Global drivers of reef fish growth

2.1 Setting the stage: bioenergetics of fish growth

A bioenergetic model describing animal growth was developed by von Bertalanffy, (1938, 1949, 1957) and has been extensively applied to fish growth, especially in fisheries biology (e.g. Beverton & Holt, 1957; Hilborn & Walters, 1992; Pauly, 1979). We acknowledge the effectiveness of other more recent growth models (e.g. West et al., 2001), but we use Von Bertalanffy's one because: (a) the parameters required are mathematically simple to obtain and easy to interpret; and (b) it has been widely used. Thousands of growth curves have been produced using this model over the last seven decades. In the context of the Von Bertalanffy Growth Model (VBGM), growth is the net result of two opposite metabolic processes: anabolism, the production of body substances; and catabolism, the consumption of body substances. Its underlying mathematical formulation, the Von Bertalanffy Growth Function (VBGF) follows as

(1)

in which is the instant rate of change in fish weight over time; is a term that represents anabolism; and is a term that represents catabolism. Growth may, thus, be either positive, when the organism increases in body mass, or negative, when the organism decreases in body mass. Biologists are most frequently interested in positive growth, which, for multicellular organisms, is mainly due to an increasing number of cells (von Bertalanffy, 1938). An increase in the number of cells leads to a proportional increase in catabolism because all living cells consume body substances (Pauly, 1979; von Bertalanffy, 1938). Therefore, the catabolic term should be proportional to weight, with n = 1. For fishes and other aquatic organisms, it has been proposed that anabolism is limited by the rate at which oxygen can diffuse through the gills and become available for cell synthesis (Pauly, 1979; von Bertalanffy, 1957). In this case, the anabolic term would increase proportionally to gill surface area and not to overall body weight (Pauly, 1979; von Bertalanffy, 1949), with m = 2/3 (Pauly, 1979). However, empirical evidence strongly suggests that m is closer to 3/4 than to 2/3 (Pauly, 1979; Ricker, 1979; Savage, Gillooly, Woodruff et al., 2004). The most likely explanation to this is that anabolism is proportional to the area of the circulatory network rather than to the gill surface area (West, Brown & Enquist, 1997). Nevertheless, integrating the VBGF with m = 2/3 generates a simplified mathematical formulation, the so-called special VBGF (Beverton & Holt, 1957; Pauly, 1979). Not surprisingly, the simple formulation of the special VBGF is the most widely employed facet of the VBGM, and the one used by most growth studies.

The integrated special VBGF assumes two forms:

(2)

and

(3)

relating the body size of a fish at time t (in length, L_t, or weight, ) to the average asymptotic size of the population to which it belongs (L_∞ and W_∞), the theoretical age when size = 0 (t₀), and the rate at which fish in this population, on average, approach the population asymptotic size (K). Of these parameters, t₀ holds little biological information (Kritzer, Davies & Mapstone, 2001; Pauly, 1979) and has frequently been constrained to zero or estimated after constraining size when age = 0 to the settlement size (e.g. Berumen, 2005; Kritzer et al., 2001). The exponent b on Equation 3 is equal to the species-specific length–weight regression parameter b (Froese, 2006). The most fundamental parameters to characterize growth are, thus, L_∞ (or W_∞) and K, which can also be used to statistically estimate t₀ (Pauly, 1979, 1980).

2.2 A database of VBGF parameters: assembling and processing

The VBGM can be fitted to individual- or population-level growth data. Individual-level data include repeated measures of the same individual over time, as in captivity or mark–recapture studies (Francis, 1988). Population-level data include length–frequency analyses (Pauly & Morgan, 1987) and size-at-age data from temporally deposited rings in hard structures such as vertebrae, dorsal spines, scales, but mainly otoliths (Campana, 2001; Choat & Robertson, 2002). However, caution should be exercised when comparing growth data derived from different methods for two reasons. First, because in the VBGM from individual- or population-level data, L_∞ values have distinct meanings (Francis, 1988). For individual-level data, it is the length at which the expected growth increment of an individual is zero, whereas for population-level it is the average asymptotic size of a population (Francis, 1988). Second, because different methods can derive different VBGF parameters’ estimates, even from the same population (e.g. Schwamborn & Ferreira, 2002). Indeed, length–frequency and age-based methods have been used simultaneously to improve VBGF parameter estimates (Campana, 2001; Morales-Nin, 1989). In this study, we compiled an extensive reef fish growth database that includes both individual- and population-level growth data. We accounted for the potential issues listed above by first standardizing K relative to the maximum size of a species instead of L_∞, and then explicitly considered the type of data used for fitting the VBGM as a covariate in our model. Details of both procedures are given below. We then examine the effects of environmental factors and species morphological and behavioural traits on growth.

The assembled database included the VBGF parameters, length–weight regression parameters, species morphological and behavioural traits and environmental variables associated with the geographic location of the compiled reef fish growth curves. We used the family list provided by Bellwood and Wainwright (2002) to define a minimum list of “reef fish” families, with the addition of important commercial groups that eventually use reef habitats: Rachycentridae, Scombridae and Sebastidae. It is important to make clear that we use a broad concept of “reef fish” that encompasses both coral reef taxa and families restricted to the rocky coasts of temperate regions (i.e. Sebastidae). Within the selected families, we kept only those genera and species known to use reefs or that are likely to be seen in the vicinity of a reef. The main source of data was FishBase (Froese & Pauly, 2016) and the references therein, but we included 151 additional growth curves. Some of the growth curves from short-lived small cryptobenthic fishes were modelled by linear regressions in the original references (Depczynski & Bellwood, 2006; Kritzer, 2002; Winterbottom, Alofs & Marseu, 2011; Winterbottom & Southcott, 2008). However, linear growth can be expected under the VBGM if longevity is smaller than that necessary to reach the asymptotic size. Thus, we fitted a VBGM to raw data extracted from the graphs in these studies.

With the whole VBGF parameters dataset, we implemented a multistep quality control procedure, excluding curves that were:

We converted all estimates of the parameter L_∞ to TL (Total Length in cm) using length–length conversion factors obtained from FishBase or directly from photographic records. When both sex-specific and combined growth curves were reported, we used only the combined curve; when only sex-specific curves were reported, we averaged parameters between males and females to exclude the influence of sex. We acknowledge that this procedure places equal weights on sample sizes that might have differed between sexes. However, in many cases this information was not accessible. We therefore averaged growth parameters to reduce the effect of differences in growth between sexes. Following these quality control criteria, 484 curves were excluded or aggregated, leaving a final database with 1,921 growth curves from 588 species of reef-associated fish (Supporting Information – DS1, See Data accessibility section).

2.3 Compiling and processing of explanatory variables

We modelled reef fish growth as a function of morphological and behavioural traits (i.e. maximum body size, diet, schooling behaviour, position relative to the reef and body shape), environmental variables (i.e. sea surface temperature and pelagic primary productivity) and the method used to obtain the growth data.

Maximum body size is the maximum recorded length (TL in cm) for a referred species, either based on the literature or the authors’ unpublished data (provided in the Supporting Information—DS1, See Data accessibility section). “Body size” here was taken to be a synonym of “species body size,” an evolutionary property of a lineage (often a species). It is explicitly distinguished from “individual body size,” which is a property of an individual and a function of both ontogeny and the individual's environment. Moreover, we acknowledge that the VBGM theory and much of the field of allometry quantifies body size in terms of body mass rather than length (von Bertalanffy, 1938, 1949, 1957); however, we chose to use length because: (a) growth has been traditionally expressed in terms of length in fisheries biology; and (b) because reef ecologists primarily collect length data of fish (e.g. from underwater visual census). Seven dietary categories were considered: herbivores/detritivores, herbivores/macroalgivores, omnivores, planktivores, sessile invertivores, mobile invertivores, and fish and cephalopod predators (Mouillot et al., 2014; Parravicini et al., 2014). Schooling behaviour (or gregariousness) measures the extent of intraspecific aggregations in five levels: solitary, pair, small groups (3–20 individuals), medium groups (20–50 individuals) or large groups (>50 individuals) (Mouillot et al., 2014; Parravicini et al., 2014). Position relative to the reef combines horizontal and vertical components, resulting in six levels (Bellwood, 1988). The horizontal component represents the degree of association of a fish to the reef: reef dwelling (more likely to be found on the reef than in other adjacent habitats) and reef-associated (more likely to be found in adjacent nonreef habitats than on the reef). The vertical component represents the position in the water column: benthic, benthopelagic and pelagic (Mouillot et al., 2014). The body shape factor is a continuous variable derived from the length–weight regression coefficients of fish (termed “body form factor” in Froese, 2006) that measures the extent to which a fish is elongated or deep-bodied. It can be perceived as the a parameter value a fish species should have if its b = 3. As a and b can be sensitive to methodological issues (Froese, 2006), we compiled a database on these parameters estimated from the Bayesian Hierarchical Model described by Froese, Thorson and Reyes (2014). This model starts with priors reflecting broad shape categories and is improved by the hierarchical addition of length–weight parameters from studies of closely related species or from different populations of the species of interest. The parameter estimates are given in the Supporting Information—DS1 (See Data accessibility section). The logical basis of the shape factor calculation is provided in Froese (2006).

Environmental data (sea surface temperature and pelagic net primary productivity) were acquired by georeferencing the locality of each of the growth curves. Growth curves were only included if the referred areas were biogeographically discrete with no major disparities in oceanographic features, regardless of size. Thus, “Ionian Sea” was acceptable, but not “Eastern Australia.” Within the area, the centroid was estimated, and its coordinates used to extract mean sea surface temperature, mean chlorophyll concentration and mean photosynthetically active radiation from Bio-ORACLE (Tyberghein et al., 2012). To decrease the chance of bias due to the centroid estimate, we averaged the values from across the closest four cells (each cell has a width of ~9.2 km in Bio-ORACLE). Pelagic net primary productivity was estimated from chlorophyll concentration and photosynthetically active radiation using the model described in Behrenfeld and Falkowski (1997). Details on the calculation of productivity can be found in the Supporting Information—SUPP SCRIPT.

Finally, given the possibility that the method used to derive the growth curves would affect the final VBGF parameter estimates (see above in A database of VBGF parameters: assembling and processing), we included method as a covariate in our model. Method consisted of six levels: mark–recapture, length–frequencies, scale rings, otoliths rings, rings from other structures and unknown. Although we aimed to tease apart the confounding effects that different methods can have on growth estimates, we were mainly interested in predicting for otoliths rings only, as this is the most widely used ageing technique nowadays (e.g. Campana, 2001; Choat & Robertson, 2002).

2.4 Accounting for phylogenetic nonindependence

Our dataset included species with varying degrees of shared ancestry, as well as multiple observations from the same species. These features result in nonindependence among observations and require a phylogenetic correlation structure to be specified (Symonds & Blomberg, 2014). To do this, we first created a supertree by combining phylogenies that included our species using the “rotl” package (Michonneau, Brown & Winter, 2016) in the software R (R Core Team 2017). This package is an interface to the Open Tree of Life (Hinchliff et al., 2015). Nonmatching species were manually included in the phylogeny alongside congeneric species (e.g. the Doederlein's cardinalfish (Ostorhinchus doederleini, Apogonidae) with the Yellowstriped cardinalfish (Ostorhinchus cyanosoma, Apogonidae) or the Fusca drum (Umbrina ronchus, Sciaenidae) with the Shi drum (Umbrina cirrosa, Sciaenidae) or with the most closely related families according to Betancur-R et al. (2017) (Supporting Information—Phylogeny). Branch lengths were computed using the method of Grafen (1989). Each species was represented in the phylogeny by as many tips as its number of growth curves, and intraspecific branch lengths were set to zero. At last, we used the phylogeny to generate a correlation structure by applying a Brownian motion model of trait evolution (Symonds & Blomberg, 2014). All phylogenic procedures and manipulations were carried out with the packages “ape” (Paradis, Claude & Strimmer, 2004) and “phytools” (Revell, 2012) in R.

2.5 The correlation between VBGM parameters

Different populations of the same species vary in their growth trajectories depending on environmental factors, such as temperature and food availability (Choat & Robertson, 2002; Pauly, 1980; Ricker, 1979; von Bertalanffy, 1957). VBGF parameters’ estimates can also be affected by methodological issues such as small sample sizes and underrepresented body size ranges (Berumen, 2005; Kritzer et al., 2001). This can result in large disparities in L_∞ (or W_∞) and K among populations of the same species (Figure 1a) or even among studies of the same population. Although these disparities could preclude direct comparisons, it has been argued that they conform to a theoretical and empirical pattern. Pauly (1979) suggested that, in the special VBGF, K varies with W_∞ with a slope of s_w = 2/3 and with L_∞ with a slope of s_L = - 2, when all parameters are log₁₀ transformed (Munro & Pauly, 1983; Pauly, 1979, 1980). If we assume a VBGF with (Pauly, 1979; Savage, Gillooly, Woodruff et al., 2004), then K should vary with W_∞ and L_∞ with and S_L slopes that differ from the values above. Following Pauly (1979) reasoning, we can define

(4)

where m is the VBGM anabolic term exponent and b is the species length–weight regression exponent (for simplicity, we will only refer to the length slope S_L from now on). The anabolic exponent can be taken as the metabolic scaling exponent, which Savage, Gillooly, Woodruff et al. (2004) found out to be on average 0.761 (CI₉₅ 0.68–0.86) for fishes. Froese et al. (2014) found that, for all body types of fish, b averages 3.04 (CI₉₅ 2.81–3.27). Substituting the mean and extreme (CI₉₅) values of these parameters in Pauly's equation results in the average slope, , being −2.31 (CI₉₅ from −2.75 to −1.91). As b can vary among species, S_L is probably better characterized by a distribution centred on −2.31 and ranging from −2.75 to −1.91 (Figure 1b).

2.6 Standardizing growth curves for among populations and species comparisons: the Ø and K_max parameters

The practical meaning of the relationship between K and L_∞ can be better represented in a plot like Figure 2. Variation among growth curves of a species along a theoretical line with slope S_L in such a plot could, for example, reflect incomplete sampling of the population size range. However, residual variation, that is variation in any direction other than along this line, will likely be due to environmental factors (e.g. temperature, productivity). This “residual variation” (quoted because it is actually the variation in which we are interested) can be isolated by regressing each growth curve along the theoretical line towards a specific size value (Figure 2). By regressing the curves towards the y-axis, we obtain the rate at which a fish population with the VBGF parameters specified would converge to its asymptotic size, L_∞, if it grew to L_∞ = 1 cm (Figure 2a). This approach is a standardization procedure that allows one to compare growth among populations at a constrained minimum body size. The resulting parameter has been named the growth performance index by Pauly (1979) and has been represented by the characters P, a, φ, or Ø. It will be hereafter referred as Ø. In practical terms, Ø is calculated as

(5)

for length data (Froese & Binohlan, 2003).

Instead, one can regress each growth curve towards the point where it intercepts a line projecting the maximum size reported for that species (L_max, Figure 2b). This standardization procedure results in an estimate of the rate at which a fish population with the specified VBGF parameters would approach its L_∞ if and is termed K_max. With respect to mathematics, it is obtained by

(6)

It is important to clearly distinguish between the meanings of K, K_max and Ø. K is the rate of convergence towards a population (or individual) asymptotic body size, with meanings as discussed above (section “A database of VBGF parameters: assembling and processing”). K_max and Ø, however, are theoretical projections of K at specific body lengths. By standardizing K to a constrained body length (L_∞ = 1 cm or ), the derived parameters (K_maxor Ø) concentrate all growth information and allow for comparisons across populations and species.

The growth performance index (Ø) and the expected growth coefficient at the theoretical maximum species size (K_max) are, for any one species, opposite ends of the same line (Figure 2). As we consider K_max to be easier to interpret biologically than Ø, K_max will be the main focus of this work. A potential caveat is that K_max is first standardized by species maximum size, and then modelled by this same variable. We evaluate possible issues of this approach by, first, checking the relationship between K_max and Ø (see below in Procedures for modelling K_max and Ø), and then performing all modelling procedures using Ø as well as the response variable. We report all the alternative modelling results in the Supporting Information.

2.7 Contrasting theoretical and empirical estimates of s_L

To check whether the theoretical range of S_L values is supported by our data, we first filtered our growth curves dataset to retain all species that had six or more growth curves. This resulted in 74 species for which S_L could be estimated by regressing log₁₀ transformed K and L_∞ values. Then, we calculated a weighted average of these estimated S_L values in a meta-analytical Bayesian framework using the R package “brms” (Bürkner, 2017). This procedure incorporates standard errors, weights and a prior distribution when averaging values of a variable. We used the standard errors of the S_L estimates from the K and L_∞ regressions; and also included the R² of these regressions as the weights. The theoretical range of S_L values was used to delimitate the prior distribution of the intercept. The model was run with four chains of 3,000 iterations, with 1,500 warm-up steps and a thinning of every third step for each chain. The output of this procedure is a posterior distribution of S_L values whose 95% credibility interval can be used for inference. To check for mismatches between our data and the posterior distribution, we visually compared the distribution of S_L among the species in our dataset with values simulated from the posterior distribution. Complete overlap between the simulated and the empirical data would reveal that incorporating quality metrics (standard errors and weights) to the species S_L estimates did not affect the posterior distribution; that is, the data quality was uniform and no meta-analysis was required.

2.8 Procedures for modelling K_max and Ø

Prior to fitting the model, we checked the explanatory variables for collinearity using two approaches. First, we plotted the relationship among these variables using Local Weighted Scatterplot Smoothing regressions (LOWESS, Supporting Information Figure S1) and also checked for correlations. Second, we fitted a simple linear regression with all the covariates and calculated the Variance Inflation Factor (VIF). Only one correlation higher than 0.5 was found between schooling and position. Further checking the VIF suggested that both of these variables and diet had some degree of collinearity. The exclusion of schooling resulted in all variables remaining with a VIF < 4, a value that we deemed satisfactory. We also assessed the assumptions that the response variable K_max included information that was different from the parameters K, L_∞ and Ø. We modelled these relationships using LOWESS regressions. If these assumptions were true, then K_max would be related to both K and L_∞ with a high residual variation, but not be related to Ø.

To determine the main drivers of reef fish growth, we modelled K_max and Ø relative to morphological and behavioural traits, and environmental variables, in a Phylogenetic Generalized Least Squares Model (PGLS, Symonds & Blomberg, 2014). As there are currently no methods to fit a phylogenetic model with a Gamma distribution, we log₁₀ transformed K_max to achieve Gaussian distribution (Supporting Information Figure S2). We log₂ transformed body size and primary productivity to decrease dispersion. At last, to assist with model convergence, all continuous variables were centred. We fitted the models using the package “nlme” (Pinheiro, Bates, DebRoy & Sarkar, 2017) in R. We contrasted the full model with nested submodels by iterating the model fit with one explanatory variable excluded each time. All models were fitted using Maximum Likelihood for comparing fixed effects and the comparisons were based on Akaike Information Criterion (AIC) metrics: ΔAIC and wAIC (Bartoń, 2016; Burnham & Anderson, 2002). Finally, we assessed the importance of each predictive variable using the proportional change in the R² from the full model to submodels excluding each variable. As GLS techniques do not allow R² calculation in the same way as Ordinary Least Squares, we instead calculated a prediction R². This was achieved by fitting a linear regression of the raw data values by the predicted values from the PGLS, and then using the R² from this regression to do the calculations. After the fitting procedure, we performed model validation as recommended by Zuur, Ieno, Walker, Saveliev and Smith (2009) and refitted the final model using Restricted Maximum Likelihood.

2.9 Predicting growth coefficients for trait combinations and environmental settings and assessing prediction accuracy

We used XGBoost, a Gradient Boosted Regression Tree (GBRT) method to predict reef fish stadardized growth coefficients K_max. The goal of this step was to derive a table that can be used to predict growth trajectories for unsampled species using the combinations of morphological and behavioural traits, and the environmental settings evaluated here. Machine learning techniques, such as GBRTs, are considered superior in predicting when compared to statistical methods (Elith, Leathwick & Hastie, 2008). XGBoost, in particular, is regarded as the state-of-the-art tree boosting system, yielding very fast and accurate predictions (Chen & Guestrin, 2016; Mitchell & Frank, 2017). One of the main advantages of GBRTs over statistical methods is the possibility of efficiently modelling multilevel variable interactions (Elith et al., 2008).

The same model structure as in the final PGLS was used for prediction, except that the response variable, K_max, was included in its raw form and the XGBoost model was fitted with a Gamma distribution. Two tuning steps were executed before running the prediction model. First, we fit the model multiple times with combinations of model parameters (learning rate, maximum tree depth, gamma and subsampling rate) that were varied systematically, and recorded the combinations that yielded the minimum root mean square error (rmse). These values were as follows: learning rate = 0.15, maximum tree depth = 7, gamma = 0.15 and subsampling = 0.5. Other parameters were kept in their default values. Then, we refit the model multiple times with combinations of values randomly drawn from a uniform distribution bound by the recorded parameter values from the previous round ± 10%, and again selected the parameters that minimized rmse. These tuning steps reduced model rmse from 0.32 to 0.27, a substantial improvement in terms of prediction consistency.

To evaluate the accuracy and precision of XGBoost in predicting from our data, we used a cross-validation procedure. This consisted in randomly splitting the growth coefficients database into independent training and testing datasets. The training dataset contained 80% of the data points and was used to refit the final model in order to generate coefficients for prediction. The testing dataset contained the remaining 20% of the data points and was used exclusively to contrast with predictions from the training dataset model. Using different datasets to fit the model and to predict, cross-validation makes these steps independent, and, therefore enhances bias detection. We calculated a bias metric by subtracting each K_max predicted by the xgboost from its estimate in the database (the “measured” value). An accurate model would have a bias at or very close to zero. Precision was assessed by a prediction R² analogous to the one calculated for the PGLS. These cross-validation procedures were repeated 1,000 times.

At last, prediction was carried out for all diet and position groups, for body sizes between 2 and 200 cm TL, for sea surface temperatures between 10 and 30°C, and for the ageing method of otolith's rings only (see above Compiling and processing of explanatory variables). We bootstrapped the model for 1,000 iterations to generate a distribution of K_max predictions. All prediction-related analyses were conducted with the R package “xgboost” (Chen, He, Benesty, Khotilovich & Tang, 2018).

4.1 Body size and temperature effects

The fact that reef fish growth rates depend on body size and temperature is a reflection of underlying physiological processes: All mass-specific physiological rates follow body size and temperature, as these factors determine metabolism (Gillooly et al., 2001). Therefore, they also determine energetic demands. Mass-specific metabolic rates decrease with size and increase with temperature (Brown et al., 2004), the same trends we observed for K_max. This relationship between rates and body size stems from physiological constraints on molecule transport (e.g. amino acids or carbohydrates) across body surfaces to individual cells (West et al., 1997). By contrast, the temperature dependence of physiological rates follows a simple kinetic relationship: higher temperatures increase the rates of chemical reactions (Brown et al., 2004; Gillooly et al., 2001). All types of chemical reactions, from lyses to syntheses, are kinetically affected. As a result, organisms in warmer temperatures have higher metabolic rates, and also higher growth rates, than similar-sized organisms in cooler temperatures.

4.2 Resource availability and acquisition effects

Although the energetic demands of an organism are determined by size and temperature (Brown et al., 2004; von Bertalanffy, 1957), its energetic supply is mediated by resource acquisition. Reef fishes encompass a wide array of morphological, physiological and behavioural traits that allow them to explore a broad spectrum of feeding resources (Wainwright & Bellwood, 2002). Feeding resources also vary largely in space and time. Thus, the interplay between resource availability and traits used to explore them should result in some level of growth disparities among feeding modes (Beverton & Holt, 1959; Ricker, 1946). Our results partially support this expectation: diet and the degree of association with the reef affected reef fish growth coefficients. To a remarkable extent, after accounting for body size and temperature, herbivores/macroalgivores had higher growth coefficients than all other trophic groups. This includes fish with “better quality” diets (sensu Harmelin-Vivien, 2002), such as planktivores or fish and cephalopod predators.

Marine prey items exhibit considerable variability in energetic and protein content (Bowen, Lutz & Ahlgren, 1995; Brey, Müller-Wiegmann, Zittier & Hagen, 2010; Choat & Clements, 1998), as well as in their structural and chemical defences against predation (Burns, Ifrach, Carmeli, Pawlik & Ilan, 2003; Hay, 1991). Depending on these factors, food resources for marine organisms have been categorized as “low quality” or “high quality” (Choat & Clements, 1998; Harmelin-Vivien, 2002). Low-quality items include sessile invertebrates and macroalgae that have low protein and/or energy content, and frequently also structural and/or chemical defences. High-quality items, such as mobile invertebrates and fish, have a high protein and energy content and relatively few structural or chemical defences. One may therefore assume, based on these differences, that fishes with “high-quality” diets would grow faster than fishes with “low-quality” diets (Harmelin-Vivien, 2002). However, “low-quality” dietary items are readily available on reefs, and exploiting them may be a trophic opportunity rather than a constraint (Harmelin-Vivien, 2002). Niche expansion from “high-quality” to “low-quality” diets in reef fish lineages has, for instance, been followed by rapid evolutionary diversification (Lobato et al., 2014). Fishes have many behavioural and physiological mechanisms to deal with their preferred food (Choat & Clements, 1998; Clements et al., 2009). The fact that many fishes rely on apparently “low-quality” diets such as algae and particulates suggest that the purported obstacles posed by these diets (i.e. defences, scarcity of nutrients) are generally overcome. A possible trade-off between lower nutrient levels but higher and more predictable availability may mean that these “low-quality” items may indeed provide fishes with superior nutritional rewards (e.g. Choat, Clements & Robbins, 2002; Wilson, Bellwood, Choat & Furnas, 2003). There is increasing evidence that feeders of “low-quality” diets, such as herbivores and detritivores, do not grow markedly slower than feeders of “high-quality” diets (Choat & Axe, 1996; Choat & Robertson, 2002; Trip, Raubenheimer, Clements & Choat, 2011). Our results add further support to these findings. After accounting for differences due to other factors (mainly body size and temperature), sessile invertivores and herbivores/detritivores grew similarly to planktivores or mobile invertivores, whereas herbivores/macroalgivores grew faster than the other trophic groups. It is clear that, the constraints imposed by a herbivorous diet are not as severe as previously thought.

We see a similar but unexpected pattern in pelagic primary productivity, a component of resource availability for fishes. Although pelagic fishes associated with reefs had higher growth coefficients than all other position categories, we did not find a relationship between growth and pelagic primary productivity. This pattern, again, disconnects apparent food quality/availability from potential for growth. The gradient in primary productivity here investigated included very productive temperate reefs and also oligotrophic tropical coral reefs. The fact that fish growth did not respond to this gradient shows that, in the scale investigated, the different strategies that fish employ to acquire resources are optimized to deal with resource availability.

Pelagic primary productivity can play an important role in the energetics of both temperate and tropical reefs (e.g. Truong, Suthers, Cruz & Smith, 2017; Wyatt, Waite & Humphries, 2012). However, some of the most productive marine habitats frequently occur in tropical oligotrophic waters: coral reefs (Crossland, Hatcher & Smith, 1991; Hatcher, 1988). This observation is partially explained by coral reefs’ high efficiency in uptake rates and recycling of nutrients, especially through the detritus pathway (Arias-González, Delesalle, Salvat & Galzin, 1997; Crossland et al., 1991; de Goeij et al., 2013). There may also be scale-dependent factors involved, for example, the use of the pelagic environment adjacent to reefs. Ocean currents provide reef food chains with large transient zooplankton from the open ocean (Hamner et al., 1988; Hobson, 1991). As currents move closer and through the reef, this large zooplankton is depleted by feeding from planktivorous fishes, that is the “wall of mouths” (Hamner et al., 1988). Thus, the pelagic environment adjacent to reefs provides a highly rewarding food source for those fishes capable of exploring it (Bellwood, 1988; Hamner et al., 1988). This pelagic environment also provides predators with the opportunity to feed on fishes that live far from the protection of the reef structure (Hobson, 1991). Fish that live in the open have few chances of escaping predators other than schooling, swimming fast or getting large quickly (Hobson, 1991). A similar reasoning might be applied to the predators themselves. It seems likely that growing fast in the pelagic environment adjacent to reefs is an outcome of opportunities and pressures: opportunities provided by abundant, high-quality feeding resources (zooplankton and zooplanktivorous fishes); and the need to quickly achieve large body sizes to escape predation.

4.3 Reef fish growth in a changing world

This study has demonstrated the major importance of body size and, to a smaller degree, also of temperature on reef fish growth, as predicted by theory. Rising sea temperatures and disruption of fish size structure are ongoing threats to tropical reefs (Hughes et al., 2017; Jackson et al., 2001). Both are likely to disturb normal fish growth trajectories. For example, although fish growth coefficients increased with temperature in the present study, the temperature range investigated herein only encompasses present sea conditions (up to ~31°C). Many tropical reef fishes already live in temperatures close to their metabolic optimum, with further temperature increases resulting in diminished aerobic scope (Barneche et al., 2014; Rummer et al., 2014). Despite the fundamental ties between metabolism and growth, it is unlikely that reef fish growth coefficients will keep on increasing linearly with further rises in sea temperature. Moreover, reef fish size structure can be severely disrupted by size-selective fishing activities (Jennings & Blanchard, 2004; Jennings & Kaiser, 1998; Robinson et al., 2017). This type of fishing can also induce nonrandom genetic changes to fish populations, for example, by selecting for lineages that grow to smaller sizes, mature, and attain their asymptotic sizes more quickly (Kuparinen & Merilä, 2007). Although this scenario could potentially result in either increased or decreased growth rates (Kuparinen & Merilä, 2007), any potential benefits may be outweighed by detrimental consequences to reproductive output or larval survival (e.g. Birkeland & Dayton, 2005; Hixon, Johnson & Sogard, 2014). Hence, exploring the links between population asymptotic size, growth rates, rising sea temperatures and fishing-induced size changes is likely to be of increasing interest to reef fish ecologists in the near future.

Variables that represent resource availability and acquisition had a minor, albeit significant role on growth in this study. We expect that downscaling from the global reef fish assemblage, examined herein, to local assemblages will increasingly emphasize links between growth and resource-related variables. For example, Gust et al. (2002) documented abrupt demographic changes between populations of parrotfishes and a surgeonfish from outer and mid-shelf reefs in the Great Barrier Reef. Populations from outer-shelf reefs had smaller asymptotic size and higher growth coefficients, as well as higher abundances, when compared to mid-shelf reefs. The authors concluded that differences in growth were an outcome of density-dependent processes triggered by limited production of detritus, the main feeding resource of the species evaluated (Gust et al., 2002). On an even smaller spatial scale, Clifton (1995) observed varying growth rates of a Caribbean parrotfish between adjacent reefs subject to distinct wave action. This was attributed to wave action mediating the population dynamics of benthic filamentous algae targeted by that parrotfish species, thus determining its growth rates. Moreover, local communities include only a small subset of the potential environmental variability and, most often, also of the size range used in this study. Hence, resource-related variables are likely to be more important, and useful, to explain differences in growth at a reduced scale. Some of the most interesting departures from expectations in this paper resulted from investigating resource variables. In particular, our model showed that growth rates of herbivores/macroalgivores, theoretically “low-quality” feeders, were higher than fish and cephalopod predators, and mobile invertebrate predators, considered as “high-quality” feeders. This supports the idea that fish have developed behavioural, physiological and anatomical mechanisms to deal with their preferred food and illustrates how studying fish growth might help to clarify other aspects of reef ecology.

4.4 Predicting growth coefficients

In addition to identifying the drivers of reef fish growth, we apply a state-of-the-art machine learning technique to predict growth coefficients for combinations of these drivers. Thus, we provide an accurate and precise means of estimating the growth trajectories of unsampled reef fish species. This can be particularly useful if one wishes to characterize whole-assemblage patterns of fish growth (e.g. Depczynski, Fulton, Marnane & Bellwood, 2007). To facilitate this use, we provide the raw growth dataset (Supporting Information—DS1, See Data accessibility section) and an easy-to-use table with predicted coefficients (Supporting Information—DS2, See Data accessibility section). The prediction table includes most of the range of morphological and behavioural traits and environmental variables that tropical and temperate reef fishes are likely to encounter.

Ours is not the first study to provide predictions of fish life history traits. Thorson, Munch, Cope and Gao (2017), for example, used a multivariate probabilistic model to derive estimates of four life-history traits, including growth parameters, of all fish species. This impressive task was not without challenges, and the authors recognize three drawbacks of their approach: (a) the use of a taxonomic, rather than phylogenetic, structure to model correlations among species; (b) the absence of resource-related variables in their model; and 3) the lack of discrimination between high- and low-quality input data. We believe that, by focusing our attention to reef fishes, we were able to overcome these three drawbacks and, as such, to provide more accurate growth predictions for our targeted group.

Growth is primarily a physical phenomenon driven by body size and temperature. Biological features related to resource acquisition are important but only to a minor extent, and some do not affect growth as expected. The model derived herein can be used as an easily available method for estimating growth trajectories of unsampled species and, as such, to bridge the gap between individual- and community-level growth patterns. This will contribute to a better understanding of the role of fish growth in ecosystem processes, such as energy flow and nutrient cycling, which ultimately result in biomass accumulation.