France

Metabolism is a fundamental property of organisms as it underpins all life-sustaining processes. The relationship between metabolic rate (R) and body size (M) has become a central topic in ecology, yet the mechanism(s) that underlie this mass dependence (termed scaling) and its variation, remain enigmatic. Metabolic scaling can be affected by temperature and activity, as warming and muscular work not only accelerate metabolic level (L), but often lead to changes in the scaling exponent (or slope b, in log R vs. log M). This change has been explained through a shift of resource supply from volume- to surface-area related processes. However, whether the same supply constraints apply among and within species is unclear, as the quantitative relationship between b and L remains largely untested within species. Only by understanding these patterns we will be able to address proximate and ultimate mechanisms behind metabolic scaling variation. Through a meta-analysis, we quantitatively compare the intra-specific change in b when L is increased by either temperature or locomotor activity in a wide range of ectothermic vertebrates, including fish, amphibians, and reptiles. We show that b decreases with temperature-increased L in water-breathing (fish) but not in air-breathing species (amphibians and reptiles), whereas b increases with activity-increased L in air-breathing but not in water-breathing species. Our findings in the most comprehensive intra-specific analysis of ectothermic vertebrates to date indicate that b varies differently with temperature and activity in water- and air-breathers, and suggest that oxygen availability in water may constrain metabolic scaling of fish.

Why and how does metabolic rate scale with body size?

Intraspecific variation in metabolic scaling with temperature and activity differs between water- and air-breathing ectothermic vertebrates

body mass

ontogeny

animals

oxygen limitation

ecophysiology

ecology

constraints

The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

Model predictive control (MPC) is indisputably one of the advanced control techniques that have significantly affected control engineering practice with thousands of controllers implemented in various fields, spanning from the process industry to automotive and robotics. This is due to its unique ability to handle constraints, take preview information about disturbances and setpoint changes into account, and optimize performance. Furthermore, MPC allows the consideration of various types of dynamics, from linear to nonlinear, discrete to continuous, as well as an online adaptation of models and parameters. The research community on MPC is very active, with hundreds of papers published every year. Over the past decades, many theoretical, as well as implementation results, have been achieved.

### **All content presented at NMPC2021, including videos, papers and slides will be available only to registered (regular/student) participants. The content can be accessed until August 31st, 2021.**



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Nonlinear Model Predictive Control Conference 2021

The IFAC Conference on Nonlinear Model Predictive Control (NMPC 2021) aims to bring together researchers interested in and work in the MPC field from both academia and industry. This allows us to reflect and establish the current state-of-the-art and focus on the future development of the MPC field towards relevant directions.

technical paper

Metabolic rate is closely related to body size (body mass), but when mass increases, metabolic rate usually increases less. This allometric scaling relationship between metabolic rate and body mass is fundamental to biology and widely applied, but also one of the most debated concepts in integrative and comparative physiology, ecology, and evolutionary biology.

Several theories and hypotheses have been put forward to explain why and how metabolic rate scales with body mass, and why there appears to be variation in how steep this scaling relationship is among different taxa and physiological or ecological conditions (e.g. 'surface area', 'cell size', 'fractal distribution network', ‘dynamic energy budget’, and ‘metabolic-level boundaries’ theories or hypotheses). However, the lack of consensus on these important topics is a major barrier to our understanding of the pace at which organisms of different sizes and species expend energy and need to consume resources such as food and oxygen from the environment. It also limits our ability to predict how metabolic rate and body size (co)evolves, and how climate change affects metabolic demands and body sizes, as metabolic scaling exponents are used to model how these key organismal traits are affected by changing temperature and oxygen levels. The importance of metabolic scaling is clear, yet it remains one of the most controversial concepts in biology.

The overall aim of this satellite meeting is to bring together researchers working with metabolic scaling, to: (1) bring the field up to speed on state-of-the-art knowledge and research on metabolic scaling; (2) help understand how the vastly different views and opinions on metabolic scaling can persist despite more than a century of research (e.g. scaling in proportion to surface area or not, universal ¾-power scaling or not, governed by ecological vs. physical or geometric factors); and (3) identify and help streamline specific areas of research on metabolic scaling that will be particularly important for our further understanding of why and how metabolic rate scales with body size.

The meeting is being organised as part of the Animal Section of the SEB and will therefore have a focus on metabolic scaling of animals, but work on other organisms is welcome where this can provide insight into metabolic scaling in general.

The overall aim of this satellite meeting is to bring together researchers working with metabolic scaling, to: bring the field up to speed on state-of-the-art knowledge and research on metabolic scaling; help understand how the vastly different views and opinions on metabolic scaling can persist despite more than a century of research (e.g. scaling in proportion to surface area or not, universal ¾-power scaling or not, governed by ecological vs. physical or geometric factors); and identify and help streamline specific areas of research on metabolic scaling that will be particularly important for our further understanding of why and how metabolic rate scales with body size.

Living organisms use energy to grow and reproduce, so the processes of energy metabolism and biological production should be tightly bound. Based on this fundamental tenet, we develop new theory that predicts the relationships between three fundamental aspects of life: metabolic rate, growth, and reproduction. We test and validate this theory using empirical data for more than 10,000 species from 12 phyla, and show that the optimisation of these processes yields the observed allometries of metazoan life. We conclude that metabolic rate, growth, and reproduction are inextricably linked and together determine fitness, and, in contrast to longstanding dogma, that no single component drives another.

Metabolic scaling is the product of life history optimization

The dependence of metabolic rate on body mass, or metabolic scaling, during animal growth varies among species. Some of this variation is systematic, varying with species habitat. For instance, in aquatic ectotherms, pelagic species have steeper metabolic scaling than benthic ones. Although the selection pressures producing this variation remain insufficiently tested, we can use this variation to predict the degree of phenotypically plastic reduction in size-at-maturity in response to warmer growth conditions. We produce a new Emergent Scaling model, which fit the data significantly better in strength and direction of response, when assessed against the influential Gill Oxygen Limitation Model. We then explore how this model may be used to help quantify the combined effect of multiple stressors on growth and mature size in warming waters. We propose that reductions in animal growth and mature size in nature may be compared against a standardized “no-stress” response to temperature that is observed or predicted in controlled studies in which warming is benign, resources are abundant, and mortality is negligible. Such “no-stress” body size reductions, predicted using variation in metabolic scaling, may therefore be able to provide a standard against which combined stress impacts in the field can be compared.

Evolutionary significance and ecological consequences of variation in metabolic scaling in aquatic ectotherms

Metabolic rates of fish scale with body mass according to power-law relationships with a scaling exponent generally lower than 1. This means that animals use proportionally less oxygen as they grow; a concept which is widely accepted in experimental biology. The mechanisms driving this relationship, however, are hotly debated. The gill surface area (GSA) dictates the oxygen availability for metabolic processes and thus represents a promising candidate for explaining potentially “supply-limited” metabolic scaling relationships in fish. Here, we conducted a literature review to explore the relationships between body mass, GSA and metabolic rates of various fish species. Furthermore, we reared barramundi under optimal (29℃), warm (35℃) and cold (23℃) conditions and measured metabolic rate and GSA on multiple occasions throughout the trial. In our analyses, we introduced a new parameter, the ratio S, which provides a measure of GSA in relation to the metabolic requirements for maintenance (SSMR) and maximum activity (SAMR). We show that the scaling exponents for SSMR and SAMR are consistently close to zero, with only a few exceptions where S either increased or decreased. We furthermore show that S only decreases with body size when fish are acclimated to cooler-than-optimal temperatures. These findings suggest that GSA is sufficient to meet fish oxygen requirements throughout life, even if the temperature rises, and that growth is not universally restricted by oxygen supply limitations at the gills.

Scaling relationships of metabolic rate and gill surface area: Is oxygen demand limited by oxygen supply as fish grow?

Size at the start of life reflects the initial per offspring parental investment – including both the embryo and the nutrients supplied to it. Initial offspring size can vary substantially both within and among species. Within species, increasing offspring size can enhance growth, reproduction, competitive ability, and reduce susceptibility to predation and starvation later in life, that can ultimately increase fitness. Previous work has suggested that the fitness benefits of larger offspring size may be driven by energy expenditure during development – or how offspring metabolic rate scales with offspring size. Despite the importance of early life energy expenditure in shaping later life fitness trajectories, consideration of among-species scaling of metabolic rate at the time of birth as a potential source of general metabolic scaling patterns has been overlooked by theory. Here we review the patterns and processes of energy expenditure at the start of life when mortality is often greatest. We compile existing data on metabolic rate and offspring size for 184 ectotherm species spanning eight phyla and use phylogenetically-controlled methods to quantify among-species scaling patterns across a 109-fold mass range.

The evolution of offspring size: a metabolic scaling perspective

Understanding how and why metabolic rate scales allometrically with body mass in fish is of particular interest given the observed decline in the maximum body size of aquatic ectotherms under climate warming. Size-dependent oxygen limitation has been proposed to drive these body size declines, particularly at warmer temperatures. If this is true, then in warm settings and with an excess oxygen supply (hyperoxia) we would expect scaling exponents to steepen as larger fish would require comparatively more oxygen to fulfill their proposed debt. To test this, we measured the aerobic metabolic performance of Galaxias maculatus upon acute exposure to hyperoxia (150% air saturation) and following five months of acclimation to hyperoxia, at 15°C and 20°C. Despite hyperoxia acclimation, scaling exponents for standard and maximum metabolic rates did not differ from normoxia-acclimated conspecifics, implying that oxygen limitation does not regulate allometric scaling. Interestingly, the scaling exponents for standard metabolic rate in normoxia- and hyperoxia-acclimated fish at 15°C were particularly high (1.05 and 1.08, respectively). Further investigation revealed that these high exponents were likely driven by differences in the reproductive state of smaller (immature) vs. larger (mature) fish, illustrating the increased energetic demands of the reproductive process and the need to account for reproductive stage when assessing metabolic scaling in fish.

Effects of hyperoxia and reproductive state on the metabolic scaling of a temperate fish Galaxias maculatus

"Various well-known growth models, including the Bertalanffy model, the models developed within the framework of the Metabolic Theory of Ecology (MTE), and the standard DEB model, will be introduced and compared, with special emphasis on the interspecific scaling of the model parameters. 
At first sight, it seems that MTE and DEB would come up with assumptions that give rise to totally contradictory predictions concerning the relationship between metabolic rate and ultimate size. Whereas DEB points to the area-specific assimilation rate as the characteristic that differs among species of different ultimate size, MTE thinks that differences in ultimate size are basically due to differences in the volume-specific maintenance. Further explorations, however, yield the surprising result that under certain conditions both theories predict a similar relationship between metabolic rate and ultimate mass.

"Various well-known growth models, including the Bertalanffy model, the models developed within the framework of the Metabolic Theory of Ecology (MTE), and the standard DEB model, will be introduced and compared, with special emphasis on the interspecific scaling of the model parameters. 
At first sight, it seems that MTE and DEB would come up with assumptions that give rise to totally contradictory predictions concerning the relationship between metabolic rate and ultimate size. Whereas DEB points to the area-specific assimilation rate as the characteristic that differs among species of different ultimate size, MTE thinks that differences in ultimate size are basically due to differences in the volume-specific maintenance. Further explorations, however, yield the surprising result that under certain conditions both theories predict a similar relationship between metabolic rate and ultimate mass.

"

The scaling of metabolic rate: a comparison between predictions based on DEB theory and other approaches

"Time integrated Field Metabolic Rate (FMR) is arguably the most ecologically relevant measure of the energetics of wild animals, but the relative complexity of determining FMR routinely means that we have relatively few large datasets describing variation in energy use in free-living wild animals, particularly for aquatic ectotherms where double labelled water methods cannot be used.
Emerging proxies based on stable isotope systematics associated with respiration allow retrospective estimation of time integrated field metabolic rate, experienced temperature and growth in any free-living marine teleost fish. Here we present FMR data obtained for 780 individuals from 10 species of fishes sampled within a one month period in the Barents Sea. The dataset includes individual Atlantic cod with a body size range over 4 orders of magnitude, dramatically increasing the body size range over which scaling of field metabolic rates have been assessed for any single species. 
The allometric exponent for body size scaling of FMR is 0.9 across all taxa. Within-species scaling exponents range from 0.7 – 1.2. Mass scaling exponents may be non-linearly related to body size, but these field data are confounded by size-dependent temperature preferences. In all but one species, FMR is relatively insensitive to temperature, implying that FMR is not strongly constrained by external temperatures for fish populations operating within environmental conditions to which the population is adapted/acclimated. 



"

Body size and temperature scaling of field metabolic rate in wild marine fishes

Adult body size in insects can be influenced by environmental conditions during larval growth. The effect of such intraspecific variation in body mass on flight performance is poorly understood. In Batocera rufomaculata, a large tree boring beetle, often engaging in dispersal flight, adults emerging from larvae that developed in a dying host tree under nutrient-deprived diet conditions, are smaller than individuals who developed in nutrient rich environments. This leads to a large variation in adult body mass (1 to 7 g) with an expected effect on flight Metabolic Rate (MR). Measuring MR poses a formidable challenge in free-flying insects who can’t breathe into masks or be trained to fly in controlled settings. Consequently, flight MR has been predominantly measured on hovering or tethered insects flying in closed systems. In this study we applied the ‘bolus injection of isotopic 13C Na-bicarbonate’ method to explore the relationship between intraspecific body size and power expended during tethered steady forward flight and free flying B. rufomaculata. While the method was previously used solely on vertebrates, we report a 90% accuracy of the method in our beetle when compared to direct respirometry. We found that free FMR and tethered FMR increased in relation to body mass as 99·𝑀0.54 and 36∙M^0.56 respectfully showing that while the free FMR is ~3 times higher than FMR recorded in tethered flight, the mass exponent remains unchanged. This mass exponent of ~0.55 is lower than the expected exponent for interspecific variation in body mass of M^0.74 to M^0.98.

The scaling of free flight energetics of the mango stem borer beetle, Batocera rufomaculata

Metabolic scaling theory: New Insights in Scaling Form, Function & Diversity

Metabolic rate (MR) usually changes (scales) out of proportion to body mass (BM) as MR = aBM^b, where a is a normalisation constant and b the scaling exponent that reflects how steep this change is. This scaling relationship is fundamental to biology, but over a century of research has provided little consensus on the value of b, and why it appears to vary among taxa and taxonomic levels. Here, I show that individual variation in fish growth under naturally restricted food availability can explain variation in within-individual (ontogenetic) b for standard metabolic rate (SMR) of brown trout (Salmo trutta); the fastest growers had the steepest metabolic scaling, and within-individual b varied much more widely than previously assumed from work on different individuals or different species, from –1 to 1. The negative b for some individuals was caused by reductions in metabolic rate, likely to maintain positive growth, which resulted in a mean within-individual b that was significantly lower than the across-individual (‘static’) b, a difference that also existed for another species, cunner (Tautogolabrus adspersus). I also show that across-species (‘evolutionary’) b for SMR of 134 fishes is significantly steeper than the mean ontogenetic b for the trout and cunner. I hypothesise that the steeper evolutionary than ontogenetic scaling for fishes could arise as a by-product of natural selection for fast-growing individuals with steep metabolic scaling early in life, where size-selective mortality is high. I support this by showing that b for SMR tends to increase with natural mortality rates of fish larvae within taxa.

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Metabolic scaling is the product of life history optimization

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Reducing the computational effort of min-max model predictive control with regional feedback laws

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