Skip to main content
SpringerLink
Log in

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

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Adamson MW, Morozov AY (2012) Revising the role of species mobility in maintaining biodiversity in communities with cyclic competition. Bull Math Biol 74(9):2004–2031

    Article  MathSciNet  MATH  Google Scholar 

  • 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):115–122

    Article  Google Scholar 

  • 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):4532–4542

    Article  Google Scholar 

  • 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):303–311

    Article  Google Scholar 

  • 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

  • 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):032415

    Article  Google Scholar 

  • 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 11:651–688

    Article  MATH  Google Scholar 

  • Beppu K, Izri Z, Gohya J, Eto K, Ichikawa M, Maeda YT (2017) Geometry-driven collective ordering of bacterial vortices. Soft Matter 13(29):5038–5043

    Article  Google Scholar 

  • Bernard EP, Krauth W (2011) Two-step melting in two dimensions: first-order liquid-hexatic transition. Phys Rev Lett 107(15):155704

    Article  Google Scholar 

  • Birch C, Oom S, Beecham J (2006) Rectangular and hexagonal grids used for observation, experiment and simulation in ecology. Ecol Model 206(3):347–359

    Google Scholar 

  • Buss LW (1979) Competitive networks: nontransitive competitive relationships in cryptic coral reef environments. Am Nat 113(2):223–234

    Article  Google Scholar 

  • Chang HC, Wang LC (2010) A simple proof of Thue’s theorem on circle packing. arXiv preprint, pp. 1–4. arXiv:1009.4322

  • Finke DL, Denno RF (2006) Spatial refuge from intraguild predation: implications for prey suppression and trophic cascades. Oecologia 149(2):265–275

    Article  Google Scholar 

  • Ginovart M (2002) INDISIM, an individual-based discrete simulation model to study bacterial cultures. J Theor Biol 214(2):305–319

    Article  Google Scholar 

  • Gonnella G, Lamura A, Suma A (2014) Phase segregation in a system of active dumbbells. Int J Mod Phys C 25(12):1441004

    Article  Google Scholar 

  • 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):2760–2768

    Article  Google Scholar 

  • Hurlbert SH (1978) The measurement of niche overlap and some relatives. Ecology 59(1):67–77

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE conference on neural networks, vol 4, pp 1942–1948

  • 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):171–174

    Article  Google Scholar 

  • Kirkup BC, Riley MA (2004) Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature 428(6981):412–414

    Article  Google Scholar 

  • Kreft JU, Booth G, Wimpenny JWT (1998) BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144(12):3275–3287

    Article  Google Scholar 

  • Kreft JU, Picioreanu C, Wimpenny JWT, van Loosdrecht MCM (2001) Individual-based modelling of biofilms. Microbiology 147(Pt 11):2897–2912

    Article  Google Scholar 

  • Laird RA, Schamp BS (2008) Does local competition increase the coexistence of species in intransitive networks? Ecology 89(1):237–247

    Article  Google Scholar 

  • Laird RA, Schamp BS (2009) Species coexistence, intransitivity, and topological variation in competitive tournaments. J Theor Biol 256(1):90–95

    Article  MathSciNet  MATH  Google Scholar 

  • Landau L, Lifshitz E (1986) EM Lifshitz theory of elasticity, 3rd edn. Pergamon Press, New York

    Google Scholar 

  • Lloyd M (1967) Mean crowding. J Anim Ecol 36(1):1–30

    Article  Google Scholar 

  • 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):e1790

    Article  Google Scholar 

  • Mattson W, Rice BM (1999) Near-neighbor calculations using a modified cell-linked list method. Comput Phys Commun 119(2):135–148

    Article  Google Scholar 

  • May RM, Leonard WJ (1975) Nonlinear aspects of competition between three species. Soc Ind Appl Math 29(2):243–253

    Article  MathSciNet  MATH  Google Scholar 

  • Neuhauser C (2001) Mathematical challenges in spatial ecology. Not AMS 48(11):1304–1314

    MathSciNet  MATH  Google Scholar 

  • 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):1–34

    Article  Google Scholar 

  • Railsback SF, Grimm V (2011) Agent-based and individual-based modeling: a practical introduction. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Railsback SF, Lytinen SL, Jackson SK (2006) Agent-based simulation platforms: review and development recommendations. Simulation 82(9):609–623

    Article  Google Scholar 

  • Reichenbach T, Mobilia M, Frey E (2007) Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448(7157):1046–1049

    Article  Google Scholar 

  • Reynolds C (1987) Flocks, herds, and schools: a distributed behavioral model. Comput Graph 21(4):25–34

    Article  Google Scholar 

  • Schelling TC (1969) Dynamic models of segregation. J Math Sociol 1(2):143–186

    Article  MATH  Google Scholar 

  • 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):67–81

    Article  Google Scholar 

  • Taylor DR, Aarssen LW (1990) Complex competitive relationships among genotypes of three perennial grasses: implications for species coexistence. Am Nat 136(3):305–327

    Article  Google Scholar 

  • Touhami A, Nysten B, Dufrêne Y (2003) Nanoscale mapping of the elasticity of microbial cells by atomic force microscopy. Microbiology 19(11):4539–4543

    Google Scholar 

  • Verlet L (1967) Computer “experiments” on classical fluids. Phys Rev 159(1):98–103

    Article  Google Scholar 

  • 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):1–8

    Article  Google Scholar 

  • Wilsey BJ (2004) Realistically low species evenness does not alter grassland species-richness: productivity relationships. Ecology 85(10):2693–2700

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Author notes

  1. Aisling J. Daly and Ward Quaghebeur: shared first authors.

Authors and Affiliations

  1. KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure links 653, 9000, Ghent, Belgium

    Aisling J. Daly, Ward Quaghebeur, Tim M. A. Depraetere, Jan M. Baetens & Bernard De Baets

Authors
  1. Aisling J. Daly
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ward Quaghebeur
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tim M. A. Depraetere
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jan M. Baetens
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bernard De Baets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aisling J. Daly.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Daly, A.J., Quaghebeur, W., Depraetere, T.M.A. et al. Lattice-based versus lattice-free individual-based models: impact on coexistence in competitive communities. Nat Comput 18, 855–864 (2019). https://doi.org/10.1007/s11047-019-09767-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-019-09767-1

Keywords

Search

Navigation