Fundamental insights into ontogenetic growth from theory and

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 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 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. We suggest that the the same speed, as fast as possible, if they are at the same tem- within-species scaling reflects shared ontogenetic development perature. It follows that after adjusting for temperature the relative growth rate at hatching when mass = 0.001 g, g0.001, should be the programs, which are modified by natural selection over phyloge- = 2 − same for all fish. Setting m 0.001 in Eq. , and noting that netic evolution toward the optimum of 1/4 predicted by meta- 1=3 1=3 ðm∞=mÞ is then 1, gives g0.001 ≈ 10 K m∞ .Ifg0.001 is the bolic scaling theory. Because much of the protein in human 1=3 diets worldwide comes from fish that are either caught in the wild same for all fish then K m∞ must also be constant, in other words: in the oceans or cultured on fish farms, these theoretical and − 1 empirical aspects of fish growth should be important in imple- K ∝ m∞3, menting fishery regulations and aquacultural practices to ensure

sustainable and economical yields. giving a regression coefficient of –1/3 in a regression of loge K on log m∞. Theory e So hypotheses 1 and 2 differ in the value of the coefficient or Here, we derive two mathematical models producing contrasting the slope of the regression line in a plot of loge K on loge m∞. predictions about the scaling of growth rate with final body mass. Hypothesis 1 predicts that the coefficient is –1/4, whereas hy- The predictions apply to both within- and across-species scaling, pothesis 2 predicts it is –1/3. which we expected to be the same. We start from the premise that The following analysis aims to evaluate these alternative pre- growth is well described by the Bertalanffy growth equation (1, 12) dictions both among closely related populations and across dif- (examples in Fig. 1). A common form of the Bertalanffy growth ferent species, and to explore their implications. Because the growth data in FishBase are presented in terms of the Bertalanffy equation has three parameters: neonate mass, m0;asymptoticma- ture mass, m∞; and growth coefficient, K. The equation specifies coefficient, K, we are unable to comment on the consequences individual juvenile mass, m, as a function of age, t,asfollows: of using other, more explicitly mechanistic growth models (e.g., refs.4,6,and9).

" ! # 1 = 3 3 Results m0 —Kt=3 m = m∞ 1 − 1 − e . [1] m∞ We obtained data on K, m∞, and water temperatures of ray- finned fishes (Class ) from FishBase as described in Differentiation of Eq. 1 gives the Bertalanffy growth equation in Materials and Methods. Data were available for 3,119 noncaptive an alternative form: populations belonging to 576 species, with populations varying in their K and m∞ values, but data on water temperatures were

1 = available for only 136 species. To find the value of the within- and 1 dm m∞ 3 g = = K − 1 , [2] across-species regression coefficients in a regression of loge K on m dt m loge m∞ and 1/cT, we used a phylogenetic generalized linear mixed model (PGLMM) (18) separating within-species variation from the where g is relative growth rate, so the proportionate increase in overall relationship across species using the within-subject centering body mass per unit time when the fish is of mass m. Note that approach of ref. 19 with two fixed effects: average m∞ per species, according to this formulation, g is inherently a mass-specific m∞across, and within-species deviation from m∞across, m∞within. growth rate, because it is indexed in terms of m. Additional Across-species variations in the effects of m∞within were included consideration of Eq. 2 gives the two hypotheses investigated in as random effects. To obtain a single indicator of water tem- this paper. perature, T, we calculated the average of the species minimum

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1518823112 Sibly et al. Downloaded by guest on September 30, 2021 and maximum temperatures, expressed it in kelvin, and included A it as an additional species-level fixed-effect parameter. The phylogenetic regression equation for the model without temperature, illustrated in Fig. 2A, was as follows:

log K = − 0.23ð± SE 0.01Þlog m∞ e e across [5] − ð± Þ + ð± Þ 0.35 SE 0.01 loge m∞within 0.25 SE 0.65 ,

with phylogenetic heritability (h2; Materials and Methods) 0.90 ± SE 0.01, n = 576, and this accounted for 17% of the variance 2 [R adj (20)]. The phylogenetic regression equation for the model with tem- perature, illustrated in Fig. 2 B and C, was as follows: B = − ð± Þ loge K 0.23 SE 0.02 loge m∞across − ð± Þ − ð± Þ = 0.36 SE 0.02 loge m∞within 0.31 SE 0.07 1 cT + 12.75ð± SE 2.77Þ, [6]

with phylogenetic heritability 0.85 ± SE 0.027, n = 136, and this 2 accounted for 27% of the variance (R adj). So including temper- ature did not change the value of the coefficients of m∞, but it substantially increased the variance accounted for. The data are illustrated in bivariate plots in Fig. 2. Because the C value of the regression coefficient, −0.23, in the across-species – regression of loge K on loge m∞across is very close to 1/4 and ECOLOGY significantly different from −1/3 for the within-species analysis, we reject hypothesis 2 in favor of hypothesis 1. However, the within- species regression coefficient of loge K on loge m∞within was −0.35, much closer to and not significantly different from −1/3 but signif- icantly different from −1/4 (Fig. 2D). Although the main effect of loge m∞within was – 0.35, there was across-species variation in the effect of m∞within,asshowninFig.2D (ΔDIC less than −200; Materials and Methods). The within-species relationship was not significantly affected by any of the lifestyle variables: environment, D reproductive guild, reproductive mode, fertilization type, or feeding type, but there was a small effect of trophic level (Materials and Methods and Supporting Information). A negative relationship be- tween loge K and loge m∞ within fish species was shown by D. Pauly (e.g., refs. 12 and 15), but his reported coefficient [−0.67 (ref. 15, p. 62)] was much less than ours (−0.35 ± 0.01) in part because more data are now available. The finding that the regression coefficient in the across-spe- cies regression of loge K on loge m∞ is −0.23 has important implications for the growth of fry. For fry of mass m = 0.001, Eq. 1=3 2 gives g0.001 ≈ 10 K m∞ , and because we have shown that − 0.23 −0.23 0.33 K ∝ m∞ , it follows that g at size 0.001 g scales as m∞ m∞ , Fig. 2. Effects of final body size, m∞, and temperature, T, on the Berta- 0.1 lanffy growth coefficient K of ray-finned fishes. (A) K as a function of m∞ for i.e., as m∞ .Sog0.001 increases with increasing m∞. To in- dependently assess whether fish species that grow to be larger 576 species without temperature correction, one point per species. The slope of the regression line, illustrating Eq. 5,is−0.23. (B) Temperature-corrected grow faster as fry, we searched for empirical studies that mea- 0.31=cT sured initial growth rate directly. Winemiller and Rose (14) K (Ke ) as a function of m∞ for 136 species where temperature data are provide relevant data for 221 species of North American marine available, one point per species. The slope of the regression line, illustrating Eq. 6, is again −0.23. (C) Mass-corrected K (Km0.23) as a function of tem- and freshwater fishes, where juvenile growth was measured as (i) ∞ “ ” perature, plotted as 1/cT, one point per species. The slope of the regression larval growth : the mean increment in total length from line is −0.31. (D) Within-species variation in K as a function of m∞ for the hatching to an age of 1 mo; and (ii) “young of the year growth” 58 species with at least five populations and more than a 10-fold variation in (YOY): the mean increment in total length from hatching to age m∞, one regression line per species (gray lines). The black line is the across- 1 y. The dataset encompassed substantial variation in final size species regression from A with the slope of −0.23; 71% of the within-species across species: up to two orders of magnitude in m∞. A phylo- slopes are steeper than this. genetic correlation between K and m∞ for the 203 species in these data that are also present in the phylogeny confirms that species with larger maximum adult sizes do indeed grow faster as Discussion both larvae (Fig. 3A; r = 0.22, Bayes factor = 4.7) and young of Growth is fueled by metabolism, so growth rates—like rates of the year (Fig. 3B; r = 0.62, Bayes factor = 60.1). However, nei- metabolism and most other biological processes—are predicted ther larval nor YOY growth rates are correlated with egg size to scale with body mass and temperature according to Eq. 3. The (Fig. 3 C and D; Bayes factors, <2). These results corroborate across-species scaling with body mass of growth rate, measured the analysis of Winemiller and Rose (14) and demonstrate that empirically by the slope of the relationship between loge K and direct empirical measurements of juvenile growth across differ- loge m∞ was −0.23 ± SE 0.01 (Fig. 2A). This is very close to and ent fish species support the prediction of hypothesis 1. within the confidence intervals of the value of −0.25 predicted by

Sibly et al. PNAS Early Edition | 3of6 Downloaded by guest on September 30, 2021 metabolic scaling theory (4, 11, 17, 21). It is also close to the The phenomenon that young of larger species grow faster than value of −0.21 ± SE 0.01 (although this was not phylogenetically similar-sized individuals of smaller species is actually a very adjusted) for the slope of mass-specific metabolic rate on loge general feature of empirically measured growth in many animal m∞ across species reported in ref. 22. The temperature de- taxa in addition to fish (e.g., refs. 5 and 6). We believe that this pendence of growth rate is given by the slope of the relationship phenomenon results from two trade-offs: (i) Between growth between loge K and 1/cT. Our value of −0.31 (±SE 0.06) is and maintenance/reproduction such that individuals of smaller similar to the value of −0.43 obtained by Clarke and Johnston species start to produce more mature kinds of cells, tissues, and (22) for the temperature dependence of metabolic rate. Both organs at sizes when individuals of larger species are still allo- values are somewhat less than the value of 0.65 eV predicted by cating mostly to structures and functions devoted to growth (8, metabolic scaling theory (17, 23), but well within the range of 25). A dwarf goby (m∞ = 5 mg) is already slowing growth and values reported in empirical studies of various taxa, including allocating to maintenance and reproduction when it weighs only = fish (23, 24). Some of the variation in the relationship between 2.5 mg, whereas a 2.5-mg tuna (m∞ 500,000 g) is still a tiny larva allocating to juvenile structures and functions so as to grow loge K and loge m∞ may reflect imprecision in the estimation of environmental temperature during ontogeny, as many fish move at near-maximal rate. (ii) Between growth and survival, such that between water masses and temperatures over ontogeny, and larger species obtain high rates of food acquisition and growth at some of it is related to variation across species in gill area (12, the expense of high rates of juvenile mortality (cf. refs. 8, 26, and 13). This is because metabolism is fueled by oxygen taken up 27). Fish species of large size, such as tunas, billfish, and ocean across the gills, so that gill surface area correlates with metabolic sunfish, which start life as tiny hatchlings weighing about 1 mg, rate. These results support the theoretical and mechanistic linkage must have extremely high rates of energy assimilation to support their very high growth rates. Their larvae feed on planktonic of growth rate to metabolic rate. However, the finding that the organisms, and their morphology and physiology reflect extreme across-species relationship between log K and log m∞ is −0.23 has e e specialization for capturing, ingesting, and digesting prey, and the implication that fish species that grow to larger mature size grow this results in higher assimilation rates than individuals of smaller faster as small juveniles. This is supported by the measured growth mature size (8). A consequence of this lifestyle is a very high rate rates of juveniles (Fig. 3) (14). This may seem puzzling because, as of juvenile mortality, presumably due to some combination of mentioned in developing hypothesis 2, one might expect hatchlings, predation and starvation, which is balanced by enormous fe- regardless of species and adult size, to grow as fast as possible. cundity of the very few individuals that manage to survive to Contrary to expectation, the within-species relationships be- maturity (females lay millions of eggs in one spawning and they tween loge K and loge m∞ differed from the across-species re- − spawn many times as they grow from reproductive size to max- lationship; the average slope within-species was 0.35, very close imum size). By contrast, a tiny goby that also lays eggs weighing − to and not significantly different from 1/3. This is surprising in about 1 mg, can lay only a few small clutches in its lifetime. In view of the fact that metabolic rate generally appears to scale order for enough offspring to survive and reproduce, juvenile similarly with body size within individuals over ontogeny as gobies must minimize mortality due to predation and starvation across species within large taxonomic groups (9, 10). Moreover, by allocating to “maintenance” traits. −1=4 it shows that it is biologically possible for fish of very different So if K scaling as m∞ represents the evolutionary optimum, mature sizes to have very similar growth rates in early ontogeny. why does not hypothesis 1 and the above theoretical explanation If everything else were equal, natural selection should seemingly also apply to within-species growth rates? We believe the reason is act to maximize growth rate and all fish would grow equally fast that most of the within-species variation reflects suboptimal phe- −1=4 when very small. The fact that K scales as m∞ across species notypic and genetic changes over a few generations (Fig. 4). Fish- implies that it is not optimal in the long term for all juveniles to Base does not indicate the cause of the variation in m∞ within grow as fast as possible; juveniles of species with small final sizes species, but some fish species are well known to exhibit extreme grow more slowly. So what else is not equal? variation in mature size due to stunting in response to low food

AB

CDFig. 3. Fish species that grow to larger final size have higher growth rates as juveniles. (A) Larval growth rate, measured as millimeters per month during the first month (n = 96), and (B) “young of the year” (YOY) growth rate, measured in millime- ters per year (n = 144), both plotted as a functions of final length on log scales. (C and D) Growth rates of juveniles are not correlated with egg size, measured as diameter in millimeters (n = 86 for C and n = 122 for D). Data from ref. 14 were kindly provided by K. O. Winemiller and are also available from www. infotrieve.com/support.

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1518823112 Sibly et al. Downloaded by guest on September 30, 2021 supply, and to morphological, physiological, and behavioral spe- 1 dm B m1−α cializations for different trophic roles or reproductive tactics (e.g., = 0 ∞ − 1−β β−1 [7] 1−α 1−α m∞ m refs. 28–30). These divergent phenotypes have been shown to be m dt Emm∞ m due to some combination of phenotypic plasticity and a few genes of (rearranging ref. 9, equation 2 and appendix equations), where α large effect (e.g., refs. 31 and 32). Each fish species has an onto- β genetic program that has been honed by natural selection over and are the metabolic scaling exponents for the rate of energy assimilation during growth and the rate of energy expenditure for its phylogenetic history to closely integrate ontogenetic growth and maintenance, respectively; B is a normalization constant; and E development in adaptation to intrinsic traits, such as body form, 0 m is the quantity of metabolic energy required to create a unit of life history, and breeding system, and to extrinsic environmental biomass. This and the Bertalanffy model in Eq. 2 can both hold conditions, such as water velocity, oxygen concentration, food sup- identically over a range of values of m only if α = 2=3, β = 1, and ply, population density, and predation regime. We suggest that when fish of similar genetic stock grow to different mature sizes, the = B0 [8] common ontogenetic program constrains the growth trajectory so K 1=3. E m∞ that individuals grow at similar rates when they are small juveniles m even though they mature at different sizes. This leads to the testable −1=3 This gives K ∝ m∞ if B0 and Em are constants. To have the hypothesis that, as populations adapt to different environments over −1=4 observed interspecific scaling of K ∝ m∞ would require that ei- evolutionary time, the ontogenetic program is modified by natural ther B0 or Em scale with m to a 1/12 power. If instead of the −1=3 −1=4 selection so that scaling of K changes from m∞ to m∞ . Bertalanffy K a growth coefficient from the OGM had been The way this played out in evolution is seen in the high phy- recorded by fish workers, the analyses might—or might not—give logenetic heritabilities of the across-species relationship between different results. This highlights the potential for compiling and 5 6 loge K and loge m∞ (Eqs. and ). It indicates that species that analyzing data on important parameters of fish growth in addition have relatively recently diverged from common ancestors tend to to Bertalanffy’s K, to allow development of alternative models. have similar values of K and m∞. Additional support for the Our findings, together with earlier studies of fish growth (e.g., ontogenetic program explanation comes from extrapolating the refs.8,12–14, and 15) have important practical implications. Fish within-species regression lines for individual species in Fig. 2C to harvested from both wild populations and aquaculture operations

the entire range of fish body sizes. It is immediately apparent supply a large and increasing fraction of the protein that is essential ECOLOGY that some species would grow unrealistically slowly or fast, up to in the human diet. The growth rates of these fish are directly rel- evant to the capacity of wild and cultured stocks to provide sus- an order of magnitude slower or faster than any extant species of tainable commercial food supplies for at least three reasons. First, such extreme size (Fig. 4). high growth rates of wild populations should contribute to their Can our results be related to the ontogenetic growth model capacity to sustain yields under harvest. So it is not surprising that (OGM) of ref. 4 (see also refs. 6 and 9)? We were unable to do some fish with exceptionally high growth rates such as Pacific this, because the OGM is written in the 1/4 powers of metabolic (Onchoryunchus spp.) and mahi mahi (Coryphaena hip- scaling theory, whereas our analysis used the coefficient K purus) support relatively sustainable commercial fisheries. Sec- obtained by fitting the Bertalanffy growth equation, which is ond, high growth rates should also be important in choosing written in terms of 1/3 powers. To illustrate the problem, con- species for aquaculture and domestication. So it is not surprising sider the OGM written in its most general form as follows: that fish used in aquaculture, such as Atlantic salmon (Salmo salar), some (species of Oreochromis, Sarotherodon,and Tilapia), and catfish (Pangasianodon spp. and Ictalurus punctatus), exhibit high growth rates. Third, some domesticated stocks have additionally been modified to increase growth rates using a combination of artificial selection and genetic modification. Comparing the growth trajectories and life history traits of wild and farmed fish offers insights into both the patterns and processes of ontogenetic growth and development that have evolved under natural selection in the ancestral populations and the extent to which these patterns and processes can be altered by artificial selection and genetic modification. For example, AquaBounty Technologies have created AqauAdvantage salmon from a stock of Atlantic salmon (Salmo salar), which was previously subjected to strong artificial selection. AqauAdvantage salmon have been genetically modified to produce all-female triploid individuals containing two inserted genes: the opAFP-GHc2 promoter from ocean pout ( americanus) and a growth hormone from the much larger (Oncorhynchus tshawytscha) (https://en.wikipedia.org/wiki/AquAdvantage_salmon). In aquacul- ture, where they are supplied with abundant, high-quality food, caged to exclude predators, and treated with antibiotics to control diseases, some stocks of salmon have growth rates, measured as Bertalanffy K, two to three times faster than wild populations. [This Fig. 4. Schematic depiction of how evolutionary changes occur in scaling of is according to our analysis of published data; claims that some K with m∞. Individuals within closely related populations are constrained to “ ” scale with slope −1/3 (dashed line). Due to trade-offs between growth and transgenic stocks exhibit growth enhancement more than 17 times maintenance, natural selection favors faster growth in species that attain greater than wild populations appear to be based on differences in large sizes (upward arrows) and slower growth in species that mature at mature sizes (33).] The exceptionally high growth rates of domes- small sizes (downward arrows). Over evolutionary time, the ontogenetic ticated stocks have been achieved by selecting for high rates of en- program changes until the optimal scaling is attained (solid line with slope ergy intake (food assimilation) and for allocation of metabolic −1/4). Note that if the steeper within-species scaling were continued to ei- energy to growth (rapid biomass production) at the expense of ther extremely small or large sizes, the fish would have unrealistically slow or energy expenditure on activity (lower swimming speed), predator fast growth rates, respectively (Fig. 2D). avoidance (reduced vigilance and escape behavior), and reproduction

Sibly et al. PNAS Early Edition | 5of6 Downloaded by guest on September 30, 2021 (reduced mating behavior and lower egg production) (e.g., refs. We used the species-level phylogeny of ray-finned fishes (Class Actino- 34 and 35). So, greatly accelerated growth has been achieved at the pterygii) presented in ref. 37. Species names were matched between the expense of traits for survival and reproduction under natural phylogeny and the data using official synonym lists extracted from FishBase. conditions as discussed above. Like factory-farm turkeys, fryer In two cases (Salmo trutta and Sarotherodon galilaeus), multiple synonyms chickens, and hogs, some farmed fish stocks have been so modified for a single species were found in the tree. In both cases, the data were to grow fast to produce food for humans that they have lost many excluded from the analysis. A total of 576 of the species in our phylogeny is traits required to survive in the wild. found in the data. We used the deviance information criterion (DIC) to assess the contribution Our theoretical and empirical analysis of fish growth highlights of individual variables to a PGLMM, where lower DICs are preferred (18). A the insights that can come from combining mathematical theory ΔDICoflessthan−3 when comparing models with and without a given char- with compilation and analysis of large, high-quality databases. It acter is considered evidence of a significant contribution of that variable (38, 39). is apparent that fish exemplify general patterns and processes We calculated phylogenetic heritability (h2), identical to Pagel’s lambda (40), observed in other animals. For example, higher juvenile growth from the phylogenetic variance of our models, to determine the importance of rates in species that grow to larger adult sizes are also seen in species’ shared ancestry: values close to 1 indicate strong phylogenetic signal. All mammals and birds (see, e.g., refs. 3, 10, 16, and 36). It is also models were implemented within a Bayesian framework and were run for a apparent that we are still some ways from having a general total of 1,000,000 iterations, sampling every 1,000 after removing the first unified theory of growth. We need more explicitly mechanistic 100,000. All chains were run multiple times to ensure convergence. models for how the life history evolves in response to trade-offs For the reanalysis of data from Winemiller and Rose (14), we matched 203 between growth and survival, and to energy allocation trade-offs of the 221 species in the original data to the fish phylogeny. We report mean between maintenance, growth, and reproduction. Additional phylogenetic correlations (r) in a Bayesian framework using the same model studies of fish will continue to have much to contribute, especially if conditions described for the PGLMMs and using all available data (Fig. 3). FishBase or other databases can be expanded to include additional Significance was assessed by comparison with a noncorrelational model us- quantitative data on growth beyond the Bertalanffy K values used in ing Bayes factors estimated using a stepping-stone sampler (41) (1,000 this study. stones with 100,000 iterations per stone) as implemented in BayesTraits (42). A Bayes factor of >2 is considered positive support for the correlation, Materials and Methods and >10 is considered to give very strong support (43).

Values of K and m∞ were extracted from FishBase on September 30, 2014, ACKNOWLEDGMENTS. We thank both referees for constructive comments together with species-level data where available for water temperature on the manuscript. For financial support, we are thankful for Leverhulme and six additional lifestyle variables (environment, reproductive guild, re- Trust Research Project Grant RPG-2013-18 (to C.V.) and a University of productive mode, fertilization type, trophic level, and feeding type). Reading PhD studentship (to J.B.).

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