A re-examination of the relationship between thermal conductance and body weight in mammals

A RE-EXAMINATION BETWEEN THERMAL WEIGHT S. ROBERT

OF THE RELATIONSHIP CONDUCTANCE AND BODY IN MAMMALS and

BRADLEY

DANIEL

R. DEAVERS

Department of Zoology, Iowa State University. Ames. Iowa 5001 I, U.S.A. and Department of Physiology and Biophysics, School of Medicine. University of Louisville. Louisville. Kentucky 40206. U.S.A. (Rrwicrd

19 July 1979)

Abstract-l. The following equation based on 230 conductance values for 192 species of mammals of body weights ranging from 3.5 to 150,OOOg describes the relationship of conductance below thermal and W neutrality to body weight in mammals: C = 0.760 W-0.4Zh, where C has units of mlO,/g.h.‘C is body weight in g. 2. Bats. order Chiroptera, have conductance values higher than predicted from body weight; conductance is predicted by the equation : C = 1.54 Wmo.54. 3. Heteromvid and cricetid rodents have conductance values below predicted and the following and C = 1.03 Wm”.‘r C = 0.62 Wi).44 equations predict conductance in these two families. respectively.

INTRODUCTIOK

Although there is a controversy (Kleiber, 1974) as to which physical law describes

1972; Swan. heat loss in

biological systems, biologists for some time have used either Newton’s Law of Cooling or Fourier’s Law of Heat Flow. These laws state that the rate of heat loss from a body is the product of some proportionality coefficient, C, and the temperature difference or gradient between the object and its environment: dH ~ = C(T, - T,) dr where Tb is the temperature of the object and T. is the ambient temperature. In mammals, which have a relatively constant Tb at thermal neutral or subthermal neutral zone temperatures, this steady state condition is maintained over time by heat loss to the environment being equaled by metabolic heat gain or heat production. The equation can then be rewritten: MR = C(T, - T,)

(2)

where MR is weight-specific metabolic rate and the proportionality coefficient, C. is thermal conductance. Thermal conductance thus is a measure of the ease of heat transfer from the body by radiation, conduction, convection and evaporation and is the reciprocal of insulation (Scholander et al., 1950a.b~). In energetic terms conductance is the rate of increase of weightspecific metabolic rate with decreasing ambient temperature and represents the ease of total heat transfer from the body by the four avenues of heat loss. Conductance may be calculated in one of two ways: (1) It is the slope of the line describing weight-specific metabolic rate us ambient temperature below the zone of thermal neutrality. This approach involves the assumptions that conductance is constant and minimal below the thermal neutral zone (TNZ), that Tb remains constant, that the curve extrapolates to Tb where it intersects the T, axis (MR = O), and that it 465

can only be calculated at temperatures below the TNZ. (See King [ 19641 and Tucker [ 1965b] for assumptions implicit in this method.) (2) Conductance can be calculated at any given T, by rearranging the previous equation to: MR c=

~

Th - To

(3)

MR is weight specific metabolic rate. The classical concept of thermal conductance as developed by Scholander et a/. (1950a,b,c) will be used in this paper since it is widely accepted (e.g. Bartholomew & Rainy, 1971; Dalby & Heath, 1976; Dawson & Bennett, 1971; Hill, 1975; Hudson et al., 1972; Hulbert & Dawson, 1974a,b). It should be pointed out that this usage differs from the restrictive use of the term “thermal conductance” referring to heat exchange by physical contact between two parallel surfaces differing in temperature. Thermal conductance values for species comparisons are generally expressed as minimum conductance, or conductance below the TNZ. Conductance as used in this paper refers to the minimum values of thermal conductance at ambient temperatures below thermal neutrality. Conductance is inversely related to body size (Scholander et al.. 1950~) because heat is lost from surfaces and because a small mammal has a larger surface to volume or mass ratio than a large mammal. Herreid & Kessel (1967) quantified this relationship and derived the following equation from data available for 24 species of placental mammals: where

C = 1.023 w-O.505 where W is weight in grams and units of conductance are m102/g. h. “C. Within the limits imposed by this conductance-size relationship, species may show adaptations of conductance to environment. Scholander et al. (1950a,b,c) measured several factors concerned with temperature regulation in birds and mammals from different cli-

S. RORI.KT BKAIILI:Y and DANII.L R. DI.AVI:KS

466

They examined body temperature, basal metabolism and conductance and concluded that only conductance was adaptive to environment. That is, animals living in colder climates had lower conductance or higher insulation values than similarly sized tropical species. As another example of adaptation of conductance to environment, McNab (1966) reported high conductance values in several species of fossorial rodents. and he attributed high conductance to evolution of adaptations for existence in a closed subterranean environment where heat dissipation may be difficult. There is. however, some disagreement about conductance values for fossorial rodents. Gettinger (1975) examined metabolism and conductance in the pocket gopher. Thor?lor~~~ talpoides, and found conductance values lower than predicted from body weight. He also recalculated McNab’s data and concluded that the data showed lower than expected conductance in these fossorial rodents. He attributed the lower than predicted conductance to adaptation for life in a cool, highly conductive substrate. His data, however, do not extrapolate to Th = r, at MR = 0. There is also some indication that conductance may show phylogenetic relationships. with some taxa showing uniformly higher or lower conductance than predicted from body weight. Hudson tgr ul. (1972) reported conductance values in several species of ground squirrels that were generally higher than predicted from the equation of Herreid & Kessel (1967). Several measurements were more than ISO>; of predicted values. MacMillen & Nelson (1969) found conductance values for 12 species of dasyurid marsupials to be slightly higher. although not statistically different. than predicted values for placental mammals. McNab (1978) has recently reported conductance values for 10 neotropical marsupials. He found somewhat higher conductances than in the Australian species. He attributes this to high. stable environmental temperatures. The objectives of this paper were: (1) to derive a regression equation describing the relationship between C and W,, from a larger number of mammals with a much wider range of body weights than were available to Herreid & Kessel (1967): (2) to examine thermal conductance in several mammalian taxa and where sufficient data are available to determine to what extent group differences occur; and (3) to quantify any existing differences. mates.

MATERIALS

AND METHODS

Some conductance values utilized in this study were extracted from available literature. Where conductance was not given per se either the regression coefficient of metabolic rate PS To below the TNZ was used or conductance was calculated from metabolic rate, T, and T,. An appraisal of each conductance value was made to ascertain that the appropriate assumptions as discussed above were adhered to in the calculation of conductance. Where body temperature was given and the slope of the line intercepted the u-axis at other than body temperature. values were calculated according to equation 3. Where actual body temperature was not reported. a Th representative of closely related species was used as the reference and for calculating conductance where necessary. Where conductance values were not constant below the TNZ, minimal values where T,, = r, at MR = 0 were used. Other values are unpublished measurements by the authors using an

open flow system in which carbon dioxide-free. dry air entered a paramagnetic oxygen analyzer (Beckman G-2). Oxygen c&sumption measurementswere made by thr, methods given bv Bradley & Hudson (1974). Measurements were made-on post-absorptive animals during theirinactive period. Metabolic values were calculated according to the method of Depocas & Hart (1957) and conductance was calculated from the metabolic data. Values are given in m102/g~ h ‘C. since these are the units most often used in the iitcraturc. Animals were maintained at least I month prior to measurement in a windowless room at 20 + I ‘C on a 14L:lOD photoperiod and wcrc given food and water ud lihilunl.

RESULTS AND DlSCUSSlON

We have extracted from the literature conductance values for a large number of mammalian species spanning a wide range of body weights and have treated this data in two ways. First, we derived a regression equation for all mammals based on a much larger sample size and weight range than has previousl) been assembled. Second. in order to discern any pass. ible phylogenetic trends in conductance, we havt grouped the data according to taxa and have derived regression equations which describe the relationship of conductance to body weight for these taxa. Where sufficient data were available. WC grouped conductance values by family. There are only a few families in which there exist enough data for this type of treatment. Regression equations were calculated by the least squares method using log transformed data and a linear model. Correlation coefficients apply to the log-transformed data. Where confidence intervals were used, values were converted to the antilog form before use. In interpreting our results it must bc recognized that when using data from the literature a wide variety of factors may vary including such things as techniques of measurement. age and condition of animals, sample size, and season of year. These variables cannot be controlled in a literature review and increase the amount of variability. Experimental variability should tend to obscure rather than strengthen any underlying physiological relationships. Thus any significant physiological relationships which are uncovered as a result of this literature review are considered to be representative of the taxa involved. In view of the fact that there are not and probably will not be sufficient data representing sample sizes and weight ranges large enough to make a sufficiently accurate estimate of the true relationship of conductance and body weight for many taxa, it would be valuable to derive a regression line which describes the relationship of conductance to body weight for mammals as a whole, remembering that phylogenetic differences may exist. Figure I presents 230 conductance values for 192 species of mammals prepresenting 41 families with a range in size from 3.5 to 150,OOOg. Data for the various mammals included in Fig. I are presented in Tables l-6. The regression equation which describes the relationship of conductance to body weight for mammals as a group is: C = 0,760 W-0.4’h It is of note that the confidence intervals for the regression line (Fig. 1) arc quite narrow and the correlation coefficient is high (0.94) indicating that it is

Thermal

conductance

and body weight

BODY

WEIGHT,

461

in mammals

g

Fig. 1. Relationship of thermal conductance to body weight in mammals. Dashed line IS from Herreid & Kessel (Herreid & Kessel, 1967). Solid line is from the present study. Dotted lines represent 95”/(, confidence interval for solid line.

Table

1. Body weight and thermal

conductance Body

Species

weight g

of mammals

not included

in subsequent

Conductance ccO2/g.h.'C

Reference

Sorex -~

cinereus

Sorex --

minutus

3.5 4.6

sorex --

araneus

7.6

0.53

Gebczynski,

8.5

0.47

HacMillen

12.8

0.28

Gebczynska

I3

0.258

Morrison

I4

0.25

HacMillen

14.5

0.29

Gebczynska

13

0.42

Kennedy

20.3

0.27

Neal

22.1

0.25

MacMiIlen

22.1

0.25

This

24.2

0.21

MacMillen

39.2

0.45

McNab,

1966

40

0.194

HcNab,

1978

43.1

0.14

MacMillen

70

0.15

Bartholomew

85

0.167

Bradley

86

0.14

Kennedy

88.5

0.128

McNab,

Antechinus Neomys -~

maculatus

anomalus

Harmosa

microtarsus

Sminthopsis Neomys --

crassicaudata

fodiens

Sminthopsis Blarina

crassicaudata

brevicauda

Antechinus Blarina

stuartii

brevicauda

Antechinus

spenceri

Heterocephalus Monodelphis

glaber brevicauda

Pseudantechinus cercaertus Thomomys

macdonnellensis

nanus umbrinus

Dasycercus

cristicaudata

Heliophobius Dasycercus

kapeti cristicaudata

Dasyuroides

byrnei

0.59

Morrison

0.56

Gebczynski,

et al., --

1965 6 Nelson,

& HcNab,

6 HacFarlane,

1969

t Nelson,

1963

t Nelson,

etc.,

6 MacFarlane,

0.12

MacMillen

t Nelson,

1969

83.0

0.13

HacHillen

8 Nelson,

1969

Bradley

Gettinger,

III

0.120

HcNab,

1978

122

0.111

McNab,

1978

126.4

0.090

Bradley

153

0.122

Brown

157.2

0.08

MacMillen

185

0.070

McNab,

1970

Phascogale Cyclopes

tapoatafa didactylus

1971

88.8

0.10

frenata

1962

1974

1966

0.110

Hustela --

I969

t Hudson,

110.8

gl

1973

study

106

Tupaia

1965

1971

t Nelson,

talpoides

brevicauda

1969

G Gebczynski,

t Lustick,

1965

1962

B Nelson,

talpoides

robinsoni

I969

t Gebczynski,

Thomomys

Monodelphis

1959

1971

Thomomys

Marmosa -___

tables

et al., --

1974

1975

6 Hudson, t Lasiewski, b Nelson,

Geomys

pinetis

202.8

0.075

McNab,

1966

Spalax --

leucodon

207.7

0.068

McNab,

1966

1974 1972 1363

(continued

on next page)

S. RORI:RT

BKAI)LEY

Table Body

Tachyoryctes Mustela

splendens

frenata

Caluromys

derbianus

Metachirus

nudicaudatus

g

DANIEL.

R. DI.AV~RS

1 (continued)

weight

Specie5

and

Conductance ccOp/g.h."C

Reference

233.6

0.073

HcNab,

297

0.079

Brown

1966

305

0.083

HcNab,

I978

G Lasiewski,

1972

336

0.083

McNab,

1978

derbianus

357

0.063

HcNab,

1978

Hemiechinus

auritus

397

0.082

Shkolnik

t Schmidt-Nielsen,

1976

Paraechinus

aethiopicus

453

0.051

Shkolnik

t Schmidt-Nielsen,

1976

semispinosis

498

0.055

McNab,

Caluromys

Proechimys Satanellus

hallucatus

Herpestes Aotus

auropunctatus

trivirgatus

Perameles ~-

nasuta

Ornithorhynchus Mustela ~-

anatinus

vison

Tenrec --

ecaudatus

1973

584.4

0.06

MacMillen

611

0.06

Ebisu

625

0.031

Morrison

645

0.06

Hulbert

693

0.03

Martin,

1902

704

0.046

Farrell

6 Wood,

720

0.07

Hildwein,

6 Nelson,

G Whittow, 6 Simoes,

europeaus

749

0.047

Shkolnik

opossum

751

0.066

McNab,

I978

812

0.053

McNab,

1978

824

0.044

Hildwein

860

0.055

Kinnear

946

0.056

McNab,

crassicaudata europaeus

Pseudocheirus Chironectes

occidentalis minimus

Perodicticus Didelphis

potto

marsupialis

1968

t Schmidt-Nielsen,

t Malan,

1970

E, Shield,

I975

981

0.037

Hildwein

1000

0.054

Enger,

6 Goffart,

lagotis

1011

0.05

Hulbert

tridactylus

1120

0.026

Nicol,

brucei

1310

0.039

Bartholomew

marsupialis

1329

0.050

McNab,

I978

1354

0.036

Arnold

6 Shield,

1500

0.018

Smyth,

1973

1520

0.020

Kinnear

1548

0.032

McNab,

Dasyurus

g eoffroii

Onrithorhynchus Macrotis

lagotis

Didelphis lsoodon

anatinus

virginiana rn~c~o"~"s

americanus

Lepus

Lepus __~

1970

t Shield,

1975

1978

Hulbert

6 Dawson,

1974a,b

1782

0.04

MacMillen

0.031

Taylor

6 Sale,

1969

2250

0.031

Taylor

E Sale,

1969

2300

0.021

Schmidt-Nielsen

brachyurus

2510

0.022

Kinnear

capensis

2630

0.020

Taylor

t Sale,

2660

0.020

Dawson

t Bennett,

2750

0.016

Taylor

t Sale,

3000

0.028

Dawson

E Schmidt-Nielsen,

3000

0.022

Schmidt-Nielsen

brucei

Lagorchestes Procavia

conspicillatus

johnstoni

alleni

Tachyglossus Didelphis

aculeatus

et al., --

1965

F, Nelson,

1969

et&.,

t Shield,

1969 1971

1969

et al., --

virginiana

3257

0.025

McNab,

3700

0.029

Johansen,

Choloepus

hoffmani

3770

0.018

Scholander,

Phalanger

maculatus

4250

0.021

Dawson

4440

0.018

Irving 6 Krog. Irving -et al.,

1954 1955 1969

Vulpes --

fulva

Macropus

eugenii

Sarcophilus Erethizon Canis

harrisii dorsatum

familiaris

1966 1966

I978 I961 1950a

t Degabriele,

4960

0.017

Dawson

5050

0.03

HacMillen

5530

0.015

Irving G Krog. Irving -et al.,

et al., --

t Nelson,

6666

0.019

Hellstrom

scrofa

48000

0.011

Irving, 1956 Irving et al.,

Taurotragus

150000

0.016

Taylor

sus --

1965

1975

novemcinctus

Dasypus

1971

2000

maculatus

habessinica

Procavia

6 Rainy,

Hart

californicus

Setonix

1974a,b

0.029

Heterohyrax

Lepus

0.071

t Dawson, 1976

1581

Dasyurops ___~

Procavia

1551

1975

1957

Potorous

Didelphis

1976

1978

Macrotis

Heterohyrax

1974a,b

1970

Philander Lutreolina

1962

t Dawson,

Erinaceus ~___

Erinaceus ______

1969

1976

I969

1954 1955

6 Hamnel,

d Lyman,

1973

1956 I967

I967

Thermal

and body weight in mammals

conductance

Table 2. Body weight and thermal Body

conductance

weight

Species

of Sciuridae

Conductance cc02/g.h.“C

9

469

Reference

Eutamias ___-

minimus

46.6

0.112

Jones

8 Wang,

1976

Eutamias ~-

amoenus

57.3

0.095

Jones

B Wang,

1976

Eutamias ___-

merriami

78.9

0.093 0.115

Wunder

,

0.126

Hudson

I970

Hudson,

Spermophilus

tereticaudus

Spermophilus

spilosoma

1.29 152.0

Spermophilus

tridecemlineatus

171

0.107

Pohl

1964 s

&II_.

E Hart,

, 1972 1965

Tamiasciurus

hudsonicus

225

0.085

Irving

--et

Tamiasciurus

hudsonicus

0.086

Irving

G Krog,

1954

Spermophilus

lateralis

229 264.2

0.067

Hudson

--et

al.,

1972

Spermophilus

richardsoni

267.2

0.086

Hudson

--et

al.,

1972

Spermophilus

beldingi

0.078

Hudson

--et

al.,

1972

--et

al.,

1972

armatus

219.4 300.6

0.071

Hudson

Spermophilus

undulatus

600

0.048

Hock,

Spermophilus

undulatus

998

0.029

Erickson,

Spermophi

lus

probably a very good estimate of the true line representing all mammalian species. The line of Herreid & Kessel (1967) falls within the confidence intervals of our line for the weight range of about 3CMOg which is the range of body weights that includes most of their data points. Above and below this range their line doesn’t fit the data as well and misleading conclusions might be drawn from it. For animals less than 30 g, the line of Herreid & Kessel (1967) would overestimate conductance leading to the conclusion that a species has lower than predicted conductance when in fact conductance may be close to predicted. The converse would be true for animals more than 80g. For example, based on the Herreid & Kessel line, Hudson et al. (1972) concluded the ground squirrel species they studied had higher conductances than would be predicted from body weight. However, with the newer line, which includes numerous mammals in the weight range of these squirrels, sciurids do not have higher than predicted conductance (Table 2, Fig. 2). It appears from Fig. 1 that mammals weighing more than about 5 kg may not show a relationship of conductance to body weight, and this may mean that

al.,

IV55

I960 1956

there is a minimum constant conductance for larger mammals. Before this possibility can be tested more data from animals weighing more than 5 kg are needed. Conductance values for members of seven families in the order Chiroptera are available and these seven families have higher than predicted conductance (Table 3; Fig. 3). Thus these animals were grouped at the ordinal level. Higher than predicted conductance in this order may be a consequence of heat loss from the large, relatively unfurred wing surface area. Conductance in chiropterans is higher than predicted in all except two large (362 & 598 g) megachiropteran species. Bartholomew et al. (1964) found that these two species enhance insulation by wrapping their wings around the body forming dead air pockets. Higher than predicted conductance may be adaptive in bats because flight with its associated high level of heat production may necessitate the ability to quickly dissipate large amounts of heat. This may be effectively done by vasodilation in the relatively unfurred wings and other parts of the body (Reeder & Cowles. 1951). The following equation describes the relation-

SCIURIDAE

0.01,~

IO' BODY

Fig. 2. Relationship

of thermal

conductance

’ WEIGHT,

’

’ 102

’

2

’

IO’

g

to body weight

in the family Sciuridae.

470

S. ROBERT BRAULEY and DANIEL R. DEAVERS Table 3. Body weight and thermal Body Species Rhinophyl

la

Histiotus ___Anoura -~

fer

HcNab,

1969

HcNab,

1969

II.2

0.34

McNab,

1363

11.5

0.36

HcNab,

1363

HcNab,

1363

Carollia

perspicillata

14.9

ilolossus ~~

molossus

15.6

0.35 0.44

Uroderma ______

bi labatum

16.2

0.30

McNab,

17.5

0.28

Bartholomew

19.7 21.3

0.27

HcNab,

0.32

Bartholomew

21.9

0.22

McNab,

1363 1363

austral

Artebius ___~

is

concolor

Paranyctimene

raptor

Vampyrops ___-

lineatus

--Sturnia

Iilium

Leptonycteris Noctilio ______

sanborni labialis

Tonatia ___-

bidens

McNab..lY63 I369

21.9

0.25

HcNab.

22

0.252

Carpenter

27.0

0.30

McNab,

1363

27.4

0.20

HcNab,

1363

ecaudata

27.8

0.22

HcNab,

1363

Desmodus ___-

rotundus

29.4

0.19

McNab,

I363

33.5 36.6

0.21

McNab,

1363

0.17

McNab,

1363

jamaicensis

45.2

0.17

McNab,

1363

hirsutus

43.5

0.18

Carpenter

56

0.15

Leitner,

Diaemus

youngi

Artebius Artebius -~ Eumops

discolor

Perot

is

Noctilio ~~

leporinus

61 .O

0.18

NcNab,

1969

1ituratus

70.1

0.14

NcNab,

1363

84.2

0.15

NcNab,

I363

87.0

0.113

Bartholomew

96.1

0.14

McNab,

lostomus

Dobsonia ___-

hastatus

minor

Chrotopterus Macroderma

auri

tus

u

c.,

5

$_.

t

Graham,

1367

c

1364

al.,

1363

148

0.095

Leitner

362

0.053

Bartholomew

--et

al.,

Pteropus

poliocephalus

598

0.031

Bartholomew

s

$_.

in chiropterans

c = 1.54 W-0.5’. The rodent family, Heteromyidae, has conductance values (Table 4; Fig. 4) that are 76 and 81% of that predicted by the equation of Herreid & Kessel (1967) or the equation derived in the present study

1970

1367

scapulatus

to body weight

,

G Graham,

Pteropus

(Fig. 3):

1364

1966

Artebius ~___ Phyl

5

I363

Diphylla ______

Phyllostomus

of conductance

Reference

0.37 0.45

3.5

9.6

velatas caudi

Syconycteris

ship

1io

soricina

of Chiroptera

Conductance cc02/g.h.OC

g

pumi

Glossophaga

weight

conductance

G Nelson,

1367 1364

,

1364

respectively. Heteromyids have conductance values as low as’37-42% of predicted. These well-insulated animals may show adaptation to nocturnal activity in desert areas often characterized by low ambient temperatures during the night (Carpenter, 1966). Two subtropical species of the genus Liomys are exceptional in that they have higher than predicted conductances. Liomvs are primitive heteromyids which may

CHIROPTERA

Fig. 3. Relationship

of thermal

conductance

to body weight

in the order Chiroptera.

Thermal conductance and body weight in mammals

471

Table 4. Body weight and thermal conductance of Heteromyidae Body

weight

Species

Conductance ccO2/g.h."C

g

Reference

Perognathus

longimembris

7.8

0.273

Brewer,

Perognathus

longimembris

a.2

0.277

Chew -et al.,

I2

0.185

Brown

14.5

0.115

Brewer,

Microdipodops Perognathus

pallidus parvus

Microdipodops

pallidus

1970 1967

C. Bartholomew,

15.2

0.12

Bartholomew

Perognathus

pencillatus

15.5

0.202

Brewer,

1970

Perognathus

formosus

16.8

0.198

Brewer,

1970

Perognathus

fallax

17.7

0.187

Brewer,

Perognathus

formosus

17.7

0.216

Mullen

Perognathus

californicus

22

0.18

Tucker,

lv65a

t MacMi

hispidus

31.0

0.196

Brewer,

1970

merriami

35.4

0.136

Brewer,

1970

Oipodomys

merriami

36.8

0.109

Brewer,

I970

Oipodomys

merriami

38.3

0.108

Carpenter,

43.8

0.186

Hudson

agilis

47.2

0.134

Brewer,

irroratus

48.1

Liomys --

salvani

Oipodomys Liomys -___

0.176

Hudson

.P

o.toa

Brewer,

1970

Dipodomys ~-

ordi

56.0

0.091

Brewer,

1970

Dipodomys

agilis

60.6

0.080

carpenter,

Dipodomys

panamintinus

77.0

0.083

Scelza

Dipodomys

desert;

0.065

Brewer,

have evolved in a moist environment (Wood, 1935) and higher than predicted conductance may be an adaptation to inhabiting hot, humid environments where heat dissipation may be difficult. The following equation describes the regression line relating conductance to body weight in heteromyid rodents: C = 0.62 W-o.44. Cricetid rodents generally have conductance values below predicted (Table 5; Fig. 5). It might be argued that most of the bats studied live in the tropics and that their high conductance may in reality reflect the normally high ambient temperatures to which these species are exposed rather than a phylogenetic relationship. However, the cricetid species share no common factor in their behavior or environment which

1973

I966

I370

54

103

1961

1966

G Rummel,

panamintinus

Dipodomys

Ilen,

1970 6 Chew,

Oipodomys

Perognathus

1969

1370

t Rummel,

1966

1966

G Knoll,

1975

1970

would explain their better than predicted insulation. They inhabit a wide variety of habitats throughout the world. Many are nocturnal while others may be active at any time during the day or night. Their only apparent similarity is that they are related closely enough to be included in the same family. The generally similar insulation or conductance of cricetids appears to have a phylogenetic basis. Perhaps conductance in cricetids is a conservative evolutionary trait which has not been greatly modified to meet environmental stresses. If this is the case, then the principle set forth by Scholander et al. (1950a,b.c) that insulation is adaptive to environment may operate to a limited extent in cricetids. Conductance for cricetid rodents is described by the equation: c = 1.03 w-O.‘4.

HETEROMYIDAE

C=O76OW

Y

1

S

o.,

-0.426

cz;h,,

, = 0.78

g S

BODY

WEIGHT,g

Fig. 4. Relationship of thermal conductance to body weight in the rodent family Heteromyidae.

S. ROBERT

472

BRADLEY

and

DANIEL

R. I>EAVERS

Table 5. Body weight and thermal conductance of Cricetidae Body Species

g

taylori

Baiomys

Reithrodontomys Peromyscus

megalotis

crinitus

Clethrionomys Peromyscus

glareolus

crinitus

Onychcmys ~.

torridus

Ochrotamys

weight

nuttalli

Conductance ccO2/g.h."C

Reference

7.3

0.38

Hudson,

2.0

0.28

Pearson.

1965

16

0.13

McNab,

18.0

0.210

Jansky,

18.4

0.180

McNab

19.1

0.21

Whitford

19.2

0.18

Layne

1959 t Morrison,

maniculatus

19.5

0.239

Hayward,

Peromyscus

maniculatus

20.0

0.185

McNab

20.0

0.19

Janskv,

arvalis

1965

glareolus

20.5

0.160

Pearson,

rutilus

21.0

0.22

Rosenmann

Clethrioncxnys

glareolus

21.0

0.25

Gorecki,

1962 et al., --

eremicus

21.5

0.160

McNab

Peranyscus

leucopus

22.1

O.iYY

This

23.5

0.23

I(aiabukhov,

23.5

0.234

Dalby

23.8

0.20

Chew

lagurus

Onychcxnys --

torridus

E Morrison,

1970

t Heath, & Chew,

Percxnyscus

maniculatus

24

0.17

McNab

maniculatus

24.6

0.206

Hayward,

1976 1970

5 Morrison,

25.1

0.189

This

study

longicaudus

25.2

0.18

Beck

G Anthony,

Microtus ~~

pinetorum

25.9

0.191

This

study

25.9

0.20

Layne

21.2

0.169

This

Peromyscus Microtus --

floridanus mexicanus

1963

1965

Microtus

gapperi

1363

study

Percmyscus

Clethrioncmys

1975

IV66

Peromyscus

azarae

1963

1359

Ciethrionomys

Lagurus

1971

1975

6 Morrison,

Clethrioocmys

Akodon ~-

1963

G Conley,

G Dolan,

Peromyscus

Microtus --

1360 1366

t DoIan*

1971

1975

study

27.5

0.130

pearson,

1962

Percxnyscus

sitkensis

28.3

0.180

Hayward,

1965

Percmyscus

f loridanus

29.9

0.17

tayne

E Dolan,

1975

Ochrotcmys

nuttalli

30.6

0.192

Layne

t Dolan,

1975

30.8

0.18

Packard,

30.9

0.17

Layne

31.1

0.173

Heldmaier,

Clethrioncmys

Microtus -~

rufocanus

montanus

Percmyscus Phodopus

gossypinus sungorus

Percmyscus

1968

F. Dolan,

truei

33.2

0.140

NcNab

Microtus ~-

nivalis

34.9

0.15

Bienkowski

Hicrotus

pennsylvanicus

37.3

0.151

This

study

Microtus

californicus

study

Peromyscus Microtus

californicus ochrogaster

Dicrostonyx Arvicola

groenlandicus

NcNab

50.2

0.128

This

B Morrison,

Scholander

0.317

This

61.0

0.110

Hart & Heroux, Hart, 1971

megalops

66.2

0.099

Musser

unguiculatus

70.0

0.15

Robinson,

81.8

0.12

Kalabukhov,

97.5

0.071

Pohi,

groenlandicus

luteus

Mesocricetus

auratus

100.2

0.088

Drozdz

0.102

Robinson

Neotcxna lepida -__

110.3

0.071

Brown

Perwnyscus

110.8

0.088

Fusser

138.5

0.062

Brown

thomasi

Percmyscus

pirrensis

1955

1970

et al.,

1971

t Henrickson,

B Lee,

s Shoemaker, t Lee,

0.083

Hill,

1375

150.6

0.056

Brown

& Lee,

1969

Neotana

albigula

173.0

0.058

Brown

t Lee,

1969

Neotoma

fuscipes

186.7

0.059

Drown

t bee,

1969

Neotdma --

cinerea

201.3

0.063

Drown

6 LG.

1969

obesus

Neotcma --

cinerea

Ondatra

zibethicus

1965

1969

140.8

cinerea

IV61

1963

aibigula

Psammomys --

1365

1359

Neotdma

Neotoma ~-

lYSOa,c

1965

108.5

lepida

et al., --

6 Shoemaker,

pyramidum

Neotcma

1963

study

terrestris

Gerbillus ~~

1974

study

0.10

Percmyscus

Arvicola

This

0.105

1963

G Marszalek,

51.0

Dicrostonyx

Lagurus

0.138

t Morrison,

51.4

richardsoni

Meriones

43.4 47.6

1975

1975

224

0.045

Frenkel

B Kraicer,

288.9

0.048

Brown t

Lee,

1963

299.0

0.044

Brown

t Lee,

1969

1100.0

0.027

Hart,

1971

1972

Thermal

conductance

and body weight

in mammals

413

CRICETIDAE

1

0.01

I

,,,I

BODY

Fig. 5. Relationship

of thermal

WEIGHT,

conductance

Body

weight

minutus

Apodemus

agrarius

103

9

conductance

6.0

family Cricetidae.

of Muridac

Conductance ccO2/g.h.'C

g

Hicrcmys

,I,,

to body weight in the rodent

Table 6. Body weight and thermal Species

I 102

IO’

100

Reference

0.35

Smirnov,

l957a

20

0.24

Smirnov,

lT5Jb

MUS musculus -___

26

0.13

Hart.

Notomys --

alexis

32.3

0.192

MacHillen

t Lee,

IT70

Notomys

cervinus

34.2

0.179

MacMillen

t Lee,

ITJO

cahirinus

41.3

0.117

Shkolnik

t Borut,

43.9

0.128

Kalabukhov,

50.3

0.122

Shkolnik

6 Borut,

51

0.16

Smirnov,

1957b

Acomys -~ Apodemus Accmys -~ Apodemus

flavicollis russatus sylvaticus

1950

1969

I953

Rattus

fuscipes

75.7

0.095

Collins,

l973b

Rattus ~~

fuscipes

77.1

0.101

Collins,

l973b

1969

lTJ3a

Rattus -___

lutreolus

109.1

0.071

Collins,

Rattus --

rattux

132.0

0.081

Collins

Rattus

norvegicus

160

0.10

Gelineo.

Rattus

norvegicus

170

0.090

Kirmiz,

IT62

Rattus

villosissimus

186.7

0.053

Collins

t Bradshaw,

Rattus

norvegicus

225

0.071

Krog -et al.,

Rattus

norvegicus

350

0.067

Herrington,

Rattus

norvegicus

390

0.048

Oepocas

t, Bradshaw,

1973

1934

I973

1955 1940

et al., --

1957

MURIDAE

I

0.01 IO0

BODY Fig.

6.

Relationship

of thermal

.

,,,I

conductance

I IO2

IO’ WEIGHT,

,*,I IO’

q

to body weight in the rodent

family

Muridae.

474

S. ROBLHT BRAI>LEYand DANI~:L R. DI.AVERS

Murids appear not to differ greatly from the line predicting conductance for mammals as a whole (Table 6; Fig. 6). For most mammalian families there are not enough data to derive regression lines that accurately describe the relationship of conductance to body weight. Even 25 or so points may not give an accurate description of this relationship for a taxon, particularly if the regression line is based on a narrow range of body weights. There are sufficient data for an accurate assessment of the relationship of conductance to body weight in the order Chiroptera and the rodent family Cricetidae. Statistical tests (t-test) for comparing the slopes of lines were made, and indicate that for Cricetidae and Chiroptera the slope of the lint is different than for mammals as a group (P < 0.01 for Chiroptera and P < 0.001 for Cricetidae). For data comparisons involving conductance of species in these two taxa. we recommend that workers use the regression equations we have derived. And until more data are available for other groups, we feel that the general mammalian regression line is more applicable.

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