body weight and the energetics of temperature regulation · body weight and energetics of...

J. Exp. Biol. (1970). 53. 329-348 3 2 9With 9 tcxt-figuru

Printed in Great Britain

BODY WEIGHT AND THE ENERGETICS OFTEMPERATURE REGULATION

BY BRIAN K. McNAB

Department of Zoology, University of Florida,Gainesville, Florida 32601

{Received 10 April 1970)

INTRODUCTION

The recent rebirth of interest in the 200-year-old field of homoiothermic energeticsmay be dated from three papers published in 1950 by Scholander, Irving and col-leagues. These papers furnished many data and a theoretical analysis of the energeticsof temperature regulation in tropical and arctic birds and mammals. A massive bodyof data has since become available through the efforts of many workers. Unfortunately,there has been little effort to extend Scholander and Irving's model (which was basedon Newton's law of cooling) to meet the challenge of new data. One of the peculiaritiesof this model is that it is presented in a weight-independent form, although two of itsparameters, basal rate of metabolism and thermal conductance, are well-known to beweight-dependent.

In this paper the influence of weight on the energetics of homoiotherms will bere-examined; special attention will be given to the applicability of Newton's law ofcooling.

NEWTON'S LAW OF COOLING

Since Newton's law of cooling will be the analytical basis for the discussion in thispaper, it is first necessary to understand what it says and to know the limitations thatare imposed upon it. As originally formulated Newton's law states that the rate atwhich the temperature of a body falls is proportional to the difference in temperaturebetween the body and the environment: dTbjdt = <p(Tb-Ta), where <f> is a coolingconstant (see the Table of Symbols for all definitions and units). But a fall in tem-perature can be related to a loss of heat, since ATb — AQ/s. W. Therefore,

dQldt = s.W.<t>{Tb-Ta)

= C{Tb-Ta) (1)

which is the form of Newton's law to be used in this paper.Equation (1) indicates that the net heat loss from an object warmer than its sur-

roundings is proportional to the temperature differential between the object and itsenvironment. A proportionality constant C (usually referred to as thermal conductance,but maybe more properly called the coefficient of heat transfer) is defined such thatC( Tb — Ta) is equal to the rate of heat loss (not C, as erroneously stated by me, 1966 a, b).If an animal regulates its temperature perfectly, Tb is constant and the rate of meta-bolism equals C(Tb— Ta) when there is no thermal source for regulation other thanmetabolism.

330 B. K. M C N A B

Two aspects of this relationship must be kept always in mind: (i) C(Tb—Ta) is anapproximation of the summed heat loss by a warm animal to a cool environment, and(2) there are biological limits placed on this approximation. Each of these conditionsmust be examined briefly to avoid any misunderstandings.

Newton's law of cooling is an approximation to the sum of the amounts of heat lostby radiation, convection, conduction, and evaporation, respectively

M = eaAin- T^ + hA^T.-T^ + kA^-T^ + LA.fv. (2)

One might therefore argue that it would be best to represent the rate of metabolismof an endotherm by equation (2). There are two reasons why this is not usually done.(1) It is an unnecessarily complex statement as shown by the rather simple linearrelationship usually existing between the rate of metabolism and the temperaturedifferential (e.g. Tucker, 1965), if for no other reason than that the biological variabilityof intact animals is sufficiently great to obscure the mathematical intricacies of thetheoretically rigorous statement. (2) Equation (2) is difficult to apply because of thevariable nature of the effective surface areas in each term and because of the com-plexities of the convective constant. Although Newton's law is a rough approximationof heat loss, the uncertainties in the application of equation (2) are sufficient to deny ita practical advantage in spite of its theoretical security.

Newton's law of cooling can be derived from equation (2). Note that (T%— T%) isapproximately equal to \T^(Tb — Ta) when Tb — Ta is small, as is the case in biologicalsystems. Therefore,

M = (evA^T* + hAt + kA3) (Tb - Ta) + LAtw

= c 1 ( r 6 - r o ) + L44w. (3)

(When temperature is incorporated into the term for radiation as either T3 or 71*, it mustbe in °K, but when a temperature differential is used either °C or °K may be used.)Equation (3) is applicable over all biologically relevant temperatures. It has two terms,one for heat loss based on a temperature differential and the other for evaporative heatloss. Biologically meaningful measurements of both oxygen consumption (metabolism)and evaporative water loss are difficult to make simultaneously (Lasiewski, Acosta &Bernstein, 1966). There is value, then, in a still simpler formulation when it is notpracticable to measure evaporative water loss. This simplification can be made becausethe amount of heat lost by the evaporation of water at moderate to low environmentaltemperatures is a small, rather constant fraction of the total heat loss (e.g. Schmidt-Nielson et al. 1965; Calder & Schmidt-Nielsen, 1967). Equation (3) therefore maybe rewritten

M = (c1 + c2) (Tb-Ta) = C(Tb-Ta) (4)

which, again, is Newton's law of cooling.Newton's law of cooling, as represented in equations (1) and (4), resembles the

Fourier equation for heat exchange with two exceptions. (1) A core temperature isused in Newton's law, which is justified by being easier to measure and by the fact thatmost of the temperature gradient between an endotherm and its environment existsbetween the surface and the environment (Porter & Gates, 1969), so that a surfacetemperature can be replaced by a core temperature with little error, except in animalsthat are both large and naked. (2) The surface area is not generally used in Newton's

Body weight and energetics of temperature regulation 331

law. The units for thermal conductance in this paper are cal/g-h °C (or equivalent).It has been argued that these units are not appropriate because heat loss occurs perunit of surface area, not per unit of weight. There is no question that the surface areais an important parameter of heat loss, but it is nearly impossible to measure theeffective area, since it may be modified by postural changes and by changes in con-ductivity brought about by local vasoconstriction and vasodilation. Faced with thisdifficulty some observers advocate that surface area measurements be replaced by(constant) W0'67. But surely it is better to use the simpler weight-specific units forconductance than to calculate a pseudo surface-specific conductance.

There are biological limits to the application of Newton's law. It is an appropriateexpression only at cooler ambient temperatures, since the evaporative heat loss (whichdoes not depend upon a temperature differential) becomes the predominate means ofheat dissipation at higher temperatures. Another complication derives from thebehaviour of C. As the ambient temperatures fall from moderate values, C graduallydecreases to a minimal value. Any further fall in Ta requires an increase in heat produc-tion by the animal to maintain a constant body temperature. The ambient temperatureabove which changes in C are the major means of thermal adjustment to a varying Ta

and below which changes in M predominate is called the lower limit of thermo-neutrality (Tt). If the separation between the temperatures at which changes in C orM are used is sharp, the curve of metabolism on Ta below Tt has a slope equal to Cand extrapolates to Tb when M = o. But if an animal does not rigidly distinguishbetween ' physical' and ' chemical' regulation, C will decrease and M will increasewith a fall in ambient temperature. As a result the slope of the curve of M on Ta belowTx is not equal to C and the curve extrapolates to a temperature greater than T6 whenM = o. Contrary to the opinion of some authors, this result does not invalidate theapplication of Newton's law to the heat exchange of homoiotherms, since this law issimply a mathematical approximation of the physics of heat exchange and per se doesnot incorporate any biological features, except for the dependence upon non-evaporative heat loss.

The two major criticisms of Newton's law, then, are that it is either physically toosimple or that it is biologically inappropriate. But as long as the Newtonian simplifica-tion is used within its proper limits, e.g. at ambient temperatures below the mid-pointof thermoneutrality, its great mathematical convenience can be profitably employed.

THE ENERGETICS OF MAMMALIAN THERMOREGULATION

Homoiotherms accommodate their energetics to unique environments mainlythrough a modification of thermal conductance and the basal rate of metabolism, Mb

(McNab, 1966ft). Since both parameters vary as a function of weight, species thatdiffer greatly in weight may be compared if Mb and C are expressed relative to thevalues expected by weight from some 'standard', such as the curves of Kleiber (i960)for Mb and Herreid and Kessel (1967) for C. This transformation demonstrates thatmuch of the observed variation in the level of Tb is due to relative variation in thebasal rate and thermal conductance. The reason for this influence may be seen fromrearranging Newton's law: Tb = MjC+Ta. Thus, Tb increases with an increase inthe ratio MjC, which becomes MbjC, when evaluated at the lower limit of thermo-neutrality.

332 B. K. MCNAB

What is the physical basis for the influence of MJC on T6 ? This ratio is a measureof the temperature differential between a homoiotherm and the environment at thelower limit of thermoneutrality. Although temperature determines the rate of chemicalreaction, the rate of chemical reaction may also determine the temperature of thesystem. Consider a furnace having a steady-state temperature distribution and con-suming coal at a fixed rate. If the amount of coal fed to the furnace is increased, therate of combustion will increase (assuming no other limiting factors) and the tempera-ture of the furnace will rise to a new steady-state distribution, the level of which is

100 200Basal rate of metabolism (% of expected)

300

Fig. i. Thermal conductance in mammals and birds aa a function of the basal rate of metabolism(data from Tables i and 3). Each parameter ia expressed as a percentage of the values expectedfrom weight in mammals (see the text).

dictated by the temperature differential needed to dissipate the heat produced by thefurnace. Endotherms can be compared to small furnaces, their temperatures deter-mined, in part, by the proportionality existing between the rate of heat productionand the temperature differential.

The biological significance of variations in the ratio MbjC may be seen in Fig. 1.Temperate species generally have higher basal rates of metabolism than expected fromweight, but they have only a modest increase, if any, in conductance (unless they arevery large). The ratio MJC in these species tends, then, to be higher than expected


from weight, a condition that leads to the high, precisely regulated body temperaturestypical of species living in a thermally unstable environment. Temperate species thatlive in deserts have a low Mb (to minimize water exchange) and in compensation havea low conductance. Fossorial rodents have both low basal rates and high conductancesto reduce the threat of overheating in closed burrows. Tropical mammals also havelow basal rates and high conductances, but like fossorial mammals, can tolerate theresulting low body temperatures by living in environments characterized by thermalstability.

Recent data on tropical bats (McNab, 1969) have shown that body weight alsoinfluences the level of Tb (contrary to the conclusion of Morrison & Ryser, 1952, but

a.E

30

25

• 7"(, determined byWand (MbIQr

lower than expectedfrom Wand (MbIQr

10 15

I I J I

20

111S 10 50 100

Weight (g)500 1000

Fig. 2. A. The relation between Tb, (MJC)r, and (MJC), expected from equation (5). B. Bodytemperature in bats as a function of the ratios (MJC), and (M6/C), (data from McNab, 1969).Values for (M,JC)r indicated for each hollow point.

in agreement with Rodbard, 1950). If it is recalled that the absolute values of Mb and Care weight-dependent, the possibility arises that the level of body temperature isdetermined by the weight-dependent relationships of Mb and C, as well as the extentto which actual values conform to these expectations. Thus, the measured ratio Mb\Cmay be represented by the product (Mb\C)^Mb\C)ty where the expected ratio {MbjC)e

= (3-4W-0M)/(i-o2W-01>1) = 3-33PF°-M (McNab, 19666; Herreid & Kessel, 1967)and the relative ratio (Mb/C)r is the dimensionless fraction: (measured ratio)/(expectedratio) = {MbJC)l(MbjC)e. The relative ratio is identical to that described in previousanalyses (McNab, 19666, 1969).

334 B - K - MCNAB

Applying this analysis to Newton's law of cooling and rearranging

Tb = (5a)

(sb)If this suggestion for the weight-dependency of body temperature is correct, a plotof body temperature against 3-33 W0'26 should give a family of linear curves, the slopesof which are equal to (MbjC)r (see Fig. 2 A). Such curves are plotted in Fig. 2B forbats and in Fig. 3 for other mammals. The expectation holds in both cases: Tb depends

40 1 -

E 3 5

a.Ev

30 Tj determined byW and (MbIC)r

lower than expectedfrom Wand (Mb/Qr

higher than'expectedfrom W and {MJC)r

10 20 30 40 50 60 70 80

II III I 11 10 100 1000 10000 20000

Weight (g)50000 100 000' 200000

Fig. 3. Body temperature in mammals other than bats as a function of the ratios (MJC), and) , (data from Table 1). Values for (MtJC)r indicated for each hollow point.

upon the ratio (M6/C)e up to 37 or 38 °C. (beyond which Tb is nearly constant). More-over, body temperature varies with the ratio {MbjC)T at a constant weight in a mannerexpected from equation (5). A similar dependency of Tb on Mb, C and W can be seenin the data of MacMillen & Nelson (1969) on marsupials. Equation (5), then, is simplyNewton's law rewritten in a form that permits the influence of body weight on Tb toappear. The precision of regulation and the sensitivity of Tb to variations in Ta

are also compatible with this analysis (McNab, 1969).The weight at which body temperature shifts from being (Mb/C)e dependent to

being (MbjC)t independent may be called the 'critical' weight. This weight varies


with the ratio (Mb/C)r in a manner such that a high relative ratio may compensate fora small weight in the maintenance of a high temperature (Fig. 4). The equation for thisrelationship is

= 3-4S W^° (6)whether obtained by extrapolating the curves in Figs. 2B and 3 to a common bodytemperature (38 °C), or by taking the critical weights from the (Mb/C)r constantcurves in these figures. A similar equation is obtained from equation (5 a) by sub-stituting Tb = 38 °C and Tt = 27 °C (the mean T, for all mammals in Table 1).

100

50

? 10

0-5

0-1

10r

0-5

-C?

00

- -OS

L - 1 0 1 1 1 1

0-0 0-2 0-4 0-6 0-8 10 1-2 1-4 1-6 1-8 20

0-1 1 00-5

1 1 1 1

10 1005-0 50

Weight (g)

1000 10000 100000500 5000 50000

Fig. 4. The relation between (Mb/C)r and (Mb/C), in mammals either at a fixed temperatureor at the point beyond which Tb no longer depends upon (MJC),. The data were taken fromFigs. 2 and 3.

A ' critical' weight results from the mathematical form of equation (5) and from thesetting of a maximal Tb. Mammalian temperatures seem set near 38 °C, all deviationsbeing due either to a small weight or to deviations from the 'standard' curves ofmetabolism and conductance on weight.

A high, precisely regulated temperature, therefore, can be attained at any weight,provided that an appropriate energy expenditure, relative to conductance and weight,is made. The exact balance differs somewhat among mammals, but it has a consistentpattern: to regulate temperature precisely a species weighing 10 kg must have theratio {MbjC)T equal to or greater than 0-3, one weighing 500 g (in bats about 250 g)must have a ratio equal to 0-7, and one weighing 100 g (in bats 70 g) must have aratio equal to i*o.

A very small species must pay a high price for a high Tb. Morrison, Ryser & Dawe(1959) have shown that a common shrew, Sorex cinereus, even though weighing only3-3 g, maintains a temperature of 39 °C by having (MbjC)r equal to about 2-9 (assuming

23 E3CB 33

OJ

Tab

le i

. T

he e

nerg

etic

s of

mam

mal

s

Bas

al m

etab

olis

m

Con

duct

ance

Spe

cies

Tac

kygl

ossu

s ac

ulea

tui

Orm

thor

kync

hus

anat

imu

Mar

mos

a nu

crot

arsu

sD

idel

plri

i m

arsu

pial

isC

erca

ertu

s na

nus

Sore

x dn

ereu

sA

otus

tr

ivir

gatu

sC

yclo

pes

dida

ctyl

usB

rady

pus

sp.

Cho

loep

us

hoff

man

niD

asyp

us n

ovem

cinc

tus

Vul

pes

vulp

es

Can

is f

amiU

aris

Tam

iasc

iuru

s hu

dson

icus

Geo

mys

pin

etis

Dip

odom

ys

mtr

riam

D.

agili

sP

erom

yscu

s er

emic

usP

. ca

lifor

nicu

sP

. cr

initu

sP

. m

anic

ulat

usP

. tr

uei

Neo

tom

a le

pida

N.

fusc

ipes

Mic

rotu

s m

onta

nus

Spal

ax l

euco

don

Tac

kyor

ycte

s sp

lend

ens

Wei

ght

(g)

30

00

693 13

1000 70 3

362

518

52

60

03

77O

37°o

4440

6666 22

9

203 38 61 22 46 16 24 33 no

187

312

08

23

4

(Mj/

C),

*

26

7

18

2

6-5

20-1

IO

I

4-6

17

71

30

25

72

83

28

22

96

36-2

13

5

13

38-

69

77'

49

06

97

68-

3n

-31

30

8-i

13

41

38

(c.c

. OJ

g-h)

O-2

2

O-2

8i-

440-

520

85

70

04

50

58

01

80

16

02

5

o-55

O-3

4

1-50

0-74

11

31-

051-

481-

031-

581

67

i-53

07

9

O7

92-

650

79

07

9

%t

48 42 80 85 72

28

0 66 63 38 37 57 13

4

10

0

172

81 83 86 94 81 92

no

10

9 76 91 185 89 90

(c.c

. OJ

g-h

°C)

00

26

00

30

02

6

0-0

54

0-1

40

54

00

31

0-0

70

0-0

24

0-0

18

0-0

27

0-0

18

O-O

22

0-08

6

0-07

5O

il

00

73

0-16

o-n

0-1

90-

170-1

40-0

70

00

59

0-1

90068

0073

%t

137 79 93 169

118 98 82 95

12

0

"3

155

12

4

24

4

134

10

7 65 56 74 74 76 84 80 74 81 106

IO

I

11

2

(M6/C

) r§

O-3

5

O-5

3o-

860-

50o-

6i2

86

o-8o

o-66

03

2

o'33

03

71-

08

04

1

12

8

07

6[•

26

i-53

[•27

[•09

[-21

[•31

1-36

[•03

[-12

17

5o-

88<3

-80

Tb

30

7

34

03

32

35

03

56

38

83

80

32-5

33-o

34

434

-53

87

37-8

40

0

36-1

37-o

37

O3

61

35

93

68

37-6

37-4

36

83

66

37-8

37'°

36-2

T,\

\(°

C)

22

— 27 25 31 23 23 •— — — —

8 — 20

25 27 28

30

28

29

29

27 26 23 26

25 27

Ref

eren

cesH

Sch

mid

t-N

iels

en e

t a

l.(1

966)

H He H H Mo

rris

on

et a

l. (

1959

)M

orr

iso

n&

Sim

des

(196

2]M

cNab

, u

np

ub

lish

ed

H H H Irv

ing

& K

rog

(195

4),

Irvi

ng e

t al

. (1

955)

Hel

lstr

om &

Ham

mel

(196

7)Ir

vin

g &

Kro

g (1

954)

,Ir

ving

et

al.

(195

5)H

eC

arp

ente

r (1

966)

Car

pen

ter

(196

6)H

eH

eH

eH

eH

eH

eH

eP

acka

rd (

1968

)H

eH

e

fcd

o

Spe

cies

Ere

thiz

on

dors

atum

Hel

ioph

obiu

s ka

peti

Het

eroc

epha

lus

glab

erL

epus

am

eric

ama

L.

alle

ni

L. c

alif

orni

cus

Hct

eroh

yrax

br

ucei

Pro

cavi

a ca

pens

isP

. jo

knst

omSu

s sc

rofa

Tau

rotr

agus

or

yx

• (M

JC),

=t

M>

(%)-

-X

C{

%)

=§

(MJC

) r =

Wei

gh

t(g

)

5 53

O 89 39

1 58

130

00

2300

2000

2630

2750

4800

0

1500

00

= 3-

33H

™"*

-

31

3

10

7

8-6

22

626

-7

24

9

24-0

25

82

61

54

9

74-6

•-o-

u

100

mea

n/i

-o2p

F~°

'11.

= M

b (%

)/C (

%).

|| T

( =

low

er l

imit

of

ther

mo

neu

tral

ity

.U

In

dic

ates

th

at r

efer

ence

s ar

e fo

und in

Bas

al m

etab

olis

m

(c.c

. 0

,/g-

h)

0-40

1 0

40

77

0-96

o-55

05

7

0-36

04

2

0-45

O-3

5

0-24

%t

10

3

91 56 178

12

0

11

9

71 88 961

52

14

1

Tab

le 1

co

nt.

1 C

ondu

ctan

ce

(c.c

. OJ

g-h

°C

)

0-01

5

0-13

o-45

0-02

90-

029

O-O

2I

O-O

28O

-O2O

0-01

6o

-oio

0-01

6

%x 116

12

1

281

12

1

153

10

5

133

II

I 8924

3

615

Tab

le I

V o

f M

cNa

b (1

066I

: c

ind

icat

es t

hat

vi

(Mj/

C)r

§

08

9

o-75

O-2

O

1-47

07

8

11

3

o-S3

07

91

080-

63

0-23

alue

s fo

r A

fi

(°C

)

37

4

35

O2

94

39-8

37

9

39

2

36-7

38

03

88

38-4

36-6

ha

ve

hfff

tn c

7

28

— 10

20 14 24 15 10 4

24

'.nrr

wt̂

H

Ref

eren

ces^

Irvi

ng &

Kro

g (1

954)

,Ir

vin

g et

al.

(19

55)

He

Uc(r

,,atr

o=

2o

to2

5oC

)H

art

eta

l. (

1965

)D

awso

n &

Sch

mid

t-N

iels

en (

1966

)S

chm

idt-

Nie

lsen

et

al.

(190

5)T

aylo

r &

Sal

e (1

969)

Tay

lor

& S

ale

(196

9)T

aylo

r &

Sal

e (1

969)

Irv

ing (

19

56

); I

rvin

g e

t al.

(i9

55

. 19

56)

Tay

lor

& L

ym

an (

1967

)

to m

pfln

vn

lufM

i

to I £L Crq ettcs •**

2 CO

338 B. K. MCNAB

that the mean minimal rate of metabolism measured in Sorex was equal to 1-4 Mb,due to the specific dynamic action of protein metabolism). Small shrews are near thelower limit of weight for continuous homoiothermy. Animals of still smaller weightsare theoretically capable of continuous homoiothermy, but apparently it is prohibi-tively expensive. For example, a mammal weighing 0-25 g requires a ratio (Mb/C)r

equal to about 4-9 for Tb to be independent of weight. The intermittently endothermicsphinx moth (Celerio, thorax weight = 0-25 g) has {Mb(C)r equal to o-6, only 12%of the expenditure needed for continuous homoiothermy (Heath & Adams, 1967).As a result this moth can thermoregulate only with the high heat production associatedwith wing movements; during quiescent periods the moth is poikilothermic.

In the evolution of a small weight, then, an endotherm has two alternatives: (1) tomaintain the relative levels of Mb and C, as may well be dictated by its habits and itsenvironment, and suffer a reduction in the level and precision of thermoregulation,or (2) maintain thermoregulation by means of a compensatory increase in the relativerate of metabolism, or a compensatory decrease in the relative conductance. It appearsthat the second 'choice' is utilized whenever energetically (that is, ecologically)feasible (e.g. McNab, 1969).

It is of interest at this point to examine the constant appearing in equation (5).First, let us consider the behaviour of K within a group of mammals, such as bats,rodents or edentates. Graphically, K, represents the level of Tb when (MbIC)e = o-o.(Fig. 2A). It also represents the lower limit of thermoneutrality, Tt, since that is theenvironmental temperature at which the basal rate of metabolism intersects the curvewhose slope is the minimal thermal conductance. One may ask how Tx is influencedby the ratio (MbJC)T and by body weight. The effect depends upon whether or notbody temperature is independent of weight. According to Newton's law, Tt= Tb — MbjC.If body temperature depends upon weight, equation (5a) may be applied:

T, = (MbIC)r(MbIC)6+K-MbIC

= MJC+K-MJC

= K, (7)

that is, the lower limit of thermoneutrality should be independent of weight and ofthe relative ratio (MJC),. If, however, Tb is dependent of weight, then fromequation (5 b)

^ = r6-3-33(M6/C)rFF°-*«; (8)

T, should decrease as each weight and (MbjC)r increases.Data on the lower limit of thermoneutrality in mammals (Table 1) are plotted in

Fig. 5 as a function of weight. Clearly the variation in Tlt whether found amongspecies or seasonally within species, conforms to the predictions of equations (7)and (8).

There is another source of variation inherent in K. It will be noticed in Figs. 2 B and3 that the curves below the ' critical' weight, although similar in form in the variousgroups of mammals, do not extrapolate to a common K; K is higher in bats than inmonotremes and edentates (Fig. 6a). And K is even higher in Australian marsupials.It should be re-emphasized that the analysis used above accounts for variations inthe size of the temperature differential Tb — K= Tb—Tt and will account for Tb


only when K is equal in all mammals. This is shown in Fig. 6 B by the fact that muchof the variation in Tb among the mammals in Fig. 6 A disappears when the differentialT6 — Tt is used. In this case the differential approaches o-o as either (Mb/C)r or(MbjC)e approaches o-o. Therefore, the variation of K represents a variation in the

30

20

£10

0

-10

- 2 0

, o 0 1-0 0-90

0-2

o Tb weight-dependent• Tb weight-independent

1 0 20 30Log10 W

40 50

5 10 50 100 5001000

Weight (g)

500010000

50000100000

Fig. 5. The lower limit of thermoneutrality, Tj, in mammals as a function of body weight(data from Table 1). Numbers near solid points indicate values for (M,JC)r. Dotted curvesexpected from equation (8) for given values of (Afj/C)^ S and W refer to summer and wintervalues, respectively.

Table 2. Variation in the set point of body temperature in bats as a function of food habitsand distribution in South America

Species

RkinophyUa pumilioDesmodus rotundusGlossophaga soricinaUroderma bilobatumNoctilio labialisCarollia perspicillataMolosnu molossusEumops perotisPhyllostomus discolorArtibeus concolorNoctilio leporinusVampyrops lineatusTonatia bidensPhyllostomus hastatusSturnira liliumArtibeus jamaicensisHistiotus velatusAnoura caudiferDiphylla ecaudataDiaemus youngi

•7*it

7-26-66-56-45 9S-95 95-75-65-65-24 94 74-64'54-24-24-°3 93'2

Trop.

X

X

X

X

X

XX

X

X

X

XX

X

X

X

X

?X

X

X

Distribution

Marginal Temp.

— —x —— —— —— —— —X —

— —

— —— —

X ? -— —— —

— —

X - ?

X —

X X

— —

— —— —

Food habitat

Type

FruitBloodNectar, fruitFruitInsectsFruitInsectsInsectsFruit, meatFruitFish, insectsFruitMeatMeat, fruitFruitFruitInsectsNectarBloodBlood

Range

N ?BBB?BBBBBB?B?BBBBBBN ?NN

• Z = Tb-{MtIC) -22-2.t Range of foods used within a food typt either broad (B) or narrow (N).

34° B. K. MCNAB

placement of the differential along a temperature axis and not in the ability of MJCto predict the size of the differential.

If there is significance in the variation of K, it should follow some meaningfulpattern. The search for such a pattern is facilitated by substituting TQ + z for K, whereTo is the lowest limit of thermoneutrality for any mammal whose Tb depends upon{MbjC)e (here equal to 22-2 °C in Tachyglossus), and z is the difference between theactual Tj for a particular species and To. The range of z, then, is a measure of the

o Monotremesx Didelphls• Edentates

20

I H-10

H h15 20 25 30

•4 -

1 510 50 100 500 1000Weight (g)

5000

1 0 -

O

o

I

- 5

Numbers indicatevalues of (M6/C)r

10 15 20 25 30

Fig. 6. A. Body temperature in selected mammals as a function of (MfJC)r and (MJC)fB. The temperature differential between the body and the environment at the lower limit ofthermoneutrality as a function of (MJC)r and (M^JC),.

flexibility of the set point of body temperature independent of the influence of W,Mb, and C. Of two mammals having the same weight, basal rate of metabolism, andconductance, the species with the highest set point for temperature regulation, that iswith the largest z, will have a higher rate of metabolism at all ambient temperaturesbelow the lower limit of thermoneutrality of the warmer species. One may therefore


expect that mammals that live in cold climates or that have unusually narrow foodhabits might have small values for z, since this may be a means of reducing energyexpenditure at a fixed weight without sacrificing the effectiveness of thermoregulation.These conclusions agree with the data on bats (Table 2). Furthermore, Didelphis hasthe lowest z for known marsupials, and it has moved farther into the temperate zonethan any other marsupial; Sorex has a low z, which insures that its rate of metabolismis less than it would be for a mammal of its size with a large z; and z is small inedentates and monotremes, tropical mammals with specialized food habits. Bodytemperature thus seems to be capable of some variation independent of Mb, C andW in a manner adaptive to the climate. It is not clear what sets the limits of variationin z.

45 r-

U 40

"8OQ 3 5

30

20 o 1 ' 5

x °

Mammalsweight-dependent

, weight-independentBirds

8 0,

0 0 10 2 0 30

Fig. 7. The influence of (Mb/C)r on body temperature in mammals and birds (data from Tables1 and 2). All values of (M,JC)r for both birds and mammals use (Mb/C), = 3-33^°"" as astandard. Numbers on graph indicate W".

Beyond the ' critical' weight, body temperature is influenced by the ratio {MbjC)r.One can expect from equation (5 b) that the slope of the curve of body temperature onthe relative ratio would be equal to 3-33, irrespective of weight, since variation inW02S is compensated for by variation in Tv The same relationship between Tb and{MbjC)r should also exist when Tb depends upon (MJC),., provided that weight and zare constant. Both of these expectations generally hold (Fig. 7), except at some lowvalues for {MbjC)n where there is variation in z.

Since a large weight can compensate for a low ratio (MJC), in the maintenance ofprecise thermoregulation, large mammals tend to have lower ratios (MbjC)r (Fig. 1)and therefore lower body temperatures than species of an intermediate size (Figs. 2 B

342 B. K. MCNAB

and 3). This trend raises the possibility that the largest of mammals, the pachydermsand cetaceans, have even lower relative ratios and temperatures. One can concludefrom Fig. 7 that Tb in mammals whose temperature is independent of {MbjC)e shouldapproach 35-7 °C as (MbjC)T approaches o-o and weight becomes infinitely large.Unfortunately, there are no adequate measurements of the energetics of large mam-mals; it is even difficult to obtain reliable measurements of their body temperatures.

4 0 1 -

u

a 350)Q.

IV

•vom

30

0-85

^-Mirounga

11

00511

LX WhalesA PinnipedsA Bears• Elephants

• RhinocerosO Hippopotamus• Other Artiodactyla

50 100 150 200 250 300 35a 400

I I I 110° 104 103 106 107

Weight (g)10"

Fig. 8. Body temperatures in large mammals as a function of body weight. Dashed curves arefor Tt when (MJC)r is constant. The data (mean ± ranges) were taken from Allbrook et al.(1958), Bartholomew (1954), Benedict (1935), Bligh & Harthoorn (1965), Bligh et al. (1965),Buss & Wallner (1965), Irving & Krog (1954), Luck & Wright (1959), Morrison (1962), andRay & Fay (1968).

The few data indicate a continuing decrease in temperature with an increase in weight,an asymptote in accord with the argument above occurring near 36 °C (Fig. 8). Thedecrease in temperature with an increase in weight occurs intraspecLfically both in thewalrus (Odobenus rosmarus; Ray & Fay, 1968) and in the northern elephant seal(Mirounga angustirostris; Bartholomew, 1954).

It is clear from this discussion that the parameters Tb, T{, Mb, C, and W have inter-relations that are consistent with the Newtonian model of thermoregulation proposedby Scholander and Irving. It may also be tentatively concluded that the level of tem-perature regulation in mammals is determined in the following manner:

Climate ̂ ^ Food habits


THE THERMOREGULATION OF BIRDS

Birds usually have higher resting temperatures than mammals; this has beenexplained as due to the high basal rates of metabolism and low thermal conductancesof birds (McNab, 1966a). Two problems with this explanation have since arisen. Oneis that the higher level of metabolism in birds has been questioned by Lasiewski &Dawson (1967) and the lower conductances disputed by Herreid and Kessel (1967).Secondly, it remains to be determined what effect bringing weight into the analysisof mammalian temperatures has upon the conclusion that bird temperatures aredetermined in the same manner as those of mammals.

Lasiewski & Dawson (1967) suggest on the basis of energetics that birds can bestbe broken into two groups, passerines and non-passerines, the curve of metabolismon weight for each having an exponent similar to that of mammals and differing eachfrom the other and from mammals only by a coefficient. Without doubt marked

40 -

e

Q.

S

30

p 1 30 1-65CD

/I

1

1 1-00

o

1

0-0

• Tb determined byW and (Mb/Qr

O 7*t lower than expectedfrom W and (Mb/Qr

_

-

53

-

-

1 i l10 20

I I I I I

30 40

(MbIQ. = 8-59 W "50 60

I

70

10 100 1000 10000Weight (g)

100000

Fig. 9. Body temperature in birds as a function of the ratios (MJC)r and (M,JC),.Data from Table 3.

differences exist among birds, but one could as well divide birds into familial orgeneric groups (e.g. Zar, 1968). How animals are divided into categories depends uponthe questions being asked, not simply upon whether one can find statistically significantdifferences. Thus, one may be interested in the differences existing between homoio-therms and poikilotherms, as was Hemmingsen (i960), who combined mammals andbirds into one equation. Or, one may be interested in the differences existing betweenmammals and birds (King & Farner, 1961; McNab, 1966a). Each of these viewpointsis legitimate.

344 B - K - MCNAB

Herreid & Kessel (1967) measured cooling constants for dead birds from whichthey calculated thermal conductances; they also summarized the data available in theliterature on the conductances of live mammals. They concluded that there is nodifference between the conductances of mammals and birds. However, conductancesmeasured on live animals and those calculated from the cooling curves of dead indi-viduals often do not give identical results (e.g. McNab & Morrison, 1963), which mayhave obscured any inequality in conductance occurring between birds and mammals.This suggestion is borne out by Lasiewski, Weathers & Bernstein (1967), who describedan equation for the conductances of live birds as a function of weight that is identicalin the exponent to that of Herreid and Kessel for mammals, differing only in thecoefficient, which is 17% less than that for mammals. Thus, birds do in fact havelower conductances than mammals of the same weight.

The question remains whether these differences are sufficient to account for thehigher temperatures of birds, especially given the effect of weight in mammals. Thatis, if a mammal of a given weight had the rate of metabolism and conductance of abird of the same weight, would the mammal have the same temperature as the bird ?Or do mammals operate at lower temperatures than birds for reasons other than thoseof Mb and C ? Unfortunately, there are very few complete sets of data on birds.

The expected ratio (MJC)efor birds is equal to (7-3 FF-°**)/(o-85 W**1) = 8-59 W0'"(McNab, 1966a; Lasiewski et al. 1967). Therefore, if the analysis described formammals works for birds as well, Tb should be given by

Tb = 8-s9(Mb!C)rW°"+K. (9)

Since 8-59W017 = (z-sSW-0^) fa^W028), the ratio {MbjC)T in birds is equal to2-58J-F-"0'09 times that of mammals, which will insure that the temperatures of smallbirds will be appreciably higher than those of mammals of the same weight.

The body temperatures of birds are plotted in Fig. 9 as a function of 8-59W017

(data from the literature, see Table 3): there is an acceptable agreement between thetemperatures measured in birds and the parameters of {Mb(C)T and W017. Furthermore,the interactions that exist between Tb, (MbjC)r, and W026 in these birds are similarto those found in mammals (Fig. 7), the major difference between these groups beingthat birds have higher values for the ratio {MbjC)r. But an important point must bemade here: in spite of the many comparative studies on the metabolism of birds, mostof these data have little or no value in studies of the energetics of temperature regulationbecause body temperatures corresponding to the rates of metabolism were not reported.This deficiency is very important, since conductance cannot be evaluated without Tb,especially when a bird's response to a change in Ta involves both M and C. To interpretrates of metabolism in terms of temperature regulation, one must have at least thefollowing data: (1) W, (2) Ta, (3) Tb, and (4) the animal's activity.

Obviously, more complete data on the energetics of birds are required over a largeweight range. Nevertheless, one can tentatively conclude that temperature regulationin birds is determined as it is in mammals; the differences in body temperature betweenthese groups are primarily due to differences in Mb and C. The variation of Mb and Camong birds depends upon their body weight and the conditions existing in theirnormal environments (Fig. 1).

Spec

ies

Stru

thio

cam

elus

Ard

eola

ib

isL

agop

us l

eucu

rus

Lop

hort

yx

calif

orm

cus

Scar

dafe

lla

inca

Pha

laen

optil

us

nutta

lli

Cho

rdei

les

min

orP

asse

r do

mes

ticus

Ric

hmon

dena

ca

rdm

alis

Est

rild

a tr

oglo

dyte

sT

aeni

opyg

ia

cast

anot

isZ

onot

rick

ia

leuc

ophr

ys

Wei

ght

(g)

IOO

OO

O

35

032

6

139 40

s4

0

70 25-8

40 6-

2n

-72

86

(Af t

/O/

60

823

-322

-918

-41

61

16

1

17-7

14

91

61

n-7

13

115

-2

Tab

le 3

.

Bas

al m

etab

olis

m

(ex.

OJ

g-h)

02

7— 1

30I-

OI

11

6o-

8o

I-IO

35

82-

653

60

32

8

a-43

%t

185 — 127 74 56 38 64 148

127

91

104

104

The

ene

rget

ics

of b

irds

Con

duct

ance

(ex.

OJ

g-h

°C)

0-00

83—

0-04

10-

069

O-I

I

O-I

I

O-I

I

O-I

7o-

io0-

500

34

O'I

2

*

%t

346 93

10

0 85 85 no

106 77

152

142

80

(Mb/

C) r

§

o-53

i-oo

1-37

07

4o-

660-

45

05

81-

401

-6S

o-6i

07

3

Tb

CO

38-3

4°-S

399

40-6

39

036

-0

3T°

41

242

-03

92

40

24

20

Ref

eren

ces

Cra

wfo

rd &

Sch

mid

t-N

iels

en (

1967

)Si

gfrie

d (1

968)

John

son

(196

8)B

rush

(19

65)

Mac

Mil

len

& T

rost

(19

67)

Bar

thol

omew

et a

l. (1

962)

; B

raun

er(•

952)

Las

iew

ski &

Daw

son

(196

4)H

udso

n &

Kim

rey

(196

6)D

awso

n (1

958)

Las

iew

ski

et a

l. (1

964)

Cal

der

(196

4)K

ing

(196

4)

to 0 1 i 1 fro if* 5S

Not

e. I

talic

ized

num

bers

rep

rese

nt q

uest

iona

ble

valu

es o

r va

lues

tha

t ar

e po

orly

sub

stan

tiat

ed.

• (M

bIO

. =

8-59

W-"

.t

Mb{

%)

= 1

00 m

ean/

7-3

W-*

**.

J §

OJ

346 B. K. MCNAB

SUMMARY

1. The interactions of basal rate of metabolism, thermal conductance, body tem-perature, lower limit of thermoneutrality, and body weight in mammals are compatiblewith Newton's law of cooling.

2. A small body weight will normally reduce the level and preciseness of bodytemperature, but a high basal rate of metabolism or a low thermal conductance maycompensate for a small size and permit a high, precise temperature to be maintained.

3. The parameters of energetics that fix the level and preciseness of body tempera-ture in mammals are ultimately correlated in turn with the environmental parametersof climate and food habits.

4. Birds generally have higher temperatures than mammals because the basal ratesof metabolism are higher and the conductances lower in birds than in mammals ofthe same weight.

I should like to thank the many people with whom I have discussed these ideas;special thanks must go to Drs A. Carr, C. Johnson, D. Johnston, and F. Nordlie andto Mr T. Krakauer, all of whom critically read this manuscript. Mr P. Laessle drewthe figures for this paper. Finally, I would like to express my thanks to the NationalScience Foundation (GB-3477) and the American Philosophical Society (PenroseFund 4225) for sponsoring the research that led to the ideas found within this essay.

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BARTHOLOMEW, G. A., HUDSON, J. W. &HOWELL, T. R. (1962). Body temperature, oxygen consumption,evaporative water loss, and heart rate in the poor-will. Condor 64, 117—25.

BENEDICT, F. G. (1935). The Physiology of the Elephant. Carnegie Inst. of Wash. Publ. 474. Washington,D.C.

BLIGH, J. & HARTHOORN, A. M. (1965). Continuous radiotelemetric records of the deep body tem-perature of some unrestrained African mammals under near-natural conditions. J. Physiol. 176,145-62.

BLIGH, J., INGRAM, D. L., KEYNES, R. D. & ROBINSON, S. G. (1965). The deep body temperature ofan unrestrained Welsh mountain sheep recorded by a radiotelemetric technique during a 12-monthperiod. J. Physiol. 176, 136-44.

BRAUNER, J. (1952). Reactions of poor-wills to light and temperature. Condor 54, 152—9.BRUSH, A. H. (1965). Energetics, temperature regulation and circulation in resting, active and defeathered

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rats Dipodomys agilis and Dipodomys merriami. Univ. Calif. Pub. Zool. 78, 1—36.DAWSON, T. J. & SCHMIDT-NIELSEN, K. (1966). Effect of thermal conductance of water economy in the

antelope jack rabbit, Lepus aUeni. J. Cell Physiol. 67, 463-72.DAWSON, W. R. (1958). Relation of oxygen consumption and evaporative water loss to temperature in

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Can.J. Zool. 43, 73i~44-

Body weight and energetics of temperature regulation 347HEATH, J. E. & ADAMS, P. A. (1967). Regulation of heat production by large moths. J. exp. Biol. 47,

21-33-HBLLSTROM, B. & HAMMEL, H. T. (1967). Some characteristics of temperature regulation in the

unanesthetized dog. Am.J. Pkytiol. 313, 547-56.HEMMINCSEN, A. N. (i960). Energy metabolism as related to body size and respiratory surfaces, and

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LASIEWSKI, R. C. & DAWSON, W. R. (1967). A re-examination of the relation between standard metabolicrate and body weight in birds. Condor 69, 13—23.

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LUCK, C. P. & WRIGHT, P. G. (1959). The body temperature of the hippopotamus. J. Physiol. 147,53-4^-

MACMILLEN, R. E. & NELSON, J. E. (1969)- Bioenergetics and body size in dasyurid marsupials. Am.J.Pkysiol. 317, 1246-51.

MACMILLEN, R. E. & TROST, C. H. (1967). Thermoregulation and water loss in the Inca dove. Comp.Biochem. Pkysiol. 30, 263-73.

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B. K. MCNAB

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Symbol

Table of Symbols

Factor Units

AC

cu c,hKkLMMb

QsTa

Tb

Tt

T,tWwze<j>a-

Surface areaThermal conductance

(coefficient of heat transfer)Thermal coefficientsConvective coefficientTemperature constantConductive coefficientHeat of vaporizationRate of metabolismBasal rate of metabolismHeatSpecific heatAmbient temperatureBody (core) temperatureLower limit of thermoneutralityTemperature constantTimeBody weightRate of water lossTemperature constantEmissivityCooling constantStefan-Boltzmann constant

cm1

c.c. 0,/g-h °C, or cal/h °C

c.c. O,/g-h °C, or cal/h °Ccal/cm«-h °K°Ccal/cm«-h °K(c. 540) cal/g H,Occ. O,/g-h, or cal/hc.c. 0,/g-h, or cal/hcalcal/g °C°C, or °K°C, or °K°C°ChggH,O/h°CNonei / h

(488 x 10-') cal/cm1 h °K«

body weight and the energetics of temperature regulation · body weight and energetics of...

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