population waves [15]. More complicated regimes in which the traveling
fronts become transient or oscillatory before the formation of spatial patterns
can be observed in a heterogeneous environment, or under the influence of other
species [16, 17]. Additionally, the topological and dynamical features of the ecological interacting networks exhibit scaling behaviors highly unlikely to be generated
through uncorrelated random processes but instead to be a product of a slow
evolution in which stability is a major natural selection mechanism [18].
The race of plants, microbes, and even cells (e.g., within a tumor) for adaptation
to the chemicals synthesized by their neighbors may drive species coexistence and
community composition. This view contrasts with the conventional explanations
of biodiversity as passively shaped by niche differentiation, density-dependent
predation pressure, habitat heterogeneity, or fluctuations in the resources required
by these communities. However, the astonishing high diversity observed within
microorganism communities in seemingly uniform environments – the famous
paradox of the plankton [19] – challenges the conventional resource competition
framework. Indeed, even a highly structured habitat can hardly maintain such
astronomical species numbers.
Nowadays, evidence is mounting that resource competition only is insufficient to
explain even the diversity in communities of macrobial organisms such as higher
plants and animals. For instance, positive nontrophic interactions between
physiologically independent plants also play a major role in plant communities
[20, 21]. Also, a theoretical work on the ecosystem stability reveals that mutualism
supports biodiversity when the direct competition is weak [22]. An analysis of 59
empirical data sets representing mutualistic plant-pollinator networks provides support to this theoretical work [23].
In this chapter we review single and multiscale mathematical models proposed to
investigate the dynamics of competing species in which at least one of them produces secondary metabolites (allelochemicals) affecting the others. The review is
focused on models proposed by our group. Models range from deterministic to
stochastic, involving either continuous or discrete populations, with or without
explicit spatial information, and describing either a single or multiple scales.
In this way we hope to provide a wide view of the mathematical tools for modeling
the biochemical warfare between living organisms to survive.
2
Mathematical Models for Two Species
As aforementioned, competitions mediated by the production of toxic chemical
compounds are ubiquitous in biological communities, and allelopathy is certainly
involved in bacterial and plant invasions. Hence, understanding the dynamics
of species involving allelochemicals becomes a main issue in both theoretical
ecology (emergence of biodiversity in communities) and practical issues (biological
invasions and ecosystems conservation). In this section, models for the biochemical warfare involving two species that also compete for common environmental resources are discussed.
20 Biochemical Warfare Between Living Organisms for Survival: Mathematical. . .
469
fronts become transient or oscillatory before the formation of spatial patterns
can be observed in a heterogeneous environment, or under the influence of other
species [16, 17]. Additionally, the topological and dynamical features of the ecological interacting networks exhibit scaling behaviors highly unlikely to be generated
through uncorrelated random processes but instead to be a product of a slow
evolution in which stability is a major natural selection mechanism [18].
The race of plants, microbes, and even cells (e.g., within a tumor) for adaptation
to the chemicals synthesized by their neighbors may drive species coexistence and
community composition. This view contrasts with the conventional explanations
of biodiversity as passively shaped by niche differentiation, density-dependent
predation pressure, habitat heterogeneity, or fluctuations in the resources required
by these communities. However, the astonishing high diversity observed within
microorganism communities in seemingly uniform environments – the famous
paradox of the plankton [19] – challenges the conventional resource competition
framework. Indeed, even a highly structured habitat can hardly maintain such
astronomical species numbers.
Nowadays, evidence is mounting that resource competition only is insufficient to
explain even the diversity in communities of macrobial organisms such as higher
plants and animals. For instance, positive nontrophic interactions between
physiologically independent plants also play a major role in plant communities
[20, 21]. Also, a theoretical work on the ecosystem stability reveals that mutualism
supports biodiversity when the direct competition is weak [22]. An analysis of 59
empirical data sets representing mutualistic plant-pollinator networks provides support to this theoretical work [23].
In this chapter we review single and multiscale mathematical models proposed to
investigate the dynamics of competing species in which at least one of them produces secondary metabolites (allelochemicals) affecting the others. The review is
focused on models proposed by our group. Models range from deterministic to
stochastic, involving either continuous or discrete populations, with or without
explicit spatial information, and describing either a single or multiple scales.
In this way we hope to provide a wide view of the mathematical tools for modeling
the biochemical warfare between living organisms to survive.
2
Mathematical Models for Two Species
As aforementioned, competitions mediated by the production of toxic chemical
compounds are ubiquitous in biological communities, and allelopathy is certainly
involved in bacterial and plant invasions. Hence, understanding the dynamics
of species involving allelochemicals becomes a main issue in both theoretical
ecology (emergence of biodiversity in communities) and practical issues (biological
invasions and ecosystems conservation). In this section, models for the biochemical warfare involving two species that also compete for common environmental resources are discussed.
20 Biochemical Warfare Between Living Organisms for Survival: Mathematical. . .
469