Short Note The strength of simulated indirect interaction modules in a real food web Nerta Gjata, Marco Scotti, Ferenc Jorda ´n * The Microsoft Research – University of Trento Centre for Computational and Systems Biology, Piazza Manifattura 1, 38068 Rovereto (TN), Italy 1. Introduction Network modules (or motifs) are increasingly studied in various systems ranging from food webs to gene regulation networks. The key questions are (1) how to define modules, (2) how frequent they are, (3) how strong their functional effects are and (4) how do they differ among different biological (and non-biological) systems? The last, comparative problem is already quite heavily studied (Milo et al., 2002), even if we still do not really know the answers to the previous, more basic questions. Studying network modules can be a key to better understanding complex biological networks, e.g., food webs (Fig. 1). In ecological research, network modules have already been richly analysed, both experimentally (Menge, 1995) and theoreti- cally (Brose et al., 2005; Mullon et al., 2009). In this paper, by ‘‘network modules’’ we refer to a particular set of small food web subgraphs shown in Fig. 2: these are richly described experimen- tally and seem to have solid ecological relevance. Although the nomenclature differed, the interest in indirect effects (especially interaction chain effects, Wootton, 1994) is very old (Elton, 1927) and experimentally inspired (Ohgushi, 2005). Moreover, indirect effects between two groups can be stronger than a direct interaction (Patten, 1982; Higashi and Patten, 1989; Palomares et al., 1995), giving a strong justification for studying small network modules as the building blocks of food webs. In a broader sense, studies on dense subgraphs also belong to this problematics (Melia ´n and Bascompte, 2004). One of the key problems of food web research is over- emphasizing structural (topological) properties. It is the same in studying modules: counting them, determining their frequency distribution and checking whether it is significantly non-random, although excellent first steps, do not help enough to better understand their functioning. Dynamical approaches are basically lacking (but see Melia ´n et al., 2005). It is a major task, thus, to study the behaviour of modules in suitable dynamical modelling frameworks. However, these modelling approaches should proba- bly be motivated by experimental findings (relative strength and frequency distribution; see Menge, 1995; Abrams et al., 1996). Here we dynamically simulate a food web and compare the relative strength of some kinds of modules. Computing module strength is based on sensitivity analysis in a stochastic simulation model. Our results may contribute to better understand the behaviour of indirect interaction modules. 2. Data We study the Prince William Sound food web (Okey and Pauly, 1999; Okey, 2004; Okey and Wright, 2004; Fig. 1). It is composed of 51 trophic components but we only analyze the subgraph of the 48 living ones (S = 48), containing L = 355 trophic links (directed connectance, C = L/S 2 = 0.154), including 12 cannibalistic ones. The reason is that living-living interactions refer to ingestion/ assimilative events, with a different dynamics in comparison to transfers involving non-living nodes (Whipple, 1998). Here we focus more on community dynamics than ecosystems nutrient Ecological Complexity xxx (2012) xxx–xxx * Corresponding author. Tel.: +39 0461 882826; fax: +39 0461 882814. E-mail address: jordan.ferenc@gmail.com (F. Jorda ´ n). A R T I C L E I N F O Article history: Received 6 April 2011 Received in revised form 21 November 2011 Accepted 18 January 2012 Available online xxx Keywords: Food web Network module Stochastic simulation Indirect effects Interaction strength A B S T R A C T There is an increasing body of literature on the topological analysis of modules (motifs, building blocks) in different networks. Most of these results are of descriptive, comparative and statistical nature, while dynamical simulations of their behaviour are missing. We present a stochastic food web simulation and study the relative strength of different simple food web modules. We found that (1) the effects of prey groups on predators are significantly stronger than other effects, (2) indirect loops have strong effects only on mean population sizes, not on their variabilty, and (3) some short indirect interactions are not stronger than some longer ones. We believe that these findings may contribute to systems-based conservation practice in the future. ß 2012 Elsevier B.V. All rights reserved. G Model ECOCOM-337; No. of Pages 5 Please cite this article in press as: Gjata, N., et al., The strength of simulated indirect interaction modules in a real food web. Ecol. Complex. (2012), doi:10.1016/j.ecocom.2012.01.005 Contents lists available at SciVerse ScienceDirect Ecological Complexity jo ur n al ho mep ag e: www .elsevier .c om /lo cate/ec o co m 1476-945X/$ – see front matter ß 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ecocom.2012.01.005