# PhD proposal: Statistical and dynamical properties of mutualistic interactions, in natural and social systems

For example, ecologists are interested in systems where groups of animals and plants help each other to fulfill essential biological functions such as feeding or reproduction. They are usually known as seed dispersal or pollination networks, because it may be described in terms of complex networks, where the nodes represent animal or plant species and the links, an interaction between them. In the case of mutualistic ecosystems, only interactions between nodes belonging to different guilds are allowed, leading to a bipartite network. The bipartite adjacency matrix of the network shows that real ecosystems are not a random collection of interacting species, but that they display instead, a high degree of internal organization, called nestedness. This particular topology of the network is such, that if the columns (rows) of the bipartite adjacency matrix are ordered in, say, decreasing degree, then the rows (columns) appear to be ordered in the same way [1].

The origin and the importance of such ordering is a matter of strong debate. It is fairly obvious that a detailed explanation of the interaction mechanism of individual species can be of little help to understand the generalized pattern that is found across ecological systems of very different sizes and types, involving plants of different nature and animals that range from insects to birds.

Interestingly, different socio-economic systems may also be described in the same way. For example in the country-product network, one kind of nodes represents the countries and the other, the products they make/sell. The mathematical tools developed for the study of ecosystems proved to be useful to describe the evolution of such systems [2]. While these networks often show nestedness, the degree distributions of the corresponding two guilds are often different from those in mutualistic ecosystems. Moreover, nowadays the relevance of nestedness itself, is also under discussion [3].

In a recent work [4] it has been proposed that the observed organization of mutualistic ecosystems contributes to the persistence of biodiversity. This result is based on the study of a dynamical population model that includes the mutualistic interaction along with the intra-guild competition treated in mean field approximation. It is then interesting to study the dynamics where the competition term takes into account the topology of the network.

In this project we focus on the study of the statistical properties of natural and socio-economic systems presenting mutualistic interactions, using complementary approaches. On one hand, we propose a data based study of these systems, in order to look for stylized facts. This may help to understand the role of mutualism in the observed organization of man-made systems with respect to that of natural ones. On the other hand, it is necessary to understand which interactions are at the origin of the observed organization of each type of system. To study the dynamics of a model based on the interactions assumed to be relevant for different cases, is then essential to compare with observations on real systems.

**References:**

[1] J. Bascompte, P. Jordano, C.J. Meli ́an, and J.M. Olesen, The nested assembly of plant-animal mutualistic networks Proc.Nat. Acad. Sci. USA 100,9383(2003).

[2] The Atlas of Economic Complexity: Mapping Paths to Prosperity, Ricardo Hausmann, César Hidalgo, Sebastián Bustos, Michele Coscia, Sarah Chung, Juan Jiménez, Alexander Simoes, Muhammed. A. Yildirim, The MIT Press,Cambridge, Massachusetts, London, England (2013).

[3] The ghost of nestedness Phillip P.A. Staniczenko, Jason C. Kopp and Stefano Allesina, Nature Comm. DOI: 10.1038/ncomms2422 (2012).[4]The architecture of mutualistic networks minimizes competition and increases biodiversity, U. Bastolla et al Nature 458, 1018, (2009).

[5] Two classes of bipartite networks: Nested biological and social systems. Enrique Burgos, Horacio Ceva, Laura Hernández, R. P. J. Perazzo, Mariano Devoto, and Diego Medan,, Phys.Rev. E 78, 046113, (2008).

[6] Understanding and characterizing nestedness in mutualistic bipartite networks. Enrique Burgos, Horacio Ceva, Laura Hernández, R. P. J. Perazzo, Comp. Phys. Comm. 180, 532 (2009).

**Procedure:**

Interested candidates should send an email, quoting in the subject: “PhD application”, including CV, transcripts of undergraduate studies and a recommendation letter to: Laura.Hernandez@u-cergy.fr and Yamir.Moreno@gmail.com

**Deadline: May 15 th 2015.**

The selected candidate will be proposed for a financial support to the Doctoral School EM2P (Economie, Management Mathématiques et Physique) of Cergy-Pontoise University. Answer middle of June 2015

The PhD student will register to the Cergy-Pontoise University, and is expected to start in September 2015. He/She will be based at LPTM, and will work under the supervision of Dr (HDR) Laura Hernández and the co-direction of Prof. Yamir Moreno BIFI, Zaragoza, Spain.

**Skills the student will develop:** Based on his/her knowledge on Statistical Mechanics, Phase Transitions and Dynamical Systems, the PhD student will acquire an interdisciplinary formation through the different case studies, along with experience in numerical simulations, agent based models, and complex network theory.

**Requirements:** Interest in the interdisciplinary approach, good knowledge of Statistical Mechanics, Phase Transitions and programming (C or Fortran at least).