Natural Computing

, Volume 18, Issue 4, pp 855–864 | Cite as

Lattice-based versus lattice-free individual-based models: impact on coexistence in competitive communities

  • Aisling J. DalyEmail author
  • Ward Quaghebeur
  • Tim M. A. Depraetere
  • Jan M. Baetens
  • Bernard De Baets


Individual-based modelling is an increasingly popular framework for modelling biological systems. Many of these models represent space as a lattice, thus imposing unrealistic limitations on the movement of the modelled individuals. We adapt an existing model of three competing species by using a lattice-free approach, thereby improving the realism of the spatial dynamics. We retrieve the same qualitative dynamics as the lattice-based approach. However, by facilitating a higher spatial heterogeneity and allowing for small spatial refuges to form and persist, the maintenance of coexistence is promoted, in correspondence with experimental results. We also implement a directed movement mechanism allowing individuals of different species to pursue or flee from each other. Simulations show that the effects on coexistence depend on the level of aggregation in the community: a high level of aggregation is advantageous for maintaining coexistence, whereas a low level of aggregation is disadvantageous. This agrees with experimental results, where pursuing and escaping behaviour has been observed to be advantageous only in certain circumstances.


Cyclic competition Coexistence Individual-based model Directed movement 



The authors acknowledge funding from a UGent–BOF GOA project “Assessing the biological capacity of ecosystem resilience” (Grant BOFGOA2017000601) and FWO grant number 3S79219. The computational resources (Stevin Supercomputer Infrastructure) and services used in this paper were provided by the VSC (Flemish Supercomputer Center), funded by Ghent University, the Hercules Foundation and the Flemish Government, department EWI.


  1. Adamson MW, Morozov AY (2012) Revising the role of species mobility in maintaining biodiversity in communities with cyclic competition. Bull Math Biol 74(9):2004–2031MathSciNetCrossRefGoogle Scholar
  2. Arsenault DJ, Himmelman JH (1996) Size-related changes in vulnerability to predators and spatial refuge use by juvenile Iceland scallops Chlamys islandica. Mar Ecol Prog Ser 140(1–3):115–122CrossRefGoogle Scholar
  3. Ashby MN, Rine J, Mongodin EF, Nelson KE, Dimster-Denk D (2007) Serial analysis of rRNA genes and the unexpected dominance of rare members of microbial communities. Appl Environ Microbiol 73(14):4532–4542CrossRefGoogle Scholar
  4. Auchincloss AH, Riolo RL, Brown DG, Cook J, Diez Roux AV (2011) An agent-based model of income inequalities in diet in the context of residential segregation. Am J Prev Med 40(3):303–311CrossRefGoogle Scholar
  5. Avelino PP, Bazeia D, Losano L, Menezes J, de Oliveira BF (2017) Spiral patterns and biodiversity in lattice-free Lotka–Volterra models. arXiv preprint. pp. 1–5. arXiv:1710.05066
  6. Avelino PP, Bazeia D, Losano L, Menezes J, de Oliveira BF, Santos MA (2018) How directional mobility affects biodiversity in rock-paper-scissors models. Phys Rev E 97(1–3):032415CrossRefGoogle Scholar
  7. Baetens J, De Loof K, De Baets B (2013) Influence of the topology of a cellular automation on its dynamical properties. Commun Nonlinear Sci Numer Simul 11:651–688CrossRefGoogle Scholar
  8. Beppu K, Izri Z, Gohya J, Eto K, Ichikawa M, Maeda YT (2017) Geometry-driven collective ordering of bacterial vortices. Soft Matter 13(29):5038–5043CrossRefGoogle Scholar
  9. Bernard EP, Krauth W (2011) Two-step melting in two dimensions: first-order liquid-hexatic transition. Phys Rev Lett 107(15):155704CrossRefGoogle Scholar
  10. Birch C, Oom S, Beecham J (2006) Rectangular and hexagonal grids used for observation, experiment and simulation in ecology. Ecol Model 206(3):347–359Google Scholar
  11. Buss LW (1979) Competitive networks: nontransitive competitive relationships in cryptic coral reef environments. Am Nat 113(2):223–234CrossRefGoogle Scholar
  12. Chang HC, Wang LC (2010) A simple proof of Thue’s theorem on circle packing. arXiv preprint, pp. 1–4. arXiv:1009.4322
  13. Finke DL, Denno RF (2006) Spatial refuge from intraguild predation: implications for prey suppression and trophic cascades. Oecologia 149(2):265–275CrossRefGoogle Scholar
  14. Ginovart M (2002) INDISIM, an individual-based discrete simulation model to study bacterial cultures. J Theor Biol 214(2):305–319CrossRefGoogle Scholar
  15. Gonnella G, Lamura A, Suma A (2014) Phase segregation in a system of active dumbbells. Int J Mod Phys C 25(12):1441004CrossRefGoogle Scholar
  16. Grimm V, Berger U, DeAngelis DL, Polhill JG, Giske J, Railsback SF (2010) The ODD protocol: a review and first update. Ecol Model 221(23):2760–2768CrossRefGoogle Scholar
  17. Hurlbert SH (1978) The measurement of niche overlap and some relatives. Ecology 59(1):67–77CrossRefGoogle Scholar
  18. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE conference on neural networks, vol 4, pp 1942–1948Google Scholar
  19. Kerr B, Riley MA, Feldman MW, Bohannan BJM (2002) Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature 418(6894):171–174CrossRefGoogle Scholar
  20. Kirkup BC, Riley MA (2004) Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature 428(6981):412–414CrossRefGoogle Scholar
  21. Kreft JU, Booth G, Wimpenny JWT (1998) BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144(12):3275–3287CrossRefGoogle Scholar
  22. Kreft JU, Picioreanu C, Wimpenny JWT, van Loosdrecht MCM (2001) Individual-based modelling of biofilms. Microbiology 147(Pt 11):2897–2912CrossRefGoogle Scholar
  23. Laird RA, Schamp BS (2008) Does local competition increase the coexistence of species in intransitive networks? Ecology 89(1):237–247CrossRefGoogle Scholar
  24. Laird RA, Schamp BS (2009) Species coexistence, intransitivity, and topological variation in competitive tournaments. J Theor Biol 256(1):90–95MathSciNetCrossRefGoogle Scholar
  25. Landau L, Lifshitz E (1986) EM Lifshitz theory of elasticity, 3rd edn. Pergamon Press, New YorkGoogle Scholar
  26. Lloyd M (1967) Mean crowding. J Anim Ecol 36(1):1–30CrossRefGoogle Scholar
  27. Luisa M, Merler S, Rizzo C, Ajelli M, Massari M, Furlanello C, Tomba GS, Iannelli M (2008) Mitigation measures for pandemic influenza in Italy: an individual-based model considering different scenarios. PLoS ONE 3(3):e1790CrossRefGoogle Scholar
  28. Mattson W, Rice BM (1999) Near-neighbor calculations using a modified cell-linked list method. Comput Phys Commun 119(2):135–148CrossRefGoogle Scholar
  29. May RM, Leonard WJ (1975) Nonlinear aspects of competition between three species. Soc Ind Appl Math 29(2):243–253MathSciNetCrossRefGoogle Scholar
  30. Neuhauser C (2001) Mathematical challenges in spatial ecology. Not AMS 48(11):1304–1314MathSciNetzbMATHGoogle Scholar
  31. Osborne JM, Fletcher AG, Pitt-Francis JM, Maini PK, Gavaghan DJ (2017) Comparing individual-based approaches to modelling the self-organization of multicellular tissues. PLoS Comput Biol 13(2):1–34CrossRefGoogle Scholar
  32. Railsback SF, Grimm V (2011) Agent-based and individual-based modeling: a practical introduction. Princeton University Press, PrincetonzbMATHGoogle Scholar
  33. Railsback SF, Lytinen SL, Jackson SK (2006) Agent-based simulation platforms: review and development recommendations. Simulation 82(9):609–623CrossRefGoogle Scholar
  34. Reichenbach T, Mobilia M, Frey E (2007) Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448(7157):1046–1049CrossRefGoogle Scholar
  35. Reynolds C (1987) Flocks, herds, and schools: a distributed behavioral model. Comput Graph 21(4):25–34CrossRefGoogle Scholar
  36. Schelling TC (1969) Dynamic models of segregation. J Math Sociol 1(2):143–186CrossRefGoogle Scholar
  37. Schreiber SJ, Lipcius RN, Seitz RD, Long WC (2006) Dancing between the devil and deep blue sea: The stabilizing effect of enemy-free and victimless sinks. Oikos 113(1):67–81CrossRefGoogle Scholar
  38. Taylor DR, Aarssen LW (1990) Complex competitive relationships among genotypes of three perennial grasses: implications for species coexistence. Am Nat 136(3):305–327CrossRefGoogle Scholar
  39. Touhami A, Nysten B, Dufrêne Y (2003) Nanoscale mapping of the elasticity of microbial cells by atomic force microscopy. Microbiology 19(11):4539–4543Google Scholar
  40. Verlet L (1967) Computer “experiments” on classical fluids. Phys Rev 159(1):98–103CrossRefGoogle Scholar
  41. Vukov J, Szolnoki A, Szabó G (2013) Diverging fluctuations in a spatial five-species cyclic dominance game. Phys Rev E Stat Nonlinear Soft Matter Phys 88(2):1–8CrossRefGoogle Scholar
  42. Wilsey BJ (2004) Realistically low species evenness does not alter grassland species-richness: productivity relationships. Ecology 85(10):2693–2700CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Aisling J. Daly
    • 1
    Email author
  • Ward Quaghebeur
    • 1
  • Tim M. A. Depraetere
    • 1
  • Jan M. Baetens
    • 1
  • Bernard De Baets
    • 1
  1. 1.KERMIT, Department of Data Analysis and Mathematical ModellingGhent UniversityGhentBelgium

Personalised recommendations