Louis E. DeversInstitut de Mathématiques de Toulouse (IMT)Université Paul Sabatier Toulouse III118 Rte de Narbonne, 31400 Toulousedevers.louis@gmail.comPerrine BonavitaCentre de Recherche sur la Cognition Animale (CRCA-CBI)Université Paul Sabatier Toulouse III118 Rte de Narbonne, 31400 Toulouseperrine.bonavita@univ-tlse3.frChristian JostCentre de Recherche sur la Cognition Animale (CRCA-CBI)Université Paul Sabatier Toulouse III118 Rte de Narbonne, 31400 Toulousechristian.jost@univ-tlse3.frMarch 20, 2024ABSTRACTTermites form complex dynamical trail networks from simple individual rules when exploring their environment. To help identify those simple rules, we reconstructed trail networks from time-lapse images of roaming termites. We quantified the trails’ frequentations over time and compared them to the ones obtained by a null model. Arena borders were preferred in both simulated and observed data. Yet, the amplification phenomenon was higher with real termites, underlining the role of pheromones.Keywords Dynamical Networks · Social Insects · Network Reconstruction · Termites · Biological Networks
As seen in Fig.2B and D, the observed and simulated termite densities are not distributed in the same way. So, an absolute filter above which an edge is considered "active" will not suffice. To discriminate active and non-active edges, we propose a method inspired by social insects like ants and termites: pheromones. The amount of pheromones on a given edge increases with passing termites but decreases through evaporation at a constant rate . Pheromones are usually key to understanding routing problems and path selection in social insects Theraulaz and Bonabeau , Dorigo et al. . Here, we computed the amount of pheromones on each edge P hij for each time step as follows : dP hij(t) dt = P hij(t) +
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Nij Lij (3) In Eq. (3), the concentration of pheromones P hij(t) on edge ij evaporates at rate . Previous work estimated the half life of Procornitermes araujoi of being 16 minutes Fouquet and Jost . Implying a rate of evaporation of = 7.26 104s1. The concentration of pheromones increases with the number of individuals present in edge ij. We need to divide by the length of the edge Lij to obtain concentrations of pheromones per cm. From there, we conserved the edges with the higher amount of pheromones that totalled pthresh per cent of all the pheromones at time t. In our case,pthresh = 0.8 meant that active edges were the biggest ones representing a total of 80% of all pheromones. Such criterion allows easy comparison between the observed and simulated networks.
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In Fig.4, is represented both observed (A-C) and simulated (D-F) networks over time (t = 10, 100, 1000s). Concerning the observed network (A-C), we first observe a spread of the termites through the whole arena, followed by a selection of edges. The edges on the border are mainly selected. Concerning the networks simulated by our null model, we also observe a spread, but not followed by a drastic edge selection. However, border edges seem to be preferred as well. The main difference thus lies in the intensity of the filtering, rather than the edges being filtered.
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The dynamics of the formed networks properties can be extensively studied. We propose here preliminary results concerning the total length of the networks and the number of conserved edges over time. Future work will be needed to focus on metrics like efficiency, robustness or meshedness for instance Buhl et al. [2004, 2006, 2009]. In Fig.5, we represented (A) the total number of edges and (B) the total length of the network in cm over time. Both observed 5 Emergence of dynamical networks in termites
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