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Evaluating Thermoregulation in Reptiles: An Appropriate Null Model.Author(s): Keith A. Christian, Christopher R. Tracy, and C. Richard TracySource: The American Naturalist, Vol. 168, No. 3 (September 2006), pp. 421-430Published by: The University of Chicago Press for The American Society of NaturalistsStable URL: http://www.jstor.org/stable/10.1086/506528 .

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vol. 168, no. 3 the american naturalist september 2006 �

Notes and CommentsEvaluating Thermoregulation in Reptiles: An Appropriate Null Model

Keith A. Christian,1,* Christopher R. Tracy,1,† and C. Richard Tracy2,‡

1. School of Science, Charles Darwin University, Darwin, NorthernTerritory 0909, Australia;2. Department of Biology, University of Nevada, Reno, Nevada 89557

Submitted November 18, 2005; Accepted May 22, 2006;Electronically published August 7, 2006

Online enhancement: appendix.

abstract: Established indexes of thermoregulation in ectothermscompare body temperatures of real animals with a null distributionof operative temperatures from a physical or mathematical modelwith the same size, shape, and color as the actual animal but withoutmass. These indexes, however, do not account for thermal inertia orthe effects of inertia when animals move through thermally hetero-geneous environments. Some recent models have incorporated bodymass, to account for thermal inertia and the physiological controlof warming and cooling rates seen in most reptiles, and other modelshave incorporated movement through the environment, but noneincludes all pertinent variables explaining body temperature. We pre-sent a new technique for calculating the distribution of body tem-peratures available to ectotherms that have thermal inertia, randommovements, and different rates of warming and cooling. The ap-proach uses a biophysical model of heat exchange in ectotherms anda model of random interaction with thermal environments over thecourse of a day to create a null distribution of body temperaturesthat can be used with conventional thermoregulation indexes. Thisnew technique provides an unbiased method for evaluating ther-moregulation in large ectotherms that store heat while movingthrough complex environments, but it can also generate null modelsfor ectotherms of all sizes.

Keywords: body size, body temperature, ectotherms, null model, op-erative temperature, thermal inertia.

* Corresponding author; e-mail: [email protected].

† E-mail: [email protected].

‡ E-mail: [email protected].

Am. Nat. 2006. Vol. 168, pp. 421–430. � 2006 by The University of Chicago.0003-0147/2006/16803-41441$15.00. All rights reserved.

The paradigm-shifting article by Cowles and Bogert (1944)caused biologists to recognize that reptiles employ behaviorto interact with their thermal environments as a means toregulate their body temperatures. Two decades of field andlaboratory studies subsequent to the article by Cowles andBogert gave birth to the field of animal physiological ecologyand to an expanding literature documenting how some rep-tiles regulate body temperature by behaviorally and physi-ologically exploiting diverse thermal environments. Nearlyfifty years ago, Heath (1964) published an admonition thatsimply measuring body temperature or correlating bodytemperature with air temperature was inadequate to char-acterize complex environments in which thermoregulationmight occur. In the late 1960s, some studies applied thephysics of heat transfer and thermodynamics to add un-derstanding to observations of reptile interactions with theirthermal environments (Bartlett and Gates 1967; Norris1967). Subsequently, biophysical models describing the en-ergy budgets of animals put the thermal biology of reptilesinto an ecological perspective (Porter and Gates 1969; Porteret al. 1973; Christian and Tracy 1981; Tracy 1982; Wald-schmidt and Tracy 1983; Stevenson et al. 1985). Contem-poraneously, the concept of “operative temperature” (Te)was developed to incorporate both animal and environ-mental factors into a mechanistic index of the driving forceof the thermal environment on the body temperatures ofanimals under a given set of environmental conditions (Bak-ken and Gates 1975; Bakken 1981; Roughgarden et al. 1981;Tracy 1982; Bakken et al. 1985).

The Te of an animal incorporates surface areas (areasexposed to various forms of radiation and convective heatexchange), but, by definition, it is a “massless” index,meaning that it is an index of the interaction of an animalof a particular size, shape, and posture with its thermalenvironment, assuming that the animal has no body mass(and therefore no heat capacity or “thermal inertia” thatcan result in a lag in change of body temperature whensubjected to a new thermal environment). Although amassless index normally can be used for studies of smallanimals, its use for larger animals can be misleading be-cause larger animals tend to have thermal inertia, and their



422 The American Naturalist

body temperature depends on both the instantaneous Te

and also the body temperatures that the animal had in therecent past, because bodily thermal inertia causes a lag inbody temperatures during warming or cooling (Spotila etal. 1973; Spotila 1980; Tracy 1982; Stevenson 1985a; Turnerand Tracy 1986). Biophysical models can incorporate ther-mal inertia and physiological control of heat exchange,and some models have been developed to calculate bodytemperatures for large ectotherms in the warmest andcoolest parts of their thermal environment (Christian etal. 1983; Stevenson 1985a; Tracy et al. 1986; Christian andWeavers 1996), to provide context to the body tempera-tures attained by the animals.

Based on earlier work employing a cost-benefit ap-proach to thermoregulation (Huey and Slatkin 1976),Hertz et al. (1993) drew attention to the fact that thequestion “How carefully does an animal thermoregulate?”is a complex of several distinct and interacting questions.The answer to that complex question requires not simplyan examination of the pattern of the animal’s Tb but alsoa comparison with the thermal options available in theenvironment. One part of this complex question is “Howvariable is the animal’s Tb (‘precision’ of thermoregula-tion)?” A second question that must be addressed is “Howclosely do Tb’s match the preferred or set point range ofthe species (‘accuracy’ of thermoregulation)?” A thirdquestion is “To what extent do thermoregulatory behaviorsactually enhance the accuracy of Tb’s relative to those ofa nonregulating control (the ‘effectiveness’ of thermoreg-ulation)?” On the basis of these questions, Hertz et al.(1993) have provided methods to evaluate data bearing onthe quantification of thermoregulation. These methodsrepresent a conceptual advance and have since becomecommonly used in studies of reptilian thermoregulation(e.g., Bauwens et al. 1996; Blouin-Demers and Weather-head 2001; Fitzgerald et al. 2003; Ibarguengoytıa 2005),despite having some well-discussed limitations to their use(e.g., Christian and Weavers 1996; Wills and Beaupre2000). The thermoregulatory indexes of Hertz et al. (1993)have been modified and extended by various authors(Christian and Weavers 1996; Brown and Weatherhead2000; Blouin-Demers and Weatherhead 2001; Blouin-Demers and Nadeau 2005), but all of theses indexes requirea null model (the body temperatures of a nonregulatinganimal) with which to compare empirical data.

Indeed, one of the major contributions of the Hertz etal. (1993) article (see also Hertz 1992a, 1992b) was tocompare the animal’s Tb to a null model. They suggestedusing a random distribution of Te as the null distributionfor comparison. However, they also pointed out that Te

does not accurately reflect the temperatures available forlarge animals or for small animals that move quicklyamong thermal environments, and so they cautioned

against using their approach with large ectotherms. Chris-tian and Weavers (1996) addressed this problem by usingbiophysical equations to incorporate the effects of thermalinertia. This resulted in a predicted body temperature fora stationary large lizard that could then be substituted forthe massless Te in the indexes proposed by Hertz et al.

Seebacher and Shine (2004) pointed out that the effectsof thermal inertia in ectotherms can be substantial whenlarge ectotherms move about in a thermally heterogeneousenvironment. They offered equations and a table of coef-ficients to correct Te when applying the thermal indexes ofHertz et al. (1993). Their technique explicitly models animalmovement through the environment at regular intervals.The approach illustrates that large ectotherms with largethermal inertia have a reduced range of attainable bodytemperatures. While this work draws attention to the prob-lems associated with thermal inertia, it does not create atrue null model of available body temperatures for largeectotherms because that would require both random move-ments (both in terms of time and in terms of directionrelative to thermal environments) and the option that anyrandom “decision” to move would include not moving.

A second problem in the Seebacher and Shine (2004)model is that it apparently (as evidenced by their fig. 1b)does not incorporate physiological (cardiovascular) con-trol of heat exchange that typically allows reptiles to warmat a faster rate than they cool, sometimes twice as fast(Bartholomew 1982; Turner and Tracy 1983; Dzialowskiand O’Connor 1999, 2001, 2004; O’Connor 1999). Thus,the 5-kg animal (in fig. 1b of Seebacher and Shine 2004)should warm faster than it cools. Cardiovascular controlof thermoregulation creates efficiencies in thermoregula-tion that can be critically important to homeostasis inindividuals, especially for large-bodied ectotherms (seeTracy et al. 1986).

Seebacher and Shine’s (2004) model also predicts verylarge second-order body temperature dynamics (seeTurner 1987 for discussion of second-order body tem-perature dynamics). Systems with second-order dynamics(so named because the dynamics are better described bysecond-order differential equations) have an initial timelag (the second-order dynamics) before body temperaturesbegin to change in response to a change in thermal en-vironment. Thereafter, body temperatures change in re-lation to the heat capacitance of the body (the first-orderdynamics). The first-order dynamics are dominated by theheat capacitance of the body, resulting in a lag in changein body temperature with respect to time due to mass-related thermal inertia (appropriately described in termsof a “time constant” t). The second-order dynamics, incontrast, are likely related to establishing a new gradientof temperatures within the body after a change in thermalenvironment. There is some theoretical basis for conclud-



Null Model for Ectotherm Thermoregulation 423

ing that animals can exhibit second-order body temper-ature dynamics (Turner 1987), but there is a dearth ofempirical evidence that second-order effects are importantin the thermal biology of lizards. This may be becausephysiological control of temperature gradients in the bodyby cardiovascular mechanisms can rapidly establish newtemperature gradients in the body. Thus, a 6.9-kg landiguana has been shown to have no second-order lag inresponse to an experimentally controlled change in ther-mal environment (see Tracy et al. 1986), and a 5-kg Var-anus varius appears not to have second-order temperaturedynamics in response to change in thermal environment(fig. 3 in Seebacher and Shine 2004). Nevertheless, See-bacher and Shine’s model (likely incorrectly) predictedthat a 5-kg lizard would respond to a novel thermal en-vironment so slowly that it would show no discerniblechange in body temperature even after 15 min. This con-cept of second-order dynamics needs to be studied further(see Turner 1987, 1994a, 1994b, 1994c), but here we acceptthe empirical evidence that large second-order body tem-perature dynamics are not likely to be very important inpredicting body temperatures of lizards in changing ther-mal environments.

Here, by using a randomly generated null model againstwhich one can compare the body temperatures achievedby an animal, we address the problems associated withdata for ectotherms with large body size that move througha thermally heterogeneous environment. We contend thatour method overcomes the inadequacies associated withprevious approaches and that it offers a robust techniquefor evaluating thermoregulation, according to the pre-scriptions in Hertz et al. (1993). The method is particularlyuseful for animals with substantial thermal inertia (largeanimals) but also can be used more generally.

A New Null Model Incorporating Size and Movement

In our approach, we first establish the extreme tempera-tures available in the environment at a given time by cal-culating the maximum ( ) and minimum ( ) bodyT Te emax min

temperatures from a steady state biophysical model (Porterand Gates 1969; Porter et al. 1973; Porter and James 1979;Porter and Tracy 1982; Tracy 1982; Waldschmidt and Tracy1983). Input data included animal characteristics (e.g., so-lar absorptivity and surface areas) and microclimate datafrom days when lizards were followed with telemetry(Christian and Weavers 1996). The and representT Te emax min

the way in which the animal integrates its thermal envi-ronments in the most hot and most cool environmentsavailable, and the following procedures were used to cal-culate predicted body temperature ( ), within thisTbpred

range of thermal environments, of an animal with thermalinertia using and as driving variables.T Te emax min

We developed a computer program (in True BASIC) toconstruct a null distribution of . The representsT Tb bpred pred

the body temperatures achievable by the animal based onthe animal characteristics, Te, and the body temperatureof the animal in the recent past (as the animal is warmingor cooling). Calculation of is accomplished by firstTbpred

assigning a random starting situation (corresponding to asite in which the microclimate, at that time, is either

or ) and a random length of time for the modeledT Te emax min

animal to remain in that spot. Then, ’s are calculatedTbpred

for the animal in that place for each minute that the animalremains in that place. This is done using Te as the drivingforce and the thermal time constant t to incorporate bodymass. Each place is assigned a random proportion of thedistance between and as an indicator of theT Te emax min

animal being in full sun, full shade, or any intermediatepartial shade. The proportion remains constant until theanimal’s next move, but the and are updatedT Te emax min

every minute of the day such that the predicted Tb alsomay change while an animal is in one place as the dailyconditions change. The time constant t is taken from re-gression equations generated from data in Dzialowski andO’Connor (2001). Different time constants are used forwarming ( ) and cooling (0.434t p 1.96 # mass t ph c

). Alternatively, time constants could be0.3622.34 # massmeasured for an individual species. The form of the first-order equation for the predicted body temperature of theanimal adjusted for thermal inertia and time in a givenplace is , where T0 is the�1/tT p T � (T � T ) # eb 0 e 0pred

temperature at the time the animal first enters the newplace. Next, the program chooses a new random place andtime, calculates the corresponding predicted Tb, and con-tinues these steps over the course of the entire day (24 h).The animal could be modeled as remaining above groundfor the full period or as retreating into a refugium, so longas and are adjusted accordingly. Finally, theT Te emax min

model repeats this process for as many days as desired (weused 1,000 replicate days) to generate a distribution ofrandom predicted Tb achievable over the day (i.e., a nulldistribution).

The term was defined by Hertz et al. (1993) as thedb

mean deviation of an animal’s field-active body temper-atures from its set point (or preferred) range. This indexis an indication of the accuracy of thermoregulation, buton its own, this index cannot be used to determine whetheran animal is thermoregulating because it lacks informationabout the availability of thermal opportunities in the en-vironment, as Hertz et al. (1993) noted. The term wasde

defined as the mean deviation of Te from the animal’s setpoint range and is thus a measure of the thermal qualityof the animal’s environment (Hertz et al. 1993). For largeectotherms, it is appropriate to substitute the mean achiev-able body temperature ( ) for mean Te to calculateTbpred




Figure 1: Examples of predicted body temperatures as a function of time of day for lizards differing in body size, as calculated from a model thatassumes random movements through the thermal environment. A total of 1,000 replicates (days) of the model were used to determine the nulldistribution, which was then used in thermoregulatory indexes. The shaded area represents the middle 950 replicates, or the 95% confidence intervalof the distribution; lines are representative individual replicates for lizards of each size.

. The calculated for each hour of each iteration ofd Te bpred

the model was compared to the set point range to yield a, and then a (mean) was calculated for 1,000 iterations¯ ¯d db e

for comparison with hourly values of .db

The simplest use of these indexes is a direct comparison:when , it suggests that the animal is regulating its¯ ¯d ! db e

body temperature because the selected body temperaturesare closer to the set point range than would be the caseif the animal were randomly selecting body temperaturesin its environment (as represented by the null model; Hertzet al. 1993). We used a one-tailed paired t-test to compare

with .¯ ¯d db e

The “effectiveness” of thermoregulation is defined byHertz et al. (1993) as , where a value for¯ ¯E p 1 � (d /d )b e

E of 0 indicates a random selection of thermal environ-ments and a value for E of 1 indicates careful thermoreg-

ulation (Hertz et al. 1993). Others have argued that a betterindex of effectiveness of thermoregulation is simply thedifference, , with higher values indicative of more¯ ¯d � de b

effective thermoregulation (Blouin-Demers and Weath-erhead 2001; Blouin-Demers and Nadeau 2005). The “ex-ploitation” of the thermal environment (Ex) is defined asthe amount of time an animal has a body temperaturewithin its set point range divided by the amount of timeduring the day in which it is possible for the animal toachieve its set point range (Christian and Weavers 1996).

Example

To illustrate the methods developed in this article, we havereanalyzed data shown in figures 1A and 1B of Christianand Weavers (1996) on body temperatures of two species




Figure 2: Mean predicted Tb as a function of time of day, calculated for lizards ranging from 10 to 1,000 kg. The means were calculated from 1,000iterations (replicate days) of the model for each body size. Error bars (95% confidence interval) are shown for 0.01–1,000-kg animals.

of varanid lizards. These lizards include the floodplainmonitor Varanus panoptes and the sand monitor Varanusgouldii, studied during the wet season in northern Aus-tralia. The two species are sympatric, and the data for theselizards and their environments were collected simulta-neously. In this study, individuals of each species of ap-proximately 1.5 kg body mass were selected (Christian andWeavers 1996), and, except where specifically stated oth-erwise, a mass of 1.5 kg was used in the models below.During the period of data collection, the thermal envi-ronment was such that lizards could attain body temper-atures within the set point range during most of the day-light hours (Christian and Weavers 1996). Despite thesimilarities between the two species (body mass, samestudy site, and simultaneous data collection), the patternsof body temperatures selected by the species were strikinglydifferent (fig. 1 in Christian and Weavers 1996). For com-parison, we additionally used the methods suggested bySeebacher and Shine (2004; using equations from theirtable 1) for the two varanid lizards, assuming regular shut-tling movements between thermal patches every 5 min,every 15 min, and every 30 min (namely, three separatesimulations).

Our model calculated predicted body temperatures( ’s) that fluctuate widely, as would be expected for aTbpred

null distribution of random “thermoregulation” (fig. 1).

There was no obvious pattern in the mean for lizardsTbpred

ranging from 200 to 5,000 g, except that the body tem-peratures of the 5,000-g lizard seemed to lag behind bodytemperatures of the smaller lizards (fig. 2).

Measured body temperatures for V. gouldii during theactivity period of the day were always within the set pointrange (central 50% of Tb’s selected in a thermal gradient;Christian and Weavers 1996) for this species (fig. 3),whereas measured body temperatures for V. panoptes werenever within its set point range (fig. 4). Nevertheless, theTe’s and the mean ’s indicate that both species shouldTbpred

have been able to bring their body temperature to withinthe set point range. Thus, although these two species areof similar size, inhabit the same environment, and weremeasured simultaneously, they interact with their thermalenvironments very differently, and this is consistent withobservations of the behavior and activity patterns of thesetwo species (Christian et al. 1995; Christian and Weavers1996). The body temperatures predicted from the modelsof Seebacher and Shine (2004) were far from the set pointrange for either species (figs. 3, 4), and this indicates aproblem in their approach to correcting for thermalinertia.

The indexes of thermoregulation for V. gouldii indicatethat it is an excellent thermoregulator (table 1), whereasthe indexes indicate that V. panoptes is a much less precise




Figure 3: Temperatures during a typical day in the wet season in tropical Australia for Varanus gouldii. The temperatures include mean Tb (asmeasured by telemetry), mean predicted Tb (as determined by the model in the appendix in the online edition of the American Naturalist), ,Temin

and , and three “available Tb” lines determined using the techniques recommended by Seebacher and Shine (2004), assuming that the animalsTemax

shuttle between warm and cool thermal environments every 5, 15, and 30 min.

thermoregulator. The former species actively selects a sub-set of the thermal conditions available in its environment,whereas the latter species moves through the thermal en-vironment with little regard to its set point range of bodytemperatures.

Discussion

The new techniques presented here are an easy supplementto the prescriptions in Hertz et al. (1993) for studies ofthermoregulation of large ectotherms. They represent anapproach for creating a sophisticated null model that canbe used in conjunction with the indexes of Hertz et al.

(1993) and Christian and Weavers (1996). Users need anarray of Te values (either calculated or estimated fromphysical models; Tracy 1982; Bakken 1992), Tb’s of realanimals, and the ability to generate the null distribution(see appendix in the online edition of the American Nat-uralist). Although we have applied these methods to meanvalues of body temperature among animals (to provide adirect parallel with the data in fig. 1 of Christian andWeavers 1996), other questions can be addressed by ap-plying the techniques and indexes to data collected fromeach individual in a study (Hertz et al. 1993). The modeleasily could be modified to reflect different spatial andtemporal distributions of thermal patches at a particular




Figure 4: Temperatures during a typical day in the wet season in tropical Australia for Varanus panoptes. The temperatures include mean Tb (asmeasured by telemetry), mean predicted Tb (as determined by the model in the appendix), , , and three “available Tb” lines determinedT Te emin max

using the techniques recommended by Seebacher and Shine (2004), assuming, in separate simulations, that the animals shuttle between thermalenvironments every 5, 15, and 30 min.

study site by using weighted proportional distributionsbetween and .T Te emax min

The Te integrates and reflects the thermal environmentof an organism of a particular size, shape, posture, andcolor. As such, Te is the “driving force” for heat exchangebetween an organism and its environment. For example,when an ectotherm has a body temperature of 35�C in anenvironment with , the organism will typicallyT p 40�Ce

tend to warm toward 40�C. However, large ectotherms,with large thermal inertia, respond to both their currentTe and the Te from the immediate past. For example, ifan ectotherm with a body temperature of 35�C moves froman environment with Te of 40�C to an environment witha Te of 30�C, the core Tb of that organism (as opposed tosurface temperature) might continue to rise due to a lag-

ging response to its immediate past thermal environment.This is in spite of the fact that the animal is currently ina cooling environment. Thus, it is simply not enough toknow Te for large ectotherms to predict how the animal’sTb will respond in particular environments because thethermal response of a large ectotherm is complexly relatedto present and past Te’s.

Seebacher and Shine (2004) laudably drew attention tothe problems associated with a large ectotherm movingthrough a complex environment, but their model does notyield a “null” distribution of body temperatures becausethat model assumes behavioral thermoregulation by lizardsthat is not random; indeed, it assumes mechanical move-ment between environments with regular periodicity. Inaddition, their model does not incorporate physiological




Table 1: Thermoregulatory indexes for two species of var-anid lizards from the wet season in tropical Australia

Indexes Varanus gouldii Varanus panoptes

(�C)db .0 2.6(�C)de 1.9 1.8!¯ ¯d db e t p 5.9,

df p 7, P p .0003t p 3.5,

df p 7, P p .99�¯ ¯d de b 1.9 �.8

E 1.0 �.4Ex 1.0 .0

Note: Calculated, in part, from original data of Christian and Weavers

(1996), these indexes demonstrate that V. gouldii thermoregulate very

carefully but V. panoptes do not. The field data were collected from the

same study site simultaneously for the two species. A paired t-test of

the � index (Blouin-Demers and Weatherhead 2001) revealed that¯ ¯d de b

the index was significantly greater for V. gouldii than for V. panoptes

( , , ), indicating that V. gouldii is the moret p 13.7 df p 7 P ! .0001

effective thermoregulator. One-tailed paired t-tests were used to deter-

mine whether within each species. of ther-¯ ¯d ! d E p effectivenessb e

moregulation; of the thermal environment. IndexesE p exploitationx

are defined in the text.

control of warming and cooling, and this may also explainthe unusually high second-order body temperature dy-namics predicted by their model. These modeling short-comings doubtlessly contributed to their underestimate ofthe abilities of animals with body masses around 5 kg tochange temperature.

The biological conclusions drawn here about thermo-regulation of two varanid lizards are the same as the con-clusions drawn by Christian and Weavers (1996). Obser-vations of these two species reveal dramatic differences inbehaviors of the two species (K. A. Christian, personalobservation), and the conclusions drawn from the ther-moregulatory indexes in Christian and Weavers (1996) andhere (figs. 3, 4) are consistent with those observations.However, the methods of Seebacher and Shine (2004) failto identify these species differences. “Available Tb’s” mod-eled according to Seebacher and Shine (2004; fig. 3) arealmost always lower than the actual Tb’s of Varanus gouldii.Thus, the “correction” techniques proposed by Seebacherand Shine (2004) result in unrealistic estimates of bodytemperatures of large ectotherms.

Large body mass results in less variance around themeans of (figs. 1, 2), and the body temperatures ofTbpred

larger lizards lag behind those of smaller individuals duringthe initial warming phase (fig. 2). However, the extensivelyoverlapping mean ’s (fig. 2) indicate that randomTbpred

movements of animals up to around 10 kg can largelyerase the effects of body size. Although body size is oneimportant factor in determining how an animal interactswith its thermal environment, it is only one of many im-portant factors (e.g., Stevenson 1985b; Tracy et al. 1986).Behavioral and physiological characteristics (such as

warming faster than cooling) can neutralize the effects ofthermal inertia (Stevenson 1985a, 1985b). Thus, effects ofthermal inertia for small to medium-sized ectotherms (upto approximately 10 kg), although real and measurable,should not be overstated in the broader context of therange of possibilities due to behavior, physiology, and an-imal-environment interactions. Animals on the order of100 kg or larger, however, have substantial thermal inertia(fig. 2).

The tools we provide here generate null models of ther-moregulation in ectotherms by using properties of animalsand environments and the physics of heat exchange be-tween animals and their environments. These tools makeit possible to investigate the thermal relations of large ec-totherms that move about in complex thermal environ-ments. However, the technique provides a mechanism forgenerating null models for ectotherms of all sizes. Even ifTe’s are measured with physical models, unless Te’s arespatially normally distributed, it would require a prohib-itively large number of models to adequately create a nullmodel representative of the thermal heterogeneity in theenvironment. Thus, the techniques presented here are ap-propriate in studies of thermoregulation regardless of bodysize.

Acknowledgments

We thank the Australian Research Council (ARC grantDP0559093 to K.A.C.), the National Science Foundation(grant INT-0202663 to Christopher R. Tracy), Charles Dar-win University, and the Biological Resources Research Cen-ter at the University of Nevada, Reno, for financial support.

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Associate Editor: Raymond B. HueyEditor: Jonathan B. Losos

Floodplain monitor lizard, Varanus panoptes (photograph by Keith Christian).



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