Metabolic Theory of Ecology (MTE) and Ecological Stoichiometry (ES) are two common frameworks used to predict energy and nutrient budgets at various biological levels of organization [4, 7]. By comparing both theories, we found that the ES variables (diet, body N:P, “armor”) were outperformed by body size, which indicates that the ES framework has relatively little predictable effect on nutrient excretion compared to the role of body size. Also, we saw that the scaling coefficients for the relation between N excretion and body size were lower than the 0.75 coefficient predicted by MTE.
Similarly to previous studies, our results show that body size is a key control on excretion of N and P by fish[12, 24, 25, 26]. Bigger fish excreted more nutrients per capita when compared to smaller fish, however they excreted less nutrients per mass. This result was expected since MTE states that there is an allometric relation between metabolism and body size, described by ¾-power scaling . In fact, Allgeier et al. (2015)  found quantitative support for ¾-power scaling of nutrient excretion rates with body mass using data from marine fish and invertebrates. In our study, the lower scaling coefficients for both N and P were closer to a 2/3 factor than ¾, perhaps echoing debates in metabolic ecology about the most appropriate scaling factor [27, 28, 29]. Our results are similar to Vanni and McIntyre (2016) , who found scaling coefficients comparable to ours (0.68 for N; 0.56 for P). The ecological significance of these low scaling coefficients is that size-based increases in nutrient excretion are smaller than would be expected.
The reasons for these lower-than-expected scaling coefficients are uncertain because the ingestion and assimilation of nutrients should be directly related to metabolic rates, hence it is reasonable to expect that release of nutrients in wastes would be as well. One possibility is that focusing on dissolved wastes while excluding solid wastes could create a bias in studies like ours . Alternatively, biochemical mechanisms have received little attention. For instance, Delong et al. (2010)  found a gradient of size-scaling coefficients from 1.0 to 0.75 in a survey of metabolism across prokaryotes, unicellular eukaryotes and metazoans, and argued that the differences reflected the number of membrane-bound sites where ATP synthesis and proton pumping occur, as well as differential constraints on resource supply and vascular systems. Although MTE refers to metabolism instead of excretion, it is reasonable to assume the theory also applies to any biological rate that is derived from metabolism . Therefore, it could be that our lower than ¾ power-scaling is related to fish growth and ingestion rates or to ontogenetic diet shifts.
A novel aspect of our study was the range of temperature variation during our excretion incubations (9.9 to 25.7º C), and we were surprised to find no evidence that temperature affected nutrient excretion rates of fish. Both the MTE framework and many previous studies [13, 31–35] have suggested that temperature should have discernable effects. This is a surprising result since fish are poikilotherms, which means their body temperature is determined by the external temperature of the water they inhabit and should have direct influence on metabolic rates, feeding rates and activity levels . It could be that in the tropics, as the rate of diel temperature change is usually slow [12, 37], fish can acclimate and perform metabolic compensation . Consequently, because of fish acclimation, we see no apparent changes in nutrient excretion rates.
As for the effects of ES variables, diet and body stoichiometry, our results revealed counterintuitive patterns. Many studies have demonstrated that diet can directly influence fish nutrient excretion rates [38, 39]. The nutritional quality of the diet of aquatic consumers progressively increases from detritivores, to omnivores, to invertivores and, finally, to piscivores . Therefore, according to ES, it is expected that piscivores present the highest nutrient excretion rates compared to detritivores, for example. However, similarly to other comparisons of MTE and ES variables [12, 13], our results do not reflect this pattern. Vanni and McIntyre (2016)  attribute the lack of a diet effect to the absence of information on growth, ingestion, and egestion data, and Allgeier et al. (2015)  question how useful diet is for predicting nutrient excretion rates. Clearly, we need future studies to investigate the importance of diet by measuring growth, ingestion, excretion and egestion rates across a range of feeding and taxonomic groups.
As expected, armored catfish species presented up to 3x more P in their body composition than the other fish species. Therefore, according to ES predictions, it was expected that they would excrete less P because of their higher P demand for building their boney plates. However, armored and non-armored fish did not differ in their P excretion rates. One possible explanation for this deviation from our prediction is that we sampled primarily adult fishes whose bony skeletons have already been formed, such that further assimilation of dietary P reflects only tissue maintenance. Perhaps if we had sampled individuals in different life stages, we would see growing individuals with a higher P demand and consequent low P excretion.
Surprisingly, differentiating between armored and non-armored fish proved to be more efficient than using actual data on body NP for our model selection. This classification captures the major differences in body composition among our study species, so relying on a simple classification of armor investment by fish could be a sufficient proxy for differences in body stoichiometry. Given that directly measuring body composition is both time-consuming and requires specialized lab facilities, the use of such proxies is appealing in lieu of systematic characterization of body P and stoichiometry across aquatic animals.
Our work built upon the previous studies of Vanni and McIntyre (2016)  and Allgeier et. al (2015)  to integrate the MTE and ES frameworks for predicting animals’ nutrient excretion rates, and all three studies found that body size was by far the strongest influence on nutrient excretion. However, these prior studies tested a much wider range of body sizes (1µg to 500g dry mass , 0.04 to 2,597g ) than body N:P ratio. That disparity could yield a bias in favor of detecting the influence of MTE variables, so we designed our study to focus on a single taxon with a more limited range of body size (0.021 to 22.01g dry mass) yet similarly variable body stoichiometry. However, we still found that body size is the key control on N and P excretion rates.
Conceptual integration of MTE and ES in this study and others revealed that body size is the key control on nutrient recycling by aquatic animals. Even though our study included a wide range of temperatures, body stoichiometry, and diets, these factors had little detectable influence. While our statistical models provide a useful way to estimate nutrient excretion rates in our study system, they are not a replacement for collecting field data. The mass balance constraints embodied in the ES framework are a fundamental constraint on nutrient recycling, hence researchers seeking accurate estimates of nutrient excretion by aquatic animals should gather direct measurements to verify the applicability of predictive models to their focal species or ecosystem.