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Chapter 1
Geophysiological modeling: a new approach
at modeling the evolution of ecosystems
By Francesco
Santini (1)(2), Lodovico Galleni (2), Paola Cerrai (2)(3)
(1) Department
of Zoology, University of Toronto. fsantini@zoo.utoronto.ca
(2) Centro Interdipartimentale per lo Studio dei Sistemi Complessi (CISSC), Universitá di Pisa.
lgalleni@agr.unipi.it
(3) Dipartimento di Matematica, Universitá di Pisa. cerrai@dm.unipi.it
1. The theoretical framework.
In the recent years many of the inherent problems in the neo-darwinian view of evolution have been underlined by
several authors. These include, among others, a lack of attention for biological hierarchies; for the importance of
adaptive mutational systems and the epigenetic inheritance systems; for the developmental constrains caused by
morphogenetic fields; for the relationships that exist between thermodynamics, information and evolution
[Goodwin 1984, 1994; Wan Ho 1984; Eldredge 1985; Brooks and Wiley 1988; Jablonka et al. 1998].
Living organisms, of course, evolve within ecological associations (ecosystems, landscapes, biomes, the
biosphere) that are constituted by a biological component and a physico-chemical component. Until recently the
attention of evolutionary ecologists has been mainly directed towards the understanding of the effects that the
interactions between the biological components of ecosystems have on the dynamics of populations and
communities. Such interactions (that is, infra- and interspecific competition and predation) were supposed to be,
by far, the main cause for the observed organization of ecosystems. This was due to the fact that only the
eukaryotic component (but it would be better to say: multicellular component) of ecosystems was investigated. At
these levels competition and predation do indeed have a main role in shaping the constitution and interactions of
the community. However, when microbial communities, and especially the prokaryotic ones, are taken into
consideration, a very different picture emerges [Margulis and Sagan 1991; Markos 1996]. At this point two
additional factors have to be taken into account, in order to be able to understand correctly the functioning of
ecological systems: cooperation among organisms and the interactions between the living and non living parts of
the ecological systems.
We believe that in the search for a more comprehensive theory of evolution a much greater attention
should be paid to the ways in which the physico-chemical environment interacts with the living organisms. This
aspect is mainly based on the suggestion of taking into consideration the Biosphere as a whole evolving object,
which was the very basis of Geobiology, the science of the Biosphere proposed by Teilhard de Chardin [Galleni
1995, 1996].
These concepts are at the core of the Gaia theory (formerly Gaia hypothesis), advanced by the British
Scientist James Lovelock in the early seventies [Lovelock and Margulis 1974; Lovelock 1995a, 1995b]. The Gaia
theory claims that it is not possible to talk about an independent evolution of the biological and chemico-physical
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components of the biosphere, because both parts are strongly linked and influence and direct the evolution of
each other. Hence, according to Lovelock, we should think about a unique integrated system, that is Gaia, in
which the self-regulation that leads to the homeostasis of certain parameters is a self-emergent property obtained
by the interactions between the several parts of the system [Lovelock 1995a]. To try to better visualize his
concept, Lovelock recurred to the metaphor of the “Superorganism”, claiming that the Earth is, as a
superorganism, able to maintain the homeostasis of some of its components, such as the salinity of the oceans and
the atmospheric composition, being for example all the gasses of the Earth’s atmosphere of biological origin
[Lovelock and Margulis 1974]. Hence the name Geophysiology to describe the new science of Gaia; the science
that studies ecological systems as if their components were co-evolving and influencing each other, and not just a
mere sum of independently functioning parts.
2. Where are we now ?
Mathematical models have always been massively used by ecologists in an attempt to simulate the dynamics of
biological populations and communities and hence predict the behavior of ecological systems. Until recently,
however, only few attempts have been made to try to include also the physico-chemical environment and the
interactions that exist between the living and non living part of the ecosystems in the mathematical modeling of
temporal evolution [Watson and Lovelock 1983; Maddock 1991]. In our opinion, in order to be able to develop
more realistic models, it is of paramount importance to take into consideration these interactions.
According to this line of thought, in our opinion [Benci and Galleni 1998] the factors that influence the
evolution of ecosystems can be split in 3 groups:
1) X factors, which represent the living beings and the interactions among themselves.
2) Y factors, which represent the “non-living species”, that is the environmental parameters which are subject to
the influence of the biota. In reality, as first foreseen by the American Biologist Lotka and the Russian
geochemist Vernadsky [Lovelock 1995a], X and Y factors are tightly bound and heavily influence the evolution of
each other.
3)  factors. These are environmental parameters that are out of the biota’s control, such as, for example the
increase in luminosity of the sun, or the tectonic plate drive. All these events are often not taken into consideration
in the vast majority of attempts to simulate the evolution of ecosystems through modeling, despite the great
importance that they have on evolutionary processes (e.g. mass extinctions caused by asteroids and comets).
Interacting with the X and Y factors the  factors are also constituents of natural selection.
3. The model applied to Ecosystem studies
For our study, we have decided to apply this approach to a recently discovered new kind of ecosystems: the
hydrothermal vents. These vents are produced by the geological processes that drive plate tectonics and are
responsible for the genesis of oceanic crust at spreading centers. The biological communities of these particular
ecosystems do not depend on photosynthesis but on bacterial chemosynthesis, which obtains carbohydrates and
other biological molecules from inorganic compounds, such as CO2, exploiting as electron donors the reduced
inorganic compounds present in the heated fluid. Thus the source of energy is not solar light but is geothermal
energy produced by the Earth’s interior. The main reduced compounds used in chemosynthetic reactions are
dissolved sulphides [Jannasch and Mottl 1985; Tunnicliffe 1991]. Chemoautolithotrophic bacteria are the only
primary producers in deep-sea hydrothermal ecosystems. They form the base of the trophic structure of the
communities. Vent communities have a much bigger biomass than that of the classic hadal communities even if
they show a more limited diversity. Chemoautotrophy and symbiosis are the reason for the presence of a great
amount of biomass. Heterotrophic bacteria, protists and several species of invertebrates, many of which are in
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symbiosis with chemotrophic bacteria, make up the remaining part of these communities. The fauna of the
inhabitants of the hydrothermal vents is endemic and taxonomically distinct from that of the normal deep-sea
environment [Tunnicliffe 1991].
For the purposes of this study this kind of ecosystems presents many advantages, including a short life-time that
makes it easy to test theoretical predictions.
4. Our Geophysiological model
Given that it is possible to identify among the several components of ecosystems both biotic and abiotic,
phenomena of “self-limitation”, “competition” and “predation”, the mathematical model that we propose is a
Lotka-Volterra variation [Murray 1989]. This kind of modeling in our opinion presents several advantages that
have convinced us of its validity for our research. It was in fact created by Volterra to study the dynamics of
biological populations, and independently by Lotka to model chemical reactions (and in our model we have both
kinds of interactions). This is a standard modeling technique, and for the purposes of our study it gives acceptable
results, even considering the degree of approximation of those.
In order to simplify the ecological interactions we have divided the biota into producers, called X 1, and
consumers, called X2. Producers include not only the free-living chemoautotrophic bacteria, but also the
chemosynthetic bacteria that live in symbiosis with macroinvertebrates and their metazoan hosts in cases where
these have no other mean of finding food if deprived of their associates. Consumers include both primary (grazers
and filter feeders) and secondary consumers.
In our model we have also decided to take into account the main chemical compounds that perform the
role of electron donors and acceptors. These two roles are performed mainly by hydrogen sulphide and molecular
oxygen. Molecular oxygen is produced by the activity of living organisms outside the thermal ecosystem, while
the hydrogen sulphide is mainly produced by venting, making the production of these compounds beyond the
control of living beings inhabiting the hydrothermal vents. Oxygen and sulphide are indicated as 1 and 2
respectively. In our investigation of hydrothermal ecosystems we could not identify any Y factor that has a vital
role in the functioning of these ecosystems. Being the chemical elements used as source of energy and as source of
matter mainly of thermal origin or coming from non-thermal organisms (such as in the case of O2), we decided to
label them as  factors. However Y factors are usually extremely important in any other kind of ecosystem
investigated [Benci and Galleni 1995, 1998].
Due to needs of model manageability, we have decided to limit it to a set of 4 differential equations in 4
variables.
 d1
 dt  1    C1  1   2   2

 d 2   2    C2  1   2
 dt

 d1  1   1  1  1     2
 dt
 d 2
  2   2  1   2  D  1  C  1

 dt
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X1, X2, 1,2represent respectively the density of autotrophic organisms, heterotrophic organisms, electron
acceptors and electron donors. dX1/dt, dX2/dt, d1/dt and d2/dt represent the variations through time of those
densities. The coefficients that appear in the equations are all positive, and to make matters simple we have put
the coefficients of self-limitation, competition and predation for X1, X2, 1, 2 equal to 1. A, B, C, D, C1, and C2
are coefficients. As in the Lotka-Volterra models, the advantages and the disadvantages that are obtained by every
species/compound from the interactions with other components of the ecological system are supposed to be
directly proportional to the density of the interacting species/compounds.
The first equation represents the variation through time of the producers. In the absence of 2 we would
have an exponential decrease to zero, with a decrease coefficient C1, to which is added the internal self-limitation
(that is, competition) and predation. The advantage given by the presence of inorganic reduced compounds, which
are necessary for chemosynthesis, is represented in the model by the expression X12. The disadvantage,
determined by the competition for resources among autotrophs and the predation from heterotrophs, is represented
by -X1X1 and -X1X2 respectively.
The second equation, dX2/dt, represents the evolution of the consumer’s guild. Without autotrophs,
represented by X1, there would be an exponential decrease to zero with coefficient C2, to which is added the
effect of self-limitation. X2 receives advantage in the form of predation from the presence of X 1, always with a
coefficient considered to be 1. The advantage, here represented by the expression +X 1X2, is still considered to be
directly proportional to the density of the 2 populations.
The equation d1/dt represents the variation in time of molecular oxygen. This would tend to reach,
through a sigmoid growth, a maximum concentration that corresponds to that of sea water, which we have
considered to be 1. However this is altered by the presence of reduced compounds, which perform what might be
considered to be the equivalent of a biological “predation” with coefficient A. The disadvantage caused by the
reduced inorganic compounds for the molecular oxygen is given by the expression -A12, and is still considered
to be directly proportional to the densities of the interacting species, even if now chemical and not biological
anymore. We have not considered in our equation the consumption of oxygen through respiration of the biota,
given the fact that this quantity is extremely low, compared to the consumption caused by sulphides.
The last equation, d2/dt, represents the variation through time of the hydrogen sulphide. This also
depends on the tendency of this compound to reach its maximum concentration, which corresponds to the one of
the thermal fluid, also in the sea water, and even this maximum concentration is considered to be 1 in the model.
The consumption by chemotrophs and by oxygen, represented by - D2X1 and - C12, keeps the concentration of
hydrogen sulphide much lower.
By selecting the growth coefficients in accordance to the experimental evidences, it is now possible to
simulate the evolution of these ecosystems and their associated biological communities.
5. Results
Given that it is not possible to graphically represent the evolution of the four components at the same time, we
decided to split them and analyze the evolution of the biological and the chemical components of the ecosystem
separately. Figure 1 and figure 2 show that the amount of sulphide and oxygen that is present in the hydrothermal
ecosystems remains constant since the early stages of the life of a vent. Soon after the beginning of the emission of
thermal fluids a stable state is reached, and this state is maintained for the whole life of the vent. At the end of the
emission of thermal fluids (figure 3), the concentration of sulphides in the hydrothermal ecosystem tends to drop
to zero, given that no new sulphides are emitted by the vent and all the sulphides already emitted are either
consumed by the living organisms or oxidized by the molecular oxygen present in the sea water. Hence, given that
sea water represents a continuous source of oxygen while the H2S concentration goes to zero, the concentration of
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O2 in the hydrothermal ecosystem approaches the same level present in the sea water, which in our model we have
considered to be 1.
For the biological components, the model shows that in the early stages of the life of a vent, producers
start to increase quite rapidly, while consumers are more slow to follow (figure 4). As time passes by, the
population of producers tends to reach a climax stage more quickly than the population of consumers, which
keeps growing, as illustrated by figure 5. When the hydrothermal emissions stop, primary producers tend to
collapse very rapidly, while the population of consumers converges towards zero more slowly (this because they
find preys to consume even within their own category), as can be seen from figure 6.
6. Conclusions
Our model shows that when there is a flow of thermal fluids rich in hydrogen sulphide, and presence of oxygen in
the marine water, in the area of mixing of fluids rich biological communities flourish and start to modify their
surrounding environment (e.g. the chemotrophs lower the concentration of sulphides in the water). In order to
keep the biological communities alive, there has to be a constant supply of both oxygen and sulphides. The
amount of these two elements that is present in the area surrounding a single vent is massively influenced not only
by the interactions among the chemical species, but also by those among biological species. Furthermore, the fate
of living organisms of thermal communities, is determined not only by the classic biological phenomena, such as
competition and predation, but also by the interactions between biological and chemical species. When the flow of
thermal fluids is reduced, available sulphides are rapidly oxidized and this event leads to the death of
chemoautotrophs and the collapse of the thermal community. This illustrates the need to take into consideration
also the chemico-physical environment and its interactions with the biota when modeling ecosystem functioning.
Otherwise it would be very difficult (not to say impossible) to explain the disappearance of the hydrothermal
communities if only the biological interactions are considered.
We hope that our model may illustrate that in order to be able to predict in a more realistic way the functioning of
ecosystems, it is not possible to avoid considering the core idea of the Gaia theory. Evolution is not just a process
that concerns living organisms. It is a phenomenon that should be investigated with a “Biospherocentric”
perspective, keeping in mind that living organisms cannot be taken into consideration without also considering
their surrounding environment, which they have a great influence in forming [Lowenstam, 1981; Lovelock,
1995a].
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