EPIAL
An Epigenetic Approach for an Artificial Life Model
Jorge Sousa and Ernesto Costa
Evolutionary and Complex Systems Group
Centre of Informatics and Systems of the University of Coimbra, Portugal
Keywords:
Artificial life, Epigenetics, Regulation, Dynamic environments, Environmental influence.
Abstract:
Neo-Darwinist concepts have always been questioned and, nowadays, one of the sources of debate is epi-
genetic theory. Epigenetics study the relation between phenotypes and their environment, and the way this
relation can regulate the genetic expression, while producing traits that can be inherited by offspring. This
work presents an Artificial Life model designed with epigenetic concepts of regulation and inheritance. A
platform was developed, in order to study the evolutionary significance of the epigenetic phenomena, both
at individual and population levels. Differences were observed in the evolutionary behavior of populations,
regarding the epigenetic variants. Agents without epigenetic structures display difficulties thriving in dynamic
environments, while epigenetic based agents are able to achieve regulation. It is also possible to observe the
persistence of acquired traits during evolution, despite the absence of the signal that induces those same traits.
1 INTRODUCTION
150 years after the publication of “On the Origin of
Species” (Darwin, 1859), Darwin’s theory of evolu-
tion by means of natural selection is still a source
of inspiration, but also of debate. Neo-Darwinism
(Dawkins, 1976), the idea that evolution is gene cen-
tric and that the organisms’ structures are untouchable
by the environment, is due for a revision, as defended
by some authors (Jablonka and Lamb, 2005). Differ-
ent theories claim that the modern synthesis provides
for an incomplete view of evolution, regarding the
separation between organism and nature (Wadding-
ton, 1942). Genetic structures are far more com-
plex than previously thought, due to the non linear
nature of the mapping between genotype and phe-
notype. Epigenetics posit the existence of environ-
mentally based regulatory operations, and the pos-
sibility for inheritance of structural marks (Jablonka
and Lamb, 2005). Several approaches in Artificial
Life (ALife) attempt to model biological phenomena,
mostly focusing on the Neo-Darwinist point of view
in evolution. Most models perceive the environment
solely as a factor of selection, discarding interrela-
tions between agents and their world, such as the in-
fluence of the environment in the developmental pro-
cesses (Rocha, 2007), which could provide for an al-
ternative evolutionary approach (Jablonka and Lamb,
2005). In this work, we present an approach for an
ALife model that considers epigenetic concepts, fo-
cusing on the regulation of organisms and the possible
inheritance of epigenetic acquired marks. By includ-
ing regulatory elements in the agents’ structures, our
model enables the study of the evolutionary signifi-
cance of epigenetic concepts, while contributing to an
enriched ALife model. The remainder of this article
is organized in the following way: section 2 briefly
tackles epigenetic theory; section 3 presents the cur-
rent state of the art in epigenetic or related ALife mod-
els; section 4 describes the developed model, EpiAL;
in section 5, some experimental results are shown; fi-
nally, section 6 discusses some final remarks pointing
to some future work directions.
2 EPIGENETICS
Epigenetics is conceived as a set of genetic mech-
anisms and operations involved in the regulation of
gene activity, allowing the creation of phenotypic
variation without a modification in the genes’ nu-
cleotides. Some of these variations are also pos-
sibly inheritable between generations of individuals
(Gilbert and Epel, 2009). The focus is on the ma-
jor importance of development in organisms, but also
on the relationship between the mechanisms of devel-
90
Sousa J. and Costa E. (2010).
EPIAL - An Epigenetic Approach for an Artificial Life Model.
In Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Artificial Intelligence, pages 90-97
DOI: 10.5220/0002732500900097
Copyright
c
SciTePress
opment and the genetic system and, ultimately, with
evolution itself (Jablonka and Lamb, 2005). In terms
of phylogeny, epigenetics refers to the traits that are,
or can be, inherited by means other than DNA nu-
cleotides. Epigenetics in relation to ontogeny refers
to the influence, through epigenetic effects, of struc-
tural genetic parts of an individual during its lifetime
(Gorelick, 2004). Although epigenetic marks can be
inheritable, their frequency of inheritance is lower
than nucleotide sequences (Holliday, 1994). This is
due to the fact that epigenetic signals are much eas-
ier to alter through environmental disturbances and,
therefore, it could result in a high and undesirable
variability (Gorelick, 2004). Four types of (cellular)
epigenetic inheritance systems (EIS) have been theo-
rized (Jablonka and Lamb, 2005): (i) self-sustaining
regulatory loops; (ii) structural templating; (iii) chro-
matin marking systems; (iv) RNA-mediated inheri-
tance . The one that is used for our work is the chro-
matin system, in which methylation is one of the pos-
sible marks (Jablonka and Lamb, 2005). Methylation
of DNA refers to the addition of a methyl group to
the base sequence, that although does not change the
coding properties of the base, can influence its gene
expression (Bender, 2004; Boyko and Kovalchuk,
2008). It is known (Gorelick, 2004) that stress re-
sponses (tolerance, resistance, avoidance or escape)
from the organisms, which are induced from environ-
mental conditions, can lead to responses of methy-
lation or demethylation of a binding site of chromo-
somes. The effects of these responses can both be her-
itable and remain present during more than one gener-
ation (Gorelick, 2004). Most individuals, during de-
velopment, possess mechanisms that erase the methy-
lation marks from the parents, sometimes resetting the
genome to the original state (Youngson and Whitelaw,
2008). Nevertheless, there are cases in which these
erasure operations are not fully accomplished, with
epigenetic variation persisting through meiosis, and
being retained by the offspring (Jablonka and Lamb,
2005).
3 STATE OF THE ART
Artificial Life (ALife) is a scientific area whose main
goal is the study of life and life-like phenomena by
means of computational models, aiming at a better
understanding of those phenomena. As a side ef-
fect, ALife has also produced nature-inspired solu-
tions to different engineering problems. At the core
of ALife activity, we find the development of mod-
els that can be simulated with computers. Although
some works use epigenetic theory (or related con-
cepts) for problem solving techniques, to the best of
our knowledge, none tackles the question of exper-
imenting with epigenetic ideas regarding the evolu-
tionary questions posed by the concept itself. This
is a flaw that is pointed out by other authors as well
(Rocha, 2007). There are some approaches for prob-
lems solving model that take inspiration in epige-
netic, or epigenetic related ideas. In (Rocha and Kaur,
2007), the authors model an agent structure that is
able to edit the genotype, allowing the same genotype
to produce different phenotypic expressions. This
edition, however, is not influenced by environmen-
tal conditions. A dynamic approach for the envi-
ronment is presented in (Clune et al., 2007), where
an Avida (Ofria and Wilke, 2004) based model pro-
motes a time based symmetric environment in order
to induce the agents to produce phenotypic plastic-
ity (Pigliucci, 2001). In (Tanev and Yuta, 2008), epi-
genetic theory is used in order to model a different
sort of genetic programming, with the modelling of
different life phases (development, adult life) being
used to adapt the agents to the environment. During
the simulations, the agents adapt to the environment
using epigenetic based processes, that are separated
between somatic and germ line structures. Finally,
in (Periyasamy et al., 2008), epigenetic concepts are
used for the formulation of an Epigenetic Evolution-
ary Algorithm (EGA). The algorithm is used in order
to attempt an optimization for the internal structures
of organizations, with a focus on the autopoietic be-
havior of the systems.
4 EPIAL MODEL
EpiAL aims at studying the plausibility for the exis-
tence of epigenetic phenomena and its relevance to an
evolutionary system, from an ALife point of view. In
this section, we first describe the conceptual design
and notions used in EpiAL, focusing in the agent, the
regulatory mechanisms and the environment. Then
we present the dynamics of the system, explaining
how to evaluate the agents and the mechanisms of in-
heritance of EpiAL.
4.1 Conceptual Design
In our model, epigenetics is considered as the ability
for an agent to modify its phenotypic expression due
to environmental conditions. This means that an agent
has regulatory structures that, given an input from the
environment, can act upon the genotype, regulating
its expression. We also consider the possibility for the
epigenetic marks to be inherited between generations,
EPIAL - An Epigenetic Approach for an Artificial Life Model
91
through the transmission of partial or full epigenetic
marks (methylation values), allowing the existence
of acquired traits (methyl marks) to be transmitted
through generations of agents. The proposed model
is based on two fundamental entities, the agent(s) and
the environment. Their relation and constitution are
conceptually depicted on figure 1. The environment
Figure 1: EpiAL conceptual model.
provides inputs that are perceived by the sensors of
the agent (S). These sensors are connected to the el-
ements that compose the epigenotype (EG), i.e., the
epigenetic code of the agent. The epigenotype is com-
posed of structures that can act over the agents’ geno-
type (G), performing regulatory functions. This regu-
lation occurs in methylation sites that are assigned to
each of the genes, controlling their expression. The
methylation value for a gene is a real value compre-
hended between 0 (not methylated at all) and 1 (fully
methylated). It is this value that determines, stochasti-
cally, the type of expression for each of the genes. Fi-
nally, genes are expressed, originating the phenotype
of the agents, which is composed of a set of traits (T).
This mapping from expressed genotype to phenotype
is performed according to a function (f) that relates
sets of genes with the traits. In figure 2, we show an
example where each trait is dependent of 3 genes.
Figure 2: Genotype to phenotype mapping.
4.2 Regulation
The regulatory actions are taken under control of the
epigenes. An agent can contain one or several epi-
genes, that have the structure shown in figure 3. Epi-
genes are composed of two main parts, sensory and
(a) Generic epigene structure.
(b) Concrete example of an epigene.
Figure 3: Epigene structure.
regulatory (figure 3(a)). The sensory section is a tu-
ple that states (i) the sensor to which the epigene is
connected and (ii) the reference value that is going
to be used to compare with an environmental effect.
The possible reference values (for instance, the mean
values for each range of environmental effects) are
previously setup by the experimenter. The other con-
stituent of the epigenes, the regulatory section, con-
tains a list of tuples, with each tuple representing a
gene and a regulatory operation. During a regulatory
phase, the reference value encoded in the epigene is
compared against the environmental value perceived
by the sensor corresponding to the epigene. If the epi-
gene detects an activation, it acts on the genotype by
firing the rules that it encodes. Formulas 1 and 2 are
used to define the update of the methylation sites, with
m(g) representing the methylation value of gene g,
BaseMethyl a methylation constant and AcValue the
activation value perceived from the sensory operation,
proportional to the level of activation perceived. The
rules can be to methylate (formula 1) or demethylate
(formula 2) a certain gene, which means that a methy-
lation value is either increased or decreased for that
gene.
m(g)
new
= max(1,m(g)
old
+(BaseMethyl AcValue))
(1)
m(g)
new
= min(0, m(g)
old
(BaseMethyl AcValue))
(2)
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4.3 Environment
The environment is modelled as a 2D grid with each
location being transposable or not (a wall). Each
of the locations also has different attributes - tem-
perature, light and food - that can vary along time.
These attributes are used to define the favoured traits
for the locations. A certain location in the world
favours agents which have the traits more adequate
for the current environmental conditions. Therefore,
a change in an environmental condition might also
imply a change in the trait that is favoured. This is
shown in figure 4, where a modification in the tem-
perature state also implies a modification in the set
of favoured traits. However, environmental dynamics
are also used to promote the regulatory expression of
agents. This allows for an influence of the environ-
ment over the agents not only by performing selec-
tion, but also by inducing possible structural changes
(either adaptive or disruptive) within the agent. Be-
cause the agents sense environmental conditions, if
there is a change in the environment then it is possible
that regulatory actions are undertaken in the agents
structures.
Figure 4: Environmental traits setup of favoured traits.
4.4 System Dynamics
The simulation of the agents in the environment is
performed in evolutionary steps, as shown in figure
5. Agents are born and, either during their develop-
ment phase or their adult life, are subject to regula-
tory phases. Here, by sensing environmental condi-
tions, they regulate their expression. At the core of
Figure 5: EpiAL system cycles.
the evolutionary system is a Darwinian evolution and,
as such, agents are subject to selection, with the best
ones being chosen for reproduction and new agents
being subject to mutation. The agents live for a num-
ber of generations, originate offspring periodically
and die of old age, with the possibility for different
generations to live at the same time in the environ-
ment. The time step of the agents is independent from
the one in the environment. An agent can perform
several internal cycles of regulation or food digestion
during only one environmental cycle.
4.5 Evaluation
As agents do possibly have different performances
during their lifetime, due to their different regulation
status, it is relevant to possess means for this evalua-
tion to take into account not only the immediate per-
formance, but also an account of the past behaviour
of the agent. Moreover, recent values are more im-
portant to evaluate an agent. In order to evaluate the
agents in EpiAL, two measures are used: direct fitness
evaluation, i.e., the immediate fitness of the agents.
This value is obtained by comparing the agents’ trait
values with the favoured ones for the location (cell)
in which the agent currently stands (formula 3). From
the formula, it is clear that the lower the sum of the
module value of the differences, the better. Therefore,
agents attempt to minimize this direct fitness. Dur-
ing the life of the agents, these evaluations are stored.
When one desires to evaluate the global performance
of an agent, the weighted evaluation is performed.
This calculation is based on the exponential moving
average method, proposed in (Achelis, 2000). In sim-
ple terms, this method assigns more weight to recent
evaluations. The weighted sum calculated in formula
4 is used to obtain the weighted fitness, as depicted
in formula 5 ( f (t) is the direct fitness evaluation for
time t). This allows to perceive if the current regula-
tory state of the agent is beneficial or detrimental. At
the same time, allows agents that are born later to be
evaluated without prejudice from the older agents.
EPIAL - An Epigenetic Approach for an Artificial Life Model
93
Fitness =
3
i=1
|Phenotype
i
CellFavouredTrait
i
|
(3)
wSum(t) = w(1) f (1) + w(2) f (2) + . . . + w(t) f (t)
(4)
WeightedFit =
1
wSum
if wSum > 0.2
5 if wSum <= 0.2
(5)
4.6 Inheritance
During reproduction, crossover operations are used,
so the genetic material of the parents is combined to
form the offspring genetic material. The genotype is
immutable during an agent’s life, but there is, how-
ever, the possibility for the methylation marks to be
inherited by the offspring. In EpiAL, there are three
different mechanisms of epigenetic methylation mark
transmission: (i) faithful transmission, in which the
methylation marks are transmitted entirely to the off-
spring; (ii) complete erasure, where all the marks
are deleted from parent to offspring, being reset in
the new organism; or (iii) partial and stochastic era-
sure, in which some of the marks may be partially
erased. This partial erasure is either performed uni-
formly over the whole genotype or independently for
each gene, according to formulas 6 (DeltaMax be-
ing the maximum erasure value) and 7. Partial in-
heritance of methyl marks is exemplified in figure 6.
Here, methylation values of genes 1, 4 and 9, for
the first offspring, and genes 3, 7 and 9, for the sec-
ond offspring, are slightly decreased, compared to the
original parents’ marks. They have suffered a partial,
stochastic erasure.
Erase = Rand(0, DeltaMax) (6)
g: methyl(g)
new
= methyl(g)
current
Erase (7)
5 EXPERIMENTAL RESULTS
Several types of experiments were performed with the
EpiAL model, in order to study the mechanisms that
influence the evolution of the agents. Agents were
subject to environments where the three conditions
encoded in the world (temperature, light and food)
were modified, either periodically or non periodically.
Figure 6: Partial transfer of methylation marks.
Populations without epigenetic mechanisms are com-
pared against epigenetic ones. The epigenetic mech-
anisms - encoded in the agents’ epigenotype - remain
static and are not subject to evolution. In table 1 are
shown the main parameters used or tested, while table
2 presents the different major mechanisms that were
also experimented with in our simulations. These val-
ues were applied in several different simulations in
which the environmental setup would vary from mod-
ifying one or more conditions, periodically or non pe-
riodically, with higher or lower modification values.
As available space does not permit the exhaustive pre-
sentation of all these results, we present two types of
experiments that demonstrate the typical behavior of
the EpiAL platform.
Table 1: Parameters for the simulations.
Parameter Value
Agent Step 1
Fitness Smooth Factor 0.5
Aging Step 1
Aging Value 0.5/1/1.5
Dying Age Base 100
World Step 1
Mating Step 10
Initial Agents 15
Offsprings (per mating) 6
Agents Initial Age [-10;-5;-1]
Epigenetic Sensing Factor [3;4]
Methyl Base Value [0.1;0.3;0.5;0.7]
Genetic Mutation Rate [0.01; 0.1]
Losers’ Hype (Tournament) [0.05; 0.15]
Figure 7 shows a simple environment where the
temperature is modified, periodically, each 100 itera-
tions.
The results (average fitness values for sets of 30
runs) for this environment are shown in figure 8.
Non epigenetic populations, using tournament selec-
tion with a mutation rate of 0.01, perform poorly in
this sort of environment, whereas the epigenetic pop-
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Table 2: Methods for the simulations.
Action Method
Agent Aging Fitness Related
Agent Death Stochastic
Selection Tournament (2 Pair)
Reproduction Sexual (Crossover)
Genetic Crossover Trait Based (Gaps of 3)
Partial Methyl Erasure Overall
Figure 7: Dynamic, periodic temperature.
Figure 8: Average fitness results for different populations,
regarding the environment shown in 7.
ulations, subject to the same evolutionary operations
of selection, crossover and mutation, are able to en-
dure such an environment. Along the evolutionary
time, epigenetic agents adapt to the dynamic envi-
ronment by adapting also to the epigenetic structures
they possess. Agents which evolve to take advan-
tage of the epigenetic layer, regarding the environ-
ment, are preferentially selected to reproduce. This
is performed indirectly, by selecting the agents with
the best weighted fitness - i.e., during the agents’ life-
time, the ones that performed better, by regulating to
in adequate terms with the environment. As such,
along time, the population increases their adaptation
to the dynamic environment. One can, however, ob-
serve different evolutionary behaviors, regarding the
different epigenetic inheritance mechanisms. In the
case where the methylation marks are not inherited,
the spiked’ behavior is due to the fact that the new
agents are born from parents that are regulated with
methyl marks for the colder environment, with no
change on the genotype. As the epigenetic marks are
not transmitted, the agents are born with the genotype
for warmer environments - which are the ones actu-
ally coded in the genotype -, but are not regulated to
colder ones. Thus, there is a drop in the mean fitness
values because part of the population is not epigenet-
ically adapted to the colder environment. The case
where there is no methyl mark inheritance is the worst
of the epigenetic variants, while the cases where the
inheritance occurs in full terms, or only partially, are
very similar in terms of performance.
We also experimented with non periodic, more dy-
namic environmental effects, where both temperature
and light values are non periodically modified. This
is shown in figure 9.
Figure 9: Dynamic, non periodic temperature and light.
Figure 10: Average fitness results for different populations,
regarding the environment shown in 9.
The results for this scenario are shown in figure
10. The results are very similar to the previous ones,
with the non epigenetic agents showing bad perfor-
mance, whereas the epigenetic populations are able
to adapt to such an environment. The apparently sig-
nificant difference in the evolutionary behavior of the
agents regarding the possession or absence of epige-
netic mechanisms poses some interesting questions
that can be tackled with the EpiAL model. For in-
stance, we experimented with a basic movement be-
havior, where some of the agents would be able to
move into different locations, while others would be
fixed into the place where they are born. At the same
EPIAL - An Epigenetic Approach for an Artificial Life Model
95
time, the environment changes not as a whole, but
only in some specific locations (the environmental
modification in these areas occurs as depicted in fig-
ure 7). Some of the agents can, therefore, move out
of unfavorable locations, while others have to endure
the conditions from their birth location. The results
for this sort of simulation is presented in figure 11.
Figure 11: Average fitness results for different populations,
regarding an environment modified in some of the areas ac-
cording to dynamics in figure 7.
Results indicate that the impact of either possess-
ing epigenetic mechanisms or not, regarding popula-
tions that can move is not nearly as significant as for
populations that cannot move. The moving popula-
tions have a fairly similar performance whether they
are epigenetic or not. In the case of the grounded pop-
ulations, however, as they cannot move from the mod-
ified areas, they are subject to harsher environments,
unless they regulate their genotypes to the new con-
ditions. This is in agreement with the epigenetic the-
ory, in which plants, organisms that, indeed, cannot
move, posess biological mechanisms that are much
more plastic than the ones in animals. Some of these
mechanisms can be considered epigenetic (Boyko and
Kovalchuk, 2008).
Regarding the results of the model in general, a
legitimate question arises, related to whether there is
a memory role at play, a way in which the agents re-
member the environmental modifications and inherit
those memories. Memory, in the terms that the agents
remember that cycles occur at a certain time, is dis-
carded by the exposure to non periodic environments
(figure 10) and the consequent adaptation of the epi-
genetic agents. There are no hard coded mechanisms
that the agents can take advantage of, in order to re-
member timed, cyclic conditions in the environment
and transmit that information to their offspring. Nev-
ertheless, it can be stated that the main role is played
by both regulation and a genetic memory factor. If
we consider that the construction of the methylation
marks are a mechanism of life-time adaptation, and
if those marks are inherited, it is only fair to state
that there is some ’knowledge’ inherited by the off-
spring. However, and because the mechanics were
built around the regulatory theory of epigenetics, that
sort of ’memory’ is derived from regulatory mecha-
nisms. The agents have no means to remember a spe-
cific state from the environment, unless the epigenetic
components allow them to mark their genotypes with
such knowledge. And, even then, such knowledge has
to evolve (genetically, at least) in order to be of any
use. Methylation, by itself, is worthless if the genetic
elements are not evolved to cooperate with the epi-
genetic mechanisms. Despite some evidence regard-
ing the partial inheritance of these acquired marks (as
studied in (Gorelick, 2004), for instance), the EpiAL
model enables the possibility to consider that this ge-
netic memory does not operate. The results obtained
from the experiments have shown that, although these
results are usually worse than the simulations with
methyl mark inheritance, there can be improved re-
sults from this solely regulatory behavior, compared
with the absence of epigenetic mechanisms at all. As
such, we can consider that the key role of the epige-
netic dimension modelled in EpiAL is mostly regula-
tory, with the genetic memory variants improving on
the results obtained by regulatory mechanisms.
6 CONCLUSIONS AND FUTURE
WORK
EpiAL, the model hereby presented, is designed with
a biological enhancement regarding epigenetic mech-
anisms. The dynamics of the environment are able
to handle multiple conditions, like temperature, light
and food, in cyclic or non periodic modifications. The
artificial agents, in turn, possess mechanisms to incor-
porate and process these environmental conditions,
allowing an epigenetic influence in their coding struc-
tures. This enables the simulation with different me-
chanics regarding the epigenetic effects, ranging from
the regulatory aspects to the inheritance methods. Us-
ing an abstraction for the phenomena of methylation
in the genome, the model is able to represent regula-
tory operations for adapting to different, dynamic en-
vironments and allows different inheritance patterns
to be experimented with. The results show that there
could be a significant difference regarding the agents’
possession of epigenetic mechanisms. The non epige-
netic populations find it hard to thrive in dynamic en-
vironments, while the epigenetic populations are able
to regulate themselves to dynamic conditions. More-
over, results regarding a simple behavior in the agents,
i.e., movement, have been presented, in the light of
epigenetic constraints. However, different sorts of ex-
perimentations can be performed with the actual im-
plementation of the model. It would also be inter-
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96
esting to perceive if nocive effects of the epigenetic
mechanisms can be found, namely the application of
mutational events either to the methylation sites or the
epigenetic structures themselves. It would also be in-
teresting to perceive if the application of these mech-
anisms could be used in the scope of problem solving
techniques. This work is but a first step, in which we
attempted to show that there is a difference, in evo-
lutionary terms, in considering agents with an epige-
netic variant. By pursuing this work further, we can
hope to achive a better understanding of the field of
epigenetics. The subject of epigenetics is young and
still maturing, but, as a hot subject in biology, it pro-
vides an example of an excellent opportunity to capi-
talize over the knowledge achieved in the past years,
regarding the modelling of biological phenomena. We
intend to pursue the continuous development of the
model, with a focus on two dimensions: the first is re-
garding the biological knowledge that we believe the
EpiAL model can assist in studying and better under-
standing. The emergent fields of developmental bi-
ology (evo-devo) tackle this issues and have use for
simulation tools that can assist in theoretical specula-
tion. The other dimension is related to problem solv-
ing techniques. Problems with dynamic environments
are tackeld by several algorithmic approaches, and we
believe that the conceptual basis of the EpiAL model
has some evolutionary and adaptational mechanisms
that could provide a different approach in tackling
these problems. This twofold path is but another hint
that ALife models can be used concurrently with the
discoveries found on the field of epigenetics and de-
velopmental biology, providing an actual relation of
biomutualism between the fields of computation and
biology.
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