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J Comp Physiol B
DOI 10.1007/s00360-007-0193-0
123
REVIEW
The “minimal boundary curve for endothermy” as a predictor
of heterothermy in mammals and birds: a review
Christine E. Cooper · Fritz Geiser
Received: 22 March 2007 / Revised: 11 July 2007 / Accepted: 12 July 2007
© Springer-Verlag 2007
Abstract According to the concept of the “minimal
boundary curve for endothermy”, mammals and birds with
a basal metabolic rate (BMR) that falls below the curve are
obligate heterotherms and must enter torpor. We examined
the reliability of the boundary curve (on a double log plot
transformed to a line) for predicting torpor as a function of
body mass and BMR for birds and several groups of mam-
mals. The boundary line correctly predicted heterothermy
in 87.5% of marsupials (n= 64), 94% of bats (n= 85) and
82.3% of rodents (n= 157). Our analysis shows that the
boundary line is not a reliable predictor for use of torpor. A
discriminate analysis using body mass and BMR had a sim-
ilar predictive power as the boundary line. However, there
are suYcient exceptions to both methods of analysis to sug-
gest that the relationship between body mass, BMR and
heterothermy is not a causal one. Some homeothermic birds
(e.g. silvereyes) and rodents (e.g. hopping mice) fall below
the boundary line, and there are many examples of hetero-
thermic species that fall above the boundary line. For mar-
supials and bats, but not for rodents, there was a highly
signiWcant phylogenetic pattern for heterothermy, suggest-
ing that taxonomic aYliation is the biggest determinant of
heterothermy for these mammalian groups. For rodents,
heterothermic species had lower BMRs than homeothermic
species. Low BMR and use of torpor both contribute to
reducing energy expenditure and both physiological traits
appear to be a response to the same selective pressure of
Xuctuating food supply, increasing Wtness in endothermic
species that are constrained by limited energy availability.
Both the minimal boundary line and discriminate analysis
were of little value for predicting the use of daily torpor or
hibernation in heterotherms, presumably as both daily tor-
por and hibernation are precisely controlled processes, not
an inability to thermoregulate.
Keywords Basal metabolic rate · Body mass ·
Hibernation · Daily torpor
Abbreviations
BMR Basal metabolic rate
TaAmbient temperature
TbBody temperature
Introduction
The concept of a “minimal boundary curve for endo-
thermy” in mammals and birds (McNab 1983) postulates
that mammals and birds whose basal metabolic rate (BMR)
falls below this allometric curve must use torpor; conse-
quently they are obligate heterotherms. In contrast, species
with a BMR above the boundary curve are predicted to be
capable of continuous endothermy or, in other words,
homeothermic thermoregulation. The minimal boundary
curve for endothermy was derived by “placing a linear
curve on the left margin of the relation between basal rate
and mass for fossorial mammals and hedgehogs” and is
described by the equation BMR (ml O2h¡1) = 15.56 m(g)0.33
Communicated by I.D. Hume.
C. E. Cooper (&)
Department of Environmental Biology,
Curtin University of Technology,
PO Box U1987, Perth, WA 6845, Australia
e-mail: C.Cooper@curtin.edu.au
C. E. Cooper · F. Geiser
Centre for Behavioural and Physiological Ecology,
Zoology, University of New England, Armidale,
NSW 2351, Australia
J Comp Physiol B
123
(McNab 1983) and consequently the double-log plot of this
relationship forms a line, henceforth referred to as the
boundary line. The boundary line and Kleiber’s (1932) line
intersect at a body mass of approximately 80 g, below
which the BMR of homeothermic species is predicted to
scale according to the boundary line, whereas heterother-
mic species are thought to scale according to Kleiber’s line.
In this way the boundary line claims to provide a clear dis-
tinction of the species that should employ torpor and those
who do not (McNab 1983). The same concept of a minimal
boundary line has been reiterated in recent publications
(McNab and Bonaccorso 2001; McNab 2002) and the con-
cept is widely used by other authors.
Some mammals, such as ground squirrels, marmots and
large carnivores, have a BMR that falls above the boundary
line, but nevertheless use torpor. These exceptions to the
boundary line concept have been explained by claiming
that seasonal torpor in these hibernating species is “an
actively regulated state: it is not an inability to thermoregu-
late, as tends to be the case for those species whose BMR
falls below, especially far below, the boundary curve”
(McNab 2002). The implicit assumption here is that species
who enter daily torpor (daily heterotherms, with torpor
bouts lasting less than 1 day) and hibernators (species capa-
ble of prolonged torpor, with torpor bouts that can last
longer than 1 day up to several weeks) diVer fundamentally
in their thermoregulatory ability, and that hibernation is
regulated whereas daily torpor is not.
The purpose of our paper is to quantitatively assess the
reliability of the boundary line in separating homeothermic
and heterothermic mammals and birds, and for heterother-
mic species, in distinguishing between species that use
daily torpor and those that enter prolonged torpor (hiberna-
tion). We also explore an alternative method for predicting
patterns of heterothermy based on the relationship between
mass and BMR, and examine phylogenetic patterns in body
temperature regulation.
Methods
Body mass, BMR and mode of body temperature regulation
were taken from original references or from reviews (Hays-
sen and Lacy 1985; McNab 1988; Geiser and Ruf 1995;
McKechnie and Lovegrove 2002; Lovegrove 2003; Geiser
2003, 2004; Cruz-Neto and Jones 2006). We found suY-
cient and reliable data for homeothermic or heterothermic
monotremes (n= 3), marsupials (n= 64), bats (n= 84),
rodents (n= 157), and birds (n= 28) for our analysis. Het-
erothermic species were deWned as those whose minimum
metabolic rate during torpor is less than BMR and/or mini-
mum body temperature (Tb) >5°C below the normothermic
resting Tb (Geiser et al. 1996). Species with a minimum
MR not lower than BMR, or a <5°C Tb reduction were con-
sidered to be homeothermic (we recognise that homeo-
thermy in at least some of these species may not withstand
vigorous investigation of thermal biology in the Weld, but
these are our best estimates based on available data). BMR
and body mass for mammals and birds with known patterns
of thermoregulation were plotted along with the minimal
boundary line for endothermy. DiVerences between residu-
als (obtained by least squares regression of log transformed
body mass and BMR data for each of the respective groups)
for heterothermic and homeothermic mammals (excluding
monotremes) were evaluated using a one-factor ANOVA
both before and after correction for phylogenetic history
(see below).
Discriminate analysis was used to produce classiWcation
functions to separate homeothermic and heterothermic spe-
cies and for heterotherms, to separate those that use daily
torpor and hibernation, using data for log body mass (g;
logm) and log BMR (ml O2h¡1; logBMR). Of the two
resulting functions, whichever equation produces the larg-
est value indicates to which category a species belongs.
Regression, ANOVA and discriminate analyses were con-
ducted using statistiXL v1.6.
The signiWcance of a phylogenetic signal in patterns of
heterothermy for each group was assessed by cluster analy-
sis after Vanhooydonck and Van Damme (1999). Random
reallocations (1,000) of trait categories (daily heterotherm,
hibernator or homeotherm) were assessed for Wt (minimum
cumulative distance of each species with a particular trait to
each of the other species sharing that trait) and compared to
the actual Wt for the phylogenetic tree for each group. Phy-
logenetically independent residuals were calculated from
phylogenetically corrected allometric regressions for each
group using independent contrasts (IC; Felsenstein 1985;
Garland et al. 1993). Phylogenetic trees for each group
were obtained from Withers et al. (2006; marsupials), Jones
et al. (2002; bats) and Lovegrove (2003; rodents). Cluster
analyses and IC were conducted using custom-written
Visual Basic software (P.C. Withers). Monotremes and
birds were excluded from ANOVA, discriminate and phy-
logenetic analyses because insuYcient species numbers or
data on torpor use were available for these groups.
Results
Monotremes
Members of the three extant genera of monotremes are
large (body mass 1.3–10.3 kg) and all have a BMR that lies
near or below the marsupial regression, but are above the
boundary line because of their large mass (Fig. 1). Long-
beaked echidnas (Zaglossus spp.) and platypus (Ornitho-
J Comp Physiol B
123
rhynchus anatinus) appear to be homeothermic (Grant
1983; Grigg et al. 2003). In contrast, short-beaked echidnas
(Tachyglossus aculeatus) may hibernate for extended peri-
ods in winter and also enter short bouts of torpor in summer
(Grigg and Beard 2000; Nicol and Andersen 2000),
although their BMR is above the boundary line.
Marsupials
Marsupials have BMRs that conform exceptionally well to
an allometric relationship (r2= 0.99, n= 64). The residuals
from this allometric relationship for heterothermic and
homeothermic marsupials do not diVer, before or after cor-
rection for phylogenetic history (F1,59 =0.81, P= 0.372;
F1,59 = 0.531, P= 0.469 respectively). The allometric line of
BMR for marsupials and the boundary line intercept at a
body mass of 87.9 g and a BMR of 67.7 ml O2h¡1. Hetero-
thermic marsupials range in body mass from »5 to »1,500 g
and have BMRs that fall both above and below the boundary
line (Fig. 1). At body masses of less than 87.9 g all marsupi-
als have BMRs that are lower than the boundary line. While
all of these species are heterothermic, they include species
that use both short-term daily torpor (e.g. dasyurids) and
those that undergo prolonged seasonal hibernation (e.g.
pygmy-possums, Burramyidae). Eight marsupial species
with body masses greater than 87.9 g are known to be hetero-
thermic (Dasyuroides byrnei, Dasyurus geoVroyi, D. viverri-
nus, Marmosa robinsoni, Monodelphis brevicaudata,
Myrmecobius fasciatus, Petaurus breviceps, Phascogale
tapoatafa) and, although their BMRs fall above the boundary
line, they all enter daily rather than prolonged torpor (Geiser
2003; Cooper and Withers 2004). Therefore the boundary
line correctly classiWes 87.5% of marsupials as either hetero-
or homeothermic (73.3% of heterothermic and 100% of
homeothermic marsupials). However, it fails to distinguish
between seasonal hibernators and daily heterotherms.
A discriminate analysis of BMR and mass data for mar-
supials produced the following equations:
Homeothermic: ¡31.7 log m+55.45logBMR ¡26.18
Heterothermic: ¡35.02 log m+ 53.98 log BMR ¡15.25
Of all marsupial species 93.5% were correctly classiWed
(97.1% of homeothermic and 90% of heterothermic species
classiWed correctly). A similar discriminate analysis to sep-
arate daily heterotherms from hibernators produced the fol-
lowing equations:
Hibernation: 0.419 log m+ 51.83 log BMR ¡14.78
Daily Torpor: 18.44 log m+ 50.88 log BMR ¡15.02
However this prediction was not robust, with only 47.9% of
species being classiWed correctly (50% of hibernators and
45.8% of daily heterotherms).
There was a highly signiWcant (P< 0.001) phylogenetic
signal for the pattern of heterothermy amongst marsupials,
with none of the 1,000 reallocations of trait categories
Wtting the marsupial phylogenetic tree better than the actual
pattern i.e., the actual pattern of trait characters had a lower
minimum cumulative distance of each species with a partic-
ular trait to each of the other species sharing that trait, than
any of the 1,000 random rearrangements.
Bats
The BMR of bats conforms well to an allometric relation-
ship (r2=0.915; n= 85; Fig. 2). There was no signiWcant
diVerence between the residuals from this relationship for
heterothermic and homeothermic species, either before or
after correction for phylogenetic history (F1,82 = 0.481,
P=0.490; F1,82 = 0.829, P= 0.368 respectively). The
boundary line intercepts the allometric equation at a mass
of 54.6 g and a BMR of 58.1 ml O2h¡1. Heterothermic bats
have body masses that range from »4 to »74 g and have
BMRs that fall both above and below the boundary line
(Fig. 2). Five species of known heterothermic bats (Anoura
caudifer, Artibeus hirsutus, Artibeus jamaicensis, Dobsonia
minor and Tonatia sylvicola) fall above the boundary line
(Fig. 2), and all Wve use daily torpor. Two of these (Dobso-
nia minor and Tonatia sylvicola) have body masses above
54.6 g, whereas the remaining three have body masses less
than 54.6 g but BMRs that are higher than the boundary
line. Both daily heterotherms and species that use long-
term hibernation are below the boundary line. No homeo-
thermic bats fall below the boundary line. Thus the bound-
ary line correctly classiWes 94% of bats as either hetero- or
homeothermic (93% of heterothermic and 100% of homeo-
thermic bats). However, it fails to distinguish between hib-
ernators and daily heterotherms.
Discriminate analysis of body mass and BMR for bats
and insectivores produced the equations:
Fig. 1 Relationship between mass and basal metabolic rate (BMR) for
monotremes (n= 3; data from Dawson 1983) and marsupials (n= 64;
data from Withers et al. 2006) relative to the boundary line. Homeo-
thermic species are represented by dark symbols, heterothermic spe-
cies by light symbols. Species that use daily heterothermy are
represented by circles and those that use hibernation by squares. Tri-
angles represent monotremes
J Comp Physiol B
123
Homeothermic: ¡5.11 log m+36.71logBMR ¡34.69
Heterothermic: ¡12.15 log m+ 32.45 log BMR ¡15.205
These correctly separated 94% of heterothermic and 93%
of homeothermic species (combined success 93%). Daily
heterotherms and hibernators were separated using the fol-
lowing discriminate functions:
Hibernation: ¡8.38 log m+29.43logBMR ¡14.27
Daily torpor: ¡7.65 log m+ 32.36 log BMR ¡19.05
with 70% of species using hibernation and 70% using daily
torpor separated correctly (70% overall correct classiWcation).
There was a highly signiWcant (P< 0.001) phylogenetic
signal for the pattern of heterothermy amongst bats, with
none of the 1,000 reallocations of trait categories Wtting the
bat phylogenetic tree better than the actual pattern.
Rodents
The relationship between BMR and body mass for rodents
(r2= 0.69; n= 242; data from Hayssen and Lacy 1985;
Lovegrove 2000a) is not as strong as for marsupials and
bats. The residuals from the allometric line of BMR for
rodents are signiWcantly lower for known heterothermic
species than those for homeothermic rodents both before
and after phylogenetic correction (F1,156 = 9.1, P=0.003;
F1,156 =10.1, P= 0.002 respectively). The intercept
between the allometric line of BMR (data from Lovegrove
2000a) and the boundary line occurs at a body mass of
32.2 g and a BMR of 48.9 ml O2h¡1. Both daily hetero-
therms and seasonal hibernators have BMRs that fall below
as well as above the boundary line; »53% of heterothermic
rodents are above the boundary line (Fig. 3). An extreme
case is the woodmouse (Apodemus Xavicollis), which has a
BMR that is well above the boundary line but enters daily
torpor (Aeschimann et al. 1998). The Siberian hamster
(Phodopus sungorus) is a daily heterotherm with strongly
seasonal torpor. It has a BMR that is above the boundary
line both in summer and winter, but the species enters tor-
por only in winter (Heldmaier and Steinlechner 1981b).
The BMR of the majority of small homeothermic
rodents appears to scale with the boundary line (Fig. 3).
However, unlike for marsupials, the BMR of a few species
of rodents considered to be homeothermic (the spinifex and
fawn hopping mice, Notomys alexis and N. cervinus; Mac-
Millen and Lee 1970; Withers et al. 1979; Dawson and
Dawson 1982) and the swamp rat (Rattus lutreolus; Collins
1973) fall under the boundary line (residuals ¡28.6, ¡8.0
and ¡9.3 ml O2h¡1 respectively; Fig. 3). Overall, the
boundary line correctly classiWes 82.3% of rodents as either
hetero- or homeothermic (51.2% of heterotherms and
98.1% of homeotherms), whereas the line separates 65.9%
of hibernators and 83.3% of daily heterotherms correctly.
The discriminate functions for hetero- and homeother-
mic rodents were:
Homeothermic: 19.21 log m+ 39.52 log BMR ¡20.79
Heterothermic: 17.21 log m+ 36.22 log BMR ¡16.87
These correctly separated 68% of rodents into the two cat-
egories (66.5 % of homeothermic and 69.5% of hetero-
thermic rodents correctly). Daily heterotherms and
hibernators were separated using the following discrimi-
nate functions:
Hibernation: 17.69 log m+ 28.2 log BMR ¡18.91
Daily torpor: 14.11 log m+27.54logBMR ¡13.61
with 92.5% of species using daily torpor and 71.9% using
hibernation separated correctly (81.7% overall correct clas-
siWcation).
There was no signiWcant phylogenetic pattern
(P= 0.766) for heterothermy in rodents. Of the 1,000 real-
locations of trait categories, 766 Wtted the rodent phyloge-
netic tree better than the actual pattern.
Fig. 2 Relationship between mass and basal metabolic rate for bats
(n= 85; data from Cruz-Neto and Jones 2006) relative to the boundary
line. Homeothermic species are represented by dark symbols, hetero-
thermic species by light symbols. Species that use daily heterothermy
are represented by circles and those that use hibernation by squares
Fig. 3 Relationship between mass and basal metabolic rate for rodents
(n= 157; data from Lovegrove 2000a) relative to the boundary line.
Homeothermic species are represented by dark symbols, heterothermic
species by light symbols. Species that use daily heterothermy are rep-
resented by circles and those that use hibernation by squares
J Comp Physiol B
123
Birds
Heterothermic birds range in mass from »3 to »500 g
(Schleucher 2001; McKechnie and Lovegrove 2002) and
have BMRs that fall both above and below the boundary
line in similar proportions (Fig. 4). The BMR of the poor-
will (Phalaenoptilus nuttallii) falls below the boundary
line. The poorwill is the only known avian hibernator and
enters prolonged torpor bouts in winter but also short bouts
of torpor in summer (Jaeger 1948; Bartholomew et al.
1957; French 1993; Brigham et al. 2006).
Some birds considered to be homeothermic have BMRs
below the boundary line (Fig. 4). For example, silvereyes
(Zosterops australis) can maintain a normothermic Tb at an
eVective ambient temperature (Ta) as low as ¡40°C, have a
circadian variation in Tb of only 3–4°C and do not enter tor-
por (Maddocks and Geiser 1999) despite their BMR (both
in summer and winter) falling below the boundary line
(mean residual = ¡8.8 ml O2h¡1; Fig. 4). Todies (Todus
mexicanus) have a BMR that is well below the boundary
line (residual = ¡20.8 ml O2h¡1), and whereas females
enter torpor as predicted, males appear to be homeothermic
(Merola-Zwartjes and Ligon 2000).
Discussion
Our analyses suggest that McNab’s (1983) minimal bound-
ary line for endothermy is not a reliable predictor of hetero-
thermy and homeothermy in endotherms. Although
classifying a high proportion of species correctly, we iden-
tify examples of heterothermic species, from a range of tax-
onomic groups with BMRs above this line, and there are
some examples of apparently strictly homeothermic rodents
and birds that fall below the boundary line. The classiWca-
tion functions produced by our discriminate analysis to
distinguish between heterothermic and homeothermic spe-
cies (based also on body mass and BMR) had an overall
similar success rate to McNab’s (1983) boundary line,
being slightly better for marsupials, similar for bats and
appreciably worse for rodents. However, neither method
proved reliable for distinguishing between daily hetero-
therms and those that enter prolonged torpor. For marsupi-
als and bats, patterns of heterothermy are best predicted by
phylogenetic history, although there is no signiWcant phylo-
genetic pattern in heterothermy for rodents. We discuss fur-
ther the relationship between body mass, BMR and
heterothermy, and examine the limitations of using this
relationship to predict heterothermy in endotherms.
Body mass is clearly a major factor inXuencing hetero-
thermy. Torpor is a mechanism important for both energy
and water conservation, and is particularly important for
small species (Morrison 1960; Bartholomew 1972; Barnes
and Carey 2004). A small body mass enhances heat loss,
due to a high surface area to volume ratio, so the relative
advantages of heterothermy are especially pronounced for
small endotherms. Small species cool faster, have a high
mass-speciWc energy requirement, have a greater reduction
of metabolic rate in comparison to normothermic values,
and the overall energetic costs of re-warming are smaller
due to reduced thermal inertia at smaller body masses
(Bradshaw 2003; Speakman and Thomas 2003).
Whereas some species that use torpor do have a signiW-
cantly lower BMR than those that do not (e.g. rodents) this
is not true for marsupials and bats. There are suYcient
exceptions amongst all groups to suggest that not all small
species with a low BMR are obligate heterotherms, and that
a high BMR is due not only to the cost of homeothermic
regulation. Several examples presented here (e.g. silver-
eyes, hopping mice) indicate that small endotherms, with
low BMRs (below the boundary line) are capable of main-
taining a high and stable Tb during cold exposure. Such
examples are few however, due to the prevalence of hetero-
thermy in small species (Geiser and Ruf 1995). In addition,
not all small species with a high BMR (e.g. bats, rodents)
are homeothermic, suggesting that a high BMR in small
species is not inextricably linked to the cost of permanent
homeothermy. A priori one might even predict that species
with a high BMR and the associated high costs of energy
expenditure during normothermia are more likely to enter
torpor, to compensate for this high energy expenditure.
However species with a low BMR often live in an environ-
ment that requires frugal use of energy and presumably use
torpor for the same reason. A low BMR has been associated
with environments with low primary productivity (e.g.
deserts) and with diets with a low net energy yield (e.g.
myrmecophages, folivores). Heterothermy, which is impor-
tant for the conservation of both energy and water, is an
important additional strategy for species occupying low-
Fig. 4 Relationship between mass and basal metabolic rate for birds
with known thermoregulatory strategies (n= 28, data from Ascho
V
and Pohl 1970; McKechnie and Lovegrove 2002) relative to the
boundary line. The homeothermic silvereye (Zosterops australis) is
represented with a dark symbol, heterothermic species by light sym-
bols. Daily heterotherms are represented with circles, the hibernating
poorwill (Phalaenoptilus nuttallii) with a square
J Comp Physiol B
123
energy niches (Lovegrove 2000b). Thus, species with a low
BMR may also enter daily torpor because they have a life-
style that requires a frugal use of energy during the inactive
phase of the day or year when fuels are not replenished.
Thus any association of a low BMR and heterothermy need
not be causal.
Although both the boundary line and our discriminate
analysis were reasonably successful in discriminating het-
erotherms and homeotherms, a number of species were not
correctly classiWed by either method. The limitations of
both are presumably due to factors other than the inXuence
of the relationship between body mass and BMR on pat-
terns of heterothermy. For marsupials and bats, the pattern
of heterothermy is strongly related to phylogeny. For mar-
supials, all dasyurids studied to date use daily torpor, and
all of the Burramyidae (pygmy-possums) use prolonged
hibernation (Geiser 2003; Geiser and Körtner 2004). Spe-
cies of these two groups are heterothermic regardless of
whether their BMR falls above or below the boundary line.
Other marsupials (e.g. peramelids, macropodids) are all
larger than the 87.9 g intercept of the BMR/boundary lines
but are all presumably homeothermic due to phylogenetic
aYliation rather than a relationship between mass and
BMR. The Tasmanian devil (Sarcophilus harrisii) is the
largest extant dasyurid, and although it has been suggested
that it uses daily torpor (Nicol and Maskrey 1980), its ther-
mal biology has not been investigated in suYcient detail to
conWrm torpor. The use of torpor by this largest extant
dasyurid would conWrm a strong phylogenetic rather than
mass/BMR inXuence on heterothermy. For bats, there are
also strong phylogenetic patterns. Vespertilionids show a
predominance of hibernation, small pteropodids are daily
heterotherms and large pteropodids apparently are charac-
terised by homeothermy. For these groups, phylogenetic
history and size are better predictors of patterns of hetero-
thermy than a relationship between mass and BMR.
For rodents the relationship between phylogeny and het-
erothermy is not signiWcant and the occurrence or otherwise
of heterothermy is complex, presumably further inXuenced
by a suite of habitat, climate and life history factors such as
diet. Most homeothermic species are above the boundary
line, but the exceptions suggest that species with a BMR
below the boundary line are not necessarily obligate hetero-
therms, and that species above the line may not necessarily
be homeothermic. For Phodopus sungorus BMR is above
the boundary line both in summer and winter, although the
species only enters daily torpor in winter. Winter acclima-
tised P. sungorus are capable of maintaining a homeother-
mic Tb at Ta as low as ¡69°C. Nevertheless, P. sungorus
enter spontaneous (food ad libitum) torpor in winter, even
at mild, thermoneutral Ta of 23°C (Heldmaier and Stein-
lechner 1981a; Geiser and Heldmaier 1995). In summer, P.
sungorus does not enter spontaneous torpor, although its
thermogenic capacity is substantially reduced to about 70%
of the winter capacity (Heldmaier and Steinlechner 1981a,
b). Thus data on thermoenergetics of P. sungorus do not
support a link between BMR and torpor use, nor a link
between thermoregulation and thermogenic capacity and
torpor. For birds insuYcient data are available to fully
understand the relationship between BMR, body mass and
heterothermy, and the use of torpor by birds in general is an
area that requires further investigation. Presumably, hetero-
thermy in rodents and birds is primarily determined by
adaptation to Xuctuating energy and/or water availability
(Lovegrove 2000b), with in turn is related to factors includ-
ing distribution, habitat, climate and life history traits such
as diet.
For heterothermic species, both the boundary line and
our discriminate analysis have substantial limitations for
predicting patterns of torpor. Heterothermic species with a
BMR above the boundary line are not restricted to hiberna-
tors, contradicting McNab’s (1983, 2002) suggestion; many
of the species are daily heterotherms, which use daily tor-
por exclusively. In fact, all of the heterothermic marsupial,
bat and bird species with a BMR above the boundary line
use daily torpor, whereas all hibernators fall below the
boundary line. For rodents, the BMRs of a mix of daily het-
erotherms and seasonal hibernators fall above and below
the boundary line. Our discriminate analysis had a similar
low success rate to the boundary line in separating species
that use daily torpor and those that use hibernation. The
inability of these techniques to separate these two groups of
heterotherms is presumably due to a conceptual weakness–
–daily torpor is not a reXection of poor thermoregulatory
ability or failure of heat production, and there appears to be
no physiological reason for these two groups to be divided
based on the relationship between body mass and BMR.
Both daily torpor and hibernation are precisely con-
trolled processes and there is no known physiological
diVerence in proportional thermoregulation during daily
torpor and seasonal hibernation. Although Tb in both
groups may vary over a wide temperature range when tor-
pid individuals are thermoconforming, Tb in all species
investigated so far is regulated above a species- or popula-
tion-speciWc set point by proportional thermogenesis as
during normothermia, albeit at a lower Tb (Heller and Ham-
mel 1972). There are examples of thermoregulation during
torpor by daily heterotherms for birds (e.g. hummingbirds;
Hainsworth and Wolf 1970; Hiebert 1990), marsupials (e.g.
Dunnarts and Kowaris; Geiser and Baudinette 1987) and
placentals (e.g. Siberian hamsters, shrews; Heldmaier and
Steinlechner 1981b; Nagel 1985) as well as for thermoregu-
lation during hibernation from several mammalian orders,
including marsupials (e.g. pygmy-possums; Song et al.
1997), rodents (e.g. ground squirrels, dormice; Wyss 1932;
Heller and Hammel 1972), bats (Hock 1951), and insecti-
J Comp Physiol B
123
vores (Fowler and Racey 1990). Although the average min-
imum Tb for hibernators is »6°C and is »17°C for daily
heterotherms, Tb minima show substantial overlap between
the two groups (Geiser and Ruf 1995), some daily hetero-
therms have a Tb minimum <10°C (e.g. honey possum
Tarsipes rostratus, Withers et al. 1990; hummingbird
Oreotrichilus estella, Carpenter 1974), and some hiberna-
tors have a Tb minimum >10°C (e.g. tenrecs Tenrec ecaud-
atus, Setifer setosus, Kayser 1964; Hildwein 1970) and
consequently Tb minima are not a reliable trait for separat-
ing the two groups of heterotherms. To our knowledge
diVerences in thermogenic capacity between daily hetero-
therms and hibernators have not been investigated, but
maximum re-warming rates from torpor are indistinguish-
able between daily heterotherms and hibernators (Geiser
and Baudinette 1990) suggesting that, as for thermoregula-
tion, thermogenic capacity does not diVer between the two
groups of heterotherms.
Our analyses raise the question as to why BMR should
be a predictor for torpor use. Torpor is predominantly
employed by small species in which BMR comprises only a
small component of daily energy expenditure. Conse-
quently, BMR is not likely to have a strong selective pres-
sure on torpor use by various birds and mammals. Body
mass, together with phylogenetic history is a signiWcant
determinant of heterothermy for marsupials and bats, but
not rodents. For rodents, it is highly likely that body mass
combined with habitat or food availability will provide
strong selective pressures on torpor use as well as on BMR.
Thus, our analyses suggest that it is not simply the relation-
ship between BMR and body mass alone, but rather a com-
bination of factors including body mass, phylogeny, diet,
climate and other life history traits that determine whether
or not a species is heterothermic.
Acknowledgments We are grateful to Dr. Mark Brigham for con-
structive comments on the manuscript and Dr. Phil Withers for advice
and use of his IC and cluster analysis program. Dr. Ariovaldo Cruz-
Neto kindly provided some data and references. The work was sup-
ported by the Australian Research Council and a UNE Vice Chancel-
lor’s postdoctoral fellowship to CEC.
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