The University of Chicago

Temperature, Activity, and Lizard Life Histories Author(s): Stephen C. Adolph and Warren P. Porter Source: The American Naturalist, Vol. 142, No. 2 (Aug., 1993), pp. 273-295 Published by: The University of Chicago Press for The American Society of Naturalists Stable URL: http://www.jstor.org/stable/2462816 . Accessed: 05/09/2013 17:33 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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The AmericanNaturalist

Vol. 142, No. 2

August 1993

TEMPERATURE, ACTIVITY, AND LIZARD LIFE HISTORIES STEPHEN

C.

ADOLPH AND WARREN P. PORTER

Departmentof Zoology, Universityof Wisconsin-Madison, Madison, Wisconsin53706 SubmittedDecember 23, 1991; Revised June 8, 1992; Accepted July10, 1992 characteristicsvarywidelyamongspecies and populations.Most Abstract.-Lizard life-history patterns,which are usually authorsseek adaptive or phylogeneticexplanationsforlife-history presumedto reflectgeneticdifferences.However, lizard lifehistoriesare oftenphenotypically factors. plastic, varyingin response to temperature,food availability,and otherenvironmental Despite the importanceof temperatureto lizard ecology and physiology,its effectson life historieshave received relativelylittleattention.We presenta theoreticalmodel predictingthe proximateconsequences of the thermalenvironmentfor lizard life histories.Temperature,by affectingactivitytimes, can cause variationin annual survivalrate and fecundity,leading to a thermal negativecorrelationbetween survivalrate and fecundityamongpopulationsin different environments.Thus, physiologicaland evolutionarymodels predictthe same qualitativepattern data from variationin lizards. We tested our model with published life-history of life-history fieldstudies of the lizard Sceloporus undulatus,using climate and geographicaldata to reconstructestimatedannual activityseasons. Amongpopulations,annual activitytimeswere negatively correlated with annual survival rate and positively correlated with annual fecundity. variaProximateeffectsof temperaturemay confoundcomparativeanalyses oflizardlife-history tion and should be included in futureevolutionarymodels.

characteristics varywidelyamonglizardspeciesand populations Life-history (Tinkle1967,1969;Fitch1970;Ballinger1983;Stearns1984;Dunhamand Miles mostauthorssoughtadaptiveexplanations 1985;Dunhamet al. 1988).Initially, on thebasis ofpredictions fromlife-history theory forlizardlife-history patterns (Tinkle1969;Tinkleet al. 1970;TinkleandBallinger1972;Stearns1977;Ballinger 1979;Tinkleand Dunham1986;Dunhamet al. 1988).A second,morerecent underlievariationin life approachexamineshow body size and/orphylogeny histories(Ballinger1983;Stearns1984;Dunhamand Miles 1985;Dunhamet al. assumethat 1988;Miles and Dunham1992).These approachesoftenimplicitly variation based. However,commongardenexperiments is genetically life-history onlya fewtimeswithlizards(Tinkle (Clausenet al. 1940)have been performed 1970;Ballinger1979;Fergusonand Brockman1980;Sinervoand Adolph1989; Sinervo1990;Fergusonand Talent 1993).Therefore, we knowlittleaboutthe eitheramongorwithinspecies(Stearns1977; geneticbasisoflizardlifehistories, Ballinger1979,1983;Fergusonet al. 1980;Bradshaw1986;Sinervoand Adolph by a number in naturalpopulationsare affected phenotypes 1989).Life-history of environmental factors(Bervenet al. 1979;Ballinger1983;Bervenand Gill and moistureare knownto foodavailability, temperature, 1983).In particular, exertproximate on lizardlifehistories(Tinkle1972;Ballinger1977, influences Am. Nat. 1993. Vol. 142, pp. 273-295. ? 1993 by The Universityof Chicago. 0003-0147/93/4202-0005$02.00. All rightsreserved.

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THE AMERICAN NATURALIST

274

|

Tpreferred

....

.............

(inactive)

-a--

active

-

P

. ..................... .W...

(inactive)

TIME OF DAY FIG. 1.-Idealized daily body temperature(Tb) profileof a diurnal,heliothermiclizard. Value of Tb is typicallyhighand relativelyconstant(around Tpreferred) duringactivitybecause The Tb value of active lizardsoftenvariesrelativelylittleover thecourse ofthermoregulation. environments.However, the of the activityseason and among populationslivingin different and therefore amountof timelizards can attainTpreferred depends on the thermalenvironment can vary substantiallyboth seasonally and geographically.In addition,Tb of inactivelizards is likelyto vary seasonally and geographically.

1983;Dunham1978,1981;Abts1987;JonesandBallinger1987;Joneset al. 1987; Sinervoand Adolph1989;Sinervo1990). to lizard ecology and physiology Despite the importanceof temperature (Cowles and Bogert1944; Bartlettand Gates 1967;Norris1967;Avery1979; havereceivedlittleformalattention until Huey 1982),itseffectson lifehistories recently(Huey and Stevenson1979; Ballinger1983;Nagy 1983;Beuchatand Ellner1987;Jonesand Ballinger1987;Joneset al. 1987;Dunhamet al. 1989; Porter1989;Sinervoand Adolph1989;Sinervo1990;Grantand Dunham1990; can Grantand Porter1992).In thisarticlewe discussthewaysthattemperature lizardlifehistories.We presenta generalmechanistic modelforthe influence oftemperature on fecundity and survivalrate,based on lizard proximate effects thermalphysiology.Specifically, we addressthe question:Whatkindof lifethermalenvironments historyvariationwould we expect to see among different

due simplyto proximate effectsin theabsenceof geneticdifferentiation among feaOur modelpredictsthe same associationbetweenlife-history populations? turesthatis predicted different by evolutionary theories,butbecauseofentirely causes. We thenprovidea testof our modelusingpublisheddata frompopulationsof theeasternfencelizard,Sceloporusundulatus.Finally,we discussthe limitations ofourmodel,itsimplications forlife-history evolution, anditsimplicawillrespondto climatechange. tionsforhowpopulations TEMPERATURE AND LIZARD LIFE HISTORIES: POSSIBLE MECHANISMS

on lizardlifehistories oftemperature is complicated The effect bythefactthat Diurnallizardsoftenmaintaina relatively high, manylizardsthermoregulate.

constantbody temperature(Tb) duringdaytimeactivity(fig. 1) throughvarious behavioraland physiologicalmechanisms(Cowles and Bogert 1944; Avery 1979,

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AND LIZARDLIFE HISTORIES TEMPERATURE

275

1982;Huey 1982;Bradshaw1986).As a result,themeanTbofactivelizardsoften littledespitedaily,seasonal,andgeographical variesrelatively variation inthermal environments (Bogert1949;Avery1982).However,twoaspectsoflizardTbare environments and seasonallyin thesameenvironlikelyto varyamongdifferent is largelydetermined ment(fig.1). First,Tbduringinactivity bysubstrate andair whichrestricts temperatures, thermoregulatory options(butsee Cowlesand Bogert1944;Porteret al. 1973;Huey 1982;Huey et al. 1989).Second,and more theamountoftimeperdaythata lizardcan be activeat itspreferred important, environment and Gates 1967;Porteret Tbis constrained by thethermal (Bartlett et al. 1983;Porterand Tracy al. 1973;Huey et al. 1977;Avery1979;Christian 1983;Grantand Dunham1988,1990;Sinervoand Adolph1989;Van Dammeet timeof activityis one of theprimary al. 1989).Indeed,modifying mechanisms by whichlizardsthermoregulate (Huey et al. 1977;Grantand Dunham1988). environments Thus, althoughlizardsin two different mightmaintainthe same meanTbduringactivity,thecumulativeamountof timespentat highTbcould Annualactivitytimeis thenroughly differ substantially. equivalentto thetotal amountoftimespentat highTbandcan be considereda measureofphysiological timeforlizards. Lizards are foundin a wide varietyof thermalenvironments, hot including tropicallowlands,temperate deserts,and cool, highlyseasonalhabitatsat high in thermal elevationor highlatitude(Pearsonand Bradford1976).Thisvariation inactivity variation andconcomitant season(Huey 1982),is likely environments, inlifehistories tocause someoftheobservedvariation amongspeciesandamong widespreadpopulationsof singlespecies (Grantand Dunham1990).Here, we can directlyinfluence describesome of the ways thattemperature life-history characteristics. Many of theseeffectsare mediatedthrough activitytimesand energybudgets. ActivityTime and Energetics

Energyallocatedto reproduction ultimately dependson thedailyenergybudget,whichin turndependson activitytimein severalways.Energyacquisition and by therate bothby therateat whichresourcesare harvested is determined at whichtheyare processed(Congdon1989).Daily preycapturerate should thatlizardsare foraging increasewithdailyactivitytime,undertheassumption whileactive(Avery1971,1978,1984;Averyet al. 1982;Karasovand Anderson et al. 1986).In addition,highTbmayincreasepreycapture 1984;Waldschmidt ratesand handling efficiency (Averyet al. 1982;Van Dammeet al. 1991).Daily shouldincreasewithactivity energyassimilation time,becauseratesofdigestion are temperature at ornearactivity andassimilation andaremaximized dependent and Louw Tb's(Avery1973,1984;Skoczylas1978;Harwood1979;Buffenstein 1982;Huey1982;Waldschmidt etal. 1986,1987;Dunhametal. 1989;Zimmerman andTracy1989;Van Dammeet al. 1991).On thedebitsideoftheenergybudget, shouldalso increasewithactivitytime,bothbecause dailyenergyexpenditure resting metabolicratesare higherat activityTb's(BennettandDawson 1976)and because activelizardsoftenincuradditionalmetaboliccosts in pursuingprey, and the like (Bennett1982;Karasov and Anderson1984; defending territories,

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276

THE AMERICANNATURALIST

Marlerand Moore 1989).The difference betweenenergyassimilated and energy expendedrepresents discretionary energythatcan be allocatedto reproduction, growth, or storage(Porter1989).Thus,energyallocatedto reproduction depends on activity timevia dailyandannualenergybudgets(Congdonetal. 1982;Anderson and Karasov 1988;Dunhamet al. 1989;Porter1989;Grantand Porter1992). Potential timeis likelyto be correlated activity withthesize oftheannualenergy budgetand consequently withthe amountof energythatcan be allocatedto reproduction. Growth,ActivityTime, and Age at Maturity

distorts therelationship betweenphysiological In ectotherms, and temperature time(Taylor1981;Sinervoand Doyle 1990).For example,lizards chronological seasonsspendmoretimeathighTbandtherefore withlongeractivity areexpected at a youngerage (Pianka1970; to growfasterand reachreproductive maturity are supported Jamesand Shine1988).Thesepredictions byfieldstudiesshowing ratesoflizardsincreasewithannualactivity time(Davis 1967; thatannualgrowth Tinkle1972;Ballinger1983;GrantandDunham1990)andbydirectobservations underlongergrowingseasons (Tinkleand Ballinger1972; of earliermaturation Goldberg1974;Grantand Dunham1990).In addition,severallaboratory studies ofactivity timeon growth effects havedemonstrated rates.GrowthratesofjuvenileLacerta vivipara,Sceloporus occidentalis,and Sceloporus graciosus increase

withdailyactivitytime(i.e., access to highTb via radiantheat; Avery1984; Sinervoand Adolph1989;Sinervo1990;B. Sinervoand S. C. Adolph,unpubis frequently observedin animalsmaintained lisheddata). Acceleratedmaturity underoptimalthermalconditionsin thelaboratory (e.g., A. Muth,unpublished data,citedin Porterand Tracy1983;Fergusonand Talent1993).The observed effects oftemperature and activity timeon growth fromtheenerfollowdirectly outlinedabove. geticconsiderations ReproductiveCycles

Temperature typicallyservesas a proximatecue forinitiating reproductive cycles in temperate-zone lizards,eitherdirectlyor by entraining endogenous circannualrhythms (Duvall et al. 1982;Marion1982;Licht 1984;Mooreet al. 1984; Underwood1992). Correspondingly, populationsin warmenvironments ofteninitiate at an earlierdate(Fitch oraltitudes) (e.g.,lowlatitudes reproduction can often 1970;Goldberg1974;Duvall et al. 1982;Licht1984)and consequently reproducemorethanonce per year,whereascool environments usuallylimit to one clutchor broodper year(McCoy and Hoddenbach1966; reproduction Tinkle1969;Goldberg1974;Parkerand Pianka 1975;Gregory1982;Ballinger 1983;Joneset al. 1987;Jamesand Shine1988). ActivitySeason and SurvivalRate

orlatitudes oftenhavehigher at highaltitudes annualsurvivalrates Populations at to those low altitudes/latitudes compared (Tinkle1969;Pianka 1970;Tinkle andBallinger1972;Smithand Hall 1974;Turner1977;Ballinger1979;Jamesand risk(notablyriskofpredation) is higher Shine1988).Thisimpliesthatmortality

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TEMPERATURE AND LIZARD LIFE HISTORIES

277

foractivelizardsthanforinactiveones (Rose 1981).Severalstudieswithin populationssupportthisconclusion.Wilson(1991; B. Wilson,personalcommunication)foundthatdailymortality ratesin Uta stansburianaare highestin spring, intermediate in summer, and lowestduringthewinter;dailyactivity timesfollow thesamerankorder.Marlerand Moore(1988,1989)experimentally manipulated testosteronelevels in male Sceloporus jarrovi and found that individualswith

testosterone implants hadlongerdailyactivity periodsandsuffered higher mortalityrelativeto controls. Acute Effectsof Temperatureon SurvivalRates All lizards have upper and lower criticalthermallimitsbeyond which the animals perish (Cowles and Bogert 1944; Dawson 1967; Spellerberg 1973). How

oftentheselimitsare approachedin natureis unknown.Deaths due to winter coldhavebeenreported (Tinkle1967;Vitt1974;reviewinGregory1982);deaths are probablyless common(Dawson 1967).Acuteeffectsof due to overheating temperature may also influencesurvivalrates indirectly, throughthe thermal andTracy1981;Huey 1982; dependenceoflocomotion(Bennett1980;Christian vanBerkum1986,1988).In somecases lizardsareactiveat Tb'sthatsignificantly

impairsprintspeed, which could lead to greaterriskof predation(Christianand

Tracy 1981;Huey 1982; Crowley1985;van Berkum1986;Van Dammeet al. thatlead to lowersprintspeeds 1989,1990).However,the cool environments theoveralleffect mayalso reduceactivity times,whichwouldtendto ameliorate on annualsurvivalrates.Temperature mayalso affectresistanceto disease. For

example, the abilityof desertiguanas (Dipsosaurus dorsalis) to survivebacterial infectionimproveswithincreasingTb(Kluger 1979). Energetics of Hibernation

Lizards can be inactive more than halfthe year, particularlyat highlatitudes or highaltitudes(Gregory1982; Tsuji 1988a). Duringthistimetheyrelyon stored

energy, particularly lipids(Derickson1976;Gregory1982).Because temperature conditions affectmetabolicrates(Bennettand Dawson 1976; duringhibernation Tsuji 1988a,1988b),energystoresmustbe adequateforboththedurationand theTb'sexperienced duringhibernation. Temperatureand EmbryonicDevelopment

affects In lizards,temperature and(insome eggincubation time,eggmortality, species)sexualdifferentiation (Bull 1980;Muth1980;PackardandPackard1988). shorter In warmerenvironments, incubation timesmaylengthen theactivity seathemto reacha largersize priorto son experiencedby hatchlings, permitting

hibernation.Laying several clutches of eggs in a single activityseason is more

incubation times.The significance oftemperafeasibleifaccompaniedby shorter forlizardlifehistories sex determination is notwellunderstood. ture-dependent inducedcorrelation One possibleeffectis an environmentally betweenhatching dateand sex, whichcouldlead to a correlation betweenjuvenilesize and sex by theend of theactivityseason. Because mostlizardsreachmaturity within1-2 couldpersistintoadulthood. yr,thissexualsize difference

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DAY OF ACTIVITYSEASON, j

a

24 .

-150

-50

-100

50

0

100

150

18

O 120

b

J

F

M

A

J

FMAMJ

J

F M

M

J

J

A

S O

N

D

24 a

24

~18

0

6_ 0

JASMN

D

24

c

~18 0

0

A M

J J A SON

MONTH

D

FIG. 2.-Seasonal variationin potentialactivitytimeof diurnallizards, as determinedby thethermalenvironmentand thermalphysiologyof thelizard. NorthernHemisphereseasons are illustrated.Unshaded region indicates times when thermalconditionspermitactivity; shaded region indicates periods of inactivity.Individuallizards may not be active as often as the thermalenvironmentpermits(see, e.g., Nagy 1973; Porteret al. 1973; Simon and Middendorf1976; Rose 1981; Beuchat 1989). a, Elliptical activityseason characteristicof manydiurnaltemperate-zonelizards. b, Activitypatternoftenobserved in lizards livingin desertsor otherseasonally hot environments,where highsummertemperaturescause midday inactivity(hence bimodal activity;Porteret al. 1973; Grant 1990; Grant and Dunham 1990). c, Rectangularactivityseason characteristicof some lowland tropicallizards (see, e.g., Heatwole et al. 1969; Porterand James 1979).

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AND LIZARDLIFE HISTORIES TEMPERATURE

279

Thus,temperature potentially affects lizardlifehistories through variousmechanisms.However,thereis no generaltheoryincorporating theseproximate influences.A fewstudieshaveexaminedtheeffect oftemperature on lifehistories of individual detailedphysiological speciesthrough modelstailoredtothelifehistory of the species in question(Beuchatand Ellner 1987;Grantand Porter1992). Here,we presenta generalmodeloftheeffect oftemperature on annualfecundity and annualsurvivalrates.Othertraits,suchas age and size at maturity, could be modeledsimilarly. A GENERAL

MODEL

Annual and Daily ActivityTime

For mostdiurnaltemperate-zone lizards,potentialdailyactivitytimevaries timesare typically shortin thespringandfallandlong seasonally.Daily activity insummer, becauseofseasonalchangesintemperature (Porteret al. 1973;Porter theannualactivity andTracy1983}.Here, we approximate patternas an ellipse (fig.2a), wherethe lengthof the activityseason is 2y d and the lengthof the maximumactivityday is 2d h. For an ellipticalactivityseason the potential numberofhoursofactivity perdayis givenby h = 2d/ 1-_(j2/y2),

(1)

wherej represents day of theyear;j = 0 at themiddleof theactivityseason, whenh is maximal.The area of theellipseTryd equals thecumulative potential hoursofactivity peryear. effectson potentialactivitytimeare reflected Temperature in thevaluesofy and d. These valuesare affected in air primarily by dailyand seasonalvariation and solarradiation.Warmlow-latitude temperature environments usuallypermit inlargey,whereaslizardsat highlatitudes formuchoftheyear,resulting activity or altitudescan have activityseasonsas shortas 4-5 mo (Tsuji 1988a).Factors and cloud cover can also affectthesevalues; heavy such as habitatstructure wouldtendto decreased becauseoftheshadowscastinearlymorning vegetation Thermalphysiological andlateafternoon. characteristics ofthelizardalso influencey andd. For example,somespeciesrequirerelatively hightemperatures for theirpotentialactivitytime(reducingbothy and whichwouldrestrict activity, thermal allowslongeractivity d). Conversely, relaxing requirements periods(PorterandTracy1983;Grant1990). fordifferent Shapes otherthanellipsesmightbe moreappropriate thermal For example,desertlizardsoftenhavebimodaldailyactivity environments. patternsduringthesummer,to avoid hotmiddaytemperatures (Porteret al. 1973; Grant1990;Grantand Dunham1990;fig.2b). Lizardsin tropicallowlandsmay be activeyear-round duringdaylighthours(Heatwoleet al. 1969;Porterand we willrestrict James1979;Huey 1982;fig.2c). For simplicity, ouranalysisto elliptical activity seasons,butourmodelcan be extendedto anyseasonalactivity pattern.

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THE AMERICAN NATURALIST

280

b

a ma:

1.0 0.8:

1.0

0.0001

0.60 ir 0

0.8

0.4

0

activity 0.2' cn

0.0003

0OU

0.3

0.6

0.6 e.(.uvartce0.0005s

saneg(uutehroatiyafr

_1

m

z [lotte on z 0.1030006 FIG.

1000

0.0

~~~~~~~~~~~~~~~~~~~~

0m00vm6

00i00o3aeSa

nulautsria

La,3.Mdlpeitosfrepce

0.05

0.4

2000

0.2

3000

10~00

2000

uciono

0.00009

3000

ANNUALACTIVITYTIME(HOURS)

ANNUALACTIVITYTIME(HOURS)

of FIG. 3.-Model predictions forexpectedannualadultsurvivalrateS as a function seasonlength(cumulative hoursof activity, a), fromeq. (3). Survivalratecurves activity are plottedon a logarithmic scale forseveraldifferent values Of Ma and mi (thehourly and inactivity, valuesof risksduringactivity a, Effectofdifferent mortality respectively), valuesofini, setting ofdifferent Ma equal to 0.0003. in'al setting miequal to 0; b, effect

SurvivalRates

We assumethateach individual has constantprobabilities ofmortalityMaper oftimeofyearortime andmiperhourofinactivity, independent hourofactivity amongindividuofday.Undertheassumption thatmortality riskis independent is givenby als, expectedannualsurvivalrate(S) forthepopulation S

= (1 - ma)a (1 - mi)i,

(2)

andinactivity fortheyear, wherea andi are thetotalnumberofhoursofactivity Thisis closelyapproximated by respectively. S = exp(-ama

- im )

(3)

risksless than0.01 perhour;typicalvaluesare less than forper-hour mortality data). Because 0.002 (see below; S. C. Adolphand B. S. Wilson,unpublished = in can as a + i number of hours this a year), expression be rewritten 8,766(the S = exp[a(mi

-

ma) -

8,766mi].

(4)

(e.g., becauseof In thespecialcase in whichall mortality occursduringactivity avianpredation), S = exp(-ama).

(5)

withdifferent risks activityseasonsbutthesamehourlymortality Populations seasons willdiffer inexpectedannualsurvivalrates.In particular, longeractivity willresultin lowerS ifma > mi; theempiricalstudiesdiscussedabove suggest thatthismayoftenbe true.The degreeofvariationin S dependson thevalues twofold overa typical ofmaandmi(fig.3). For example,S variesapproximately rangeofactivityseasonsif ma = 0.0005and mi = 0.0. However,S variesrelaover the same rangeif ma = 0.0001and mi = 0.0. Similarly, tivelyslightly

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TEMPERATURE AND LIZARD LIFE HISTORIES b

a 0

0

03

--~~~~~~~ -

00

ir .1~~~0

-

UJ~~~~~~~~~~~~~~~~ z

281

-zM

HOURS OF ACTIVITYPER DAY, h

ENERGY ASSIMILATED PER DAY, Ea

FIG. 4.-Model assumptionsfordaily energyassimilationand allocationtowardreproduction by individuallizards. a, Daily energyassimilationEa (in arbitraryunitsof energy)as a functionof activitytimeh. Dashed line illustratesthe special case where c2 = 0. b, Amount of energyallocated per day to reproduction,Er, as a functionof Ea. Above a daily energy thresholdEt (daily maintenancerequirements),a constantfractionfofeach day's assimilated energyis allocated to reproduction.

of deathsoccur variationin S is reducedas mi increases;as a greaterfraction in variation season will have a smallereffect.Figure3 duringinactivity, activity in survivalrate(i.e., greaterthantwofold) thatlargedifferences also illustrates amonglizardpopulationsor betweenyearsin a singlepopulationare likelyto in mortality differences risksin additionto differences in activity. reflect Thisis the between S and to due a; doublinga reducesS by exponentialrelationship less thana factoroftwo. Ourmodelforsurvivalrateassumesthatvaluesformaandmiare independent ofactivity wouldbe violatedby patterns (thevaluesofa and i). Thisassumption that are either to animals activetoo infrequently obtainenoughfoodor are so activethattheycannotmaintaina positiveenergybalance(Marlerand Moore to estimatea priori;however,they 1988,1989).Valuesformaandmiare difficult can be estimated fromsurvivalratedata.In ourtestofthemodel(see below)we givean example.We knowof no otherpublishedestimatesforhourlymortality risksin reptiles. EnergyAssimilationand Allocation to Reproduction We model energyintake and allocation to reproductionon a daily basis. An individual'sdaily energyassimilation(Ea) may be limitedby eitherpreycapture

rate or by digestionand absorptionrates(Congdon1989). In eithercase, Ea shouldvarypositivelywithhoursof activity:morepreycan be captured,and will be fasterwhena lizardspendsmoretimeat a digestionand assimilation higherTb.We assumethatEa increaseswithdailyactivitytimeh accordingto therelationship Ea=

clh-C2h2,

(6)

unitsof energy(fig.4a) and cl and c2 are whereEa is expressedin arbitrary as h variesfrom0 to 12 h constantschosenso thatEa increasesmonotonically

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THE AMERICAN NATURALIST

282

and is maximizedat h = 12 h. Thatis, energyassimilatedper hourdecreases Theformofthisrelationtime(diminishing withincreasing dailyactivity returns). due to gut size, foodpassage rate, limitations shipcould reflectphysiological satiation,and the like. Variationin preycaptureprobability (amongdifferent reform.Finally,diminishing timesof day) wouldlikewiseyieldthisfunctional turnscouldresultfrombehavior,iflizardsdo notuse all ofthepotential activity timeavailableto them(Sinervoand Adolph1989;Sinervo1990;see also Simon and Middendorf 1976;Rose 1981). is supported forEa (diminishing Thisgeneralrelationship returns) bythelaboraabove (Avery1984;Sinervoand torystudieson lizardgrowthratesmentioned Adolph1989;Sinervo1990).Dependingon thepopulationand species,growth to c2 = 0) to curvilinear linear(corresponding curvesvariedfromapproximately withpeaks near 12 h (C2 = 0.04 cl). This suggeststhatenergyintakein these form. juvenilelizardshad a similarfunctional each day duringthe We assumethatfemalesallocateenergyto reproduction reproductive season, iftheirintakeexceeds a minimum dailyenergythreshold Abovethisthreshold, maintenance allocationto requirements). Et (representing ofenergyassimilated. reproduction (Er) is assumedto be a linearfunction Thus, , E = t?for r f(E -Et),

Ea2Et,

(7)

wheref is a fractionless thanone (fig.4b). The difference Ea - Er includes and growth.For simplicity metaboliccostssuchas locomotion we assumef and oftimeofyear. Et to be independent We assumethatlizardsallocateenergyto reproduction throughout thereproductiveseason,whoselengthis 2y - n d, where2yis thelengthoftheactivity season(as above) and n is thelengthin daysofthenonreproductive season.The minimum valueofn is set by theamountoftimenecessaryforeggsto hatch(in to acquiresufficient oviparousspecies) and forhatchlings energyreservesfor We also assumethatn does not varyamongdifferent overwintering. environments.In reality,n couldbe shorterin warmenvironments becauseeggswould lizardsin warmenvironments incubatein less time;alternatively, mightcurtail in longern. reproduction earlier,resulting Totalannualenergyassimilatedis then = Eannual

(8)

Ea aij

where Ea

2cd

1 -7ly2

-

4C2d2(1

_ j2/y2).

(9)

Thisyields Eannual = dy[c Tr - (16dC2/3)],

(10)

whichshows thatthe annualenergybudgetincreaseswiththe lengthsof the season2yand themaximum activity activity day 2d.

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TEMPERATURE AND LIZARD LIFE HISTORIES

283

annualreproductive Similarly, investment is givenby = Rannual

f_y rY

Erai

=

f

V- 1

-itf(Ea

-

()

Et)ai,

where It=

-

I

c-

4C2Et

(16d2C2)

(12)

limit(y - n) is thefinalday andEa[h(j)] is givenabove; theupperintegration limit-ji is necessaryto of thereproductive season, and thelowerintegration avoid havingnegativevalues forEr earlyin the activityseason whenEa < Et season (-jt is thevalueofj forwhichEa = Et). We assumethatthereproductive endsbeforeEa againfallsbelowEt (i.e., that[y - n] < jt). The solutionto this is integral = fc, d/yx {(y Rannual

-

n) Vy2

-

(y

-

n)2 +jt

y2 _

+ y2sin-1[(y- n)/y]+ y2sin-l(it/y)} - 4fd2c2/3y2[2y3 + 3y2jt - 3yn2 + n3 - j3]

-

fEt(Y

(13) -

n + it)

Because thisexpressioninvolvesmanyterms,the effectsof activityseason and energeticparametersare not immediately apparent.In the simplestcase (setting c2, n, and Et equal to zero) thissolutionreducestofdyclr, showingthe on the area of the activityellipseand the energy lineardependenceof Rannual We assumethatRannual intakeandallocationparameters. is proportional to annual thisincludestheassumption thattheenergetic costperoffspring fecundity; does notvaryamongenvironments. We exploredthegeneralsolution(eq. [13]) by evaluating fordifferent Rannual valuesanddifferent parameter activity ellipsesizes. We choseseasons(2y)rangand maximum ingfrom120to 300 d (30-dincrements) day lengths(2d) ranging from8 to 12 h (1-hincrements), thevarietyof thermalenvironapproximating lizardsat different mentsencountered bytemperate-zone latitudesandaltitudes. 5a. Note thattherelationship An exampleis shownin figure betweenRannual and linearovera widerangeof ellipsearea (= annualactivity time)is approximately termsin theintegral solutionabove. Also activityseasonsdespitethenonlinear involvessome variationin Rannual fora givenellipse notethattherelationship area. This is because of thecurvilinear betweenenergyintakeand relationship time(fig.4a). For activityellipseswiththesamearea, an ellipsewitha activity highervalueofy (longerseason)buta lowervalueofd (shorter days)willresult in a largerannualenergybudgetand a largerallocationto reproduction. While values (forf, Et, and n) affectthequantitative different parameter relationship and annualactivity betweenRannual does notchange. time,thequalitative pattern In general,a twofoldincreasein annualactivity timeincreasesRannual bya factor of 1.4-3.5.

Underourmodelbothpredictedannualsurvivalrate(fig.3) and annualreproductiveinvestment (fig.5a) varywiththe lengthof the activityseason. This suggeststhatlizardlifehistoriescould differsubstantially amongpopulations

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THE AMERICAN NATURALIST

284

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Annual ActivityTime (hours)

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Annual Adult Survivorship

FIG. 5.-Model predictionsof annual reproductiveallocation(Rannual) evaluatedforactivity seasons rangingfrom=750 to =3,000 h yr-'. Values ofRannual are normalizedto themaximum as a functionof activityseason length.In thisexample, value of 404.6 energyunits.a, Rannual cl = 1.0, c2 = 0.042, f = 0.3, n = 60, and Et = 0.0. Otherparametervalues yield similar graphsthatdiffermainlyin overall slope. Connected points representactivityseasons with the same numberof days (2y) but different maximumday lengths(2d); nonlinearitiesresult fromthediminishing-returns assumptionforenergyassimilation(fig.4b). b, Predictedpattern and annual adult survivalrateamongpopulationsfromdifferent ofcovariationbetweenRannual thermalenvironments,combiningreproductiveoutputfromfig.5a and survivalrate curves fromfig. 3b (with ma = 0.0003 and mi = 0.00003). This negative relationshipbetween survival rate and reproductiveoutput is a proximateconsequence of variationin activity season length.Similarly,data presentedby Tinkle (1969) show a negativerelationship(r = -0.88, P < .001) between annual adult survivalrate and annual fecundityon the basis of empiricalstudies of 14 lizard populations(13 species). These data matchpredictionsof both our mechanisticmodel and evolutionarymodels.

ofdifferent simplybecauseoftheproximate effects thermal environments, without any geneticdifferences. This possibility has been givenless attention than evolutionary explanations (Tinkleand Ballinger1972;Stearns1977,1980,1984; Ballinger1983;Joneset al. 1987;Dunhamet al. 1988;Jamesand Shine 1988), almostnothing is knownaboutthegeneticbasis of lizardlifehistories although (Ballinger1983;Sinervoand Adolph1989;Fergusonand Talent1993). Evolutionary life-history theorypredictsthathighannualreproductive investmentwill evolve whenannualadultsurvivalrateis low (Tinkle1969;Stearns 1977;Pianka 1988). Underthistheory,comparisonsof speciesor populations betweensurvivalrateand fecundity shouldshowa negativecorrelation (Tinkle based model offersthe same prediction, 1969). Our physiologically without betweenpopulations evolveddifferences (fig.5b). Thus,thenegativecorrelation betweenannualfecundity and annualsurvivalrateobservedby Tinkle(1969) couldreflecttheproximate influence of temperature ratherthan(or in addition to) adaptiveevolutionof reproductive investment to compensateformortality. Ourmodelsuggeststhatthermal effects on reproductive outputwillautomatically compensate(at least partially)forthermaleffectson survivalrate,if foodresourcesare not limiting. Because bothevolutionary and physiological models

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predictthe same phenotypic patterns,simplecomparisons of wildpopulations willnotdistinguish betweenthem. TESTING

THE MODEL:

DATA FROM SCELOPORUS

UNDULATUS

and annualadultsurvivalratewill Our modelpredictsthatannualfecundity We testedthesepredictions co-varywithannualhoursofactivity. usingpublished datafrom11populations oftheeasternfencelizard(Sceloporusundulife-history in montane, latus).This species is widespreadin the UnitedStates,occurring woodland,prairie,and deserthabitats(Smith1946).These data werecollected by severaldifferent researchers and weresummarized in Dunhamet al. (1988). EstimatingActivitySeasons

We calculatedpotentialactivityseasonsforeach populationusingcomputer and animalTbon thebasis of heattransfer modelsthatestimatemicroclimates principles (Porteret al. 1973;Porterand Tracy1983).For each population, we andmaximum obtainedclimatedata(monthly airtemperatures) averageminimum fromthenearestavailablelocationforeach yearofthefieldstudy(U.S. Weather wereadjustedfordifferences in altitudebetweenstudy Bureau).Temperatures sitesand climatestationsat the theoretical adiabaticcoolingrateof 9.9?C per kilometer ofaltitude(Sutton1977).Detaileddiscussionofthismodelis presented in Porteret al. (1973).Solarradiation was calculatedon thebasis ofMcCullough andPorter(1971;software SOLRAD [developedbyW. P. Porter]availprogram ablethrough WISCWARE,University ofWisconsinAcademicComputer Center, alti1210WestDaytonStreet,Madison,Wis. 53706).Exceptfortemperatures, tudes,andlatitudes, we assumedall studysiteswereequivalentintheirmeteorologicalcharacteristics (e.g., windspeed,cloudcover,soil thermal conductivity) becauselocallyspecificinformation was unavailable.Table 1 liststhevaluesof we used in thesesimulations. parameters and simulations estimatedair and soil temperature The microclimate profiles forthefifteenth at ?1-h intervals radiation conditions dayofeach month.These modelthatcalculatedtheequilibrium datawerethenused as inputto a computer and Lizardmorphological Tbattainable bya lizardwithgiventhermal properties. 1. We assumed in table used in thisanalysisare given thermalcharacteristics a typicaladultbody size forS. undulatus(Dunhamet al. 1988)and obtained forabsorptivity measurements and Gates (Norris1967)and emissivity (Bartlett assumed that lizards We could be of radiation. active whenever 1967) potentially in them to reach a their microclimates permitted Tb preferred bodytemperature rangeof32?-37?C(Bogert1949;Avery1982;Crowley1985).Themodelcalculated at