modeling and simulating morphological evolution in an artificial life environment by silveira et

7/29/2019 Modeling and Simulating Morphological Evolution in an Artificial Life Environment by Silveira Et

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COMPUTERS AND BIOMEDICAL RESEARCH 31, 117 (1998)ARTICLE NO. CO971464

Modeling and Simulating Morphological Evolution in an

Artificial Life Environment

Paulo Sergio Panse Silveira and Eduardo Massad

Discipline of Medical Informatics, School of Medicine of the University of Sao Paulo

and LIMQ1/HC-FMUSP, Sao Paulo, Brazil

E-mail: [email protected]

Received January 16, 1997

This paper presents a computer-based environment designed to study biological evolutionconsidering morphological aspects. It was inspired on cellular automata and evolutionaryalgorithm principles. Simple rules are used to determine the genotype and phenotype ofindividuals and their relationships with behavioral aspects in a square matrix environment,where individuals can evolve. Two methods to simulate mutational errors and to introducevariability of mutations are discussed. A series of four simulations show that the modelpromotes phenotype evolution depending on the distribution of food over the environment;morphology evolved as to favor movement of the individuals towards the portion of theenvironment in which the food has been distributed or to capture falling food. 1998 Aca-demic Press

Key Words: computer simulations; artificial life; genetic algorithm; cellular automata;medical informatics; ecology; modeling.

INTRODUCTION

Morphogenesis is certainly one of the most complex problems in biology (6,7), but evolutionary rules that generate patterns of development may be simplerthan we may think. Computer simulations of the evolutionary aspects are basedon very rudimentary rules that, sometimes surprisingly, mimics real life. If weconsider the fact that the whole biosphere evolved through a process of verytiny errors in the transcription of a 4-letter alphabet, together with selection of

the favorable new words, we may be led to the somewhat simplified conclusionthat life started based on a simple set of rules. Development can be viewed asinvolving only a small set of rules of cellular and mechanochemical interactionsthat can generate complex morphologies (1, 2, 8). This does not imply that, if itis possible to use computer algorithms to simulate complex behaviors using aset of simple rules, so Nature evolved in a similar fashion. Otherwise, we mustthink about how simple are the rules for DNA duplication in relation to theeffects we can observe, namely, life or ecosystems. Natural life on earth is

organized into molecular level, cellular level, organism level, and population-1


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SILVEIRA AND MASSAD2

ecosystem level. A living thing at any of these levels is a complex adaptive systemthat emerges from the interaction of a large number of elements from the levelbelow (13).

Another matter of contention is that computational rules may not be the same

set of natural rules, or, in other words, if a model correlates well with a process,it does not necessarily mean that the process was generated by the same set ofrules in the simulation. We believe that the answer would be, most often, a no.It is almost certain that we are not building a natural set of rules, since they area computational, artificial, and ad hoc set of rules. According to Prusinkiewicz(10), the relationship between the rules expressing the behavior of individualcomponents and the resulting developmental processes, patterns, and forms isoften nonintuitive and difficult to grasp, and computer simulations play an essen-

tial role in the study of morphogenesis.Taylor and Jefferson (13), assume that there is a major intellectual divide

between the modeling tools designed to accomplish some complex tasks (evenif only distantly related to the way natural systems accomplish it) and systemsmeant to accurately model biological systems and intended for testing biologicalhypotheses. We think it is a didactic way to classify the computational models,but there is not a clear limit between them.

The model discussed in this paper was inspired in cellular automata (CA)

and evolutionary algorithm principles. It intends to study biological evolutionconsidering morphological aspects by offering a computer-based environment.The individual morphology evolves on the conditions of the environment,applying artificial rules. We believe that, if this model is able to follow its rulesconsistently, it is useful to be applied to solve some complex tasks as predator/prey emergence, populational strategies, parasitism evolution, evolution, anddifferentiation of a species in another two species, and so on, testing biologicalhypotheses, even if it is distantly related to the way natural systems accomplish it.

The environment presented here is a matrix represented on a computer, seenas a chessboard. Each position can contain an individual, a portion of food, anobstacle or another kind of element in study. All algorithms have local scope,i.e., as is in biological systems, all decisions are not taken by demographic parame-ters, but they depend only on individual state and the state of its nearby neighbor-hood. In the model presented here, most of decisions are influenced by theindividual shape like its movement, its probability of mating, and its energyconsumption; i.e., individual shape is used as a decisional parameter by the

algorithms. This is an aspect of the model inspired in CA methodology.The model is also inspired by techniques from artificial life (Alife) and evolu-

tionary algorithms. This field of study emerged in the last few years and hasbeen developed by some independent groups (4). It consists of five great divisions:genetic algorithms (GA), evolutionary programming (EP), evolution strategies(ES), classifier systems (CFS), and genetic programming (GP). As a commonaspect, all of them are related with Darwinian evolutionary theories and thesurvival of the fittest. The inspired algorithms are thus termed evolutionary

algorithms (see [4] for a detailed discussion about GA, EP, ES, CFS, and GP


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SIMULATING MORPHOLOGICAL EVOLUTION 3

differences). Evolutionary algorithm models are applicable to complex tasks,mainly if the space of searching is very large. Although these methods have beenapplied in many areas of human knowledge, their applications in biologicalmodeling are a direct consequence. Our model codifies artificial genes in each

individual, used as parameters to the decisional algorithms, whose copies arepropagated to the descendants during the reproduction when the genes aresubmitted to mutational errors.

It is important to emphasize that we are not stating that the shapes evolvedby this model use the same set of rules as natural morphogenesis. We intend todemonstrate that shapes may evolve from simple rules in a simple and artificialenvironment. The model just reproduces some basic principles of Darwinianevolution, accumulating favorable variations by mutation and selection, promot-

ing morphogenesis as a complex dynamic process in which development takesplace in a sequential way, and morphological forms depend on the historyof their past forms; i.e., the appearance of novel phenotypic forms is not ran-dom (7).

METHODS

The program was developed in a computer environment based on a CISC

architecture in C computer language. Details of the initial conception of ourcomputer program can be found in Silveria et al. (12). An example of its applica-tion in studies related to infectious diseases can be found in Silveira et al. (11).

The computational environment is represented by a square matrix and individ-uals are placed in it. The square matrix is 200 200 positions.

Each individual is represented by its variables of life and genetic components(genotype) used as parameters by the algorithms. Simple rules are used to deter-mine the genotype and phenotype of individuals, and their relationships with

behavioral aspects and individual decisions, like the reproductive age, movement,and the rules to reproduce and form gametes with variation (mutation), the twobasic requisites to selection in a Darwinian sense (see below).

Simple algorithms are applied to each individual in repeated life cycles. Thescopes of these algorithms are local, mimicking a biological system, where individ-ual decisions use inputs provided by the neighborhood and the current state ofthe individual.

The main variables of life are: age, amount of ingested food and its spatial

position (x, y) in the environment. The genotype is described by two genes:recursion gene (R) and morphology gene (M).

R determines the size of the individual, whose body is generated by R iterationsfrom (x, y) initial position of the individual. Recursion may assume values from0 to 31 (5 bits). Mis an array, where each element of the array may assume valuesfrom 0 to 3, representing the orientation of growing, namely: 0 downwards;1 rightwards; 2 upwards; 3 leftwards. For instance, an individual withgenotype as in Table 1 is six cells large. Its adult shape (phenotype) is shown in

Fig. 1.


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TABLE 1

Example of Genotype of an Individual

R M0 M1 M2 M3 M4 M5 M6 M7 ... M31

5 2 2 3 3 2 ? ? ? ... ?

Note. R Recursion Gene; M0 to M31 morphologic array gene.

The model is able to: save and retrieve the configuration supplied by the researcher; interrupt a simulation and continue at that point; execute simulations in batch; exhibit graphics and data during simulations to allow visual control; generate files to store, cycle by cycle, the status of the variables involved

in the simulations that can be read by other computer systems.When a simulation is running, the program creates a split screen with an

environment where the individuals can live, and the information window wherethe graphics and the census appear. Inside the environment the individualsare represented by composition of points (cells), and the food by single points.A simulation is initiated by setting the initial conditions, as in Table 2.

All simulations are initiated with R 0 and random values in M array toguarantee that any growing direction is favored. Ages are equal to zero and theindividuals are positioned randomly over all the environment in cycle 0.

The simulations are based on the following steps: Random distribution of food over the upper portion of the environment

(explained in Table 2). Generation of the body of each individual based on its genetics (see Table

1 and Fig. 1). An individual can contact a point of food. In this case the individualeats this point and increases its reserve of food. In case of contact with anotherindividual, mating and generation of descendants can occur. As each cell has anarea of influence (Table 2) the phenotype of the individual influences itsfeeding and mating success.

FIG. 1. Phenotype of individual generated by chromosome sequence described in Table 1. The

initial cell is denoted by (x, y). The M array from M5 to M31 is not read by this individual.


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TABLE 2

Parameters of the Model

Final cycle Total duration of the simulation in life cycles (number of itera-

tions)Initial number of individuals Initial number of individuals in cycle 0.Area of influence Distance that each cell of each individual can reach to mate or

feed.Metabolic parameter Used to determine how many points of food are consumed for an

individual to maintain its body.Agitation The position (x, y) of each individual is disturbed by (x agita-

tion, y agitation) in each cycle, determined randomly.Floor depth The basement of the environment cannot be occupied by (x, y)

cell. An individual may be able to grow in this direction (by

predominance of alleles 0 in M) in order to acquire accumu-lated food.

Food by cycle Amount of food randomly distributed over the environment ineach cycle.

Area of food distribution Determines the depth (from top downwards to the bottom) thatfood is distributed in the environment.

Initial food Amount of food that each individual has in cycle 0.Food donation Proportion of food that each parental individual donates to the

offspring when reproducing (see main text).Food by descendant Each newborn receives a determined amount of food from the

parents. Depending on parental reserve of food, more or lessoffspring are generated in each reproduction.

Mutation Mutation rate is determined by one of two ways: (1) acting oneach bit that represents the genotype of each individual ineach cycle or (2) on the whole gene (see main text).

Probability of fatal accident All individuals are submitted to a constant probability of deathby accident in each cycle.

Maximum age Maximum age that an individual may achieve.

Movement of each individual. The new position that will be occupied byan individual is a function of three components: agitation of the environment(described in Table 2), force of gravity (acting over individuals and food), andmorphology. Considering the individuals in Fig. 2 it is possible to understandhow those influences act upon each individual.

Reproduction. To reproduce, individuals must be at a certain minimum age.Although the R gene determines the number of recursions, if the age (a) of anindividual is smaller than R, the number of recursions performed by the systemwill be a. In this case the individual is assumed to be still at a growing stageof life and therefore immature to reproduce. When R a the individual isable to reproduce.

Gamete formation is subject to errors (mutations). Two ways to implementmutation are applied, named as bit-mutation and gene-mutation. As each

gene is represented by an integer number, bit-mutation assumes that each bit


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FIG. 2. Examples of different phenotypes: (a) a one-celled individual is unable to move itself byits own resources and it tends to fall downwards. (b) a two-celled individual that tends to moveupwards by one position in each cycle; since the force of gravity move it downwards the sameamount, this kind of individual is able to float in the environment. (c) an example of heavyindividual; it tends to move downwards two positions each cycle, one by itself and one by force ofgravity. (d) a light individual able to move up by one position in each cycle. (e) this individualdisplays a composed movement, moving upwards by two positions and moving rightwards by twopositions. (f) a more complex morphology, showing a heavy individual that tends to move leftwards.

is analogous to a DNA base (ATCG) and each of them is submitted to a probabil-ity of error during the gamete formation. This means that, from a gene 00000(decimal value0), a single mutation may generate, for instance, 01000 (decimalvalue 8). Gene-mutation is to assume the decimal value of the gene and weallow steps of one unity (from gene 2 a mutation may generate a 1 or a 3).

Offspring result from the combination of parental genes. Reproduction de-pends on the participation of two, but all individuals are haploid like in somebacteria. Crossovers are not considered in this model in order to simplify the

TABLE 3

Initial Conditions to the Simulation Described in Fig. 3

Final cycle 10000 Food by cycle 150 pointsInitial number of in- 100 individuals Area of food distribution 10 positions depth

dividualsCarrying capacity 500 individuals Initial food 10 pointsArea of influence 1 position Food donation 0.10 of parental

reserveMetabolic parameter 0.50 Mutation rate 5 104/bitAgitation 21 positions Probability of accident 0.01Floor depth 10 positions Maximum age 1000 cycles


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FIG. 3. (a) Evolution of a population showing initial oscillation. The amount of distributed foodin each cycle is the main parameter to limit the amount of living individuals. (b) When the populationstabilize the average age oscillates around a certain average. (c) The amount of ingested food percapita did not change during this simulation. (d) Causes of death by accident (constant to all agesand all individuals during simulations) and by lack of food. (e) Evolution of recursion gene R showingtwo phases. Simulation was initiated with R 0 (binary 00000). Allele R 8 (binary 01000)was initially successful. Allele R 24 (binary 11000) won the competition. (f) Position occupied

by the individuals during the simulation. The food is distributed in the upper fraction of the environ-ment and light individuals evolved.


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FIG. 4. Snapshots of a simulation from cycle 0 to 2100 showing aspects of evolution of phenotypesthat are able to move upwards. Individuals represented in black and food in gray. Observe thatsome favorable individuals were able to move upwards at cycle 100 but they reproduced in significantnumber around cycle 200 competing by food. This caused lack of food for the individuals livingclose to the floor at cycle 350. In the sequence larger individuals were able to evolve.

algorithm and we assume that each gene (R or an element of the M array) isindependently segregate from the others.

The new individual receives food from each parental individual that donatesa proportion of its own food during the process. The percentage of food donatedfrom parental reserves and the amount of food received by each descendant are

FIG. 5. Simulation A: (a) distribution of food over the upper 10 lines of the environment generateslight individuals, able to move upwards; (b) succession of some prevalent phenotypes during the

simulation. Initial cells are assigned by .


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always the same. As the reserve of parental food is variable, probably dependingon its fitness, this is a supersimplification of real life, although somewhat realis-ticin biological species this donation varies in a range from the parents thatdonate all their bodies to the descendants (like bacteria) to parents that donate

part of their reserves depending on their nutritional state (as mammals). In thismodel the amount of the parents food would be an indirect consequence of itsshape, and available food is the major constraint in the environment. Therefore,individuals with higher fitness would have more reserve and would be able togenerate more offspring.

The initial age is zero and the position of the offspring is an average of theparental positions: Aging. All individuals become one cycle older at each simulation cycle.

Energy consumption. It corresponds to the basic metabolism of an individualand determines how many points of ingested food it spends in each cycle. Thecalculation of this amount of consumed food depends on the size of its body.Considering that a one-celled individual with an area of influence equals to1 has 8 neighboring positions, this means that it has 8 possibilities to find food.A two-celled individual has 7 neighboring positions around each cell. We canpresume that if this individual consumes two points of food, it is disadvantagedin comparison to the one-celled individual.

In order to allow the appearance of larger individuals, a metabolic parameterm (ranged from 0 to 1) is applied to calculate the food consumption, C, in eachcycle as a function of the size s (number of cells) of the body, according to

Cs

i1

mi.

Probability of death by accident. Census: values of the variables in the study are stored in a hard disk. Removal of dead individuals. All points of food drop one position (force of gravity). Updating the screen so as to show the environment and data to the researcher

(visual control). If not interrupted by the user, go to step 1.

RESULTS

Typical simulation parameters and results are shown in Table 3 and Fig. 3.Observe that the bit-mutation model (Fig. 3e) generated gene R equal to 0,8, and 24 in rapid succession. This is not desirable since it may be difficult fine-

FIG. 6. Simulation B: (a) distribution of food over 40 lines of the environment generates individualswith force to move upwards of two cells (one of them opposed by force of gravity); (b) successionof some prevalent phenotypes during the simulation. Observe the lateral appendices developed to

capture falling food.


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tuning the system. For instance, if the fittest individual would be, for instance,R 15 (binary 01111), the system would take a long time to find this value.Compare it with the results below (Fig. 9).

Figure 4 shows selected aspects of the computer screen. Observe that the

simulation begins with food randomly distributed over the environment, exceptin its upper portion, where food will be distributed at each cycle in the subsequentsnapshots. One-celled individuals (R 0) are also randomly distributed overthe environment. At cycle 50 the force of gravity is concentrating the individualsclose to the floor and part of food is concentrated below floor depth as describedin Table 2. At cycle 100 few light individuals emerge and begin to movetowards the upper portion of the environment. When they are well establishedno more food falls over the heavy variety. Part of food escaped from these

individuals during their transition from the bottom portions of the model. Ataround cycle 350 all food has been consumed. The result is the extinction of theheavy variety. Larger individuals were able to be developed on the upperportion of the environment presumably as a function of the evolution of a moreefficient morphology.

In order to show that it is possible to observe evolutionary issues out of thesesimulations, the following are results from simulations performed with the sameinitial conditions except by the area of food distribution. All the following simula-

tions used the gene-mutation model (as defined in the description of the stepsof a simulation under Reproduction).

Four simulations were performed. On simulation A, food was distributed closeto the upper fraction of the environment. In this case, individuals evolved towardsa shape able to move upwards (Fig. 5a). This movement generated a populationexhibiting high demographic concentration. In consequence, a convex shape,probably by maximizing food capture, evolved (Fig. 5b). It is suggested that thecompetition for food was more difficult in this simulation than in the following,

since the deaths caused by lack of food (Fig. 9) was higher in simulation A thanthe others, except simulation B.

In simulation B (Fig. 6), the distribution of food was over the quarter upperfraction of the environment. In this case, light individuals evolved, but theyare less efficient than individuals of simulation A (compare Figs. 5b and 6b)since these individuals have only two cells to move upwards and one of them isopposed by the force of gravity. The evolved individuals are able to occupy theupper fraction of the environment, without the disadvantage of high concentra-

tion as in simulation A. On the other hand, they evolved a kind of plate usefulto capture falling food.

In simulations C and D (Figs. 7 to 8) food was spread over the upper threequarters and over all the environment. In both cases, floating individuals

FIG. 7. Simulation C: (a) distributing food over 140 upper lines generates floating individuals;

(b) succession of some prevalent phenotypes during the simulation. Note the lateral appendices.


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evolved. Both populations developed plates to capture falling food. In conse-quence, the individuals were more spread over the environment.

Although simulations C and D were similar to each other, it is possible toobserve, by comparing Figs. 7a and 8a, that the individuals occupy all the environ-

ment only in simulation D. It appears to be a heavy subpopulation livingclose to the floor in simulation D, which was not possible in the conditions ofsimulation C.

FINAL COMMENTS

Instead of describing populational behavior as a function of equations wedescribe individual behaviors as computer algorithms. This kind of model is ableto mimic some real life situations and it deals with the problem of the incompleteinformation necessary to simulate real systems based on mathematical modeling,by circumventing some of the steps involved in the process of model construction.The model can also avoid some of the difficulties of dealing with heterogeneity,due to the construction of algorithms that act on each individual of the population.The two main disadvantages of Alife models against equatorial models are that(1) Alife models are time-consuming to run in the currently available personalcomputers and (2) a subjective component provided by the researcher interveneswith the model building. The first problem could be solved with technology

evolution. The second is also true for equational models, but it is minimizedwith progressive mathematical formalization.

If the populational behavior of a simulation correlates well with a biologicalobservation, the model may be useful as an exploring tool. The set of rules maybe not the same for a biological environment, since it is a more controlled modelthan reality. For instance, if we are studying mortality and each individual hasa gene D that determines its probability of death, it is not relevant if a naturalindividual has its mortality based on a single gene. Probably not, but the model

would be an initial approach to the question, devoted to clarify some basicmechanisms and influences in an overall evolution of the mortality of the speciesin a poligenic universe.

This discussion gains importance when we consider the processes of mechaniza-tion of real systems in the form of a computer simulation. Through this technique,we state certain rules, for instance, mathematical functions or maps or proceduralalgorithms, which generate outputs that can be compared to real systems aftera set of iterationcorrection processes. Simpler tools, such as CA, are proving to

be extremely useful to simulate complex patterns, like the evolution of biologicalshapes and sizes, based on comparatively simple rules (10).

FIG. 8. Simulation D: (a) distributing food over all environment generates floating individuals.On the other hand, there are heavy phenotypes living close to the floor of the environment;(b) succession of some prevalent phenotypes during the simulation. The usual lateral appendices

were developed.


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FIG. 9. Graphical results from simulations A, B, C, and D.

In this paper we intended to demonstrate that models based on cellular auto-mata and evolutionary algorithms may be useful in evolutionary studies. Manyimprovements may be done in the future in order to implement more realisticfeatures to the model. This kind of model may reflect a biological reality fromsimple rules. By constructing a model of reality many hypotheses can be tested.If the model fails, it should be modified or abandoned. Models and hypotheses

that do not agree with reality are substituted by others that are better able toreflect the real environment (9).Although it is possible to apply complex algorithms to this kind of model, we

believe that simpler rules may mimic the biological behavior. The present modelassociates morphology with interactions among individuals and their environ-ment to allow evolution to act and select the more advantageous individuals.

ACKNOWLEDGMENT

We thank CNPq for financial support.


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