Data accessibility statement:
Data and code to reproduce this study (including GitHub repository) are
available on OSF at
https://osf.io/n6m5j/
Abstract
Metabolism underpins all
life-sustaining processes and varies profoundly with body size,
temperature, and locomotor activity. A current theory explains some of
the size-dependence of metabolic rate (its mass exponent, b )
through changes in metabolic level (L ). We propose two predictive
advances that: (a) combine the above theory with the evolved avoidance
of oxygen limitation in water-breathers experiencing warming, and (b)
quantify the overall magnitude of combined temperatures and degrees of
locomotion on metabolic scaling across air- and water-breathers. We use
intraspecific metabolic scaling responses to temperature (523
regressions) and activity (281 regressions) in diverse ectothermic
vertebrates (fish, reptiles and amphibians) to show that bdecreases with temperature-increased L in water-breathers,
supporting surface area-related avoidance of oxygen limitation, whereasb increases with activity-increased L in air-breathers,
following volume-related influences. This new theoretical integration
quantitatively incorporates different influences (warming, locomotion)
and respiration modes (aquatic, terrestrial) on animal energetics.
1. Introduction
Metabolism is a fundamental
property of life, comprising all biochemical processes that transform
energy and materials from the environment into life-sustaining functions
and body structures (Humphries & McCann 2014). Metabolic rate
(indirectly estimated by respiration rate R in aerobic organisms)
is strongly linked to body size (m ), through a relationship
commonly expressed as a power function, R = amb(Kleiber 1932), where a is a constant, and b is the
scaling exponent, or allometric slope of a linear regression between logR and log m . The slope b describes the change in
log respiration rate as log body mass increases. Understanding and
quantifying the influence of body size on respiration rate has become a
central topic in ecology, where the emphasis is placed on combinations
of both physical principles and organismal adaptations (Brown et al.
2004; Kooijman 2010; Glazier 2005, 2022; White et al. 2022). The classic
description of b as having a value of 0.75 across all life forms
(Hemmingsen 1960; West et al. 1999; Savage et al. 2004) is challenged by
systematic variation in its value across taxa, lifestyles, ontogeny, as
well as with environmental conditions and physiological states (White et
al. 2007; Makarieva et al. 2008; DeLong et al. 2010; Hirst et al. 2014;
Hatton et al. 2019; Glazier 2010, 2014, 2020, 2022).
The ‘Metabolic-Level Boundaries
Hypothesis’ (MLBH; Glazier 2005,
2010, 2014) offers a mechanistic explanation for the variation in
metabolic scaling. This hypothesis proposes that variation in the
allometric slope b is influenced by factors related to body
volume (V), such as tissue maintenance and locomotive power, and factors
related to surface area (SA), such as resource uptake or waste
elimination. The relative contribution of volume or surface area-related
factors alter as the metabolic level changes. Metabolic level
(L ) increases with overall energy use, and is often quantified as
the mass-specific metabolic rate at the geometric midpoint of the mass
range covered by the metabolic scaling relationship (Glazier 2010).
According to the MLBH, for organisms that conserve body shape as they
grow, b should approach a value of 2/3 (Rubner 1883), if
SA-related processes through external exchange surfaces predominate, but
should approach 1 if V-related processes predominate (proportional to
body mass or volume). Following
the MLBH, the amount of locomotor activity and increased environmental
temperature, which both increase L , can change the slope b(Glazier 2010) by changing the relative contributions of SAversus V-related processes.
The MLBH predicts that increased
active movement and associated energy demands of locomotor musculature,
whose mass is typically proportional to whole body mass (Glazier 2005,
2010), will increase the metabolic scaling slope relative to that at
rest. During bursts of strenuous activity (maximal L ), metabolic
rate should be mainly driven by resource demand (and hence be
proportional to m1 ; Fig. 1), rather than by
surface-dependent resource supply or waste removal (Weibel & Hoppeler
2005). This extreme response is only possible because of short-term
storage of oxygen and energy in muscles and their temporary tolerance to
accumulation of wastes, such as lactic acid (Glazier 2009).
Temperature appears to affect metabolic scaling in more complex ways.
Contrary to influential models that assume that temperature affects only
metabolic level and not b (e.g., Gillooly et al. 2001), the MLBH
predicts changes in b . As temperature increases, resting
metabolic demands increase; consequently, the mass-scaling of metabolic
rate may decrease if it is increasingly dictated by fluxes through
external exchange surfaces (m2/3 in isomorphic
growers), as limits on resource supply become more influential (Fig. 1).
Glazier (2020) observed such a predicted negative relationship between
temperature and b in 10 of 13 sedentary ectothermic animals and
one plant. However, warming not only increases maintenance demands in
ectotherms, but accelerates other energy-demanding processes such as
growth, even in resting individuals (Parry 1983; Rosenfeld et al. 2015).
Importantly, although whole-body growth has been described as a
V-related process (Glazier 2010, 2020), its contribution to metabolic
scaling will depend on whether mass-specific growth rate remains
constant as the organism gets bigger. Exponential growers continue to
add new tissue in direct proportion to body mass (i.e., ∝m1 ), which some species achieve by changing
shape, thereby maintaining a high ratio of SA for resource uptake
relative to mass, as in various pelagic invertebrates (Hirst et al.
2014). But more generally, mass-specific growth rates decline during
ontogeny, as widely observed in vertebrates and several benthic
invertebrates (von Bertalanffy 1951, 1957; Lee et al. 2020).
Therefore, increasing overall
growth rate and its attendant costs in most animals, whose growth
decelerates during ontogeny, is expected to contribute to loweringb below 1. Another effect of temperature on metabolic scaling
depends on how it affects locomotor activity. Glazier (2020) found that
in contrast to 71% of 14 sedentary species that showed a negative
relationship between b and temperature, significantly fewer (18%
of 165) mobile species showed a negative relationship, supporting the
idea that warming-enhanced locomotion, which includes contribution of
muscular output (considered approximately proportional to body mass),
mostly countered SA-influenced reduction in b . Clearly,
therefore, the mass-scaling of metabolic rate predicted by the MLBH
depends on the relative influence of different processes that scale
differently with body mass (e.g., SA- versus V-related
processes). A major challenge for predictive ecology is to identify
situations when particular influences on metabolic scaling
predominate.
We propose that combining a second theoretical approach with the MLBH
may help to identify when particular processes with certain
mass-dependences (e.g., SA-related versus V-related) predominate.
Specifically, the effects of temperature and activity on metabolic
scaling may differ between aquatic and terrestrial organisms due to
different physical properties of their environments. Water is 800-fold
denser, 60-fold more viscous and contains 43-fold less oxygen than air,
making breathing in water more energy-costly than in air (Dejours 1981;
Makarieva et al. 2008; Gillooly et al. 2016). Moreover, the ability of
water-breathers to increase their oxygen bioavailability tends to be
less sensitive to warming (Einum et al. 2021; Deutsch et al. 2022) than
does oxygen demand (metabolic rate), which typically doubles with 10 ℃
of warming in both water- and air-breathers (Seebacher et al. 2015). For
water-breathers, warmer temperatures and larger sizes are expected to
combine to place a greater challenge on supplying sufficient oxygen, as
the SA ratio for respiratory exchange relative to body mass is reduced
(Atkinson & Sibly 1997; Rubalcaba et al. 2020). Aquatic ectotherms,
whose ancestors had experienced oxygen limitation at large sizes under
warm conditions (the ‘Ghost of Oxygen Limitation Past’; Verberk et al.
2021; Atkinson et al. 2022), are predicted to have evolved adaptations
that enable them to avoid oxygen shortage as size and temperature both
increase.
Such
avoidance strategies could include reduction in the rates of growth and
metabolism as size and temperature both increase, and hence reduceb . While Glazier (2020) anticipated that oxygen availability may
underpin more negative b -temperature relationships in aquaticvs . terrestrial ectotherms (25 vs . 16%), aquatic species
conversely showed greater increases in b between resting and
maximally active states (Glazier 2009), adding uncertainty to this idea.
Here, we combine these two
theoretical approaches to quantitatively investigate impacts of
temperature and activity on intraspecific metabolic scaling in
ectothermic vertebrates. Ectothermic vertebrates are ideal to test the
MLBH predictions quantitatively, because they belong to a monophyletic
clade (Subphylum Vertebrata) showing diverse ontogenetic changes in
metabolic scaling, but which otherwise share common biological traits,
namely: (i ) near-isomorphic and indeterminate (continuous
post-maturational) growth; (ii ) closed circulatory systems and
specialised respiratory organs, such as lungs or gills, facilitating the
comparison between water- and air-breathing species (Shelton et al.
1986); and (iii ) physiological performance and body temperature
intrinsically linked to ambient temperature (Angilletta et al. 2002),
making it easier to control for temperature when examining the effect of
activity alone. Studying vertebrates rather than the phylogenetically
diverse invertebrates with varied respiratory and circulatory systems
avoids complications from profound and variable body-shape changes over
ontogeny that affect surface area for respiratory exchange, hence
metabolic scaling, observed in diverse aquatic zooplankton and
cephalopods (Hirst et al. 2014).
A key feature of this investigation is to quantify how the relative
importance of two influences on energy use – temperature and locomotor
activity – on the metabolic scaling slope b , depend on whether
animals are air-breathers or water-breathers. We first hypothesise thatb decreases more steeply with warming in water-breathers, which
are influenced by (SA-related) avoidance of oxygen shortage. Secondly,
we expect that b increases more steeply with activity level in
air-breathers, due to increasing metabolic contributions from
(V-related) musculature, whereas the muscular contribution in
water-breathers may be countered by pressures to reduce oxygen
consumption. Through a meta-analysis that compares water- and
air-breathing vertebrates, we test the degree to which b changes
as metabolic level (L ) increases within species: (1) with warming
of inactive individuals and (2) with increasing activity.
We,
therefore, quantify for the first time the overall magnitude of
intraspecific change in b with L across the range of
activity levels and temperatures in water- and
air-breathers.
As
predicted, our findings show that b decreases with
temperature-increased L only within water-breathers, whereasb overall increases with activity-increased L within
air-breathers. Our findings
highlight the value of combining more than one theoretical approach to
increase the predictive potential of ecological theory.
2. Materials and Methods
2.1. Data collection
To test the relationship between the slope (b ) and metabolic
level (L ) with increasing temperature, we searched the literature
for studies that measured metabolic scaling during ontogeny in at least
two temperature treatments of the same species, complementing the
intraspecific datasets of Glazier (2005, 2020). Searches were carried
out with Google Scholar, Web of Science and OATD (Open Access Theses and
Dissertations), using the names of the target taxa (i.e., ‘fish’,
‘amphibian’ or ‘reptile’) followed by terms as ‘<name of
taxon> + metabolism’, ‘+ metabolic + rate’, ‘+ respiration
+ rate’, ‘+ oxygen + consumption’, all including ‘temperature’. Finally,
we checked the reference lists and citations of all relevant papers
(i.e., those including the search terms in the title) for related
studies. Here, we only included estimated parameters from scaling
regressions in non-active, unstressed animals (i.e., showing no or
minimal locomotion), to minimise the effects of muscular activity on
metabolic scaling (Glazier 2020). Sets of regressions from studies were
grouped by experimental conditions (e.g., metabolic states, such as
resting or routine metabolism, if different states were measured) in the
same species.
Second, to test the relationship between b and L with
increasing locomotor activity, we searched the literature for studies
that measured ontogenetic metabolic scaling in at least two activity
levels in the same species at the same temperature, complementing the
dataset of Glazier (2009). The literature search was identical to that
above but replacing ‘temperature’ with ‘activity’. Again, we grouped
regressions according to experimental conditions, into single studies,
and the same species. Active metabolic rates here were usually measured
during sustained activity, including freely moving animals (e.g.,
Wood et al. 1978;
Du Preez et al. 1988),
measurements of active (e.g.,
Brett & Glass 1973) and maximum
metabolic rate through experimentally forced exercise at peak locomotory
performance (e.g., Rao 1968;
Garland 1984), activity sustained
to near or complete exhaustion (e.g.,
Brett 1965;
Walton
1988), or immediately after (e.g.,
Killen et al. 2007).
Species were grouped into their principal respiration modes (water-vs . air-breathers). For air-breathing fish, we preferred
regressions based on bimodal respiration (i.e., aquatic + aerial) when
available, as this is their normal behaviour in nature
(Graham & Wegner 2010). We
excluded regressions measured in fish larvae only, given that this life
stage exhibits different metabolic influences from those on non-larval
stages (Glazier 2005), related to exponential growth and high
surface-area of respiratory organs
(Post & Lee 1996). All
regressions of amphibian species were based on aerial respiration. We
disregarded non-statistically significant regressions (p ≥ 0.05,
which excluded only 6). When equation parameters or mass ranges were
missing in a study, data were extracted from figures using
WebPlotDigitizer v4.4 (Rohatgi
2020), performing regressions, if needed, through ordinary least squares
models of log-log data. Metabolic
levels were calculated as the mass-specific metabolic rate at the
geometric mass-midpoint of the mass range of each regression, and
converted to mg O2 g wet mass-1h-1.
All
regressions were given equal weight in subsequent analyses, rather than
giving more weight to regressions with lower uncertainty in b ,
because for many studies the information needed to perform such
weighting was not available.
2.2. Data analyses
We assessed data comparability by
checking for systematic differences between datasets (see Appendix S1 –
S2). Specifically, we checked whether scaling regressions covered
similar mass ranges in water- and air-breathing species, and whether
experiments measured comparable increases in metabolic level by either
temperature or activity, as differences in these factors might influence
the change in slope b (Glazier 2020). We also checked that
acclimation duration showed no obvious influence on b . Moreover,
to minimise the variation in metabolic level due to variation in mass
between regressions within experiments, we excluded regressions whose
mass-midpoints were too dissimilar (i.e., differing by >
0.5 orders of magnitude) to the rest of the set (Appendix S3)
We determined whether temperature and activity underpin the
intraspecific variation in slopes b of ectothermic vertebrates
through their effects on metabolic level (L ), and whether these
effects differ between air- and water-breathers, using Bayesian
phylogenetic multilevel models. We used linear models with b as
the response variable and log10 L as an
explanatory variable because: (i ) the MLBH predicts a linear
relationship between b and log-transformed L (Glazier
2010) when only one of temperature or activity is varied (Fig. 1);
(ii ) the change in b is expected to be mediated through
the change in L , but not the opposite; and
(iii )
multilevel models allow estimation of variance in b within
species and experiments (Bürkner
2018). Moreover, using log10 L as an explanatory
variable enabled us to examine the increase in metabolism with warming
or activity in a continuous manner, and hence quantify and compare the
effects of these influences on b .
To determine the effect of temperature-increased L on b,and whether this effect differs between water and air-breathers, we
fitted a regression model with a global intercept (β0),
and the fixed effects of log10 L(βL), animal
group according to respiration mode (air- or water-breather,
βg) and the interaction between log10L and group (βLg), as described in the Appendix
(S4). We used a Student’s t distribution to describe errors inb , since this distribution is robust against outliers (Gelman &
Hill 2006). We included two random effects: species relatedness with a
variance-covariance matrix estimated from a phylogenetic tree (with
species-specific intercepts ψk) and an experiment effect
(with experiment-specific intercepts ϕ0j and slopes
ϕLj).
We
included the phylogenetic relationship among species as a random effect
because evolutionary history influences metabolic scaling in vertebrates
(Uyeda et al. 2017), possibly through its effects on geometry. We
searched species names in the Open Tree of Life
(https://tree.opentreeoflife.org) and built phylogenetic trees through
package ‘rotl’ (Michonneau et al. 2016). Polytomies (> 2
species sharing a direct ancestor) were resolved using the functionmulti2di in package ‘ape’ (Paradis & Schliep 2019), which
transforms polytomies into a series of random dichotomies with one of
several branches of length close to 0. Variance-covariance matrices on
these trees were calculated following Grafen’s method (Grafen 1989)
using ‘ape’ package. We also
assessed the relevance of phylogenetic signal to our analysis by
comparing with models that included species identity but not
phylogenetic effects (Appendix S5). By allowing experiment-specific
slopes, we accounted for variation in the strength of the relationship
between b and log10 L (Harrison et al.
2018), which is expected under varying experimental conditions (Glazier
2020). To analyse the effect of
activity-increased L on b , we fitted a similar model but
also including the effect of experimental temperature (in ℃,
βT), since temperature and activity exert opposite
effects on b according to MLBH predictions (Fig. 1).
We used a mix of weakly informative and informative priors. We applied
an empirical estimate of the effect of log10 Lbetween species (Killen et al. 2010) and MLBH predictions of the
intercept (Glazier 2010), as means of the normal prior distributions for
βL, and β0, respectively. We fitted
models using package ‘brms’ (Bürkner 2017, 2018) in R v. 4.2.0 (R Core
Team 2022), with the NUTS algorithm and four chains of 3000 warm-up and
16000 sampling iterations (Hoffman & Gelman 2014). Convergence was
checked through potential scale reduction factors
(R̂ , Gelman et al. 2003).
Residuals and trace plots were inspected using packages ‘ggmcmc’
(Fernández-i-Marín 2016),
‘bayesplot’ (Gabry et al. 2019),
and ‘tidybayes’ (Kay 2022). We
checked that we could recover
known parameters by simulating 10 data sets under the temperature-effect
model, with posterior mean parameter values and the same structure as
the real data, and fitting the model to these simulated data sets
(Appendix S4). Data and code are available on GitHub
(https://github.com/GuilleGarciaG/Metabolic_scaling_ectothermic_vertebrates).
2.3. Extending the MLBH: quantifying
effects of increased L onb
To quantitatively extend the MLBH, we calculated active metabolism by
adding a term aʹm to the inactive metabolic rate
(Rmin ), so that active respiration isRmin + aʹm . The term aʹm (in mg
O2 h-1) reflects how muscular power
elevates metabolic rate, with aʹ = 0 for an inactive organism,
and increasing with activity. The active term is thus assumed to be
proportional to m (Glazier 2009, 2010). We examined the change inb with activity-increased L using the first derivative of
total log R with respect to log m , evaluated at a standard
body mass of 10 g (see Appendix S6). This equation (eq. [S7])
predicts the effect of activity on b . The change in b andL (mean ± standard deviation) between inactivity and maximal
activity from the literature was compared visually with that expected
under this model for water- and air-breathing species.
3. Results
We collected 523 metabolic scaling regressions for 69 water-breathing
species (66 teleosts and 3 elasmobranchs) at temperatures between −1.8
°C and 37 °C, and 43 air-breathing species (4 amphibians and 39
reptiles) at temperatures between 4 °C and 45 °C (Table S1). These
experiments covered, on average, similar increases of metabolic level
(L ) in inactive water- and air-breathers (0.12 vs . 0.19 mg
O2 g-1 h-1,
respectively). Moreover, we compiled 281 scaling regressions at
different activity levels, from inactive to maximal metabolic rates, for
37 aquatic species (35 teleosts and 2 elasmobranchs), and 10 terrestrial
species (4 amphibians and 6 reptiles) (Table S2). The latter experiments
comprised, on average, smaller increases in L due to locomotor
activity in water- than in air-breathing species (0.24 vs . 0.90
mg O2 g-1 h-1,
respectively). This is partially because only a third of experiments
measured minimal and maximal L in water-breathers, whereas all
but one experiments included both measures in air-breathers.
Additionally, the difference in activity-increased L may relate
to water-breathing species exhibiting lower mean aerobic scopes (i.e.,
the difference between max. and min. L ) than air-breathing
species (0.34 vs . 1.35 mg O2g-1 h-1). Last, mass-midpoints of
regressions varied over 4 orders of magnitude across species in the
datasets, whereas mass ranges covered by the regressions were similar
between water- and air-breathers, spanning on average over one order of
magnitude.
Our models showed that the values of slopes b were not clearly
different between water- and air-breathing species, as 95% equal-tailed
credible intervals (CI) of the effect of groups overlapped 0 (Table 1),
under both warming (βg = −0.03, CI: (−0.21, 0.16)) and
increasing activity (βg = −0.11, CI: (−0.44, 0.23)).
However, the effect of increasing log10 L by
warming and by increasing activity on b did vary between water-
and air-breathers (Table 1). Under warming conditions (Fig. 2A, B),
water-breathers showed strong evidence of a negative relationship
between b and log10 L(βL+ βLg = −0.09, CI: (−0.13, −0.05)), yet this coefficient
was strongly centred on zero in air-breathers (βL =
−0.002, CI: (−0.04, 0.04)), which showed a species’ mean b = 0.74
(±0.14 standard deviation). Conversely, under increasing activity (Fig.
2C, D), b showed a positive relationship with
log10 L in air-breathers
(βL = 0.19,
CI: (0.09, 0.30)), but no overall
effect in b was found in water-breathers
(βL +
βLg = 0.04, CI:
(−0.02, 0.10)). Furthermore, the
mean estimate of global intercept (i.e., predicted b at Lof 1 mg O2 g-1 h-1)
fell between 2/3 and ¾ in the model for temperature-increased L(β0 = 0.73, CI: (0.58, 0.87)), whereas this estimate was
close to 1 in the model for activity-increased L(β0 = 0.98, CI: (0.68, 1.27)).
The quantitative prediction of changes in b associated with
activity-increased L , utilising the MLBH assumption that muscular
demands were proportional to body mass (see Methods: 2.3. Extending the
MLBH), could predict well the changes seen in air-breathing amphibians
and reptiles, but not in fish (Fig. 3): the mean b and its
standard deviation for fish at maximal activity fall below the expected
value under the MLBH for a given increase in L .
4. Discussion
By combining two theoretical approaches – \soutfrom the MLBH and the
Ghost of Oxygen Limitation Past – we extended predictions of metabolic
scaling beyond those of either hypothesis individually. Increased
locomotor activity is predicted by the MLBH to increase metabolic
scaling slopes (b ) towards 1, whereas the Ghost of Oxygen
Limitation Past predicted that warming – beyond any increase inb due to locomotor activity (Glazier 2020) – contributes to
reducing b in water-breathers only, as expected from an evolved
avoidance of oxygen limitation at large sizes. Our analysis, using a
diverse set of ectothermic vertebrates, temperatures, and activity
levels, supported these predictions (Fig. 2; Table 1).
We showed that intraspecific
slopes b decreased as log10 metabolic level
(L ) increased with temperature only within water-breathing
vertebrates (teleosts and elasmobranchs). Conversely, we found an
overall increase in b as log10 L increased
with activity only within air-breathers (amphibians and reptiles). Our
theoretical approach to understanding intraspecific variation in
metabolic scaling combines extrinsic (temperature) and intrinsic
(activity) influences on organismal physiology, together with different
respiration modes and their evolutionary pressures.
4.1. The effect of
temperature
We suggest that metabolic scaling
slopes generally decrease with warming in fish, but not in air-breathing
amphibian and reptiles, because of greater risks in water-breathers of
oxygen becoming limiting at increased temperatures as individuals grow
(Fig. 4A, B). Specifically, metabolic rates of water-breathers at
increased temperatures are likely influenced to a greater extent than
for air-breathers by surface area for oxygen uptake, because energetic
costs of increasing water flow over respiratory surfaces to meet
increased demand are higher (and oxygen-demanding) (Verberk et al.
2021). Oxygen is thus expected to become limiting in fish when
respiratory SA, hence oxygen-supply capacity, is unable to satisfy the
increased demand with increasing temperature and body size
(von Bertalanffy 1964;
Pauly 2021), providing there are
no physiological or behavioural adjustments that avoid oxygen shortage
(Atkinson et al. 2006; Atkinson
et al. 2022). However, if increased temperature is associated with
increased risks of oxygen shortage at large sizes in a predictable
manner, such adjustments could evolve as adaptive plastic responses to
warming such that water-breathers avoid insufficient oxygen (‘gasping
for breath’; Pauly 2010), especially under conditions of low exertion
and non-extreme warming (Verberk et al. 2021).
Besides measures to improve oxygen-supply capacity at increased
temperatures as water-breathers grow (e.g., Nilsson et al 2012; Funk et
al. 2021; Woods et al. 2022), oxygen demands may be reduced. Metabolic
costs are not just from tissue maintenance, but also include overhead
costs of growth, which contribute strongly to metabolic rate
(Parry
1983), even in resting individuals (Rosenfeld et al. 2015). Growth rate
and its metabolic cost increase with temperature mostly in young, small
individual fish, but barely change in large, old ones
(Imsland &
Jonassen 2001; Barneche et al.
2019), which would lead to lower slopes b with warming.
Fast-growing fish in warm waters are therefore expected to show lowerb values than slow-growing fish in cold waters, as the latter
exhibit slower but generally more sustained growth throughout ontogeny
(see Imsland & Jonassen 2001; e.g., Björnsson & Steinarsson 2002;
Lefébure et al. 2011).
Conversely, air-breathing species
do not seem to show such abrupt deceleration of growth rates over
ontogeny with increasing temperature
(e.g.,
Rhen & Lang 1995;
Roosenburg & Kelley 1996;
Steyermark & Spotila 2001), yet
further research is needed to test this hypothesis. This increasingly
steep reduction in both mass-specific growth and mass-specific metabolic
rates over fish ontogeny with warming may have evolved as a plastic
response to maintain a safety margin for oxygen uptake (i.e., aerobic
scope; Atkinson et al. 2006), thus avoiding oxygen shortage under
specific conditions (Jutfelt et
al. 2021). Complementarily, high b values in cold, viscous waters
may result from large fish experiencing less drag and smaller boundary
layers than small individuals, hence improved oxygen-uptake capacity
(Verberk & Atkinson 2013). In resting, slow-growing individuals at cool
water temperatures, b would thus approach 1 following predominant
V-related influences from body maintenance.
The absence of a general relationship between b and
temperature-increased L within air-breathing amphibians and
reptiles (Fig. 4B), supports the prediction from the metabolic theory of
ecology that warming affects only metabolic level but not the predicted
¾-power scaling (Gillooly et al.
2001; Brown et al. 2004), albeit within a specific set of species and
conditions. This lack of relationship between b and L with
temperature in amphibians and
reptiles could be attributed to a balance between influences from
SA-related processes (e.g., water loss avoidance or heat conservation)
and V-related maintenance (discussed in Glazier 2020).
4.2. The effect of activity
Following the MLBH prediction
that increased muscular activity during locomotion increases the
relative influence of V-related over SA-related processes (Glazier 2008,
2009), we found that the slope b increased with L as
activity increases in amphibians and reptiles. However, no such overall
effect of activity on b was observed within fish species.
These results contrast with the
higher intraspecific b values with locomotion in aquatic
ectotherms found by Glazier (2009), possibly because that study compared
resting vs . maximal activity measurements, whilst we investigated
a wider range of activity levels and species (see Appendix S7). Our
quantitative prediction for the effect of activity on b –
assuming a metabolic cost of locomotor activity proportional to body
mass – was consistent with the
observed b values at maximum activity in air-breathing but not in
water-breathing species (Fig. 3), which provides further evidence of an
influence that prevents b from increasing during muscular power
production in fish (Fig. 4C, D). Again, we propose that evolved
avoidance of oxygen shortage in water-breathers may explain this
finding. We posit that the oxygen costs of aerobically fuelled
locomotion will not generally be proportional to body mass (or V) in
water-breathers, but will be disproportionately less at larger sizes,
following selection against large individuals that over-exert themselves
to the extent that oxygen shortage reduces fitness.
High activity and warm temperature would therefore be expected to
combine to lower b in water-breathers, but increase it in
air-breathers. Indeed, warming-induced reductions in aerobic scope were
predicted in a recent quantitative model and supported by empirical data
on 286 teleost species (Rubalcaba et al. 2020), suggesting that larger,
active individuals may be more susceptible to oxygen limitation in
warmer water. Conversely, aerobic scopes exhibit no such decrease with
warming in amphibians and reptiles (e.g., Wright 1986; Gifford et al.
2013).
4.3. Intraspecific variation in metabolic scaling:
Improving explanatory
power
Theory to explain and predict
variation in ecological energetics in general, and intraspecific
metabolic scaling in particular (see comments on interspecific variation
in Appendix S7), need to account for context, which includes: metabolic
state or activity level; body and ambient temperature; and selection
pressures on resource supply, demand and allocation among metabolic
activities (Glazier 2022). For example, Glazier (2020) partly explained
why thermal effects on metabolic scaling in ectotherms were not uniform,
because of their dependence on activity level, consistent with the MLBH.
Building upon previous work
(Glazier 2010, 2020), we have extended the explanatory power of the MLBH
by incorporating the idea of evolved avoidance of oxygen limitation in
warm, large, and active water-breathers. We found that responses of
intraspecific metabolic scaling to warming and activity did indeed
differ as predicted between air- and water-breathing ectothermic
species. We have also presented new quantitative predictions for the
effects of locomotion on metabolic scaling, assuming locomotor costs
were proportional to body mass. In so doing, we have bridged empirically
the predictions from two hypotheses, the MLBH and the Ghost of Oxygen
Limitation Past.
5. Acknowledgements
We are grateful to Professor Douglas S. Glazier for insightful
discussions, and for generously providing data. We also thank Dr Wilco
Verberk and Dr Félix Leiva for their advice on statistical analyses, Dr
Alejandro Martínez for his helpful suggestions, and three anonymous
referees for their thorough feedback on a previous version of this
manuscript. GGG was funded by a PhD studentship from the School of
Environmental Sciences, University of Liverpool (UK).
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7. Tables
Table 1. Posterior mean
estimates, 95% credible (equal-tailed) intervals and effective sample
size of posterior distributions for the fitted parameters of the model
examining the variation in slopes b with log10metabolic level (L , in mg O2h-1 g-1) as temperature or activity
level increase. These models incorporated the respiration mode (water or
air) and the interaction effect with log10 L , to
test whether b changes differently with L between water-
and air-breathers under warming conditions or increasing locomotion.
Experimental temperature (℃) was included as an additional covariate in
the model analysing the effect of activity, as temperature and
activity-increased L are expected to show opposite effects onb (Fig. 1).