Fundamental insights into ontogenetic growth from theory and fish Richard M. Siblya,1, Joanna Bakera, John M. Gradyb, Susan M. Lunac, Astrid Kodric-Brownb, Chris Vendittia, and James H. Brownb,d,1 aSchool of Biological Sciences, University of Reading, Reading, Berkshire RG6 6AS, United Kingdom; bBiology Department, University of New Mexico, Albuquerque, NM 87131; cFishBase Information and Research Group, Inc. (FIN), International Rice Research Institute (IRRI), Los Baños, 4031 Laguna, Philippines; and dSanta Fe Institute, Santa Fe, NM 87501 Contributed by James H. Brown, September 28, 2015 (sent for review May 4, 2015; reviewed by Andrew J. Kerkhoff and Kirk O. Winemiller) The fundamental features of growth may be universal, because body mass is generally around −1/4, but there has been debate as to growth trajectories of most animals are very similar, but a unified whether the same scaling applies to ontogenetic growth (9–11). mechanistic theory of growth remains elusive. Still needed is a Theoretical models and empirical studies of fish growth have synthetic explanation for how and why growth rates vary as body the potential to inform how metabolic processes fuel and regu- size changes, both within individuals over their ontogeny and late growth (4, 6, 9, 12). Fish vary in mature body size by nearly between populations and species over their evolution. Here, we nine orders of magnitude, from less than 5 mg for the dwarf use Bertalanffy growth equations to characterize growth of ray- pygmy goby (Pandaka pygmae) to more than 2 tons for the ocean finned fishes in terms of two parameters, the growth rate sunfish (Mola mola), and show substantial within-species as well coefficient, K, and final body mass, m∞. We derive two alternative as across-species variation in final body size. Interestingly, how- ever, with the exception of a few freshwater species the vast majority empirically testable hypotheses and test them by analyzing data ∼ from FishBase. Across 576 species, which vary in size at maturity of fish species start life at a nearly constant size, eggs 1mmin −0.23 diameter and 1 mg in mass (13, 14). To reach mature size, they grow by almost nine orders of magnitude, K scaled as m∞ . This sup- ports our first hypothesis that growth rate scales as m−0.25 as pre- less than 1 order of magnitude for the smallest species, such as the ∞ dwarf goby, and about 11 orders of magnitude for the largest fish, dicted by metabolic scaling theory; it implies that species that ECOLOGY such as ocean sunfish and giant tunas (www.fishbase.org). Fish oc- grow to larger mature sizes grow faster as juveniles. Within fish −0.35 cur in an enormous variety of environments, including nearly all species, however, K scaled as m∞ . This supports our second m−0.33 marine and fresh waters and a range of temperatures from below hypothesis, which predicts that growth rate scales as ∞ when freezing (0 °C) in the Antarctic Ocean to above 40 °C in hot springs. all juveniles grow at the same rate. The unexpected disparity be- It has long been known that mass-specific growth rates of fish, tween across- and within-species scaling challenges existing theo- like other animals, decrease with increasing body size, both retical interpretations. We suggest that the similar ontogenetic within individuals over ontogenetic development and across taxa m−0.33 programs of closely related populations constrain growth to ∞ over phylogenetic evolution (12, 15). Data on fish growth are scaling, but as species diverge over evolutionary time they evolve typically quantified using the Bertalanffy model, which has three the near-optimal m−0.25 scaling predicted by metabolic scaling theory. ∞ parameters: neonate mass, m0; final body mass, m∞;andagrowth Our findings have important practical implications because fish supply rate coefficient, K. We developed two models to account for how essential protein in human diets, and sustainable yields from wild K might scale with m∞. Scaling according to the −1/3 power is harvests and aquaculture depend on growth rates. expected if growth rate after hatching is the same for all fish. This is plausible if the fish are all of the same species, but might also metabolic theory of ecology | Bertalanffy growth | scaling theory hold across species because most start life at similar sizes, about 1 mg in mass. On the other hand, metabolic scaling theory predicts rowth is a universal attribute of life. All organisms have life Gcycles that include growth. Growing organisms take up en- Significance ergy and material resources from their environment, transform them within their bodies, and allocate them among maintenance, Understanding growth of fish is important, both for regulating growth, and reproduction. Over ontogeny, large, multicellular, harvests of wild populations for sustained yields, and for using complex animals increase in mass by many orders of magnitude, artificial selection and genetic engineering to increase pro- from microscopic zygotes to much larger mature adults. In such ductivity of domesticated fish stocks. We developed theory to animals, growth necessarily entails integration of three phenomena. account for how growth rate varies with body size, within in- First, growth is fueled by metabolism as energy-rich carbon com- dividuals as they grow to maturity and across species as they pounds are respired to generate the ATP that powers the assembly evolve. Data on fish growth in FishBase supported our theo- of organic molecules and essential elements to synthesize biomass. retical predictions. We found that growth rates scaled differ- Second, mass and energy balance are regulated so that uptake ently in populations of the same species than they scaled exceeds expenditure and a stock of biomass accumulates. Third, across species. We suggest that similar developmental pro- the synthetic process is integrated with ontogenetic development so grams of close relatives constrain growth, but as species di- that growth is regulated as body size increases by orders of mag- verge over evolutionary time they evolve the near-optimal −1/4 nitude and differentiated tissues and organs are produced. power scaling predicted by metabolic scaling theory. Growth trajectories of most animals are nearly identical when rescaled by body mass at maturity and time to reach mature size Author contributions: R.M.S., J.B., C.V., and J.H.B. designed research; R.M.S., J.B., C.V., and (Fig. 1). This suggests that the fundamental features of growth may J.H.B. performed research; S.M.L. extracted the data from FishBase; R.M.S., J.B., C.V., and be universal or nearly so (1–7; www.fishbase.org). Nevertheless, how J.H.B. analyzed data; and R.M.S., J.B., J.M.G., A.K.-B., C.V., and J.H.B. wrote the paper. energy and materials are processed to regulate growth as body size Reviewers: A.J.K., Kenyon College; and K.O.W., Texas A&M University. changes over both ontogeny and phylogeny remain poorly un- The authors declare no conflict of interest. derstood (8). Because growth is powered by metabolism, scaling of 1To whom correspondence may be addressed. Email: [email protected] or jhbrown@ metabolic rate, both within individuals over ontogenetic develop- unm.edu. ment and across species over phylogenetic evolution, is relevant. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. Across species, the scaling of mass-specific metabolic rate with adult 1073/pnas.1518823112/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1518823112 PNAS Early Edition | 1of6 Downloaded by guest on September 30, 2021 −1=4 i) Hypothesis 1: K scales as m∞ . Consider first g when the fish is at a specified proportionn of finalo body mass—e.g., 1/2 m∞. 1 = 2 = 3 − Then Eq. gives gð1=2Þm∞ K 2 1 . Viewed in this way gð1=2Þm∞ is proportional to K,soK is an index of growth rate (16). Hence K is a biological rate, and metabolic theory predicts that mass-specific biological rates generally scale across species negatively with body size and positively with temperature T as follows: −α −E=cT K = K0m∞ e , [3] where K0 is a normalization constant; α is the allometric scaling exponent, which usually is ∼1/4; T is environmental temperature in kelvin (= °C + 273.2); E is an “activation energy,” which is usually ∼0.65 eV for processes governed by respiration; and c is − − Boltzmann’s constant (c = 8.62 × 10 5 eV·K 1) (11, 17). Taking logarithms, we get the following: = −α − = + [4] loge K loge m∞ E cT loge K0. So in a regression of loge K on loge m∞ and 1/cT the regression coefficients are predicted to be –α or approximately −1/4 and –E Fig. 1. Individual body mass plotted against age for the southern mouth- − brooder, Pseudocrenilabrus philander, and the guppy, Poecilia reticulata. or approximately 0.65, respectively. −1=3 The curves represent fitted Bertalanffy growth equations. ii) Hypothesis 2: K scales as m∞ . Our second hypothesis is also developed from Eq. 2. With the exception of a few freshwater species, offspring of nearly all bony fish hatch at very similar size, −1/4 scaling across species. We tested these predictions using around a millimeter long, corresponding to a mass of around 0.001 g empirical growth data from FishBase and found some support for (13, 14). So, neonate mass, m0, is nearly invariant, and rapid both models. Within-species coefficients scaled close to the −1/3 growth after hatching would seem to confer a large fitness advan- power, but across species they scaled close to −1/4. This un- tage. According to this idea, we might expect all juveniles to grow at expected disparity challenges existing theory.