modeling the costs and benefits associated with the ... · research article modeling the costs and...

RESEARCH ARTICLE

Modeling the costs and benefits associated with the evolutionof endothermy using a robotic pythonJ Alex Brashears12 Ty C M Hoffman3 and Dale F DeNardo2

ABSTRACTEndothermy provides considerable benefits to an organism butrequires large energy investment To understand potential drivingforces that would lead to the evolution of endothermy it is important tounderstand the energy costs and potential benefits of intermediatesteps between ectothermy and homeothermic endothermy as wellas the influences of environmental conditions on energetic costsHowever efforts to examine intermediate conditions are greatlylimited by the predominant natural dichotomy between ectothermyand endothermy Facultative endothermy by brooding pythonsprovides a fortunate study system where endothermy is beneficialbut not essential As one cannot control the extent of energyinvestment in heat production by a female python we created anartificial snake with controllable heating capability This enabled us todetermine the energetic costs of maintaining a clutch at a preferredtemperature and to determine the relative thermal benefit of limitedenergy-producing capability (ie 50 of the required energy tomaintain the preferred developmental temperature) We manipulatedthe pseudoserpentrsquos clutch size (5 10 15 eggs) diel ambienttemperature cycle (2 4 6degC) and insulation (with and without) at eachof these power levels unlimited power half required power and nopower We found no significant effect of clutch size on either powerrequirements or developmental temperature Energy requirementsincreased with the amplitude of the diel cycle and decreased with theaddition of insulation while the quality of the thermal environmentdecreased with the amplitude of the diel cycle Interestingly thequality of the thermal environment also decreased with the additionof insulation We discuss these results within the context of thereproductive model of the evolution of endothermy

KEY WORDS Facultative thermogenesis Nest site selectionParental care Pseudoserpent

INTRODUCTIONThe maintenance of high and relatively constant temperature bymetabolic means (homeothermic endothermy) constitutes a majorinnovation that appeared independently in two vertebrate lineagesbirds and mammals (Bennett and Ruben 1979) While daily andseasonal heterothermic endothermy are widespread among birdsand mammals and mitigate energetic costs (Grigg et al 2004) theextreme complexity and energetic demands of homeothermic

endothermy suggest that there must have been substantialselective advantages driving its evolution (Bennett and Ruben1979 Koteja 2004) While one can postulate advantages to theability to maintain elevated temperature it is unclear whichselective forces may have initiated the evolution of endothermy(Hayes and Garland 1995 Koteja 2000 Ruben 1995)

The evolution of homeothermic endothermy has generatedconsiderable scientific controversy and several hypotheses havebeen advanced (Hayes and Garland 1995 Ruben 1995) Theseinclude thermoregulation per se (Crompton et al 1978 Heinrich1977) increased aerobic capacity (Bennett and Ruben 1979) andintense parental care (Farmer 2000 2003 Koteja 2000) Thereproductive model was formulated by Farmer (2000) and it dividesthe evolution of homeothermic endothermy into two steps As a firststep increased thermogenesis was selected for (at low associatedcosts) to provide embryos with a developmental environment thathad a relatively high mean temperature and low variation Duringthe second step additional benefits such as the capacity forprolonged physical activity would have then permitted theemergence of extensive postnatal parental care including foodprovisioning to progeny a common feature of birds and mammals(Koteja 2000) This second step would thereby result in the fixationof high performance (and thus high-energy demand systems) andhomeothermic endothermy as displayed by birds and mammalsThe reproductive model is distinct from previous theories in thatendothermy is primarily beneficial to the progeny rather than theadult (Farmer 2000)

The reproductive model has been extensively discussed anddebated (Angilletta and Sears 2003 Farmer 2003) with the debatecentering on whether the thermal benefits accrued by the offspringduring development (eg increased survivability decreasedincubation period) outweigh the energetic costs exacted on theparents Opponents not only suggest that these benefits are unlikelyto exceed the costs but also point to the mixed results attained bystudies that have attempted to quantify these benefits (Andrewset al 2000 Shine et al 1997) Accurate assessment of the problemhowever requires that the energetic costs to the parent must beassessed relative to these benefits including factors that may affectsuch costs (eg nest site insulation)

While studies on heterothermic organisms have providedvaluable comparative data (Grigg et al 2004) empirical tests ofany model for the evolution of homeothermic endothermy are rareThe unique characteristics of pythons in which females of somespecies are facultatively endothermic during egg brooding (Vinegaret al 1970) have been used to support arguments for and againstthe reproductive model (Angilletta and Sears 2003 Farmer 2000)More recently Tattersall et al (2016) provided evidence that therelatively large tegu lizard Salvator merianae also employsfacultative endothermy to support reproductive efforts Howeverlittle work has been conducted to empirically examine therelationship between the energetic costs to the female and theReceived 17 January 2017 Accepted 18 April 2017

1Natural Sciences Department LaGuardia Community College Long Island CityNY 11101 USA 2School of Life Sciences Arizona State University Tempe AZ85287 USA 3School of Mathematical and Natural Sciences New College ofInterdisciplinary Arts and Sciences Arizona State University at the West CampusPhoenix AZ 85069 USA

Author for correspondence ( jbrashearslagcccunyedu)

JAB 0000-0003-4809-8812

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copy 2017 Published by The Company of Biologists Ltd | Journal of Experimental Biology (2017) 220 2409-2417 doi101242jeb151886

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thermal benefits to the developmental environment or how bioticand abiotic factors related to the reproductive event mayinfluence these costs and benefits In fact while pythonbrooding is widely mentioned in discussions of facultativeendothermy only a few species are known to have significantthermogenic capability (Brashears and DeNardo 2015Stahlschmidt and DeNardo 2010)As female snakes cannot be induced to produce heat or refrain

from producing heat we designed a pseudoserpent (an artificialsnake) that mimicked the insulating properties of a Childrenrsquospython (Antaresia childreni) a species that has become an effectivemodel for examining parental care tradeoffs (Lorioux et al 2012Stahlschmidt and DeNardo 2009ab) While A childreni does notuse facultative thermogenesis when brooding we were able toregulate the thermogenic capability of the pseudoserpent We usedthis pseudoserpent to (1) calculate the power required to create aconstant preferred developmental temperature under variousconditions with respect to environment and clutch and (2)determine the thermal consequences of the various conditionswhen thermogenic capability was absent or limited to 50 of thepower required for developmental homeothermy Specifically weconducted thermometric sets of trials that included threethermogenic potentials (homeothermy ectothermy and anintermediate condition) We imposed these three sets of conditionunder multiple diel cycles of ambient temperature (2 4 6degCamplitude with the zenith at the preferred developmentaltemperature) and multiple clutch sizes (5 10 and 15 eggs)Additionally we conducted trials in both non-insulated andinsulated nest conditions As heat production depended on thepower supplied to the pseudoserpent for each trial condition wewere able to directly estimate the energetic costs and thermalconsequences for the developmental environment

MATERIALS AND METHODSPseudoserpent constructionThe pseudoserpent was designed to mimic the size shape andinsulation properties of a brooding Childrenrsquos python (A childreni)The body of the pseudoserpent was constructed by inserting a130 cm spring into a 135 cm length of latex tubing (outsidediameter 24 mm inside diameter 18 mm McMaster-Carr Santa FeSprings CA USA) To provide the pseudoserpent with the ability togenerate heat we soldered 18 resistors (033 Ω All ElectronicsCorporation Van Nuys CA USA) in series with sufficient distancebetween them that the total length approximated the length of thepseudoserpentrsquos body A piece of 18 G wire was soldered to eachend of the resistor string and then the resistors were enclosed in apiece of waterproof heat shrinkable tubing The sealed resistorarray was then inserted into the body of the pseudoserpent A no3 rubber stopper was inserted into each end of the tubing with thecircuit wire exiting through a small (sim3 mm) hole in each of thestoppers Additionally a syringe needle (18 G 25 cm) fittedwith a stopcock penetrated one of the stoppers The stopcock andneedle were used for filling the pseudoserpent with water prior toeach set of trials

The complete pseudoserpent was then coiled into a beehiveposture typical of a brooding female and secured in that positionusing fine wire (Fig 1) To mimic the seal typically provided by thesnakersquos head we secured a piece of latex over the opening at the topof the coil Antaresia childreni females coil so effectively aroundtheir clutch that the eggs are completely confined when the female isin a tightly coiled position (Stahlschmidt and DeNardo 2008)Therefore we placed the brooding female and her clutch on a thinbed of synthetic insulation and filled any small gaps between coilswith small pieces of the same insulation Pseudo-eggs were made byremoving the fingers of large-sized latex gloves and filling themwith 15plusmn05 ml of water before knotting the end The desirednumber of eggs (depending on trial set see below) was then placedwithin the femalersquos coils The insulating properties of theresulting brooding pseudoserpent closely mimicked those of a liveA childreni female brooding her eggs (Fig 2)

To regulate the thermogenic activity of the pseudoserpent wesupplied power to the pseudoserpent through an amplifying circuitthat was controlled by a datalogger (21X micrologger CampbellScientific Instruments Logan UT USA) The program increasedpower to the pseudoserpent and thus current and heat production inproportion to the difference between the pseudoserpentndashpseudo-egginterface temperature (TInt) and the target incubation temperature(TSet 305degC which approximates the preferred incubationtemperature of A childreni Lourdais et al 2007)

List of symbols and abbreviationsGLM generalized linear modelTClutch clutch temperatureTEnv environmental temperatureTInt pseudoserpentndashpseudo-egg interface temperatureTNest nest temperatureTSet target incubation temperatureΔT temperature differentialΔTClutch difference between set temperature and clutch temperatureΔTInt difference between set temperature and interface

temperature

BA Fig 1 Pseudoserpent constructionA Childrenrsquos python (Antaresia childreni)brooding her clutch in a beehive posture (A)and the pseudoserpent brooding a clutch ofpseudo-eggs in a similar posture (B)

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TrialsTrials were conducted in a darkened temperature-controlledtest chamber that had a sinusoidal diel thermal cycle tightlycontrolled by the same datalogger used to power thepseudoserpent Chamber temperature was controlled usingfeedback from a 3-thermocouple array that surrounded thepseudoserpent at a distance of 10 cm thus averaging itsimmediate environmental temperature (TEnv) The environmentalchamber was equipped with a small fan to maximize thermalhomogeneity within the chamberIn addition to chamber temperature the datalogger also

recorded input from a thermocouple at the center of theclutch (TClutch) and from a thermocouple array averaging TIntover three points of contact During sets of trials with nestinsulation TEnv was measured just outside the insulating box andwe additionally measured nest temperature using a thermocoupleplaced within the insulating box but not in contact with thepseudoserpent (TNest)Trial sets were designed to test the relationship between power

consumption TClutch and TInt at a specified set point (TSet) in thepresence of a diel cycle Each trial set lasted 80 h and consisted ofconstant environmental conditions and clutch characteristics (seebelow) but variable thermogenic capability as the trial setprogressed On day 1 the pseudoserpent was supplied withunlimited power (up to 4 W which was sim300 mW above thepower needed to maintain TClutch even in the most demandingconditions) On day 2 the power limit was set to half of themaximum power consumed on the previous day At the end of day2 power to the pseudoserpent was discontinued (ie anectothermic condition was imposed) The first 8 h of day 3 wereused as an equilibration period to assure that starting temperatureswere the same for all three power conditions After the 8 hequilibration period we recorded all temperatures for a continuous24 h period

Diel cycle amplitude trialsTrial sets were conducted with TEnv following a sinusoidal dielcycle with a zenith temperature of 305degC and a nadir temperature of285 265 or 245degC (a 2 4 or 6degC diel cycle respectively) Thisrange of temperature cycles reflects the range reported for free-ranging nesting females of a python species that is sympatric toA childreni (Shine et al 1997) Three sets of trials were conductedat each of the three diel cycles and clutch size for these trials was 10eggs which approximates a typical clutch size for A childreni(Stahlschmidt and DeNardo 2008)

Clutch size trialsTrial sets were conducted in triplicate for clutch sizes of 5 10 and 15eggs which approximates the clutch size range of captiveA childreni (DFD unpublished data)

Insulation trialsWhile the sets of trials using clutch size as a treatment mimicked thesituation of brooding a clutch in open space on the surface this set oftrials provided insulation similar to what might be provided if afemale broods her eggs in a more restricted environment (eg withina burrow chamber) We examined both conditions as pythons ingeneral are known to brood either on the surface or within burrowsand the location of brooding in A childreni is unknown Trial setswere similarly conducted in triplicate for clutch sizes of 5 10 and 15eggs but for these trial sets we placed the pseudoserpent within arectangular box (24times17times16 cm) constructed by pinning a singlelayer of shade cloth (Synthesis Commercial 95 Arizona Sun SupplyInc Phoenix AZ USA) to the six faces of a wooden frame Wedetermined the thermal conductivity (k W degCminus1 mminus2) of the shadecloth by inserting a high wattage ceramic resistor within the centerof the box suspended from the top layer We placed the box withinthe test chamber and set the chamber to maintain 255degC to provide aconstant heat sink Thermocouples were placed at three points on theinner surface of the shade cloth and three points on the outer surfaceof the shade cloth We then provided constant power (16 W) acrossthe resistor and allowed the system to reach steady-state conditions(sim15 h) To calculate the thermal conductivity of the system weused the equation

k frac14 Q DdA DT

eth1THORNwhereQ is heat flow inW Δd is the thickness of the shade cloth A isthe surface area of the box and ΔT is the temperature differentialacross the shade cloth We did this under two conditions first withno air circulation within the environmental chamber then with thesmall fan turned on which we used during trials to ensurehomogeneity of the thermal environment For our material k=06plusmn02 W degCminus1 mminus2 with no air circulation and 20plusmn02 W degCminus1 mminus2

with air circulation

Data analysisData were analyzed by fitting multiple models to the data andcomparing Akaike information criterion (AIC) values Independentfactors were the type of diel cycle (2 4 6degC) the clutch size (5 1015 eggs) and insulation (no insulation one layer) Supplied power(zero half full) fitted as an independent factor produced the lowestAIC values but as these power levels were programmed into thetrials and we were interested in the relationships within the levelsthe final model was a general linear model (GLM) with suppliedpower as a covariate All data were tested for parametricassumptions The percentage of time the clutch (TClutch) and

Time of day (h)

Tem

pera

ture

(degC

)Air

Brooding Childrens pythonPseudoserpent

0000 0400 0800 1200 1600 2000 2400

24

26

28

30

32

34

Fig 2 Comparison of clutch temperatures Temperature is shown for aclutch being brooded by a female Childrenrsquos python and an artificial clutchsurrounded by a similarly sized pseudoserpent simultaneously maintained in a6degC diel cycle As A childreni is ectothermic the model was set to zerothermogenic potential to compare the insulating properties of the female andthe pseudoserpent Air temperature is also shown

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interface (TInt) spent at suboptimal temperatures (ΔT10degC) wascalculated for each trial then arcsine transformed and tested acrosseach treatment (diel clutch size insulation) with supplied power asa covariate All data are presented as meansplusmnsem Analyses wereperformed using R 2140 (R Development Core Team 2011) andmodels were run using the lme4 package (Bates et al 2011)

RESULTSThe power required by the pseudoserpent during the trials reflectedthe energetic costs of maintaining TClutch above TEnv (Table 1)Power metrics modeled a femalersquos metabolic rate during broodingThe maximum recorded power during a 3 day trial increased withthe amplitude of the diel cycle (F271=31431 Plt0001) but was notsignificantly decreased with the addition of insulation (F171=3190P=0078) The total power supplied during a single 24 h periodreflected the average power over that period Total power wasincreased by the diel cycle amplitude (F271=33734 Plt0001) aswell as clutch size (F271=5928 P=0004) The addition ofinsulation strongly decreased total power (F171=18866 Plt0001)The mean interface temperature difference (ΔTInt=TSetminusTInt)

increased with diel cycle amplitude (F271=34417 Plt0001) andwas weakly decreased by the addition of insulation (F271=3806P=0055 Table 2) Both the maximum recorded ΔTInt and thepercentage of time during which ΔTInt was at a suboptimaltemperature (ΔT10degC) increased with diel cycle amplitude(maximum ΔTInt F271=57623 Plt0001 percentage timeF222=25672 Plt0001 Table 2) but decreased with the additionof insulation (maximum ΔTInt F171=6790 P=0011 percentagetime F165=14045 Plt0001 Table 2) The variance of TIntincreased only in response to the amplitude of the diel cycle(F271=20107 Plt0001 Table 3) Clutch size had no effect on anyinterface metricsThe amplitude of the diel cycle significantly increased the

amount of time TClutch experienced a suboptimal environmentaltemperature by all metrics of TClutch the calculated mean ΔTClutch(ΔTClutch=TSetminusTClutch F271=72722 Plt0001) the maximumrecorded ΔTClutch (F271=87118 Plt0001) the percentage of time

the clutch spent at a suboptimal temperature (F222=15411Plt0001) and the variance in temperature the clutch experienced(F271=23053 Plt0001) Interestingly the addition of insulationalso increased the mean ΔTClutch (F171=6921 P=0010) themaximum recorded ΔTClutch (F171=8406 P=0005) the thermalvariance that the clutch experienced (F171=3610 P=0062) and thepercentage of time the clutch spent at a suboptimal temperature(F165=26398 Plt0001) Clutch size did not affect most metricsbut larger clutches increased the percentage of time a clutchexperienced suboptimal temperatures (F243=8357 Plt0001)

DISCUSSIONCosts and benefits of homeothermic endothermyWe designed an artificial snake model (pseudoserpent) to estimatethe cost and benefits associated with reproductive endothermy inpythons The pseudoserpent mimicked a brooding Childrenrsquos python(A childreni) which although not facultatively endothermic hasbecome a useful model for examining brooding tradeoffs (Loriouxet al 2012 Stahlschmidt and DeNardo 2009ab)

The unlimited thermogenic pseudoserpent was able to maintainthe temperature of the clutch within an optimal range (Table 2Fig 3) but doing so required considerable amounts of energy(Table 1 Fig 3) At the 6degC amplitude with a 10-egg clutch thepseudoserpent used 148plusmn4 kJ over the 24 h trial (Table 1) Incomparison a much larger (16 kg) brooding and facultativelyendothermic Burmese python (Python molurus) maintaining a 6degCgradient averages approximately 772 kJ dayminus1 (21 g fat dayminus1Brashears and DeNardo 2013) Despite heating a much largerclutch mass (50-fold) energy requirements to maintain a similardevelopmental homeothermic state are only 5-fold higher for theBurmese python Such large differences in energy requirementsper gram of clutch are a result of the high thermal conductivityof smaller females Using the maximum recorded power andthe temperature differential the pseudoserpent maintained at thatpower the thermal conductivity of our pseudoserpent is 063plusmn01 W kgminus1 degCminus1 closely matching the thermal conductivity of065 W kgminus1 degCminus1 reported for the slightly larger ball pythons

Table 1 Maximum power mean energy and total energy used by an artificial snake during trials

Diel cycle clutch sizePowersupplied

Max power(mW)

Meanenergy (J)

Totalenergy (kJ)

Relative cost(no of eggs)

No insulation 10-egg clutch 2degC Full 1213plusmn16 37plusmn1 53plusmn2 07Half 618plusmn10 27plusmn1 39plusmn2 05

4degC Full 2323plusmn18 70plusmn1 100plusmn1 13Half 1172plusmn7 49plusmn1 71plusmn2 09


No insulation 6degC diel cycle 5 eggs Full 3802plusmn29 76plusmn1 109plusmn1 14Half 1369plusmn33 56plusmn5 81plusmn8 10

10 eggs Full 3903plusmn72 84plusmn1 121plusmn1 16Half 1414plusmn16 58plusmn1 84plusmn1 11


Insulation 6degC diel cycle 5 eggs Full 3554plusmn18 64plusmn1 93plusmn1 12Half 1112plusmn14 45plusmn1 65plusmn2 08



Power supplied was the thermogenic limit put on the pseudoserpent (see Materials and methods for details) Wemanipulated the amplitude of the diel cycle (2 4or 6degC) using a 10-egg clutch size as well as clutch size (5 10 or 15 eggs) using a 6degC diel cycle under both insulated and non-insulated conditions (seeMaterialsand methods) Total energy is expressed as the cost relative to egg production using a 15 g egg with a composition of 14 lipid All trials were conducted intriplicate and values are presented as meansplusmnsem

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(Python regius) (Ellis and Chappell 1987) In contrast the twofacultatively endothermic species the Burmese python (P molurus)and the diamond python (Morelia spilota) are considerably larger andhave reduced thermal conductivity (027 and 0114 W kgminus1 degCminus1respectively) (Ellis and Chappell 1987)In addition to energy savings resulting from size-based

differences in conductivity larger snakes also have greater energyreserves At 148 kJ dayminus1 a female A childreni would use 188 g offat over a species-typical 48 day brooding period (Lorioux et al2012) or 63 of body mass assuming a 300 g post-parturient bodymass (Stahlschmidt and DeNardo 2008) If shewere to maintain themaximum power we recorded during the entirety of the same trialshe would need to use over the 48 day brooding period 375 g fatwhich is more than her entire body mass However over a species-typical 60 day incubation period (Ramesh and Bhupathy 2010) thefemale Burmese python at 772 kJ dayminus1 would require a total of12 kg of fat which represents only 75 of her body mass a veryfeasible investmentWhile endothermy buffers the developmental thermal environment

from ambient conditions the costs of endothermy are still highlysensitive to ambient conditions Thus even for facultativelyendothermic brooders nest site selection can be critically importantfor balancing the costs and benefits of endothermy For thepseudoserpent the cost of heating a 10-egg clutch for 48 days wentfrom 188 g of fat (63 of bodymass) for the 6degC diel cycle to 67 g offat (22 of body mass) for the 2degC cycleIn addition to the thermal variation of a nest heat loss through

conductivity also greatly influences the cost of endothermy(Tattersall 2016) While reptiles do not possess an insulating coat(eg fur or feathers) it is plausible that an endothermic python could

reduce the energy costs of regulating the egg developmentalenvironment by altering blood perfusion and directing greaterperipheral flow to her body wall that faces her eggs while reducingflow to the side away from the eggs Alteration in blood flow is awell-documented component of thermoregulation in squamates(Porter and Witmer 2015 Tattersall et al 2016 Weathers 1971)and peripheral flow adjustments associated with brooding remainunexplored and deserve attention

While we could not evaluate changes in conductivity associatedwith altered perfusion we could evaluate the effect of nestinsulation on conductive heat loss which assuredly wouldinfluence the cost of regulating the developmental environment(Farmer 2001 Tattersall 2016) The addition of a single layer ofinsulation during the 6degC diel cycle required 132 g of fat (44 ofbody mass) which is 30 less than the 188 g of fat calculated forour non-insulated trials The thermal conductivity of the insulatednest environment we created for our experimental trials was 20plusmn03 W degCminus1 mminus1 In comparison the thermal conductivity of soilcan range widely from 03 to 4 W degCminus1 mminus1 depending on the typeof soil and the amount of moisture For dry soil the thermalconductivity is approximately 1 W degCminus1 mminus1 (Somerton 1992)and a burrow with this conductivity would reduce the energeticcosts of our model even further requiring 98 g of fat (31 bodymass) during a 48 day brooding period

It is pertinent to note that convection within our test chambercreated by a small fan used to avoid thermal stratification may haveled to an overestimation of the energetic costs associated withbrooding if the female nested in a location with minimal air flowHowever the natural nesting environments of A childreni arecurrently unknown and both facultatively endothermic species

Table 2 Differences between set temperature (TSet) of the pseudoserpent and both clutch (TClutch) and interface temperature (TInt) during trials

Diel cycleclutch size Power

TClutch (degC) TInt (degC)

Mean ΔTClutch Max ΔTClutch Time ΔT1degC Mean ΔTInt Max ΔTInt Time ΔT1degC

No insulation 10-egg clutch 2degC Full 017plusmn001 024plusmn002 00plusmn00 001plusmn000 005plusmn000 00plusmn00Half 048plusmn001 106plusmn002 108plusmn14 031plusmn001 092plusmn002 00plusmn00None 132plusmn007 223plusmn006 617plusmn16 112plusmn006 206plusmn005 542plusmn13

4degC Full 018plusmn006 026plusmn006 00plusmn00 002plusmn000 006plusmn001 00plusmn00Half 075plusmn005 191plusmn009 345plusmn12 059plusmn002 180plusmn005 342plusmn23None 222plusmn002 401plusmn002 740plusmn03 206plusmn005 392plusmn004 694plusmn05


No insulation 6degC diel cycle 5 eggs Full 073plusmn009 128plusmn061 00plusmn00 008plusmn001 024plusmn001 00plusmn00Half 152plusmn015 308plusmn005 425plusmn14 091plusmn015 257plusmn008 384plusmn02None 310plusmn016 575plusmn011 799plusmn07 273plusmn005 547plusmn009 755plusmn05

10 eggs Full 069plusmn019 119plusmn017 00plusmn00 008plusmn001 044plusmn031 00plusmn00Half 148plusmn022 319plusmn029 427plusmn03 086plusmn003 256plusmn009 371plusmn03None 337plusmn014 588plusmn012 791plusmn05 295plusmn007 559plusmn007 795plusmn05


Insulation 6degC diel cycle 5 eggs Full 10plusmn04 20plusmn10 177plusmn11 03plusmn04 10plusmn13 00plusmn00Half 18plusmn07 39plusmn14 524plusmn23 14plusmn09 35plusmn16 358plusmn01None 91plusmn103 140plusmn140 892plusmn26 89plusmn106 138plusmn144 802plusmn15



Power refers to the thermogenic limit put on the pseudoserpent (see Materials and methods for details) We manipulated the amplitude of the diel cycle (2 4 or6degC) using a 10-egg clutch size as well as clutch size (5 10 or 15 eggs) using a 6degC diel cycle under both insulated and non-insulated conditions (see Materialsand methods) All trials were conducted in triplicate and values are presented as meansplusmnsem

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(P molurus and M spilota) have been reported brooding on thesurface where convection could easily equal or exceed that presentin our chamber (Ramesh and Bhupathy 2010 Slip and Shine1988)The tight brooding posture of A childreni (Fig 1) reduces clutch

evaporative water loss 15-fold (Lourdais et al 2007) but water lossstill occurs from the female and her clutch and the entropy ofvaporization associated with this water loss contributes to heat lossfrom the brooding female In a previous study water loss frombrooding females and their eggs was calculated to be on average9047 mg hminus1 (Lourdais et al 2007) which would result in 724 gof water lost over an 80 h period Over the 80 h experimental trialsthe pseudoserpent and her artificial eggs lost an average of 81 g allattributable to water loss These similar values suggest aninsignificant difference in heat loss due to vaporization betweenthe natural and artificial systems

Clearly microhabitat selection altered blood perfusion andbehaviors such as intermittent basking (Slip and Shine 1988) canreduce the cost of homeothermic endothermy and these influencesare especially important to small snakes which have limited energyreserves to support endothermy Even using such mechanisms toreduce costs homeothermic endothermy might still be beyond thecapability of some female pythons as they invest enormous amountsof fat and muscle reserves into the production of the clutch(Lourdais et al 2013) and brooding occurs immediately followingthis investment

The effect of the thermal developmental environment on offspringfitness is still being explored in pythons Early studies showed thatP molurus eggs are sensitive to increases in ΔTClutch with survivalrates quickly approaching zero when ΔTClutchgt3degC (Vinegar 1973)In the ectothermic water python (Liasis fuscus) however eggsurvival seems robust to daily temperature fluctuations (maximum

Incubation temperatureTe

mpe

ratu

re (deg

C)

Full power

Half power

Zero power

Power consumption

Full powerHalf power

Pow

er (W

)

Time of day (h)0000 0400 0800 1200 1600 2000 2400 0000 0400 0800 1200 1600 2000 2400

2degC

4degC

6degC

24

26

28

30

32

24

26

28

30

32

24

26

28

30

32

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

Fig 3 Pseudoserpent and artificial clutchmetrics over a 3 day trial Example ofpower consumed and temperature datacollected during a single trial using apseudoserpent model with variable powerpotential (4 W half the maximum powerrequired for clutch homeothermy and nopower) and variable thermal diel cycles (2 4and 6degC) set to maintain interfacetemperature (the temperature at the contactzone between the pseudoserpent andartificial clutch) at 305degC Trials wereconducted in triplicate at different thermaldiel cycles (amplitude of 2 4 or 6degC) and thepseudoserpent was programmed to have aheating potential of either full or half powerPlots on the left show the incubationtemperatures of the artificial clutch (TClutchsolid lines) and the interface between thepseudoserpent and clutch (TInt dotted lines)Gray lines are air temperature Plots on theright show the power consumed by the snakewhen it was provided full power potential andhalf power potential

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ΔTClutch=8degC) although higher developmental temperatures decreasethe length of incubation (Shine et al 1997) which can result in anincrease in hatchling survival rate (Madsen and Shine 1999)The pseudoserpent was able to maintain an optimal environment

for the artificial clutch with unlimited power mimicking athermogenic python capable of homeothermic endothermy Thefraction of time the clutch spent at suboptimal temperatures wasgreatly reduced as were the mean ΔTClutch (Table 2) and thevariance of TClutch (Table 3) When the pseudoserpent was suppliedwith zero power mimicking the ectothermic condition the meanΔTClutch increased by approximately 3degC and the maximumΔTClutch increased by approximately 5degC during the 6degC diel cycle(10-egg clutch Table 2) Additionally the clutch was belowoptimal developmental temperature 61ndash83 of the time (Table 2)and the variance of TClutch increased by approximately 35degC(Table 3)As there is considerable overlap in the ranges of A childreni and

L fuscus it is likely that the egg development in A childreni issimilarly robust to the effects of temperature Although pre-oviposition body temperature in a female has been shown toaffect offspring fitness (Lorioux et al 2012) no data currently existon the relationship between clutch temperature and offspring fitnessin A childreni Even if the A childreni eggs are as thermallysensitive as those of P molurus it seems highly improbable that thebenefits to offspring fitness provided by a fully thermogenic femalewould outweigh the energetic costs to the female even if theseenergetic costs were reduced environmentally Thus we concludethat the high thermal conductance of small females combined with

their inability to store the large fat reserves that thermogenesiswould require prohibits them from being facultatively endothermic

Costs and benefits of limited thermogenesisThe reproductive model for the evolution of endothermy posits thatthermogenesis was initially selected for the benefits it provided tothe developing offspring (Farmer 2000) In pythons this wouldhave entailed small increases in thermogenesis that providedsufficient offspring benefits to drive full facultative endothermyAs much of the debate regarding the reproductive model centers onhow the costs of such limited thermogenesis would be offset byincreases in offspring benefits (Angilletta and Sears 2003 Farmer2003) we examined these costs when the maximum amount ofpower supplied to the pseudoserpent was reduced by halfmimicking a limited thermogenic state

In the limited thermogenic state the pseudoserpent spent moretime drawing its maximum power Thus mean and total energy didnot decrease by 50 but decreased by around 30 acrosstreatments This reduced the total energy cost that an unlimitedthermogenic 600 g female would have to expend during 60 daysunder a 6degC diel cycle from 235 g of fat (39 body mass) to 165 gof fat (28 body mass) These costs were offset by substantialbenefits to the clutch over the fully ectothermic state Under a 6degCdiel cycle the maximum ΔTClutch and the percentage of time theclutch spent below optimal developmental temperature decreasedby 52 and 46 respectively The mean ΔTClutch decreased by58 and the variance of TClutch decreased by 73 This trend wasrepeated under the 2 and 4degC diel cycles Thus a limitedthermogenic female under a 2degC diel cycle would lose only 62 gof fat (10 initial body mass) but still gain a 50ndash75 reduction inthermal costs

These results suggest that the evolution of limited thermogenesismight confer disproportionate benefits to the offspring especiallyin the reduction of thermal variance which can affect fitness(Bozinovic et al 2011 DuRant et al 2013 Shine et al 1997)Although the high thermal conductivity of a small species wouldlikely still make the energetic cost prohibitive a full explanatorymodel must include the reduction in costs conferred by environmentalvariables (eg tropical environment nest site selection) Our resultsalso suggest that a femalersquos maximum metabolic rate might be aconstraint in the evolution of limited thermogenesis

Relationship of the model to the evolution of endothermyOur results highlight several novel aspects of python endothermyUnexpectedly clutch size had no significant effect on any energeticor thermal metric except the percentage of time the clutch spent atoptimal temperature (ΔT10degC Tables 1ndash3) with a large clutchsize slightly depreciating the thermal environment (Fig 4) Thisresult suggests there might not be an increased energetic costassociated with the thermal inertia of larger clutches a resultsupported by data from P regius showing that energy expenditurefrom coiling does not increase even with a 50 increase in clutchsize (Aubret et al 2005) The depreciation of the thermalenvironment however might act as a selective force indetermining species clutch size

Previous work has indicated that brooding P molurus regulatetheir own body temperature during facultative endothermy and onlyindirectly regulate clutch temperature (Brashears and DeNardo2013) Similarly the pseudoserpent increased heat production inproportion to the magnitude of ΔTInt As the thermocouples were indirect contact with the inner surface of the pseudoserpent ΔTInt waspresumably largely driven by the pseudoserpentrsquos temperature This

Table 3 Variance of clutch (TClutch) and interface temperature (TInt)

Diel cycleclutch size

Powersupplied

TClutchvariance (degC)

TInt

variance (degC)

No insulation10-egg clutch

2degC Full 0001plusmn0001 0000plusmn0000Half 0105plusmn0008 0123plusmn0005None 0405plusmn0010 0432plusmn0013



No insulation6degC diel cycle

5 eggs Full 0064plusmn0053 0003plusmn0001Half 0921plusmn0047 0921plusmn0047None 3276plusmn0241 3276plusmn0241



Insulation6degC diel cycle




Power supplied was the thermogenic limit put on the pseudoserpent (seeMaterials and methods for details) We manipulated the amplitude of the dielcycle (2 4 or 6degC) using a 10-egg clutch size as well as clutch size (5 10 or 15eggs) using a 6degC diel cycle under both insulated and non-insulated conditions(see Materials and methods) All trials were conducted in triplicate and valuesare presented as meansplusmnsem

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had the counter-intuitive effect of reducing the benefits to the clutchwhen insulation was added (Table 2) Under the insulated conditionthe pseudoserpent consumed less power (Table 1) to regulate itsown temperature (Table 2) which ultimately decreased heattransference to the clutch Thus the presence of a nestenvironment during the evolution of endothermy would only havebeen adaptive if the lowered energetic costs were not offset by adepreciated nest environmentAs pythons are capital breeders energy allocated to

thermogenesis would likely come at a cost in the form of reducedclutch size Although the exact composition of A childreni eggs isunknown lipids are responsible for 14 of the wet mass of eggs inL fuscus (Speake et al 2003) For a 15 g pseudoserpent egg thiswould translate into a minimal cost of 777 kJ per egg At themaximum diel cycle and without insulation providingdevelopmental homeothermy would cost almost two eggs(Table 1) In addition to lipids eggs contain protein and othernutrients and their production requires metabolic energy(Thompson and Speake 2003) Therefore this approximationmay overestimate the relative costs It would not be surprising iffacultatively endothermic pythons had reduced clutch sizes relativeto female body mass a line of inquiry that is becoming moretractable as comparative reproductive data emergeOur results provide some insight into the costs and benefits that

may have driven the evolution of endothermy The mean powerconsumed by the pseudoserpent increased dramatically in responseto increased diel cycle amplitude in both the limited and fullthermogenic states (Fig 5A) However increasing diel cyclesincreased only the thermal variance of the clutch for pseudoserpentsmimicking the ectothermic and limited thermogenic states but notthe full thermogenic state (Fig 5B) An intuitive interpretation isthat environmental temperatures could have driven the evolution offacultative endothermy by initially increasing offspring fitnessthrough a reduction of clutch variance but afterwards

environmental temperatures would mainly select for a reductionof energetic costs (eg increased insulation) The achievement oflower energetic costs could then allow new selective pressures todominate As heterothermy is likely the ancestral condition for birdsandmammals (Grigg et al 2004) a scenario in which new selectionpressures extended endothermy to other life stages is plausible

In summary our results demonstrate that pseudoserpentthermometry is a useful tool for investigating the evolution ofpython endothermy and it provides insight into the evolution ofendothermy in general Our model was able to quantify many of theenergetic costs and thermal benefits associated with pythonbrooding Future research will benefit from the expansion of themodel to facultatively endothermic python species to gain greaterunderstanding of the role played by body size in the evolution ofendothermy

AcknowledgementsWe would like to thank C Garcia for early work with developing the pseudoserpentand two anonymous reviewers whose comments improved this manuscript

Competing interestsThe authors declare no competing or financial interests

Author contributionsConceptualization DFD Methodology TCMH DFD Software TCMHValidation TCMH DFD Formal analysis JAB Investigation JAB Writing -original draft JAB Writing - review amp editing JAB TCMH DFD Fundingacquisition DFD

FundingThis work was supported by a National Science Foundation grant to DFD(IOS-0543979)

ReferencesAndrews R M Mathies T and Warner D A (2000) Effect of incubation

temperature on morphology growth and survival of juvenile Sceloporusundulatus Herpetol Monogr 14 420

Angilletta M J Jr and Sears M W (2003) Is parental care the key tounderstanding endothermy in birds and mammals Am Nat 162 821-825

Clutch size (no of eggs)

Pro

porti

on o

f tim

e at

ΔTge

10deg

C

5 10 15

Full powerHalf powerZero power

0

20

40

60

80

100

Fig 4 Proportion of time clutches spent at suboptimal temperature as aproduct of clutch size Suboptimal temperature was ΔT10degC from thepreferred developmental temperature of 305degC Supplied power was acovariate A clutch size of 10 eggs reduces the amount of time a clutchexperiences suboptimal temperatures when the pseudoserpent is suppliedwith power Data are averages of three replicate trials

Diel cycle

Mea

n to

tal p

ower

(mW

)

2degC 4degC 6degC 2degC 4degC 6degC

A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

40

60

80

0

05

10

15

20

25

30

Fig 5 Energetic costs to pseudoserpent and thermal benefits to clutchThe mean total power used by the pseudoserpent (A) and the clutch thermalvariance (B) during three 24 h diel cycles with different maximum amplitudes2 4 6degC Each diel cycle was run in triplicate and averaged

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Aubret F Bonnet X Shine R and Maumelat S (2005) Energy expenditure forparental care may be trivial for brooding pythons Python regius Anim Behav 691043-1053

Bates D Maechler M and Bolker B (2011) Lme4 Linear mixed-effects modelsusing S4 classes R package version 0999375-38 URL httpsCRANR-projectorgpackage=lme4

Bennett A F and Ruben J A (1979) Endothermy and activity in vertebratesScience 206 649-654

Bozinovic F Bastıas D A Boher F Clavijo-Baquet S Estay S A andAngilletta M J (2011) The mean and variance of environmental temperatureinteract to determine physiological tolerance and fitness Physiol Biochem Zool84 543-552

Brashears J A and DeNardo D F (2013) Revisiting python thermogenesisbrooding Burmese pythons (Python bivittatus) cue on body not clutchtemperature J Herpetol 47 440-444

Brashears J and DeNardo D F (2015) Facultative thermogenesis duringbrooding is not the norm among pythons J Comp Physiol A 201 817-825

Crompton A W Taylor C R and Jagger J A (1978) Evolution ofhomeothermy in mammals Nature 272 333-336

DuRant S E Hopkins W A Hepp G R and Walters J R (2013) Ecologicalevolutionary and conservation implications of incubation temperature-dependentphenotypes in birds Biol Rev 88 499-509

Ellis T M and Chappell M A (1987) Metabolism temperature relationsmaternal behavior and reproductive energetics in the ball python (Python regius)J Comp Physiol B 157 393-402

Farmer C G (2000) Parental care the key to understanding endothermyand otherconvergent features in birds and mammals Am Nat 155 326-334

Farmer C G (2001) A new perspective on the origin of endothermy In NewPerspectives on the Origin and Early Evolution of Birds Proceedings of theInternational Symposium in Honor of John H Ostrom February 13-14 1999 NewHaven Connecticut (ed J A Gauthier and LF Gall) pp 389-412 New HavenCT Yale University Peabody Museum

Farmer C G (2003) Reproduction the adaptive significance of endothermy AmNat 162 826-840

Grigg C G Beard L A and Augee M I (2004) The evolution of endothermyand its diversity in mammals and birds Physiol Biochem Zool 77 982-997

Hayes J P and Garland T (1995) The evolution of endothermy testing theaerobic capacity model Evolution (N Y) 49 836-847

Heinrich B (1977) Why have some animals evolved to regulate a high bodytemperature Am Nat 111 623-640

Koteja P (2000) Energy assimilation parental care and the evolution ofendothermy Proc Biol Sci 267 479-484

Koteja P (2004) The evolution of concepts on the evolution of endothermy in birdsand mammals Physiol Biochem Zool 77 1043-1050

Lorioux S DeNardo D F Gorelick R and Lourdais O (2012) Maternalinfluences on early development preferred temperature prior to ovipositionhastens embryogenesis and enhances offspring traits in the Childrenrsquos pythonAntaresia childreni J Exp Biol 215 1346-1353

Lourdais O Hoffman T C M and DeNardo D F (2007) Maternal brooding inthe Childrenrsquos python (Antaresia childreni) promotes egg water balance J CompPhysiol B 177 569-577

Lourdais O Lorioux S and DeNardo D F (2013) Structural and performancecosts of reproduction in a pure capital breeder the Childrenrsquos python Antaresiachildreni Physiol Biochem Zool 86 176-183

Madsen T and Shine R (1999) Life history consequences of nest-site variation intropical pythons (Liasis fuscus) Ecology 80 989-997

Porter W R and Witmer L M (2015) Vascular patterns in iguanas and othersquamates blood vessels and sites of thermal exchange PLoS ONE 10e0139215

Ramesh C and Bhupathy S (2010) Breeding biology ofPython molurusmolurusin Keoladeo National Park Bharatpur India Herpetol J 20 157-163

R Development Core Team (2011) R A Language and Environment for StatisticalComputing Vienna Austria Foundation for statistical computing URL httpwwwR-projectorg

Ruben J (1995) The evolution of endothermy in mammals and birds fromphysiology to fossils Annu Rev Physiol 57 69-95

Shine R Madsen T Elphick M and Harlow P (1997) The influence of nesttemperatures and maternal brooding on hatchling phenotypes in water pythonsEcology 78 1713-1721

Slip D J and Shine R (1988) The reproductive biology and mating system ofdiamond pythonsMorelia spilota (Serpentes Boidae) Herpetologica 44 396-404

Somerton W H (1992) Thermal Properties and Temperature-Related Behavior ofRockFluid Systems Amsterdam Elsevier Science

Speake B K Thompson M B Thacker F E and Bedford G S (2003)Distribution of lipids from the yolk to the tissues during development of the waterpython (Liasis fuscus) J Comp Physiol B 173 541-547

Stahlschmidt Z R and DeNardo D F (2008) Alternating egg-broodingbehaviors create and modulate a hypoxic developmental micro-environment inChildrenrsquos pythons (Antaresia childreni) J Exp Biol 211 1535-1540

Stahlschmidt Z R and DeNardo D F (2009a) Obligate costs of parental care tooffspring Egg brooding-induced hypoxia creates smaller slower and weakerpython offspring Biol J Linn Soc 98 414-421

Stahlschmidt Z R andDeNardo D F (2009b) Effect of nest temperature on egg-brooding dynamics in Childrenrsquos pythons Physiol Behav 98 302-306

Stahlschmidt Z and DeNardo D F (2010) Parental care in snakes InReproductive Biology and Phylogeny of Snakes (ed R D Aldridge and D MSever) pp 673-702 Enfield NH Science Publishers Inc

Tattersall G J (2016) Reptile thermogenesis and the origins of endothermyZoology 119 403-405

Tattersall G J Leite C A C Sanders C E Cadena V Andrade D V AbeA S and Milsom W K (2016) Seasonal reproductive endothermy in tegulizards Sci Adv 2 e1500951

Thompson M B and Speake B K (2003) Energy and nutrient utilisation byembryonic reptiles Comp Biochem Physiol A 133 529-538

Vinegar A (1973) The effects of temperature on the growth and development ofembryos of the Indian python Python molurus (Reptilia Serpentes Boidae)Copeia 1973 171-173

Vinegar A Hutchison V H and Dowling H G (1970) Metabolism energeticsand thermoregulation during brooding of snakes of the genus Python (ReptiliaBoidae) Zoologica 55 19-48 2 plates

Weathers W W (1971) Some cardiovascular aspects of temperature regulation inthe lizard Dipsosaurus dorsalis Comp Biochem Physiol A Physiol 40A503-515

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thermal benefits to the developmental environment or how bioticand abiotic factors related to the reproductive event mayinfluence these costs and benefits In fact while pythonbrooding is widely mentioned in discussions of facultativeendothermy only a few species are known to have significantthermogenic capability (Brashears and DeNardo 2015Stahlschmidt and DeNardo 2010)As female snakes cannot be induced to produce heat or refrain

from producing heat we designed a pseudoserpent (an artificialsnake) that mimicked the insulating properties of a Childrenrsquospython (Antaresia childreni) a species that has become an effectivemodel for examining parental care tradeoffs (Lorioux et al 2012Stahlschmidt and DeNardo 2009ab) While A childreni does notuse facultative thermogenesis when brooding we were able toregulate the thermogenic capability of the pseudoserpent We usedthis pseudoserpent to (1) calculate the power required to create aconstant preferred developmental temperature under variousconditions with respect to environment and clutch and (2)determine the thermal consequences of the various conditionswhen thermogenic capability was absent or limited to 50 of thepower required for developmental homeothermy Specifically weconducted thermometric sets of trials that included threethermogenic potentials (homeothermy ectothermy and anintermediate condition) We imposed these three sets of conditionunder multiple diel cycles of ambient temperature (2 4 6degCamplitude with the zenith at the preferred developmentaltemperature) and multiple clutch sizes (5 10 and 15 eggs)Additionally we conducted trials in both non-insulated andinsulated nest conditions As heat production depended on thepower supplied to the pseudoserpent for each trial condition wewere able to directly estimate the energetic costs and thermalconsequences for the developmental environment

MATERIALS AND METHODSPseudoserpent constructionThe pseudoserpent was designed to mimic the size shape andinsulation properties of a brooding Childrenrsquos python (A childreni)The body of the pseudoserpent was constructed by inserting a130 cm spring into a 135 cm length of latex tubing (outsidediameter 24 mm inside diameter 18 mm McMaster-Carr Santa FeSprings CA USA) To provide the pseudoserpent with the ability togenerate heat we soldered 18 resistors (033 Ω All ElectronicsCorporation Van Nuys CA USA) in series with sufficient distancebetween them that the total length approximated the length of thepseudoserpentrsquos body A piece of 18 G wire was soldered to eachend of the resistor string and then the resistors were enclosed in apiece of waterproof heat shrinkable tubing The sealed resistorarray was then inserted into the body of the pseudoserpent A no3 rubber stopper was inserted into each end of the tubing with thecircuit wire exiting through a small (sim3 mm) hole in each of thestoppers Additionally a syringe needle (18 G 25 cm) fittedwith a stopcock penetrated one of the stoppers The stopcock andneedle were used for filling the pseudoserpent with water prior toeach set of trials

The complete pseudoserpent was then coiled into a beehiveposture typical of a brooding female and secured in that positionusing fine wire (Fig 1) To mimic the seal typically provided by thesnakersquos head we secured a piece of latex over the opening at the topof the coil Antaresia childreni females coil so effectively aroundtheir clutch that the eggs are completely confined when the female isin a tightly coiled position (Stahlschmidt and DeNardo 2008)Therefore we placed the brooding female and her clutch on a thinbed of synthetic insulation and filled any small gaps between coilswith small pieces of the same insulation Pseudo-eggs were made byremoving the fingers of large-sized latex gloves and filling themwith 15plusmn05 ml of water before knotting the end The desirednumber of eggs (depending on trial set see below) was then placedwithin the femalersquos coils The insulating properties of theresulting brooding pseudoserpent closely mimicked those of a liveA childreni female brooding her eggs (Fig 2)

To regulate the thermogenic activity of the pseudoserpent wesupplied power to the pseudoserpent through an amplifying circuitthat was controlled by a datalogger (21X micrologger CampbellScientific Instruments Logan UT USA) The program increasedpower to the pseudoserpent and thus current and heat production inproportion to the difference between the pseudoserpentndashpseudo-egginterface temperature (TInt) and the target incubation temperature(TSet 305degC which approximates the preferred incubationtemperature of A childreni Lourdais et al 2007)

List of symbols and abbreviationsGLM generalized linear modelTClutch clutch temperatureTEnv environmental temperatureTInt pseudoserpentndashpseudo-egg interface temperatureTNest nest temperatureTSet target incubation temperatureΔT temperature differentialΔTClutch difference between set temperature and clutch temperatureΔTInt difference between set temperature and interface

temperature

BA Fig 1 Pseudoserpent constructionA Childrenrsquos python (Antaresia childreni)brooding her clutch in a beehive posture (A)and the pseudoserpent brooding a clutch ofpseudo-eggs in a similar posture (B)

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k frac14 Q DdA DT




Time of day (h)

Tem

pera

ture

(degC

)Air


0000 0400 0800 1200 1600 2000 2400

24

26

28

30

32

34


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Max power(mW)

Meanenergy (J)

Totalenergy (kJ)












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mpe

ratu

re (deg

C)

Full power

Half power

Zero power

Power consumption


Pow

er (W

)

Time of day (h)0000 0400 0800 1200 1600 2000 2400 0000 0400 0800 1200 1600 2000 2400

2degC

4degC

6degC

24

26

28

30

32

24

26

28

30

32

24

26

28

30

32

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4


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Powersupplied


TInt

variance (degC)














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Pro

porti

on o

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e at

ΔTge

10deg

C

5 10 15


0

20

40

60

80

100


Diel cycle

Mea

n to

tal p

ower

(mW

)


A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

40

60

80

0

05

10

15

20

25

30


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k frac14 Q DdA DT




Time of day (h)

Tem

pera

ture

(degC

)Air


0000 0400 0800 1200 1600 2000 2400

24

26

28

30

32

34


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Max power(mW)

Meanenergy (J)

Totalenergy (kJ)












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mpe

ratu

re (deg

C)

Full power

Half power

Zero power

Power consumption


Pow

er (W

)

Time of day (h)0000 0400 0800 1200 1600 2000 2400 0000 0400 0800 1200 1600 2000 2400

2degC

4degC

6degC

24

26

28

30

32

24

26

28

30

32

24

26

28

30

32

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4


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Powersupplied


TInt

variance (degC)














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Pro

porti

on o

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e at

ΔTge

10deg

C

5 10 15


0

20

40

60

80

100


Diel cycle

Mea

n to

tal p

ower

(mW

)


A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

40

60

80

0

05

10

15

20

25

30


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Totalenergy (kJ)












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mpe

ratu

re (deg

C)

Full power

Half power

Zero power

Power consumption


Pow

er (W

)

Time of day (h)0000 0400 0800 1200 1600 2000 2400 0000 0400 0800 1200 1600 2000 2400

2degC

4degC

6degC

24

26

28

30

32

24

26

28

30

32

24

26

28

30

32

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4


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Powersupplied


TInt

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Pro

porti

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ΔTge

10deg

C

5 10 15


0

20

40

60

80

100


Diel cycle

Mea

n to

tal p

ower

(mW

)


A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

40

60

80

0

05

10

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20

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30


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mpe

ratu

re (deg

C)

Full power

Half power

Zero power

Power consumption


Pow

er (W

)

Time of day (h)0000 0400 0800 1200 1600 2000 2400 0000 0400 0800 1200 1600 2000 2400

2degC

4degC

6degC

24

26

28

30

32

24

26

28

30

32

24

26

28

30

32

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4


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Powersupplied


TInt

variance (degC)














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Pro

porti

on o

f tim

e at

ΔTge

10deg

C

5 10 15


0

20

40

60

80

100


Diel cycle

Mea

n to

tal p

ower

(mW

)


A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

40

60

80

0

05

10

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20

25

30


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mpe

ratu

re (deg

C)

Full power

Half power

Zero power

Power consumption


Pow

er (W

)

Time of day (h)0000 0400 0800 1200 1600 2000 2400 0000 0400 0800 1200 1600 2000 2400

2degC

4degC

6degC

24

26

28

30

32

24

26

28

30

32

24

26

28

30

32

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4


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Powersupplied


TInt

variance (degC)














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Pro

porti

on o

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e at

ΔTge

10deg

C

5 10 15


0

20

40

60

80

100


Diel cycle

Mea

n to

tal p

ower

(mW

)


A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

40

60

80

0

05

10

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20

25

30


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porti

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e at

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10deg

C

5 10 15


0

20

40

60

80

100


Diel cycle

Mea

n to

tal p

ower

(mW

)


A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

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0

05

10

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25

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Pro

porti

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e at

ΔTge

10deg

C

5 10 15


0

20

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60

80

100


Diel cycle

Mea

n to

tal p

ower

(mW

)


A

Clu

tch

ther

mal

var

ianc

e (σ

2 )


B

0

20

40

60

80

0

05

10

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modeling the costs and benefits associated with the ... · research article modeling the costs and...

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