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A mathematical model shows a global trend towards mutualism between species


A team led by researchers from Universidad Carlos III de Madrid (UC3M) and Universidad Politécnica de Madrid (UPM) has developed a new mathematical model to study changes in ecological interactions between microbe populations. One of the conclusions they have found is that there is a trend towards mutualism, that is, towards a relationship in which species benefit each other.

Un modelo matemático muestra que hay una tendencia global hacia el mutualismo entre especies

There are various types of ecological interactions between species in ecosystems. One of the best known is predation (one species feeds from another, to put it simply), but there are other varieties, such as competition for resources, mutualism, commensalism, parasitism, etc. However, it is known that these are not permanent states, because there may be transitions between these interactions as a result of evolution. For example, a predation relationship between species may eventually become a mutualistic or symbiotic relationship between them during the course of evolution.

This new mathematical model makes it possible to study the type of transitions in ecological interactions. “One of the conclusions we have found is that there is a clear trend towards mutualism: ecological interactions can start in any way, but in the majority of cases they eventually lead to a mutualistic relationship”, says one of the researchers, José Antonio Cuesta Ruiz, professor in UC3M’s Mathematics Department, who recently published this work in the scientific journal Physical Review E together with researchers from UPM, Universidad Rey Juan Carlos de Madrid and Universidad del Pacífico at Lima (Peru).

In this article, they have also shown the high frequency with which these transitions occur in nature, discovering evolutionary trajectories that go through various intermediate states, according to the researchers: “Despite being a simple model, its emergent behavior is complex, it shows transitions between different ecological relationships, and is able to go through different stages of mutualism, predation and competition before reaching its final state”, add Javier Galeano and Juan Manuel Pastor, lecturers at UPM and co-authors of the work.

For their study, the researchers have used classical models of population dynamics, to which they have applied a standard technique in evolutionary theory, called adaptive dynamics. This technique allows them to find dynamic equations for the parameters of the population model, which determine the nature of ecological interactions, making it possible to study how these interactions change over time. “These types of models, despite being very simple, are able to capture essential elements to provide mechanisms of emergent phenomena. They are very useful when studying complex systems”, says Cuesta.

Bibliographic reference: Luciano Stucchi, Javier Galeano, Juan Manuel Pastor, Jose María Iriondo, José A. Cuesta (2022).  Prevalence of mutualism in a simple model of microbial coevolution. Physical Review E. Vol. 106, Iss. 5. Published 1 November 2022.


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