The paper in Nature is here: http://go.nature.com/2gHOjAA
Coevolution is the reciprocal evolutionary change observed in interacting species driven by natural selection. We have now decades of theoretical and empirical work exploring how pairs and small groups of interacting species coevolve. However, in many biological communities, a web of ecological interactions directly or indirectly connects dozens of interacting species. How does coevolution proceed in a web of interacting species? Similar problems emerge in very distinct scientific fields. How do cultural practices change in social networks? How do financial stocks change in financial markets? Evidence from disparate scientific fields indicates that indirect effects play a fundamental role in the dynamics of complex systems.
In ecology, indirect effects are the effects of non-interacting species on the ecology, evolution, or behavioral patterns of other species. For instance, the arrival of a new species of hummingbird may impose novel selective pressures on a flowering plant. In turn, the evolution of the plant may lead to new selective pressures on other species in the community, such as another pollinator.
The role of indirect effects in ecological networks fascinated me since the beginning of my PhD in 2003. I remember my former co-supervisor Marcus Aguiar (Campinas, Brazil) explaining to me and to my supervisor Sergio Reis (also from Campinas, Brazil) that there are infinite pathways connecting species in a network. My co-supervisors Jordi Bascompte and Pedro Jordano, both at that time in Seville, Spain, also pointed out the importance of indirect pathways within networks for cascading effects that, in turn, may affect the ecology and evolution of species-rich interactions.
Almost ten years ago, at the beginning of my postdoc at UC-Santa Cruz with John N. Thompson I was interested in exploring the implications of cascading effects to the coevolutionary dynamics. First, I thought about using just the network structure – such as the shortest pathways between pairs of species – to explore the coevolutionary dynamics. However, as John would point out then, this approach would not incorporate the coevolutionary dynamics explicitly. After the development of a first coevolutionary model in collaboration with my friends John and Pedro, we explored some implications of cascading effects to coevolution in networks, but we were still unable to infer about the indirect effects in an explicit way.
In 2011, I began studying different approaches to infer about indirect effects. I tried approaches derived from different fields such as statistical mechanics, information theory, and network flow to explore the role of indirect effects on coevolution within networks. However, I made little progress in inferring the contribution of indirect effects until I read a paper about a phenomenon called “pathway proliferation”: ecological networks often have much more indirect and long pathways connecting species than direct interactions between species. It is expected longer pathways to have smaller effects than direct interactions but if the number of indirect pathways is much larger than the number of direct interactions, there is a chance that indirect effects may have a non-negligible contribution to the coevolution of species interactions.
At this point, my friends Jordi and Mathias Pires joined John, Pedro, and I on the project. We had multiple discussions about the development of the approach we used to compute the indirect effects. We had many, many Skype meetings and wonderful chats at Santa Cruz, CA or at the Atlantic Rainforest, in Brazil – literally discussing our study in-between species-rich networks formed by tropical palms and trees, toucans, tanagers, jacutingas, and fruitcrows.
At some point, our group realized that if the cascading effects die off with the length of the pathway it was possible, under some assumptions, to compute the asymptotic value for the sum of all infinite pathways connecting all species in the network. More importantly, we discovered that the matrix that describes the sum of all effects of all direct and indirect pathways connecting species represents the reorganization of the adaptive landscape promoted by species interactions.
Now we had an approach to compute the contribution of indirect effects to coevolutionary dynamics in a network model parameterized with empirical data. First, we asked a very simple question: under what conditions can we ignore indirect effects? Surprisingly the answer was that whenever mutualisms are a relevant source of selection, indirect effects are also relevant to coevolutionary dynamics. Contrary to our expectations, indirect effects were especially relevant to the evolution of specialist species.
However, mutualisms vary in their network patterns, from small, highly modular networks formed by host plants and ants to species-rich, asymmetrical, highly nested networks formed by fruiting plants and fruit-eating vertebrates. We then asked: how does the relevance of indirect effects vary with the structure of the network? We found that indirect effects are particularly relevant for species-rich mutualisms that involve multiple partners such as seed dispersal by vertebrates and pollination by animals.
Our results predict that mutualisms among multiple partners should show high levels of integration due to indirect effects. This evolutionary integration may explain the emergence of convergence in traits that characterize multiple mutualisms, as illustrated by the chemical composition and color of fruits, the shape of flowers, the color patterns and behavior of cleaning fishes, and warning signals of unpalatable species. However, our numerical simulations also suggest that this high level of integration produced by indirect effects may promote weak but long-lasting cascading effects in mutualistic networks. As a consequence, under scenarios of rapid environmental change, the integration produced by indirect effects, which may have contributed to the evolution of the most beautiful ornaments of life, may also imperil the rapid evolutionary response of interacting species.
Photo by João Paulo Krajewski.