American Society of Naturalists

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“A vector-based approach to measure nutritional trade-offs within and between species”

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Juliano Morimoto and Mathieu Lihoreau (June 2019)

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A generalized approach to compare fitness landscapes within and between species in multi-dimensional data

“Eat your greens, Euclid!”

Morimoto and Lihoreau method allows for the comparison of diets that maximize (red arrows) and minimize (blue arrows) the performance of multiple species. Figure showing two performance landscapes of two hypothetical fly species (pink and magenta).<br />(Credit: Juliano Morimoto)
Morimoto and Lihoreau method allows for the comparison of diets that maximize (red arrows) and minimize (blue arrows) the performance of multiple species. Figure showing two performance landscapes of two hypothetical fly species (pink and magenta).
(Credit: Juliano Morimoto)

In Ancient Greece, somewhere around the year 300 BC, Euclid published his book Elements containing a single framework based on rigorous mathematical proof for Geometry. Little could he predict the far-reaching implications of his work. Some 22 centuries later, his life’s legacy was used to inspire biologists into creating a new framework – known as ‘nutritional geometry’, which is now widely used to investigate how animals and humans (should) eat. But how can one tell a good diet from a bad diet? And is there a universal ‘good diet recipe’ that solve all our problems?

To answer these questions, scientists need to measure the effects of different diets on morphological and physiological traits, and quantify how these diets affect these traits in relation to others in the same individual, species, or between species. To date, however, there were no quantitative framework that allowed intra- and inter-specific comparisons of these effects.

Building on previous attempts from colleagues, Morimoto and Lihoreau came up with a solution for this conundrum. They used the mathematical concept of vectors to quantify how much of each nutrient in the diet animals should eat to maximize a trait. Then, using fancy statistics that includes machine learning, they developed a model that could quantify differences in nutrient intake required to maximize traits within and across species.

This work provides a significant advance in how we tell good from bad diets. The method of Morimoto and Lihoreau has the potential to be broadly used in ecology and evolution to understand the fundamentals of animal nutrition, but also their far-reaching consequences such as how individuals interact within societies, how species coexist and co-evolve in communities. The work can also be used in conservation and medical research to gain insights into what a healthy diet means for a given species (including us humans), and how to achieve it. Many centuries later, Euclid’s fundamental mathematical legacy becomes an evidence to explain the evolution of species, the onset of diseases, and possibly, the secret for a healthy life.


Animals make feeding decisions to simultaneously maximize fitness traits that often require different nutrients. Recent quantitative methods have been developed to characterize these nutritional trade-offs from performance landscapes on which traits are mapped on a nutrient space defined by two nutrients. This limitation constrains the broad applications of previous methods to more complex data, and a generalized framework is needed. Here, we build upon previous methods and introduce a generalized vector-based approach – the Vector of Position approach – to study nutritional trade-offs in complex multi-dimensional spaces. The Vector of Position Approach allows the estimate of performance variations across entire landscapes (peaks and valleys), and comparison of these variations between animals. Using landmark published datasets on lifespan and reproduction landscapes, we illustrate how our approach gives accurate quantifications of nutritional trade-offs in two- and three-dimensional spaces, and can bring new insights into the underlying nutritional differences in trait expression between species. The Vector of Position Approach provides a generalized framework for investigating nutritional differences in life-history traits expression within and between species, an essential step for the development of comparative research on the evolution of animal nutritional strategies.