, neither the hatchling nor the adult would have experienced lethal desiccation under the activity threshold of 5% desiccation, whereas the hatchling but not the adult would have died from desiccation in her retreat under the activity threshold of 35% desiccation (Fig. 9). The strong differences seen here between hatchlings and adults are primarily a result of the consequences of surface area-to-volume ratios involved in both the metabolism and the cutaneous water exchange, which made the hatchlings far more sensitive.

Figure 8.

Trajectories of wet mass for the year 1998 for the Cunningham's Skink Egernia cunninghami simulated with NicheMapR under different scenarios of water limitation at Weetangera, near Canberra. The blue line shows the expected wet mass if fully hydrated, with variation representing only growth and body condition (reserve), while the black line shows the actual wet mass by additionally incorporating both condition and hydration level.

Figure 9.

Trajectories of body size, reproduction and desiccation level for hatchling and adult Cunningham's Skink Egernia cunninghami for the year 1998, simulated with NicheMapR under different scenarios of water limitation. Hatchling body size (a) is measured as snout-vent length (SVL), while adult reproduction (c) is measured as cumulative energy. The scenario of unlimited drinking water is represented by the solid black line, limited drinking water and 5% maximum desiccation is represented by the dashed black line, and limited drinking water and 35% maximum desiccation is represented by the solid grey line. For the panels showing desiccation level, the red dotted line represents 40% desiccation, which is assumed, for argument's sake, to be lethal.

From these preliminary calculations, it is clear that water could be an important constraint on activity and feeding in these lizards, even under the relatively high food water contents and seemingly low cutaneous resistances to water loss considered here. This could be especially the case early in ontogeny, where the trade-offs between searching for food and maintaining the water balance will be strongest. Compared with thermal traits, behavioural and physiological traits that relate to water loss are rarely measured for reptiles (e.g. Mautz 1982; Crowley 1987; Neilson 2002; Davis & DeNardo 2010). The aforementioned analyses provide a holistic perspective on how such traits interact with the heat and energy (nutrient) budget in realistic environmental settings and show how important they may be for predicting how they will respond to environmental change.

The ‘thermodynamic niche’

In this article and in previous ones (Kearney 2006, 2012; Kearney & Porter 2006, 2009; Kearney et al. 2010), we have outlined how thermodynamic principles of energy and mass transfer can be formally applied to understand the linkages between organism, environment and fitness. In this way, we can define a species' ecological niche using thermodynamically grounded equations to connect functional traits with fitness in multivariate climatic and nutritional environmental space (Kearney et al. 2010).

The distinction is often made between the ‘fundamental niche’ and the ‘realized niche’, where the former reflects constraints relating to abiotic conditions and resources (e.g. food) on the range of environmental conditions that permit population persistence, while the latter reflects the additional influences of biotic interactions (competition, predation and disease) (Hutchinson 1957). Although the approach we are advocating has, in the past, been described as a way of modelling the fundamental niche (e.g. Kearney & Porter 2004, 2009; Kearney 2006; Kearney et al. 2010), we here suggest that the term ‘thermodynamic niche’ is a better descriptor. This is in part because processes other than those we are considering in the present framework, such as dispersal and genetic system (e.g. sex vs. asex), may also be considered as constituting the fundamental niche (Holt 2009). Moreover, the subset of biotic interactions that are used to distinguish the fundamental from the realized niche is somewhat arbitrary and nebulous (e.g. what about mutualisms?) and is more a reflection of the research interests of ecologists such as Hutchinson and Macarthur during the 50s and 60s (competition and predation) than a real qualitative distinction among processes. In contrast, the concept of the ‘thermodynamic niche’ provides a more natural categorization of niche-related processes and, in a sense, represents a more ‘fundamental’ set of constraints because no organisms are at liberty to violate the laws of thermodynamics. The thermodynamic niche thus provides an obligatory constraining stage on which other ecological interactions must occur.

The ability of the thermodynamic niche framework to define such a constraining ecological stage is especially helpful in the context of the topic of this extended Spotlight in Functional Ecology – predicting the impacts of global climate change on organisms. Empirical models based on the present or past, such as occurrence-based species distribution models (e.g. Elith & Leathwick 2009), must be extrapolated to future environments under the bold assumption that the processes they have implicitly captured will continue in the same fashion into future, novel environments (Davis et al. 1998). Thus, there is uncertainty not only in the nature of future environments, but also in the suitability of the underlying model. In contrast, we can be confident that the thermodynamic basis of the responses of organisms to future environments will be the same as it is at present.

Thermodynamic niche models capture only a subset of the ecological interactions that drive distribution and abundance, albeit a fundamental and omnipresent one. In this sense, the strongest inferences that can be made when applying thermodynamic niche models in isolation are about what is not possible due to thermodynamic/physiological constraints. For example, they can show what the geographical range would look like if it was constrained only by the effects of temperature on the intrinsic rate of increase (Kearney 2012). They can, however, be integrated with models of processes that occur at other levels and thereby provide more physiologically grounded predictions to these models. For instance, Pagel & Schurr (2012) recently proposed a powerful framework for integrating models of the environmental responses (which they referred to as the niche model), population dynamics and dispersal for the purpose of forecasting range shifts. However, the niche component of their model, that is the response of the intrinsic rate of increase with environmental gradients, was descriptive. The thermodynamic niche modelling framework we propose here provides a way to make such models physiologically and behaviourally explicit. In turn, this will provide greater explanatory and predictive power in studying the responses of organisms to environmental change.


We thank Steven Chown, Warren Porter and two anonymous reviewers for suggestions that greatly improved the manuscript and R. Shine for permission to reproduce results from his honours thesis. Kearney was supported by an Australian Research Fellowship from the Australian Research Council (ARC). Simpson was supported by an ARC Laureate Fellowship. Raubenheimer was part-funded by the National Research Centre for Growth and Development, New Zealand and the Massey University Research Fund.