Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Are patterns of growth adaptive?

Models which define fitness in terms of per capita rate of increase of phenotypes are used to analyse patterns of individual growth. It is shown that sigmoid growth curves are an optimal strategy (i.e. maximize fitness) if (Assumption 1a) mortality decreases with body size; (2a) mortality is a convex function of specific growth rate, viewed from above; (3) there is a constraint on growth rate, which is attained in the first phase of growth. If the constraint is not attained then size should increase at a progressively reducing rate. These predictions are biologically plausible. Catch-up growth, for retarded individuals, is generally not an optimal strategy though in special cases (e.g. seasonal breeding) it might be. Growth may be advantageous after first breeding if birth rate is a convex function of G (the fraction of production devoted to growth) viewed from above (Assumption 5a), or if mortality rate is a convex function of G, viewed from above (Assumption 6c). If assumptions 5a and 6c are both false, growth should cease at the age of first reproduction. These predictions could be used to evaluate the incidence of indeterminate versus determinate growth in the animal kingdom though the data currently available do not allow quantitative tests. In animals with invariant adult size a method is given which allows one to calculate whether an increase in body size is favoured given that fecundity and developmental time are thereby increased.

Obesity and body fat classification in the metabolic syndrome: impact on cardiometabolic risk metabotype

Obesity is a key factor in the development of the metabolic syndrome (MetS), which is associated with increased cardiometabolic risk. We investigated whether obesity classification by body mass index (BMI) and body fat percentage (BF%) influences cardiometabolic profile and dietary responsiveness in 486 MetS subjects (LIPGENE dietary intervention study). Anthropometric measures, markers of inflammation and glucose metabolism, lipid profiles, adhesion molecules and haemostatic factors were determined at baseline and after 12 weeks of 4 dietary interventions (high saturated fat (SFA), high monounsaturated fat (MUFA) and 2 low fat high complex carbohydrate (LFHCC) diets, 1 supplemented with long chain n-3 polyunsaturated fatty acids (LC n-3 PUFAs)). 39% and 87% of subjects classified as normal and overweight by BMI were obese according to their BF%. Individuals classified as obese by BMI (± 30 kg/m2) and BF% (± 25% (men) and ± 35% (women)) (OO, n = 284) had larger waist and hip measurements, higher BMI and were heavier (P < 0.001) than those classified as non-obese by BMI but obese by BF% (NOO, n = 92). OO individuals displayed a more pro-inflammatory (higher C reactive protein (CRP) and leptin), pro-thrombotic (higher plasminogen activator inhibitor-1 (PAI-1)), pro-atherogenic (higher leptin/adiponectin ratio) and more insulin resistant (higher HOMA-IR) metabolic profile relative to the NOO group (P < 0.001). Interestingly, tumour necrosis factor alpha (TNF-α) concentrations were lower post-intervention in NOO individuals compared to OO subjects (P < 0.001). In conclusion, assessing BF% and BMI as part of a metabotype may help identify individuals at greater cardiometabolic risk than BMI alone.

On the growth of errors in data assimilation systems

Considerable progress has taken place in numerical weather prediction over the last decade. It has been possible to extend predictive skills in the extra-tropics of the Northern Hemisphere during the winter from less than five days to seven days. Similar improvements, albeit on a lower level, have taken place in the Southern Hemisphere. Another example of improvement in the forecasts is the prediction of intense synoptic phenomena such as cyclogenesis which on the whole is quite successful with the most advanced operational models (Bengtsson (1989), Gadd and Kruze (1988)). A careful examination shows that there are no single causes for the improvements in predictive skill, but instead they are due to several different factors encompassing the forecasting system as a whole (Bengtsson, 1985). In this paper we will focus our attention on the role of data-assimilation and the effect it may have on reducing the initial error and hence improving the forecast. The first part of the paper contains a theoretical discussion on error growth in simple data assimilation systems, following Leith (1983). In the second part we will apply the result on actual forecast data from ECMWF. The potential for further forecast improvements within the framework of the present observing system in the two hemispheres will be discussed.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Human microbiota in health and disease

Each human body plays host to a microbial population which is both numerically vast (at around 1014 microbial cells) and phenomenally diverse (over 1,000 species). The majority of the microbial species in the gut have not been cultured but the application of culture-independent approaches for high throughput diversity and functionality analysis has allowed characterisation of the diverse microbial phylotypes present in health and disease. Studies in monozygotic twins, showing that these retain highly similar microbiota decades after birth and initial colonisation, are strongly indicative that diversity of the microbiome is host-specific and affected by the genotype. Microbial diversity in the human body is reflected in both richness and evenness. Diversity increases steeply from birth reaching its highest point in early adulthood, before declining in older age. However, in healthy subjects there appears to be a core of microbial phylotypes which remains relatively stable over time. Studies of individuals from diverse geopraphies suggest that clusters of intestinal bacterial groups tend to occur together, constituting ‘enterotypes’. So variation in intestinal microbiota is stratified rather than continuous and there may be a limited number of host/microbial states which respond differently to environmental influences. Exploration of enterotypes and functional groups may provide biomarkers for disease and insights into the potential for new treatments based on manipulation of the microbiome. In health, the microbiota interact with host defences and exist in harmonious homeostasis which can then be disturbed by invading organisms or when ‘carpet bombing’ by antibiotics occurs. In a portion of individuals with infections, the disease will resolve itself without the need for antibiotics and microbial homeostasis with the host’s defences is restored. The administration of probiotics (live microorganisms which when administered in adequate amounts confer a health benefit on the host) represents an artificial way to enhance or stimulate these natural processes. The study of innate mechanisms of antimicrobial defence on the skin, including the production of numerous antimicrobial peptides (AMPs), has shown an important role for skin commensal organisms. These organisms may produce AMPs, and also amplify the innate immune responses to pathogens by activating signalling pathways and processing host produced AMPs. Research continues into how to enhance and manipulate the role of commensal organisms on the skin. The challenges of skin infection (including diseases caused by multiply resistant organisms) and infestations remain considerable. The potential to re-colonise the skin to replace or reduce pathogens, and exploring the relationship between microbiota elsewhere and skin diseases are among a growing list of research targets. Lactobacillus species are among the best known ‘beneficial’ bacterial members of the human microbiota. Of the approximately 120 species known, about 15 are known to occur in the human vagina. These organisms have multiple properties, including the production of lactic acid, hydrogen peroxide and bacteriocins, which render the vagina inhospitable to potential pathogens. Depletion of the of the normal Lactobacillus population and overgrowth of vaginal anaerobes, accompanied by the loss of normal vaginal acidity can lead to bacterial vaginosis – the commonest cause of abnormal vaginal discharge in women. Some vaginal anaerobes are associated with the formation of vaginal biofilms which serve to act as a reservoir of organisms which persists after standard antibiotic therapy of bacterial vaginosis and may help to account for the characteristically high relapse rate in the condition. Administration of Lactobacillus species both vaginally and orally have shown beneficial effects in the treatment of bacterial vaginosis and such treatments have an excellent overall safety record. Candida albicans is a frequent coloniser of human skin and mucosal membranes, and is a normal part of the microbiota in the mouth, gut and vagina. Nevertheless Candida albicans is the most common fungal pathogen worldwide and is a leading cause of serious and often fatal nosocomial infections. What turns this organism from a commensal to a pathogen is a combination of increasing virulence in the organism and predisposing host factors that compromise immunity. There has been considerable research into the use of probiotic Lactobacillus spp. in vaginal candidiasis. Studies in reconstituted human epithelium and monolayer cell cultures have shown that L. rhamnosus GG can protect mucosa from damage caused by Candida albicans, and enhance the immune responses of mucosal surfaces. Such findings offer the promise that the use of such probiotic bacteria could provide new options for antifungal therapy. Studies of changes of the human intestinal microbiota in health and disease are complicated by its size and diversity. The Alimentary Pharmabiotic Centre in Cork (Republic of Ireland) has the mission to ‘mine microbes for mankind’ and its work illustrates the potential benefits of understanding the gut microbiota. Work undertaken at the centre includes: mapping changes in the microbiota with age; studies of the interaction between the microbiota and the gut; potential interactions between the gut microbiota and the central nervous system; the potential for probiotics to act as anti-infectives including through the production of bacteriocins; and the characterisation of interactions between gut microbiota and bile acids which have important roles as signalling molecules and in immunity. The important disease entity where the role of the gut microbiota appears to be central is the Irritable Bowel Syndrome (IBS). IBS patients show evidence of immune activation, impaired gut barrier function and abnormal gut microbiota. Studies with probiotics have shown that these organisms can exert anti-inflammatory effects in inflammatory bowel disease and may strengthen the gut barrier in IBS of the diarrhoea-predominant type. Formal randomised trials of probiotics in IBS show mixed results with limited benefit for some but not all. Studies confirm that administered probiotics can survive and temporarily colonise the gut. They can also stimulate the numbers of other lactic acid bacilli in the gut, and reduce the numbers of pathogens. However consuming live organisms is not the only way to influence gut microbiota. Dietary prebiotics are selectively fermented ingredients that can change the composition and/or activity of the gastrointestinal microbiota in beneficial ways. Dietary components that reach the colon, and are available to influence the microbiota include poorly digestible carbohydrates, such as non-starch polysaccharides, resistant starch, non-digestible oligosaccharides (NDOs) and polyphenols. Mixtures of probiotic and prebiotic ingredients that can selectively stimulate growth or activity of health promoting bacteria have been termed ‘synbiotics’. All of these approaches can influence gut microbial ecology, mainly to increase bifidobacteria and lactobacilli, but metagenomic approaches may reveal wider effects. Characterising how these changes produce physiological benefits may enable broader use of these tactics in health and disease in the future. The current status of probiotic products commercially available worldwide is less than ideal. Prevalent problems include misidentification of ingredient organisms and poor viability of probiotic microorganisms leading to inadequate shelf life. On occasions these problems mean that some commercially available products cannot be considered to meet the definition of a probiotic product. Given the potential benefits of manipulating the human microbiota for beneficial effects, there is a clear need for improved regulation of probiotics. The potential importance of the human microbiota cannot be overstated. ‘We feed our microbes, they talk to us and we benefit. We just have to understand and then exploit this.’ (Willem de Vos).

Physical activity attenuates the body mass index-increasing influence of genetic variation in the FTO gene 1-3.

BACKGROUND: Intronic variation in the FTO (fat mass and obesity-associated) gene has been unequivocally associated with increased body mass index (BMI; in kg/m(2)) and the risk of obesity in populations of different ethnicity. OBJECTIVE: We examined whether this robust genetic predisposition to obesity can be attenuated by being more physically active. DESIGN: The FTO variant rs1121980 was genotyped in 20,374 participants (39-79 y of age) from the European Prospective Investigation into Cancer and Nutrition-Norfolk Study, an ethnically homogeneous population-based cohort. Physical activity (PA) was assessed with a validated self-reported questionnaire. The interaction between rs1121980 and PA on BMI and waist circumference (WC) was examined by including the interaction term in mixed-effect models. RESULTS: We confirmed that the risk (T) allele of rs1121980 was significantly associated with BMI (0.31-unit increase per allele; P < 0.001) and WC (0.77-cm increase per allele; P < 0.001). The PA level attenuated the effect of rs1121980 on BMI and WC; ie, whereas in active individuals the risk allele increased BMI by 0.25 per allele, the increase in BMI was significantly (P for interaction = 0.004) more pronounced (76%) in inactive individuals (0.44 per risk allele). We observed similar effects for WC (P for interaction = 0.02): the risk allele increased WC by 1.04 cm per allele in inactive individuals but by only 0.64 cm in active individuals. CONCLUSIONS: Our results showed that PA attenuates the effect of the FTO rs1121980 genotype on BMI and WC. This observation has important public health implications because we showed that a genetic susceptibility to obesity induced by FTO variation can be overcome, at least in part, by adopting a physically active lifestyle.

Sustaining growth and profits in a rapidly changing world - a Chinese perspective

The aim of this paper is to stimulate discussion about how Chinese construction and professional service companies can best equip themselves and grow sustainably and profitably in a rapidly changing world. It identifies some of the issues and risks faced by Chinese construction and professional service companies operating domestically and overseas. China has experienced a period of rapid economic growth which is also reflected in the annual construction output. China’s population is the largest in the world, but the demographic profile is changing with an ageing population and a changing dependency ratio. The population is urbanising at a fast rate, putting pressure on housing, and infrastructure. The government must plan for the future and the construction sector must be involved in that planning. The paper considers the drivers shaping China’s construction market, how companies are responding by embracing change and internationalising by seeking to exploit their skills overseas. The drivers are globalisation, urbanisation, demographic change, sustainability, safety and health, and the evolution of professional services as a core part of construction activity. Clients/owners are driving change by demanding more certainty and more sustainable projects.

Competitive fitness in coronaviruses is not correlated with size or number of double-membrane vesicles under reduced-temperature growth conditions

Positive-stranded viruses synthesize their RNA in membrane-bound organelles, but it is not clear how this benefits the virus or the host. For coronaviruses, these organelles take the form of double-membrane vesicles (DMVs) interconnected by a convoluted membrane network. We used electron microscopy to identify murine coronaviruses with mutations in nsp3 and nsp14 that replicated normally while producing only half the normal amount of DMVs. Viruses with mutations in nsp5 and nsp16 produced small DMVs but also replicated normally. Quantitative RT-PCR confirmed that the most strongly affected of these, the nsp3 mutant, produced more viral RNA than wild-type virus. Competitive growth assays were carried out in both continuous and primary cells to better understand the contribution of DMVs to viral fitness. Surprisingly, several viruses that produced fewer or smaller DMVs showed a higher relative fitness compared to wild-type virus, suggesting that larger and more numerous DMVs do not necessarily confer a competitive advantage in primary or continuous cell culture. For the first time, this directly demonstrates that replication and organelle formation may be, at least in part, studied separately during positive-stranded RNA virus infection.

How body mass and lifestyle affect juvenile biomass production in placental mammals

In mammals, the mass-specific rate of biomass production during gestation and lactation, here called maternal productivity, has been shown to vary with body size and lifestyle. Metabolic theory predicts that post-weaning growth of offspring, here termed juvenile productivity, should be higher than maternal productivity, and juveniles of smaller species should be more productive than those of larger species. Furthermore because juveniles generally have similar lifestyles to their mothers, across species juvenile and maternal productivities should be correlated. We evaluated these predictions with data from 270 species of placental mammals in 14 taxonomic/lifestyle groups. All three predictions were supported. Lagomorphs, perissodactyls and artiodactyls were very productive both as juveniles and as mothers as expected from the abundance and reliability of their foods. Primates and bats were unproductive as juveniles and as mothers, as expected as an indirect consequence of their low predation risk and consequent low mortality. Our results point the way to a mechanistic explanation for the suite of correlated life-history traits that has been called the slow–fast continuum.

Patterns of maximum body size evolution in Cenozoic land mammals: eco-evolutionary processes and abiotic forcing

There is accumulating evidence that macroevolutionary patterns of mammal evolution during the Cenozoic follow similar trajectories on different continents. This would suggest that such patterns are strongly determined by global abiotic factors, such as climate, or by basic eco-evolutionary processes such as filling of niches by specialization. The similarity of pattern would be expected to extend to the history of individual clades. Here, we investigate the temporal distribution of maximum size observed within individual orders globally and on separate continents. While the maximum size of individual orders of large land mammals show differences and comprise several families, the times at which orders reach their maximum size over time show strong congruence, peaking in the Middle Eocene, the Oligocene and the Plio-Pleistocene. The Eocene peak occurs when global temperature and land mammal diversity are high and is best explained as a result of niche expansion rather than abiotic forcing. Since the Eocene, there is a significant correlation between maximum size frequency and global temperature proxy. The Oligocene peak is not statistically significant and may in part be due to sampling issues. The peak in the Plio-Pleistocene occurs when global temperature and land mammal diversity are low, it is statistically the most robust one and it is best explained by global cooling. We conclude that the macroevolutionary patterns observed are a result of the interplay between eco-evolutionary processes and abiotic forcing

Fundamental insights into ontogenetic growth from theory and fish

The fundamental features of growth may be universal, because growth trajectories of most animals are very similar, but a unified mechanistic theory of growth remains elusive. Still needed is a synthetic explanation for how and why growth rates vary as body size changes, both within individuals over their ontogeny and between populations and species over their evolution. Here we use Bertalanffy growth equations to characterize growth of ray-finned fishes in terms of two parameters, the growth rate coefficient, K, and final body mass, m∞. We derive two alternative empirically testable hypotheses and test them by analyzing data from FishBase. Across 576 species, which vary in size at maturity by almost nine orders of magnitude, K scaled as m_∞^(-0.23). This supports our first hypothesis that growth rate scales as m_∞^(-0.25) as predicted by metabolic scaling theory; it implies that species which grow to larger mature sizes grow faster as juveniles. Within fish species, however, K scaled as m_∞^(-0.35). This supports our second hypothesis which predicts that growth rate scales as m_∞^(-0.33) when all juveniles grow at the same rate. The unexpected disparity between across- and within-species scaling challenges existing theoretical interpretations. We suggest that the similar ontogenetic programs of closely related populations constrain growth to m_∞^(-0.33) scaling, but as species diverge over evolutionary time they evolve the near-optimal m_∞^(-0.25) scaling predicted by metabolic scaling theory. Our findings have important practical implications because fish supply essential protein in human diets, and sustainable yields from wild harvests and aquaculture depend on growth rates.