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Speciation with gene flow in aheterogeneous virtual world: can physical

obstacles accelerate speciation?Abbas Golestani1,*, Robin Gras1,2 and Melania Cristescu2,3

1School of Computer Science, 2Department of Biology, and 3Great Lakes Institute,

University of Windsor, Windsor, Canada

The origin of species remains one of the most controversial and least understood topics in evolution. While it

is being widely accepted that complete cessation of gene-flow between populations owing to long-lasting

geographical barriers results in a steady, irreversible increase of divergence and eventually speciation, the

extent to which various degrees of habitat heterogeneity influences speciation rates is less well understood.

Here, we investigate how small, randomly distributed physical obstacles influence the distribution of popu-

lations and species, the level of population connectivity (e.g. gene flow), as well as the mode and tempo of

speciation in a virtual ecosystem composed of prey and predator species. We adapted an existing individual-

based platform, EcoSim, to allow fine tuning of the gene flow’s level between populations by adding various

numbers of obstacles in the world. The platform implements a simple food chain consisting of primary pro-

ducers, herbivores (prey) and predators. It allows complex intra- and inter-specific interactions, based on

individual evolving behavioural models, as well as complex predator–prey dynamics and coevolution in

spatially homogenous and heterogeneous worlds. We observed a direct and continuous increase in the

speed of evolution (e.g. the rate of speciation) with the increasing number of obstacles in the world. The

spatial distribution of species was also more compact in the world with obstacles than in the world without

obstacles. Our results suggest that environmental heterogeneity and other factors affecting demographic sto-

chasticity can directly influence speciation and extinction rates.

Keywords: speciation; gene flow; individual-based simulation; predator–prey system

1. INTRODUCTIONThe relative contribution of geography and ecology to

speciation remains one of the most controversial topics in

evolutionary biology. Models of speciation that involve geo-

graphically unrestricted gene flow (sympatric speciation) or

limited gene flow (parapatric speciation) are often con-

sidered unrealistic. The major theoretical problems with

models that assume gene flow stem from the antagonism

between selection and recombination and from the pro-

blem of coexistence [1]. It is generally assumed that while

selection acts to maximize the fitness optimum of popu-

lations, generating genetic and phenotypic divergence,

recombination continuously shuffles the co-adapted gene

complexes and brings populations together. Moreover,

sister species that are not sufficiently ecologically divergent

are believed to experience competitive exclusion that leads

to rapid extinction of emerging lineages [1]. The wide

range of theoretical conditions that diminish these major

conflicts [2,3] are considered by many critics to be biologi-

cally unrealistic, maintaining the long-lasting debate over

the likelihood of speciation with gene flow.

While placing level of gene flow at the centre of specia-

tion debates has extremely been successful in shaping

research programmes and directions [1], the simple dichot-

omy of sympatry and allopatry along with the static spatial

(biogeographical) context also has the potential to hinder

r for correspondence (golesta@uwindsor.ca).

ic supplementary material is available at http://dx.doi.org//rspb.2012.0466 or via http://rspb.royalsocietypublishing.org.

28 February 201229 March 2012 1

progress in the field. It has been suggested that conclu-

sions reached about the relative importance of various

mechanisms of speciation can be drastically different if

investigators use explicit geographical-pattern (biogeogra-

phical) concepts versus more demographic (population

genetic) criteria that imply a strict condition of original

panmixia outside the geographical context (e.g. sympatric,

allopatric) [4]. Clearly, many species have strong schooling

or homing behaviours or strong ecological preferences that

result in a non-random distribution of genetic diversity at

the onset of speciation. Moreover, habitat heterogeneity

can often enhance the local structuring of genetic variation.

Such strategies make the distinction between sympatric and

micro-allopatric speciation scenarios hard to disentangle

without very good knowledge of the early stages of specia-

tion. Moreover, the intense debate over the geography of

speciation has often left biologically relevant scenarios,

such as the intermediate parapatric conditions, out of the

research context.

There is no doubt that the complexity of natural systems

poses a great challenge when one tries to assign speciation

cases to discrete categories. Most species exhibit dynamic

changes in distribution that involve population expansions

and contractions, fragmentations and secondary contacts

across evolutionary relevant time scales [4–6]. Moreover,

macro-geographical barriers are also ephemeral on a

larger geological scale. At a fine local scale, the effect of

micro-geographical barriers depends largely on how impor-

tant the structure of the habitat is for dispersal rates. It has

recently been proposed that the complex context of specia-

tion can be better understood outside the framework of a

This journal is q 2012 The Royal Society

2 A. Golestani et al. Speciation in a virtual world

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classical geographical definition by focusing on the impor-

tant evolutionary forces such as gene flow, selection and

genetic drift [4].

In the area of ecosystem simulation, individual-based

modelling provides a bottom-up approach allowing for

the consideration of the traits and behaviour of individual

organisms. Instead of modelling an ecosystem as a whole,

individual-based models treat individuals as ‘unique and

discrete evolutionary entities’ [7]. By modelling organ-

isms with varying characteristics (such as age, mating

preferences and role in the ecosystem), the properties of

the system can emerge from their complex interactions.

This approach has advanced in various areas of appli-

cation such as forest ecology, fish recruitment modelling

and spatial heterogeneity depiction [8], and can effec-

tively be used in speciation research. Yet, few attempts

have been made to simulate a complex ecosystem. An

example of such a system is the platform Echo [8],

which includes an evolutionary mechanism allowing vir-

tual agents to evolve. However, the organisms in Echo are

relatively simple, and have no behavioural model. Another

system often used to study long-term evolution is Avida [9]

which allows studying emergence of complex behaviours in

populations of evolving digital organisms. It nevertheless

has limitations on the movement of individuals and is

based on one or more external fitness function(s), which

means that the system is more an optimization process

rather than a complex virtual world. Other models, such

as PolyWorld [10], Bubbleworld.Evo [11] or Framsticks

[12], include more complex agents and behavioural

models. They use artificial neural networks or systems of

learned rules to evolve the agent’s behavioural model

during their life or across generations. Unfortunately,

these approaches are highly computationally expensive,

allowing the implementation of populations composed of

only few hundred agents. They are, therefore, more appro-

priate for studying the evolution of learning capacities than

for studying large-scale evolutionary processes. More

specialized predator–prey models have also been proposed

[13], yet these particular models are dedicated to represent

specific schooling behaviours, and the evolution is an off-

line mechanism using a genetic algorithm suggesting that

the direction of the evolution is pre-determined.

In this study, we use an individual-based simulation

approach to investigate how physical obstacles (the rag-

gedness of the environment) influence population

connectivity (e.g. gene flow), the distribution of species

in space and time and ultimately the genomic cohesion

of species and speciation rates. We explore how randomly

placed physical obstacles that can be easily circumvented

by agents, influence the pattern and rate of speciation.

The major advantage of using an individual-based simu-

lation approach in speciation research is that it allows

for the modification and fine tuning of one property of

the whole system at a time. The effects of these modifi-

cations can be determined within a reasonable time

frame and over a large evolutionary scale.

2. MATERIAL AND METHODSIn this study, we use EcoSim (http://sites.google.com/site/

ecosimgroup/research/ecosystem-simulation) [14], a versatile

simulation platform that has been designed to investigate sev-

eral broad ecological questions (e.g. community formation),

Proc. R. Soc. B

as well as long-term evolutionary patterns and processes such

as speciation and macroevolution. In this programme, two

organism types, prey and predator, are simulated in a

torus-like discrete world which is a 1000 � 1000 matrix of

cells. Every cell can contain some amount of grass (varying

in time) which is the primary producer. To observe the

evolution of individual behaviour and ultimately ecosystems

over thousands of generations, several conditions need to

be fulfilled: (i) every individual should possess genomic

information; (ii) this genetic material should affect the indi-

vidual behaviour and consequently its fitness; (iii) the

inheritance of the genetic material has to be done with

the possibility of modification; (iv) a sufficiently high number

of individuals should coexist at any time step and their behav-

ioural model should allow for complex interactions and

organizations to emerge; (v) a model for species identification,

based on a measure of genomic similarity, has to be defined;

and (vi) a large number of time steps need to be performed.

These complex conditions pose computational challenges

and require the use of a model which allies the compact-

ness and easiness of computation with a high potential of

complex representation.

EcoSim uses a modified version of the fuzzy cognitive

map (FCM) model [15] adapted for behavioural modelling.

The FCM, coded in the genome of the individuals, is used

not only as the behavioural model of the individuals but

also as the vector of transmission of evolutionary information

[14]. The genomes are coded with real numbers, and are

therefore continuous. This approach offers compactness

with a very low computational requirement, while having

the capacity to represent complex notions. Although, each

agent is represented by a unique map, which is an inherited

modified combination of its parental genomes, the system

can still manage several hundreds of thousands of agents sim-

ultaneously in the world. This FCM contains sensory inputs

(e.g. predator_close, prey_close, food_close, mate_close,

energy_low), internal concepts (e.g. fear, hunger, sexual

need, curiosity, satisfaction) and motor concepts (e.g. escap-

ing, searching for food, eating, breeding, socializing or trying

to approach a potential sexual partner). Additionally, it

includes links and weights representing the mutual influences

(allowing feedback loops) of these concepts. Moreover, the

activation level of each motor concept depends on a complex

and a nonlinear combination of excitatory and inhibitory

influences from both sensory inputs and internal concepts.

Therefore, the action performed by an individual at a given

time step is the one corresponding to the motor concept with

the highest activation level (for details, see the electronic sup-

plementary material, §1, figure S1). Links between concepts

can appear or disappear, so that the structure and complexity

of the maps can change during the evolutionary process.

Each agent also possesses several physical or life-history

characteristics summarized in table 1. The energy is provided

by the primary or secondary resources found in their environ-

ment. For example, prey individuals gain 250 units of energy

by eating one unit of grass and predators gain 500 units of

energy by eating one prey. At each time step, each agent

spends energy depending on its action (e.g. breeding,

eating, running) and on the complexity of its behaviour

model (number of existing edges in its FCM). On an average,

a movement action such as escape and exploration requires

50 units of energy, a reproduction action uses 110 units of

energy and the choice of no action results in a small expendi-

ture of 18 units of energy. The food chain implemented in

Table 1. Several physical and life-history characteristics of individuals.

characteristic predator prey

maximum age 42 time steps+0–6 46 time steps +0–18minimum age of reproduction 8 time steps 6 time steps

maximum speed 11 cells per time step 6 cells per time stepvision distance 25 cells maximum 20 cells maximumlevel of energy at initialization of the system 1000 units 650 unitsaverage speed 1.4 cells per time step 1.2 cells per time stepaverage level of energy 415 units 350 units

maximum level of energy 1000 units 650 unitsaverage number of reproduction action during life 1.14 1.49average length of life 16 time steps 12 time steps

Speciation in a virtual world A. Golestani et al. 3

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our system consists of three levels; primary producers, preda-

tors and prey, allowing complex interactions between agents

with and between trophical levels.

One of the actions performed by the individuals is repro-

duction. Several factors play roles in reproduction. For

reproduction to be successful, the two parents need to be

in the same cell, have enough energy, choose the reproduc-

tion action and be genetically similar. The organisms

cannot determine their genetic similarity with their potential

partner. They try to mate and if the partner is too dissimilar,

the reproduction fails. The result of the reproduction action

is a unique offspring with a genome which represents a com-

bination of the parental genomes. The newborn receives an

initial amount of energy equivalent to the energy that the

two parents spend in reproduction.

EcoSim implements a species concept directly related to

the genotypic cluster definition [16] in which a species is a

set of individuals associated with the average of the genetic

characteristics of its members. The species map is computed

based on the average FCM matrices of all individuals. It is

considered that a species splits if the distance between the

genomes of the two most dissimilar agents is greater than a

predefined threshold [17,18]. Our species recognition

method involves the use of a 2-means clustering algorithm

in which an initial species is split into two new species,

each one of them containing the agents that are mutually

the most similar. Since the birth and death of individuals

influences the general composition of species [19] and spe-

ciation and extinction can occur at any time step, species

membership is evaluated at each time step. Although specia-

tion events are discrete, the complete speciation process is

spread over multiple time steps. With time, a species will pro-

gressively contain individuals that are genetically more and

more dissimilar up to an arbitrary threshold where it is con-

sidered that the species split. After splitting, the two sister

species are still very similar and hybridization events can

occur. Two individuals can interbreed if their genomic dis-

tance is smaller than an arbitrary threshold (half of the

speciation threshold) even if they are designated as members

of two sister species by our clustering algorithm (for details,

see the electronic supplementary material, §2, figure S2).

The frequency of hybridization events ranges between 2

and 5 per cent of the overall number of reproductive

events. On average, prey and predator individuals live for

12 and 16 time steps, respectively, with some individuals

living for up to 60 time steps. If we consider that a generation

is the time needed for a new born individual to have its first

reproduction, a generation is about eight time steps. This

Proc. R. Soc. B

indicates that a single run with 15 000 time steps corresponds

to about 2000 generations.

In terms of computational time, the speed of simulation

per generation is related to the number of individuals.

Recent executions of the simulation with an average of

250 000 individuals produced approximately 15 000 time

steps in 35 days. Each time step involves the time needed

for each agent to perceive its environment, make a decision,

perform its action, as well as the time required to update the

species membership, including speciation events and record

relevant parameters (e.g. the quantity of available food).

Although a run can involve the birth of more than one billion

individuals and thousands of species, all evolutionary events,

the mental state and action of every agent, are saved for every

time step of every run. This thorough tracking system enables

us to extract, to measure and to correlate parameters that are

useful to understand the underlying properties of such a

complex system.

Several studies evaluated the capacity of the EcoSim plat-

form to model real ecosystems and make realistic predictions

regarding species abundance patterns [19] and the complex-

ity levels of the simulation [18]. These studies show that the

communities of species generated by the simulation follow

the same lognormal law as natural communities and that

EcoSim can help evaluate the overall level of diversity of a

given community. Moreover, it was shown that the simu-

lation has a deterministic chaotic behaviour [20], similar to

many natural systems [21], and that the spatial distribution

of the individuals has multi-fractal characteristics [22].

In order to measure the effect of the raggedness of the

environment on population fragmentation and the speciation

process, we included small physical obstacles that obstruct

the movement (dispersal) of agents. The presence of obstacle

cells in the world is expected to impede the movement of our

agents, change their spatial distribution, and in turn influ-

ence dispersal and ultimately the gene flow between

populations (for details, see the electronic supplementary

material, §3). The reduction of gene flow should be pro-

portional to the raggedness of the world. We control the

level of gene flow by changing the percentage of obstacle

cells. We investigated how this impediment in the movement

of organisms, without any complete extrinsic barrier separ-

ating two subpopulations of an initial species, affects the

speciation frequency and the number of coexisting species.

We compared three different situations. We considered a

neutral configuration with no obstacles (the ‘density of

obstacles (0%)’ experiment). We also considered two virtual

worlds with various numbers of obstacles: 1 and 10 per cent.

(a) (b)

(c) (d)

Figure 1. An overview of the distribution of species and populations in the world with density of obstacles (10%) and the den-

sity of obstacles (0%) experiment. (a) View of the whole world in the density of obstacles (0%) experiment. (b) Magnified partof the world in density of obstacles (0%) experiment. (c) View of the entire world with obstacles. (d) Magnified part of theworld with obstacles. The blue squares are obstacle cells and dots are individuals. Different coloured dots represent differentprey species and white dots represent predator species.

4 A. Golestani et al. Speciation in a virtual world

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For example, in the experiment ‘density of obstacle (10%)’,

10 per cent of cells in the world are obstacles. For each exper-

iment, we conducted 10 independent runs using the same

parameters and averaged the results. To ensure that our

results are not dependent on special parameter values, several

speciation thresholds for prey (0.65, 1.3, 2.6) and predator

(0.75, 1.5, 3) were used. As the results for the three specia-

tion thresholds were very similar, we averaged them. All the

results represent the average of 30 experiments (10 runs�three speciation thresholds). To avoid any bias owing to a

variation in the number of free cells available after the

addition of obstacles, we maintained the number of free

cells constant by increasing the world size accordingly. We

analysed the variation of the number of species for both

prey and predator during the simulation process for several

numbers of obstacles. We also observed other properties of

the whole system, such as individual behaviours, spatial

distribution of species and the assembly and dynamics of

ecological communities.

3. RESULTS AND DISCUSSIONS(a) Global patterns

We investigated the global behaviour of our system in

different situations, by varying the number of obstacles.

We measured and monitored several representative

characteristics of the system, such as the number of

species, individual behaviour and spatial distribution of

Proc. R. Soc. B

the individuals that can give insight into the evolutionary

processes that shape the biodiversity of our virtual world.

An overview of the distribution of species reveals that

individuals show a strong clustering distribution with

circular or spiral shapes.

Individual’s distribution forming spiral waves is a com-

mon property of predator–prey models (see figure 1).

The prey near the wave break has the capacity to escape

from the predators sideways. A subpopulation of prey

then finds itself in a region relatively free from predators.

In this predator-free zone, prey individuals start disper-

sing rapidly forming a circular expanding region. The

predation pressure creates successive interactions between

prey and predators over time, the same pattern repeats

over and over again, leading to the formation of spirals.

Strong and robust spiral waves have been commonly

observed in complex and dynamic biological systems

[23]. Self-organized spiral patterns have been seen not

only within chemical reactions [24] but also among host–

parasitoid or predator–prey systems [23,25–27] even

when the world is uniform in terms of environment’s rag-

gedness [25,27]. Our system is closer to a predator–prey

system than a host–parasite system. Both the behaviour

of the species (dispersal ability), population numbers of

prey and predators, life-history characteristics (life span,

energy expenditure), reflect more a predator–prey system

than a host–parasite system. The global pattern of popu-

lation distribution in the world with obstacles is very

8000

7000

6000

5000

5000 10 000time steps

15 000

4000

3000

2000

1000

no. i

ndiv

idua

ls d

ivid

ed b

y no

. spe

cies

(pr

ey)

0

Figure 2. Comparison between numbers of (a) prey and (b) predator species in the whole world during 16 000 time steps. Eachcurve represents an average value obtained from 30 independent runs with three different speciation thresholds (blue line,density of obstacles (0%); green line, density of obstacles (1%); red line, density of obstacles (10%)).

Table 2. Average and standard deviation of the number and

size of spirals in the 30 independent runs of every configuration.

no. spiralssize of spiralsin cells

mean s.d. mean s.d.

density of obstacle (0%) 41 5 186 67density of obstacle (1%) 38 6 188 58

density of obstacle (10%) 43 8 181 73

Table 3. Average and standard deviation of the number of

species in the 30 independent runs for every configuration.

Nr prey species

version mean s.d. median

density of obstacle (0%) 27 9 25density of obstacle (1%) 68 16 61density of obstacle (10%) 94 19 82

Table 4. Measure of distribution dissimilarity by ANOVA

test for the time series representing the number of preyspecies. (Each comparison includes either two differentexperiments or a single experiment compared with itself.For two distributions, the higher the value is, the more

dissimilar the distributions are. When a single distribution isconsidered, the higher the value is, the higher the variancebetween the 30 runs of the same configuration is.)

density ofobstacle (1%)

density ofobstacle (10%)

density of obstacle (0%) 4.3016 � 103 2.5184 � 104

density of obstacle (1%) 116.629 517.2141density of obstacle (10%) 517.2141 93.1408

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similar to the one observed in the world of the experiment

with density of obstacles (0%) (figure 1) and these oscil-

latory dynamics are probably owing to the predator–prey

interaction [28]. It has been observed that the size and

number of spirals in all the experiments are almost the

same (table 2). Therefore, the existence of such patterns

is unlikely to explain the differences in speciation rates

between different experiments.

(b) Species richness and relative species abundance

The most important quantities of the system that we

monitored through time were species richness (the total

number of species), as well as species abundance (the

number of individuals per species) in the world during

the entire simulation process and across multiple simu-

lations. Our results indicate that the number of species

for both prey and predators increases directly with the

number of obstacles (figure 2). Our results reveal that

the total number of prey and predator species in the

world is higher in the two configurations with obstacles

compared with the no obstacles configuration. Moreover,

the number of species in the configuration with 10 per

cent obstacles is much higher than the number of species

for another configuration with obstacles.

The computed average and standard deviation of the

number of species during the whole process for prey

population (table 3) reveal clear differences between the

three experiments. This suggests that the speciation rate

is directly proportional to the restriction of movement

Proc. R. Soc. B

and therefore to gene flow between populations. As the

total numbers of individuals in the three configurations

are almost the same, it follows that the number of individ-

uals per species decreases when obstacles are added in

the world.

The computed ANOVA statistical tests [29] revealed

that the observed differences in species richness between

the experiments were significantly different (table 4).

Even if the values obtained are higher than the 5 per

cent confidence threshold, the difference observed

between the inter-class values and the between-classes

values strongly confirms that the variations observed for

the number of species are highly significant for prey

species. The average number of species with the density

0.25(a) (b)

(c) (d)

0.20

0.15

0.10

0.05

0

% p

opul

atio

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at f

ail

in r

epro

duct

ion

0.25

0.20

0.35 6

5

4

3

2

1

0

0.30

0.15

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opul

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at f

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epro

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ocia

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opul

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at f

ail

in s

ocia

lizat

ion

(× 1

0–3)

0 1000 2000 3000 4000 5000time steps

6000 7000 8000 1000 2000 3000 4000 5000time steps

6000 7000 80009000

Figure 3. Percentage of prey individuals that fail in (a,c) reproduction action and (b,d) socialization between the various densityof obstacles (1% and 10%) configuration and the density of obstacles (0%) configurations. The red curves represent the den-

sity of obstacles (0%) experiment and the blue curves represent the experiments with various densities of obstacles ((a,b) 1%and (c,d) 10%). Each curve is an average value obtained from 30 independent runs with three different speciation thresholds.

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of obstacles (10%) configuration is more than five times

that of the density of obstacles (0%) configuration.

Our results clearly show that the addition of obstacles

in the world is associated with an increase in the number

of species. Population genetic theory predicts that natural

selection and genetic drift cause populations to diverge

from each other while migration resulting in gene flow

acts in an opposite direction creating genetic homogen-

eity. We suggest that obstacles lead to an impediment in

dispersal, more geographical isolation, less migration

and gene flow. This overall lower level of population

connectivity leads to rapid differentiation. Eventually,

populations will contain individuals with genome dis-

similarities higher than the speciation threshold, leading

to speciation.

(c) Variation in individual behaviours

The results on species richness confirm that the restric-

tion in the movement of species owing to scattered

physical obstacles is strongly correlated with the fre-

quency of speciation events. In order to verify that the

increased speciation rate cannot be explained by other

factors such as the change in the behaviour of the

agents, we monitored the actions performed by prey

individuals in the three configurations. Most of the

actions chosen by the individuals (e.g. feeding, predator

avoidance, prey chasing) were the same in the three con-

figurations although a slight difference was identified on

reproduction and socialization (figure 3). The decision

for the individual to conduct these actions is done first

using their behavioural models. Different situations can

then lead to a failure of individuals to execute these

actions. The reproduction action fails either because the

agent cannot find a partner for reproduction, or has insuf-

ficient energy, or the two partners are genetically too

Proc. R. Soc. B

different. The action of socialization fails because the

agent cannot reach the place where the chosen partners

are located. Our results suggest that the number of

failed socialization events is much higher and much

more variable in the density of obstacles (0%) configur-

ation than in all obstacle experiments (see figure 3b,d).

This is probably a direct consequence of the fact that

the species have much smaller spatial distribution in

obstacle configurations, making the socialization action

easier to perform (the genetic similarity between agents

is not considered for this action). However, the number

of failed reproduction actions is significantly higher

when the raggedness of the world increases (figure 3c).

This is probably owing to the higher genetic distance

between individuals often found in close proximity (data

not shown). This result enforces the hypothesis that the

presence of obstacle cells in the world increases the gen-

etic distance and therefore the speciation rate even in

situations where the heterospecific individuals are more

spatially compact.

(d) Spatial distribution of populations and species

Spatial distribution of species was shown to have a strong

influence on their extinction rates [30,31] as well as the

relationship between physical distance and genetic dis-

tance [32]. For example, it has often been documented

that the risk for species to become extinct increases

when its distribution area is reduced and when its demo-

graphy is low [30]. Moreover, a regular increase of genetic

distance with increasing geographical distance has been

predicted [32] and documented often in broad phylogeo-

graphical surveys or organisms with various life-history

attributes and dispersal abilities [33].

To evaluate the spatial distribution of the species, we

used a measure, based on an average distance of all the

Table 5. The average and standard deviation of individuals’ average distances around the spatial centre of the species in the

30 independent runs corresponding to the three speciation thresholds for the three configurations.

time steps

3000 7000 10 000 13 000

density of obstacle (0%)mean of spatial average distance 173.11 184.609 154.80 118.69s.d. of spatial average distance 73.29 104.33 82.32 94.84

density of obstacle (1%)

mean of spatial average distance 135.80 107.68 93.89 79.15s.d. of spatial average distance 63.19 54.37 51.11 52.30

density of obstacle (10%)mean of spatial average distance 97.57 81.11 64.74 62.03s.d. of spatial average distance 49.62 43.19 46.38 41.37

Table 6. The median of maximum distances between

individuals around the centre of species in the 30independent runs corresponding to the three speciationthresholds for the three configurations.

density ofobstacle

(0%)

density ofobstacle

(1%)

density ofobstacle

(10%)

maximum spatial

distribution

310.45 186.13 129.58

Speciation in a virtual world A. Golestani et al. 7

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members of a species to its physical centre. This measure

is expressed in a number of cells and gives an accurate

evaluation of the distribution area of a particular species

in the world. The average and standard deviation of indi-

viduals’ average distances around the centre of each

species taken from 10 independent runs show that the

species have a more compact distribution in the obstacle

versions (table 5).

Knowing that in a torus world of size 1000 � 1000

cells the largest possible distance between two points is

about 700 cells, the average values observed for the den-

sity of obstacles (0%) configuration, which can be more

than 180 cells, are quite large. This suggests that, in the

density of obstacles (0%) configuration, many species

have a widespread spatial distribution covering a large

part of the world. By contrast, in the world with obsta-

cles, species show a much more restricted geographical

distribution which means that the species’ spatial distri-

bution decreases proportionally with the increase in the

number of obstacles. These results are also confirmed

by the strong negative correlation between number of

obstacles and the maximum observed spatial distribution

of a species (table 6). The high value of the standard devi-

ation for all configurations can easily be explained by the

high variability of the number of individuals by species.

Our communities of species display show a log-normal

distribution pattern commonly found in nature [19]. This

property leads to an important diversity in terms of

number of individuals per species, which in turn explains

the observed high variance in spatial distribution.

Obstacle cells strongly affect the spatial distribution

of the individuals by reducing the total number of subdi-

vided populations that constitute a species (for details, see

the electronic supplementary material, §3, figure S4). For

most of the species, several spatially separated popu-

lations are observed in the density of obstacles (0%)

configuration, whereas only one compact population is

observed in the obstacle configurations.

(e) Fuzzy cognitive map evolution

The composition of species in our virtual world depends

on the fine balance between speciation and extinction.

The high species richness in the obstacle worlds could

be owing to an accelerated speciation rate, a decelerated

extinction rate, or a combination of both. In order to

Proc. R. Soc. B

investigate the factors driving the biodiversity of the

three virtual worlds, we analysed the level of genetic diver-

gences between the initial genome and the genome of all

individuals at every time step. In the initial populations,

every prey or predator individual has the same genome.

However, after roughly 50 time steps (about six gener-

ations), when all the founding individuals are dead, the

genome of each agent is unique, and is the outcome of

the evolutionary process. To evaluate the speed of evol-

ution in our simulation, we compared the average

distance [14] between all existing prey or predator gen-

omes at any time step with the two initial genomes of

prey and predators.

This average distance computed for a total of 5000

time steps (figure 4) indicates that the overall genetic

divergence of the community of prey and predator species

is greater in obstacle trials than in the density of obstacles

(0%) experiment. The more obstacles in the world, the

steeper the slope of the curve. This suggests that evol-

ution accelerates with the number of obstacles.

Given that this result shows only global information

(at the community level) about speciation patterns,

changes at the intraspecific level or between closely related

species are also very informative. We measured the speed of

divergence between two sister species after a speciation

event. In EcoSim, a species is associated with a genome

which corresponds to the average genome of all its individ-

uals allowing us to compute a distance between the

‘genome’ (called centre) of two species. We considered 20

independent speciation events for each of the three con-

figurations. We then computed the distance between the

centres of the two new species after the speciation event

60005000time steps

gene

tic d

ista

nce

from

initi

al F

CM

40003000200010000

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 4. Average genetic distance between the community genomes (all individuals of prey or predators) at time zero and timex for the three configurations. Each curve is an average value obtained from 30 independent runs with three different speciationthresholds. Blue line, density of obstacles (0%); green line, density of obstacles (1%); red line, density of obstacles (10%).

0

0.66

0.64

0.62

0.60

0.58

0.56

0.54

0.52

0.50

0.48

gene

tic d

ista

nce

betw

een

two

spec

ies¢

FCM

aft

er s

pliti

ng

50 100 150 200 250time steps after spliting

Figure 5. Average genetic divergence between the FCMs of sister species after their splitting for the three configurations. Eachcurve is an average of 600 couples of sister species (30 runs � 20 couples of sister species). Blue line, density of obstacles (0%);

green line, density of obtacles (1%); red line, density of obstacles (10%).

8 A. Golestani et al. Speciation in a virtual world

on April 19, 2012rspb.royalsocietypublishing.orgDownloaded from

occurred across 250 time steps (figure 5). It can be noticed

that, as expected, sister species diverge quite quickly after

speciation. After speciation, hybridization events are quite

rare because in each of the newly emerged species the indi-

viduals are highly similar, but dissimilar from the ones of

the sister species. As a result, gene flow between the two

species is probably very low and leads to fast divergence.

More noteworthy, the speed of divergence is much higher

when there are obstacles in the world. Once again, it is

clear that this phenomenon is continuous, as the speed of

divergence increases proportionally with the number

of obstacles.

To understand if the reduction in gene flow is enough

to explain the speed of divergence, we also considered the

effect of obstacles on spatial distribution of sister species.

We computed the average geographical distance between

the physical centres of the emerging species after specia-

tion events occurred and across 250 time steps for 20

Proc. R. Soc. B

speciation events (figure 6). We observed that the physical

distance between species is smaller in the world with

obstacles than that without. This result can be correlated

to the fact that the number of individuals per species is

smaller and the spatial distribution of individuals is

more compact for an obstacle than density of obstacles

(0%) configurations. It is interesting to note that even if

there are high variations in these spatial distances, there

are no visible trends to an increase of distance between

species after speciation in the three configurations.

4. CONCLUSIONSUsing a modified EcoSim individual-based platform to

implement various degrees of physical obstacles that

restrict the movement of individuals and probably

reduce gene flow, we compared three different configur-

ations with different densities of obstacles. It is clear

100 150 200 250500300

350

400

450

500

550

time steps after spliting

spat

ial d

ista

nce

betw

een

two

spec

ies

posi

tion

afte

r sp

litin

g

Figure 6. Average spatial distance between the spatial centre of two sister species after their splitting for the three configur-ations. Each curve is an average of 600 couples of sister species (30 runs � 20 couples of sister species). Blue line, densityof obstacles (0%); green line, density of obtacles (1%); red line, density of obstacles (10%).

Speciation in a virtual world A. Golestani et al. 9

on April 19, 2012rspb.royalsocietypublishing.orgDownloaded from

that the speciation rate and species diversity is directly

proportional to the roughness of the physical environ-

ment. Our study also reveals that species are more

spatially compact in the configurations with obstacles

than in the world of the experiment with density of

obstacles (0%). Moreover, the continuous reduction in

spatial distribution as the number of obstacles increases

results in low levels of gene flow between sister species.

Therefore, the rapid genomic divergence between species

should be directly linked to the reduction of movement

owing to obstacles that result in low gene flow and rapid

divergence between subdivided populations. We investi-

gated several factors that could be involved in the

increase of speciation rate, such as the individual’s beha-

viours, the spatial distribution of the species, or the

overall speed of evolution (increase in genetic divergence

between sister species). We show that the faster divergence

between populations and accelerated speciation cannot be

explained by an increase of spatial separation during

the initial stage of speciation or different behaviours of the

individuals. We suggest that this is probably owing to the sig-

nificantly lower population sizes in obstacle configurations.

This reduced size, results in more pronounced genetic

drift and rapid differentiation between populations that

experience relatively low levels of gene flow.

It is well accepted that the effect of micro-geographical

barriers (e.g. the raggedness of the environment) to main-

tain population cohesion and the genetic homogeneity of

a species depends heavily on the intrinsic properties of the

species (e.g. dispersal ability, intra- and inter-specific

interactions). We suggest that the complex context of spe-

ciation can be better understood outside the framework of

a classical geographical definition of speciation (e.g. sym-

patric, allopatric) by focusing on the complex interactions

at the community level.

Speciation and extinctions are very important pro-

cesses that influence the species composition of an

ecosystem at a particular time and the long-term

dynamics of ecological communities. Our approach

allows testing of the unified neutral theory of biodiversity

and biogeography proposed by Hubbell [34] which

Proc. R. Soc. B

suggests that the persistence of ecologically equivalent

species in sympatry across relevant time scales might

not depend strictly on complex niche differences. Our

results suggest that factors affecting demographic stochas-

ticity (e.g. factors shaping the density of individuals in a

local area, the extent of the distribution of species in

space) can influence speciation and extinction rates and

ultimately the distribution of relative species abundance.

Our approach has demonstrated its use in modelling sev-

eral important biological problems and it seems possible

to modify it to represent many new ones. However, the

FCM model has some limitations because it cannot

evolve new sensory inputs or new actions. The complexity

of the model also grows with the square of the number of

such concepts, limiting this application to relatively

simple behavioural models. Since our simulation takes

into account spatial information and individual behaviour

while allowing the creation of new species and, more

importantly, the growth rate of species is not fixed, it is

difficult to determine if varying the growth rates of species

or predator pressure would lead to different distributional

patterns without testing it. A more in depth analysis of the

effect of reproduction rates and predator pressure on the

spiral formation is needed.

We thank D. Bock, J. Vaillant and B. MacPherson forcomments on the manuscript. This work was supported bythe NSERC grant ORGPIN 341854, the CRC grant 950–2-3617 and the CFI grant 203617 and is made possible bythe facilities of the Shared Hierarchical Academic ResearchComputing Network (SHARCNET: www.sharcnet.ca).

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