Metabolic theory, life history and the distribution of a terrestrial ectotherm

Metabolic theory, life history and the distribution of a

terrestrial ectotherm

Michael Kearney*

Department of Zoology, The University of Melbourne, Melbourne, Victoria 3010, Australia

Summary

1. Life histories, population dynamics and geographic range limits are fundamentally con-

strained by the way organisms acquire and allocate energy and matter. Metabolic theories pro-

vide general, parameter-sparse frameworks for understanding these constraints. However, they

require the accurate estimation of body temperature which can be especially challenging in

terrestrial environments.

2. Here, I integrate a metabolic theory (Dynamic Energy Budget theory, DEB) with a biophysi-

cal model for inferring field body temperatures and activity periods of terrestrial ectotherms and

apply it to study life-history variation and geographic range limits in a widespread North Ameri-

can lizard, Sceloporus undulatus.

3. The model successfully predicted trait co-variation (size at maturity, maximum size, repro-

ductive output and length-mass allometry) through changes in a single parameter. It also pre-

dicted seasonal and geographic variation in field growth rates, age at first reproduction,

reproductive output and geographic range limits (via rmax estimates), all as a function of spatial

climatic data. Although variation in age at maturity was mostly explained by climate, variation

in annual reproduction was largely a product of local body size.

4. Dynamic Energy Budget metabolic theory is concluded to be a powerful and general means

to mechanistically integrate the dynamics of growth and reproduction into niche models of

ectotherms.

Key-words: biophysical ecology, climate, dynamic energy budget theory, geographic range

limits, niche modelling, Sceloporus undulatus, species distribution modelling, thermoregulation

Introduction

Organisms take up energy and matter from their surround-

ings and use it to build and maintain their bodies and to

produce offspring. The life history, distribution and abun-

dance of species reflect the operation of these metabolic pro-

cesses in the context of varying environments, especially

temperature, water and food (Andrewartha & Birch 1954).

The set of these environmental conditions and resources

permitting population persistence represents the organism’s

‘fundamental niche’, setting the stage for understanding

biotic interactions (excluding feeding) such as predation

and competition, i.e., the ‘realized niche’ (Hutchinson

1957). Mechanistic niche models aim to capture these pro-

cesses as a function of the interaction between traits and

environmental gradients, especially climate, terrain and

vegetation (Kearney & Porter 2009).

Recent progress in mechanistic niche modelling has hap-

pened rapidly along two different fronts that are yet to be uni-

ted. On one hand, the field of biophysical ecology has been

applied to predict body temperature (and also water loss)

through space and time as a function of an organism’s biology

(size, shape, colour, behaviour) and of the increasingly rich

array of available spatial environmental data (Kearney &

Porter 2004, 2009; Helmuth, Kingsolver & Carrington 2005;

Gilman, Wethey & Helmuth 2006; Buckley 2008; Helmuth

2009; Kearney, Shine & Porter 2009). On the other hand, the

parallel emergence of ‘metabolic theories in ecology’ has pro-

vided first-principles models of the processes of energy and

matter uptake and its use for maintenance, development,

growth and reproduction (Kooijman 1986, 2010; Nisbet et al.

2000; Brown et al. 2004; van der Meer 2006b). To date, the

field of biophysical ecology has incorporated phenomenologi-

cal, static (snapshot in time) energy budgets and empirical

descriptions of physiological processes such as metabolic

rates, growth rates and feeding rates (e.g. Grant & Porter

1992; Adolph & Porter 1993, 1996; Buckley 2008; Buckley

et al. 2010; Kearney, Wintle & Porter 2010). In contrast,

applications of metabolic theory to environmental gradients

have been performed under the assumption that body*Correspondence author. E-mail: [email protected]

� 2011 The Author. Functional Ecology � 2011 British Ecological Society

Functional Ecology 2012, 26, 167–179 doi: 10.1111/j.1365-2435.2011.01917.x

temperature equals air or water temperature (e.g. Dillon,

Wang&Huey 2010), which is unrealistic formany organisms.

In this study, I integrate a metabolic theory, the Dynamic

Energy Budget (DEB) model, with the Niche Mapper system

(US Patent 7,155,377B2; [email protected]) that predicts

spatial and temporal variation in field body temperatures in

thermoregulating organisms. DEB theory is unique among

metabolic theories in capturing the metabolic process of an

organism through its the entire life cycle as an explicit function

of body temperature and food availability (Kooijman 1986,

2010). It is thus highly suited to integration with mechanistic

niche models (Kearney et al. 2010). Niche Mapper models

body temperature and thermoregulatory behaviour, including

potential foraging time, as a function of macroclimatic and

organismal data (Porter et al. 1973; Kearney & Porter 2009),

providing the environmental input for theDEBmodel.

Here, I apply the integrated models to study the fundamen-

tal niche of the widespread North American lizard Sceloporus

undulatus. This species complex (Reeder, Cole & Dessauer

2002) has been the subject of many field and laboratory stud-

ies of its ecophysiology (Niewiarowski & Waldschmidt 1992;

Angilletta 1999, 2001a,b; Angilletta, Hill &Robson 2002), life

history (Tinkle 1972, 1973; Tinkle & Ballinger 1972; Vinegar

1975; Ferguson, Bohlen &Woolley 1980; Ballinger, Droge &

Jones 1981; Tinkle & Dunham 1986; Ferguson & Talent

1993; Niewiarowski 2001) and geographic range (Buckley

2008; Buckley et al. 2010). Detailed life-history studies at 11

widely dispersed localities across the geographic range of

S. undulatus document broad variation in growth rate, size

and age at maturity, egg and clutch size and clutch frequency

(summarized in Tinkle & Dunham 1986). This wealth of

information makes S. undulatus an excellent case for testing

the approach.

In this study, I use the combinedmodels of metabolism and

behavioural thermoregulation, together with spatial climatic

data, to predict geographic variation in growth rate, age at

maturity and reproductive output in S. undulatus from first

principles. I compare the effectiveness of the model and the

relative number of parameters required with previous efforts

to model the life-history variation in S. undulatus from an

energetics perspective (Grant & Porter 1992; Adolph&Porter

1993, 1996). I also assess the implied patterns of life-history

trait co-variation stemming from DEB theory with the

observed patterns. Finally, I project this depiction of the

niche of S. undulatus across North America to infer con-

straints on its range and compare these results with recent

range predictions derived frommore empirically based, static

energy budgets (Buckley 2008, 2010).

Materials and methods

D Y N A M I C EN ER G Y BU D G E T T H E O R Y A N D I T S

I M P L E M E N T A T I O N F O R S C E L O P O R U S U N D U L A T U S

Dynamic Energy Budget theory is described in detail in Kooijman

(2010), with useful summaries by van der Meer (2006a) and Sousa,

Domingos & Kooijman (2008). The parameters for the standard

DEB model used in this study are provided in Table S1 (Supporting

information) and EXCEL spreadsheet implementing the model is avail-

able from the author on request. The author is also developing an R

package (R Foundation for Statistical Computing, Vienna, Austria)

that implements the integrated Niche Mapper and DEB model.

Because it is not widely applied in the studies of animal energetics, I

provide a brief summary of the Standard DEB model and associated

theory here.

A key feature of DEB theory is the partitioning of mass into the

abstract quantities of ‘structural volume’, V and ‘reserve’, E. The

reserve, which may consist of, e.g., fat, carbohydrate and amino acids

scattered across the body, is used and replenished and hence does not

require maintenance. The structure is the ‘permanent’ biomass such

as proteins and membranes and requires energy and matter for its

maintenance (protein turnover and the maintenance of concentration

gradients and ionic potentials) in direct proportion to structural vol-

ume. The rate of energy assimilation _pA is explicitly related to food

density through a functional response curve _pA = f{ _pAm}V2 ⁄ 3, where

f is the scaled functional response (ranging from 0 to 1) and { _pAm} is

the maximum assimilation rate per unit surface area (note that, in

DEB theory notation, square and curly brackets denote volume-spe-

cific and surface area-specific terms, respectively). DEB theory fol-

lows the flows of both energy and matter and does not necessarily

assume that energy per se is limiting.Development, growth and repro-

duction are predicted dynamically according to the j-rule whereby a

fixed (throughout ontogeny) fraction j of the energy ⁄matter in the

reserves flows to growth and to somatic maintenance, the rest to

increasing and maintaining the level of maturity EH and to reproduc-

tion once maturity is reached. The rate of change in the structural

volume at constant food density is equal to

dV

dt¼ jff _pAmgV2=3 � ½ _pM�V

jf½Em� þ ½EG�ðeqn 1Þ

where t is time, [Em] is maximum reserve density (which, at constant

food, reaches steady state at f[Em]), [ _pM] is the somatic maintenance

costs per unit volume and [EG] is the total energetic cost of structure

(tissue energy content plus overheads for synthesis) per unit structural

volume (van der Meer 2006b; Kooijman 2010). For a constant food

density, this equation is equivalent to the von Bertalanffy growth

curve, although based on very different principles (Kooijman 2010).

The rate of change of the reserve density (whichmust bemultiplied by

structural volume, converted to mass and added to the structure to

obtain a wet weight) is equal to

d½E�dt¼ f _pAmg

V1=3f� ½E�½Em�

� �: ðeqn 2Þ

Once maturity is reached under the standard DEB model, a fixed

fraction of assimilates is continually transferred from the reserve to

the reproduction buffer (after accounting for maturity maintenance)

and then ‘packaged’ as eggs and dispensed as soon as an appropriate

threshold amount for a clutch is reached. The energy allocated to the

reproduction buffer per unit time is _pr = (1 ) j) _pc ) _pj, where

_pc = ( _pAm[E]V2 ⁄ 3) ⁄ [Em] ) [E](dV ⁄ dt) is the reserve mobilization

rate and _pj = _kjEH is the maturity maintenance rate, with _kj the

maturitymaintenance rate coefficient. However, S. undulatus is a sea-

sonal breeder, with a refractory period from mid-summer until mid-

winter (Marion 1970). Following Pecquerie, Petitgas & Kooijman

(2009), I implemented seasonal reproduction whereby reserve in the

reproduction buffer continues to accumulate at all times but is only

drawn upon to produce eggs between 1st January and 1st August.

The rate that the reserve buffer is transferred to the egg buffer (J h)1)

during the reproductive season is _pB = (jR ⁄ k)((1 ) j)([Em]

� 2011 The Author. Functional Ecology � 2011 British Ecological Society, Functional Ecology, 26, 167–179

168 M. Kearney

({ _pAm} ⁄ [Em])V2 ⁄ 3) + [ _pM]V) ⁄ (1 + 1 ⁄ ([EG] ⁄ j[Em] ⁄ )) ) _pJ), where

(1 ) jR) is the overhead cost of reproduction and k is a constant that

relates to the maximum fraction of the year during which the animal

would reproduce if fed ad libitum (Pecquerie, Petitgas & Kooijman

2009), assumed here to be 0Æ58 (i.e. 7 ⁄ 12 months).

D Y N A M I C EN ER G Y BU D G E T P A R A M E T E R ES T I M A T I O N

F O R S C E L O P O R U S U N D U L A T U S

Dynamic Energy Budget parameters are not directly observable

because they relate to the abstracted state variables of structure,

reserve and maturity. To estimate DEB parameters (Table 1) for

S. undulatus, I applied a new approach called the ‘covariation

method’ (Lika et al., in press, a). The covariation method aims to

estimate all of the DEB parameters simultaneously from empirical

observations of physiological processes. I implemented this estima-

tion procedure in MATLAB (The MathWorks, Natick, MA, USA)

using the freely available package ‘DEBtool’ (http://www.bio.vu.nl/

thb/deb/deblab/debtool/).

In DEB theory, a distinction is made between ‘core’ parameters

and ‘auxiliary’ parameters. The core DEB parameters are intimately

linked to the underlying assumptions of DEB theory and relate

directly to processes controlling state variable dynamics. Auxiliary

parameters combine with the core DEB parameters and state vari-

ables to define mapping functions from the abstract quantities such as

structural volume to real world observations such as wet mass. In the

covariation method, empirical observations are obtained for a given

species (entered in the ‘mydata.m’ DEBTOOL script), mapping func-

tions are specified using auxiliary theory (contained in the ‘predict.m’

DEBTOOL subroutine) that relates the given set of empirical data to

the DEB core parameters and state variables, and the set of core and

auxiliary parameters that best reflects the empirical data is obtained

inversely through a regression proceedure.

Because core DEB parameters frequently appear concurrently in

the mapping functions for different types of data, substantial con-

straints on their possible values are imposed as the number of types of

observations used for parameter estimation increases (e.g. the primary

core parameter { _pAm} appears in the compound core parameters Lm

and [Em] which themselves appear in the mapping functions for the

von Bertalanffy growth rate, dry mass and body length). This situa-

tion allows the parameter values to be estimated via regression based

on a set of single data points (single numbers) for a range of different

physiological observations, which are hence referred to as ‘zero-vari-

ate’ data (in contrast to the more typical situation in regression of

using a list of one or more pairs of numbers, e.g., time vs. length,

which would be referred to as ‘uni-variate’ data). The general idea

behind the covariation method is to let all available information com-

pete to produce the best fitting parameter set and, to this end, it is nec-

essary to estimate all parameters from all data sets simultaneously.

In addition, the estimation proceedure may be guided by prior

knowledge of parameter values, not unlike the concept of a ‘prior’ in

Bayesian parameter estimation methods. Conceptually, this prior

knowledge is treated as data and hence it is referred to it as ‘pseudo-

data’. The pseudo-data (rates corrected to 20 �C) for the present

study were: energy conductance v = { _pAm} ⁄ [Em] = 0Æ02 cm day)1,

allocation fraction to soma j = 0Æ8, growth efficiency jG = 0Æ8(relates to [EG] and is the energy fixed in structure as fraction of the

energy required for structure), maturity maintenance rate

kJ = 0Æ002 day)1 and somatic maintenance [ _pM] = 54 J cm)3

day)1, based onLika et al. (in press, a).

Finally, when estimating DEB parameters with the covariation

method on the basis of diverse data sets, one frequently faces the issue

that certain observations have been made with greater confidence

or accuracy than others. It is therefore useful to be able to assign rela-

tive weights to the different data points on the basis of this prior

knowledge.

Table 1. (a) Observed and predicted values from the Dynamic Energy Budget (DEB) parameter estimation procedure for Sceloporus undulatus,

and (b) DEB resulting core parameter estimates and standard deviations (SD), with rates corrected to 20 �C. The shape coefficient is for snout-vent length (SVL)

(a) Observed and predicted data

Data Obs. Pred. Units Data source

ab, age at birth 62 29Æ39 days (28 �C) Andrews, Mathies &Warner (2000);

Parker, Andrews &Mathies (2004)

ap, age at puberty 152Æ5 153Æ8 days (28Æ9 �C) Ferguson & Talent (1993)

lb, length at birth 25Æ0 25Æ1 mm Tinkle (1972)

lp, length at puberty 58Æ0 57Æ3 mm Tinkle (1972)

l¥, maximum length 80Æ0 79Æ9 mm Tinkle (1972)

Wb, mass at birth 0Æ56 0Æ56 g, wet Tinkle & Ballinger (1972)

Wp, mass at puberty 6Æ9 6Æ7 g, wet Tinkle & Ballinger (1972)

W¥, maximum mass 18Æ0 18Æ4 g, wet Tinkle & Ballinger (1972)

R¥, max reproduction rate 40Æ1 39Æ6 # year)1 (24 �C) Lordsburg population

(Tinkle & Dunham 1986)

(b) Core parameter estimates

Parameter Estimate SD Units

z, zoom factor (relative volumetric length) 1Æ92 0Æ228 cm

dM, shape correction factor 0Æ2401 0Æ05914 –

v, energy conductance 0Æ0271 0Æ01098 cm day)1

j, allocation fraction to soma 0Æ605 0Æ1904 –

[ _pM], somatic maintenance 100 28Æ61 J cm)3 day)1

_kJ, maturity maintenance rate coefficient 0Æ001751 0Æ004541 day)1

[EG], cost of structure 7725 485 J cm)3

EbH, maturity at birth 1416 1080 J

EpH, maturity at puberty 3Æ649e+004 2Æ434e+004 J


Metabolic theory, life history and range constraints 169

The covariation method applies the Nelder-Mead simplex method

for estimating parameters, using either a maximum likelihood (ML)

or weighted least squares (WLS) criterion for model fit. The WLS

performs better than the maximum likelihood method when only

‘zero-variate’ data is being used for parameter estimation (Lika et al. ,

in press, b) as is the case in this study. I used data based largely on the

Utah population of S. undulatus, for which growth data in con-

trolled-environments are available (Ferguson & Talent 1993). The

observed data and their sources are summarized in Table 1a.

The associated Matlab scripts I used to estimate the parameters for

S. undulatus can be found at http://www.bio.vu.nl/thb/deb/deblab/

add_my_pet/Species.xls.

For energy ⁄mass conversions, the chemical potential of structure

lV = 500 000 J mol)1 and the chemical potential of reserve

lE = 585 000 J mol)1 were used, adjusting the default DEB values

(Kooijman 2010) based on (Vitt 1978).

For the observations in Table 1a, age at birth includes both

pre- and post-ovipositional development. Weights at birth, puberty

and maximum size were based on the observed sizes (snout-vent

length, SVL) and the relationship between SVL and mass in Tin-

kle & Ballinger (1972) (Fig. S1, Supporting information). I

assumed a body water content of 70% and an egg water content

of 50% (Vitt 1978). The value for maximum observed reproductive

rate used in the parameter estimation proceedure must relate to

the value used for the mass of the hatchlings (0Æ56 g wet mass in

this case) and the different water content of eggs and hatchlings. I

was unable to find suitable data from the literature on reproduc-

tion rate under controlled conditions (food and temperature). An

initial guess at this value was based on the maximum observed

annual reproduction for the 11 populations in the comparative

life-history study of 9Æ5 g wet mass (Lordsburg, New Mexico,

Tinkle & Dunham 1986). Assuming that the eggs (50% water)

have an average dry-mass energy content of 27Æ82 kJ g)1 (Vitt

1978), a 9Æ5 g clutch contains 132Æ2 kJ of energy. Assuming that

the hatchlings (70% water) have an average dry-mass energy con-

tent of 23Æ58 kJ g)1 (Vitt 1978), a 0Æ56 g hatchling would contain

3Æ96 kJ. Thus, a reproductive output of 9Æ5 g wet mass per year is

equivalent to 132Æ2 ⁄ 3Æ96 = 33Æ4 offspring per year. This value

resulted in underestimates of observed field reproductive output by

approximately 20%, and was adjusted accordingly, decreasing j

slightly from the original estimate.

For simulations, egg wet mass was assumed to be 0Æ36 g, based on

the Utah population (Tinkle 1972). In keeping with the assumption of

DEB theory that the specific energy content of eggs is the same as the

specific energy content of reserve (estimated in this study to be

7343 J g)1 wet weight, 70%water), I assumed that the energy content

of one egg (0Æ36 g wet weight, 50% water) was 4406 J. For simula-

tions of life-history variation, I ran the model either with the Utah

body size and clutch size values, or with the locally observed values

for these traits. In DEB theory, maximum size Lm = (j{ _pAm} ⁄[ _pM]); it is thus not a core parameter itself but is rather the outcome

of the parameters that control the ratio between the incoming

energy for growth and maintenance, and the amount of energy con-

sumed by maintenance. Variation in maximum size can be consid-

ered the outcome of proportional changes in the ‘extensive’

physical design parameters through the dimensionless ‘zoom factor’

z, where Lm2 = zLm1 = (jz{ _pAm} ⁄ [ _pM]). An adjustment of z

reflects a shift in the maximum assimilation rate { _pAm} as well as in

the parameters controlling the size at hatching EbH and maturity E

pH

(Kooijman 2010), with all other DEB parameters remaining con-

stant. The z adjustment thus imposes a covariation of these three

design parameters from a physicochemical point of view with sub-

sequent implications for the life history and provides a null expecta-

tion for the implications of size shifts unless selection acts

independently on the design parameters. Mean snout-vent length at

maturity (SVLmat) for the 11 populations of S. undulatus summa-

rized by Tinkle & Dunham (1986) is indeed tightly related to mean

adult SVLmax (linear regression: SVLmat = 0Æ951SVLmax ) 6Æ742,R2 = 0Æ874, P < 0Æ001, Fig. S2, Supporting information). I thus

determined, for each population, the value of z that the reference

size (Utah population) must be multiplied by to produce the

locally observed SVLmat and the corresponding SVLmax that this

implied (Table S2, Supporting information). The resulting relation-

ship closely matched the observed one (Fig. S2, Supporting

information).

T H E R M O R E G U L A T O R Y M O D E L A N D I N T E G R A T I O N

W I T H T H E D Y N A M I C E N ER GY BU D GE T M O D E L

The Niche Mapper system calculates hourly steady-state body tem-

peratures (Tb) from actual or interpolated weather station records

given the properties of the animal and its microhabitat (Kearney,

Shine & Porter 2009). Following previous studies (Adolph & Porter

1993, 1996; Buckley 2008), solar absorptivity was set to 0Æ9, and I

assumed that the lizards foraged between Tb of 32 and 37 �C, main-

taining a Tb of 33 �Cwhenever possible during active or inactive peri-

ods by seeking shade ⁄ changing depth within the soil profile.

Parameters for the microclimate model follow Kearney & Porter

(2004) except that climatic data were drawn from a global data set of

monthly mean daily maximum and minimum air temperature and

monthly mean daily relative humidity, wind speed and cloud cover

(1961–1990; 10’ resolution; http://www.cru.uea.ac.uk/cru/data). The

lizards were assumed to experience the predicted wind speed and air

temperature calculated for 0Æ5 cm above the ground when active on

the surface.

A FORTRAN script implementing the DEBmodel was integrated

with the Niche Mapper system and was called every hour to estimate

structural volume, reserve density and reserve allocated to reproduc-

tion, given the body temperature estimate [see Fig. S3 (Supporting

information) for an example of daily outputs across average days of

eachmonth].

The Arrhenius temperature correction (similar to Q10 correction)

was applied to all rates for a common Arrhenius temperature TA of

9600 which provides a good approximation for the observed thermal

responses of resting metabolism, assimilation and development rates

(Fig. S4, Supporting information). The Sharp adjustment (see Kooij-

man 2010, p. 21) was also applied to provide an appropriate thermal

response outside the range to which the Arrhenius relationship

applied (Table 1b, Fig. S4, Supporting information). This adjustment

causes rates to reduce outside upper and lower temperature bound-

aries (parameters TL and TH) at particular rates (TAL and TAH),

reflecting enzyme inactivation and producing a classic-shaped ther-

mal performance curve.

Feeding was only allowed when the animal was active on the sur-

face and was assumed to occur ad libitum (i.e. the functional response

f = 1). The energy (mass) of food in the stomach Ms started at zero

(at hatching) was assumed to fill at a rate dMs ⁄ dt = { _pAm}V2 ⁄ 3

(f ) Ms ⁄MsmV) (Kooijman 2000), where Msm, the maximum energy

content of the stomach per lizard mass, was assumed to be 186 J g)1

assuming an adult lizard has a stomach volume of approximately

2Æ5% of total body volume and that insect prey contain 23Æ85 J mg)1

dry mass (Buckley 2008). Assimilation was assumed to occur when

the stomach was>1% full, otherwise fwas set to zero and the reserve

density declined according to eqn 2.


170 M. Kearney

The wet mass of the animal as calculated by the DEB model

each hour was used in the biophysical calculations of body temper-

ature, dynamically capturing the effect of size on body tempera-

ture.

For simulations of the life-history study sites, hatching was

assumed to occur in July–September (as described in the original

studies, Table S2, Supporting information) and the hourly simula-

tions were run for 5 years, repeating the loop through average

monthly climatic conditions for the appropriate number of days per

month. For continent-wide simulations for predicting geographic

range, hatching was uniformly assumed to occur at the beginning of

August. The simulation was run for 4 years at each location, tallying

the total number of eggs and the total activity time for each year. A

life table was then constructed, with annual estimates of age-specific

fecunditiesmx (number of female offspring of age class x, assuming a

50 : 50 sex ratio) and survivorships lx (the survivorship to age class x).

Following Adolph & Porter (1993), survivorship was estimated

according to the empirically derived relationship between annual

activity hours a (calculated in this study) and observed adult survivor-

ship across the 11 life-history study populations (linear regression,

F1,8 = 5Æ96, P = 0Æ041, R2 = 0Æ427, )0Æ00020818a + 0Æ63854795).From this, I calculated the net reproductive rateR0 ¼

Pnx¼0 lxmx, the

average generation time T ¼ ðPn

x¼0 xlxmxÞ=R0 and the intrinsic rate

of increase rmax ¼ ln ðR0ÞT .

Results

D Y N A M I C EN ER G Y BU D G E T P A R A M E T E R ES T I M A T I O N

A N D V A L I D A T I O N

The DEB parameter estimates in Table 1b provided a

close fit to the data used in the estimation procedure, with

the exception of age at birth which was underestimated.

The resulting DEB model successfully captured a wide

range of metabolic phenomena not included in the fitting

procedure. Most fundamentally, the model predicted the

oxygen consumption rate (derived from first principles

based on a generalized stoichiometry, Fig. S5a, Supporting

information) and the assimilation rate (Fig. S5b, Support-

ing information). It also closely predicted the trajectory of

growth observed in laboratory-reared Utah individuals

(Fig. S6a, Supporting information). Reduction in the

‘zoom’ factor z to 0Æ92 provided a close fit to the growth

trajectory of the Oklahoma population (reared under the

same conditions as Utah individuals) (Fig. S6a, Supporting

information) and predicted the qualitative (and to some

extent quantitative) differences between these lineages with

respect to size at maturity, post-partum weight and egg

size (Table S3, Supporting information). The adjustment

of z also qualitatively predicted the observed differences in

the scaling of body size with body mass (Fig. S6b, Sup-

porting information), reflecting DEB predictions of the

scaling of reserve pools. Reserve was estimated to make

up approximately 60% of the wet body mass. A simula-

tion of starvation at 33 �C predicted a wet mass loss of

28% over 10 days, which compares well with the range of

20–30% observed by Dunlap (1995) at the same tempera-

ture and over the same time for the related Sceloporus

occidentalis.

F I E L D B O D Y T E M P E R A T U R E S , A C T I V I T Y B U D G E T S A N D

G R O W T H

The biophysical model accurately predicted potential field

body temperature when based on coarse climatic data

(Fig. S7, Supporting information). The estimates in the pres-

ent study of annual activity time were tightly related to those

calculated by Adolph & Porter (1993) (linear regression,

R2 = 0Æ909) but were around 700 h (30%) shorter (paired t-

test, t8 = 16Æ84, P < 0Æ001) because of the inclusion of cloud

cover (clear skies were assumed in Adolph & Porter 1993); re-

running the simulations without cloud produced statistically

indistinguishable results to Adolph & Porter (1993) (paired

t-test, t8 = 1Æ79,P = 0Æ112, linear regression,R2 = 0Æ794).The combined biophysical ⁄DEB model produced results

qualitatively and quantitatively consistent with observed field

growth rates when driven by long-term monthly climatic

averages (Fig. 1a–d). The overall relationship between

observed and predicted age-specific body sizes (SVLobs and

SVLpred) explained a similar proportion of the variance and

was similarly close to a 1 : 1 relationship, whether using the

Utah parameter set (linear regression, R2 = 0Æ856, P <

0Æ001, SVLobs = 0Æ97SVLpred + 3Æ06, Fig. 1a) or adjusting

to the local body size via the parameter z (linear regression,

R2 = 0Æ897, P < 0Æ001, SVLobs = 0Æ96SVLpred + 4Æ15,Fig. 4b).

G E OG R A P H I C L I F E -H I ST OR Y V A R I A T I O N : A G E A T

M A T U R I T Y A N D R E P R O D U C T I V E O U T P U T

Operational definitions of ‘maturity’ in the life-history studies

of S. undulatus are varied but almost always involve some

level of egg development having occurred (to be detectable ‘in

the hand’) (Tinkle 1972; Vinegar 1975) (Tinkle & Ballinger

1972; Ballinger, Droge & Jones 1981). The closest fit between

observed and predicted age at maturity occurred when a

threshold of 1 ⁄ 5th through the development of a clutch was

used, with the exception Nebraska and Kansas (Fig. 2a,b).

These latter two populations were also outliers in Adolph &

Porter’s (1996) analysis. Regression analyses including these

outlier populations indicated that SVL on its ownwas the best

predictor of age at maturity (Table 2a). However, when the

outliers were excluded, the integrated DEB ⁄biophysicalmodel predictions significantly explained large fractions of

the variation in month at maturity relative to SVL or activity

hours, with the predictions based on the Utah lineage fitting

best (Table 2a). Figure S8 (Supporting information) shows

the trajectories of body mass (with sudden drops representing

oviposition events) as well as midday body temperature and

reserve densities for the 11 sites in order of activity time and

clearly shows the trend toward earlier maturation with

increasing activity windows. Figure 4a shows the spatial vari-

ation in predicted age atmaturity when theUtah-basedmodel

was run across all of theUSA aswell as Central America.

Regression analyses comparing observed to predicted geo-

graphic variation in annual reproductive output are presented

in Table 2b. Observed annual reproductive output was



poorly explained by annual activity hours alone. Body size

alone explained 50% of the variation in reproduction, but

multiple regression with body size and annual activity

explained over 70% of the variation. Similarly, regression of

residual annual reproduction (from the regression on SVL)

against annual activity hours showed a strong positive rela-

tionship (R2 = 0Æ62, F1,8 = 13Æ1, P = 0Æ007). The DEB-

based model provided a poor prediction of reproduction

when based on a constant body size (that of Utah), unless

SVL was included as a covariate. However, the size-adjusted

DEB model explained a similarly large fraction of the varia-

tion as did the more detailed empirical energy budget model

of Grant & Porter (1992). In all cases, Arizona was a signifi-

cant outlier from the analyses, as found previously (Grant &

5

10

15

20

25

500 1000 1500 2000 2500 3000

Age

at m

atur

ity

(mon

ths)

Predicted annual activity (h)

5

10

15

20

25

500 1000 1500 2000 2500

Age

at m

atur

ity

(mon

ths)

Predicted annual activity (h)

0

50

100

150

200

500 1000 1500 2000 2500

Repr

oduc

tion

(kJ y

ear–1

)

Predicted annual activity (h) Predicted annual activity (h)

Utah body/clutch size Local body/clutch size

(a) (b)

(c) (d)

0

50

100

150

200

500 1000 1500 2000 2500

Repr

oduc

tion

(kJ y

ear–1

)

Fig. 2. Observed (crosses) and predicted (cir-

cles) age at maturity (a, b) and annual

reproductive output (c, d) plotted against cal-

culated potential activity time. Predictions

are based on either the Utah body size and

clutch size (a, c) or the locally observed body

and clutch sizes (b, d). Dotted lines are regres-

sions for observed values, and solid lines are

regressions for predicted values. All observed

data come from Tinkle & Dunham (1986).

Predictions are made based on long-term

monthly average climate, rather than the

actual weather of the observations.

20

30

40

50

60

70

80

0 5 10 15 20 25

Snou

t-ve

nt le

ngth

(mm

)

10

20

30

40

50

60

70

80

10 20 30 40 50 60 70 80Obs

erve

d sn

out-

vent

leng

th (m

m)

Predicted snout vent length (mm)

10

20

30

40

50

60

70

80

10 20 30 40 50 60 70 80Obs

erve

d sn

out-

vent

leng

th (m

m)

Predicted snout vent length (mm)

Months since hatching

20

30

40

50

60

70

80

0 5 10 15 20 25

Snou

t-ve

nt le

ngth

(mm

)

Months since hatching

Ohio

Arizona

Texas

Ohio

Arizona

Texas

Fixed size Local size(a) (b)

(c) (d)

Fig. 1. Observed and predicted field growth of Sceloporus undulatus derived from aDynamic Energy Budget model integrated with a biophysical

model of heat exchange and thermoregulatory behaviour. The first two panels show contrasting growth trajectories for three sites assuming the

Utah size (a) and the local size (b), with points representing observed data and lines representing the DEB predictions. The second two panels

show observed and predicted values for SVL at particular ages for all five sites for which there is growth data, again based on either the Utah size

(c) or the local size (d). In (c) and (d), the dotted lines represent 1 : 1 and the solid lines represent a linear regression. Observations come fromTin-

kle & Ballinger (1972) (Colorado, South Carolina, Ohio and Texas) and Tinkle & Dunham (1986) (Arizona). Predictions are made based on

long-termmonthly average climate, rather than the actual weather of the observations.


172 M. Kearney

Porter 1992). Exclusion of this site substantially increased the

variances explained but the qualitative differences among

models were largely unchanged. The size-adjusted DEB

model fitted best (adjusted AIC) when all populations were

considered, and the fit of this model was second to the model

of Grant & Porter (1992) when Arizona was excluded from

the analyses. Annual clutch frequency was predicted to

decline from 13 in Central America to 1 or 0 in northernUSA

(Fig. 4b).

G E OG R A P H I C R A N G E L I M I T S

Life-table calculations based on the UtahDEB energy budget

calculations and empirical survivorship vs. activity time curve

produced very similar results to the observed life table for this

site reported by Tinkle (1972) (Table S4, Supporting informa-

tion). When spatial variation in rmax (based on the Utah

parameters) was calculated using gridded climatic data, the

threshold where rmax > 0 provided a coarse match with the

observed geographic range limits but tended to under-predict

in the south and north west, and to over-predict in the north-

east and far west (Fig. 4c).

Discussion

C O N S T R A I N T S O N E N E R G Y A N D M AS S B U D G E T S

The characterization of energy and mass budgets is basic to

understanding life histories (Dunham &Overall 1994), popu-

lation dynamics (Nisbet, McCauley & Johnson 2010) and

range limits (Kearney, Wintle & Porter 2010). Life-history

theory aims to predict how evolution will shape the allocation

of assimilated resources to the potentially competing destina-

tions of maintenance, growth, development and reproduction

such that fitness is maximized (e.g. Stearns 1992). Although

the range of allocation ‘strategies’ that organisms could take

Table 2. Results of linear regression of observed (a) annual reproductive output and (b) age at maturity as a function of activity hours, body size

(snout-vent length, SVL) and the Dynamic Energy Budget (DEB) model predictions. ‘Utah month mature’ refers to model predictions of the

month of maturity assuming the DEB parameters for Utah, while ‘z-adjusted month mature’ holds all DEB parameters the same except the

scaling parameter, z, which alters size at maturity and asymptotic size according to the assumptions of DEB theory. AIC is the adjusted value of

the Akiaike Information Criterion, with the lowest (best model) value in bold. For multiple regressions, statistical significance of individual

predictors is indicated by asterisks. Analyses are reported with and without outlier populations

d.f. F R2 P AIC

(a) Age at maturity (months)

All populations

Activity hours 1,9 0Æ916 0Æ092 0Æ364 72Æ121SVL 1,9 6Æ057 0Æ402 0Æ036 67Æ527Activity hours + SVL 2,7 3Æ308 0Æ453 0Æ09 71Æ796Utah month mature 1,9 3Æ094 0Æ256 0Æ112 69Æ937Utah month mature + SVL* 2,7 6Æ484 0Æ618 0Æ021 67Æ826z-adjusted month mature 1,9 2Æ542 0Æ22 0Æ145 70Æ451

Excluding Kansas and Nebraska

Activity hours 1,7 8Æ834 0Æ558 0Æ021 55Æ421SVL 1,7 2Æ49 0Æ262 0Æ159 60Æ028Activity hours + SVL 2,6 3Æ937 0Æ568 0Æ081 62Æ423Utah month mature 1,7 124Æ4 0Æ947 <0Æ001 36Æ376Utah month mature** + SVL 2,6 70Æ923 0Æ959 <0Æ001 41Æ127z-adjusted month mature 1,7 28Æ283 0Æ802 0Æ001 48Æ209

(b) Annual reproduction (kJ)

All populations

Activity hours 1,8 1Æ363 0Æ146 0Æ227 104Æ385SVL 1,8 8Æ144 0Æ504 0Æ021 98Æ938Activity hours + SVL* 2,7 8Æ743 0Æ714 0Æ012 99Æ437Utah reproduction 1,8 4Æ408 0Æ355 0Æ069 101Æ569Utah reproduction + SVL* 2,7 8Æ632 0Æ711 0Æ013 99Æ528z-adjusted reproduction 1,8 9Æ488 0Æ541 0Æ015 98Æ161Grant and Porter reproduction 1,8 8Æ868 0Æ526 0Æ018 98Æ498

Excluding Arizona

Activity hours 1,7 0Æ999 0Æ125 0Æ351 96Æ695SVL 1,7 6Æ912 0Æ497 0Æ034 91Æ715Activity hours* + SVL** 2,6 12Æ36 0Æ805 0Æ007 90Æ398Utah reproduction 1,7 3Æ897 0Æ358 0Æ089 93Æ913Utah reproduction* + SVL* 2,6 11Æ008 0Æ786 0Æ01 91Æ227z-adjusted reproduction 1,7 27Æ625 0Æ798 0Æ001 83Æ508Grant and Porter reproduction 1,7 45Æ225 0Æ866 <0Æ001 79Æ809



is potentially vast (Dunham&Overall 1994), the options may

be substantially constrained by both the environment (Grant

& Dunham 1990; Grant & Porter 1992; Adolph & Porter

1993, 1996; O’Connor, Sieg & Dunham 2006) and by the

extent that the ‘architecture’ of a metabolic system imposes

mechanistic couplings among life-history traits (Lika & Koo-

ijman 2003).

The results of the present study show that the general prin-

ciples of biophysical ecology and the DEB metabolic theory

can, when integrated, capture much of the observed geo-

graphic variation in the life history of S. undulatus and, ulti-

mately, the limits on its geographic range. A distinguishing

feature of this analysis lies in the allocation rules of the DEB

model, which prescribes simple yet somewhat unorthodox

constraints on allocation. Specifically, the j-rule means that

growth does not compete directly with reproduction but only

with somatic maintenance. The ultimate, asymptotic size then

emerges from the model once the flux of assimilates assigned

to growth and somatic maintenance is fully consumed by

maintenance; the trajectory of growth is therefore predicted

to be unaffected by the transition to maturity, consistent with

observation (Kooijman 2000). The estimate for j in the pres-

ent study implies that 40% of the energy ⁄mass intake of

S. undulatus is allocated to reproduction (and maturity main-

tenance) at the point of maturity. Where were these resources

going prior to maturity, given the constant value for jassumed throughout ontogeny? The DEB theory states that

they were being allocated to maturation, i.e., to increasing the

complexity or information content within the organism (such

as general tissue differentiation, preparing reproductive

organs, developing the immune system) (Kooijman 2010). At

the transition from juvenile to adult, the DEB model predicts

a discontinuity in the respiration rate because 1 ) j of the

reserve flux is redirected from a dissipative destination (matu-

ration) to being largely fixed as reproductive biomass

(Fig. S5a, Supporting information).

The other relatively unusual concept in DEB theory is the

partitioning of mass into ‘structure’ and ‘reserve’. This study

estimates that the reserve comprises around 60% of the total

wet body mass and implies realistic starvation times com-

pared with empirical data (Dunlap 1995), as described in the

Results. Some predicted starvation times for an adult lizard

from the Utah population are: 25 days at 33 �C, 58 days at

25 �C and 117 days at 20 �C. In the simulations for this

study, which assumed food was available ad libitum when liz-

ards were able to forage (as constrained by the biophysical

model), the longest periods of time when animals were pre-

vented from feeding were during the winter dormancy peri-

ods. Because of the cool temperatures predicted in the retreat

sites at these times, reserve densities were never predicted to

drop to seriously low levels (e.g. Fig. S8, Supporting informa-

tion). However, if activity budgets were to be limited by high

temperatures (e.g. in warm environments where available

shade was minimal) and food abundance was low, death by

starvation would be predicted in the order of months. This

would be further exacerbated for juveniles, with lower abso-

lute amounts of reserve (see Kooijman 1986).

I M P L I C A T I O N S F O R L I F E - H I S T O R Y V A R I A T I O N I N

S C E L O P OR U S U N D U L A T U S

The results of the present study contribute further to our

understanding of the causes of life-history variation in the

classic example of S. undulatus. Adolph& Porter (1993, 1996)

showed that thermal constraints on activity could cause geo-

graphic variation in life-history patterns qualitatively similar

to those expected under adaptive arguments derived from

life-history theory. Using S. undulatus as a case study, they

predicted how phenomena such as age at maturity and repro-

ductive output should vary with the local potential activity

time as inferred from a biophysical model. The qualitative

predictions they made are highly consistent with the quantita-

tive predictions of the present study, which are based on

growth and maturation rates as constrained by the thermal

environment (Figs 1 and S8, Supporting information). First,

age at maturity showed threshold shifts of approximately 1-

year intervals as potential activity time increased (Figs 2a,b

and 4a). Second, the number of clutches produced per year

increased as potential activity time increased (Figs 2c,d and

4b). The results of the present study are also highly consistent

with the quantitative predictions of Grant & Porter (1992) for

annual reproductive output (Fig. 3).

0

20

40

60

80

100

120

140

0 50 100 150 200Obs

erve

d fe

cund

ity

(kJ y

ear–1

)

Predicted fecundity (kJ year–1)

0

20

40

60

80

100

120

140

0 50 100 150 200

Obs

erve

d fe

cund

ity

(kJ y

ear–1

)

Predicted fecundity (kJ year–1)

Utah body/clutch size Local body/clutch size

(a) (b)

Fig. 3. Observed annual reproductive vs. predicted values from the present study (filled circles) and from Grant & Porter (1992) (open circles).

Predictions are based on either the Utah body size and clutch size (a) or the locally observed body and clutch sizes (b). The dotted lines show the

1 : 1 relationships and the solid lines are linear regressions excluding the outlier population of Arizona. All observed data come from Tinkle &

Dunham (1986). Predictions from the present study are made based on long-term monthly average climate, rather than the actual weather of the

observations while those of Grant and Porter are based onmeteorological observations from nearby weather stations for the period of the obser-

vations.


174 M. Kearney

The advance of the present study over these important pre-

vious studies is that the predictions have been made quantita-

tively from first principles (cf. Adolph & Porter 1993, 1996)

and on the basis of a more general and formal mechanistic

framework for whole life-cycle metabolism (cf. Grant & Por-

ter 1992). This permits some novel interpretations of the fit of

the energy budget predictions with the observed life-history

patterns. First, climatic influences on reproductive output

were only strongly apparent once local variation in body size

had been accounted for, both in the previous analyses (Grant

& Porter 1992; Adolph & Porter 1993) and in the present

study (Figs 2d and 3b, Table 2b). This is because body size

dominates total reproductive output. Although body size

adjustments by Grant & Porter (1992) and by Adolph & Por-

ter (1993) were made based on the average adult size, adjust-

ments in the present study were made through the ‘zoom

factor’ z, which affects size at birth, maturity and the asymp-

totic maximum through influences on the ‘extensive’ parame-

ters EbH, E

pH and { _pAm}, respectively (see Kooijman 2010, p.

300). The DEB theory thus predicts that, all else being equal,

selection for increased size should have correlated effects on

size at birth and size at maturity. I also assumed local clutch

size was equal to that empirically observed (Table S2, Sup-

porting information). However, the fit of observed to pre-

dicted total annual reproductive output differs little whether

clutch and egg size were held constant at the values for the

Utah population (R2 = 0Æ718) or allowed to vary as

described above (R2 = 0Æ798). Thus, an increase in body size

alone increased the absolute reproductive output.

However, even once body size was accounted for, the Ari-

zona population was a consistent outlier in all studies in hav-

ing a lower than expected reproductive output. Grant &

Porter (1992) suggested that this was because reproduction at

this site was limited by ingestion rate (i.e. prey density) rather

than food processing rate. The DEB-based predictions pro-

vide support for this hypothesis in that the predicted asymp-

totic size (given the size at maturity, see Materials and

methods) was lower than observed (Figs 1b and S2, Support-

ing information), and ultimate size in the DEB model is pre-

dicted to decrease under low food availability. The generally

close match between observed and predicted field growth and

reproduction rates has the remarkable implication that S. un-

dulatus is typically not limited by prey availability in much of

its range. This is consistent with the findings of Huey, Pianka

& Vitt (2001) that only 13Æ2% of field-active lizards (and only

1Æ5% of North American iguanid lizards) are observed to

have empty stomachs.

C O N S T R A I N T S O N G E O GR A P H I C R A N G E

Biophysical models have been applied to infer geographic

range constraints by predicting regions where a necessary

physiological process fails (Kearney & Porter 2009). For

example, Kearney & Porter (2004) predicted regions in Aus-

tralia where foraging or egg development was not possible in

a nocturnal lizard. For S. undulatus, the northern range limit

has been proposed to be limited by potential for egg develop-

ment (Parker & Andrews 2007) but my calculations of poten-

tial development in shallow nests suggest otherwise (Figs S10

and S11, Supporting information). The present study also

predicts at least some annual activity is possible through the

region considered. However, the length of the active season

required for successful reproduction cannot be inferred with-

out an energy budget. The energy budget developed in the

present study predicts the northern distribution limit to occur

around the 1100 activity hours threshold (Fig. S9a, Support-

ing information). Similarly, Buckley et al. (2010) predicted

that S. undulatus could not produce sufficient eggs to offset

mortality (22Æ5 eggs per annum) below an annual activity time

of 1315 h. However, on this basis, Buckley et al.’s (2010)

model precluded S. undulatus from all but the very southern

parts ofUSA (see Fig. 1 in Buckley et al. 2010). In these areas,

the present study estimated potential annual activity of

>2000 h (Fig. S9a, Supporting information). This suggests

that the poor agreement between the observed and predicted

range limit based on the ‘biophysical threshold’ model in

Buckley et al. (2010) is because their biophysical model sub-

stantially underestimated the potential activity hours.

The integrated biophysical ecology ⁄DEB approach taken

here allowed inference of age-specific reproductive output as

constrained by the thermal environment (Fig. S9b, Support-

ing information). When combined with the empirically

observed relationship between potential activity time and sur-

vivorship (Fig. S9c, Supporting information), it was possible

to estimate rmax and, therefore, to map a more energetically

specific depiction of the niche to infer range constraints

(Fig. 4c). This prediction, being based on empirical patterns

of survivorship, is potentially more reflective of the realized

niche and is sensitive to local variations in predation pressure.

Buckley et al. made the distinction between ‘threshold’ mod-

els that delimit ranges based on an environmentally limited

physiological process vs. those that explicitly compute popu-

lation dynamics such as the ‘foraging energetic’ model of

Buckley (2008). Although the latter study estimated carrying

capacity (via a spatially implicit model of optimal foraging

and a constant empirically determined prey density) and

hence population density, the predicted range limits were in

fact a reflection of the threshold where rmax is non-negative,

as in the present study. Thus, the ‘biophysical threshold’ dis-

tinction seems inappropriate. It is perhaps more helpful to

categorize species distribution models with respect to the

extent that processes are represented explicitly (through pro-

cess models) vs. implicitly (i.e. through statistical associa-

tions), and whether explicitly stated process are depicted by

empirical functions (e.g. allometric regressions) or formal the-

ories (e.g. DEB theory or heat-transfer physics).

A D V AN T AG E S F R OM A P PL Y I N G A F O R M A L M E T A BO L I C

T H E O R Y : PA R A M E T E R S , G E N E R A L I T Y , T E S T A B I L I T Y

A number of studies have successfully integrated biophysical

principles with energy budgets to study life history, popula-

tion dynamics and range limits of ectotherms using S. undula-

tus as a model (Grant & Porter 1992; Adolph & Porter 1993,



1996; Dunham 1993; Angilletta et al. 2004; Buckley 2008).

The key distinction between the present study and these

important prior efforts is in the application of a more formal-

ized, general and mechanistic theory of metabolism. If the

core assumptions and propositions of the DEB theory are

indeed correct, then a number of practical and theoretical

gains follow from its application.

First, the models derived from DEB theory have substan-

tially fewer parameters relative to the number of processes

that are explained. To illustrate this, I have compared the

number of processes, parameters and variables involved in

the energy budget for S. undulatus as derived here and in two

previous, less formalized approaches for the same species

(Table S5, Supporting information). Grant & Porter’s (1992)

pioneering energy budget analysis of S. undulatus required 22

parameters and one environmental variable (Tb) to capture

potential reproduction at a fixed adult body size. Buckley’s

(2008) model required 29 parameters and two environmental

variables (Tb and prey density) to estimate potential repro-

duction at a fixed size, optimal foraging radius, and the impli-

cations of these for rmax and carrying capacity K. In contrast,

the DEB model applied in the present study required only 24

parameters and one environmental variable (Tb) to predict

ontogenetic growth, size- and age-specific reproduction, the

phenology of growth, maturation and reproduction, the

dynamics of the gut and the reserve (and hence starvation and

body condition), and rmax. Note also that, while the number

of parameters in these models may seem high, most of them

CONB KS

OH Months to maturity

(a)

^

^

^

^

^

^

^

^^

^

^

UT

369121518212427

AZ

LB PATX GA

SC

(b)

30333639424548

Clutches year–1

^

^ ^

^

^

^

^

123

^

^^

^

^

45678910111213

(c)

rmax^ ^

^

^

^ 0 – 0·20·2 – 0·40·4 – 0·60·6 – 0·80·8 – 1·0

^

^^

^

^

^Fig. 4. Spatially explicit predictions of (a)

age at maturity, (b) annual clutch frequency

and (c) the intrinsic rate of increase, rmax. All

predictions are based on the estimated

parameters for the Utah population. The

solid black line represents the approximate

range limit within the USA, while the filled

triangles represent the sites for which detailed

life-history data are available, summarized in

Tinkle &Dunham (1986).


176 M. Kearney

are directly observable ‘first-principle’ parameters that can be

measured with high precision (e.g. energy or water content,

multi-parameter thermal response curves).

A second advantage stems from the generality of the

model; the standard DEB model applied in the present study

was developed to be applicable tomost kinds of animal (Koo-

ijman 2010) and the scaling responses are fixed and based on

first-principles arguments, rather than through species-spe-

cific allometric curve-fitting. This should enhance the capacity

for meaningful comparisons of parameter values estimated

among populations, species and higher taxonomic groups

(Lika et al., in press, b).

The third advantage lies in the testability of the model, par-

ticularly when considering the plausibility of ontogenetic or

spatial (local adaptation) changes in parameters. For exam-

ple, Angilletta (2001a) observed that laboratory-measured

assimilation rate was higher (at one of three temperatures

considered) in a South Carolina population compared with a

New Jersey population. Although DEB theory would predict

that the South Carolina population would, as a result, reach a

larger size, in fact the converse is true (Angilletta et al. 2004).

As there is no evidence for differences in adult somatic main-

tenance rate between these population, DEB theory implies a

higher value for j in the SouthCarolina population and hence

an increased proportion of energy flowing to maturation and

reproduction rather than growth and maintenance. An expli-

cit test of this would therefore be that respiration rates during

growth and development are higher for the South Carolina

population. Another inconsistency is the substantially earlier

observed ages at maturity of the Kansas and Nebraska popu-

lations, which may reflect lower energetic thresholds for

maturity. An explicit test of this hypothesis would therefore

be that the cumulative energy invested in growth and matura-

tion (as reflected in O2 consumption per gram of tissue pro-

duced) is lower for these two outlier populations. The

important point here is that DEB theory provides clear and

testable predictions of how themetabolism of a species should

behave as a consequence of such shifts in parameter values

(e.g. Zonneveld & Kooijman 1989). Detailed empirical stud-

ies aimed at testing these predictions will provide potent tests

of the assumptions of both the DEB theory and of life-history

theory in general.

Conclusion

The aim of this study was to assess the potential for integrat-

ing DEB theory with biophysical ecology tomake first-princi-

ples estimates of the energy budget, life-history patterns and

geographic range limits of a terrestrial ectotherm. This can be

thought of as attempting to infer a species’ fundamental niche

on the basis of its functional traits and how they connect to

environmental gradients (Kearney & Porter 2004; Kearney

et al. 2010). The results for S. undulatus indicate that such an

approach is indeed feasible and effective, capturing and

explaining a wide range of phenomena ranging from basic ele-

mental fluxes to life-history variation and geographic range

limits. The overall approach should provide a firm basis for

inferring the impact of changing environments on the distri-

bution and abundance of organisms.

Acknowledgements

I thank Reid Tingley for assistance with construction of the climatic database,

and Bas Kooijman, Raymond Huey and Warren Porter for advice and

comments on the MS. This work was supported by an Australian Research

Fellowship from theAustralianResearch Council (DP110102813).

References

Adolph, S.C. & Porter, W.P. (1993) Temperature, activity and lizard life histo-

ries.TheAmericanNaturalist, 142, 273–295.

Adolph, S.C. & Porter, W.P. (1996) Growth, seasonality, and lizard life histo-

ries: age and size at maturity.Oikos, 77, 267–278.

Andrewartha, H.G. & Birch, L.C. (1954) The Distribution and Abundance of

Animals. TheUniversity of Chicago Press, Chicago, IL.

Andrews, R.M., Mathies, T. & Warner, D.A. (2000) Effect of incubation tem-

perature on morphology, growth and survival of juvenile Sceloporus undula-

tus.HerpetologicalMonographs, 14, 420–431.

Angilletta, M.J. Jr. (1999) Estimating body composition of lizards from total

body electrical conductivity and total bodywater.Copeia, 1999, 587–595.

Angilletta, M.J. (2001a) Thermal and physiological constraints on energy

assimilation in a widespread lizard (Sceloporus undulatus). Ecology, 82,

3044–3056.

Angilletta, M.J. (2001b) Variation in metabolic rate between populations of a

geographically widespread lizard. Physiological and Biochemical Zoology,

74, 11–21.

Angilletta, M.J.J., Hill, T. & Robson, M.A. (2002) Is physiological

performance optimized by thermoregulatory behavior?: a case study of the

eastern fence lizard, Sceloporus undulatus. Journal of Thermal Biology, 27,

199–204.

Angilletta, M.J., Niewiarowski, P.H., Dunham, A.E., Leache, A.D. & Porter,

W.P. (2004) Bergmann’s clines in ectotherms: illustrating a life-historical

perspective with sceloporine lizards. The American Naturalist, 164, E168–

E183.

Ballinger, R.E., Droge, D.L. & Jones, S.M. (1981) Reproduction in a Nebraska

Sandhills population of the Northern Prairie Lizard Sceloporus undulatus

garmani.AmericanMidland Naturalist, 106, 157–164.

Brown, J.H., Gillooly, J.F., Allen, A.P., Savage, V.M. & West, G.B. (2004)

Toward ametabolic theory of ecology.Ecology, 85, 1771–1789.

Buckley, L.B. (2008) Linking traits to energetics and population dynamics to

predict lizard ranges in changing environments. The American Naturalist,

171, E1–E19.

Buckley, L.B. (2010) The range implications of lizard traits in changing envi-

ronments.Global Ecology and Biogeography, 19, 452–464.

Buckley, L.B., Urban, M.C., Angilletta, M.J., Crozier, L.G., Rissler, L.J. &

Sears, M.W. (2010) Can mechanism inform species’ distribution models?

Ecology Letters, 13, 1041–1054.

Dillon, M.E., Wang, G. & Huey, R.B. (2010) Global metabolic impacts of

recent climate warming.Nature, 467, 704–706.

Dunham, A.E. (1993) Population responses to environmental change: opera-

tive environments, physiologically structured models, and population

dynamics. Biotic Interactions and Global Change (eds P.M. Kareiva, J.G.

Kingsolver & R.B. Huey), pp. 95–119. Sinauer Associates Inc., Sunderland,

MA.

Dunham, A.E. & Overall, K. (1994) Population responses to environmental

change: life history variation, individual-based models, and the popula-

tion dynamics of short-lived organisms. American Zoologist, 34, 382–

396.

Dunlap, K.D. (1995) Hormonal and behavioural responses to food and water

deprivation in a lizard (Sceloporus occidentalis): implications for assessing

stress in a natural population. Journal of Herpetology, 29, 345–351.

Ferguson, G.W., Bohlen, C.H. & Woolley, H.P. (1980) Sceloporus undulatus:

comparative life history and regulation of a Kansas population. Ecology, 61,

313–322.

Ferguson, G.W. & Talent, L.G. (1993) Life-history traits of the lizard

Sceloporus undulatus from two populations raised in a common laboratory

environment.Oecologia, 93, 88–94.

Gilman, S.E., Wethey, D.S. &Helmuth, B. (2006) Variation in the sensitivity of

organismal body temperature to climate change over local and geographic

scales.Proceedings of the National Academy of Science, 103, 9560–9565.



Grant, B.W. & Dunham, A.E. (1990) Elevational covariation in environmental

constraints and life histories of the desert lizard Sceloporus merriami. Ecol-

ogy, 71, 1765–1776.

Grant, B.W. & Porter, W.P. (1992) Modeling global macroclimatic constraints

on ectotherm energy budgets.AmericanZoologist, 32, 154–178.

Helmuth, B. (2009) From cells to coastlines: how can we use physiology to fore-

cast the impacts of climate change? Journal of Experimental Biology, 212,

753–760.

Helmuth, B., Kingsolver, J.G. & Carrington, E. (2005) Biophysics, physiologi-

cal ecology, and climate change: does mechanism matter? Annual Review of

Physiology, 67, 177–201.

Huey, R.B., Pianka, E.R. & Vitt, L.J. (2001) How often do lizards ‘‘run on

empty’’?Ecology, 82, 1–7.

Hutchinson, G.E. (1957) Concluding remarks. Cold Spring Harbour Symposia

onQuantitative Biology, 22, 415–427.

Kearney, M. & Porter, W.P. (2004) Mapping the fundamental niche: physiol-

ogy, climate, and the distribution of a nocturnal lizard. Ecology, 85, 3119–

3131.

Kearney, M. & Porter, W.P. (2009) Mechanistic niche modelling: combining

physiological and spatial data to predict species’ ranges. Ecology Letters, 12,

334–350.

Kearney,M., Shine, R. & Porter,W.P. (2009) The potential for behavioral ther-

moregulation to buffer ‘cold-blooded’ animals against climate warming.

Proceedings of the National Academy of Science, 106, 3835–3840.

Kearney, M.R., Wintle, B.A. & Porter, W.P. (2010) Correlative and mechanis-

tic models of species distribution provide congruent forecasts under climate

change.Conservation Letters, 3, 203–213.

Kearney, M., Simpson, S.J., Raubenheimer, D. & Helmuth, B. (2010) Model-

ling the ecological niche from functional traits. Philosophical Transactions of

the Royal Society of London: Series B, Biological Sciences, 365, 3469–3483.

Kooijman, S.A.L.M. (1986) Energy budgets can explain body size relations.

Journal of Theoretical Biology, 121, 269–282.

Kooijman, S.A.L.M. (2000) Dynamic Energy and Mass Budgets in Biological

Systems. University Press, Cambridge.

Kooijman, S.A.L.M. (2010) Dynamic Energy Budget Theory for Metabolic

Organisation. CambridgeUniversity Press, Cambridge.

Lika, K. & Kooijman, S.A.L.M. (2003) Life history implications of allocation

to growth versus reproduction in dynamic energy budgets.Bulletin ofMathe-

matical Biology, 65, 809–834.

Lika, K., Kearney, M.R., Frietas, V., van der Veer, H.W., van der Meer, J.,

Wijsman, J.W.M., Pecquerie, L. & Kooijman, S.A.L.M. (in press, a) The

‘covariationmethod’ for estimating the parameters of the standardDynamic

Energy Budget model I: philosophy and approach. Journal of Sea Research.

Lika, K., Kearney, M.R. & Kooijman, S.A.L.M. (in press, b) The ‘covariation

method’ for estimating the parameters of the standard Dynamic Energy

Budget model II: properties and preliminary patterns. Journal of Sea

Research.

Marion, K.R. (1970) Temperature as the reproductive cue for the female fence

lizardSceloporus undulatus.Copeia, 1970, 562–564.

van der Meer, J. (2006a) An introduction to Dynamic Energy Budget (DEB)

models with special emphasis on parameter estimation. Journal of Sea

Research, 56, 85–102.

van der Meer, J. (2006b) Metabolic theories in ecology. Trends in Ecology &

Evolution, 21, 136–140.

Niewiarowski, P.H. (2001) Energy budgets, growth rates, and thermal con-

straints: toward an integrative approach to the study of life-history varia-

tion.The AmericanNaturalist, 157, 421–433.

Niewiarowski, P.H. & Waldschmidt, S.R. (1992) Variation in metabolic

rates of a lizard: use of SMR in ecological contexts. Functional Ecology, 6,

15–22.

Nisbet, R.M., McCauley, E. & Johnson, L.R. (2010) Dynamic energy budget

theory and population ecology: lessons from Daphnia. Philosophical Trans-

actions of the Royal Society of London: Series B, Biological Sciences, 365,

3541–3552.

Nisbet, R.M., Muller, E.B., Lika, K. & Kooijman, S.A.L.M. (2000) Frommol-

ecules to ecosystems through dynamic energy budget models. Journal of Ani-

mal Ecology, 69, 913–926.

O’Connor, M.P., Sieg, A.E. & Dunham, A.E. (2006) Linking physiological

effects on activity and resource use to population level phenomena. Integra-

tive and comparative biology, 46, 1093–1109.

Parker, S. & Andrews, R. (2007) Incubation temperature and phenotypic traits

of Sceloporus undulatus: implications for the northern limits of distribution.

Oecologia, 151, 218–231.

Parker, S.L., Andrews, R.M. & Mathies, T. (2004) Embryonic responses to

variation in oviductal oxygen in the lizard Sceloporus undulatus from New

Jersey and South Carolina, USA. Biological Journal of the Linnean Society,

83, 289–299.

Pecquerie, L., Petitgas, P. & Kooijman, S.A.L.M. (2009) Modeling fish growth

and reproduction in the context of the Dynamic Energy Budget theory to

predict environmental impact on anchovy spawning duration. Journal of

Sea Research, 62, 93–105.

Porter, W.P., Mitchell, J.W., Beckman, W.A. & DeWitt, C.B. (1973) Behav-

ioral implications of mechanistic ecology – thermal and behavioralmodeling

of desert ectotherms and their microenvironment.Oecologia, 13, 1–54.

Reeder, T.W., Cole, C.J. &Dessauer, H.C. (2002) Phylogenetic relationships of

whiptail lizards of the Genus Cnemidophorus (Squamata: Teiidae): a test of

monophyly, reevaluation of karyotypic evolution, and review of hybrid

origins.AmericanMuseumNovitates, 3365, 1–61.

Sousa, T., Domingos, T. & Kooijman, S.A.L.M. (2008) From empirical pat-

terns to theory: a formal metabolic theory of life. Philosophical Transactions

of theRoyal Society ofLondon: Series B, Biological Sciences, 363, 2453–2464.

Stearns, S.C. (1992) The Evolution of Life Histories. Chapman and Hall, New

York.

Tinkle, D.W. (1972) The dynamics of a Utah population of Sceloporus undula-

tus.Herpetologica, 28, 351–359.

Tinkle, D.W. (1973) A population analysis of the Sagebrush Lizard, Sceloporus

graciosus in southernUtah.Copeia, 1973, 284–296.

Tinkle, D.W. & Ballinger, R.E. (1972) Sceloporus undulatus: a study of the

intraspecific comparative demography of a lizard.Ecology, 53, 570–584.

Tinkle, D.W.&Dunham, A.E. (1986) Comparative life histories of two syntop-

ic Sceloporine lizards.Copeia, 1986, 1–18.

Vinegar, M.B. (1975) Life history phenomena in two populations of the lizard

Sceloporus undulatus in southwestern NewMexico.AmericanMidland Natu-

ralist, 93, 388–402.

Vitt, L.J. (1978) Caloric content of lizard and snake (Reptilia) eggs and bodies

andtheconversionofweighttocaloricdata.JournalofHerpetology,12,65–72.

Zonneveld, C. & Kooijman, S.A.L.M. (1989) Application of a general energy

budget model toLymnaea stagnalis. Functional Ecology, 3, 269–278.

Received 9March 2011; accepted 23August 2011

Handling Editor: GretchenHofmann

Supporting Information

Additional Supporting Information may be found in the online ver-

sion of this article.

Figure S1. Observed and predicted relationship between body size

(snout vent length, SVL) andwet mass.

Figure S2. Predicted and observed (Tinkle & Dunham 1986) relation-

ship between body size (measured as snout-vent length, SVL) at

maturity vs. meanmaximumbody size.

Figure S3. Example hourly output for the middle day of each month

from the coupled biophysical ⁄Dynamic Energy Budgetmodels.

Figure S4. Fits of observed (points) vs. predicted (lines) development

time (a), assimilation rate (b) and resting metabolic rate (c) based on a

common Arrhenius relationship (see Table S1, Supporting informa-

tion, for parameters).

Figure S5. Predicted and observed resting oxygen consumption and

assimilation rates.

Figure S6. (a) Predicted (lines) and observed (symbols) growth trajec-

tories for laboratory-raised Sceloporus undulatus from either Utah

(grey line, triangles) or Oklahoma (dark line, squares). Dynamic

Energy Budget model predictions are based on zoom factors (z) of 1

(Utah) and 0Æ92 (Oklahoma). (b) Predicted and observed relation-

ships between snout vent length (SVL) and body mass for the same

two populations (Utah, grey; Oklahoma, black; observed relation-

ship, solid line; predicted relationship, dotted lines).

Figure S7. Observed (dots) and predicted (lines) maximum and mini-

mum available operative temperatures for Sceloporus merriami

(slightly smaller than S. undulatus) at Big Bend National Park in

Texas.

Figure S8. Predicted trajectories of wet body mass, reserve density

and 12 PM body temperatures for integrated biophysical ⁄Dynamic


178 M. Kearney

Energy Budget simulations of Sceloporus undulatus at the 11 sites for

which detailed life history data exists (see Table S1, Supporting infor-

mation, for abbreviations of place names).

Figure S9. Spatially explicit predictions of (a) annual activity hours,

(b) lifetime clutches, and (c) probability of survival to the end of

year 3.

Figure S10. Predicted fraction of egg development for Sceloporus

undulatus between June and September at two different depths in the

soil.

Figure S11. Predicted degree days of development for Sceloporus

undulatus between June and September at two different depths in the

soil, based on data fromParker &Andrews (2007).

Table S1. Parameters for the Dynamic Energy Budget model used in

the present study.

Table S2. Values used for location-specific simulations of life history

variation.

Table S3. Observed (Ferguson & Talent 1993) length, mass and egg

size for two populations of Sceloporus undulatus reared under in a

common garden compared with Dynamic Energy Budget model pre-

dictions based on zoom factors (z) of 1 (Utah) and 0Æ92 (Oklahoma).

Table S4. Observed and predicted life table statistics (x = year,

lx = survival, mx = female offspring produced, R0 = reproductive

rate) for the Utah population of Sceloporus undulatus (Tinkle 1972)

compared with predicted values from the Dynamic Energy Budget

model driven by biophysical predictions of body temperature and for-

aging period as well as the empirical relationship between annual

activity hours and survivorship.

Table S5.The relative number of processes explained, and parameters

and variables used, by the Dynamic Energy Budget model used in the

present study compared with the empirical, static energy budgets

applied byGrant & Porter (1992) and Buckley (2008).

As a service to our authors and readers, this journal provides support-

ing information supplied by the authors. Such materials may be re-

organized for online delivery, but are not copy-edited or typeset.

Technical support issues arising from supporting information (other

thanmissing files) should be addressed to the authors.



Documents

Metabolic theory, life history and the distribution of a terrestrial ectotherm