Skip to main content
SpringerLink
Log in
Book cover

Co-Evolution of Secondary Metabolites pp 467–504Cite as

Biochemical Warfare Between Living Organisms for Survival: Mathematical Modeling

  • Reference work entry
  • First Online:

Part of the book series: Reference Series in Phytochemistry ((RSP))

Abstract

Nowadays, evidence is mounting that the race of living organisms for adaptation to the chemicals synthesized by their neighbors may drive competition, coexistence, and community structures. Particularly, some bacterial infections and plant invasions disruptive of the native community rely on the release of allelochemicals that inhibit or kill sensitive strains or individuals from their own or other species. In this chapter, we review single and multiscale mathematical models proposed to investigate the dynamics of the biochemical warfare between competing species for survival.

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

References

  1. Cordero OX, Wildschutte H, Kirkup B, Proeh LS, Ngo L, Hussain F, Le Roux F, Mincer T, Polz MF (2012) Ecological populations of bacteria act as socially cohesive units of antibiotic production and resistance. Science 337:1228–1231

    Article  CAS  PubMed  Google Scholar 

  2. Starmer WT, Ganter PF, Aberdeen V, Lachance M-A, Phaff HJ (1987) The ecological role of killer yeasts in natural communities of yeasts. Can J Microbiol 33:783–796

    Article  CAS  PubMed  Google Scholar 

  3. Bérdy J (2005) Bioactive microbial metabolites. J Antibiot 58:126

    Article  Google Scholar 

  4. Bais HP, Park SW, Weir TL, Callaway RM, Vivanco JM (2004) How plants communicate using the underground information superhighway. Trends Plant Sci 9:26–32

    Article  CAS  PubMed  Google Scholar 

  5. Gatenby RA, Gawlinski ET, Gmitro AF, Kaylor B, Gillies RJ (2006) Acid-meditated tumour invasion: a multidisciplinary study. Cancer Res 66:5216–5223

    Article  CAS  PubMed  Google Scholar 

  6. Braganhol E, Wink MR, Lenz G, Battastini AMO (2013) Purinergic signaling in glioma progression. In: Baranska J (ed) Glioma signaling, Advances in experimental medicine and biology, vol 986. Springer, Dordrecht

    Google Scholar 

  7. Bais HP, Vepachedu R, Gilroy S et al (2003) Allelopathy and exotic plant invasion: from molecules and genes to species interactions. Science 301:1377–1380

    Article  CAS  PubMed  Google Scholar 

  8. Chou C (1999) Roles of allelopathy in plant biodiversity and sustainable agriculture. Crit Rev Plant Sci 18:609–636

    Article  Google Scholar 

  9. Dean WRJ (1998) Space invaders: modeling the distribution, impacts and control of alien organisms. Trends Ecol Evol 13:256–258

    Article  PubMed  Google Scholar 

  10. Drake JA, Mooney HA, di Castri F et al (eds) (1989) Biological invasions: a global perspective. Wiley, Chichester

    Google Scholar 

  11. Shigesada N, Kawasaki K (1997) Biological invasions: theory and practice. Oxford University Press, Oxford

    Google Scholar 

  12. Round JL, Mazmanian SK (2009) The gut microbiota shapes intestinal immune responses during health and disease. Nat Rev Immunol 9:313–323

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Richards MJ, Edwards JR, Culver DH, Gaynes RP (2000) Nosocomial infections in combined medical-surgical intensive care units in the United States. Infect Control Hosp Epidemiol 21:510–515

    Article  CAS  PubMed  Google Scholar 

  14. Martina Sassone-Corsi M, Nuccio S-P, Liu H, Hernandez D, Vu CT, Takahashi AA, Edwards RA, Raffatellu M (2016) Microcins mediate competition among Enterobacteriaceae in the inflamed gut. Nature 540:280–283

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  15. Petrovskii S, Shigesada N (2001) Some exact solutions of a generalized Fisher equation related to the problem of biological invasion. Math Biosci 172:73–94

    Article  CAS  PubMed  Google Scholar 

  16. Sherratt JA, Lewis MA, Fowler AC (1995) Ecological chaos in the wake of invasion. Proc Natl Acad Sci U S A 92:2524–2528

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Shigesada N, Kawasaki K, Teramoto E (1986) Traveling periodic waves in heterogeneous environments. Theor Popul Biol 30:143–160

    Article  Google Scholar 

  18. Perotti JI, Billoni OV, Tamarit FA, Chialvo DR, Cannas SA (2009) Emergent self-organized complex network topology out of stability constraints. Phys Rev Lett 103:108701

    Article  PubMed  CAS  Google Scholar 

  19. Hutchinson GE (1961) The paradox of the plankton. Am Nat 95:137–145

    Article  Google Scholar 

  20. Brooker RW, Maestre FT, Callaway RM, Lortie CL, Cavieres LA, Kunstler G et al (2008) Facilitation in plant communities: the past, the present, and the future. J Ecol 96:18–34

    Article  Google Scholar 

  21. van der Heijden MGA, Horton TR (2009) Socialism in soil? The importance of mycorrhizal fungal networks for facilitation in natural ecosystems. J Ecol 97:1139–1150

    Article  Google Scholar 

  22. Pascual-Garcia A, Bastolla U (2017) Mutualism supports biodiversity when the direct competition is weak. Nat Commun 8:14326

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. James A, Pitchford JW, Plank MJ (2012) Disentangling nestedness from models of ecological complexity. Nature 487:227–230

    Article  CAS  PubMed  Google Scholar 

  24. Fassoni AC, Martins ML (2014) Mathematical analysis of a model for plant invasion mediated by allelopathy. Ecol Complex 18:49–58

    Article  Google Scholar 

  25. Strogatz SH (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Westview Press, Cambridge, MA

    Google Scholar 

  26. Britton N (2003) Essential mathematical biology. Springer, London

    Book  Google Scholar 

  27. Fox MD, Fox BD (1986) The susceptibility of natural communities to invasion. In: Groves RH, Burdon JJ (eds) Ecology of biological invasions: an Australian perspective. Australian Academy of Science, Canberra, pp 97–105

    Google Scholar 

  28. Carvalho SA, Martins ML (2018) Invasion waves in the biochemical warfare between living organisms. Phys Rev E 97:042403

    Article  CAS  PubMed  Google Scholar 

  29. Gordon DM, O’Brien CL (2006) Bacteriocin diversity and the frequency of multiple bacteriocin production in Escherichia coli. Microbiology 152:3239–3244

    Article  CAS  PubMed  Google Scholar 

  30. Melchionda D, Pastacaldi E, Perri C, Banerjee M, Venturino E (2018) Social behavior-induced multistability in minimal competitive ecosystems. J Theor Biol 439:24–38

    Article  CAS  PubMed  Google Scholar 

  31. May RM (1973) Stability and complexity in model ecosystems. Princeton University Press, Princeton

    Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  33. Cheng H, Yao N, Huang Z-G, Park J, Do Y, La Y-C (2014) Mesoscopic interactions and species coexistence in evolutionary game dynamics of cyclic competitions. Sci Rep 4:7486

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Szabó P, Czárán T, Szabó G (2007) Competing associations in bacterial warfare with two toxins. J Theor Biol 248:736–744

    Article  PubMed  CAS  Google Scholar 

  35. Carvalho SA, Martins ML (2018) Community structures in allelopathic interaction networks: an eco-evolutionary approach. https://arxiv.org/submit/2491687. Submitted to arXiv 30 Nov 2018

  36. Edwards KF et al (2018) Evolutionary stable communities: a framework for understanding the role of trait evolution in the maintenance of diversity. Ecol Lett. https://doi.org/10.1111/ele.13142

    Article  PubMed  Google Scholar 

  37. Barabási A-L (2016) Network science. Cambridge University Press, Cambridge, MA

    Google Scholar 

  38. May RM (1972) Will a large complex system stable? Nature 238:413

    Article  CAS  PubMed  Google Scholar 

  39. Inderjit, Wardle DA, Karban R, Callaway R (2011) The ecosystem and evolutionary contexts of allelopathy. Tends Ecol Evol 26:655–662

    Article  CAS  Google Scholar 

  40. Glimm J, Sharp DH (1997) Multiscale science. A challenge for the twenty-first century. SIAM News 30(4):17–19

    Google Scholar 

  41. Krumhansl JA (2000) Multiscale science: materials in the 21st century. Mater Sci Forum 327:1–8

    Article  Google Scholar 

  42. Martins ML, Ferreira SC Jr, Vilela MJ (2007) Multiscale models for the growth of avascular tumors. Phys Life Rev 4:128–156

    Article  Google Scholar 

  43. Martins ML, Ferreira SC Jr, Vilela MJ (2010) Multiscale models for biological systems. Curr Opin Colloid Interface Sci 15:18–23

    Article  CAS  Google Scholar 

  44. Souza DR, Martins ML, Carmo FMS (2007) A multiscale model for plant invasion through allelopathic suppression. Biol Invasions 12:1543–1555

    Article  Google Scholar 

  45. Wolfram S (1986) Theory and application of cellular automata. World Scientific, Singapore

    Google Scholar 

  46. Ermentrout GB, Edelstein-Keshet L (1993) Cellular automata approaches to biological modeling. J Theor Biol 160(1):97–133

    Article  CAS  PubMed  Google Scholar 

  47. Cannas SA, Marco DE, Páez SA (2003) Modelling biological invasions: species traits, species interactions, and habitat heterogeneity. Math Biosci 183:93–110

    Article  PubMed  Google Scholar 

  48. Cohen JE (2004) Mathematics is biology’s next microscope, only better; biology is mathematics’ next physics, only better. PLoS Biol 2:e439

    Article  PubMed  PubMed Central  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade Federal de Viçosa, Viçosa, Brazil

    S. A. Carvalho & M. L. Martins

  2. National Institute of Science and Technology for Complex, Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil

    M. L. Martins

Authors
  1. S. A. Carvalho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. L. Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Carvalho .

Editor information

Editors and Affiliations

  1. Faculty of Pharmaceutical Sciences, Institute of Vine and Wine Sciences, University of Bordeaux, Villenave d'Ornon, France

    Jean-Michel Mérillon

  2. Department of Botany, University College of Science, M. L. Sukhadia University, Udaipur, Rajasthan, India

    Kishan Gopal Ramawat

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Carvalho, S.A., Martins, M.L. (2020). Biochemical Warfare Between Living Organisms for Survival: Mathematical Modeling. In: Mérillon, JM., Ramawat, K. (eds) Co-Evolution of Secondary Metabolites. Reference Series in Phytochemistry. Springer, Cham. https://doi.org/10.1007/978-3-319-96397-6_52

Download citation

Publish with us

Policies and ethics

Search

Navigation