Table Of ContentQuantifying aspects of the evolution of
endothermy
Peter Brice
School of Biological Sciences, St Lucia Campus, The University of Queensland, Brisbane, Qld 4072,
Australia, [email protected].
Various conceptual or qualitative models have been proposed to explain the evolution of homeothermic
endothermy from heterothermic ectothermy. Assessment of the feasibility of these models may benefit
from quantitative analyses of hypotheses deriving from them. In this study, a quantitative approach
was applied to a recent conceptual model which proposed a stepwise progression from ectothermy
to endothermy in a medium sized vertebrate “evolving” in a warm, mesic thermal environment. By
assuming that selection acted to maximise time available for activity, this study showed that endogenous
heat, whether from activity or shivering thermogenesis, increased time within nominal preferred body
temperatures only if low values of thermal conductance associated with insulation were already in place.
T
Further, this study demonstrated that benefits were enhanced if the insulation was by-passable and
C associated with a wide range of thermal conductance. Because aerobic scope was incorporated as a
A constraint to thermogenic capacity, increases in standard metabolic rate were relatively ineffective until
they were substantial and, at one stage, plesiomorphic daily torpor emerged, at least in the circumstances
R
modelled. Also emerging from the modelling were the thermal neutral zone and basal metabolic rate
T characteristic of homeothermic endotherms. Additionally, benefits from rudimentary turbinal scrolls were
S quantified for this modelled, hypothetical animal in this particular environment. This initial exploratory
study demonstrated how quantifying aspects of proposed models for the evolution of endothermy can
B
provide insight into their feasibility. In so doing, this quantitative modelling highlighted avenues for further
A
enquiry and demonstrated one tool for addressing debate about the evolution of endothermy.
Key words: modelling, endothermy, ectothermy, evolution, thermal conductance, metabolic rate
Introduction
Endothermy has apparently evolved independently iii) that heterothermy (torpor and hibernation) is
in a number of vertebrate clades; most prominently, plesiomorphic among endotherms, a remnant
at least amongst current vertebrates, in birds and of ectotherm heterothermy that was retained (or
mammals. Not surprisingly, endothermy has excited re-expressed) in many mammals, refined in those that
biologists and a number of models have been proposed needed to survive periodically harsh environments and
to explain its evolution (e.g. Crompton, et al. 1978; abandoned in those where energetic resources were
McNab 1978; Bennett 1991). Most such models are sufficient and reliable.
conceptual or qualitative. It would be instructive To develop their model, Grigg et al. (2004) compared
to investigate, and eventually compare, models in the thermoregulation of extant reptiles and mammals.
a quantitative way, perhaps evaluating advantages Based in part on data from brooding pythons and from
accruing to endotherms that evolved in the various heterothermic echidnas, they concluded that reptiles
ways proposed. and mammals share many thermoregulatory attributes
and that the differences between the classes are more
In a series of recent papers, Grigg and Beard (2000),
quantitative than qualitative.
Grigg (2004) and Grigg et al. (2004) proposed a stepwise
progression from an ectothermic therapsid towards a In this, an initial study, quantitative modelling was used to
variety of endothermic mammals, both heterothermic convert an ectotherm with lizard physiology into something
and homeothermic. Salient features of this progression approaching an endotherm with mammalian physiology
included, but were not limited to: using the step-wise progression of Grigg et al. (2004) as an
approximate guide. Specifically, a heat budget model was
i) that by-passable insulation evolved first and is a pre-
used to predict the body temperature of a medium sized,
requisite for effective maintenance of a high and stable
hypothetical animal living in a warm, mesic environment as
body temperature,
it progressed through various stages in this evolution. Time
ii) that even before the evolution of mammalian metabolic spent within specified preferred body temperature ranges
rates, the heat generated by activity or perhaps was used to evaluate advantages accruing to the animal at
by shivering thermogenesis, if retained, may have various stages of the evolution in such a way as to test the
advantages for temperature dependent physiological three salient features listed above as hypotheses deriving
processes and from the model of Grigg et al. (2004).
Theme edition of Australian Zoologist “Ecology meets Physiology”, a Gordon Grigg festschrift, edited by Lyn Beard,
Daniel Lunney, Hamish McCallum and Craig Franklin. Australian Zoologist Vol 35 (2) 2010.
Brice
Methods recalculated. The resultant time course of T reflects
b.t
the cooling or heating of the animal in response to ever
Quantitative Modelling changing equilibria which in these cases were determined
primarily by fluctuations in operative temperature (see
The modelling used and its verification are described in
below). In this way, environmental dynamics can be
more detail elsewhere (Brice 2008). Briefly, the modelling
incorporated into the modelling. This modelling was
solves commonly used heat budget equations for body
found to predict well the time course of T in various
temperature (T) of any medium sized animal in either
b
b animals including lizards and mammals in static and
static or dynamic thermal environments. It accomplishes
dynamic thermal environments (Brice 2008).
this by solving the cooling(/heating) curve equation:
Assumptions and Constraints
T = T – (T – T )e–δt/τ Eq. 1
b.t b.eq.t b.eq.t b.t–1
It was assumed that important physiological processes
for T at time t (T ) given that the thermal time proceed optimally at particular T, and further, that if
b b.t b
constant, τ = C/K where C is the overall heat capacity a capacity for more precise thermoregulation evolved,
o.eq.t
of the animal’s tissues and K is the overall thermal natural selection acted to increase the efficiency of
o.eq.t
conductance of the animal in equilibrium at time t. In physiological processes over ever more narrow ranges of
this study δt = 10 minutes. In equation 1, T is the T. Thus, a range of preferred body temperatures (T )
b.eq.t b pref
equilibrium body temperature at time t which is calculated was defined for the various simulations. Initially, this
for each t (= 10, 20, 30 ... min) by solving: specified range was wide (25 oC to 35 oC) but feasible
when compared to some extant lizards (Heatwole 1976)
M = K (T – T )+E Eq. 2 and allowed the virtual lizard more than a trivial part of
eq.t o.eq.t b.eq.t e.eq.t eq.t
the day for activity etc. Subsequently, T was narrowed
pref
and to reflect more typical mammalian physiology as evolution
progressed. The amount of time spent within T was
M eq.t = Meq.0Q10 ( T 1b0eq .t – Tbeq.0) Eq. 3 used as a response variable, reflecting the assumprepftion
that increasing time spent at these T had advantages for
b
simultaneously for T and M : the metabolic heat activity, foraging, digestion, reproduction and so on.
b.eq.t eq.t
production (M) of the animal when in equilibrium at time
In accordance with the step-wise progression proposed
t. In equation 2, E is the evaporative heat lost for the
eq.t by Grigg et al. (2004), metabolic heat, both from activity
animal when in equilibrium for a given K and T .
o.eq.t e.eq.t and from (shivering) thermogenesis, were added at an
T in this study was T , the operative temperature at
e.eq.t e.t early stage. To retain some realism, these thermogenic
time t and was the driving variable for the simulations.
capacities were constrained to being no more than about
K here was generally determined so as to maximise
o.eq.t 10 times the standard metabolic rate (SMR) for a T of 25
time spent within a range of preferred T (T ). That is, b
b pref oC, and this aerobic scope was retained throughout all the
K was varied automatically within the simulations. In the
o stages of the simulated evolution.
absence of sweating, evaporative cooling in general (E)
can be determined from respiratory evaporative heat loss Respiratory minute volume was set initially to be typical
alone as: for a lizard. Assuming a constant oxygen extraction
efficiency for all simulations, V was varied in direct
i
E = λ V(χ – h χ ) Eq. 4 proportion to M both within and between simulations.
Tb i (Tb–Tue) Ta Ta
Thus, as the evolution progressed, this modelling
where λ is the latent heat of evaporation at T, V is the took no account of the evolution of the anatomy of
Tb b i
respiratory minute volume (in ml.min-1) which may be the mammalian lung, except for a straight forward
varied with M (see below), χ is the absolute humidity of increase in capacity to aspirate increasing metabolic
T
air saturated at temperature T, h is the relative humidity rates. Similarly, turbinal scrolls, commonly associated
Ta
measured at T and T is the effect any turbinal scrolls may with the saving of heat and/or moisture in endotherms
a ue
have on the temperature of the expired air. For equation 2, (Hillenius and Ruben 2004), were assumed to be absent
E may be determined by substituting T and similarly in the initial virtual lizard. For the sake of simplicity,
eq.t b.eq.t
appropriate values for V, T etc. into equation 4. In equation they were omitted until after an endotherm-like animal
i ue
3, M and T are the initial M and T for the simulation, had been derived by the modelling, at which time they
eq.0 b.eq.0 b
but only if they are in equilibrium with T and other were included. In this way, the benefit of having turbinal
e
parameters at the start. If not, as in many of the simulations scrolls, even though the environment was warm and
in this study, other equilibrium values for a given T may be mesic, was quantified for an endotherm.
e
used as substitutes. A convenient choice used here was the
Sweating was assumed to be absent in the initial virtual
SMR that pertained (according to the simulations, below)
lizard and in all subsequent simulations. Therefore, all
for a given T in equilibrium with a given T.
b e evaporative water loss was assumed to be respiratory.
In summary, the modelling proceeds from a defined Additionally for simplicity, any panting response to high
starting point by determining T for each t and then body temperatures was omitted throughout. Thus none
b.eq.t
calculating the approach of T to T over each ten of the cooling mechanisms displayed by either reptiles or
b b.eq.t
minute interval. Note that the system may never reach mammals, other than changes in thermal conductance,
equilibrium at any stage because equilibria are constantly were included in these simulations.
Australian
350 Zoologist volume 35 (2) 2010
Evolution of endothermy
Initial Conditions was at its minimum (15 oC). It was allowed to adjust
its thermal conductance so that it heated as fast
The starting point for this series of simulations assumed a
as possible and cooled as slowly as possible, thus
lizard-like reptile of 4 kg. mass. This was because (i) thermal
simulating heating/cooling hysteresis. The proportion
inertia for an ectotherm of this size would enhance the
of time spent within a nominal T of 25 oC to 35 oC
importance of heating/cooling hysteresis and (ii) this was pref
was noted for the second day.
a size envisaged by Grigg (pers. com.) when considering
the stepwise progression outlined in Grigg et al. (2004). It 2. The same animal was placed in the same environment
was given a standard metabolic rate (SMR) according to as before, but this time it was allowed to adjust its
allometric equations cited in Withers (1992), that is 0.317 K to maximise the time spent within T . That is,
o pref
W when T was 20 oC. Its metabolic rate varied with body K was minimal to minimise heat exchange with the
b o
temperature according to a Q of 2.5. This commonly environment while 25 oC < T < 35 oC. Outside this
10 b
cited value for Q (Geiser 1988; Schmidt-Nielsen 1990) range, K was adjusted to quicken any approach to T
10 o pref
was retained throughout the study even though SMR and to slow any departure from T .
pref
was increased in subsequent simulations. A Q of 2.5 is 3. The animal from simulation 2 was given non-by-passable
10
consistent with that observed across a wide range of reptiles insulation to simulate the addition of an external coat
and mammals (White et al. 2006). of fur as discussed by Cowles (1946; 1958). That is,
The overall thermal conductance (K) was calculated from the minimum conductance was reduced to a value
o
the allometric relationships for the thermal time constant typical for mammals of this size according to allometric
(τ) in both heating and cooling lizards as derived by Grigg equations cited by Withers (1992). To conform to the
et al. (1979). Thus, K was varied initially between 3.82 concepts investigated by Cowles (1946; 1958), it was
o
W.oC-1 when cooling and 5.49 W.oC-1 when heating. assumed that thermal conductance could be varied only
in a restricted way. That is, the pelage lacked thermal
Respiratory minute volume (V) for the virtual lizard was
i windows and the degree of piloerection was more or
determined from the allometric equation cited by Withers
less fixed, as would be the case for a lizard wearing a
(1992) for reptiles. Thus, V was 222 ml.min-1 when M was
i mink coat. To simulate this, K was allowed to vary only
0.317 W. As M changed, V was varied in direct proportion. o
i by the same factor as lizards of this size in general, that
Operative temperature (T) of the environment was varied
e is, 1.4 fold between 0.665 W.oC-1 and 0.931 W.oC-1. The
daily between 15 oC and 45 oC for all simulations. Note
animal was then placed in the thermal environment
that as T differs from air temperature due to the presence
e fluctuating between 15 oC and 45 oC as before.
of insolation in particular, a T of 45 oC represented a
e 4. The animal from simulation 2 was given by-passable
daily opportunity to bask rather than a particularly hot
insulation so that K could be varied in a less restricted
day. Nonetheless, this temperature regime was warm o
way. Grigg et al. (2004) envisaged a situation where
compared to current global mean temperatures.
subcutaneous fat layers combined with variable
As the rate of evaporative cooling is determined by the
cutanous perfusion would allow both effective basking
absolute humidity gradient (not the relative humidity
and insulation in an otherwise ectothermic animal. In
gradient), absolute humidity of the environment was
this study, this was simulated as a capacity to vary K
calculated for 70 % saturation when air was at 15 oC and o
six fold from its minimum value, which assumes (i) that
held constant. This implies that no day to day fluctuations
the internal, sub-cutaneous insulation is as effective
of ambient absolute humidity were included in this study
as pelage in modern mammals and (ii) that altering
and renders daily fluctuations of relative humidity with
the cutanous perfusion to by-pass the insulation has
temperature irrelevant.
no more of an effect on K than altering the degree
o
Simulations of piloerection and cutaneous perfusion to thermal
windows in extant mammals. This seemed conservative
Note that while their step-wise model was used as a
given that Homo sapiens may vary K six-fold when
guide, the following simulations (and their numbers) do o
immersed in water baths of different temperatures
not necessarily coincide with stages 1 to 5 in the schema
(Kleiber 1961) and large arctic mammals may vary their
proposed by Grigg et al. (2004).
K as much as eleven-fold (Scholander, et al. 1950).
o
Note also that the starting points for the following Consequently, in this simulation, K was allowed to vary
o
simulations are often somewhat misleading. This is because from 0.665 W.oC-1 (Withers 1992) to 3.99 W.oC-1 for the
thermal inertia in an animal of this size is important and animal in the T fluctuations as before. SMR remained at
e
lags result in the time course of T. Therefore analyses of lizard levels and the Q of 2.5 still pertained.
b 10
the generated data were based on the second of two cycles
5. Grigg et al. (2004) proposed that locomotive activity in
of T fluctuation (from the second minimum to the third
e a lizard might contribute to facultative thermogenesis.
minimum) only. By the second “day” the T of the animal
b This was simulated by allowing the animal in simulation
at all times was determined by its (thermoregulatory)
2 activity at any T > 25 oC, the lower limit of its T .
history rather than by some arbitrary starting point. b pref
During activity, M ≥ 2.5 W (say) which is about 5
Fifteen simulations were explored (approximately in times SMR for that T. Where SMR > 2.5 W due to
b
sequence), as follows. the Q effect of T on SMR, the virtual animal’s M
10 b
1. A virtual lizard with the physiological variables was assumed to be SMR.
described above was placed in the virtual environment 6. To investigate the possibility that locomotive activity
for 2 days (2880 minutes) from the time when T might contribute to facultative thermogenesis once
e
Australian
2010 Zoologist volume 35 (2) 351
Brice
by-passable insulation had evolved, the animal in sufficient to maintain T was initiated at a T of 34
pref b
simulation 4 was also allowed activity at any T > 25 oC oC as long as the aerobic scope of 10 (40W) was not
b
with M ≥ 2.5 W in the same way as in simulation 5. exceeded. Other parameters, such as SMR, V, K
i o
range remained unchanged from simulation 11.
7. An alternative to the heat produced by activity might
be the heat produced by shivering thermogenesis (Grigg, 13. The SMR in simulation 12 was about eight times
et al. 2004). Therefore, the animal from simulation 2 that for simulations 1 to 8. Such an increase is
was given a thermogenic capacity which was initiated commensurate with the differences in SMR between
when T fell below the preferred range of 25 oC to 35 extant lizards and mammals of the same size
b
oC. Thus, M was set to that value required to maintain (Bennett, 1991; Withers 1992). However, under
T within, or to raise T to, T . However, maximum the conditions specified, T was not maintained all
b b pref b
thermogenesis was set to 5 W, equivalent to giving the “night” unlike in some previous simulations (see
animal an aerobic scope of 10. If the thermogenesis Results and Discussion). This was attributed to the
required to attain or maintain T was greater than this constraints imposed by a combination of the SMR
maximum, then no thermogenebsis was initiated. This used and the aerobic scope of 10. Therefore, SMR
reflects the assumption that natural selection may act was increased marginally in this simulation to 2
against individuals that spend energy without success. W at T ~ 15 oC or a little less than 10 fold the
b
original SMR. Consequently, V was increased to 1200
8. In this simulation an animal that had evolved by-passable i
ml.min-1 and maximum M was increased to 50 W (10
insulation but still with lizard SMR (simulation 4) was
times the SMR at T = 25 oC). Thermal conductance
allowed thermogenesis to a maximum of 5 W as per b
remained unchanged.
simulation 7. Again, this thermogenesis was initiated
14. To investigate the predicted thermoregulation of an
only when T < 25 oC and when it was sufficient to
b animal with mammalian metabolic rates and reptilian
maintain or attain T > 25 oC.
b thermal conductance, the animal from simulation 13
9. In this and the following two simulations, SMR was was given a K ranging from 3.82 W.oC-1 to 5.49 W.oC-1
increased incrementally to reflect increasing leakiness as per simulatoion 2.
of cell membranes. For this sequence of simulations, it
15. So far, no effect of turbinal scrolls had been included. To
was assumed that the animal had evolved by-passable
investigate any possible advantages turbinal scrolls might
insulation, as well as shivering thermogenesis which
impart in this warm, mesic environment, the expired
was limited by an aerobic scope of 10. An animal with
air for the animal in simulation 13 was reduced by (an
high SMR and no insulation is simulated later. Thus,
arbitrary) 5 oC throughout this simulation (T = 5 oC).
for this simulation, the animal in simulation 8 was ue
given SMR of 0.4 W and a V of 280 ml.min-1 at T ~ For all simulations the times spent within T were
i b pref
15 oC (T = 15 oC). A Q of 2.5 dictates that SMR was calculated (using data from the second day only) and
e 10
about 1 W when T ~ 25 oC and an aerobic scope of reported as number of minutes as well as percentage of
b
10 means that maximum thermogenesis was therefore the day. In some cases thermogenesis resulted in T that
b
10 W. As with all other simulations, T varied between were almost, but not quite, within T . In these cases the
e pref
15 oC and 45 oC on a daily basis for 2880 minutes, times spent within one degree of T were also calculated.
pref
humidity was 70% when air temperature was 15 oC Additionally, the effectivenesses of thermoregulation sensu
and data from “day 2” only were analysed. Hertz et al. (1993) (E) were also calculated.
f
10. In this simulation the animal in simulation 9 was given
Results
double SMR such that SMR = 0.8 W and V = 500
i
ml.min-1 at T ~ 15 oC and maximum M was 20 W. K
b o Simulations
varied between 0.665 W.oC-1 and 3.99 W.oC-1; unchanged
from simulation 9 (as well as simulation 8 and 4). 1. Body temperature of the initial lizard-like virtual animal
closely followed T throughout the (second) day (Figure
11. In this simulation the SMR was doubled again such e
1): E = 0.0372 (Table 1). The environment was the
that SMR = 1.6 W and V = 1000 ml.min-1 at T ~ 15 f
i b major source of heat during heating and the major sink
oC. Thermal conductance remained unchanged from
during cooling (Figure 1). Heat was exchanged rapidly
simulation 4. However, as a T ≥ 25 oC was maintained
b with the environment as K was high, being typical
throughout the second day in simulation 10 (see o
for lizards. However K was regulated so that the
Results), T was narrowed in this simulation. Here o
pref animal cooled more slowly than it heated inducing the
T ranged from 30 oC to 35 oC and the shivering
pref heating cooling/hysteresis and the different time lags
thermogenesis was initiated when T dropped below
b between T and T. Metabolic heat was only a minor
30 oC. This step towards homeothermic endothermy b e
element in the heat budget of this animal and varied
implies that there was a benefit to the animal from
with T due only to the Q effect. Evaporative cooling
physiological rates being optimal in a narrower range b 10
varied with M: there being a link between M and V as
of T. Presumably, this benefit outweighed the costs i
b well as an increased saturation of expired air at high
incurred by spending less time each day within T .
pref T. In this simulation, E more than compensated for M
b
12. The trend towards homeothermy progressed in this at high T and T ~ 45 oC (the highest T) throughout.
b e e
simulation where T for the animal in simulation 11 The animal spent 22 % of the day with T between 25
pref b
was further narrowed to 34 oC to 35 oC. Thermogenesis oC and 35 oC (Table 1).
Australian
352 Zoologist volume 35 (2) 2010
Evolution of endothermy
entage of evolution zard-type Ef .4759 .4980 .4950 .4908 .5190 .4844 (.4824) .5156 (.4518) .5156 (.4615) .5870 (.4529) .4969 (.3675)
erche h li
minutes and as a poposed stages in tan animal with hig Tpref t mint % 66046 75052 84058 76053 78054 1060 74 (1100)(76) 920 64 (1010)(70) 150 10 (360)(25) 570 40 (860)(60) 540 38 (770)(53)
Table 1. Effects of adjustments in thermal conductance (K) and metabolic rate (varying SMR and adding activity or thermogenesis) on the time (t in othe day) spent within given preferred range (l to u) of T (T) and the effectiveness of thermoregulation (E) for a 4 kg animal simulated at various prbpreffooof endothermy in a thermal environment where operative temperature (T) fluctuated daily between 15 C and 45 C. Data on the left derive from ethermal conductance; data of the right derive from an animal with low mammalian-type thermal conductance. Low insulation / high thermal conductanceHigh insulation / low thermal conductance SimFeaturesTESimFeaturespreff ooool (C)u (C)t mint %l (C)u (C) 1heating / cooling hysteresis252532022.0372 to maximise 1 + adjusts K253536025.051432 + non-by-passable insulation25352otime in Tpref 42 + by-passable insulation2535 5253535024.062462535××2 + activity at 5 SMR4 + activity at 5 SMR 2 + thermogenesis upto 4 + thermogenesis up to 7253536025.051482535××10 SMR10 SMR 92535×8 + 2 original SMR 25 35 10×8 + 4 original SMR(24)(35) 30 35 × begins 8 + 8 original SMR: T11pref(29)(35)to narrow 11 + T narrowed further: 34 35 12prefthermogenesis ceased late at night(33)(35) 2 + thermogenic capacity: 10 34 35 14253534024.125513×12 but 10 original SMR× original SMR(33)(35) 34 35 1513 + turbinal scrolls(33)(35)
Australian
2010 Zoologist volume 35 (2) 353
Brice
2. Adjusting K to maximise the time spent within 9. Doubling the SMR of the animal with by-passable
o
T increased the effectiveness of thermoregulation insulation and rudimentary thermogenic capacity
pref
marginally to E = 0.0514 and the time spent within (simulation 8) increased the time spent in T to 780
f pref
T to 25 % of the day (Table 1). However, metabolic minutes or 54 % of the day) and E to 0.5190 (Table
pref f
heat was still a minor element of the heat budget and 1). For the first time, readily identifiable thermogenesis
T was dictated predominantly by fluctuations in T: was initiated, once just before “mid-morning” as T
b e b
the animal was still essentially a thermoconformer increased towards T and once during the “night”
pref
(Figure 1). as T fell below T (Figure 2). However, these spikes
b pref
in metabolic rate were short-lived. The environment
3. Adding non-by-passable insulation significantly
still represented the major heat source for the animal
increased the time spent in T to 46% of the day and
pref while it warmed and metabolic heat was still a minor
E to 0.4759 (Table 1). Time lags for both heating and
f element of the heat budget.
cooling of the animal were substantial so that T was
pref
not attained until 400 minutes after the occurrence 10. Doubling SMR again while maintaining the aerobic
of minimum T (Figure 2). T was maintained until scope of 10 resulted in significant thermogenesis
e pref
10 minutes after the maximum T after which T “overnight” with T maintained more or less in T :
e pref b pref
was exceeded for another 390 minutes. On the other minimum T was 24.94 oC during this thermogenesis.
b
hand, the time lag ensured that T was maintained Consequently, the only real departures of T from
pref b
through the rest of the “night” until 10 minutes before T were those where T exceeded the upper limit of
pref b
the minimum T. Heat balance was still dominated by T in the absence of various cooling mechanisms in
e pref
sensible heat exchanged with the environment. these simulations. T was within T for 1060 minutes
b pref
(74 %) of the day and between 24 oC and 35 oC for
4. With by-passable insulation, T was reached sooner
pref 1100 minutes (76 %) of the day. The decrease in E
in the day as heat was absorbed more rapidly from the f
to 0.4844 may have been due to changes in variance
environment when thermal conductance was high
in the distribution of T (Hertz, et al. 1993). Such
(Figure 2). Thus, T was achieved 330 minutes after b
pref changes resulted from a reduction in the frequency
the minimum T, an hour earlier than when insulation
e of T < T on the one hand, but, because of the
was non-by-passable. Similarly T exceeded T for b pref
b pref lack of cooling mechanisms, no significant effect
340 minutes during the day, nearly an hour less than
on the frequency T > T on the other. In this
when insulation was non-by-passable (simulation 3). b pref
simulation, the increased M assumed a significant
As a result, the animal spent more (52 %) of its day
role in the heat budget of the animal throughout
within T with a higher E (0.4980) than when
pref f the day (Figure 2). Heat produced by metabolism
insulation was non-by-passable (Table 1).
and heat absorbed from the environment were, at
5. For an animal with reptilian thermal conductance (as different times, nearly equal.
in simulation 2), increasing and prolonging metabolic
11. In simulation 10 sufficient heat was produced
heat production through activity did not increase the
to maintain T more or less greater than 25 oC
time spent within T , although it did increase E b
pref f throughout the day. Doubling the SMR in simulation
slightly to 0.0624 (Table 1). In the circumstances of this
11 was sufficient to maintain T more or less above
simulation, evaporative heat loss exceeded metabolic
b
30 oC (minimum T was 29.92 oC) with significant
heat production, especially at high T where saturated
b
expired air carried more evaporated wbater (Figure 1). thermogenesis initiated when required (Figure 2).
Consequently, narrowing the T did not contribute
6. However, for an animal with mammalian thermal pref
to the reduction of time spent with T between 30 oC
conductance (as in simulation 4), increasing and b
and 35 oC (920 minutes or 64%) or between 29 oC and
prolonging metabolic heat production through
35 oC (1010 minutes or 70%: Table 1). Such a decrease
activity increased the time spent within T to 58%
pref of time in T correlates with the higher T above T
of its day, although it decreased E very marginally to pref b pref
f associated with higher SMR. E increased once again
0.4950 (Table 1). f
to 0.5156. By this stage metabolic heat production
7. Giving the animal with reptilian K (in simulation 2) and evaporative heat loss dominated the heat budget
o
a capacity for shivering thermogenesis with an aerobic of the animal with sensible heat exchanged with
scope of 10 had no effect on time spent within T the environment having become relatively minor
pref
or on E (Table 1). No thermogenesis was initiated throughout (Figure 2).
f
by the algorithm which included the constraint that
12. Narrowing T further to the range 34 oC to 35
thermogenesis should occur only if it resulted in T pref
b oC without further increases in SMR or aerobic
being raised to T .
pref capacity resulted in T not being maintained
b
8. Similarly, giving the animal with by-passable insulation throughout the day (Figure 2). T was maintained
b
(simulation 4) a capacity for shivering thermogenesis, during the early part of the “night”. Thereafter, as
again with an aerobic scope of 10, had very little effect M reached its maximum (40 W), T could not
pref
on its thermoregulation (Table 1). Time spent within be maintained, M ceased and T was allowed to
b
T increased by 10 minutes (which, given the 10 fall until such time as the environment became
pref
minute precision of the modelling, is not significant) a heat source. At this time, T increased due to
b
while E decreased marginally (Table 2). sensible heat absorbed from the environment. This
f
Australian
354 Zoologist volume 35 (2) 2010
Evolution of endothermy
Figure 1. Body temperature and energy flux resulting from selected simulations (numbered as in Table 1 and Methods) of
a 4 kg animal with high lizard-like thermal conductance. For each simulation, the upper panel depicts T (green line), T (red
e b
line), K (blue line) and T (between thin black lines) and the lower panel depicts M (red line), E (blue line), sensible heat
o pref
exchange with the environment (green line) and heat exchange with the body store (magenta line). Data derived from
simulations over two daily T fluctuations but were analysed only from the second cycle. See text for more details.
e
Australian
2010 Zoologist volume 35 (2) 355
Brice
Figure 2. Body temperature and energy flux resulting from selected simulations (numbered as in Table 1 and Methods)
of a 4 kg animal with low mammal-like thermal conductance. For each simulation, the upper panel depicts T (green
e
line), T (red line), K (blue line) and T (between thin black lines) and the lower panel depicts M (red line), E (blue
b o pref
line), sensible heat exchange with the environment (green line) and heat exchange with the body store (magenta line).
Data derived from simulations over two daily T fluctuations but were analysed only from the second cycle. See text for
e
more details.
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356 Zoologist volume 35 (2) 2010
Evolution of endothermy
Figure 2 continued.
Australian
2010 Zoologist volume 35 (2) 357
Brice
was supplemented by a short spike of (intense) ~32 oC, one value derived from the time lag between T
e
shivering thermogenesis until T returned to T and T in a cooling thermal environment, the other in a
b pref b
once again. Therefore, only 360 minutes (25 %) warming one. This was in contrast to experimental data
were spent with T between 33 oC and 35 oC; 150 from classical endotherms that are normally collected in
b
minutes (10 %) of the day within T (Table 1). stable (laboratory) thermal environments.
pref
13. Increasing SMR to about 10 times the original while 14. The animal with high “mammalian” SMR but with
maintaining the aerobic scope of 10 was sufficient to reptilian or lizard values for thermal conductance was
maintain T, at least above 33.88 oC (T was 34 oC unable to retain its heat: T remained largely coupled to
b pref b
to 35 oC) all “night” (Figure 2). 860 minutes (60 %) of T throughout the cycle despite prodigious amounts of
e
each day were spent with 33 oC < T < 35 oC. Failures metabolic energy used, including during periodic (but
b
in thermoregulation were due to the time T spent above short-lived) attempts at thermogenesis (Figure 1). Even
b
T . E was 0.5870 (34 oC to 35 oC) indicating the closest for a wide T of 25 oC to 35 oC, E was low (0.1255)
pref f pref f
approach to a perfect thermoregulator (when E = 1) so with time spent within this range not exceeding that for
f
far. This thermoregulation was particularly apparent the same animal with low (reptilian) SMR (Table 1).
from the relationship between T and T (Figure 3). The
b e 15. Giving the animal in simulation 13 turbinal scrolls
relationship between M and T for this animal in these
e that reduce the temperature of the expired air by 5
circumstances revealed the magnitude of shivering
oC throughout (T = 5 oC) substantially reduced the
thermogenesis increasing at T < ~ 28 oC. There is zone ue
e amount of energy needed to maintain T through
of T between ~ 28 oC and ~ 32 oC where M is nearly pref
e the “night”, although it increased M when T is high
constant. This pattern, purely an emergent property of e
(Figure 3). The reduction in M at low T was associated
the modelling, is reminiscent of the pattern exhibited e
with the substantial reduction in E as expired air at
by a classical endotherm, in this case, one with a basal
metabolic rate (BMR) of ~ 11 W. Above a T of about lower temperatures held less water vapour. As well as
32 oC (and in the absence of cooling mechaneisms) two reducing M at low T, adding the turbinal scrolls altered
e
values of M and T pertained for any given T. This was the “thermal neutral zone” to between 26 oC and 30 oC
due to the cyclicablly fluctuating thermal enevironment (Figure 3). As a result of the increased M at high T and
e
preventing the animal with significant thermal inertia therefore the associated increased T, E and time spent
b f
ever reaching equilibrium. That is, for any given T > within T were actually lowered (Table 1).
e pref
Figure 3. Body temperature (blue points) and metabolic rate (red points) as functions of operative temperature from
selected simulations showing the emergence of a thermal neutral zone and basal metabolic rate in the proposed sequence
from thermoconforming ectothermy to thermoregulating endothermy. Cooling mechanisms were absent precluding
thermoregulation above thermoneutrality and operative temperature fluctuated preventing the attainment of steady state.
Australian
358 Zoologist volume 35 (2) 2010
