Download Ecosystem memory is emergent from local

DOI: http://dx.doi.org/10.7551/978-0-262-32621-6-ch015
Ecosystem memory is emergent from local-level natural selection
Daniel A. Power1 , Eörs Szathmáry2 and Richard A. Watson3
1
2
Institute for Complex Systems Simulation, University of Southampton, U.K.
Center for the Conceptual Foundations of Science, The Parmenides Foundation, Germany
3
Natural Systems Group, University of Southampton, U.K.
[email protected]
Because the form of an ecosystem is shaped chiefly
through the selection and amplification of chance genetic
and environmental events at lower levels of organisation
(sensu Maynard Smith and Szathmáry (1997)), the number
of evolutionary outcomes for these systems is enormous.
Theoretical models of ecosystem evolution and function
generally show sensitivity to initial conditions and small
disturbances that result in very different behaviours for
mature systems (May, 2001). These non-linearities mean
that ecosystem function is historically contingent; we
observe path dependency (over evolutionary timescales)
as well as those non-linearities (including hysteresis) that
occur over ecological timescales. For researchers seeking
to understand the degree to which ecosystem properties
are the result of abiotic environmental conditions and the
extent to which they are emergent from self-organisation
(Levin, 1998), this contingency adds an additional intricacy:
some ecosystem features may be a result of residual selforganisational responses to prior environmental conditions
that are no longer active.
We present a mathematical model in which an ecosystem
of species, all at the same trophic level, compete for limiting resources according to Lotka-Volterra (LV) dynamics.
In common with standard LV models, competition between
species is modeled through interaction coefficients that summarise the extent to which species’ niches overlap (Pianka,
1974). We extend this framework by allowing evolutionary pressure to affect species resource utilisation profiles,
such that natural selection alters the pattern of species nicheoverlap, with the result that interaction coefficients change
over evolutionary timescales. We alternately expose this
system to two configurations of environmental forcing, each
of which favours certain species over others (through variation in environmental carrying capacities, Figure 1). In the
case where niche-space is saturated, decreases in competition with one species can only be achieved through increases
in competition with another and species are under greatest selective pressure to minimise competition with those
species with which they co-occur at the highest densities.
Figure 1: Schema of simulation showing key stages. An
initial community of 232 species, X(0) is subjected to environmental conditions C1 (a pattern of differential carrying capacities). Ecological dynamics (Eco 1) are run until
the system reaches an stable distribution of species densities
(i.e. an attractor), at which point evolutionary effects are
applied (Evo 1). The process is repeated for environmental
conditions C2. As the distribution of carrying capacities in
C1 and C2 is arbitrary, we have chosen patterns that correspond with two events that occur in alternate years.
Under these conditions, ecosystems that are exposed
to multiple patterns of environmental forcing develop
attractors for these configurations even when environmental
forcing is lifted (Figure 2b). This property enables the
system to recover these specific configurations, even from
initial conditions that are ambiguous compositions of
both of the historically experienced environments (Figure
2c). We find that the longer that an ecosystem remains
under any configuration of forcing: i) the greater the
disturbance it can withstand when forcing is removed and
still return to the same composition of species; ii) the
speed at which the system recovers from a disturbance
increases; and iii) the longer the system can spend evolving
at another attractor before the current attractor is ’forgotten’.
We recognise the presence of underlying organisational
principles that enable these interesting system-level behaviours to emerge from local-level selection. We discuss
how access to these principles has the potential to advance
our understanding of ecosystem properties such as memory,
robustness and resilience.
ALIFE 14: Proceedings of the Fourteenth International Conference on the Synthesis and Simulation of Living Systems
initial species
densities
final species
densities
(a) before evolution
initial species
densities
final species
densities
initial species
densities
(b) after evolution
(d) vector fields
final species
densities
(c) after evolution
(e) Evolution of new attractors
Figure 2: (a) Before the evolution of ecological interactions (and in the absence of any ecological forcing) the system has a
single attractor, where all species are at the same density. After evolution of ecological interactions under alternating forcing, the system is examined again without ecological forcing. Now the system has two attractors corresponding to the exact
configurations of environmental forcing it has experienced, meaning the system will return to one of these attractors from any
set of random initial conditions (b) and even return to the nearest one of these attractors from initial conditions representing
compositions of both the forcing patterns (c). These attractors are created as the system undergoes a fold bifurcation. The
system’s response to forcing is initially linear ((d): first row of panels). After an intermediate period of evolution ((d): middle
row) the system’s response to forcing is non-linear and the species densities develop increasing ’switch-like’ convergence to the
two attractors. At the final stage of system evolution ((d): last panel) ecological forcing is insufficient to move the system out
its current attractor. (e) Monte Carlo analysis shows emergence of the two attractor state at around generation 1050.
References
Levin, S. A. (1998). Ecosystems and the biosphere as complex adaptive systems. Ecosystems, 1(5):431–436.
May, R. M. (2001). Stability and complexity in model ecosystems, volume 6. Princeton University Press.
Maynard Smith, J. and Szathmáry, E. (1997). The major transitions in evolution. Oxford University Press.
Pianka, E. R. (1974). Niche overlap and diffuse competition. Proceedings of the National Academy of Sciences, 71(5):2141–2145.
ALIFE 14: Proceedings of the Fourteenth International Conference on the Synthesis and Simulation of Living Systems