Biochemical Warfare Between Living
Organisms for Survival: Mathematical
Modeling
20
S. A. Carvalho and M. L. Martins
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
2 Mathematical Models for Two Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
2.1 Allelopathically Mediated Invasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
2.2 Allelochemical Warfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
2.3 Spatial Patterns for More Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
3 Can Allelopathic Interactions Assemble a Community? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
3.1 An Eco-evolutionary Mathematical Model for Allelochemical Networks . . . . . . . . . . . 484
3.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
4 Multiscale Modeling for Allelopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
4.1 Multiple Scales in Allelopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
4.2 A Multiscale Model for Allelopathic Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
4.3 Simulational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
5 The Future of Theoretical Allelopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
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
S. A. Carvalho (*)
Departamento de Física, Universidade Federal de Viçosa, Viçosa, Brazil
e-mail: sylvestre.carvalho@gmail.com; sylvestre.carvalho@ufv.br
M. L. Martins
Departamento de Física, Universidade Federal de Viçosa, Viçosa, Brazil
National Institute of Science and Technology for Complex, Systems, Centro Brasileiro de Pesquisas
Físicas, Rio de Janeiro, Brazil
e-mail: mmartins@ufv.br
© Springer Nature Switzerland AG 2020
J.-M. Mérillon, K. G. Ramawat (eds.), Co-Evolution of Secondary Metabolites,
Reference Series in Phytochemistry, https://doi.org/10.1007/978-3-319-96397-6_52
467
Organisms for Survival: Mathematical
Modeling
20
S. A. Carvalho and M. L. Martins
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
2 Mathematical Models for Two Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
2.1 Allelopathically Mediated Invasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
2.2 Allelochemical Warfare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
2.3 Spatial Patterns for More Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
3 Can Allelopathic Interactions Assemble a Community? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
3.1 An Eco-evolutionary Mathematical Model for Allelochemical Networks . . . . . . . . . . . 484
3.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
4 Multiscale Modeling for Allelopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
4.1 Multiple Scales in Allelopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
4.2 A Multiscale Model for Allelopathic Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
4.3 Simulational Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
5 The Future of Theoretical Allelopathy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
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
S. A. Carvalho (*)
Departamento de Física, Universidade Federal de Viçosa, Viçosa, Brazil
e-mail: sylvestre.carvalho@gmail.com; sylvestre.carvalho@ufv.br
M. L. Martins
Departamento de Física, Universidade Federal de Viçosa, Viçosa, Brazil
National Institute of Science and Technology for Complex, Systems, Centro Brasileiro de Pesquisas
Físicas, Rio de Janeiro, Brazil
e-mail: mmartins@ufv.br
© Springer Nature Switzerland AG 2020
J.-M. Mérillon, K. G. Ramawat (eds.), Co-Evolution of Secondary Metabolites,
Reference Series in Phytochemistry, https://doi.org/10.1007/978-3-319-96397-6_52
467