Petri nets for modelling and analysing trophic networks

We consider trophic networks, a kind of networks used in ecology to represent feeding interactions (what-eats-what) in an ecosystem. We observe that trophic networks can be naturally modelled as Petri nets and this suggests the possibility of exploiting Petri nets for the analysis and simulation of trophic networks. Some preliminary steps in this directions and some ideas for future development are presented.

[1]  E. Odum The strategy of ecosystem development. , 1969, Science.

[2]  Robert E. Ulanowicz,et al.  A Phenomenological Perspective of Ecological Development , 1986 .

[3]  R. Conover FACTORS AFFECTING THE ASSIMILATION OF ORGANIC MATTER BY ZOOPLANKTON AND THE QUESTION OF SUPERFLUOUS FEEDING1 , 1966 .

[4]  Louchka Popova-Zeugmann,et al.  Time Petri Nets for Modelling and Analysis of Biochemical Networks , 2005, Fundam. Informaticae.

[5]  Jörg Desel,et al.  Free Choice Petri Nets (Cambridge Tracts in Theoretical Computer Science) , 2005 .

[6]  Stefano Allesina,et al.  Cycling in ecological networks: Finn's index revisited , 2004, Comput. Biol. Chem..

[7]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[8]  C. Carlson,et al.  Microbes and dissipation of energy and respiration: from cells to ecosystems , 2007 .

[9]  Daniel Pauly,et al.  The stability of trophic mass-balance models of marine ecosystems: a comparative analysis , 1997 .

[10]  R. Barnes,et al.  An introduction to marine ecology , 1982 .

[11]  T. Reinthaler,et al.  Relationship between Bacterioplankton Richness, Respiration, and Production in the Southern North Sea , 2005, Applied and Environmental Microbiology.

[12]  M. Pace,et al.  An Inverse Model Analysis of Planktonic Food Webs in Experimental Lakes , 1994 .

[13]  B. Han,et al.  On several measures concerning flow variables in ecosystems , 1997 .

[14]  O. Giovanardi,et al.  Trophic characteristics of the Manila clam (Tapes philippinarum Adams and Reeve) , 1995 .

[15]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[16]  L. Pomeroy Microbes and the Dissipation of Energy and Respiration : From Cells to Ecosystems , 2007 .

[17]  Johanna J. Heymans,et al.  Network analysis of the South Florida Everglades graminoid marshes and comparison with nearby cypress ecosystems , 2002 .

[18]  R. Wetzel Limnology: Lake and River Ecosystems , 1975 .

[19]  J. Finn,et al.  Measures of ecosystem structure and function derived from analysis of flows. , 1976, Journal of theoretical biology.

[20]  Villy Christensen,et al.  ECOPATH II − a software for balancing steady-state ecosystem models and calculating network characteristics , 1992 .

[21]  T. Platt,et al.  Food web dynamics in the ocean. I. Best-estimates of flow networks using inverse methods , 1988 .

[22]  Mogens Nielsen,et al.  Decidability Issues for Petri Nets - a survey , 1994, Bull. EATCS.

[23]  Carl J. Walters,et al.  Ecopath with Ecosim: methods, capabilities and limitations , 2004 .

[24]  Martin Schwarick,et al.  Snoopy - A Unifying Petri Net Tool , 2012, Petri Nets.

[25]  Robert E. Ulanowicz,et al.  Quantitative methods for ecological network analysi , 2004, Comput. Biol. Chem..

[26]  R. Ulanowicz,et al.  9.04 – Quantitative Methods for Ecological Network Analysis and Its Application to Coastal Ecosystems* , 2011 .

[27]  Jörg Desel,et al.  Free choice Petri nets , 1995 .

[28]  Timothy R. Parsons,et al.  Biological Oceanographic Processes , 1973 .

[29]  James L. Peterson,et al.  Petri Nets , 1977, CSUR.

[30]  Karline Soetaert,et al.  Quantifying Food Web Flows Using Linear Inverse Models , 2009, Ecosystems.

[31]  Roberto Pastres,et al.  An inverse model for the analysis of the Venice lagoon food web , 2011 .

[32]  Martin Schwarick,et al.  Charlie - An Extensible Petri Net Analysis Tool , 2015, Petri Nets.

[33]  Ferenc Jordán,et al.  Process algebra-based computational tools in ecological modelling , 2011 .

[34]  A. Sfriso,et al.  Linking food web functioning and habitat diversity for an ecosystem based management: a Mediterranean lagoon case-study. , 2014, Marine environmental research.

[35]  Monika Heiner,et al.  Petri Nets for Systems and Synthetic Biology , 2008, SFM.

[36]  H. P. Williams THEORY OF LINEAR AND INTEGER PROGRAMMING (Wiley-Interscience Series in Discrete Mathematics and Optimization) , 1989 .