links, since they modify the interaction matrix stability much less than new nodes
with many links.
Summarizing, species-rich communities can be assembled in a homogeneous
environment only at weak allelopathy, and even in this regime, species interact
with a few others. The plankton paradox stands in the context of a total biochemical
warfare between organisms. Maybe, the coexistence of positive (or activatory) and
negative (or inhibitory) interactions is necessary to generate stability and diversity.
But this will be the focus of future works.
4
Multiscale Modeling for Allelopathy
The complexity and diversity of biological phenomena; the range of spatial and
temporal scales over which they act, extending from the molecular to the organism
and ecological levels; and the intricate way in which they are interwoven make
practically unfeasible the understanding of living systems through intuition alone.
Therefore, theoretical multiscale approaches are an essential tool in the quest for
a quantitative, “ab initio” ecology. This section will highlight multiscale modeling
frameworks to understand the allelochemical warfare between living organisms.
4.1
Multiple Scales in Allelopathy
Plant invasions are intrinsically multiscale in nature. They involve phenomena
occurring over a variety of spatial scales ranging from geographic (for instance,
regional extinctions of species) to molecular length scales (e.g., use and break of
metabolites by microbial communities), while the timescales vary from seconds for
signaling events leading to cell death induced by a phytotoxin to tens of years
for doubling times of invaded areas. Moreover, all those processes, many of which
may still be unknown, are strongly coupled. Indeed, the synthesis of a secondary
metabolite may confer a competitive advantage to a given plant, increasing its
abundance and altering microbial communities, nutrients, and chemical mosaics in
the soil which, in turn, regulate the growth and spatial distribution of plants.
To survive in a phytotoxic environment, some plant species may acquire new traits
such as metabolic detoxification mechanisms that confer resistance to phytotoxins
and promote coexistence. Thus, information flows not only from the finer to coarser
scales but between any pair of scales.
The complexity of plant invasion through allelopathy manifests at least in three
scales that might be distinguished and described in mathematical models: microscopic, mesoscopic, and macroscopic [4, 7, 39]. Specifically:
• The microscopic scale refers to molecular and subcellular phenomena occurring
within the plant cell or at its plasma membrane. Examples are transcriptional
events associated with phytotoxic response, dynamics of signaling cascades, and/
or metabolic pathways triggered by oxidative stress or defense purposes, fluxes of
20 Biochemical Warfare Between Living Organisms for Survival: Mathematical. . .
491
with many links.
Summarizing, species-rich communities can be assembled in a homogeneous
environment only at weak allelopathy, and even in this regime, species interact
with a few others. The plankton paradox stands in the context of a total biochemical
warfare between organisms. Maybe, the coexistence of positive (or activatory) and
negative (or inhibitory) interactions is necessary to generate stability and diversity.
But this will be the focus of future works.
4
Multiscale Modeling for Allelopathy
The complexity and diversity of biological phenomena; the range of spatial and
temporal scales over which they act, extending from the molecular to the organism
and ecological levels; and the intricate way in which they are interwoven make
practically unfeasible the understanding of living systems through intuition alone.
Therefore, theoretical multiscale approaches are an essential tool in the quest for
a quantitative, “ab initio” ecology. This section will highlight multiscale modeling
frameworks to understand the allelochemical warfare between living organisms.
4.1
Multiple Scales in Allelopathy
Plant invasions are intrinsically multiscale in nature. They involve phenomena
occurring over a variety of spatial scales ranging from geographic (for instance,
regional extinctions of species) to molecular length scales (e.g., use and break of
metabolites by microbial communities), while the timescales vary from seconds for
signaling events leading to cell death induced by a phytotoxin to tens of years
for doubling times of invaded areas. Moreover, all those processes, many of which
may still be unknown, are strongly coupled. Indeed, the synthesis of a secondary
metabolite may confer a competitive advantage to a given plant, increasing its
abundance and altering microbial communities, nutrients, and chemical mosaics in
the soil which, in turn, regulate the growth and spatial distribution of plants.
To survive in a phytotoxic environment, some plant species may acquire new traits
such as metabolic detoxification mechanisms that confer resistance to phytotoxins
and promote coexistence. Thus, information flows not only from the finer to coarser
scales but between any pair of scales.
The complexity of plant invasion through allelopathy manifests at least in three
scales that might be distinguished and described in mathematical models: microscopic, mesoscopic, and macroscopic [4, 7, 39]. Specifically:
• The microscopic scale refers to molecular and subcellular phenomena occurring
within the plant cell or at its plasma membrane. Examples are transcriptional
events associated with phytotoxic response, dynamics of signaling cascades, and/
or metabolic pathways triggered by oxidative stress or defense purposes, fluxes of
20 Biochemical Warfare Between Living Organisms for Survival: Mathematical. . .
491