On the architectural features of ecological and biological networks

Resumo

ABSTRACT Along this thesis we study the way in which some particular architectural features of ecological and biological networks determine their overall performance. The system approach used here, based on the application of statistical mechanics of complex networks to different biological and ecological systems, makes possible the study of the emergent or collective behaviour of those living systems, such as linear stability, global directionality, hierarchical structure, robustness against extinctions or the presence of a nested structure, among others. In this way, the study of static networks has proven extraordinarily useful. Our approach can be divided in three parts: -This highly interdisciplinary approach let us contrast different systems using the same methods, leading us to identify general patterns in their architecture, (as for example the existence of a inherent directionality in ecological and biological networks). -The design of simple models, subjected to diverse in-silico experiments, constitutes our main ¿laboratory¿. It let us contrast the natural network structures with the ones generated by these simple models. Here we have tried to stick to a minimal approach, introducing the less number of parameters and assumptions needed to model some phenomena. -And last, but not least, the use of null-models is vital to analyse the statistical relevance of natural (or synthetic) structured networks, allowing us to discern whether a particular architectural feature is relevant or on the contrary, is present in random networks. It is worth noting that one should be very careful on the desing of these null-models, since this will determine the outcome. Within this minimal-system approach, we have covered different properties regarding both directed (foodwebs, transcriptional regulatory genetic networks, signaling networks, neural networks) and undirected net-works (plant-pollinator and seed-disperser bipartite mutualistic networks). In the first part of this thesis we focus our attention in directed networks, mainly in the unaccounted stability of foodwebs and the inherent directionality present in many ecological and biological networks. Regarding foodwebs the most relevant finding is the detection of a strong correlation between lineal stability and the network feature we call trophic coherence [1]. Along this line we have suggested the Preferential Preying Model as a simple algorithm for generating networks with tunable trophic coherence. Most remarkably, it is able to create ¿syntethic¿ networks with similar stability properties to the natural foodwebs. The model also predicts that networks should become more stable with increasing size and complexity, as long as they are sufficiently coherent and the number of links does not grow too fast with size. Although this result should be followed up with further analytical and empirical research, it suggests that we need no longer be surprised at the high stability of large, complex ecosystems. On a different note, but still related to systems stability, we turn our attention to the empirically observed absence of feedback loops in directed biological and ecological networks. This feature have been oftentimes associated with the required stability these systems should present. However, while the important role of feedback loops in determining dynamical properties of complex networks has been widely recognised in the literature, their statistics remained scarcely studied. Further broadening this line we hypothesize that the (empirically observed) lack of feedback loops stems from the existence of an inherent directionality. To check the hypothesis we devise a simple model with a built-in directionality, which reproduces quite well the empirical fraction of feedback loops of any length by just tuning its only parameter ¿. In this way the existence of an inherent directionality constitutes a simple yet satisfactory parsimonious explanation for the empirically observed lack of feedback loops [2]. Moving on to bipartite networks, our work is aimed both to determine which are the topological features behind the nested architecture present in mutualistic plant-animal networks and to bring forward a solid procedure to rank the importance of different species in these valuable communities. Our first contribution in this topic is the introduction of a new analytical nestedness index. It is normalized so as to provide an output equal to unity in uncorrelated random networks. We also find that the neutral expectation for finite random networks is to have some non-vanishing level of disassortativity (r < 0). Accordingly, there is a very similar tendency for finite random networks to be naturally nested. Moreover, there is a clean-cut correspondence between nestedness and disassortativity: disassortative networks are typically nested and nested networks are typically disassortative [3]. With the idea in mind of contributing to the preservation of these communities we have put forward a novel framework to asses the relative importance of species in mutualistic networks. The algorithm, that we have named MusRank, rendered a ranking which clearly outperforms all the alternative ones used as workbench in most of the empirical mutualistic networks we analysed. The emerging ordering allows for assessing the importance of individual species within the whole system in a meaningful, efficient and robust way. This novel approach may prove of practical use for ecosystem management and biodiversity preservation, where decisions on what aspects of ecosystems to explicitly protect need to be made [4]. Summing up, the approach of statistical mechanics of complex nestorks allow us to tackle different problems in ecological and biological networks. We have studied the effect of some relevant topological features (trophic coherence, inherent directionality, nestedness) have in the overall performance of biological and ecological systems. -----------------------------------------------------------------------------------------------------------------------------------------------------