Co-variation and trade-offs in ontogenetic scaling of growth and metabolic rates in teleost fish

Abstract

The influential metabolic theory of ecology proposes that metabolic rate determines growth and ecological processes in a universal, size-dependent manner, scaling with body mass^0.75. Conversely, newer life-history-optimisation theory suggests that metabolic scaling varies due to evolutionary optimisation of energy allocation, predicting negative correlation between metabolic rate and growth. However, metabolic scaling has almost exclusively been investigated across individuals or species, not within individuals through ontogeny. By measuring body mass and metabolic rate longitudinally an average 6.6 times within the same 389 individuals from seven fish species, we find that within-individual ontogenetic scaling of standard (maintenance) metabolic rate correlates positively with scaling of growth, while scaling of aerobic scope correlates negatively. Accelerating ontogenetic growth thus appears to come at a cost of reduced metabolic scope to support functions beyond maintenance. Our results suggest that underappreciated variation in growth can explain why metabolic scaling varies, challenging dogmatic ¾-power scaling and life-history-optimisation theory.

Analysis of metabolic scaling in teleost fish shows that ontogenetic scaling of growth correlates positively with maintenance metabolic demands but negatively with metabolic scope. These results help explain variation in metabolic scaling and energetic trade-offs.

Introduction

Body size and organismal biomass are major drivers of biological patterns in nature, influencing metabolic rate, growth, reproduction, and ecological interactions^1–5. Most biological rates change (scale) disproportionately with body mass following an allometric power function, rate = a × mass^b, where a is the scaling coefficient and b is the scaling exponent¹. Of all biological rates, the scaling of metabolic rate with body mass has received the most attention since Kleiber^6,7 produced his famous ‘mouse-to-elephant curve’, showing that metabolic rates of endotherms scaled with body mass with an exponent (b) of approximately 0.75. This ¾-power scaling relationship has since been proposed to be a universal law in biology^8,9, explained by the fractal nature of resource delivery networks, such as the vascular system in vertebrates and xylem in trees^10,11. This has, in turn, laid the foundation for the metabolic theory of ecology⁹, which posits that the canonical ¾-power scaling relationship between metabolic rate and body mass governs the scaling of all ecological processes, because metabolic rate controls how energy is allocated to growth, reproduction, and maintenance^9,12. The metabolic theory of ecology has had an immense influence on metabolic and life-history theory¹³. However, the notion that metabolic rate should scale equally steeply for all organisms (be constrained to a fixed value of b) has been repeatedly challenged, as multiple physiological, ecological, and taxonomic factors have been proposed to influence the steepness of metabolic scaling^2,13–21. Among these, the role of growth rate in metabolic scaling has been much debated^19,22–26.

Growth requires metabolic energy and proximally determines body size. Growth could thus be an obvious driver of variation in metabolic scaling, but the prevailing view in highly influential metabolic growth models has been that it is metabolic scaling and variation therein that governs growth, rather than the other way around^14,27,28. Others have, however, proposed that metabolic rate adjusts to growth, with the cost and regulation of growth driving metabolic rate and its scaling^2,23,29–31. Alternatively, life-history theory suggests that the mass-scaling of metabolic and growth rates has co-evolved to maximise fitness (lifetime reproductive success) under different selection pressures^{16,24,32–36}, such that one trait does not govern the other³⁵. Evidence supporting co-evolution includes artificial selection experiments on insects, which suggests evolutionary adaptability of allometric scaling between morphological traits^37,38. Selection for body size has also been found to affect the scaling of metabolic rate in snails³⁹. In addition, it has been found that natural populations of amphipods subjected to different mortality regimes vary in the scaling of both metabolic and growth rates³⁶. However, the causal relationship between the scaling of metabolic rate and growth rate remains highly debated despite a century of work on metabolic theories^2,17,19,25.

A possible explanation for the lack of consensus is that almost all previous work on metabolic scaling has investigated how metabolic rate changes with body mass across species or across individuals of different sizes within species^19,40. These types of scaling relationships are termed ‘evolutionary scaling’ and ‘static scaling’, respectively, when they are evaluated across species or individuals at comparable developmental stages^41–43. Scaling across individuals within species at different developmental stages is often termed ‘ontogenetic scaling’ (sometimes ‘across-individual ontogenetic scaling’, e.g. refs. ^23,26). While such studies have provided valuable information on how growth and metabolic rate might be connected (e.g. refs. ^14,36,39,44), they may miss key aspects of organismal development, as body growth and allocation of metabolic energy to bodily functions occur within individuals. Any past variation in ontogenetic developmental trajectories of growth and metabolic rates that could be under selection would thus be overlooked with an across-individual scaling approach, as it only provides a snapshot view of each individual’s metabolic rate at the time of measurement, and no information on its growth history or the selective removal (e.g. mortality) of individuals with specific phenotypes before measurements. This can lead to oversight of variation in across-individual scaling relationships, as they are shaped by co-variation in within-individual ontogenetic scaling and growth⁴². Across-individual ‘ontogenetic’ studies have been criticised for these reasons and may thus not be representative of true ontogenetic scaling⁴¹. The terminology is also unfortunate, as ‘ontogeny’ (or ‘ontogenesis’) refers to the development of an individual organism^45,46. However, how metabolic rate scales within individuals as they grow through ontogeny has been almost entirely overlooked (see refs. ^19,47–50). While less common in metabolic studies, work from the related field of morphological allometry has shown how variation in individual growth trajectories and ontogenetic size-scaling of morphological traits can shape static and evolutionary scaling relationships^42,43,51,52.

Thus, to further our understanding of how the ontogenetic (within-individual) scaling of metabolic and growth rates co-vary, we measured oxygen uptake rates (as estimates of metabolic rates) and body mass longitudinally within 389 individuals from seven fish species: brown trout (Salmo trutta), rainbow trout (Oncorhynchus mykiss), cunner (Tautogolabrus adspersus), blue-green damselfish (Chromis viridis), orange-fin anemonefish (Amphiprion chrysopterus), Trinidadian guppy (Poecilia reticulata), and zebrafish (Danio rerio). As each individual fish was repeatedly measured for metabolic rate and body mass on average 6.6 times (ranging between four and twelve times), our dataset contains 2449 and 1989 measurements of standard (maintenance) metabolic rate (SMR) and growth rate, respectively, with growth rate being the absolute increase in body mass over time between two consecutive measurements. In addition to our measurements of SMR, we also measured maximum (active) metabolic rate (MMR) of individuals from all species except zebrafish (1875 measurements). This further allowed us to calculate aerobic metabolic scope, the difference between MMR and SMR, which represents the total capacity to allocate oxygen and energy to activities other than maintenance. We calculated metabolic scope as both absolute aerobic scope (AS; MMR–SMR) and factorial (relative) aerobic scope (FAS; MMR/SMR). To examine variation in the ontogenetic scaling of metabolic traits (SMR, MMR, AS, and FAS) and their relationships with the ontogenetic scaling of growth rate, we correlated individual ontogenetic scaling exponents (b) for metabolic traits with those for growth rate both within and across species.

While our primary focus is on variation in within-individual ontogenetic scaling, our data also allow us to quantify scaling relationships across individuals within a species (at each individual’s average body mass across the study) and compare these to ontogenetic scaling. We refer to this across-individual scaling as ‘static scaling’ herein, because individuals from each species were from the same cohort and thus of approximately the same age. However, the precise developmental stages of all individuals at their average body masses are unknown. Thus, our across-individual scaling may not represent static scaling in its strictest sense.

Our focus on within-individual ontogenetic scaling provides a new and interesting comparison to more traditional work on the scaling of metabolic rate (mainly maintenance metabolic rate) and growth at higher taxonomic levels (e.g. refs. ^2,24,35,53). We show that variation in ontogenetic metabolic scaling among both individuals and species can be explained by variation in the ontogenetic scaling of growth rate. We also identify a trade-off whereby accelerating ontogenetic growth comes at the cost of both elevated SMR and reduced metabolic scope. Since metabolic scope represents an individual’s capacity to perform energy-demanding tasks beyond SMR, such as digestion, growth, activity, and reproduction, this is likely to have fitness consequences (e.g. refs. ^54–58).

Results and discussion

Ontogenetic scaling of metabolic rates

The overall ontogenetic scaling of metabolic rate across species was similar for SMR, MMR, and AS, with average scaling exponents (b) of approximately 0.9 for all traits (Fig. 1 and Table 1).

Fig. 1. Ontogenetic and static body-mass-scaling of metabolic traits and growth rate for seven species of teleost fish.

Body mass-scaling of A standard metabolic rate (SMR), B maximum metabolic rate (MMR), C aerobic scope (AS; MMR–SMR), D factorial aerobic scope (FAS; MMR/SMR), and E growth rate. Scaling within individuals (ontogenetic scaling) is presented as thin, solid, coloured lines. Scaling across individuals within species (static scaling) at each individual’s average body mass is presented as dotted coloured lines. The overall mean ontogenetic scaling across species is represented by the solid black line. The dotted black line is a reference line with a slope (scaling exponent, b) of 0.75. Mean scaling exponents for each species are presented in Fig. 2 and Table 1. MMR was not measured for zebrafish, wherefore AS and FAS could not be calculated. Metabolic and growth rates have been adjusted to a common temperature of 20 °C for all species for these graphical presentations (which changes the scaling intercept, a, but not the scaling exponent, b). Temperature under the different studies with each species can be found in Supplementary Table 2.

Table 1.

Mean (inverse variance weighted) ontogenetic and static scaling exponents (with 95% CIs in square brackets) for standard metabolic rate (SMR), maximum metabolic rate (MMR), aerobic scope (AS), factorial aerobic scope (FAS), and growth rate (GR) for all species

Trait	Scaling exponent (b)
	Ontogenetic	Static
SMR	0.87 [0.85, 0.88]	0.89 [0.87, 0.92]
MMR	0.89 [0.88, 0.91]	0.90 [0.87, 0.92]
AS	0.90 [0.88, 0.92]	0.90 [0.87, 0.94]
FAS	0.03 [0.01, 0.05]	0.03 [0.00, 0.06]
GR	0.60 [0.56, 0.65]	1.02 [0.95, 1.10]

Mean scaling exponents for individual species are presented graphically in Fig. 2 and numerically in Supplementary Table 1.

Within species, the mean ontogenetic scaling exponents for SMR, MMR and AS of all individuals generally ranged from approximately 0.5 to 1.1 for the different species (Fig. 2 and Supplementary Table 1). An exception to this was the ontogenetic scaling of brown trout SMR, with a mean ontogenetic scaling exponent (b_SMR) of 0.27 for the species, ranging broadly from −0.35 to 0.80 for the different individuals (Fig. 3). The broad variation in ontogenetic scaling of SMR among brown trout individuals was likely caused by the moderately restricted food regime they were maintained on⁵⁹. This resulted in SMR being down-regulated more in individuals that initially had a relatively high SMR for their size, causing the low and even negative scaling exponents for those individuals^19,59. Such a down-regulation of SMR is unlikely to be sustainable over time, making this pattern in brown trout a potential exception among the other species. Nevertheless, the brown trout data align well with the overall scaling patterns observed across species (Fig. 1). Notably, of the species’ 19 ontogenetic scaling exponents for metabolic rates (seven for SMR, six for MMR, and six for AS), only four have a 95% CI that overlap with the proposed canonical scaling exponent of 0.75^2,9, with the majority exceeding 0.75 (Fig. 2 and Supplementary Table 1).

Fig. 2. Mean ontogenetic and static scaling exponents for metabolic traits and growth rate of seven species of teleost fish.

Shown in the panels are A standard metabolic rate (SMR), B maximum metabolic rate (MMR), C aerobic scope (AS), D factorial aerobic scope (FAS), and E growth rate (GR). MMR (and thus AS and FAS) was not measured for zebrafish. Coloured circles represent individual species and grey squares are overall means for all species. Error bars are 95% CIs (hidden behind symbols for some species and means). Numerical scaling exponents for individual species are in Supplementary Table 1. The dotted black line is a reference line with a scaling exponent (b) of 0.75.

Fig. 3. Correlations between ontogenetic (within-individual) scaling exponents (b) for metabolic traits and those for growth rate (GR) for teleost fish.

Panels show A standard metabolic rate (SMR), B maximum metabolic rate (MMR), C aerobic scope (AS), and D factorial aerobic scope (FAS) of the six or seven species (MMR, and thus AS and FAS, was not measured for zebrafish). Each point is the model-predicted ontogenetic scaling exponent for an individual fish. The dotted grey line is a 1:1 reference line. The solid black lines are overall linear regressions for A $b_{\mathrm{SMR}}=0.81+0.22\cdot b_{\mathrm{GR}}$, B $b_{\mathrm{MMR}}=0.84+0.04\cdot b_{\mathrm{GR}}$, C $b_{\mathrm{AS}}=0.86+0.02\cdot b_{\mathrm{GR}}$, and D $b_{\mathrm{FAS}}=0.03-0.16\cdot b_{\mathrm{GR}}$. If brown trout are excluded, correlations become A r = 0.67 (p < 0.001) for b_SMR vs. b_GR, B r = −0.05 (p = 0.453) for b_MMR vs. b_GR, C r = −0.142 (p = 0.02) for b_AS vs. b_GR, and D r = -0.52 (p < 0.001) for b_FAS vs. b_GR (see Supplementary Figs. 1-4 for plots without brown trout). The marginal distribution plots on the sides show the density distribution of scaling exponents for each species. The overall coefficients of variation (CV) are 27.2% for SMR, 21.4% for MMR, 25.4% for AS, 575% for FAS, and 611% for GR. See Supplementary Figs. 1-4 and Supplementary Table 1 for plots and correlations for individual species. Guppies show strong sex-specific differences and are therefore shown as circles for males and triangles for females.

While limited research exists on within-individual ontogenetic metabolic scaling^19,47–49, the ontogenetic scaling exponents found here are generally higher than those reported for SMR by others for zebrafish (b_SMR = 0.65)⁴⁷ and Nile tilapia (b_SMR = 0.71)⁴⁹. However, our ontogenetic metabolic scaling exponents align well with the relatively high static and evolutionary scaling exponents observed in other studies on fish^18,60,61. The lower ontogenetic scaling exponents reported for zebrafish⁴⁷ and Nile tilapia⁴⁹ could be explained by methodological differences. Where we used intermittent-flow respirometry to estimate metabolic rates, the other studies used closed respirometry⁴⁷ or continuous-flow respirometry⁴⁹. Given the known limitations of continuous-flow and closed respirometry^62,63, we believe our approach provides a more accurate representation of the true ontogenetic scaling exponents for SMR.

Aside from our previous research on the ontogenetic scaling of metabolic rates in brown trout^19,59 and cunner⁴⁸, both of which are included in the present dataset, we are unaware of any past studies quantifying the within-individual ontogenetic scaling of MMR, and thus AS and FAS. Interestingly, while the ontogenetic scaling of SMR, MMR, and AS were generally steep, the ontogenetic scaling of FAS across species was close to horizontal (b_FAS = 0.03; Fig. 1 and Table 1). This indicates that relative aerobic metabolic scope remains constant across a wide body mass range, although with pronounced variation between species (Figs. 1D and 2). Our finding of shallow ontogenetic scaling of FAS aligns with the shallow evolutionary (across-species) scaling of FAS for both ectotherms (b_FAS = 0.04) and endotherms (b_FAS = −0.02) reported elsewhere⁶⁴.

Ontogenetic scaling of growth rate and co-variation with metabolic scaling

The mean ontogenetic scaling of growth rate (GR) across fishes (b_GR = 0.60) was significantly shallower than the mean ontogenetic scaling of metabolic rates across fishes (b ≈ 0.9; no overlap in 95% CI, Fig. 1, Table 1), with nearly all individuals exhibiting steeper ontogenetic increases (higher b) in all of SMR, MMR, and AS with increasing body mass compared to the ontogenetic increase in growth rate (female guppies being the only exception; Fig. 3). The mean ontogenetic scaling of growth rate (b_GR) of 0.60 is also significantly shallower than the canonical 0.75-value (¾-power law) invoked by fractal geometry^10,11 (95% CI does not overlap with 0.75), but consistent with earlier findings of an evolutionary (across-species) scaling exponent of 0.61 for growth rates of ten freshwater fishes⁶⁵ Similarly, comprehensive work on scaling across diverse groups of eukaryotes found shallower scaling of growth rate (b_GR = 0.74) compared to maintenance metabolic rate (b_SMR = 0.96)². That study further found that growth rate consistently scaled with an exponent of approximately 0.75 both within and across eukaryote groups, whereas the scaling of maintenance metabolic rate was more variable within versus across groups². They interpreted this consistent ¾-power scaling of growth rate as indicative of growth rate governing metabolic rate. Thus, it seems likely that the scaling of growth rate could also govern or influence the scaling of metabolic rate².

Our findings, demonstrate a strong positive relationship between the ontogenetic scaling of SMR and the ontogenetic scaling of growth rate, especially across species (p <0.001, Pearsons correlation test, Fig. 3) but also within them (Supplementary Fig. 1). The relationship is not one-to-one though; a linear regression between the ontogenetic scaling exponents for SMR (b_SMR) and those for growth rate (b_GR) across species has a slope of 0.22. Consequently, across species, the ontogenetic increase in SMR with increasing body mass is only around a fifth of the corresponding ontogenetic increase in growth rate (Fig. 3). This finding of more variable scaling of growth rate than metabolic rate at the ontogenetic level contrasts with findings at the evolutionary (across-species) level².

Moreover, the intercept of the linear regression between the ontogenetic scaling exponents for SMR and those for growth rate across the seven species is 0.81 (Fig. 3). As such, when growth rate is constant across ontogeny (b_GR = 0), SMR scales with an exponent of approximately 0.8 (b_SMR = 0.81). A decrease in growth rate as individuals grow larger across ontogeny (b_GR < 0) is thus associated with ontogenetic scaling of SMR that is shallower than b_SMR ≈ 0.8, while an increasing ontogenetic growth rate (b_GR > 0) is associated with steeper scaling of SMR. Previously underappreciated variation in growth rate both within and between species could thus be an explanation for the now century-long debate about whether and by how much metabolic scaling varies for organisms in general, and for fishes specifically. For example, large comparative studies on the static and evolutionary scaling of fishes have found mean scaling exponents (b) for SMR in the range 0.72 to 0.95, with an overall average around 0.88^{2,18,19,60,61,66,67}. Interestingly, while we find here that SMR scales steeper than growth rate across most of the range of scaling exponents (higher b_SMR than b_GR), they intersect (scale equally steeply) at b ≈ 1 (Fig. 3A). Thus, when growth rate scales isometrically (linearly) with body mass (b_GR = 1) so does SMR (b_SMR = 1.03) (Fig. 3). A doubling in mass would thus also entail a doubling of both SMR and growth rate. While this could be a coincidence, it could also imply that there is a hard ceiling to biological scaling where neither metabolic rate nor growth rate can increase faster with increasing body mass. An upper limit to metabolic scaling at b = 1 has been suggested during periods of both minimal (dormancy) and maximal (strenuous physical activity) metabolic activity, and during periods of rapid growth^16,23,68. However, it has also been suggested and observed that metabolic scaling can exceed b = 1 under some circumstances^16,20.

Within species, a positive relationship between individual ontogenetic scaling exponents for SMR (b_SMR) and those for growth rate (b_GR) existed for five of the seven species (with one of the five species showing borderline significance, p = 0.075 for rainbow trout; Supplementary Fig. 1). Four of these five species with significant correlations (including rainbow trout) all had variation in b_GR introduced through either strong sex-specific variation in growth rate (guppies) or through variation in food availability (damselfish, zebrafish) or early-life high temperature exposure before metabolic rate measurements (rainbow trout), with comparatively little effect on b_SMR (see supplementary material for details). The fifth species (brown trout) had variation in b_SMR introduced through moderately restricted feeding and associated adjustment of SMR, as detailed above, with comparatively little variation in b_GR. The remaining two species, anemonefish and cunner, either had a relatively low sample size (17 anemonefish; Supplementary Table 2), making a correlation less likely, or exhibited low variation in both b_SMR and b_GR (cunner) compared to the other species (Supplementary Fig. 1). Thus, it appears that variation in either b_SMR or b_GR is required to observe a relationship between the ontogenetic scaling of SMR and that of growth rate. This is further supported by the strong correlation across species (Fig. 3). These observations suggest that the ontogenetic development (scaling) of SMR as organisms grow larger co-vary with the ontogenetic development of growth rate whenever variation is generated in one or the other, either experimentally or due to inherent variation between species. This also means that studies on groups of fish from the same treatment might not detect small differences in the scaling of biological rates.

As all fish used in our study were fasted prior to SMR measurement, for at least the 12–24 h sufficient to halt new tissue production⁶⁹, the positive correlations between the ontogenetic scaling of SMR (b_SMR) and that of growth rate (b_GR) should not be due to the direct cost of growth being inadvertently included in measurements of SMR. However, the machinery supporting growth, such as upregulated organ size or function, may continue to be upregulated and thus costly to maintain even when new tissue is not being synthesised. Tissue synthesised during rapid growth may also have higher maintenance metabolism¹⁷. Thus, more research is needed to untangle if and how (indirect) costs of growth are driving the positive relationship between b_SMR and b_GR.

The positive relationships between the ontogenetic scaling exponents for SMR and those for growth rate support the notion that the steepness of biological scaling is malleable and not constrained by geometry or physics to a canonical value of b = 0.75 (or any other specific value). Additionally, the greater variation we observe in the ontogenetic scaling exponents for growth rate compared to those for metabolic rates (Fig. 3) challenges the prevailing assumption in influential growth models that growth is governed by metabolic rate^14,27,28. The finding that metabolic rate and growth rate do not scale the same also contradicts the metabolic theory of ecology⁹. While we are hesitant to draw a conclusion regarding causality, variation in the ontogenetic scaling of SMR (b_SMR) appear more constrained than that for growth rate (b_GR). This is seen in both a narrower range of scaling exponents and a substantially lower coefficient of variation (CV) for SMR compared to growth rate (Fig. 3A). This pattern is also true for MMR and AS, with narrower ranges of ontogenetic metabolic scaling exponents and lower CV compared to growth rate (Fig. 3).

Contrary to the patterns observed for the ontogenetic scaling of SMR, we find a strong negative correlation between the ontogenetic scaling of factorial aerobic scope (b_FAS) and that of growth rate (b_GR) across species, with a regression intercept close to zero (Fig. 3D). Thus, when growth rate remains constant as body mass increases during ontogeny (b_GR = 0), relative metabolic scope also remains constant (b_FAS = 0.03). However, when growth rate decreases during ontogeny (b_GR < 0) relative metabolic scope increases (b_FAS > 0), while increasing growth rate decreases relative metabolic scope. As FAS is the factorial difference between MMR and SMR, this means that the relative increase in SMR out-scales that of MMR when growth rate increases with increasing body mass during ontogeny, and vice versa when growth rate decreases. This negative relationship between the ontogenetic scaling of FAS (b_FAS) and that of growth rate (b_GR) reveals a trade-off between growth and metabolic scope across fishes. Faster-growing individuals experience either a shallower increase or a decrease (when b_GR > 0) in relative aerobic capacity with increasing body mass compared to their slower-growing counterparts. Interestingly, if brown trout are disregarded (because of their temporal down-regulation of SMR under restricted food availability), the correlations between the ontogenetic scaling exponents for growth rate and those for both SMR and FAS across species (Supplementary Figs. 1I and 3H) remain strong and maintain direction (positive and negative, respectively). However, the correlation between the ontogenetic scaling exponents for AS and those for growth rate changes from being positive and non-significant to being significantly negative (Supplementary Fig. 4H). For MMR, the opposite is the case, as the correlation between the ontogenetic scaling exponents for MMR and those for growth rate becomes non-significantly negative (Supplementary Fig. 2H). Similar patterns also exist within species, where the ontogenetic scaling exponents for growth rate either show no or significantly negative correlations with the ontogenetic scaling exponents for MMR and AS (Supplementary Figs. 2 and 3).

Overall, these generally negative relationships between the ontogenetic scaling exponents for growth rate and those for MMR, AS, and FAS underscore a trade-off between growth and the development of overall aerobic metabolic capacity during ontogeny, both within and across fish species. The trade-off between accelerating ontogenetic growth (steep ontogenetic scaling of growth rate) and reduced metabolic scope with increasing body size is likely to have fitness consequences, as metabolic scope has been positively linked to feeding capacity⁵⁸, offspring size⁵⁶ and lifetime reproductive success⁵⁵.

Static scaling of metabolic and growth rates and relationships with ontogenetic scaling

We did not find an overall difference between static and ontogenetic scaling of any of the metabolic traits (SMR, MMR, AS, and FAS) for all species together (no overlap in 95% CI; Table 1). This contrasts with earlier findings for the brown trout and cunner¹⁹, which have steeper static than ontogenetic scaling of SMR (Supplementary Table 1). Steeper static compared to ontogenetic scaling at the population level was proposed to result from selection for faster-growing individuals¹⁹, due to the positive correlation between the ontogenetic scaling exponents for SMR and growth rate also found in the present study. This is supported by both theoretical and empirical work on scaling of morphological traits, which shows how covariation between ontogenetic scaling and body mass at a given time causes differences between static and ontogenetic scaling⁴². This further supports that size-selective mortality would cause differences between static and ontogenetic scaling. The lack of consistently steeper static compared to ontogenetic scaling across all seven species investigated here may reflect differences in historical selection pressures, as some species were wild-caught while others originated from hatcheries or laboratory populations (see supplementary material).

The scaling of growth rate, on the other hand, was significantly different between the ontogenetic and static levels both overall and within several species, with generally (much) shallower ontogenetic than static scaling (lower ontogenetic than static b; Fig. 1 and Supplementary Table 1). These differences between ontogenetic and static scaling reveal that growth rate can increase steeply with increasing body mass across individuals within a given cohort or age class (positive static scaling) while increasing shallowly or even decreasing with increasing body mass (negative ontogenetic scaling) within the same individuals across ontogeny. This highlights how completely different and even opposing conclusions about scaling relationships can be reached depending on the level of investigation.

Conclusions

We find that the ontogenetic development (scaling) of growth rate co-varies positively with the ontogenetic development of maintenance metabolic demands (SMR) and negatively with the ontogenetic development of metabolic scope (FAS). The severity of these trade-offs between fast growth and both elevated maintenance costs and reduced metabolic scope likely depends on the environment; a steeply increasing SMR with increasing body mass may be benign or even advantageous in resource-rich and predictable environments, where higher food intake could compensate for the increased maintenance energy expenditure and allow for faster meal processing⁷⁰ and more rapid growth⁷¹. Such rapid ontogenetic growth could allow individuals to escape size-selective mortality⁷², but the associated cost of a dwindling metabolic scope could have critical negative consequences for fitness of fish and other animals alike, as metabolic scope has been tied to feeding capacity⁵⁸, swimming performance⁷³, resistance to a changing environment⁷⁴, lifetime reproductive success⁵⁵, and offspring size⁵⁶.

Accelerating growth also commonly occur as a compensatory response in individuals having experienced a period of slow growth caused by unfavourable environmental conditions⁷⁵. In addition to escaping size-selective mortality, compensatory growth allows small individuals to catch up in size with conspecifics that have been less affected by the environmental dearth, but it decreases later-life health and lifespan^75–77. Additionally, many fish naturally have a period of accelerating growth during their typically S-shaped growth curves¹⁴. Differences in environmental selection pressures and life-stage-specific growth trajectories could thus drive scenarios where accelerating ontogenetic growth (steeper scaling of growth rate) would be favourable even at the cost of increased maintenance demands (SMR) and reduced metabolic scope (FAS). This resonates with studies on amphipods, where the scaling of growth and metabolic rates were steeper for the amphipods in the absence versus presence of fish predating selectively on large amphipods³⁶.

Overall, our findings challenge the very influential idea of universal ¾-power scaling^10,11, as well as the equally influential idea outlined in the metabolic theory of ecology that metabolic rate governs growth such that the two should scale the same^4,9. Instead, we find both broad and more pronounced variation in the ontogenetic scaling of growth rate compared to that of metabolic rates, especially SMR. Thus, we show that neither metabolic nor growth rate scaling is fixed but rather covaries. The positive relationship between ontogenetic scaling of SMR and that of growth rate also contrasts with recent life-history-optimisation theory, which predicts a negative relationship between ontogenetic metabolic scaling and growth³⁵. However, the prediction from life-history-optimisation theory is made at the ontogenetic level but is based on scaling relationships across individuals³⁵. This further highlights how different and even opposing conclusions can be reached depending on the biological level under investigation.

We believe a within-individual ontogenetic scaling approach will be key to further elucidating the much-debated causes and consequences of variation in metabolic scaling and associated theories. However, we should also be mindful that repeated measurements on the same individuals may affect their physiology and behaviour. For example, consecutive fasting before metabolic rate measurements could reduce growth rate compared to individuals measured only once in life, and consecutive swimming trials could increase maximum aerobic performance through a training effect. Regardless, our findings indicate that previously underappreciated variation in growth could help explain the century-long debate about whether, and to what extent, metabolic scaling varies.

Materials and methods

Fish species and holding conditions

We collected empirical data on body mass and oxygen uptake rates as estimates of metabolic rates from 389 individuals across seven fish species. All individuals were kept at constant temperatures within the normal range for their species: brown trout (S. trutta) at 15 °C, rainbow trout (O. mykiss) at 10 °C, cunner (T. adspersus) at 15 °C, blue-green damselfish (C. viridis) at 28.5 °C, orange-fin anemonefish (A. chrysopterus) at 28 °C, Trinidadian guppy (P. reticulata) at 25 °C, and zebrafish (Danio rerio) at 28 °C. Data for brown trout and cunner were originally collected by Norin and Malte⁵⁹ and Norin and Gamperl⁴⁸, respectively. For these species, individuals were housed in a common tank and tagged for individual identification with either passive integrated transponders (brown trout) or elastomers (cunner). Individuals from the other five species were housed separately in individual tanks or containers. All fish used in the experiment were in a growing and non-reproducing state. For all the experiments we complied with all relevant ethical regulations for animal use.

Data collection and preparation

Each individual fish was measured repeatedly for metabolic rate and body mass up to twelve times during ontogeny. Individuals with fewer than four repeated measurements of both metabolic rate and body mass were excluded from analysis. This produced a final dataset comprising 4324 paired measurements of body mass and metabolic rates, with 2449 measurements of standard metabolic rate (SMR) and 1875 measurements of maximum metabolic rate (MMR), from which scaling relationships were derived as outlined below.

Metabolic rates were measured as oxygen uptake rates (mg O₂ h^–1) using respirometry. Prior to the start of every respirometry trial, fish were fasted for 12–24 h to ensure digestion would not interfere with metabolic rate measurements. SMR was measured for all species by continuously recording oxygen uptake rates overnight using intermittent-flow respirometry⁶³. The mean of the lowest 10% of these oxygen uptake rates was considered SMR. For guppies, MMR was measured as the highest oxygen uptake rate during exhaustive swimming in a small swim flume respirometer⁷⁸. For the remaining species, MMR was measured as the oxygen uptake rate immediately after an exhaustive chase using a standard chase protocol, followed by transferring fish to an intermittent-flow respirometer⁷⁹. We did not measure MMR for zebrafish. Aerobic scope (AS) was calculated as the absolute difference between MMR and SMR for each fish, while factorial aerobic scope (FAS) was calculated as the ratio of MMR to SMR.

Growth rate (mg day^–1) was calculated for each individual fish between each pair of two consecutive body mass measurements as the increase in body mass (mg) divided by the time interval (days) between measurements. Each body mass measurement was performed by placing the fish on a fine mesh and lightly dapping them with absorbent paper to remove adhering water. To quantify the ontogenetic scaling of growth rate, each growth rate value was associated with the mean body mass between each consecutive pair of measurements.

Statistical analysis

All data analyses were performed in R v 4.2.2⁸⁰. Ontogenetic and static scaling of each trait for each species were analysed using MCMCglmm models⁸¹ as ${\log }_{10}\left(\mathrm{Trait}\right)~{\log }_{10}\left(\mathrm{MassCent}\right)+{\log }_{10}\left(\mathrm{MassMean}\right)+\left({\log }_{10}\left(\mathrm{MassCent}\right)\mid \mathrm{FishID}\right)$, where $\mathrm{Trait}$ is metabolic or growth rates, $\mathrm{MassCent}$ is the centred body mass of each individual, $\mathrm{MassMean}$ is the mean body mass of each individual repeated the number of times that individual was measured, and $\mathrm{FishID}$ is a unique ID for each fish. This model structure allowed us to analyse the ontogenetic (within-individual) and static (across-individual) scaling relationships simultaneously⁸² and extract model-predicted scaling exponents (b) for individuals and species for further analysis and graphical presentation. For species where a treatment was included in the experiment (see supplementary material), this was accounted for with fixed-effects interactions between Treatment and both ${\log }_{10}\left(\mathrm{MassCent}\right)$ and ${\log }_{10}\left(\mathrm{MassMean}\right)$. The average scaling exponent between the treatments was then calculated using inverse variance weighting, taking into account the covariation between treatments. Mean ontogenetic or static scaling exponents for all species were calculated as inverse variance weighted averages of model-predicted values.

To account for differences in temperature between species for graphical presentations (Fig. 1), all measurements were standardised to a common temperature of 20 °C. This was done by running an MCMCglmm model containing all measurements for a given trait and including temperature as a fixed effect, as ${\log }_{10}\left(\mathrm{Trait}\right)~{\log }_{10}\left(\mathrm{Mass}\right)+\mathrm{Temperature}+\left({\log }_{10}\left(\mathrm{Mass}\right)\mid \mathrm{FishID}\right)$. The effect of temperature was then calculated as Q₁₀⁸³, and all measurements were up- or down-regulated using the Q₁₀ for that given trait to the common temperature of 20 °C.

Comparisons between scaling exponents

Statistical comparisons between average scaling exponents were done by evaluating if there was overlap between the 95% CIs. Covariation between ontogenetic scaling exponents were evaluated using Pearson’s correlation coefficients (r), with p-values below 0.05 considered significant.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

A. Rosén and T.N. conceptualised and did the overall design. A. Rosén, A.H.A., Z.S., J.W.E., A.F.M., S.R. and T.N. collected the data. R.B., S.C.M. and T.N. provided equipment and facilities. A. Rosén, R.B., S.C.M. and T.N. provided supervision. A. Rosén, Z.S., J.W.E., A.F.M., S.R. and T.N. data analyses. A. Rosén wrote the initial draft while Z.S., S.R., R.B., S.C.M. and T.N. provided critical feedback. Revisions were made by A. Rosén with feedback from A.H.A. and T.N. All authors read and approved the final version of the manuscript.

Peer review

Peer review information

Communications Biology thanks Douglas Glazier and the other anonymous reviewer(s) for their contribution to the peer review of this work. Primary handling editor: Michele Repetto. A peer review file is available

Data availability

Both the data used in the article and the code used to analyse it and make the figures are available in a figshare repository⁸⁴.

Competing interests

The authors declare no competing interests

Supplementary information

The online version contains supplementary material available at 10.1038/s42003-026-09588-w.