Using Secondary Inherited Characteristics During Reproductive Choice

to Replicate Allopatric Speciation

Gary B. Parker and Jay B. Nash

Department of Computer Science, Connecticut College, New London, U.S.A.

Keywords:

Allopatric, Sympatric, Speciation, Bio-Inspired, Genetic Algorithm, Artiﬁcial Life, Agent Modeling, Rule

Base, Evolutionary Computation.

Abstract:

The goal of this research is to create an environment where we can use evolutionary computation (EC) with

separate chromosomes in independent agents to replicate allopatric speciation, the process in which a species

diverges into two distinct, reproductively separate species based on geographic isolation. In previous work

done by Parker and Edwards, an environment and genetic algorithm were developed to simulate this type of

speciation. However, some aspects of the developed environment could be considered a priori knowledge. This

paper details a new system where agents do not have access to what we will refer to as “primary characteristics”

or characteristics that directly affect agent ﬁtness and success. Characteristics that have no bearing on agent

ﬁtness, referred to as "secondary characteristics", are solely used by the agents to determine reproductive

choice. This has a variety of beneﬁts, most clearly that no a priori knowledge is used in the system. This

can result in two species that have identical primary, ﬁtness affecting characteristics, but are reproductively

separated due to secondary, arbitrary characteristics. The reduction of knowledge available to the agents during

reproduction makes the system a better match for biological systems, but was expected to cause an increase

in cross species hybrids. However, it led to a higher degree of speciation than previous work on the topic.

As a result, this system improves upon the previous method used to simulate the natural process of allopatric

speciation via a genetic algorithm by reducing a priori knowledge and increasing efﬁcacy.

1 INTRODUCTION

Speciation is the biological process of creating a new,

distinct species from an ancestral species. There are a

variety of deﬁnitions and rules for what makes a dis-

tinct species; for the purposes of this research, we

consider a species distinct if it will not produce off-

spring with individuals from a different species. Spe-

ciation is a key aspect of evolution (Coyne, 1992),

which requires that new species are developed from

ancestral species. In order for a new species to de-

velop, its population must be reproductively isolated

from the original species so that the two species can

evolve to have distinct characteristics. Although there

appears to be evidence for this found in the fossil

record, observations of it in nature are difﬁcult to ﬁnd

when species is deﬁned as individuals who cannot re-

produce with other species. The Galapagos Finches

from separate islands are said to be separate species,

but they are still able to interbreed and produce vi-

able offspring. For our deﬁnition of species, which is

required for evolution, they should not be willing to

mate, even if allowed to intermingle within the same

environment.

The goal of this work is to demonstrate speciation

in a computational model, which is done by improv-

ing the results of a simulation developed by Parker

and Edwards (Parker and Edwards, 2019), and to do

so without using knowledge of an agent’s ﬁtness dur-

ing the reproductive process. This results in gene

pools separated solely by the lack of interaction be-

tween the two species, instead of being separated by

factors that affect ﬁtness. By doing this, we are more

closely replicating what might take place in nature.

In the research presented in this paper, we concen-

trate on the results of simulating allopatric speciation

(Mayr, 1963), which occurs when new species evolve

from a common ancestor due to geographic isolation.

Sympatric speciation, when a species diverges within

the same geographic area (Bolnick and Fitzpatrick,

2007), is planned for future research.

The ultimate objective of this research into repli-

cating speciation is to determine if it is possible to

simulate both allopatric and sympatric speciation us-

304

Parker, G. and Nash, J.

Using Secondary Inherited Characteristics Dur ing Reproductive Choice to Replicate Allopatric Speciation.

DOI: 10.5220/0013017900003837

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Joint Conference on Computational Intelligence (IJCCI 2024), pages 304-312

ISBN: 978-989-758-721-4; ISSN: 2184-3236

ing a genetic algorithm (GA) with the individual

chromosomes, each within and controlling separate

agents. Standard GAs (Holland, 1975) consist of a

population of individuals that are intended to be a so-

lution to a given problem. The traits of these individ-

uals are encoded in chromosomes, which in our case

are constructed from a sequence of 0s and 1s so that

genetic operations such as crossover and mutation can

easily operate on them. In general, new individuals

are evolved by ﬁnding a ﬁtness value for each cur-

rent individual, from which the highest scoring indi-

viduals are chosen as the basis for the next generation.

When two individuals reproduce, crossover is used to

combine their chromosomes into a new chromosome,

which is then used to create a new individual to be in-

troduced into the population. Our GA differs from a

standard GA, as instead of consisting of a population

of chromosomes, our GA consists of a population of

agents, each with its own set of chromosomes. In our

simulation, agents only reproduce when they are in

close proximity to each other; our simulation relies

on the fact that agents that are physically distant from

each other will reproduce less, if at all, regardless of

any other factors.

This paper presents our results for modifying the

previous GA developed by Parker and Edwards to

remove various arbitrary factors, reduce the amount

of knowledge individuals have during reproduction,

reduce knowledge of potential mates’ primary char-

acteristics, and not arbitrarily penalize mating with

agents of different sizes (Parker and Edwards, 2019).

All of these changes are intended to make our system

better represent biological systems. Although we pre-

sumed these changes would result in less successful

speciation due to agents having less information for

decision making, we found that it instead removed the

existence of cross-species hybrids after speciation.

The motivation for this work is to both test biolog-

ical theories and to ﬁnd aspects of speciation that can

be used to improve genetic algorithms. A simulation

that can accurately reﬂect speciation could provide in-

sight into real evolutionary processes. The current re-

search is solely concerned with replicating speciation.

However, it is possible that what is learned from this

could contribute to the performance of evolutionary

computation due to the species separating naturally

rather than being separated by a similarity function.

This is purely speculation and will be investigated in

a future work after further expansion of this research

into replicating speciation.

2 PREVIOUS WORKS

Speciation has been partially mimicked in other re-

search that mainly focuses on niching algorithms to

improve the ability of a GA to optimize a multimodal

function (Goldberg and Richardson, 1987). Gener-

ally, niching algorithms function by detecting a pop-

ulation of similar chromosomes and creating niche

populations manually. Although many ways have

been developed to maintain and create niches, we do

not consider them to replicate speciation as each niche

is determined by similar characteristics rather than by

the individuals themselves (Glibovets and Gulayeva,

2013). This artiﬁcially creates subpopulations, while

our research presents a possible way for individuals to

develop such subpopulations naturally via their own

mating preferences.

NeuroEvolution of Augmenting Topologies or

NEAT (Stanley and Miikkulainen, 2002) is similar to

our research in that it uses evolution to learn agent

controls and preferences; the learning is in real time,

and speciation is somewhat present. However, like

niching algorithms, NEAT uses a compatibility func-

tion to determine if two agents are part of the same

species instead of the agents themselves determining

what agents they interact with. That is not to say

this process does not have a basis in nature, how-

ever, since structurally different organisms are gen-

erally different species, regardless of the preference

of those organisms. NEAT uses historical data for

an agent to determine which gene corresponds to an-

other gene and which agents belong to which species.

Another feature of NEAT is ﬁtness sharing, this pro-

cess allows agents of a similar species to share ﬁtness

payoff, decreasing competition inside a species while

keeping high competition with other species. The sys-

tem described in this paper has a different goal; we

want species to develop naturally through reproduc-

tive isolation. Instead of restricting mating via a pro-

grammed function, the agents themselves will choose

not to mate with agents that have diverged into a dif-

ferent species. Additionally, the simulation does not

make agents share ﬁtness payoff, although resource

scarcity tends to force one species to dominate its own

area. As ﬁtness payoff is not shared between agents

of the same species, agents compete for food with all

other agents, regardless of species membership. This

encourages the formation of new species and the mu-

tation of existing species, as there is no advantage to

remain a part of an existing dominant species beyond

an increased chance of ﬁnding a compatible mate.

The work done on simulating allopatric specia-

tion focused on using purely biological processes to

optimize a GA. Unlike the Speciation Island Mode

Using Secondary Inherited Characteristics During Reproductive Choice to Replicate Allopatric Speciation

305

(Gustafson and Burke, 2006), a process which detects

new species and separates them to their own isolated

environment using a species barcode and common an-

cestry, this GA maintains the same grid and environ-

ment for all species, only using a temporary barrier to

simulate geographic and reproductive isolation. Ad-

ditionally, the species within this GA begin as a single

population that will naturally diverge into two. This

separates it from the idea of Cooperative Coevolu-

tionary Algorithms (Potter and Jong, 1994), as in that

system, the species are utilized to solve a problem to-

gether, while in the system described in this paper,

the agents are solely concerned with competition for

individual success and food resources.

Some research has been done speciﬁcally on sep-

arating species created by a GA via geographic isola-

tion, such as in a paper published by Wang Li et al.

(Li et al., 2012). This paper proposes a process in

which a standard GA is run to have a control species,

then the search domain is separated, and each sepa-

rated domain is evaluated to see if a speciﬁc species

is likely to evolve into a superior species. That pro-

cess has some close similarities with our speciation

simulation, although in that paper the agents are not

recombined. The process of agent recombination al-

lows us to see if the populations have naturally di-

verged far enough that the agents themselves consider

them different, rather than a predeﬁned analysis func-

tion.

In addition to speciation, our simulation uses the

unique method of a Genetic Algorithm with Vary-

ing Population Size, or GAVaPS. This method im-

plements a way to have the population of a GA vary

by introducing aging into the agents (Arabas et al.,

1994). In GAVaPS, individuals die when their age ex-

ceeds a speciﬁc lifetime value. The paper discusses

different ways to determine a lifetime value for an in-

dividual, which remains constant as the agent ages.

Our research is similar to the idea of GAVaPS how-

ever differs in that the lifetime value is not predeter-

mined. Instead, age increases the amount of food an

agent must consume by increasing the amount of life

(energy) an agent loses each turn. Once the agent runs

out of energy, it dies. Thus, instead of determining an

agent’s lifetime value, the agent itself determines how

long it can live based on its ﬁtness in its environment.

Other GA’s have been created to allow variable

population sizes, such as APGA, PRoFIGA, and the

PSO-GA hybrid algorithm (PGHA) (Shi et al., 2005).

The PGHA has some similarities to our research, pri-

marily in that “parents are neither dead after their

reproduction right away, nor living forever.” Agents

can, and often do, survive and outlive their children.

However, the longer they live, the higher the probabil-

ity they will die. While the PGHA uses actual prob-

ability to determine agent death, our speciation simu-

lation uses age as a factor that increases agent energy

consumption. In addition, in our work, selection is

solely based on the preferences of two agents in close

proximity.

3 ENVIRONMENT

A new model was created using the previous specia-

tion environment model developed by Parker and Ed-

wards as a baseline (Parker and Edwards, 2018). This

new model largely follows the aspects of the previ-

ously developed model, with functional changes con-

cerning agent chromosomes and reproductive func-

tions.

This model was designed to be as simple as possi-

ble to minimize the factors outside the agents’ direct

control while keeping enough complexity that specia-

tion could occur. The environment for this simulation

is a grid over which the agents can move, eat, and in-

teract with each other. This grid was designed to be

of variable size depending on testing requirements. In

the results reported in this paper, a 100 x 100 grid en-

vironment was used. Figure 1 shows what a 50 x 50

environment looks like with seeds before agents are

added.

Figure 1: Example 50x50 empty grid with random food

generation. A 100x100 grid was used in actual simulation

runs. Food is represented by a square icon, green icons rep-

resent large food, yellow icons represent medium food, and

red icons represent small food.

The grid is array based and uses discrete blocks

(spaces) which can be empty or be occupied by food

and/or an agent within the space. A seed is repre-

sented by a square of varying sizes depending on the

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306

size of the seed, and agents are represented by spheres

of varying sizes and colors depending on the size and

RGB value of the agent. During each time cycle

(turn), the agents all select an action to perform that

turn, and some food is generated within the grid.

The food generated is of three possible sizes:

large, medium, and small. The density of food gener-

ation and the size of food generated can be speciﬁed

to determine the quantity and type of food added to

the grid per turn. Differing from the previous environ-

ment, the new environment is divided into four equal

sections: far left, center left, center right, and far right.

Food generation can be speciﬁed using probabilities

for each section and given a total amount of food to

generate. For example, the ﬁrst two sections (far left

and center left) could have a 50/50 chance of gener-

ating 100 large or medium food, while the last two

sections (center right and far right) may have a 50/50

chance of generating 100 medium or small food. Hav-

ing the grid split up like this simulates differing envi-

ronments used to replicate geographical differences

like different climates or soil. Each time cycle, new

seeds are added to the grid based on the rules for each

section. The placement within a section is random;

however, each section generates a speciﬁc number of

seeds per turn. The food does not move, once placed

the seeds stay in that position until they are eaten by

an agent.

Figure 2: Example of the three different sizes of agents and

food. Agent color is determined by genes inside a chromo-

some while food color is static. Agents have a bold border

compared to the food and are circular instead of square.

4 AGENTS

Agents are able to move around the environment

freely (although they cannot move into a space oc-

cupied by another agent), eat seeds, and interact with

each other if two agents happen to occupy adjacent

spaces. The number of agents within the environment

at a given time is variable as it may increase or de-

crease depending on the variables of the environment:

food density and the type of food generated. Gener-

ally, the population size increases as the simulation

runs, due to agents becoming more ﬁt, until it even-

tually reaches a steady state. The physical aspects

of each agent differ from previous research. While

agents still have a certain size and RGB value, they

also have four arbitrary characteristics represented by

a numerical value between 0 and 15. As new agents

are created, these physical characteristics, size, and

RGB value are inherited from the parents with a small

chance of mutation. An example of agent size and

RGB values can be seen in Figure 2.

Table 1: Agent Energy Gain From Seeds.

Agent Seed Size

Size Large Medium Small

Large 100 30 15

Medium 30 100 30

Small 15 30 100

The agents’ size varies between three values:

large, medium, and small. The size of the agent is the

only factor that determines the agent’s ﬁtness for its

environment as it determines what size seed the agent

is most capable of eating (Table 1). For example, if

a large agent had to choose between eating a medium

or large seed, the best option would be the large seed.

The number of chromosomes in each agent has in-

creased from previous research done to replicate al-

lopatric speciation. The agents now have three chro-

mosomes in order to allow them to better differenti-

ate between themselves. The ﬁrst chromosome dic-

tates agent behavior (discussed in the next section),

the second chromosome dictates the agents’ physical

characteristics as discussed previously, and the third

chromosome dictates an agent’s preferences for re-

production.

One of the possible actions of an agent is to mate

with another agent in an adjacent space. If both parent

agents agree to reproduce, a child agent is produced

and placed in the environment within three spaces of

the parent agents. Differing from the previous envi-

ronment, agent reproduction cannot fail due to dif-

ferences in agent size if two agents decide to repro-

duce. All criteria of both agents must be met for re-

production to occur. This chromosome dictates the

desired partner RGB, the desired values of the four

arbitrary characteristics, and the desired age (Figure

3). Notably different from the previous reproduction

system, size preference is absent from this decision-

making process. The lack of information about the

only factor impacting ﬁtness (the primary characteris-

tic) forces the agents to use other aspects (secondary

characteristics) of a potential partner to determine if

reproduction will yield a successful offspring.

The ﬁrst three bits of the chromosome dictate the

maximum desired color difference in a partner agent

Using Secondary Inherited Characteristics During Reproductive Choice to Replicate Allopatric Speciation

307

Figure 3: Example of two agents that would successfully re-

produce with each other given their chromosomes and spe-

ciﬁc information. Note that size, age, RGB, and arbitrary

characteristics are normally stored in a chromosome. How-

ever, they were taken out of binary format for the sake of

this example.

(Table 2). This color difference is the sum of the dif-

ferences between each of the three RGB values. The

maximum possible color difference is 765 (3 * 255)

and the minimum difference is 0. This range is found

using the formula MAXDIFF = 100 + (95 * BITVAL).

Table 2: Bit Combination for the Maximum Color Differ-

ence Between Two Agents.

Max Color Difference Bit Value Decimal Value

100 0 0 0 0

195 0 0 1 1

290 0 1 0 2

385 0 1 1 3

480 1 0 0 4

575 1 0 1 5

670 1 1 0 6

765 1 1 1 7

The next six bits of the reproductive preference

chromosome decide the desired age of a mate. An

individual agent’s age is determined by how many

time cycles that agent has been alive. The age of

reproductive fertility was deﬁned to be between the

ages of 35-154. The desired age range of a possi-

ble mate was encoded into a six-bit string by using

the ﬁrst three bits to deﬁne the starting range of 15,

such as 65-79, and then using the next three bits to

expand that range by some number of index values,

in this case one index expansion would result in an

actual range of 50-94 (Table 3). The formula for the

lower bound of the initial age range, using the ﬁrst

three bits, is: LOWERAGE = 35 + (15 * BITVAL)

and UPPERAGE= 49 + (15 * BITVAL). In order to

ﬁnd the age range index increase speciﬁed by the

second three bits, the formula is: ACTUALLOWER

= MAX(35,LOWERAGE-15*BITVAL) and ACTU-

ALUPPER = MIN(154,UPPERAGE+15*BITVAL).

Table 3: Bit Combination for the Initial Age Range of a

Partner Agent.

Initial Age Range Bit Value Decimal Value

35-49 0 0 0 0

50-64 0 0 1 1

65-79 0 1 0 2

80-94 0 1 1 3

95-109 1 0 0 4

110-124 1 0 1 5

125-139 1 1 0 6

140-154 1 1 1 7

The remaining 16 bits of the chromosome deﬁne

the preferred values of four arbitrary, inherited char-

acteristics each agent has. Reﬂecting that each char-

acteristic has a total possible range of 0-15, these

16 bits are divided into four preferences of four bits

each. Each preference has a corresponding charac-

teristic and is a value between 0-15. This value is

the maximum difference two agents can have for that

characteristic for them to be willing to mate. For each

characteristic, we take the absolute difference for that

characteristic between an agent and a possible partner,

if that difference is less than or equal to the agents’

preference for that characteristic, then the agents are

willing to mate.

5 AGENT CONTROLLER

The actions of each agent are controlled by a rule-

based system, which is made up of a set of different

rules (antecedent/consequent) that control the agent’s

actions. If the antecedent of a rule is true, then the

rule ﬁres and the action in the consequent is taken.

Agents only have one possible action per time cycle,

which means they must somehow decide on the best

possible action they can take per turn. Our research

ECTA 2024 - 16th International Conference on Evolutionary Computation Theory and Applications

308

Table 4: An Example Of The Action Chromosome That Decides The Priorities For The Rule Based Agent Controller.

Rule Free Reproduce Large Seed Medium Seed Small Seed Large Seed Medium Seed Small Seed

Base Space No Eat No Eat No Eat Eat Eat Eat

Chromosome 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0

Decimal Value 13 7 14 10 0 10 7 8

The Complete Action Chromosome Is: 11010111111010100000101001111000

uses priority ordering, learned by the overall GA, to

decide which rules have the highest priority. If there

is a tie in priority, then a random tied rule is chosen.

The agents are capable of performing various ac-

tions: move to a free space, reproduce with an adja-

cent agent, move to a large seed space and eat it, move

to a medium seed space and eat it, move to a small

seed space and eat it, move to a large seed space and

do not eat it, move to a medium seed space and do not

eat it, and to move to a small seed space and do not eat

it. During each time cycle, the immediate surround-

ings of an agent (one space up, down, left, and right)

are analyzed to see which rules are possible to ﬁre.

Once the possible actions are determined, the agent

ﬁres the highest priority action possible to perform,

with a tie broken by random choice.

An agent starts with 100 energy. All actions carry

a base cost of the square root of the agents’ age, with

reproduction carrying an additional cost of 80 energy.

The additional cost of reproduction is only levied

upon production of a child agent, since if both agents

decide to reproduce; there is no chance of failure.

Conversely, if either agent decides not to reproduce,

there is no chance of reproduction. As agents age, the

cost of each action (a cost that must be paid per time

cycle as agents must take an action) increases, mean-

ing that the agent must eat more food to survive as

it ages. If an agent eats a seed, it will get a certain

amount of energy, as shown in Table 1. For example,

if we had a large agent with 200 energy, 100 age, and

it moved to and ate a large seed, the resulting energy

would be 200 + 30 – sqrt(100) = 220.

An example of an action chromosome and its re-

sultant priorities can be seen in Table 4. This table de-

picts a single agents’ chromosome broken down into

each action gene. The chromosome is split into eight

four-bit sections, and the action that has the highest

priority and is possible for the agent to perform is cho-

sen.

According to this example, the agent would most

want to move to a large seed space and not eat the food

(pseudocode for the algorithm can be seen in Algo-

rithm 1). However, if one of the adjacent spaces does

not contain a large seed, the agent cannot perform this

action. If this is the case, the next highest priority rule

will be checked to see if it can be ﬁred. In this exam-

ple, the agent would then check if there is an open free

space to move to. This process of ﬁnding the highest

rule to ﬁre continues until a rule is found that can be

ﬁred; there is at least one rule that can always be ﬁred.

6 AGENT CHARACTERISTICS

It is important to note the difference in how we treat

certain characteristics of each agent. Characteristics

that affect agent energy gain, and therefore ﬁtness, are

what we call “primary characteristics.” The only char-

acteristic that meets this deﬁnition is the size of each

agent. This primary characteristic is not available to

other agents when deciding reproductive preference.

Therefore, the agents must decide reproduction based

on other characteristics. These other characteristics

are called “secondary characteristics” and have no im-

pact on agent energy gain or ﬁtness. These character-

istics include the RGB value of an agent, the age of an

agent, and four arbitrary characteristics that are repre-

sented by 4-bit strings with a decimal value between

0-15. These secondary characteristics are available

to the agents during reproduction and are what the

agents use to decide if they want to mate with any

adjacent agent.

All these characteristics are inherited during re-

production with a small chance of mutation. Because

these values are inherited, over time and as more com-

mon ancestors appear, agents begin to hold similar

characteristics to other agents in their proximity. Us-

ing this, agents can effectively determine if an agent

is a good mate or if the agent is a different species and

not a good mate.

7 GENETIC ALGORITHM

The properties of the rule-based system, the reproduc-

tive preferences, and the agent characteristics are all

speciﬁed by a GA. This allows the agents to pass their

preferences and characteristics to their children. The

GA operates on three chromosomes (one for actions,

one for preferences, and one for characteristics), each

made up of 1s and 0s. Selection in our system is based

on physical proximity in our environment (adjacent

spaces) of the two individuals and if they both agree to

reproduce depending on the other’s RGB value, age,

and arbitrary characteristics. Speciﬁcally, size is not

Using Secondary Inherited Characteristics During Reproductive Choice to Replicate Allopatric Speciation

309

Algorithm 1: Pseudocode for the rule-based system

that decides agent movement and actions. The infor-

mation about each agent is stored in an agent class

and parsed each time cycle to decide agent actions

with updated information.

for each agent in the environment do

Get the adjacent spaces (maximum 4);

for each action do

Determine weight for the action;

if action is possible then

Add action to priority queue with

weight;

if action added is the same weight as

other action then

Randomly choose action to be

placed higher in queue;

end

View action at top of priority queue;

if action is reproduce then

Attempt to reproduce;

if mate did not agree to reproduce or no

mate is found then

Remove reproduce from priority

queue;

else

Create new agent;

Place new agent in random space

within 3 spaces of the parent agent;

end

else

Select and ﬁre rule at top of priority

queue;

if rule can move agent to more than one

space then

Randomly decide space to move

agent to;

else

Remove action from priority queue

and go back to view action at top of

priority queue step;

end

Reduce energy of agent in regard to age;

if reproduced successfully then

Reduce energy of agent by 80;

end

Add energy to agent if food consumed;

Add one age to agent;

Update agent information for new position

and time;

end

a factor in reproductive choice, even though size is

the only determining factor of an agent’s ability to

acquire energy and thus survive. The idea of selec-

tion based on agent ﬁtness does not fully apply here,

as any agent can attempt to reproduce with any other

agent. Fitter agents do have a higher chance of re-

production because they are more likely to consume

more food, have more energy for reproduction, and

will survive longer.

Notably, this simulation does not have a ﬁtness

function nor are the agents evaluated for ﬁtness. In-

stead, as the agents evolve, they will determine their

own preferences for what makes a good potential

mate. These preferences are evolved over time and

are passed down via standard crossover to offspring in

a similar way to that of the action chromosome. This

process is what we rely on for the agents to eventually

speciate, as over time the agents may develop speciﬁc

preferences that are only met by their own species.

Chromosomes inherited from the parents are pro-

duced through single point crossover with a 100%

chance of crossover, and mutation, which is bitwise

with a very low probability (1/300) of mutating a ran-

dom bit in the chromosome.

The GA used in our research is similar to a steady-

state GA, except that we do not use standard chromo-

some replacement, old individuals die when out of en-

ergy, and new individuals are added to the population

with no regard to the overall size of the population.

The size of the population does have a “soft cap” as

only so much food is generated per time cycle, but

that is the only limiting factor on the size of the pop-

ulation.

8 RESULTS

As in previous research, initial tests were done to

check the model (Parker and Edwards, 2018). These

tests showed that agent populations could evolve to

optimize for the available food sources and adjust

when both locations and types of food changed.

Tests were then created to replicate an environ-

ment that would allow allopatric speciation. A pop-

ulation of randomly generated agents was generated

on the grid while medium sized food was generated in

the center of the grid to encourage the agents to form a

single species. As expected, all large and small agents

died out during the formation of this initial popula-

tion, while a population of medium agents was estab-

lished in the center of the grid. Once this population

was fully established (around 5,000 time cycles), a

physical barrier was placed in the center of the grid,

dividing the existing population in half.

At the same time, food generation was changed.

On the left side of the wall, some medium food was

produced for a limited period while the majority of

food produced was changed to small food. On the

right side, a similar process was followed, with the

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310

Table 5: Results of Various Runs With Different Parameters.

Run Total Time Total Reproduction Total Total Attempts Total Number Of Run

Cycles Attempts Reproductions At Hybridization Hybrids Created Information

Full 1 40,000 24,214,134 586,723 789,205 0 Standard Run

Full 2 40,000 26,562,194 644,462 1,386,087 0 Only Large Food Produced

RGB 1 40,000 15,191,461 553,952 67,650 1,358 Reproduce on Age/Color

only change being that the majority of food would

now be large. After a period of adjustment (roughly

another 10,000 time cycles) all medium food genera-

tion was stopped.

As the agents evolved to adapt to their new en-

vironment, a population of small agents were estab-

lished on the left side of the wall while a population of

large agents were established on the right side of the

wall. These two populations were allowed to evolve

independently for a period of time (15,000 time cy-

cles), then the barrier was removed, and the two pop-

ulations were allowed to interact freely for a period

of time (10,000 time cycles) as food generation was

changed so that both large and small food was gener-

ated in the center of the grid.

When the barrier was removed, agents were

tagged to see if they would reproduce with a popu-

lation that was not their own (a different species). If

an agent of the left-side population reproduced with

an agent of the right-side population, their offspring

was called a ﬁrst-degree hybrid.

If this ﬁrst-degree hybrid (or any other degree of

hybrid) mated with any other agent in the population,

their offspring was called an n-th degree hybrid. We

reason that ﬁrst-degree hybrids could exist with dis-

tinct species (such as a horse and donkey making a

mule). However, for a successful test, the ﬁrst-degree

hybrid should never reproduce, meaning no n-th de-

gree hybrids.

We ran a series of runs starting from the random

agent generation stage and from there recorded the

number of hybrids produced. While many runs pro-

duced hybrids, in approximately 20% of runs the two

populations separated far enough that no ﬁrst-degree

hybrids were produced (and therefore no n-th degree

hybrids) [Table 5]. This successfully showed that our

method of using arbitrary characteristics could repli-

cate allopatric speciation without agents knowing the

ﬁtness value of other agents (as they could not see

each other’s size value).

A second test was designed to see the impact agent

size had in the separation of these populations. This

test was identical to the ﬁrst, with the change that both

sides of the barrier would generate large food. This

was done so that the agents on both sides of the bar-

rier would evolve to be large agent populations. In-

stead of a small agent population and a large agent

population, there would be two large agent popula-

tions. During this test, the agents were able to fully

speciate in some cases and produce no ﬁrst-degree hy-

brids when the two species were reintroduced [Table

5]. This test concluded that agent size had no impact

on agent reproductive choice and that agents of the

same size were able to successfully speciate.

A third test was designed to ﬁnd the impact of

adding the four arbitrary characteristics to the char-

acteristic chromosome. This test was identical to the

ﬁrst test; however, the agents were slightly modi-

ﬁed. The agent’s reproductive choice function was

changed to no longer consider the four character-

istics on the end of the characteristic chromosome

and solely determine reproductive choice based on

agent color and age. Based on the result that the

agents could not successfully speciate in a reasonable

amount of time without considering the four arbitrary

characteristics, we believe that the number of fea-

tures considered during reproductive choice directly

affects the difﬁculty of speciation. A notable aspect

of this test was that because the agents were less spe-

ciﬁc with their choice of mate, they had lower overall

energy and therefore attempted to reproduce less of-

ten. This led to a much lower number of hybridiza-

tion attempts than the previous tests while still hav-

ing roughly the same total overall reproductions. Al-

though we believe that speciation is theoretically still

possible within the parameters of this test, the less-

ened number of features considered for reproduction

seems to have increased the difﬁculty for the agents to

speciate, as the agents were never able to successfully

speciate in any of the trials that were conducted.

In the results of our testing, the agents were able

to evolve into separate species when a sufﬁcient num-

ber of features were considered during reproduction,

regardless of how those features affect ﬁtness. The

number of features seems to have directly affected the

difﬁculty the agents had in speciating and determining

if a potential mate was a member of a different species

or not.

9 CONCLUSION

The replication of allopatric speciation has been

achieved previously by Parker and Edwards, how-

ever, in that work it was recognized that agent selec-

Using Secondary Inherited Characteristics During Reproductive Choice to Replicate Allopatric Speciation

311

tion would need to be expanded in order to achieve a

more complete replication of speciation (Parker and

Edwards, 2019). In this paper, we have been able to

conclude that the goal of replicating allopatric spe-

ciation using solely agent selectivity and inﬂuential

characteristics has been achieved. Our system was,

in fact, more complete than previous work as when

the populations were reintroduced, in some cases no

ﬁrst-degree hybrids were produced whatsoever.

This increased completeness in speciation was

possibly because in the previous work, agents would

solely consider the size of a prospective mate due to

size being the primary ﬁtness deﬁning characteristic.

As this characteristic could randomly mutate, it would

be possible that this mutation could lead to an agent

that has the same size as a different species but was

not actually a member of that species. The simulation

described in this paper removes this possibility as the

chance of a random mutation affecting many different

characteristics in such a way that the agent would be

mistaken as a different species would be highly un-

likely.

Additionally, this new system of simulating al-

lopatric speciation has the added beneﬁt of being ca-

pable of producing separate species from agents of the

same size. This allows agents to evolve the features

that best ﬁt their environment, without compromising

the features used to decide mate selection. This also

decouples the number of possible species from the

number of different environments. In this system, a

large number of reproductively separate species could

develop from identical starting conditions.

In future work, we would like to explore the pos-

sibility of speciation without a hard barrier, such as

in the concept of ring species, where a chain of in-

tergrading species encircles a barrier and the terminal

species coexist without interbreeding. This alteration

would allow simulation of an alternative way for real

world speciation to occur. We also plan to attempt

sympatric speciation to see if there are conditions that

could make it possible.

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