American Society of Naturalists

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“Nutrigonometry I: Using Right-Angle Triangles to Quantify Nutritional Trade-Offs in Performance Landscapes”

Posted on by Dr. Dana Reuter

Juliano Morimoto, Pedro Conceição, Christen Mirth, and Mathieu Lihoreau, May 2023

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Pythagoras was a key figure for mathematics, discovering what's now a cornerstone theorem used across many fields. In this paper, Pythagoras reaches out to nutrition, and help us reveal the best and the worst diets.

A new way to detect and measure animal nutritional trade-offs

A butterfly drinks from flowers. Photo credit Juliano Morimoto
A butterfly drinks from flowers. Photo credit Juliano Morimoto

What tools do we have to understand the evolution of animal feeding behavior? A new study by Dr. Morimoto and colleagues is providing a new model for measuring nutritional trade-offs. The model is called Nutrigonometry and uses right-angle triangles to identify optimal feeding strategies in complicated nutritional space. It promises to be an easy-to-use model that can be applied to many kinds of diet data and will help biologists untangle the complicated nutrition landscape that animals navigate throughout their lives.

It is not uncommon for animals to have traits that have different nutritional requirements, such as reproduction requiring different amounts of protein and carbohydrates compared with the immune system. Nutritional requirements can also change throughout the lifetime of an animal as they mature and grow. A mismatch in nutritional requirements can lead to what is called a nutritional trade-off and can lead to feeding behavior that favors one trait over another. An example of an already identified nutritional trade-off is between life span and reproduction in Drosophila melanogaster. D. melanogaster females will eat foods that maximize life-time egg production instead of life span. Even though many nutritional trade-offs have been identified and described, current tools make it difficult to compare results between studies or between different diet data structures. Dr. Morimoto and colleagues realized that having better tools to quantify these trade-offs will ultimately open the door for better comparison within the field of nutritional ecology and increase our understanding of behavioral evolution.

Dr Morimoto and colleagues propose using Nutrigonometry as a solution to the many problems that arise when studying multidimensional nutritional space. The framework is simple and effective at identifying previously described nutritional trade-offs, such as the one identified in Drosophila melanogaster. The framework allows for the use of many commonly used statistical tools, such as linear regressions, to identify peaks (or valleys) in the nutritional space. This means that the model can compare the optimum balance and quantity of nutrients that animals have to eat in order to maximise (peaks) or minimize (valleys) a given life-history trait, say, lifespan or reproduction. In the past this was often done visually or with highly computationally intensive tools. They show in their study that simple linear regressions combined with the Nutrigonometry framework perform better at predicting optimal regions in multidimensional nutritional space than other methods, such as machine learning. Their finding is exciting because it shows that large scale comparative studies can now be done easily. They are hoping their tool will allow future work to dive deeper into the relationship between animal foraging decisions and fitness. Ultimately, understanding the role of nutrition in physiology, behavior, and ecology will further rely on larger comparative studies and having a simple tool like Nutrigonometry will make it all the more possible.


Animals regulate their food intake to maximize the expression of fitness traits but are forced to trade off the optimal expression of some fitness traits because of differences in the nutrient requirements of each trait (“nutritional trade-offs”). Nutritional trade-offs have been experimentally uncovered using the geometric framework for nutrition (GF). However, current analytical methods to measure such responses rely on either visual inspection or complex models of vector calculations applied to multidimensional performance landscapes, making these approaches subjective or conceptually difficult, computationally expensive, and, in some cases, inaccurate. Here, we present a simple trigonometric model to measure nutritional trade-offs in multidimensional landscapes (nutrigonometry) that relies on the trigonometric relationships of right-angle triangles and thus is both conceptually and computationally easier to understand and use than previous quantitative approaches. We applied nutrigonometry to a landmark GF data set for comparison of several standard statistical models to assess model performance in finding regions in the performance landscapes. This revealed that polynomial (Bayesian) regressions can be used for precise and accurate predictions of peaks and valleys in performance landscapes, irrespective of the underlying structure of the data (i.e., individual food intakes vs. fixed diet ratios). We then identified the known nutritional trade-off between life span and reproductive rate in terms of both nutrient balance and concentration for validation of the model. This showed that nutrigonometry enables a fast, reliable, and reproducible quantification of nutritional trade-offs in multidimensional performance landscapes, thereby broadening the potential for future developments in comparative research on the evolution of animal nutrition.

Nutrigonometry I: eesin richt-anngle trianngles tae compeer nutritional trade-affs in sindry lanscapes

Craiters sort oot foo muckle maet they ett tae mak e maist o the expression o fitness traits, bit maun niffer eemaist expression cause o odds in e nutrients nott in ilka trait (“nutritional trade-affs”). Nutritional trade-affs hiv been preeved wi experimints aat eese e Geometric Framework for Nutrition (GF). Fooivver, wyes tae mizzour sic trade-affs depen on aither eesin yer een or kittlie mathematical models pit tae sindry performance lanscapes, makin sic oncomes subjective, or ill tae unnerstan, dear tae wirk oot, an fyles jist plain wrang. Here, we pit forrit a haimalt trigonometric model tae mizzour nutritional trade-affs in sindry lanscapes (Nutrigonometry), att lippens one trigonometric sibness o richt-anngle trianngles, an sae, is aisier tae wirk oot, unnerstan an eese nor e wyes o wirkin it oot att wis eesed afore. We apply Nutrigonometry tae a lanmark GF set o data tae compeer a hantle o statistical models tae wirk oot foo weel e model’s deein in finnin regions i the performance lanscapes. Iss shewed att polynomial (Bayesian) regressions mith be eesed for preceese an exack weirds o heichest an laichest pints in performance lanscapes, regairdless o fit lies aneth e data (i.e., parteeclar intaks o maet or fixed diet ratios). Syne, we managed tae wirk oot e kent nutritional trade-aff atween foo lang life wad be an foo mony younng there wad be baith fae e pint o view o nutrient balance an concentration for validation o e model. Iss shews Nutrigonometry allooes a fest, siccar, an reproducible mizzour o nutritional trade-affs in sindry performance lanscapes, in att wye, raxin oot e possibeelity for groweth in comparative research on the evolution o craiters’ nutrition in days tae come.

Dr. Dana Reuter.<br/>Photo credit: Dana Reuter
Dr. Dana Reuter.
Photo credit: Dana Reuter

Author Bio:

Dr. Dana Reuter is an NSF Postdoctoral Fellow working with the Florida Museum of Natural History and the Department of Ecology and Conservation Biology at Texas A&M. She studies the relationship among diet, biogeography, and morphology in mammals. She is also interested in community structure changes in deep time. Her additional interests include restoring vintage clothing, gardening, and exploring the outdoors.