Global patterns and predictors of trophic position, body size and jaw size in fishes

Aim: The aim of this study was test whether maximum body mass and jaw length are reliable predictors of trophic position ( TP ) in fishes, and to compare linear and nonlinear machine-learning (ML) models incorporating biogeography, habitat and other morphological traits. Location: Global. Time period: Modern. Major taxa studied: Fishes. Methods: We compiled a global database of TP (2.0–4.5), maximum body mass, jaw length, order, ecoregion,


| INTRODUC TI ON
Body size is a driver of trophic structure and function because it influences energy demand (Rip & McCann, 2011) and predator-prey interactions (Brose, 2010;Emmerson & Raffaelli, 2004). Food webs are considered to be size-structured, whereby predators often consume smaller-bodied prey items (Brose, 2010;Brose et al., 2006). Important exceptions have been described (e.g., parasites; scavengers; hunting in packs), but size-based trophic constraints provide vital parameters that underpin contemporary macroecology (Sibly et al., 2012), fisheries (Andersen, 2019;Blanchard et al., 2017) and food web (Brose et al., 2017) concepts and models. There is an expectation that organisms feed at a high trophic position when larger owing to assumed positive allometric scaling of the morphological and physiological traits (e.g., speed; strength; jaw size) needed to catch, kill and consume large prey, and inherently that larger prey feed at a higher trophic position than smaller prey. As Elton (1927) first pointed out "spiders do not catch elephants in their webs, nor do water scorpions prey on geese", yet complex food webs are not always well described by simple body size-based rules (Jonsson et al., 2018).
Freshwater fishes are useful subjects to test global TP-body size scaling hypotheses because these species range in maximum mass from less than 1 to over 3,200,000 g (Froese & Pauly, 2019), have evolved remarkable functional diversity (Toussaint et al., 2016) and occupy trophic niches from algivores and detritivores to top predators (Winemiller, 1990). With over 14,953 fish species inhabiting freshwater systems world-wide (Tedesco et al., 2017), this group represents about 1/4 of extant vertebrates. Studies of freshwater lakes have provided strong evidence of positive TP-size scaling relationships in fish and other consumers (Cohen et al., 2003;Nakazawa et al., 2010). Nevertheless, highly diverse fish communities in tropical rivers of South America and Southeast Asia (Layman et al., 2005;Ou et al., 2017) have reported both non-significant and positive TP-body size scaling relationships, largely dependent on the trophic guild (e.g., carnivore versus non-carnivore; Keppeler et al., 2020) and taxonomic order. A global analysis by Romanuk et al. (2011) concluded that TP of fishes scaled positively with body mass, but did not test for potential differences between marine and freshwater ecosystems, and their analysis excluded herbivores and detritivores. Large-bodied herbivores and detritivores that feed at low trophic levels are relatively common in river ecosystems (Ou et al., 2017;Winemiller, 1990), which are fuelled by a complex mix of phytoplankton, vascular plants, terrestrial seeds and detritus. Conversely, pelagic systems and lakes are supported mainly by unicellular algae, so food webs are usually longer and strongly size-structured (Keppeler et al., 2020;Potapov et al., 2019). With the exception of large filter feeders, large-bodied animals that feed at the bottom of the food web may be less common in lake or pelagic ecosystems, compared to rivers, due to the energetic and physical handling limitations associated with large animals feeding on microscopic algae. Given the wide range of variability within and among previous studies, and because herbivores and detritivores are a globally diverse and functionally important group of consumers in freshwater food webs (Ou et al., 2017;Winemiller, 1990), it remains uncertain at a global scale how, or if, TP scales positively with body size, or other traits of freshwater fishes.
Adaptations associated with jaw, mouth and skull morphology linked to feeding have been vital to the diversification of freshwater fishes and to the vertebrate transition to land (Sallan & Friedman, 2011;Westneat, 2004). In fishes, reptiles and amphibians that often swallow prey whole, mouth gape size is considered to be a fundamental morphological constraint leading consumers to select smaller prey (Arim et al., 2007;Shine, 1991;Wainwright & Barton, 1995).
If larger prey items feed at a higher trophic level than smaller prey items, then the TP of gape-limited consumers should increase with jaw length or mouth gape size across species and ontogeny (Arim et al., 2007;Mihalitsis & Bellwood, 2017;Mittlebach & Persson, 1998;Wainwright & Barton, 1995). It follows that if jaw length increases positively with body mass (Wainwright & Barton, 1995) then it is logical to assume that TP also scales positively with body mass.
The aim of this study was to test whether maximum body mass and jaw length are reliable predictors of TP in freshwater fishes globally, and to compare linear and nonlinear machine-learning (ML) models incorporating biogeography, taxonomic order, habitat and morphological traits. ML methods (Ryo & Rillig, 2017) are increasingly used in ecology due to assumed higher accuracy and better ability to predict outcomes of multiple nonlinear interactions K E Y W O R D S allometric trophic network models, allometry, body mass, gape limitation, machine learning, predator-prey, random forest, trophic network theory when compared to other statistical methods such as general linear or mixed-effects models (GLMs; GLMMs). Here, we compared the performance of Bayesian linear mixed effects and ML methods in predicting the TP of freshwater fishes.
We tested five hypotheses (Table 1) associated with functional mechanisms of trophic position-size scaling theory. We expected: (1) TP would scale positively with relative jaw length as predicted by gape-limitation theory (Arim et al., 2007;Wainwright & Barton, 1995); (2) jaw length would scale positively with body mass (Wainwright & Barton, 1995); and therefore (3) TP would scale positively with body mass (Romanuk et al., 2011). We hypothesized that: (4) fish assemblages occurring in lakes (Cohen et al., 2003;Nakazawa et al., 2010) would have a steeper positive TP-body mass scaling slope compared to fishes inhabiting rivers or streams where large-bodied detritivores and herbivores are common (Layman et al., 2005;Ou et al., 2017;Potapov et al., 2019); and (5) expected the slope of TP-body mass scaling associations would be negatively correlated with the relative species richness of herbivoresdetritivores among orders since these species do not feed at a higher TP when larger-bodied. All morphological traits, other than TA B L E 1 Hypotheses tested (1-5) and associated statistical models (1-5) used to explain and predict trophic position (TP) of fishes  maximum body size, were quantified as ratios rather than raw measurements in order to minimize the potential confounding effects of intraspecific variation.

| Fish species and trait data
A global list of extant freshwater fishes, comprising 14,953 species and their occurrences in seven biogeographic regions (ecoregion), was sourced from Tedesco et al. (2017). Species were matched with a trait database described in Toussaint et al. (2016)  if it also inhabits marine or estuarine environments (fresh/marine).
Our dataset did not include entirely marine species; only diadromous and estuarine or freshwater-obligate species. All species that were listed as temporarily inhabiting marine systems also occurred in rivers, while some species also occurred in lakes, and many occurred in both.
Maximum body mass data were not available for all species, and therefore we estimated log 10 MBM from log 10 maximum length using a Bayesian linear mixed model and unpublished body elongation data (sensu Froese et al., 2014). The correlation between actual maximum mass and predicted mass in a 10-fold cross-validation yielded an r 2 of .90 and a slope of 0.98 suggesting that the model was suitable to predict maximum mass. MBM was represented as the species' maximum total mass (g) averaged across river basins of occurrence from Tedesco et al. (2017). Many species were recorded beyond their native ranges and occurred in multiple river basins in our global dataset, but to avoid pseudo-replication we used one set of averaged trait data for each species in their native biogeographic region (Tedesco et al., 2017). Intraspecific variation in traits is wide-ranging, but could not be examined here due to insufficient data available for all species at the global scale. Therefore, our analyses focused on species-level relationships.
Morphological traits aside from MBM were extracted from a database detailed in Toussaint et al. (2016). Morphological traits provided relative measures of external morphological features derived from side view photographs and, for the analyses here, included: maxillary jaw length (JlHd); eye diameter (EdHd); vertical position of the mouth (MoBd); and caudal fin aspect (CFdCPd) (Supporting Information Figure S1). All morphological traits were represented as unitless ratios of another morphological feature (Supporting Information Figure S1), but all were measured independently of body size. Allometric biases associated with morphological ratios (Albrecht et al., 1993) likely increased uncertainty in our models, but some of these issues were minimized by restricting measurements to photos of adult stages only.
The potential TP associations with morphological features including eye diameter, position of the mouth on the head, and caudal fin aspect were included in statistical models (see below) but the direction of the associations were unclear from the literature, and therefore a priori hypotheses (Table 1) were not set for these traits.
The caudal fin aspect measured here has been correlated positively with sustained swimming speed and drag reduction in a range of fishes (Langerhans, 2008), which may benefit predators, while prey often exhibit more robust caudal regions (Langerhans et al., 2004) suited to fast-start escape behaviour. Extremely large eye diameter has evolved in some prey taxa in order to detect predators (Nilsson et al., 2012), yet predators also benefit from enhanced visual acuity.
Position of the mouth on the head indicates vertical feeding position in the water column, and fishes with superior mouths tend to have higher trophic positions (Keppeler et al., 2020).

| Trophic position
TP estimates of freshwater fishes were extracted from FishBase (Froese & Pauly, 2019). A fractional TP, between 2.0 (Herbivore) and 4.5 (Apex predator), was estimated for each fish species in FishBase. FishBase calculates TP following the equation: where the sum runs from 1 to the total number of prey items in the diet of fish species i. TP is the trophic position of fish species i, Troph p is the TP of food item p, while DC ip is the fraction of food item p in the diet of fish species i. Primary producers, detritus and bacteria were assumed to have a TP of 1 which was added to each consumer. Therefore, a fish eating 50% phytoplankton/plants (TP = 1) and 50% herbivorous zooplankton (TP = 2) will have a TP of 1 + (0.5 × 1 + 0.5 × 2) = 2.5. The model used in FishBase to calculate TP represents a mean of the species across previously published studies. However, the mean TP may not represent the best estimate trophic position for each species. In particular, the trophic position of large predators has been underestimated in recent stable isotope studies (Hussey et al., 2014). Therefore, we undertook sensitivity analyses using the upper 95% confidence interval (Supporting The four guilds align with generic descriptions representing the diet composition of adults: herbivore-detritivore-fish that consume only detritus, plants, phytoplankton or algae; omnivore-trophic generalists that consume a range of phytoplankton, algae and aquatic or terrestrial plants and invertebrates, or occasionally higher level consumers; secondary consumer-fish that feed primarily on zooplankton, insects, macroinvertebrates and other crustaceans; top predator-fish that are primarily piscivores, or feed on other higher level consumers and in some cases decapod crustaceans and macroinvertebrates.

| Statistical analysis
We used Bayesian linear mixed effects and ML random forest models (full details of the models, prior distributions, and software are provided in the Supporting Information statistical analyses; full model code and datasets on github: https://github.com/jdyen/ sizetrophic) with r 2 analogues and 10-fold cross-validation, to explain and predict TP.
To test hypotheses 1, 3 and 4 (Table 1), we used a Bayesian linear mixed effects model with the full (n = 1,991) structure (model 1): log 10 TP ~ (log 10 MBM | order) + (log 10 MBM | ecoregion) + log 10 jaw length + river/lake * log 10 MBM + fresh/marine* log 10 MBM + eye diameter + position of the mouth + caudal fin aspect. We standardized all continuous predictor variables to a mean of zero and a standard deviation of one. The full model included random intercepts and slopes for ecoregion and taxonomic order. In particular, the body size of freshwater fishes varies widely among orders and biogeographic regions (Blanchet et al., 2010), and therefore we evaluated Hypothesis 3 TP-MBM (Table 1) independent of biogeographic or order-specific differences in body mass. Body mass and jaw length were log 10 transformed for all statistical analyses. The interaction between MBM * river/lake was used to test for potential differences in the TP-MBM slopes between lake and river ecosystems (Hypothesis 4 We used a conditional inference random forest model (model 2; Breiman, 2001;Horthorn et al., 2006) to relate TP to all predictors included in Bayesian linear mixed effects (model 1; hypotheses 1, 3, 4).
We trialled four additional ML methods (Supporting Information   Table S1) during model development and present conditional inference random forest models because these had the best estimated predictive performance for models of TP (based on cross-validated r 2 values; Supporting Information Table S1). Random forest model 2 used the full dataset (n = 1,991) to build an ensemble of decision trees to relate the response variable (TP) to the set of predictor variables (log 10 MBM; ecoregion; river/lake; log 10 jaw length; fresh/marine; eye diameter; position of the mouth; caudal fin aspect). This approach implicitly incorporated complex, nonlinear associations and high-order interactions among predictors but did not allow a priori interactions or hierarchical structures to be set. The ability to incorporate multiple complex and higher-order interactions, without setting model structure (e.g., random slopes and intercepts) and interactions a priori, is considered one of the reasons why ML methods have enhanced predictive power (Ryo & Rillig, 2017) when compared to GLMs or GLMMs, which are influenced by subjective decisions about model structure.
We fitted Bayesian linear (model 1) and random forest (model 2) models to the full dataset (n = 1,991) including all trophic guilds, but also to subsets of data based on four trophic guilds [herbivoresdetritivores (n = 265); omnivores (n = 350); secondary consumers (n = 1,609); and top predators (n = 254)] independently. We fitted models in this way to compare the explanatory and predictive powered among different trophic guilds and between random forest and Bayesian linear mixed methods (see Model validation below).
In all random forest models, we estimated the partial dependence of TP on each continuous predictor, and estimated variable importance to evaluate the strength of associations. Partial dependence is the marginal relationship between model predictions and a subset of predictor variables, which provides a simplified representation of a fitted random forest model. Variable importance reflects the change in model accuracy when a given variable is shuffled randomly during model fitting. We standardized importance values so that their sum over all variables is equal to one. Therefore, importance values lie between zero and one, with larger values indicating a stronger association between a given predictor variable and the model response (Strobl et al., 2007(Strobl et al., , 2008. We used the train function in the caret R package version 6.0-84 to tune and validate random forest models and the five additional ML methods (Kuhn, 2008). We used the partial_dependence function in the edarf R package version 1.1.1 to estimate partial variable effects (Jones & Linder, 2017), and used the varImp function in the party R package version 1.3-3 to estimate relative variable importance. We fitted random forest models with the cforest function in the party R package (Hothorn et al., 2006).

| Model validation and sensitivity
To compare the performance of Bayesian linear (model 1) and random forest (model 2) models we used in-sample model fit to estimate explanatory capacity and used 10-fold cross-validation to estimate predictive capacity (Roberts et al., 2017). In both cases, we measured model fit with r 2 values, based on Pearson's r. In 10-fold crossvalidation, the dataset was broken into 10 equal-sized folds, and a model was fitted with each fold held out in turn. Model fit was based on the congruence between observed values and those predicted for each holdout dataset. We note that the cross-validation used to tune model parameters was performed internally within each model (i.e., parameters were tuned with cross-validation on the nine folds used for model fitting).
We ran sensitivity analyses (Supporting Information  Figure S5).

| RE SULTS
The TP and associated data available for the 1,991 freshwater fishes represented 30 orders and 7 global ecoregions. Cypriniformes Gadiformes; Pleuronectiformes) were not considered to be reliable since these were mostly marine inhabitants, each represented by fewer than five species in our sample.
Jaw length (Hypothesis 1/model 1) had the strongest positive effect size in the Bayesian linear mixed effects model ( Figure 2) and was the most influential (variable importance = .46) predictor of TP in the random forest equivalent, model 2 (Figures 3a and 4). When  (Table 2). In-sample model fit (Table 2) was highest (31%) in the top predator guild and lowest among herbivores-detritivores (20%). Random forest model 2 had 1.9 times better predictive performance (10-fold cross-validation) than the linear model for all trophic guilds combined (Table 2), and had equal or better predictive performance for each guild separately. The random forest model 2 for all guilds explained 55% (r 2 ) of global variation in TP, which was higher than the Bayesian linear mixed effects equivalent (Table 2). All ML methods trialled outperformed the Bayesian linear mixed models, but random forests provided the greatest predictive performance (Supporting Information Table S1).
Despite robust explanatory power and improved predictive performance of nonlinear ML methods, models 1 and 2 both over-estimated the TP of herbivores-detritivores and omnivores, and underestimated the TP of top predators (Figure 7). Both explanatory and predictive performance were lowest for herbivores and detritivores regardless of the modelling method (Table 2). Bias in low and high TPs resulted in poor overall predictive performance (Table 2; 10-fold cross-validation), which was not improved by the exclusion of herbivores-detritivores from analyses (Supporting Information Figure S5). Explanatory and predictive power (Supporting Information Table S4) of random forest models improved slightly, from r 2 of .55 to r 2 of .60 and prediction from .32 to .34, after exclusion of herbivores-detritivores, while Bayesian model results were unchanged (Supporting Information Table S4).

| D ISCUSS I ON
Our study suggests that maxillary jaw length is an important constraint on TP in fishes globally. Body size determines energy demand (Rip & McCann, 2011) and can influence predator-prey interactions F I G U R E 3 Partial dependence of trophic position (TP) on log 10 jaw length (a), jaw length-log 10 maximum body mass (b) and TP-log 10 maximum body mass (c) from random forest models 2 and 4. Plots display the marginal association between TP and a given predictor, marginalizing (averaging) over all other predictor variables included in a model. Black points are observed values of TP and predictor variables. Dashed boxes on the jaw length panel (a) qualitatively illustrate the least-occupied trait-spaces of top predators (TP = 4-4.5) with short jaws, and herbivores-detritivores or omnivores (TP = 2.0-2.79) with very long jaws (Brose, 2010;Emmerson & Raffaelli, 2004), but in gape-limited consumers it is the jaw and associated mouth and skull adaptations that play a more direct role in the size and type of prey consumed. Despite variation in diet, feeding behaviour, and jaw morphology within and among species (Ferry et al., 2015;Wainwright, 2007), our results underline a steeply positive and nonlinear association between jaw length and TP among fishes globally.
In fishes, amphibians and reptiles, which often swallow prey whole, mouth gape can limit prey size-selection (Arim et al., 2007;Shine, 1991;Wainwright & Barton, 1995). Predators generally had longer jaws than fishes feeding at a lower TP and, although gape size is not directly related to jaw length, the positive association was consistent with predictions of TP increasing with gape size (Arim et al., 2007). Longer jaws can increase gape-distance for prey capture, increase mouth closing speeds, or increase suction feeding velocities in predators (Hulsey & Garcia de Leon, 2005), while shorter jaws maximize bite force needed to feed on hard-bodied prey items (Ferry et al., 2015;Westneat, 2004;Evans et al., 2019). The shape of the nonlinear association showed that top predators rarely had small jaw sizes, while species with extremely long jaws were not commonly omnivorous, herbivorous or detritivorous.
TP was positively associated with jaw length, but jaw length was weakly associated with body mass, and consequently TP was generally uncorrelated with body mass among fishes. Given the weak but statistically significant association between jaw length and body mass, it was unsurprising that body mass was a poor predic- Siluriformes), may partly explain why TP showed a weak relationship with body size. For example, in the most species-rich order of freshwater fish, many large (> 10,000 g) Cypriniformes are detritivores and herbivores with low TPs, such as European and Asian carps (e.g., Ctenopharyngodon sp. and Hypophthalmichthys sp., TP = 2), whereas most small Cypriniformes are carnivores (German et al., 2009) feeding on zooplankton or invertebrates with TPs higher than 3. isotope studies on tropical (Ou et al., 2017) and temperate rivers (Burress et al., 2016) showing negative relationships.
In another species-rich order of freshwater fish, TP scaled negatively (Characiformes) with increasing body mass, which is opposite to the positive association reported by Romanuk et al. (2011). Even after excluding herbivores-detritivores, we could not replicate the result of positive TP-body mass scaling for Characiformes. This order is a functionally diverse (Toussaint et al., 2016) group of primarily Neotropical freshwater species including very large fishes that feed at high and low TPs, with unique adaptations to eat floodplain plants, nuts and seeds (Correa et al., 2007). Other adaptions of Characiformes include specialized teeth for biting (e.g., piranha Pygocentrus sp.; Van der Sleen & Albert, 2017), and fin-and scale-eating strategies (Sazima, 1983)-all of which allow these fishes to feed on relatively large, or high trophic level, prey necessarily without a large body size. Siluriformes in this ecoregion are characterized by a large range of jaw sizes with various adaptations to filter feed, or graze on biofilm and vegetation (Lujan & Armbruster, 2012). Similar to our results, Layman et al (2005) reported no association between TP and predator body size in the Cinaruco River of the Neotropical realm.  & Winemiller, 2013;Ou et al., 2017;Romanuk et al., 2011), and the slope of the TP-MBM association was steepest in lakes. Perciformes was the dominant order inhabiting lake ecosystems in our sample and this was largely due to radiations of endemic cichlids in the African Rift Valley (Muschick et al., 2012). Since the Afrotropical ecoregion is dominated by perciform fishes, it is reasonable to expect that TP may scale positively with body size in this ecoregion, but again we found a weak relationship, and jaw length in this order was not strongly associated with body mass. Perciformes was also dominant in Australasia, but similarly we found little evidence of positive allometric scaling in this ecoregion, possibly due to the influence of fishes in other orders with no discernible TP-MBM relationship.
Traits other than jaw length and body size examined here were not particularly influential predictors in the random forest models, but caudal fin aspect was significantly and positively associated with TP in the Bayesian linear mixed models. Caudal fin aspect is positively correlated with sustained swimming speed and drag reduction (Langerhans, 2008), and therefore this result may indicate that predators are more likely to have faster sustained swimming speeds than fishes feeding at lower TPs. However, the strength of the TP-caudal fin aspect association in random forest models was very weak. Differences in how predators find and capture prey (e.g., ambush; searching etc.) and other aspects of their Our results contribute to evidence suggesting that size-structured trophic dynamics differ between river and lake ecosystems. The weak association we observed between TP and body size of freshwater fishes in rivers is consistent with two previous global food web analyses (Potapov et al., 2019;Riede et al., 2011). Likewise, the more positive allometric scaling of TP in lake fishes matched results from lake food web analyses (Cohen et al., 2003;Nakazawa et al., 2010;Potapov et al., 2019;Riede et al., 2011). Brose et al. (2019) reported positive predator-prey mass scaling in lake and stream food webs globally, but noted that data on large species, including fish, were needed to confirm the relationship in streams. Contrasting TP-MBM scaling relationships between lakes and rivers may be explained partly by size-compartmentalization hypotheses discussed (Potapov et al., 2019). They hypothesized that differences in TP-MBM slopes among ecosystem types (freshwater, marine, terrestrial) were attributed to differences in the size-structure of primary producers fuelling food webs. For instance, river-floodplain food webs are fuelled by a complex mix of phytoplankton, vascular plants, terrestrial seeds and detritus (Layman et al., 2005;Winemiller, 1990) and generally have not conformed to simple assumptions of positive allometric scaling of TP. By contrast, lake ecosystems are more often characterized by longer and linear food chains fuelled by small-sized phytoplankton (Cohen et al., 2003;Vander Zanden & Fetzer, 2007;Vander Zanden et al., 2011) and conform to positive allometric scaling of TP (Cohen et al., 2003;Nakazawa et al., 2010;Potapov et al., 2019;Riede et al., 2011 Note: Estimates of variation explained and predicted are based on insample model fit r 2 (bold) and 10-fold cross-validation (in parentheses), respectively.
shallow and strongly supported by multicellular autotrophs whereby TP-body mass associations may be weak. The contrasting TP-MBM patterns suggest that body size-based assumptions derived from lake or marine ecosystems may not apply to rivers or floodplain ecosystems, and therefore differences among ecosystem types and underlying trophic complexity (Jonsson et al., 2018) should be considered in size-based fisheries, food web and macroecology models (e.g., Andersen, 2019;Blanchard et al., 2017;Brose et al., 2017;Sibly et al., 2012).
With 1.9 times better predictive performance compared to the linear method, our study supports the use of nonlinear ML approaches to improve the predictive capacity of macroecology models. Despite explaining 55% of the global variation in fish TP, our best random forest model over-estimated the position of herbivores-detritivores and omnivores, and under-estimated the position of top predators. A recent review showed that few studies test the predictive capacity of their most supported models (Mac Nally et al., 2018). Our findings reiterate the importance of validating predictive capacity, especially in macroecology and ML models, which often rely on global datasets with large sample sizes. Here, we have highlighted that a series of traits that are clearly associated with TP, supported by our results and mechanistic theory, cannot accurately predict TP per se. Our results caution against the use of traits-including body size-as predictors of TP, at the species level, in freshwater fishes. The addition of jaw length substantially improved performance relative to body size but global predictive capacity remained poor.
Incorporating other functional feeding traits (e.g., jaw shape and mechanics, absolute rather than relative jaw size, gape, digestive tract anatomy), behavioural feeding mode (e.g., Ferry et al., 2015), and intraspecific variation (e.g., Wainwright & Barton, 1995) are likely to yield more accurate predictions of TP. Furthermore, the same fractional TP (e.g., TP = 3.0) can be achieved via different diets (e.g., zooplankton, macroinvertebrates), and therefore future studies would benefit from exploring the more direct functional links between consumer morphology and prey morphology and their respective TPs. For example, prey type and size may also be a determinant or constraint on maximum size or gape size in consumers.
Therefore, examining consumer-food type traits together in combination with feeding mode (e.g., filter feeding; grazing) and TP may offer useful insight.

ACK N OWLED G M ENTS
Thanks to S. McDonald for assistance with collating datasets. R.K.K.