take place in the interaction topology. In fact, the study in [2]
demonstrates that intransitivity is at least feasible in SOO when
using a topologically constrained fitness metric. Future studies
will investigate whether the self-organizing topology
evolutionary algorithms studied in [2] can also display
coevolutionary behavior similar to that demonstrated here in
multi-objective environments.
4.2 Theories of Evolution
The origin of punctuated dynamics in natural evolution has
been hotly debated over the years with much attention given to
the theory of Self-Organized Criticality (SOC) [22] [23]. SOC
theory attempts to explain how the spatial and temporal
patterns in some distributed systems can spontaneously evolve
such that changes in the system can reach any size with non-
negligible probability. In particular, the theory claims that
some coupled dynamical systems are driven or attracted to a
critical state where the system displays self-similarity in both
space and time as is commonly indicated by power law
relations. SOC behavior is different from other critical
phenomena (e.g. phase transitions) where an environmental
parameter (e.g. temperature) must be tuned in order for the
system to reach a critical state.
Power law relations are also displayed in the spatial and
temporal properties of natural evolutionary dynamics including
extinction sizes, species lifetimes (although this is debated),
and taxonomic structure [24] [25], leading some to speculate
that natural evolution may be an example of an SOC system
where initially small perturbations can grow to large extinction
events [26]. Others, notably Kauffman, have argued that
critical phenomena could play other roles in evolution [27]
[28].
More recently, David Green’s Dual Phase Evolution theory
(DPE) has argued that the punctuated dynamics in natural
evolution are a consequence of external environmental factors
(e.g. changes to the physical landscape’s connectivity) that can
facilitate exploration during the evolution of individual species
and can also enable speciation events [29] [30] [31]. In
particular, DPE describes two phases for evolution; one
involving a highly connected phase where exploitive selective
pressure predominates and the overall system is relatively
stable, and the other a disconnected phase where variation and
exploration predominates. The disconnected phase is initiated
by disruptions to the ecosystem but afterwards, the ecosystem
reorganizes, often times with greater complexity than it had
previously [31].
The experiments in this paper also appear to result in two
distinct phases of evolutionary behavior: one where the system
converges /stabilizes and another where disruptions (changes in
species interaction topology) lead to short bursts of new
evolutionary activity (e.g. see Figure 4). Based on this
interpretation, the results of our study seem to support the
argument that external events can cause meta-stability in
evolving populations.
In our experiments, external perturbations come in the form of
migration events however the end effect is a change in
population connectivity which is arguably similar to changes
in a physical landscape as is used in most DPE studies (e.g. see
[32]). On the other hand, most supporting evidence for DPE
seems to suggest (if not demand) that external perturbations be
destructive (e.g. by mass extinctions or redistribution of
resources). This is not supported by our results, which instead
suggests that changes in connectivity alone might be sufficient
in models of coevolution. Such a statement can be clearly and
unambiguously made due to our removal of direct competition
in the EA. Notice that if we had allowed direct competition to
exist in the algorithm, then the observed punctuated dynamics
would have been off-handedly attributed to genetic takeover
by a newly migrated species. Such genetic takeover would be
viewed as a highly disruptive and destructive process that
allows for the punctuated dynamics to occur and would be in
strong agreement with current explanations of DPE theory.
5 Conclusions
In this paper, we have shown that multi-objective evolutionary
algorithms can exhibit several features commonly labeled as
coevolutionary behavior. We demonstrate that this occurs in a
species model when i) individual species participate in
defining the fitness of others in a multi-objective environment
and ii) when the system is exposed to external perturbations
(migrations between islands). We have also explained how
these results appears to support a recent theory of evolution
known as Dual Phase Evolution Theory, which claims that
many features of natural evolution including punctuated
dynamics, speciation, and increasing organizational
complexity can be partly attributed to events that are initiated
by the external environment.
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