Metabolic size scaling reflects growth performance effects on age-size relationships in mussels (Mytilus galloprovincialis)

RESEARCH ARTICLE Metabolic size scaling reflects growth performance effects on age-size relationships in mussels (Mytilus galloprovincialis) Irrintzi Ibarrola, Kristina Arranz, Pablo MarkaideID, Enrique Navarro* Departamento de Gene ´tica, Antropologı ´a Fı ´sica y Fisiologı ´a Animal, Facultad de Ciencia y Tecnologı ´a, Universidad del Paı ´s Vasco/Euskal Herriko Unibertsitatea (UPV/EHU), Bilbao, Spain *[email protected] Abstract Body-size scaling of metabolic rate in animals is typically allometric, with mass exponents that vary to reflect differences in the physiological status of organisms of both endogenous and environmental origin. Regarding the intraspecific analysis of this relationship in bivalve molluscs, one important source of metabolic variation comes from the large inter-individual differences in growth performance characteristic of this group. In the present study, we aimed to address the association of growth rate differences recorded among individual mussels (Mytilus galloprovincialis) with variable levels of the standard metabolic rate (SMR) resulting in growth-dependent shift in size scaling relationships. SMR was measured in mussels of different sizes and allometric functions fitting SMR vs. body-mass relationships were compared both interand intra-individually. The results revealed a metabolic component (the overhead of growth) attributable to the differential costs of maintenance of feeding and digestion structures between fast and slow growers; these costs were estimated to amount to a 3% increase in SMR per unit of increment in the weight specific growth rate. Scaling exponents computed for intraindividual SMR vs body-mass relationships had a common value b = 0.79 (~ ¾); however, when metabolic effects caused by differential growth were discounted, this value declined to 0.67 (= ⅔), characteristic of surface dependent processes. This last value of the scaling exponent was also recorded for the interindividual relationships of both standard and routine metabolic rates (SMR and RMR) after long-lasting maintenance of mussels under optimal uniform conditions in the laboratory. The above results were interpreted based on the metabolic level boundaries (MLB) hypothesis. Introduction Metabolism constitutes an integrated system of the energy yielding and utilization processes involved in supporting life; and most activities of organisms are reflected in their metabolic rates. The relationship between metabolism and the size of individuals has been the subject of thorough analysis for decades as a particularly meaningful case among the basic organismal attributes stemming from structural constraints set on functional properties. Partly for historical reasons, most of the studies on this subject have focused on animals and they rely on PLOS ONE PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 1 / 21 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Ibarrola I, Arranz K, Markaide P, Navarro E (2022) Metabolic size scaling reflects growth performance effects on age-size relationships in mussels (Mytilus galloprovincialis). PLoS ONE 17(9): e0268053. https://doi.org/10.1371/journal. pone.0268053 Editor: Erik V. Thuesen, Evergreen State College, UNITED STATES Received: April 20, 2022 Accepted: August 8, 2022 Published: September 1, 2022 Peer Review History: PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0268053 Copyright: ©2022 Ibarrola et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the manuscript and its Supporting Information files. determinations of the standard metabolic level based on oxygen consumption recorded under resting post-absorptive conditions, which is assumed to account for the energy requirements of both tissue maintenance and basic processes of homeostatic regulation [1]. As such, this metabolic level is considered as a standard for comparative purposes in multiple studies involving both interand intra-specific analyses. Body-size scaling of metabolism in animals is typically allometric, expressed by a power function in the form: R = a W b , where R is the metabolic rate, W is the body mass, ais the scaling coefficient (or proportionality constant), and bis the scaling exponent (or slope of the loglog relationship). The vast majority of these scaling exponents reported in animals in both interand intra-specific comparisons is approximately close to ⅔or ¾, but is significantly lower than 1, implying that weight-specific metabolic rate (i.e. per unit of body mass) decreases with the increasing body size that encompasses both ontogenetic development and the evolutionary processes underlying wide-range speciation. This metabolic restriction imposed by size increments is a fundamental trade-off in all biological processes and is one of the topics of the most persistent and intense debates in the subject. Earlier studies have considered bto approach the value ¾in a variety of animals [2–5]; subsequently, this trend was interpreted as the expression of universal properties of resource-transport networks underlying a “¾power law” for metabolism that is applicable to virtually all organisms [6–10]. However, several studies have recently questioned the universality of the “¾power law” based on extensive surveys of available data sets for metabolic size-scaling that showed bvalues to exhibit substantial variation among taxa and physiological states [11–14]. A potential approach to address the variability in scaling exponents is to assume that different constraints act as boundaries in the various processes that make up the organism’s metabolic rate [13,15–17], which would hence have different scaling characteristics. A derivation of the Dynamic Energy Budget (DEB) theory [18] considers that the acquisition of both energy and resources is proportional to surface area, while energy demand is proportional to volume; thus, variable scaling exponents would result from the specific balances between both types of processes achieved under the different conditions experienced by organisms. This view is consistent with the observation that most metabolic scaling exponents are between ⅔and 1 according to Glazier [13], who developed the metabolic level boundaries (MLB) hypothesis as an extension of this approach to explore the dependence of scaling exponents on the level of metabolic activity of organisms [13,16]. The MLB hypothesis assumes the above differential mass scaling for supply and demand processes, and states that the relative weight of these boundary constraints depends on the metabolic level (L = metabolism per unit mass) to predict a complex (U-shaped) relationship between the two parameters aand bof the allometric equation for metabolism vs. body mass. The MLB approach has proven useful in interpreting variations in scaling exponents associated with a diversity of conditions that shift metabolic activity across successive levels of maintenance, resting, routine, and active states of metabolism [13,14,16,19]. Intra-specific analysis of metabolic size scaling, recorded in specimens covering an ample size range within the population, forms the majority of cases in scaling exponent determination for two reasons: a) some of the explicative causes of metabolic scaling are better approached through intra-specific analysis where, in opposition to inter-specific comparisons, patters of body organization are conserved, thus “avoiding the phylogenetic effects that plague inter-specific analysis” [13] and b) precise knowledge of allometric scaling exponents is required for size standardisation in studies of metabolism, allowing to “subtract” the effects of body mass on metabolic rate in order to discern other influences such as growth rate. This especially applies to those studies based on comparing groups of individuals that may inherently be size-heterogeneous as a consequence of large inter-individual differences in growth performance. PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 2 / 21 Funding: Funder1 MINECO (https://sede.mineco. gob.es) Project FIGEBIV (AGL2013-49144-C3-1-R) Awarded: E.N., I.I. and P.M. Funder2 UPV/EHU (www.ehu.es) Project: GIU20_064 Awarded: I.I. and K.A. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interest exist. This is the case for bivalve molluscs, where extremely high rates of endogenous variability in growth have been reported [20–26]. For instance, long-lasting maintenance of spats of different bivalve species under homogenous conditions in the laboratory resulted in the progressive size-differentiation of the individuals spanning over a range of 5to 10-fold (eventually up to 30x) [25–31], thus revealing a strong growth component of possible genetic origin. Phenotypes that are segregated as fast and slow growing, using extreme groups of such size distribution, exhibit noticeable differences in physiological behaviour that accounts for differences in growth performance [25,26,28,32]. As suggested by these cases, ontogenetic growth in bivalves would include two differentiated components: the sequential phases of ontogenetic development, roughly related to age, and the overlaid inter-individual variability in growth rate that is responsible for size-to-age difference between fast and slow growers. One important point is that both sources of size variation in the population may generate different size constraints on standard metabolism and thus contribute differently to scaling effects. Consequently, an accurate characterisation of intra-specific scaling relations would require an analytical approach in which mass exponents fitted to the full size range of the population might be compared with those reflecting pure ontogenetic effects as based on the intra-individual size variation with age. Despite obvious interest [13], this type of approach has been addressed on very few occasions [33–35]. In this study, we analysed the size scaling of respiratory metabolism in individual mussels— Mytilus galloprovincialis—of a population. This study was mainly based on standard metabolic rate (SMR) determinations and aimed to differentiate two sources of individual size variation (time vs. rate of growth) as regard their effects on metabolic size scaling. Mussels from a uniformly-sized sample were allowed to differentiate in size under uniform feeding and thermal conditions in the laboratory, during which, their SMR and individual growth rate were recorded. On the other hand, SMR was determined in a heterogeneous sample of mussels covering the full size range found in the population. Parameters of allometric equations relating metabolism to body mass were then compared for two sets of data: a) intraindividual allometries with size ranges given by body-mass increments achieved during the growth period and b) inter-individual (intra-specific) allometries with size ranges given by natural size dispersion within the population. Material and methods Experimental design Over 400 mussels were collected from monolayer mussel beds grown in a rocky intertidal area of Antzorape (Ibarrangelua, Bizkaia, Spain) on February 2013. Mussels ranged from approximately 7–35 mm in shell length, representing the minimum and maximum sizes observed in the bed, respectively. Mussels were placed inside tanks containing seawater set in a recirculating system regulated at ambient temperature (15˚C) and salinity (34 psu), and fed a ration of Isochrysis galbana in 2 mm 3 particulate volume per litre (equivalent to 1.5 mg POM L -1 ) continuously for two weeks. Subsequently, two experimental groups of mussels were created and were maintained in separate tanks for approximately seven months (February–August) under the above-mentioned temperature and feeding conditions. Group 1. One hundred juvenile mussels of uniform size 10 mm (9.189 ±0.907) were arranged in individual numbered chambers for six months (from March 5 th to August 12 th ). The Shell length (SL), live weight including shell mass (LW), and SMR of each individual were recorded on eight occasions (approximately every three weeks). These measurements allowed for the calculation of individual growth rates of selected mussels and establishment of allometric scaling of metabolic rate with body weight at two different levels: PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 3 / 21 a. Intra-individual allometry: The scaling of SMR with LW for each individual mussel was determined by fitting power functions to metabolism and body size data recorded on eight occasions (n = 8). As a result, a series of 100 functions (k = 100) was obtained. b. Inter-individual allometry: Similarly, for each sampling occasion, power functions were fitted to the SMR vs. LW data for the full sample. As a result, a series of eight power functions relating the metabolic rate to body size (k = 8) was obtained for n = 100 mussels. On the 7 th sampling date, additional measurements of routine metabolic rate (RMR) and clearance rate (CR) were individually determined (n = 100), and allometric scaling of these two parameters with LW was established as described for SMR. Subsequently, the gill surface area was recorded in 30 selected mussels covering an ample range of body sizes to establish the allometric relationship of this parameter with the LW. Group 2. Fifty mussels covering the size range observed in the sampled population (7–35 mm SL) were used to analyse the intra-specific allometric relationship between SMR and LW. Allometric relationships were analysed on two occasions: a) immediately after the group was created (Intra-specific 1: 18 th of February) and b) four months post their maintenance in the laboratory under constant water temperature and continuous food supply (Intra-specific 2: 17 th of June). Determination of SL, LW, and growth rate of juvenile mussels On each sampling date, mussels were removed from the seawater tanks and carefully dried with tissue paper. Individual LWs (g) were determined in a 10 −4 g precision balance and SL (mm) was measured using digital callipers. These measurements allowed the computation of individual growth rates for different time intervals over a 6-month period. Growth rate in terms of LW was expressed as i) total growth rate (GR LW : g day -1 ): individual LW increment per day and ii) size-specific growth rate (SGR LW : %): GR LW divided by the initial LW of each interval, expressed as a percentage. Experimental determination of physiological parameters Clearance rate (CR; L h -1 ). CR determinations were performed in a static system by recording the exponential decay in particle concentration over time [36]. Mussels were individually placed in glass flasks (volume varied from 0.5 to 1.0 L according to mussel size) containing aerated sea water and particles of Isochrysis galbana (�40 particles μl -1 ). Particle concentration was measured every 10 minutes for 1–2 hours with a Coulter Counter Z1 analyser. A control chamber without mussels was used for correction of the sedimentation rate of the particles. Metabolic rates. Both SMR and RMR were estimated as the rate of oxygen consumption (VO 2 :mlO 2 h -1 ). RMR was measured after the fed mussels were directly transferred from the feeding tanks to respirometers. For SMR determinations (the majority of VO 2 recordings in this work), mussels were transferred to tanks filled with aerated filtered (1 μm) sea water and starved for three days before determination of oxygen consumption. Individual mussels were confined in chambers (the size of the chamber varied between 30 and 150 ml according to the size of the mussel) sealed with luminescent dissolved oxygen probes connected to oximeters (HATCH HQ 40d); oxygen consumption rates were estimated from the decrease in oxygen concentration over time (4–8 h). Control chambers without mussels were used to check the stability of oxygen concentration during the measurement period. In cases where both metabolic levels were determined, the metabolic scope for feeding and growth (MSFG; [26]) was calculated as the difference between RMR and SMR. PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 4 / 21 Determination of gill-surface area (GA: mm 2 ) At the end of the experiments, 30 mussels from Group 1, covering the entire size range of the group, were dissected by cutting their adductor muscles to expose the gills. One outer demibranch of each individual was photographed with a digital camera placed next to a piece of graph paper to set the scale, and the area of the demibranch was determined using ImageJ software (National Institutes of Health; Bethesda, MD, USA). The areas estimated in this manner were doubled to account for each side of the demibranch and multiplied by the number of demibranchs (4) to estimate the gill surface area (GA; mm 2 ). Statistical procedures One-way analysis of variance (ANOVA) was performed to test significance of differences in growth rate recorded for the different time intervals along the period of study. Post-hoc test (Tukey) was then applied to identify growth phases based on significant mean differences. Inter-individual and intra-individual allometric relationships between the SMR and LW were expressed according to the expression SMR = LW b . The proportionality constant aand massexponents bwere obtained by fitting logarithmically transformed individual SMR and LW data with regression equations. Mass-exponents (slopes) and proportionality constants (elevations) obtained in both the intraand inter-individual treatments were compared using analysis of covariance (ANCOVA). The null hypothesis (H 0 ) with equal slopes (b 1 = b 2 = b 3 . . ..= b k ) were tested using the F-statistic value. If H 0 was rejected, Tukey’s multiple comparison test was performed to determine the significant differences between each pair of slopes. If H 0 is accepted, a common slope b c is computed and the null hypothesis (H 0 ) of equal elevations (a 1 = a 2 = a 3 . . ..= a k ) were subsequently tested using the F-statistic value. If H 0 was accepted, then a common elevation a c and common regression were computed. If H 0 was rejected, Tukey’s multiple comparison test was performed to determine the significance between each pair of elevations. All statistical analyses were performed using a custom R script based on the procedures described by Zar [37]. Complementarily, SMR data used in both the intraand inter-individual analyses of Group 1mussels were plotted against multiple factors, using LW, growth rate (SGR LW ), and the interaction term as potential predictors, and a simultaneous function was fitted by multiple regression procedures using SPSS (IBM SPSS Statistics V. 25). Results Group 1: Mussels of initial uniform size Growth and size distribution. The time-course of size change of 100 mussels during 150 days of maintenance in the laboratory is shown in Fig 1A and 1B for both LW and SL. Different size trajectories were illustrated by the progressive divergence of these lines, accounting for great differences in growth rates among individuals. An almost continuous decline in values for condition index (CI: mg LW /mm SL 3 ), from >0.1 to <0.1 (Fig 1C), indicated that LW increments are majorly driven by shell growth. Underlying inter-individual variability, sequential phases of fast/slow growth were recorded for growth rates computed for LW (Fig 2A), with average values of 7 and 12 mg day -1 for the early and late phases of fast growth, respectively, and a minimum average of 3 mg day -1 in the slow growth phases. Change in growth trend was particularly intense from day 84 to 119, with growth rates increasing from 2.5 to 17 mg day -1 . When growth is expressed as a weight-specific rate (i.e., as a percentage of daily increment per unit weight or SGR LW ) (Fig 2B), all individual data points can be fitted to a negative exponential function with time (curve in Fig 2B), PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 5 / 21 representing the natural decline in the specific growth rate with size increment. Phases of fast/ slow growth can be identified by points departing from the overall trend described by the curve, especially those corresponding to days 42 (4%), 84 (0.58%), and 119 (2.7%). After 119 days till the end of the experiment, there was a decrease in growth rate (both in absolute and relative terms) that might represent the onset of a subsequent period of slow growth, in agreement with the observed ~ 6-week (40 days) sequence of differential phases of growth. The frequency distribution of SGR LW calculated for the entire growth period (from day 7 to 147) is plotted in Fig 3 on a logarithmic scale for normalisation purposes, removing skewness. Specific growth rates ranged from approximately 1–20% of initial LW increment per day. Fourteen individuals (approximately 15% of the group) displayed the lowest GRW SPC of 1.0– 3.4% LW day -1 and were considered a group of slow growers (S), whereas the 11 other mussels achieved the highest GRW SPC values, from 11.5 to 21.0% LW day -1 and were considered a Fig 1. Growth trends of mussels (Mytilus galloprovincialis) from Group 1 during the maintenance period, given in terms of: A) Shell length (SL: mm) and B) Live weight (LW: g); C) mean values of shell length (hollow symbols) and condition index (CI: LW / SL 3 ) (full symbols). Bars represent ±SE. https://doi.org/10.1371/journal.pone.0268053.g001 Fig 2. Mean rates of daily growth along the period of study, given in both A) absolute terms (GR: mg LW day -1 ) and B) relative weight specific terms (SGR: % day -1 ). Error bars represent ±SE. For reference, an exponential function was fitted to all individual data for SGR vs time (line in B): SGR = 3.621 (±2.189) �e (-0.008 ±0.006) � Time . Results of post-hoc test following ANOVA: Different letters denotate significant mean differences. https://doi.org/10.1371/journal.pone.0268053.g002 PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 6 / 21 group of fast growers (F). Thus, the same range interval (1.8x) was accomplished in the selection of either F or S groups, and the computed growth rate difference between the two groups was 8.5x on average. A comparison of growth trends for both groups (Fig 3) indicated differences in the intensity of changes during the transition between growth phases, with S individuals showing almost nil growth during the slow growth phase. Intra-individual allometries of SMR. Allometric equations relating SMR to LW for 100 individuals in Group 1 were fitted using linear regression after log transformation of both variables (Fig 4). LW range was achieved through the growth of the individuals and varied between ~ 400 mg in the S group (LW-range of ~5x) and ~ 1800 mg in the F group (LW-range of ~20x). Only 5 out of the 100 individual regressions were found not significant (P >0.05) and were excluded from further analysis. The minimum and maximum values of the scaling exponents of the SMR were 0.570 ±0.080 and 1.171 ±0.127, respectively. Possible significant differences among the slopes and elevations of the 95 intra-individual allometries were analysed using ANCOVA. No significant differences in either the slopes or elevations were found (Table 1), indicating that all individuals share a common mass-exponent and proportionality constant. Results of ANCOVA analysis for testing significant differences between slopes and elevations of the 95 intra-individual allometric relationship (on log-log scale) between standard metabolic rate (VO 2 : ml O 2 h -1 ) and body weight (LW: g). Size ranges varied between a minimum 5x to a maximum 30x. For about half these relationships, ranges varied between 10 and 20x. Therefore, a common equation accounting for intra-individual scaling of SMR to body weight was calculated as follows: Fig 3. Frequency distribution vs growth intervals. For normality, SGR values were logarithmically transformed. Two groups of slow (S) and fast (F) growers were created with the extremes of the distribution. Insert: Growth trends of segregated groups of fast (F) and slow (S) growing mussels. Data are mean live weight (LW) values ±SE. https://doi.org/10.1371/journal.pone.0268053.g003 PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 7 / 21 Fig 4. Regression lines fitted to log-log transformed data of SMR (ml O 2 h -1 ) vs LW (g) in 100 individuals. Size ranges correspond to the weight increment experienced by each individual mussel. Only 5 of these regressions were not significant (P >0.05). https://doi.org/10.1371/journal.pone.0268053.g004 Table 1. Analysis of covariance (ANCOVA) of intra-individual SMR vs LW relationships. Term of comparison Slopes Elevations Hypothesis H 0 = b 1 = b 2 =. . . = b 95 H 0 = a 1 = a 2 =. . . = a 95 F tab 1.278 (0.05, (1), 94, 579) 1.275 (0.05, (1), 94, 673) F0.752 1.257 P0.956 0.063 Conclusion Do NOT reject H 0 Do NOT reject H 0 Common value b c = 0.789 a c = -1.331 https://doi.org/10.1371/journal.pone.0268053.t001 PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 8 / 21 • Log SMR = 0.789 (±0.013) ×Log W– 1.331 (±0.007); R2¼0:824; P<0:0001 ð1Þ The mean values (±SD) of the slopes band elevations log a are plotted in Fig 5. A significant correlation (R 2 = 0.61; P <0.001) was found between these two parameters (Fig 5A), indicating a positive effect of metabolic level on the steepness of the lines scaling SMR to body size. However, neither of the two parameters correlated with individual growth rates (weight-specific values) (Fig 5B and 5C), very likely due to heteroskedastic distribution of variances along the SGR axis, where larger variances in slow growers (low SGR) can be attributed to the narrower size-ranges over which regression analysis were deployed compared with fast growers (high SGR). This poses a methodological constraint on the attempt of exploring the effects of individual growth rates on rates of metabolism. Thus, a further attempt was made by fitting a multiple regression model in which the SMR of each individual on a given sampling date was given as a simultaneous function of both the body weight and the weight-specific growth rate (SGR LW ) recorded on that date. Together with these independent variables, potential predictors in the model also included the combination of body weight and growth rate, although this interaction term did not significantly affect the SMR. The fitted equation (n = 665) with the two remaining variables is: • Log SMR = 0.677 (±0.016) ×Log W + 0.014 (±0.003) ×SGRLW−1.382 (±0.009) R2¼0:745; F: 921:3; P<0:0001 ð2Þ The weight-spec(3)ific growth rate exhibited by individuals exerted, along with body size, highly significant positive effects on SMR, and thus contributed to a more detailed description of factors affecting SMR. Particularly, this model accounts for the finding that, after the metabolic effects of growth were subsumed in the corresponding coefficient, body size scaling exponents were found to decrease from 0.79 (1) to 0.68 (2). Inter-individual allometries of standard metabolic rates. Inter-individual allometric relationships between SMR and LW were fitted using the size distribution of 95 mussels in Group 1 on the eight sampling dates during the growth period. The parameters of the fitted log-transformed equations are presented in Table 2, together with size ranges that varied between a minimum (3.3x) on day 7 and a maximum (18.1x) on day 147. ANCOVA results Fig 5. A) Relationship between proportionality constant (log a) and mass exponents (b) of individual allometric relationships of standard oxygen consumption and live weight. B) Mass-exponents b(±SD) and C) Proportionality constant, log a (±SD) of intra-individual allometric relationships of standard oxygen consumption and live weight plotted as a function of specific growth rate of live weight (SGR LW ). https://doi.org/10.1371/journal.pone.0268053.g005 PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 9 / 21 the values of growth coefficients for metabolism in other temporal phases, such F vs. S differences tended to lessen as growth activity was resumed. A similar behaviour of metabolic scaling along phases of ontogenetic growth have been reported for terrestrial gastropods, with slope values declining between juvenile (fast growth) and adult (slow growth) stages of development [55,56]. Second, mussels in Group 2 belonged to different cohorts of the population; therefore, the size variation in the allometric relationships (Fig 7) was mainly caused by age differences between individuals. In Group 2, the scaling exponent decreased significantly from 0.813 with mussels recently transferred to the laboratory from the natural intertidal environment (intraspecific1) to 0.709 with mussels acclimated for four months in the laboratory (intraspecific2). Such a shift in the scaling exponent might reflect the fact that inter-individual differences in growth conditions due to environmental factors (very likely associated with the trophic and thermal heterogeneity characteristic of the intertidal habitat) were attenuated after the 4-month maintenance of individuals under the optimal and stable conditions in the laboratory, thus reducing the original growth variability within this group, along with the already discussed effect of this variability on the size exponent. This interpretation is consistent with the hypothesis postulated by Glazier and collaborators [13,54,57,58] that ecological factors such as the presence of predators or changes in available diet or thermal environment affect the scaling exponent of intra-specific allometry of SMR. This scaling exponent of Group 2 (differentially aged mussels) after acclimation to laboratory conditions (b= 0.709) differed significantly from the common exponent of lines fitted to intra-individual SMR values (b= 0.79) or the average value of slopes recorded in the interindividual analysis of Group 1 mussels in the initial period (2 months) of growth under laboratory conditions (Table 2), when endogenous inter-individual differences in growth rate were considered to greatly contribute to the size variation of this single cohort of mussels. However, irrespective of some irregularities represented by growth phases, these differential growth effects tended to decline with the age of mussels, as indicated by the general behaviour of weight-specific growth rates during the maintenance period (Fig 2B), with a corresponding decline in the slope from day 63 onwards to values (average b= 0.68) that were not significantly different from those for Group 2 mussels (b= 0.709) or other reported values (b= 0.71) for a similar size range of the species [46]. Concluding remarks The scheme shown in Fig 8 was elaborated to help summarise some concluding points concerning size-scaling dependence on the variable levels of standard metabolism achieved by mussels exhibiting differences in growth conditions. These conclusions have been mainly inferred from the results of the present analysis of intra-individual SMR vs. body weight relationships in 95 juvenile individuals, although they were also supported by different approaches to the intra-specific (inter-individual) relationships reported herein. For argumentative convenience, the full size-range in this scheme has been plotted as the addition of two components: the first component is strictly dependent on the time of growth (age) and the second component is associated with differential growth accounting for size differences among individuals of the same age. Curves for SMR vs. body size were then plotted for the two categories of F and S group individuals, where the level of demand for tissue maintenance constitutes the specific difference regarding resting metabolism, according to reasons that have already been discussed. The assumption is that for the S group individuals, metabolic demands for the homeostatic regulation of body functions (e.g., surface-related processes of resource supply and waste disposal) are a prevalent component of PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 16 / 21 SMR over tissue maintenance, resulting in metabolic scaling of body size according to a surface/volume exponent (b=⅔). Conversely, in the F group individuals, SMR increment resulted from the higher demands for tissue maintenance. These demands are assumed to scale isometrically (b= 1) the size span achieved through differential growth, thus imposing a shift (as indicated by the arrow) in the weight exponent to values close to b=¾. This shift was observed irrespective of the origin of differences in growth conditions, either endogenous (Group 1 experiments) or exogenous (when maintenance in the laboratory of Group 2 mussels tended to smooth the original variability in growth conditions of freshly collected specimens), indicating that variable demands for tissue maintenance constitute a basic feature inherent to differences in growth performance. Since the present interpretation was based on assumptions underlying the MLB hypothesis [16] it is necessary to discuss how the present analysis supports the finding of a positive dependence in the relationship between the mass exponent and the level of resting metabolism (as represented by the slope and elevation of allometric functions in the intra-individual analysis; Fig 5A); while the opposite tendency (see Fig 2 in [16]) constitutes the core of MLB hypothesis predictions for resting metabolism, supported by empirical observations performed on a wide range of animal species, both ectotherms and endotherms [13,16,52]. The consideration of some distinctive features of bivalve molluscs, partly shared by other marine invertebrates of indeterminate growth, might help explain the above disagreement based on differences in the nature of variations in metabolic resting levels between the present case and the more general case presented by Glazier [13,16]. In the latter, minimum values are assumed to represent Fig 8. Proposed scheme accounting for a shift in the scaling exponent for the standard metabolic rate vs body size relationship, between slow growers (low maintenance demands) and fast growers (high maintenance demands). See text for details. https://doi.org/10.1371/journal.pone.0268053.g008 PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 17 / 21 constant tissue maintenance requirements (b= 1); the addition of regulatory demands (including expensive homeothermy, when applicable) satisfied through fluxes of metabolic resources, wastes, and (or) heat, which are surface-area-limited (b=⅔), to this minimum value would result in increased levels of the resting metabolism [16]. This is seen to differ in bivalve molluscs, whose growth heterosis has been rated among the highest in the animal kingdom [59], resulting in large inter-individual differences in growth rate, typically reaching up to 10-fold in the mussels of our study. Here, variable levels of resting metabolism would stem from growthrelated differences in tissue maintenance requirements superimposed on the rather weak regulatory demands that is characteristic of conforming organisms. Isometric size dependence of this metabolic component will thus prevail in faster growers, accounting for higher mass exponents when SMR scales the size ranges that are mostly dependent on growth rate differences among individuals, as in the case of intra-individual analysis of a single cohort of juveniles subjected to progressive size differentiation in the laboratory. The progressive decline of this differential factor in SMR with the aging of mussels would result in mass exponents approaching the ⅔value characteristic of metabolic demands driven by surface-to-volume-dependent processes. This also applies to additional demands set for activity, as in the metabolic scope for feeding and growth (MSFG) and is consistent with the bvalue of 0.65 recorded for the RMR. Supporting information S1 Data. (XLSX) Acknowledgments Authors are indebted to Douglas S. Glazier and one anonymous reviewer for valuable comments and suggestions that greatly contributed to improve the manuscript in the phase of revision. Author Contributions Conceptualization: Irrintzi Ibarrola, Enrique Navarro. Data curation: Kristina Arranz, Pablo Markaide. Formal analysis: Irrintzi Ibarrola, Kristina Arranz, Pablo Markaide. Funding acquisition: Irrintzi Ibarrola, Enrique Navarro. Investigation: Irrintzi Ibarrola, Kristina Arranz, Enrique Navarro. Methodology: Irrintzi Ibarrola, Kristina Arranz, Pablo Markaide. Project administration: Enrique Navarro. Resources: Kristina Arranz, Enrique Navarro. Software: Pablo Markaide. Supervision: Kristina Arranz, Pablo Markaide, Enrique Navarro. Writing – original draft: Irrintzi Ibarrola. Writing – review & editing: Enrique Navarro. PLOS ONE Metabolic size scaling and growth performance in mussels PLOS ONE | https://doi.org/10.1371/journal.pone.0268053 September 1, 2022 18 / 21 References 1. Hochachka PW, Somero GN. Biochemical Adaptation: Mechanism and Process in Physiological Evolution. Oxford University Press, New York, 2002. 2. Kleiber M. Body size and metabolism. Hilgardia 1932; 6: 315–353. 3. Hemmingsen AM. Energy metabolism as related to body size and respiratory surfaces, and its evolution. Reports of the Steno Memorial Hospital and the Nordisk Insulin Laboratorium (Copenhagen). 1960; 9: 1–110. 4. Peters RH. The Ecological Implications of Body Size. 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