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DIGITAL SEX: CAUSES AND CONSEQUENCES OF RECOMBINATION
By

Dusan Misevic

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Zoology
Ecology, Evolutionary Biology, and Behavior Program

2006

ABSTRACT
DIGITAL SEX: CAUSES AND CONSEQUENCES OF RECOMBINATION
By
Dusan Misevic
The evolution of sexual reproduction has long been a major problem in biology. It is a
vibrant and fascinating area of research, rich with theories but poor in experimental
results. The crux of the sexual paradox is the dominance of the sexual mode of
reproduction in the natural world in spite of the apparent costs associated with
recombination. In this dissertation I test two different theories about the evolution of
sexual reproduction and also investigate effects of recombination on genetic architecture.
According to one theory, sex opposes the fitness-destroying process of Muller’s

ratchet, which occurs by the stochastic loss of high-fitness genotypes in small
populations. Sex opposes the ratchet by allowing genotypes with different deleterious
mutations to produce mutation-free offspring. In Chapter 1 I used the Avida digital-
evolution Sofiware to investigate sex in relation to Muller’s ratchet. Populations of
digital organisms mutated, competed, and evolved in a complex environment.
Populations were either asexual or sexual; in the latter case, parental genomes
recombined to produce offspring. I also varied genomic mutation rates and population
sizes, which at extreme values often caused mutational meltdowns and population
extinctions. My results demonstrate that sex is advantageous for population survival
under some conditions. However, differences in extinction probabilities were usually
small, occurred over a narrow range of mutation rates and population sizes, and the mean

fitness of surviving asexual populations was often greater than in sexual populations.

Theory suggests that modularity promotes evolvability, and that aggravating
(synergistic) epistasis among deleterious mutations facilitates the evolution of sex. In
Chapter 2, by contrast, I investigate how genetic architecture is shaped by reproductive
mode. I allowed 200 populations of digital organisms to evolve for over 10,000
generations while reproducing either asexually or sexually. For ten randomly chosen
organisms from each population, I constructed and analyzed all possible single mutants
as well as one million mutants at each mutational distance from two to, ten. The genomes
of sexual organisms were more modular than asexual ones; sites encoding different
functional traits had less overlap and sites encoding a particular trait were more tightly
clustered. Net directional epistasis was alleviating (antagonistic) in both groups,
although the overall strength of this epistasis was weaker in sexual than asexual
organisms. My results Show that sexual reproduction profoundly influences the evolution
of the genetic architecture.

In Chapter 3 I demonstrate that sex can evolve de novo and outcompete the
asexual mode of reproduction under changing environmental conditions. I evolved large
populations of digital organisms for thousands of generations in six environments with
different periods of substrate change. Sex was the dominant mode of reproduction when
the environments were changing rapidly, with up to 65% of populations evolving to
reproduce sexually. The ancestral reproductive mode and genetic architecture had only
weak effects on whether populations evolved to be sexual or asexual. I also found that in
the environmental conditions where sex was prevalent, the sexual populations on average
had higher fitness than asexual ones. Chapter 3 experimentally demonstrates the

importance of changing environments for the evolution of sex.

ACKNOWLEDGEMENTS

The road to my Ph.D. degree has definitely been long and winding, but fortunately has
been lined by a great number of colleagues, collaborators, and friends. While in more
ways than one I typically avoided a straight and narrow path, they helped keep me on
track, and I certainly would have never made it without their support, advice, and help.

First and foremost, I must acknowledge and deeply thank my advisor, Richard. E.
Lenski. For years I have been jokingly proclaiming that “I want to be a scientist when I
grow up” and Rich has been instrumental in getting me much closer to that goal. I look
forward to conducting independent research in the future, but sometimes wish I could
spend 6 more years learning from and working with Rich. He is a truly incredible mentor
and scientist, and I can just hope that a bit of his excellence has rubbed off on me over the
years. The opportunity and privilege of being Rich’s graduate student made the six long
years in the cold and very Midwestern city of East Lansing well worth it.

Charles Ofn'a, my co-advisor, has been a great asset and help on the
computational side of things, patiently introducing me to the world of Avida, Matlab, and
C++. Also a wonderful friend, Charles never hesitated to offer a helping hand, whether it
was a couch to crash on or a ride to the airport. Charles is an impressive rising-star
scientist as well as a warm, open, and good-natured person. Just by being himself he has
been an incredible role model, and will remain someone I look up to.

My committee members, Donald J. Hall and Robert T. Pennock readily jumped
into the world of digital evolution bringing a diverse and substantial expertise. Their

objective and novel views constantly challenged me, for which I am very thankful.

Chris Adami, my “academic grandfather”, has left a Significant imprint on my
graduate career in spite of the geographical distance separating us. His probing and
insightful comments and questions have helped me on many occasions and will continue
to motivate me in the future.

Members of the Lenski and Ofria labs have created an uniquely challenging and
supportive working environment, each and every person contributing to numerous
discussions that have shaped my scientific thinking and growth. My thanks go to all of
them: Elizabeth Ostrowski, Bob Woods, Tim Cooper, Kristina Hillesland, Chris Borland,
Christopher Marx, Paco Moore, Susi Remold, Daniel Rozen, Gabriel Yedid, Sean
Sleight, Zachary Blount, Brian Baer, Kaben Nanlohy, Neerja Hejela, Donna Ellis, Sherri
Goings, Jeffery Clune, Jason Stredwick, Art Covert, Matthew Rupp, David Michael
Bryson, Dehua Hang, Wei Huang, Larry Wisne, and Anastasha Kamps.

Never a true workaholic, I would have not been capable of completing my
graduate studies without some quality down time. The diverse group of great friends that
I have made in East Lansing kept me happy and sane, put up with my quirks, shared the
good and bad times with me. While working on my laptop and drinking numerous
espresso shots in the “Espresso Royal Cafe” (where these acknowledgments are being
written) and relaxing at the neighboring “Peanut Barrel” (where I will go after these
acknowledgements are completed, and do my best not to drink numerous non-espresso
shots) I have found a community of incredible people that took me in and made my stay
in East Lansing more fun than I expected or even hoped for. I could never list or truly
thank them all and can just hope they remain in my life for many years to come: Dan

Ducat and his family, Anthony Wittman, Ashley Nebe and her family, Elizabeth

Ostrowski, Bob and Andrea Woods, Keron Greene, Seth Walk, Chris Cobb and his
family, Jason Bryans and his family, Billy Baldwin, Martha Sedivec, Billy Bewick,
Tristan Zamp, Pete and Drew Weiss.

I have been gone from my home in Belgrade, Serbia for over 11 years and yet so
many great friends still remain there: Sasa Novakovic, Aleksandar and Dubravka
Antonijevic, Jelena Gaus, Jelena Milic, Ana Tomic, Ksenija Simic, Marjana Todorovic,
Dejana Gajic, and Dusan Maljkovic. Always accepting me for who I am, they helped me
though many hard times and are always in my heart and mind.

I must also express my thanks to the amazing educators and friends Borka Pesic,
Vida Ognjanovic, Radmila Stefanovic, Tordis Isselhardt, and Jill Hayes. They thought
me mathematics, literature, and English language but, more importantly, they recognized
and nourished a potential in me that I hope I am beginning to fulfill.

My many relatives, most notably my aunts and uncles Petar and Lepa Hristovic
and Dusanka and Dragan Nikolic, have sincerely celebrated and appreciated my
academic achievements and have always lent a helping hand to my family and me.

My final words are about my parents Ljubica Hristovic Misevic and Mirko
Misevic. They have not only unconditionally loved me and supported all my endeavors,
but have also sacrificed so much for my benefit, always putting my future and well being
first. My dad is now with me only in spirit but I know he would share my joy and
happiness at this time. I remain forever indebted to my parents, humbled by the
examples their lives set, and hopeful all my gratitude and love is at least somewhat
reflected in my personal and professional accomplishments. I hope they are just half as

proud to have me as their son as I am to have them as my parents.

vi

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................... ix
LIST OF FIGURES ......................................................................................................... xi
CHAPTER 1

SEXUAL REPRODUCTION AND MULLER’S RATCHET IN DIGITAL
ORGANISMS

Abstract ................................................................................................................... 1
Introduction ............................................................................................................. 2
Materials and methods ............................................................................................ 4
The Avida system ............................................................................................... 4
First evolutionary stage ...................................................................................... 7
Second evolutionary stage .................................................................................. 8
Results and discussion ............................................................................................ 9
Adaptation and decay ......................................................................................... 9
Population survival and extinction ..................................................................... 9
Mean fitness of surviving organisms .................................................................. 12
Distribution of mutational effects ....................................................................... 14
Summary and future directions ........................................................................... 15
CHAPTER 2

SEXUAL REPRODUCTION RESHAPES THE GENETIC ARCHITECTURE OF
DIGITAL ORGANISMS

Abstract ................................................................................................................... 17
Introduction ............................................................................................................. 1 8
Materials and methods ............................................................................................ 21
The Avida system ............................................................................................... 21
Modularity .......................................................................................................... 23
Mutational sensitivity and epistasis .................................................................... 26
Statistics .............................................................................................................. 27
Results ...................................................................................................................... 27
Evolved sexual organisms have higher fitness and longer genomes .................. 27
Evolved sexual organisms have more modular genomes ................................... 30
Mutational sensitivity and epistasis differ between sexual and asexual
organisms ............................................................................................................. 31
Discussion ............................................................................................................... 35
Relationships between the genetic architectural parameters .............................. 37
Implications for the evolution of sexual reproduction ....................................... 39

vii

CHAPTER 3

EXPERIMENTAL EVIDENCE OF EVOLUTION OF SEX IN CHANGING
ENVIRONMENTS

Abstract ................................................................................................................... 41
Introduction ............................................................................................................. 41
Methods ................................................................................................................... 43
Results and discussion ............................................................................................. 48
APPENDIX
Phenotypes in Avida ................................................................................................ 73
Resolving genome length issues .............................................................................. 74
Reduced data set ................................................................................. 75
Genome doublings prevented .................................................................................. 76
REFERENCES ............................................................................................................... 78

viii

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

Table 10.

Table 1 1 .

Table 12.

Table 13.

LIST OF TABLES

Survival of sexual and asexual populations when population size is small
and Muller’s ratchet operates ...................................................................... 11

Distribution of one-step mutational effect on fitness in sexual and asexual
ancestor of some second-stage populations ................................................ 14

Comparison of properties between sexual and asexual evolved
populations .................................................................................................. 29

Two-way AN OVA testing the effects of the period of environmental
change and the substrate metabolic values on the proportion of time
populations were dominated by sexual organisms ..................................... 53

Two—way ANOVA testing the effects of the initial mode of reproduction
and period of environmental change on the proportion of time
populations were dominated by sexual organisms ..................................... 58

Two-way ANOVA testing the effects of the initial mode of reproduction
and period of environmental change on the proportion of time
populations were dominated by sexual organisms ..................................... 58

Discriminant analysis for the final mode of reproduction under six
periods of environmental change ................................................................ 61

Discriminant analysis for the final mode of reproduction under six
periods of environmental change ................................................................ 62

One-way ANOVA testing the effects of the period of environmental
change on the proportion of time populations were dominated by sexual
organisms .................................................................................................... 69

Linear and quadratic fits of proportion of time spent sexual to log“)

transformed period of environmental change for populations evolving
with 10 or 25 nutrients at a time ................................................................. 69

Two-way ANOVA testing the effects of the mode of reproduction and
the period of environmental change on mean fitness ................................. 71

Truth table for nine logic operations .......................................................... 74

Comparisons of properties between sexual and asexual evolved
populations in the reduced data set ............................................................ 77

Table 14. Comparisons of properties between sexual and asexual evolved
populations with genome doublings prevented .......................................... 77

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 1 1.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

LIST OF FIGURES

Trajectories for maximum fitness and resource use during evolution in
large and small asexual populations ........................................................... 10

Distribution of mean fitness in asexual and sexual populations that
survived Muller’s ratchet ............................................................................ 13

Genotype-phenotype maps illustrating physical and functional

modularity ................................................................................................... 25
Final distribution of average fitness (a) and genome length (b) in sexual

and asexual populations .............................................................................. 28
Genomic modularity of sexual and asexual organisms ............................... 33

Average fitness as a function of the number of one point mutations in
evolved sexual (a) and asexual (b) organisms ............................................ 34

Principal component analysis for average fitness, genome length, a, B,

PM and FM of sexual and asexual digital organisms ................................. 38
Different periods of change in substrate metabolic values ......................... 47
Proportion of sexual organisms present in a population over time ............. 50
Prevalence of sexual reproduction under 24 different treatments ............... 52

Relationship between the prevalence of sex and the ancestral mode of
reproduction ................................................................................................. 56

Proportion of time during experimental evolution that each population
was predominantly sexual ........................................................................... 57

Number of times each ancestral population evolved to be sexual .............. 65

Prevalence of sexual reproduction in environments with different
numbers of nutrients .................................................................................... 67

Average fitness of predominantly sexual and predominantly asexual
populations ................................................................................................... 70

xi

CHAPTER 1

SEXUAL REPRODUCTION AND MULLER’S RATCHET IN DIGITAL
ORGANISMS

ABSTRACT
The evolution of sexual reproduction has long been a major problem in biology.
According to one theory, sex opposes the fitness-destroying process of Muller’s ratchet,
which occurs by the stochastic loss of high-fitness genotypes in small populations. Sex
opposes the ratchet by allowing genotypes with different deleterious mutations to
produce mutation-free offspring. We used the Avida digital-evolution software to
investigate sex in relation to Muller’s ratchet. Populations of digital organisms mutated,
competed, and evolved in a complex environment. Populations were either asexual or
sexual; in the latter case, parental genomes recombined to produce offspring. We also
varied genomic mutation rates and population Sizes, which at extreme values often
caused mutational meltdowns and population extinctions. Our results demonstrate that
sex is advantageous for population survival under some conditions. However,
differences in extinction probabilities were usually small, occurred over a narrow range
of mutation rates and population sizes, and the advantage of sex for population survival
required many generations. Also, the mean fitness of surviving asexual populations was
often greater than in sexual populations. This last result indicates the need for work that
compares the statistical distribution of mutational effects and epistatic interactions in

asexual and sexual populations.

INTRODUCTION
The mixing .of genomes via sexual reproduction and the resulting recombination of
genetic variants are widespread and important to life on Earth (Bell 1982; Maynard Smith
1978). For over a century, biologists have sought to explain the evolutionary origin and
maintenance of sex (Ghiselin 1988; Weismann 1889; West et al. 1999). While there have
been important advances, there are still more questions than answers, making this
research area both interesting and active (Rice 2002).

There are many potential costs associated with sexual reproduction, including
time and energy spent in searching for a suitable mate and in the act of mating (Lewis
1983). Moreover, at the genetic level there often exists a two-fold cost of sex, which is
variously called the cost of meiosis or the cost of males. This cost alone implies that
asexual populations should grow twice as fast as sexual ones, all else being equal
(Maynard Smith 1971 ). This two-fold cost presents a major hurdle that must be
overcome if the evolution of sex is to be understood. Many theories have been proposed
to explain why sex arose and how it persists despite these costs, but most have not been
adequately tested (Kondrashov 1993) and none are broadly supported by those tests that
have been performed to date (West et al. 1999). One of the main theories is attributed to
the famous geneticist H. J. Muller, and it proposes that sex is beneficial in opposing what
is now referred to as Muller’s ratchet.

Muller’s ratchet is a stochastic process that leads to the loss of genetic
information from asexual populations via the loss of those high-fitness genotypes that are
free of any deleterious mutations (F elsenstein 1974; Muller 1964). The ratchet depends

on both mutation and drift, where drift refers to changes in gene frequencies caused by

the random sampling of a finite number of genes from the previous generation. Drift is
especially important, and selection is relatively weak, in small populations that are most
sensitive to sampling effects. By chance, the most fit genotypic class can be lost from a
small population, especially if the genomic mutation rate is high. Once this class is lost
from an asexual population, it cannot be recovered owing to the low probability of
beneficial mutations in a small population. The metaphorical ratchet has thus advanced
one notch and its action is irreversible; each subsequent loss of the most fit genotypic
class advances the ratchet another notch. By contrast, in a sexual population the most fit
class can potentially be reconstructed, even after it has been lost, via recombination
between two genotypes that carry different mutations. The harmful effects of Muller’s
ratchet are thus opposed by sex.

Small populations subject to the ratchet may even go extinct if the resulting
fitness decay causes the birth rate to drop below the death rate. This feedback can
produce a vicious cycle, in which declining fitness leads to a drop in population size,
which speeds up the ratchet causing further fitness loss. This cycle has been described as
a mutational meltdown (Lynch et al. 1993; Lynch et al. 1995). In this study, we use
population survival as one metric to compare the effect of Muller’s ratchet in sexual and
asexual populations.

Several experiments have shown the fitness-destroying effect of Muller’s ratchet
in diverse microorganisms including viruses (Chao 1990; Duarte et al. 1992), bacteria
(Andersson and Hughes 1996), and protozoa (Bell 1989). At least one study with viruses
further showed that genetic recombination could Oppose the ratchet (Chao and Tran

1997). Research in evolutionary computation has also examined the ratchet, with an

emphasis on designing strategies to eliminate its adverse effects from applied
optimization algorithms (Laumanns et al. 2001; Nowak and Schuster 1989; Piirgel-
Bennett 1997; Zitzler et al. 2000). However, questions about the operation of Muller’s
ratchet and its interaction with reproductive mode are difficult to answer using biological
systems (Kondrashov 1982; Maynard Smith 1988). In this paper, we therefore use digital
organisms to examine the effects of Muller’s ratchet over a range of population sizes and
mutation rates, and we test whether sexual reproduction can substantially impede the

ratchet’s harmful effects.

MATERIALS AND METHODS
The Avida system. We use digital evolution software called Avida to study Muller’s
ratchet and its interaction with reproductive mode. Avida maintains and monitors
experimental populations of digital organisms, which are self-replicating computer
programs written in a customized assembler-like language (Adami 1998; Ofria and Wilke
2004). Avida has been used for several other studies of evolutionary dynamics and
outcomes (Lenski et al. 1999; Lenski et a1. 2003; Wilke et al. 2001). Digital organisms in
Avida evolve on rugged fitness landscapes characterized by diverse epistatic interactions,
they have intricate genotype-phenotype maps that emerge from a complex developmental
program, and they can exhibit quasi-species dynamics (Adami et al. 2000; Lenski et al.
1999; Lenski et al. 2003; Wilke et al. 2001). They approach the level of complexity of
organic viruses, making results obtained with Avida biologically relevant and of general
interest (Adami 2002; Wilke and Adami 2002). In Avida, genomes have 26 possible

instructions at each position. All organisms descend from an ancestral program used to

seed a population. Organisms execute the programs encoded by their genomes, including
commands that enable them to copy and divide their genomes. The copy instruction
duplicates a single instruction. During this duplication process, the instruction has a
probability of being miscopied and changed to a different instruction in the offspring’s
genome; mutations from one instruction to any other are equally likely. In this study, we
held the genome length constant by setting rates of insertion and deletion mutations to
zero. The genomic mutation rate, U, equals the mutation probability per instruction
copied multiplied by the genome length. The value of U is controlled by the investigator
and was varied in our experiments.

Each digital organism occupies a cell in a rectangular lattice. The size of the
lattice sets the maximum population size, which was also varied in our experiments.
After a divide instruction is executed, the genome is split into two; the duplicated genome
(the offspring), is placed into a random cell in the lattice, which kills the organism that
previously occupied that position. Although death is random, the danger of being
overwritten provides a selective advantage to organisms that replicate faster. Also, if any
organism has not reproduced after executing its instructions an average of 15 times each,
it dies and is removed from the population. If all the individuals in a population fail to
reproduce within this allotted time, then the population has become extinct. In this study,
organisms could accelerate the execution of their genomic instructions, and thus their
reproduction, by performing certain logic functions (Lenski et al. 2003). If an organism
performs one of these functions, then it receives some corresponding resource that
provides energy and accelerates execution of its genomic program. Aside from

differences in their ability to perform logic functions, all organisms would execute their

genomes at the same rate. Even in that case, fitness can vary among organisms
depending on their relative gestation time (number of executed instructions necessary to
produce an offspring). An organism’s expected fitness equals the product of the baseline
energy available to all organisms (made proportional to genome length to eliminate
selection on genome size per se) and bonuses received for performing logic operations,
divided by the gestation time. Organisms do not have access to, and cannot manipulate,
their expected fitness. Realized fitness is affected, however, by population structure and
interactions among organisms.

In this study, we introduce a new command to Avida that causes the digital
organisms to reproduce sexually. We use this variant command to compare evolution in
asexual and sexual populations. When executed, the divide-sex command separates
a copied genome from its parent, but it does not immediately place that new genome into
the population. Instead, the new genome goes into a separate location called the birth
chamber. If the chamber is empty, the new genome remains there until a second genome
arrives. When two genomes are present, they recombine and then both resulting
offspring are placed at random into the population. (Notice that this mechanism for
sexual reproduction does not involve the two-fold cost of sex, although we could have
introduced such a cost by placing only one of the two recombinant offspring in the
population. It is likely that the most primitive biological forms of sex did not have to
overcome this two-fold cost (Maynard Smith 1978), and so we began this research by
placing both recombinants in the population. Even so, as we show below, the conditions
favoring sexual reproduction with respect to Muller's ratchet are fairly narrow.)

Recombination occurs by taking a single continuous region (with two random endpoints)

from one genome and swapping it with the corresponding region from the other genome.
Genomes are circular and fixed in length; genomic positions are defined by distance from
the first command executed and direction of execution. The initial speed of execution of
an offspring’s genome is set to the weighted average of its two parents, with weights
based on the proportion that each parent contributed to the offspring’s genome. Under
asexual reproduction, the initial speed is inherited from the sole parent.

We performed the evolution experiments with Avida in two stages. Briefly, the
first stage used large populations in order to evolve digital organisms that were well
adapted to their environment. For the second stage, these organisms were moved into
much smaller populations to examine the effects of Muller’s ratchet. Maximum
population size was identical in all cases during the first stage, but this size was varied in
the second stage. Mutation rates were also varied across runs, but the rate was held
constant in both stages of a given lineage. Similarly, reproductive mode (asexual or
sexual) varied across runs, but this mode was held constant during both stages of any
lineage. Further details on the two evolutionary stages are provided below.

First evolutionary stage. All runs started with a hand-written ancestor, which
had a genome of 100 instructions. The ancestor was capable of self-replication, but it
could not perform any logic functions. Ten replicate experiments were run with each of
five genomic mutation rates (U = 0.1, 0.3, 1, 3, 10) and with reproduction being either
strictly asexual or sexual for the population. Thus, there were 100 runs of the first stage.
Replicates differ only in the random number seed, which then affects all the stochastic
events during the run, such as mutations and offspring placement. The maximum

population size (N) was 3600 organisms for all runs in the first stage. Genome length

was held constant in all runs. Nine different resources could be obtained by digital
organisms that evolved the ability to perform logic functions; these resources were
available in infinite supply. Experiments ran for 100,000 updates, where an update is an
arbitrary unit of time in Avida corresponding to the execution of 30 instructions, on
average, per individual organism. In these first-stage runs, one generation required
roughly 10 updates; the exact value depends on the number of instructions needed to
produce an offspring, which often changes during evolution. At U = 0.1 and 0.3, the
experiments ran for an additional 500,000 updates in order to compensate for the slower
adaptation at these lower mutation rates; this extension ensured there were genotypes that
could use all nine resources in each first-stage treatment. During each run, we recorded
the numbers of organisms using each resource as well as the mean and highest fitness in
the population. At the end of each run, we saved the most fit genotype (provided it was
able to use all nine resources) for use in the second evolutionary stage.

Second evolutionary stage. These runs used the pool of well-adapted genotypes
from the first evolutionary stage as starting material to investigate the effect of Muller’s
ratchet on small populations. Each small population had the same mutation rate and
same reproductive mode as its first-stage progenitor. For each of the five mutation rates,
one sexual and one asexual organism were randomly chosen from the pool of genotypes
saved at the end of the first-stage runs. Each of these ten genotypes (also referred to as
proximate ancestors) was then used to start 100 replicate experiments at each of six small
population sizes (N = 4, 8, 16, 32, 64, or 128), for a total of 6000 second-stage runs. All
parameters other than population size were identical to those in the first-stage

experiments. The second—stage runs lasted for 500,000 updates, during which we again

recorded the number of organisms using each resource, as well as the mean and highest

fitness. We also recorded whether the population had gone extinct by the end of the run.

RESULTS AND DISCUSSION
Adaptation and decay. In the first stage of the evolution experiments, several
populations at each mutation rate produced highly adapted genotypes that could perform
all nine logic functions and thereby obtain the corresponding resources. Figure la shows
the maximum-fitness trajectory over the first 10,000 updates for a representative first-
stage population that evolved with U = 0.3 while reproducing asexually. Figure 1b
shows the corresponding trajectory for a second-stage population founded by the most fit
genotype from the first stage, but with the maximum population size now reduced from
3,600 to 16 organisms. The step-like changes in maximum fitness are typical of the
experiments. The steps reflect, in large measure, the adaptive gains and maladaptive
losses of logic functions that occurred in the large and small populations, respectively
(Figures 1c and 1d).

Population survival and extinction. In order to test if sexual reproduction could
substantially impede Muller’s ratchet, we compared the number of sexual and asexual
populations that survived to the end of the second stage. Recall that mutation
accumulation by Muller’s ratchet can cause individuals to fail to reproduce and die,
leading to a decline in population size which, if severe, might cause a mutational
meltdown and eventual extinction. In total, we compared the fate of asexual and sexual
populations under 30 different combinations of mutation rate and population size (Table

1). For 13 combinations with relatively large population sizes, low mutation rates, or

 

fitness
p—t
o
A

 

 

 

 

 

 

 

0 2 4 6 8 10 0 2 4 6 8 10

time (1000 updates) time (1000 updates)
0_ 1200 2400 3600 16 10
number of organisms number of organisms

Figure 1. Trajectories for maximum fitness and resource use during evolution in large
and small asexual populations. (a) Maximum fitness in a large population (N = 3600)
during the initial 10,000 updates with genomic mutation rate U = 0.3; (b) Maximum
fitness in a small population (N=l6) that began with the most fit genotype from (a), and
which continued at the same mutation rate; (c) Number of organisms performing each of
the nine rewarded logic functions, indicated by shading intensity (scale below), in the
same large population as in (a); ((1) Number of organisms performing these logic

functions in the same small population as in (b). Note the different scales in (c) and (d).

both, all 100 asexual and all 100 sexual populations survived to the end of the

experiment. In 4 combinations subject to both high mutation rates and small population

sizes, all 200 populations went extinct, regardless of their reproductive mode. In the

remaining 13 combinations of mutation rate and population size, the number of surviving

sexual populations was greater than the number of surviving asexual populations. For 4

of these combinations, the difference was significant based on Fisher’s exact test (two-

tailed P < 0.05) with a Bonferroni correction to adjust for performing 30 tests (Sokal and

Rohlf 1995). Also, the likelihood that all 13 cases in which there was a difference would,

 

 

 

Reproduction: Genomic mutation rate, U
asexual, sexual 0.1 0.3 l 3 10
4 75, 80 8, 41 0, l 0, O 0, 0
Z 8 98, 100 92, 98 60, 87 0, 3 0, 0
.:.S: 16 100, 100 100, 100 98, 99 67, 95 0, 0
g 32 100, 100 100, 100 100, 100 97, 99 18, 70
E 64 100, 100 100, 100 100, 100 99, 100 98, 99
128 100, 100 100, 100 100, 100 100, 100 100, 100

 

Table 1. Survival of asexual and sexual populations when population size is small and

Muller’s ratchet operates. The two numbers in each cell show the number (out of 100

runs) of surviving asexual and sexual populations, respectively, for each combination of

genomic mutation rate and maximum population size. Paired values are shown in hold

when they were significantly different (see text for details).

ll

by chance, trend in the same direction is very small (binomial test, P < 0.001). The data
on population survival and extinction therefore support the hypothesis that sexual
reproduction can slow the advance of Muller’s ratchet and prevent mutational meltdown.
On the other hand, most of the differences in extinction probabilities are fairly small, they
depend on the particular parameter values for mutation rate and population size, and the
survival advantage to sex requires thousands of generations to be manifest.

Mean fitness of surviving organisms. While the data on population survival are
consistent with the hypothesis that sex is beneficial in opposing Muller’s ratchet, the
mean fitness values of survivors suggest a more complicated picture. Owing to the large
number of experiments (100 populations for each of 60 combinations of population size,
mutation rate, and reproductive mode), we cannot present all of the fitness data.
However, Figure 2 shows the most important patterns. All of the populations in this
figure evolved with genomic mutation rates set to 0.3; the three panels show data
obtained for population sizes of 4, 16, and 64. Fitness values are expressed relative to the
proximate ancestor, and were transformed owing to their tremendous range. At the
lowest population size (Figure 2a), surviving sexual populations had slightly higher mean
fitness values than did their surviving asexual counterparts, although this difference was
not significant (two-tailed t-test, P > 0.5). For both reproductive modes, the final mean
fitness values were very low relative to the ancestors. The situation was more
complicated, however, at somewhat larger population sizes (Figures 2b and 2c). As
expected, the mean fitness under both reproductive modes was much higher at N = 16
than at N = 4, and mean fitness was higher still with N = 64. Unexpectedly, however, the

asexual populations had higher mean fitness than did the sexual populations at these

12

 

 

 

 

 

 

 

 

 

3 (a) 41 100 (b) 100 100 (c) 100

0.02 l +

+ +
w + +
8 ‘l' f 2
g + E s ’2‘?
0.01 + ., 4 ()5 93 098 .. l...
:3 F. "ii" :l: a
'f . . ,
e + i +
0 + + ‘ 0 0.96

 

 

 

asex sex

m
('0
>4

asex SCX asex

Figure 2. Distributions of mean fitness in asexual and sexual populations that survived
Muller’s ratchet. Panels (a), (b), and (c) correspond to maximum population sizes of 4,
16, and 64, respectively. All populations shown here evolved with a 0.3 genomic
mutation rate. Asexual and sexual populations are shown at the left and right,
respectively, in each panel. Each + symbol shows the mean fitness of one surviving
population; the horizontal bar shows the mean value across the surviving populations for
each treatment. The numbers of surviving populations in each treatment are shown along
the top (see Table 1). Owing to the tremendous range of fitness values within and
between treatments, mean fitness, W, is transformed as log(W+1)/log(W0), where W0 is
the fitness of the proximate ancestor. Note the changes in fitness scale between panels.

Images in this dissertation are presented in color.

larger population sizes (two-tailed t-test, both P < 0.0001). In appears that sexually
reproducing populations, while better able to survive Muller’s ratchet in very small
populations, may accumulate more harmful mutations than asexual populations at
somewhat larger population Sizes. Data obtained from other combinations of population
size and mutation rate gave similar results.

Distribution of mutational effects. As a first effort to understand one factor that
might have contributed to lower mean fitness of sexual than asexual populations, we
subjected the proximate ancestors to an in-depth mutational analysis. We constructed all
2500 one-step mutants (25 alterative instructions at each of 100 genomic sites) for the
first-stage sexual and asexual genotypes that were ancestral to the populations shown in
Figure 2. Table 2 shows the fraction of one-step mutations that were lethal, deleterious
(non-lethal), neutral, and beneficial. The asexual genotype had a substantially higher

proportion of mutations that were lethal, while the sexual type had a correspondingly

 

 

Lethal Deleterious Neutral Beneficial
Sexual 0.2420 0.6392 0.1088 0.0100
Asexual 0.4236 0.5052 0.0708 0.0004

 

Table 2. Distribution of one—step mutational effects on fitness in sexual and asexual
ancestors of some second-stage populations. The proportion of the 2500 different
mutations are Shown for one sexual genotype and one asexual genotype that evolved
during the first stage with U = 0.3, and which then served as the ancestors for the second-

stage evolution shown in Figure 2.

l4

higher proportion of deleterious but non-lethal mutations. Those populations derived
from this asexual genotype would have had a higher risk of extinction, especially in the
smallest populations, as a consequence of the higher fraction of lethal mutations. But
surviving asexual populations might also have been purged of their most deleterious
mutations, leaving these survivors with higher fitness than those from the sexual
populations. The generality of these differences as a function of reproductive mode
remains to be seen, as do such other factors as the extent and form of epistatic
interactions between mutations (Lenski et al. 1999). But these preliminary data do
suggest that prior evolution under the different reproductive modes can influence
subsequent evolution. In other words, there are multiple interacting and dynamical
feedbacks that shape evolving genomes, and they will complicate efforts to discern the
various forces responsible for the origin and maintenance of sexual reproduction (Lenski
1999).

Summary and future directions. Sexual reproduction has several disadvantages
relative to asexual reproduction, which begs the question of why sex is common in
nature. Many potential advantages of sex have been hypothesized, including that sexual
reproduction opposes the maladaptive effect of Muller’s ratchet in small populations. We
used the Avida software to perform evolution experiments with digital organisms that
would test this hypothesis. Our results demonstrate the effect of Muller’s ratchet in small
populations. At high mutation rates and in very small populations, the ratchet often led to
mutational meltdowns caused by the vicious cycle of mutation accumulation and
population decline. Sexual populations survived this effect significantly better than

asexual populations, but only over a fairly narrow range of parameter values. Opposing

15

this advantage, surviving organisms in asexual populations unexpectedly had higher
mean fitness than those in sexual populations at some other parameter values. This last
result points toward the need for systematic analyses of the effect of reproductive mode
on genetic architecture, including the distribution of mutational effects on fitness as well
as the extent and form of epistatic interactions among mutations. Avida is well-suited for

such analyses, which we intend to pursue in our future work on the evolution of sex.

16

CHAPTER 2

SEXUAL REPRODUCTION RESHAPES THE GENETIC ARCHITECTURE OF
DIGITAL ORGANISMS

ABSTRACT
Modularity and epistasis, as well as other aspects of genetic architecture, have emerged
as central themes in evolutionary biology. Theory suggests that modularity promotes
evolvability, and that aggravating (synergistic) epistasis among deleterious mutations
facilitates the evolution of sex. Here, by contrast, we investigate the evolution of
different genetic architectures using digital organisms, which are computer programs that
self-replicate, mutate, compete, and evolve. Specifically, we investigate how genetic
architecture is shaped by reproductive mode. We allowed 200 populations of digital
organisms to evolve for over 10,000 generations while reproducing either asexually or
sexually. For ten randomly chosen organisms from each population, we constructed and
analyzed all possible single mutants as well as one million mutants at each mutational
distance from two to ten. The genomes of sexual organisms were more modular than
asexual ones; sites encoding different functional traits had less overlap and sites encoding
a particular trait were more tightly clustered. Net directional epistasis was alleviating
(antagonistic) in both groups, although the overall strength of this epistasis was weaker in
sexual than asexual organisms. Our results show that sexual reproduction profoundly

influences the evolution of the genetic architecture.

17

INTRODUCTION
Modules are ubiquitous in biological systems, and they appear to be a critical aspect of
biological organization (Hartwell et al. 1999; Schlosser and Wagner 2004). Defined as
groups of characters serving the same function that are integrated into a unit largely
independent from other such units (Wagner 1996), modules occur in such diverse
contexts as the Hox gene cluster (Ferrier and Holland 2001 ), butterfly wing development
(Beldade et al. 2002), and metabolic networks in bacteria and eukaryotes (Ravasz et al.
2002). Modular organization of genomes may facilitate the exchange of independent
“building blocks’ via recombination, increase phenotypic variability, and promote
evolvability (Kirschner and Gerhart 1998). While sexual reproduction with obligatory
recombination is also common (Bell 1982), the selective forces responsible for its origin
and maintenance — in the face of substantial costs — remain largely unknown even after a
century of discussion and investigation (Kondrashov 1993; Maynard Smith 1978; Michod
and Levin 1988; West et al. 1999; Williams 1975). One hypothesis emphasizes genetic
architecture and suggests that aggravating (synergistic) epistasis between deleterious
mutations may favor sex (Kondrashov 1982; Wolf et al. 2002), but various experiments
Show no excess of aggravating relative to alleviating epistasis (Chao 1988; De Visser et
al. 1997; Elena and Lenski 1997; Lenski et al. 1999; Wilke et al. 2003). While these and
other studies have considered the effects of genetic architecture on the evolution of sex
(Kondrashov 1982; Rice and Chippindale 2001), the effects of reproductive mode on
genetic architecture have received less attention (but see Lawrence and Roth 1996;
Lenski 1999; Malmberg 1977; Pal and Hurst 2003; Pal and Hurst 2004). Here, by

contrast, we measure both modularity and epistasis in the genomes of sexual and asexual

18

evolving computer programs. We expect sex to promote more modular genomes, which
may accelerate the origin of new traits and avoid disrupting existing traits. We expect
sexual and asexual reproduction to yield different patterns of epistasis for two reasons.
First, sex favors those mutations that enhance fitness across different genetic
backgrounds, while asexuality favors mutations that are beneficial in the background in
which they occur. Thus, stronger epistatic tendencies may evolve in asexual rather than in
sexual reproduction (Malmberg 1977). Second, sex may promote aggravating epistasis
relative to alleviating epistasis, because recombination would then facilitate the efficient
removal of deleterious mutations. This explanation has been proposed for the evolution
of sex (Kondrashov 1982), but the causal link might also be reversed.

In this study, we used ‘digital organisms’ to examine the effects of reproductive
mode on the evolution of genetic architecture. These digital organisms are computer
programs that replicate, mutate, and evolve in populations maintained by the Avida
software (Ofria and Wilke 2004; Wilke and Adami 2002). They can perform various
functions by executing the series of instructions encoded in their genomes, including
instructions that enable them to copy their genomes line by line and thereby reproduce.
Depending on the genetic program encoded by their genome, instructions may be
executed out of order or multiple times. Point mutations, insertions, and deletions occur
randomly during this process. Organisms compete for the energy they need to execute
their genomic programs, and the resulting selection acts on heritable differences in their
performance that are generated by mutations and, in sexual populations, recombination.
Evolution therefore modifies the genome, with selection tending to reduce the number of

instructions that must be executed to reproduce while increasing the energy available for

19

execution. Organisms can augment the basal energy obtained at birth by performing
computations in a manner analogous to metabolizing resources. In this study, nine
distinct resources occur in unlimited quantities in the environment, but an individual can
make use of each resource only once during its life cycle. The ancestor cannot perform
any of these computations, but populations can evolve the ability to perform them.
Several studies of evolutionary dynamics and outcomes have taken advantage of
the speed of evolution, flexible experimental design, and extensive data that can be
obtained with Avida (Adami et al. 2000; Chow et a1. 2004; Lenski et al. 1999; Lenski et
al. 2003; Misevic et al. 2004; Wilke et al. 2001). Here, we examine the evolution of two
key features of genetic architecture — modularity and epistasis — as a function of
reproductive mode. To do so, we extended Avida to allow the possibility of sexual
reproduction. Following the requisite site-by-site copying of a genome, the asexual
divide instruction performs a genomic division and places the offspring into the
population. The new sexual divide instruction requires the exchange of genetic material
between two separately copied genomes before the recombinant offspring are placed in
the population. Therefore, all offspring are the product of recombination under the
sexual regime in Avida. We used two ancestors, capable of self-replication but not of
performing any computations, and differing only in their divide instruction, to seed 100
sexual and 100 asexual populations in identical environments. Such experiments and
subsequent analyses simply cannot be performed with any organic system at the scale,
scope, and precision that digital organisms allow. We realize, of course, that the detailed
results of similar experiments and analyses would undoubtedly differ between digital and

organic systems (as they probably would also for different organic systems, if such work

20

could be performed). Our intent, however, is to test general hypotheses about genome

architecture in relation to mode of reproduction.

MATERIALS AND METHODS
The Avida system. We performed experiments with the Avida software, which is
available without cost at http://devolab.cse.msu.edu/software/avida/. All experiments
used default settings unless otherwise indicated. Reproductive mode is determined by
whether the divide-sex or divide-asex instruction is included in the instruction
set. All genomes used the default set of 25 instructions plus one of these divide
instructions. Point, insertion, and deletion mutations occurred at rates of 0.002, 0.0005,
and 0.0005 per instruction copied, respectively. Point mutations swap an instruction in
the genome with a random one from the instruction set, while insertion and deletion
mutations add or delete a random instruction. Besides their mode of reproduction,
populations differed only in a random—number seed that affected all stochastic events
during an experiment, including mutations and offspring placement. Each population had
a maximum size of 3,600 organisms and was propagated for 100,000 updates. An update
equals the time in which 30 instructions, on average, are executed per organism in the
population. A typical generation is 5-10 updates, with the exact value depending on the
complexity of organismal phenotypes, which changed during evolution. With asexual
reproduction, an offspring is created by a division and immediately placed in the
population. In sexual reproduction, the genome of an incipient offspring is first placed in
a ‘birth chamber’ following a division. If the chamber is empty, the genome remains

there until a second one arrives. (Sexual reproduction thus introduces a delay associated

21

with the requirement for pairing. In principle, this delay might slow evolution in sexual
populations relative to asexual ones. Pilot experiments in which some asexual
populations experienced a corresponding delay, while others did not, showed that this
delay had no appreciable effect on the rate of adaptation.) When two genomes are
present, they recombine by swapping a continuous region of code. The relative locations
of the beginning and end of that region are chosen from a uniform random distribution in
the 0 to 1 range; the absolute locations are calculated by multiplying the random numbers
by genome lengths. Genomes are circular and sites are numbered starting with the first
one executed after birth. After recombination, both offspring are placed at random
locations in the population. Organisms have no means of mate choice, and thus sexual
selection is absent from this system. For both reproductive modes, offspring placement
kills the organism that previously occupied that location, introducing genetic drift while
maintaining a constant population size. All new organisms receive a basal amount of
energy, which is scaled by genome length, thereby eliminating direct selection for small
genomes. If, in the course of executing its genomic program, an organism inputs one or
two 32-bit strings and outputs the result of one of nine basic logic operations performed
in a bit-wise fashion on those strings, then it obtains additional energy at a rate roughly
proportional to the operation’s complexity. There are many different ways to perform
each operation, and the number and identity of instructions used varies among organisms.
The energy obtained by this computational metabolism is combined multiplicatively with
the basal energy, and the product determines the relative speed with which each organism
executes its genomic program. An organism’s expected fitness is calculated as its total

energy divided by the time used to produce an offspring and corresponds to the rate of

22

offspring production. Fitness is expressed relative to the common ancestor; in our
analyses of evolved populations, relative fitness was averaged over all organisms from a
population and then loglo transformed.

Modularity. We obtained an organism’s genotype-phenotype (GP) map by
separately mutating each site in its genome and recording any resulting changes in the
computational traits performed by the mutants. Physical deletions often produce
confounding effects caused by changes in genome length; therefore, we mutated sites to
an inert instruction (outside the default set available during evolution) that acts as a
placeholder only. The GP map identifies those genomic regions that encode different
traits. From the GP map, we then calculated two indices, physical and functional

modularity.

Physical modularity, PM, measures the mean distance between sites encoding all

computational traits:

 

2 2 (10.1)
tET i,jES, jag]: "(St) ' ("(St) - l)
L- n(T)

PM=l-2

 

where L is genome length, T is the set of an organism’s traits, n(T) is the number of traits,

S, is the set of all sites encoding trait t, n(S,) is the number of sites encoding trait t, and

d(i,}') is the distance between sites i and j. The index averages the distance between two
sites encoding a trait over the number of site pairs for each trait and the number of traits,
and normalizes by genome length, which allows comparisons between organisms that
differ in length and number of expressed traits. The normalized average is then doubled
and subtracted from unity, yielding a score from 0 to 1, with higher values indicating

more modular architectures. Characteristic distributions of instructions within a trait and

23

 

 

 

the corresponding PM values are illustrated using hypothetical organisms in Figure 3a;
evolved digital organisms generally require many more instructions to perform functional
traits than these examples, which serve only to illustrate features of the PM metric.
Organism 1 has the lowest possible modularity because the trait is encoded by only two
instructions that are located as far apart from each other as possible given a circular
genome. Organism 2 is more modular than 1 because, while the relevant instructions also
lie in two distant regions, the multiple instructions within each region are very close
together and thus lower the average distance. Organism 4 is more modular than 3
because all of the relevant instructions in 4 are within a single genomic region. Organism
5 has the highest physical modularity because the trait is encoded by just two adjacent
instructions. While the PM for Organism 5 is not quite equal to the theoretical upper
bound of 1, it would asymptotically approach that bound with increasing genome length.
Functional modularity, FM, measures the average overlap in the genomic sites

that encode two or more different traits:

2 2 (l-m(s,b))

= abET,a=-=b sESa
L' n(T)'(n(T) - 1)

FM

 

where m(s, b) specifies whether Site s is required for expression of trait b, with m(s,b) = {I
if 565‘ ; 0 if siSb}. The number of non-overlapping sites for two traits is averaged over
all trait pairs and normalized by genome length, again allowing comparisons between
organisms that differ in length and number of expressed traits. Characteristic types of

overlap between traits and the corresponding FM values are shown for hypothetical

24

 

(a) physical modularity (b) functional modularity (c) evolved organisms

 

 

 

 

 

 

 

 

 

 

 

 

0 0.43 0.62 0.73 0.98 0 0.25 0.67 1
H _. F 100-
: sex asex
.l j- 25:3
S
I 0 50 ’
Ll ul g
c:
S
Li _ u 0 .
1 2 3 4 5 1 2 3 4 phenotypic phenotypic
organism organism trait trait

Figure 3. Genotype-phenotype maps illustrating physical and functional modularity.
Phenotypic traits are arrayed as columns and genomic sites as rows. For simplicity, the
circular genomes are shown in a linear fashion. An open cell indicates that the
instruction at that site can be deleted without eliminating the trait; a filled cell marks the
site of an instruction required for expression of the trait. If a mutation not only disrupts a
trait but also prevents the organism from replicating, then that site is not filled in the GP
map. (a) Five hypothetical organisms of equal length that express a single functional
trait, with physical modularity values indicated above. (b) Four hypothetical organisms
of equal length that express two traits each, with functional modularity values indicated
above. (c) Representative GP maps for sexual (left) and asexual (right) organisms. PM
and FM values for this sexual organism are 0.796 and 0.841, respectively; PM and FM
values for the asexual organism are 0.689 and 0.746, respectively. Each value is within

5% of the overall mean for the corresponding reproductive mode.

25

organisms in Figure 3b. When there is complete overlap between the instructions
encoding different traits, then FM is 0, as in Organism 1. By contrast, FM equals 1 when
the instructions encoding different traits have no overlap at all, as in Organism 4.
Intermediate values of FM are represented by Organisms 2 and 3. Organisms that do not
express any computational traits (including those sampled before any functions evolved
and, later, those with severe mutations) have undefined physical modularity and were
excluded from the analysis. Similarly, FM is defined only for organisms expressing at
least two functions because it measures the overlap in the instructions that encode them.
Modularity has joined the ranks of biological properties, such as fitness and
species, that are often difficult to define and measure, resulting in a multitude of different
and sometimes even conflicting definitions (Beldade et al. 2002; F errier and Holland
2001; Hartwell et al. 1999; Ravasz et al. 2002; Schlosser and Wagner 2004; Wagner
1996; Winther 2001). In pilot experiments, we explored several different modularity
metrics ranging from quite simple (e.g., average number of tasks affected by an
instruction) to more complex ones (e.g., FM further normalized by the expected overlap
given the density of instructions in the GP map). Results obtained with all the metrics led
to qualitatively similar conclusions. Therefore, we chose to focus on PM and FM, which

measure different, yet intuitive and meaningful, aspects of genomic architecture.

Mutational sensitivity and epistasis. We mutated each site in an organism’s
genome to every alternative state (e.g., 50 x (26-1) = 1,250 mutants for length 50
genomes and 26 different possible instructions) and measured the resulting fitness. For
each organism, we also examined random samples of a million mutants for each

mutational distance from two to ten; these samples included more than 18-billion mutants

26

in all. Parameters 0t and B define an organism’s average sensitivity to individual
mutations and the overall form of epistatic interactions among mutations, respectively
(Elena and Lenski 1997; Lenski et al. 1999). We calculated each organism’s or exactly as

-log10W(1), where III/(1) is the average fitness of all single mutants expressed relative to

the unmutated state. We then estimated each organism’s [3 by minimizing the sum of
squared deviations between the actual average fitness values for 1 S m _<_ 10 and those

predicted by the power function logm W(m) = -aml3, using or as obtained above.

Statistics. We used Systat 10.2 software (881. Richmond, CA) for all statistical

tests.

RESULTS
Evolved sexual organisms have higher fitness and longer genomes. Sexual
populations adapted significantly better to the environment, on average, than did asexual
populations, as indicated by average fitness values after 100,000 updates (P = 0.006;
Table 3; Figure 4a). Sexual populations also evolved larger genomes, on average, than
asexual populations (P < 0.001; Table 3; Figure 4b), but this difference was strongly
influenced by the fact that 35 sexual populations evolved genomes more than twice the
ancestral length of 50 whereas only 9 asexual populations did so. Similarly, there was
more diversity in genome length within individual sexual populations (data not shown),
probably caused by the larger changes in genomes allowed by recombination. The large
genomes typically evolved via genome doublings that occurred when, owing to some

mutation, the genetic program failed to detect that the genome had already been copied

27

 

 

507 ' 7
(a)

 

 

   

 

 

 

 

 

 

25' sex
E"
.2
*5
'2.
8.
“-1
o
B
E
c:
25* asex
SOI ‘ l A # i > A ‘ _ c
2 4 6 8 1.5 2 2.5 3
log(f1tness) Iog(length)

Figure 4. Final distributions of average fitness (a) and genome length (b) in sexual and

asexual populations. Open sections show populations with average genome length 2100

instructions.

28

and repeated the site-by-site replication. Sexual reproduction in Avida evidently
increased the chance of genome doubling, created more favorable genetic combinations
in the larger genomes, or both. To preclude genome doublings from possibly biasing our
analyses of genetic architecture, we reduced the data set by excluding all populations
with mean length 2100 (i.e., at least twice the ancestral length; Appendix). We also
performed additional experiments in which we actively prevented genome doublings
from occurring (Appendix). In both cases, the resulting asexual populations had, on
average, longer genomes than sexual ones, thus reversing the direction of potential bias.
The alternative analyses also eliminated the significant fitness difference between sexual

and asexual populations, with higher fitness shifting, albeit insignificantly, to the asexual

 

 

response variable mean sexual (2 s.d.) mean asexual (: s.d.) P

loglo fitness 5.762 (1.610) 5.198 (1.228) 0.006
loglo genome length 2.022 (0.414) 1.853 (0.114) < 0.001
physical modularity, PM 0.824 (0.098) 0.699 (0.073) < 0.001
functional modularity, FM 0.838 (0.091) 0.766 (0.079) < 0.001
average effect of single point 0.546 (0.292) 0.768 (0.190) < 0.001

mutations on fitness, or

net directional epistasis, B 0.929 (0.057) 0.862 (0.088) < 0.001

 

Table 3. Comparisons of properties between sexual and asexual evolved populations.

The P values are based on two-tailed t-tests.

29

populations. Importantly, all of the qualitative effects of reproductive mode on genetic
architecture remained in the same direction, and significant in all but one case, under both
alternative analyses. Therefore, these architectural differences are robust with respect to
differences in genome length between sexual and asexual organisms.

Evolved sexual organisms have more modular genomes. We performed all of
the analyses of genetic architecture on a random sample of ten viable organisms from
each population at the end of the evolution run; occasional non—viable genotypes were
excluded. For each organism, we first deleted each genomic site (replacing it with an
inert placeholder instruction) in order to construct genotype-phenotype (GP) maps; these
maps identify the set of sites required to express a particular trait (compute a logic
operation). We used the independently evolved populations as the unit of replication in
statistical comparisons, because organisms sampled from the same population inevitably
share much of their ancestry.

Using the GP maps, we then calculated physical modularity (PM), which reflects
the average distance between two sites encoding a particular trait, and functional
modularity (FM), which captures the average overlap between sites encoding different
traits. PM and FM can range from 0 to 1, with high PM values indicating that traits are
encoded in compact regions of the genome and high FM values corresponding to low
overlap between traits. Representative GP maps illustrate the difference in modularity
between sexual and asexual organisms: sites encoding the various traits in sexual
organisms tend to be more compact (shorter, more continuous vertical filled blocks) and
less overlapping (shorter, fewer horizontal filled lines) than those in asexual organisms

(Figure 3). We averaged PM and FM across organisms within a population, and then

30

compared the populations with different reproductive modes. Over time, the genomes of
sexual organisms became increasingly more physically modular than asexual ones
(Figure 5a), and this difference was highly significant at the end of the experiment (P <
0.001; Table 3; Figure 5b). The difference in PM remained highly significant when
populations with genome length 2100 were excluded from the analysis (P < 0.001;
Appendix). Similarly, sexual organisms evolved genomes with a significantly higher FM
than asexual ones (P < 0.001; Table 3, Figure 5c), a difference that also holds in the
reduced data set (P = 0.002; Appendix).

Mutational sensitivity and epistasis differ between sexual and asexual
organisms. We further examined genetic architecture by quantifying the form and extent
of epistasis in the same organisms used to assess modularity. For each organism, we
made all possible one-step point mutants and obtained random samples of a million
organisms carrying from two to ten mutations; for each mutant, we measured its fitness
relative to its unmutated parent. We averaged relative fitness over the organisms in a
mutational class from each population. We then used a power fimction, log“) W(m) = -
amB, to relate average mutant fitness, W, to the number of mutations, m. Here, a
expresses the rate of change in average fitness expected if mutations acted independently,
and B describes the overall form of epistasis. If B = 1, then mutational effects are on
average multiplicative (no epistasis); if B < 1, then additional mutations tend to reduce
fitness less than expected from their individual effects (alleviating epistasis); and if B > 1,
then additional mutations reduce fitness more than expected from their individual effects

(aggravating epistasis).

31

Figure 5. Genomic modularin of sexual and asexual organisms. (a) Trajectories of

a\ erage ph} sical modularity in ex'oIVing sexual (red) and asexual (blue) populations.
Note the logarithmic time scale and that the first time-point represents 1.000 updates.
Frror bars are standard errors of the mean. (b) Final distributions of physical modularity
\ alaes. 0;\‘n sutions sho“ populations with ax erage genome length 2100 instructions.

let Reiazit aship 1e.“ een the final physical and functional modularity Values. Each point

represents a si'x'e independent!) ex ol\ ed sexual (red) or asexual (blue) population.

ncs‘.
‘

0.85 .

 

 

 

 

 

 

g 0.8
§ 0.75 -
E
g 0.7
‘9.
a 0.65 -

0.6 . A . . . 1 4 L

l 10 100
time (1,000 updates)
20 e
sex

10'

number of populations
o

 

(b)

 

 

 

 

 

 

 

 

 

 

 

10 . J
20 . n
0.5 0.75 1
physical modularity
1 - .
(C) '3
3s . .'.- .s
g . '.3.?‘-'-t-"-"-. .'
"8 .<'-‘.:"'.' '
5 0,75. ."-"..'. «
g .1»: -.
.2 °
8 O
G
E
0.5 r . _
0.5 0.75 1
physical modularity

33

 

 

log(fitness)
,L

 

 

 

 

 

 

 

0 5 1‘0 0 3 10
number of mutations number of mutations
Figure 6. Average fitness as a function of the number of random point mutations in
evolved sexual (a) and asexual (b) organisms. Dashed lines indicate the fitness decay
functions expected under a multiplicative model of mutation interactions, using the
corresponding average value for or and setting B = 1. Solid curves are the decay functions

based on average values for both or and B parameters.

34

Sexual populations became more robust, on average, to individual mutations than
did asexual ones (Figure 6), with sexual organisms having significantly lower 0. values (P
< 0.001; Table 3). The predominant form of epistasis was alleviating in both sexual and
asexual organisms (B < 1 based on t-tests, both P < 0.001), although this directional
epistasis was weaker in sexual organisms (P < 0.001; Table 3). The differences between
sexual and asexual populations remained significant even when those with genome length

2100 were excluded (P = 0.019 for or, P < 0.001 for B; Appendix).

DISCUSSION
In nature, organisms Show considerable variation in their reproductive mode as well as in
certain features of their genetic architecture. While there has been substantial interest in
the relationship between reproductive mode and features of genetic architecture, it is
difficult to establish causation (Beldade et al. 2002; Chao 1988; De Visser et al. 1997;
Elena and Lenski 1997; Ferrier and Holland 2001; Hartwell et a1. 1999; Kirschner and
Gerhart 1998; Lawrence and Roth 1996; Lenski 1999; Lenski et al. 1999; Malmberg
1977; Pal and Hurst 2003; P511 and Hurst 2004; Ravasz et al. 2002; Rice and Chippindale
2001; Schlosser and Wagner 2004; Wagner 1996; Wagner and Altenberg 1996; Wilke et
a1. 2003; Wolf et al. 2002). This difficulty reflects several challenges including a
multitude of potential feedbacks between the biological features of interest, the inability
to manipulate such critical features in most biological systems, and the infeasibility of
performing long-term experiments to observe how manipulating one factor would impact

the evolution of other features.

35

In this study, we have overcome these challenges by investigating the
evolutionary relationship between reproductive mode and genetic architecture in digital
organisms, which are self-replicating computer programs that mutate, compete, and
evolve. By comparing evolutionary outcomes in populations that evolved in identical
environments and initially differed only in whether they reproduced asexually or
sexually, we demonstrated that several features of genetic architecture were shaped by
reproductive mode. The genomes of sexual organisms were significantly more modular
than those of asexual organisms by two different measures (Figure 5). Sexual organisms
were also more robust with respect to the average effect of single mutations, while
asexual organisms tended to have stronger epistatic interactions among multiple random
mutations (Figure 6).

An unexpected complication arose because sexual organisms often evolved much
longer genomes than asexual organisms (Figure 4b), evidently reflecting a greater
propensity of the sexual populations to generate or retain genome doublings. Genome
length was itself correlated with other features of genetic architecture such as modularity
(Figure 5b), which raised the question of whether differences between sexual and asexual
populations in genome length might be solely responsible for the other differences in
their genetic architecture. We examined this issue in two ways (Appendix). First, we
excluded from our analyses all evolved populations in which genome length had at least
doubled. Second, we performed an additional set of experiments that prevented genome
doublings and other large changes in genome size from occurring. In both cases, the
difference in genome length became shifted in the opposite direction such that asexual

organisms were in fact longer. Yet, the other differences in genetic architecture between

36

sexual and asexual organisms retained their original form, with the genomes of sexual
organisms being more modular and more robust to the fitness effects of individual
mutations, while exhibiting weaker epistatic interactions among mutations.

Relationships among the genetic architectural parameters. Previous research
has demonstrated negative correlations between mutational parameters or and B using
both analytical models and simulations of RNA folding (Wagner et al. 1998; Wilke and
Adami 2001). We, too, observe a strong negative correlation between a and B in the
combined data set that includes both sexual and asexual digital organisms (r = -0.694, P <
0.001 for all 100 evolved populations, and r = -0.613, P < 0.001 for the reduced data set
that excludes populations with genome length 2100). We also examined the relationship
between the two measures of modularity, FM and PM, and found that they are positively
correlated (r = 0.685, P < 0.001, and r = 0.491, P < 0.001 for the reduced data set). All
else equal, genomes with more compact regions expressing different traits would have
less overlap if those regions were randomly distributed throughout a genome, which may
contribute to this association. However, the observed correlation coefficient is only
moderate in magnitude, and therefore we conclude that these two modularity measures
capture somewhat different aspects of the genetic architecture.

To examine the relationships among all the genetic architectural and performance
metrics in this study, we next performed a principal component analysis (PCA) on log-
transforrned fitness, log-transformed genome length, PM, FM, or and B (Figure 7a). The
first two components explain over 70% of the total variance in the data. The first

principal component, pc I , largely reflects the two modularity measures. PM and FM,

whereas pcz reflects the directional epistasis parameter, B, and fitness (Figure 7b). Both

37

 

 

 

 

 

 

 

 

 

 

 

 

3"
1.5-
N
8, O
—l.5'
-3'. - a
-3 -15 0 15 3
P01
1-' ' .
(b) [3 fitness
length
PM
N
a 0. fl; .
FM
(X
-1 . .
—1 0 1
P91

Figure 7. Principal components analysis for average fitness, genome length, or, B, PM,
and FM of sexual and asexual digital organisms. (a) Transformed data for sexual (red)
and asexual (blue) populations, with 95% confidence ellipses. (b) Loadings for the two

principal components.

38

components also Show substantial loadings for genome length and mutational sensitivity,
a, with these two metrics being negatively correlated, such that longer genomes tend to
be less sensitive, on average, to single mutations.

We also performed a discriminant function analysis using the same six properties
as in the PCA in order to examine which ones best capture the observed differences
between sexual and asexual organisms. The discriminant function gives the largest and
nearly equal weights to PM and B, and it would correctly classify a given organism as
sexual or asexual in over 80% of all cases (data not shown). We therefore conclude that
epistasis and modularity evolve differently in sexual and asexual populations and,
moreover, with sufficient independence that no single feature of the genetic architecture
can explain all the differences between sexual and asexual organisms.

Implications for the evolution of sexual reproduction. Our experiments do not
specifically address the long-standing question of why sex evolved (Bell 1982; De Visser
et a1. 1997; Elena and Lenski 1997; Kondrashov 1982; Kondrashov 1993; Lenski et al.
1999; Maynard Smith 1978; Michod and Levin 1988; West et al. 1999). Nevertheless,
some of our findings bear on this issue. In particular, our results support previous studies
[Chao, 1988; Wilke et al. 2003; Williams 1975) that failed to find a preponderance of
aggravating (synergistic) epistasis, which is an essential component of the mutational
deterministic hypothesis (Kondrashov 1982). Importantly, we extend this conclusion by
showing that an excess of alleviating epistasis exists even in sexual populations (Figure
6). Our experiments also suggest two alternative hypotheses for the evolution of sex, one
that is immediate and the other longer term in its consequences. First, sexual populations

evolved lower values of on (Table 3), indicating reduced sensitivity to the usually harmful

39

effects of individual mutations. Thus, sexual progeny are more robust than asexual
progeny owing to differences in the genetic encoding of their phenotype (e. g.,
canalization), as opposed to the role of recombination in purging deleterious mutations
that is posited under various other hypotheses (Kondrashov 1982). In this respect, it is
important to recognize that distributions of mutational effects and forms of epistatic
interactions evolved freely in our experiments as populations moved across fitness
landscapes, whereas these quantities are usually fixed in population-genetic analyses.
This finding suggests that theoreticians should give more attention to understanding the
structure of fitness landscapes and how different modes of reproduction influence where
populations settle on those landscapes. Second, an indirect benefit to sex could arise
from higher genomic modularity, which may increase their evolvability and thereby
promote greater fitness (Earl and Deem 2004; Wagner and Altenberg 1996). This
hypothesis is more relevant to the maintenance of sexual reproduction than to its origin,
however, because the benefit would not be manifest immediately (Bell 1982; Kondrashov
1982; Kondrashov 1993; Maynard Smith 1978; Michod and Levin 1988; West et al.
1999; Williams 1975). Finally, our results demonstrate that reproductive mode
substantially shapes the evolution of the genetic architecture. We therefore emphasize
the importance of distinguishing between the evolutionary causes and consequences of

sexual reproduction.

CHAPTER THREE

EXPERIMENTAL EVIDENCE OF EVOLUTION OF SEX IN CHANGING
ENVIRONMENTS

ABSTRACT
The evolution of sex is a vibrant and fascinating area of research, rich with theories but
poor in experimental results. The crux of the sexual paradox is the dominance of the
sexual mode of reproduction in the natural world in spite of the apparent costs associated
with recombination. Here we demonstrate that sex can evolve de novo and outcompete
the asexual mode of reproduction under changing environmental conditions. We evolved
large populations of digital organisms for thousands of generations in six environments
with different periods of substrate change. Sex was the dominant mode of reproduction
when the environments were changing rapidly, with up to 65% of populations evolving to
reproduce sexually. The ancestral reproductive mode and genetic architecture had only
weak effects on whether populations evolved to be sexual or asexual while adapting to
the rapidly changing environment. We also found that in the environmental conditions
where sex was prevalent, the sexual populations on average had higher fitness than
asexual ones. Our study experimentally demonstrates the importance of changing

environments for the evolution of sex.

INTRODUCTION
Why sex? This complicated and often costly mechanism of reproduction dominates the

biological world and continues to motivate a multitude of research studies, theoretical

41

models, and diverse hypotheses (Bell 1982; Michod and Levin 1988; Rice 2002;
Weismann 1889). The underlying benefit of sex has most often been related to the
genetic variation that is created by recombination and to the faster adaptation resulting
from that genetic variation (Maynard Smith 1978; West et al. 1999; Williams 1975).
Faster adaptation is especially important when populations are facing a novel or changing
environment. A number of experiments demonstrate the benefit of sex for adaptation to
new or harsh environments. For example, sex increases the efficiency of selection during
adaptation to a novel environment in yeast (Goddard et al. 2005), and a high
recombination rate accelerates the evolution of drug resistance in bacteriophage T4
(Malmberg 1977), while a low recombination rate slows down the response to artificial
selection in fruitflies (McPhee and Robertson 1970). Conceptually, evolution in a
changing environment is similar to repeated bouts of adaptation to a novel environment.
Much theoretical work indicates that changing environments promote the evolution of
sex, but experimental support is sparse (Barton 1995; Charlesworth 1993; Kondrashov
and Yampolsky 1996; Otto and Michalakis 1998; Sasaki and Iwasa 1987; Waxman and
Peck 1999; Wolf et a1. 1987). In an exceptional example from nature, host-parasite
interactions create a biotically changing environment that modulates the frequencies of
sexual and asexual snails and supports the popular Red Queen hypothesis (Lively 1987;
Lively and Dybdahl 2000). Here, we perform experiments with a digital system and
demonstrate that sexual organisms can invade and outcompete asexual ones when the
environmental conditions are changing rapidly, thereby providing direct experimental

evidence for a benefit of sexual reproduction.

42

METHODS
To test whether environmental change promotes the evolution of sex, we use the Avida
experimental evolution software. Avida populations comprising of thousands of self-
replicating computer programs are propagated inside computers. These digital organisms
mate and reproduce, mutate, compete, metabolize some substrates while being poisoned
by others, adapt, and evolve for thousands of generations. Avida captures evolution in a
computer and has been used to study a variety of questions about evolutionary processes
and outcomes. Most notably, previous studies have investigated the evolution of
complex features, genetic architecture and speciation in digital organisms (Chow et a1.
2004; Lenski et al. 2003; Misevic et a1. 2006).

Avidians reproduce by executing the instructions present in their digital genomes.
However, the organisms’ genetic programs may also contain instructions that input,
output, and manipulate random numbers. The environment contains multiple substrates
that organisms can metabolize to gain additional energy and speed up their replication.
Each substrate is associated with a particular mathematical logic operation. An organism
receives an energy bonus if it evolves and executes a sequence of instructions that inputs
random numbers, performs substrate-associated logic operation on those numbers, and
outputs the result. Energy received via digital metabolism is combined with the
organism’s basal energy to determine its relative replication rate. We measure replication
time and metabolic energy gains to determine fitness. As discussed below, certain
substrates may also be toxic at some points in time and their metabolism would then
decrease organism’s energy level. Fitness values are averaged over all organisms in the

population and log 1 0 transformed.

43

Reproduction in Avida is typically asexual — organisms replicate their genomes
and create offspring by simple division. Recently, recombination was introduced in the
system (Misevic et al. 2004) and this is the first study in which sexual and asexual digital
organisms mutate from one reproductive mode to the other and thus directly compete in
the same population. During sexual reproduction, two sexually generated offspring
randomly pair up and exchange a continuous region of their genomes. The physical
position of the exchanged region within the genomes is equivalent and its size is
proportional to the parental genome length. After the recombination process is complete,
both incipient offspring are placed at random locations in the population. A single
instruction in the organisms’ genetic program performs the division and determines the
mode of reproduction. The offspring produced by the divide-sex instruction will
undergo recombination, while the ones produced by divide-asex will bypass the
recombination step and immediately start their lifecycle. We can limit populations to
being purely sexual or asexual by including only one of the two possible divide
instructions in the mutationally accessible instruction set. However, if mutations to and
from both divide instruction are possible, as they were in all the experiments here, we can
directly examine evolution and competition between organisms with different modes of
reproduction.

In Chapter 2 (Misevic et a1. 2006) fifty ancestral populations evolved for over
10,000 generations under obligatory sexual or obligatory asexual conditions while their
fitness, genome length, and genetic architecture were recorded. Here, we continued
propagating those populations and preserved all but two experimental settings. Firstly,

digital organisms in any population can evolve to be either sexual or asexual through

mutations. Secondly, the environments in which populations evolve are continuously
changing. The environments are characterized by the substrates they contain,iand the
environmental change is caused by the fluctuation in the metabolic values of those
substrates. The range of metabolic values a substrate can have and the time between
changes in a substrate’s metabolic value, are the two aspects of the environmental change
that we consider here. The environment in Chapter 2 contained 9 substrates, with
metabolic values 1, 1, 2, 2, 3, 3, 4, 4 and 5, with higher values associated with more
complex computational functions. When an organism metabolizes a substrate with a
value 3, for example, it receives 23-fold increase in its current energy level. The
organism’s energy level determines the speed of execution of its genetic program and
thus its speed of replication. All substrates in Chapter 2 had positive metabolic values,
making their metabolism beneficial and so we designate them as nutrients. However,
substrates may also have negative metabolic values, and their consumption would then
slow down the organism’s reproduction, making those substrates poisonous to the
organism. In this study, all environments contained the 9 substrates present in Chapter 2;
those substrates were always nutrients, with the same metabolic values as in Chapter 2.
In addition, 68 more substrates were present in environments in this study. Those
substrates took one of two possible metabolic values, “stick” (5) and “carrot” (c), with s <
0 and c > 0. During evolution, 25 randomly chosen substrates were always nutritious,
while the remaining 43 were poisonous; however, the identity of those substrates changed
randomly over time. All 68 changing substrates in a particular environment share the
same (3, c) values. We evolved populations in environments with four different (s, c)

values: (-1, 1), (-1, 3), (-l, 5), and (-3, l). The substrates that are sometimes nutritious

45

and sometime poisonous provide a two-fold impetus for adaptation: (1) energy gained
from metabolizing a nutritious substrate (“carrot”) and (2) energy lost from metabolizing
a poisonous one (“stick”) which may have been nutritious a short while ago.

Besides the metabolic values of the substrates, each changing environment is
characterized by the period of time between changes in those values. The environments
change gradually, by a swapping the metabolic values of two randomly chosen substrates
at a time. For example, at the environmental change period of 10u, every 10 updates one
of the 25 nutritious substrates becomes poisonous and one of the 43 poisonous substrates
becomes nutritious. The change from a nutrient to a poison is achieved simply by
changing the substrate’s current metabolic value from c to s. An update equals the time
in which, on average, 30 genomic instructions are executed per organism in the
population. A typical generation is 5-10 updates, with the exact value depending on the
complexity of organismal genotypes and phenotypes, which may change during
evolution. Here, we studied evolution in environments with six different periods of
change: lu, 3u, 10u, 30u, 100u, and 300u (Figure 8). For each of the four metabolic
value pairs and each of the six periods of environmental change, we propagated 20
initially sexual and 20 initially asexual populations from Chapter 2 for additional 100,000
updates, a total of 4 x 6 x 2 x 20 = 960 populations. Over the course of evolution, many
of those populations switched their mode of reproduction, which we recorded.

All the experiments were performed using Avida software, which is available
without cost at http://devolab.cse.msu.edu/software/avida/. We used the default settings,
unless otherwise indicated. The organism’s mode of reproduction was determined by

whether it executed divide-sex or divide—asex to reproduce. All genomes used

substrates

\ 9|
' ' o l. ‘
- ‘-‘ . ' . - 1' -. ‘- ‘

.. 2 s, .t. M, 35 a .w : .

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‘ , _ Q: . ‘ 9 . 'p ' . . .
. . r 1“? T 1’ v f ' i l a '

substrates

substrates

 

0 50 100
time ( 1000 updates)

Figure 8. Different periods of change in substrate metabolic values. The 9 fixed
ancestral and 68 changing substrates are at various positions on the y-axis. Black
indicates that a substrate has a positive metabolic value (nutrient), while white indicates
that a substrate has a negative metabolic value (poison) at that particular point during the
experiment. Light grey marks the initial period where all changing substrates had a
metabolic value of zero. Panels (a), (b), and (c) represent 3u, 30u, and 300u periods of

environmental change, respectively.

47

the default instruction set with 25 instructions plus the two divide instructions. Three
different types of mutations occur in the system: point, insert, and delete, at rates of
0.002, 0.0005, and 0.0005 per instruction copied, respectively. The carrying capacity is
3,600 organisms and when a population is full, each new birth results in a death of a
randomly chosen organism, thus maintaining constant population size. After restarting
the populations from Chapter 2 here, we allowed them to acclimate and evolve for 1,000
updates in the constant, familiar environment from Chapter 2 before introducing the

additional changing substrates.

RESULTS AND DISCUSSION
The trajectories of the relative abundance of sexual organisms over time showed great
diversity across different populations in our study (Figure 9). Some populations started
and remained either primarily sexual or asexual, while others switched their mode of
reproduction multiple times. Most populations were, at any given moment, homogeneous
in terms of their reproductive mode, being comprised of either only sexual or only
asexual organisms. The most common exceptions were the rapid transitions between the
sexual and asexual types when both coexisted for up to a few dozen generations. Only in
a handful of populations did a mixture of sexual and asexual organisms persist for an
extended period of time (c. g. Figure 9c). We analyzed the data in two different ways:
first, by recording the dominant mode of reproduction at the end of the study; second, by
calculating the proportion of time during which each experimental population was

predominantly sexual.

48

We found that sexual reproduction was frequently present and often favored over
asexual (Figure 10a). For example, when the environmental change period was lOu and
metabolic values were (-1 , 5), more than 65% of populations were predominantly sexual
at the end of the study. However, because many populations repeatedly switched the
mode of reproduction throughout the study, our data may depend on the choice of the
final time point. For example, a population that spent the majority of its history as
asexual might better be classified as such, even if it evolved to sexual reproduction
shortly before the end of the experiment (e.g. Figure 9b). Thus, we also measured the
proportion of time during which a population was dominated by sexually reproducing
organisms. Fortunately, both the final (top) and time-average (bottom) measures of
reproductive mode yield the same general pattern (Figure 10). Populations are likely to
be dominated by sexual organisms when substrates are rapidly changing between
nutrients and poisons, and when the benefits of metabolizing nutritious substrates are also
high. Both effects of the environmental period of change and of the metabolic values are
highly significant (two-way ANOVA, F5936 = 10.153, P < 0.001 for the period of
environmental change and F3936 = 74.983, P < 0.001 for the metabolic values, Table 4),
as is the interaction between these two factors (F1 5,936 = 5.039, P < 0.001, Table 4). In
the two environmental regimes where the value of metabolizing a nutrient was less then
or equal to that the cost of consuming a poison, (-1, 1) and (-3, 1), asexual reproduction
dominated regardless of the period of environmental change. By contrast, in the two
regimes where nutrient benefits outweighed the poison cost, (-1, 3) and (-1, 5), sexual
reproduction prevailed as often as asexual when substrate metabolic values were

changing rapidly, while asexual reproduction prevailed in more slowly changing

49

(a) (b) (c) (d)

 

 

 

 

 

 

 

 

 

 

 

 

 

1
E
5” 0.5
a
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'3 0
g
.3 (e) (0 (g) (h)
g 1
'E I
a
a 0.5

0

o a so a so 3 8° a s
time (1000 updates)

Figure 9. Proportion of sexual organisms present in a population over time. Ancestral
populations were asexual for panels (a)-(d) and sexual for panels (e)-(h). All the
populations evolved at the 3u period of environmental change with (-l , 5) metabolic
values. Populations were chosen to illustrate the different types of population trajectories

observed in the full data set.

50

Figure 10. Prevalence of sexual reproduction under 24 different treatments. (a) Number
of sexual populations that evolved in environments with different periods of
environmental change and metabolic values. Populations were categorized as sexual if
more than half of the organisms at the end of the experiment reproduced sexually. (b)
Proportion of time populations spent as sexual during evolution was measured for each
population and then averaged over the 40 populations that evolved at each period of

environmental change and substrate value combination. Error bars represent one

standard error of the mean.

51

 

 

4

300

300

100
100

period of change (updates)

substrate values
— (-1. 1)

30

10

 

(a)

\l
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52

3

environments. Our results show that sex is beneficial only in environments with certain
combinations of the rates and magnitudes of environmental change and the metabolic
values, and, moreover, that the interaction between these two factors is also important for
the evolution of sex.

To this point, our experiments Show that asexual reproduction dominates in
slowly changing environments while sexual reproduction prevails — or at least holds its
own — when the environmental change is rapid and the benefits of consuming nutrients
sufficiently great. We now turn to several subsidiary experiments to examine four related
issues. First, we examine whether the initial reproductive mode exerts an influence on
the prevalence of sex. Second, we examine whether ancestral features of genetic
architecture matter for the evolution of sexual reproduction. Third, we explore whether,
at some point, environmental change is so rapid that populations simply cannot adapt fast

enough and sex again loses its advantage. Fourth, we ask whether sexually reproducing

 

 

Source of variation Sum of squares df Mean square F P
Period of change 3.584 5 0.717 10.153 < 0.001
Metabolic values 15.881 3 5.294 74.983 < 0.001
Interaction 5.337 15 0.356 5.039 < 0.001
Error 66.081 936 0.071

 

Table 4. Two-way ANOVA testing the effects of the period of environmental change
and the substrate metabolic values on the proportion of time populations were dominated

by sexual organisms. Using all treatments and data from Figure 10b.

53

organisms evolve to have higher fitness than asexual ones. In these additional
experiments, we focus on the populations that all evolved with the same metabolic
values, namely (-1, 5). To increase our statistical power, we generated 60 additional
populations (30 initially sexual and 30 initially asexual) at each of the six different
periods of environmental change used previously, for a total of 600 populations that
experienced the (-1, 5) metabolic values.

We first examined the potential effect of the mode of reproduction of the ancestral
population on the prevalence of sex during evolution in changing environments. We
found that sexual organisms dominated the populations that started as sexual for a greater
proportion of time than the populations that started as asexual (Figure 11, Figure 12b).
Sexual populations were also more common overall at the end of the evolution (Figure
12a). The effect of initial mode of reproduction on the time averaged dominant mode of
reproduction during evolution in changing environments was highly significant (two-way

ANOVA, F1588 = 5.267, P < 0.001, Table 5), while the interaction between the initial
mode of reproduction and the period of environmental change was not significant (F5588
= 1.783, P = 0.114, Table 5). The lack of a significant interaction reinforces the fact that
sex was more common, regardless of ancestral mode, in more rapidly changing
environments (F5588 = 21.207, P < 0.001, Table 5). However, a significant lag in
response to selection for a particular reproductive mode could also yield this data. For
example, if populations that start as sexual do not immediately switch to asexual
reproduction when asexual reproduction is favored, then our data could show a greater
proportion of time spent sexual and incorrectly suggest that sex is favored. To address

this issue, we reanalyzed the data by calculating the proportion of time that populations

54

Figure 11. Relationship between the prevalence of sex and the ancestral mode of
reproduction. Fifty populations evolved from sexual and 50 from asexual ancestors in
environments with (-1, 5) metabolic values. Number of sexual populations (a) and
proportion of time spent sexual (b) were measured as before (see text, Figure 10), and are

shown here separately for populations with different ancestral reproductive modes. Error

bars represent one standard error of the mean.

55

 

 

ancestral reproduction

(a)

asexual

 

sexual

300

100

 

30

10

 

10 30 100 300

3

 

 

period of change (updates)

56

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l
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g" 0.5
a
8
5
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1 3 10 30 100 300
period of change (updates)

Figure 12. Proportion of time during experimental evolution that each population was
predominantly sexual. Dark shades indicate populations that were mostly sexual over
time, while light ones indicate populations that were mostly asexual. All populations
evolved in environments with metabolic values (-1, 5). Populations with asexual

ancestors are presented in panel (a) and populations with sexual ancestors in panel (b).

57

 

Source of variation Sum of squares df Mean square F P

 

Initial reproductive mode 5.267 1 5.267 48.824 < 0.001
Period of change 11.439 5 2.288 21.207 < 0.001
Interaction 0.962 5 0.192 1.783 0.1 14
Error 63 .431 588 0.108

 

Table 5. Two-way ANOVA testing the effects of the initial mode of reproduction and
period of environmental change on the proportion of time populations were dominated by

sexual organisms. Using only treatments and data from Figure 11b.

 

 

Source of variation Sum of squares a’f Mean square F P
Initial reproductive mode 2.623 1 2.623 17.021 < 0.001
Period of change 14.694 5 2.939 19.071 < 0.001
Interaction 1.143 5 0.229 1.484 0.193
Error 90.608 588 0.154

 

Table 6. Two-way ANOVA testing the effects of the initial mode of reproduction and
period of environmental change on the proportion of time populations were dominated by
sexual organisms. Only the data from the second half of the evolutionary experiments

shown in Figure 11b are used (see text).

58

were sexual only during the second half of the experiments. We found the same
qualitative pattern to hold, with significant effects of the initial mode of reproduction and
period of change, but no significant interaction between them (Table 6). The overall
effect of the initial mode of reproduction was reduced, however, and during the second
part of the study, the proportion of time that sexual reproduction was dominant differed
by less than 10% between populations started with the two modes of reproduction.

A change in the mode of reproduction is inherently more difficult than simply
the maintenance of the existing mode. Moreover, asexual organisms may have evolved
genomes that are physically organized in such a way that it is more difficult to evolve
sexual reproduction; for example, favorable genetic combinations assembled within
asexual genomes may easily be disrupted by recombination. Because our work builds on
the evolutionary experiments from Chapter 2, we have an abundance of information
about the ancestral populations from which all the populations in this study evolved.
Using the data from Chapter 2, we investigate whether the properties of the ancestral
populations (besides their mode of reproduction) influence the evolution of sex in
changing environments.

The populations in Chapter 2 evolved either strictly sexually or strictly asexually
for over 10,000 generations. At the end of that evolution we measured their fitness,
genome length, modularity and fitness decay under random mutations. We found that
sexual genomes tended to be bigger, on average, and had evolved to be more modular in
two different ways. The regions of the genome responsible for metabolizing different
nutrients overlapped less (high functional modularity, FM) and were more condensed

(high physical modularity, PM) in sexual organisms than in asexual organisms. To

59

determine the effects of random mutations as well as their interactions, we constructed
millions of mutants and measured their fitness. We then fit the power function to the

data, loglOW = -0tMl3, where W is fitness and M the number of random mutations.

Parameters 0t and B reflect robustness to individual mutations and mutational
interactions, respectively. We found that sexual organisms were, on average, more robust

to mutations (0tsex < orasex) than asexual organisms. Interactions among mutations were
on average antagonistic, but less so in sexual then in asexual organisms (Basex < Bsex < 1).

There are at least two distinct ways in which genetic architecture in general, and
modularity and epistasis in particular, might promote sexual reproduction. First, more
modular genomes may allow faster exchange of the modules (metabolic building blocks),
making sexual organisms more evolvable (Schlosser and Wagner 2004; Wagner and
Altenberg 1996). Second, synergistic epistatic interactions between deleterious
mutations may facilitate removal of those mutations through recombination and thus
promote sexual reproduction (De Visser and Hoekstra 1998; Kondrashov 1982; Michod
and Levin 1988; Wolf et al. 2002). To test whether modularity and epistasis influenced
the evolution of sex in the experiments in changing environments, we performed
discriminant analysis on the ancestral parameters using the 600 populations evolved with
(-1, 5) metabolic values. In particular, for the six treatments with different periods of
environmental change, we constructed discriminant functions that would categorize the
final populations from this study as sexual or asexual based on their ancestral fitness,
genome length, PM, FM, or, and B. Here, the population is categorized as sexual or

asexual depending on the most prevalent reproductive mode at the end of the study. The

60

 

 

Period of change Wilks' lambda F 6,93 P % correct
lu 0.8791 2.1321 0.0568 60
3u 0.9190 1.3666 0.2363 53
10u 0.9111 1.5115 0.1829 56
30u 0.9325 1.1224 0.3554 52
100u 0.9512 0.7947 0.5764 48
300u 0.9352 1.0736 0.3840 53

 

Table 7. Discriminant analysis for the final mode of reproduction under six periods of

environmental change. Each discriminant function was constructed using the ancestral
fitness, genome length, PM, FM, on, and B values (see text). The P values indicate
whether the function was significant as a whole. The percentages reflect the number of

populations that were correctly classified as sexual or asexual using the discriminant

function.

six discriminant functions were, on average, able to correctly classify 53.67% of the final
populations, but none of the functions were statistically significant (Table 7). When we
included the initial mode of reproduction as an additional variable for the discriminant
function, on average, 54.83% of populations were correctly classified. Those
discriminant functions were significant in only two out of six cases (Table 8). However,
both Si gnificant discriminant functions assigned the largest weight to the initial mode of

reproduction, whose influence was already apparent as described earlier (Figure 11,

61

 

 

Period of change Wilks' lambda F6993 P % correct
1u 0.8600 2.1394 0.0470 63
3u 0.9141 1.2353 0.2917 51
10u 0.8049 3.1848 0.0046 63
30u 0.9316 0.9649 0.4616 50
100u 0.9358 0.9010 0.5094 50
300u 0.9352 0.9108 0.5018 52

 

Table 8. Discriminant analysis for the final mode of reproduction under six periods of

environmental change. Each discriminant function was constructed using the ancestral

mode of reproduction, fitness, genome length, PM, FM, on, and B values (see text). The P

values indicate whether the function was significant as a whole. The percentages reflect

the number of populations that were correctly classified as sexual or asexual using the

discriminant function.

Figure 12). We conclude that genetic architecture had little effect on the subsequent

propensity to evolve or maintain sexual reproduction in changing environments.

Further support for this essentially negative result came from the analysis of the

number of times sex evolved from each starting population. The same ancestral at each

period of environmental change. If a certain population was strongly predisposed to

evolve or maintain sexual reproduction, it might be sexual in a disproportionate number

of those 6 experiments. Here, we used the predominant final mode of reproduction to

categorize a population as sexual or asexual. We first counted the number of times each

starting population evolved to be sexual and categorized the populations accordingly
(observed values, Figure 13). There were 7 categories, corresponding to ancestral
populations that evolved (or remained) sexual 0 through 6 times. We then preformed a
randomization test by comparing the observed distribution with a random null-
distribution. In generating the null-distribution, we started by randomly selecting a
hypothetical collection of sexual populations for each period of environmental change.
The number of populations in the collections was determined by the actual number of
populations that were dominated by sexual organisms at the end of our experiments. We
then counted the number of times each population was in collections from different
periods of change. This was repeated 1000 times and the average number of populations
in each category was the random distribution (expected values, Figure 13). Finally, we
compared the random and the observed distributions, treating populations that evolved
from sexual and asexual separately. There was no statistically significant difference
between the observed and randomly generated distributions in either case (Chi-square =
10.855, df = 6, P = 0.0930 for asexual ancestors; Chi-square = 4.339, df = 6, P = 0.6309
for sexual ancestors). This result supports the interpretation that the general properties of
the ancestral populations do not strongly affect the outcome of evolution of sexual
reproduction in changing environments.

Contrary to our expectations, sexual reproduction dominated in the experiments
with energy values of (-1, 5) even at the shortest period of environmental change, with
one substrate changing from a nutrient to a poison and another from a poison to a nutrient
at every update (Figure 11). A closer consideration of our environmental setup suggests

that, while the environment may extremely variable, nutrients must also reoccur very

63

Figure 13. Number of times each ancestral population evolved to be sexual. Populations
evolved in environments with metabolic values (-1, 5). Populations with asexual
ancestors are presented in panel (a), and populations with sexual ancestors in panel (b).
Black bars represent the observed number of times individual ancestral populations
became or remained sexual after evolution in environments with 6 different periods of

change. White bars represent the expected values based on the randomization procedure

described in the text.

 

20

y—s
LII

number of populations
8

20

15:

number of populations
8

UI

 

 

 

 

 

 

 

M

(a) [:1 expected
- observed

0 2 3
(b) [:1 expected

 

J

O

- observed

  

 

 

 

 

 

2 3 4 5 6 7
number of times sexual

65

frequently. For example, when the period of environmental change is 1 update, each
substrate on average oscillates though periods of 25 updates (~3 generations) as a
nutrient, followed by 68 updates (~8 generations) as a poison. As we have a finite
number of substrates available in the system, we cannot create environments that will
continuously present the evolving populations with completely novel nutrients and
poisons. However, we can lower the number of nutrients present at one time, and thus
extend the time between occurrences of individual nutrients in the environment. We
conducted additional experiments at the metabolic values (-1, 5) with only 10 of the 68
variable substrates as nutrients at any given time, in contrast to the 25 present as nutrients
in all our previous experiments, with all else equal. The environment was changing in
the same way as in the previous experiments and 20 initially sexual and 20 initially
asexual populations evolved at every lu, 3u, 10u, 30u, 100u, and 300u period of change.
We find now that the asexual reproduction dominated at all periods of environmental
change (Figure 14). We contrast these experiments to those in which the 40 populations
evolved with identical metabolic values (-1, 5), but with 25 nutrients present at a time
(Figure 10). We find that in the 25-nutrient experiments the proportion of time spent as
sexual continues upward (or perhaps levels off) at the shortest periods of environmental
change, while in the lO-nutrient experiments it clearly peaks at the intermediate values
and then declines as the environment changes even faster. The period of environmental
change had a significant effect on the reproductive mode in the 10-nutrient experiments

(one-way ANOVA, F5234 = 2.964, P = 0.013, Table 9). We fit linear and a quadratic

function to both sets of data to characterize the shape of the observed relationship

between the period of change and prevalence of sex. Given that the period of change

66

 

 

 

 

 

 

number of nutrients
_. 25
a: 0.8”
g — 10
E
93’,» 0.6-
e..- 1\T J
a; f i
g 0.4”
.2
1:
8.
o
‘5. 0.2
O 1 r 1 r 1
1 3 10 30 100 300
period of change (updates)

Figure 14. Prevalence of sexual reproduction in environments with different numbers of
nutrients. All populations evolved in the environments with (-1, 5) metabolic values.
Populations had either 25 or 10 nutrients present any the time among the 68 changing
substrates. Data for populations with 25 nutrients are reproduced from Figure 10 for
comparison. Proportion of time spent sexual was measured as before (see text, Figure

10). Error bars represent one standard error of the mean.

67

spans three orders of magnitude, we loglo transformed the values for the period of

change prior to the regression analysis. In 10-nutrient environments, linear function was
not significant, while the quadratic function was highly Significant (Table 10). In
contrast, in the 25-nutrient populations, the linear function was significant, but the
quadratic term did not significantly reduce the unexplained variation (Table 10). Our
results suggest that while sex may thrive in rapidly changing environments, there can also
be too much change under certain scenarios, in which case asexual reproduction prevails
again.

Finally, we examine the fitness values of sexual and asexual organisms evolved in
the 600 populations with metabolic values (-1,5). We identify the periods of time during
the evolution of each population when the majority of organisms were sexual, and we
calculate the mean of the fitness values recorded during those times. (Because the
environments are constantly changing while maintaining the same number of resources
and poisons, averaging fitness values across time is reasonable.) The same calculation is
done for the periods when a population was primarily reproducing asexually (Figure 15).
The mode of reproduction did not have a significant major effect on fitness (two-way

ANOVA, FI,IO70 = 2.102, P = 0.147, Table 11), but the period of environmental change
did (F5,1070 = 2.555, P = 0.026, Table 11). The interaction between the mode of

reproduction and the period of the environmental change was also marginally significant

(F5,1070 = 1.974, P = 0.080, Table 11). The general trend in relative fitness of sexual and

asexual populations confirms our previous results. In rapidly changing environments,

sexual organisms were favored over asexual ones, and the mean fitness of sexual

68

 

Source of variation Sum of squares df Mean square F P

 

Period of change 1.081 5 0.216 2.964 0.013

Error 17.070 234 0.073

 

Table 9. One-way ANOVA testing the effects of the period of environmental change on
the proportion of time populations were dominated by sexual organisms. Using data

from the 10-nutrient treatment shown in Figure 14.

 

 

Number of nutrients Type of function R2 F 1,596 P
10 Linear < 0.001

Quadratic 0.051 31.368 < 0.001
25 Linear 0.154

Quadratic 0.156 1.412 0.235

 

Table 10. Linear and quadratic fits of proportion of time spent sexual to loglo
transformed period of environmental change for populations evolving with 10 or 25
nutrients at a time. We conducted the Partial F test for significance of the marginal
improvement associated with the addition of the quadratic term to the model. We Show
the R2 values for both linear and quadratic fit, the Partial F statistic and the P value for

the Partial F test.

69

17' . . . .

 

 

 

 

 

current reproduction
8
O asexual
E
.5 sexual
H
0 ..
5
a:
8
a.
2
>.
.o
m
U)
(D
.2
“-1
0.)
DJ.)
M
II-r
0
>
M
1 3 10 100 300

30
period of change (updates)

Figure 15. Average fitness of predominantly sexual and predominantly asexual
populations. Fitness values that were recorded when a population was predominantly
sexual were averaged, and the same was done for the fitness values from the times when
a population was predominantly asexual. The fitness while sexual or asexual was then
averaged over the 100 populations that evolved at each period of environmental change.
All populations evolved in the environments with (-1, 5) metabolic values. Error bars

represent one standard error of the mean.

70

 

Source of variation Sum of squares df Mean square F P

 

Initial reproductive mode 93.575 1 93.575 2.102 0.147
Period of change 568.782 5 1 13.756 2.555 0.026
Interaction 439.337 5 87.867 1.974 0.080
Error 47630451 1070 44.514

 

Table 11. Two-way ANOVA testing the effects of the mode of reproduction and the
period of environmental change on mean fitness. Using only treatments and data from

Figure 15.

populations was higher than that of asexual populations. Conversely, in more slowly
changing environments (3 0n, 100u, 300u), asexual organisms dominated the populations
most of the time and the mean fitness of asexual populations was slightly higher than that
of the sexual populations.

Over the past century, much thought has gone toward understanding the evolution
sexual reproduction (Bell 1982; Michod and Levin 1988; Weismann 1889), but
experiments in the area difficult and rare (Rice 2002). Here, we use digital organisms to
experimentally investigate the conditions in which sex can persist or even invade when
sexual and asexual organisms directly compete with each other. The potential for sex to
evolve in changing environments has been theoretically established in many studies, but
not experimentally tested in the past (Otto and Michalakis 1998). We find that sex can
prevail when populations evolve in rapidly changing environments. The maintenance
and invasion of sexual reproduction were only weakly affected by the ancestral mode of

reproduction, and other ancestral properties, such as genome length and genetic

71

architecture, also had little effect on evolution of sexual reproduction in changing
environments. Our experiments cannot say whether changing environments are the only
or the most important factor promoting the evolution of sex in the natural world (West et
al. 1999), but our study does demonstrate experimentally that environmental factors and

their interactions can play a very significant role in the evolution and maintenance of sex.

72

APPENDIX

PHENOTYPES IN AVIDA
As described in the main text, when an organism performs one of nine basic logic
operations on one or two random 32-bit strings and then outputs the bitwise-correct
result, it obtains additional energy that accelerates the execution of its genomic program.
The logic rules for all the operations are presented in Table 12 below. For example, if bit
A = 1 and bit B = 0, then (A OR B) = 1. These rules are defined on single-bit inputs; for
an organism to be rewarded for any operation, it must correctly perform it on all 32 bits
of the number strings.
Consider an organism that obtained the following two inputs and then output the
string below.
lnputA: 01010101110000000011101010101100
InputB: 10000110101000111101010110011110
Output: 11010111111000111111111110111110
The organism would receive the energy reward for performing the OR operation,
because it correctly calculated the OR function for all 32 pairs of the corresponding bits
in Input A and Input B and output the correct result.
The ability to perform a logic operation is scored as a phenotypic trait in the GP
maps. Figure 3c (main text) shows two different organisms that can perform eight of the
nine rewarded operations. In these examples, both the sexual and asexual organisms

have evolved the ability to perform the NOT, NAND, AND, ORN, OR, ANDN, NOR,

73

and EQU operations, but neither one can perform the XOR operation that is represented

by the penultimate column.

 

 

Input Logic operation
A B NOT NAND AND ORN OR ANDN NOR XOR EQU
0 0 1 1 0 1 0 0 1 0 1
0 1 1 1 0 0 1 0 0 1 0
1 0 0 1 0 1 1 1 0 1 0
1 1 0 0 1 1 1 0 0 0 1

 

Table 12. Truth table for nine logic operations. NOT is preformed only on Input A,

while the other eight operations are functions of both inputs

RESOLVING GENOME-LENGTH ISSUES
In the main text, we reported that sexual populations evolved larger genomes, on average,
than did asexual populations. This difference was driven by a subset of populations that
had evolved very large genomes. Out of the 100 populations with each reproductive
mode, 35 sexual populations evolved genomes that averaged at least twice the ancestral
length of 50 instructions, while only 9 asexual populations did so. These very large
genomes typically evolved via genome doublings, and sexual reproduction in Avida
evidently increased the rate of genome doubling events, created more favorable genetic

combinations in larger genomes, or both.

74

To determine whether genome doublings and the resulting difference in average
genome length between evolved sexual and asexual populations might bias or confound
the comparisons of their genetic architectures, we performed two supplementary analyses
described below. The first analysis excluded all those populations that evolved average
genome lengths twice or more the ancestral length. The second analysis used 100
additional populations with each reproductive mode, in which genome doublings were
prevented during the experiment itself.

Both supplementary analyses eliminated the greater average genome length of the
sexual populations and, in fact, they reversed the difference such that the asexual
populations had on average significantly longer genomes. Both also eliminated the
higher mean fitness values of the sexual populations relative to the asexual populations.
However, both supplementary analyses confirmed all the differences in genetic
architecture between sexual and asexual populations: (i) sexual genomes were more
modular (higher PM and FM); (ii) sexual populations were more robust to the effects of
single mutations (lower or); and (iii) asexual populations had stronger net directional

epistasis tending to alleviating interactions (lower B).

REDUCED DATA SET
We excluded all populations with average genome length 2100 instructions, which is
twice the ancestral length. We repeated the original analyses on this reduced data set,
which included 65 sexual and 91 asexual populations. The differences between sexual
and asexual populations in PM, FM, 0t, and B remained significant and in the same

direction as in the full data set (Table 13). However, average genome length was now

75

significantly greater in the asexual organisms, the opposite outcome to the full data set, so

that genome length cannot be driving these differences in genetic architecture.

GENOME DOUBLINGS PREVENTED
Analysis of the reduced data set shows that the larger tail of long genomes in the sexual
populations was not responsible for the evolved differences in genetic architecture
between sexual and asexual organisms. We sought fin‘ther confirmation by evolving an
additional 200 populations with the experimental conditions identical to the original runs
in all but one respect: genome doublings were prevented from ever occurring in these
experiments by imposing a 10% limit on the difference in genome length between parents
and offspring. Whenever a divide instruction (sexual or asexual) was about to be
executed, the Avida program checked the genome length of the incipient offspring. If the
potential genome was more than 10% longer (or shorter) than its parent’s genome, the
divide instruction was skipped and the execution proceeded to the next instruction in the
genome. Thus, no offspring were ever produced with genome doublings or other radical
changes in genome length. Very large genomes did not evolve in these modified runs
and, in fact, sexual populations had significantly shorter genomes, on average, than did
asexual populations. However, the genetic architectural features PM, or, and B differed
significantly and in the same direction as observed in the original experiments (Table 14).

The difference in FM was no longer significant but remained in the same direction.

76

 

response variable

mean sexual (: s.d.)

mean asexual (: s.d.) P

 

logm fitness

loglo genome length
physical modularity, PM
functional modularity, FM
average effect of single point
mutations on fitness, or

net directional epistasis, B

4.835 (1.230)
1.752 (0.100)
0.775 (0.057)

0.803 (0.084)

0.724 (0.173)

0.904 (0.051)

5.033 (1.104)
1.826 (0.059)
0.689 (0.066)

0.761 (0.077)

0.792 (0.176)

0.854 (0.088)

0.303

< 0.001

< 0.001

0.002

0.019

< 0.001

 

Table 13. Comparisons of properties between sexual and asexual evolved populations in

the reduced data set. The P values are based on two-tailed t-tests.

 

response variable

mean sexual (1 s.d.)

mean asexual (: s.d.) P

 

loglo fitness

loglo genome length
physical modularity, PM
functional modularity, FM
average effect of single point

mutations on fitness, or

net directional epistasis, B

4.678 (1.107)
1.703 (0.013)
0.717 (0.064)

0.771 (0.078)

0.765 (0.162)

0.901 (0.056)

4.944 (1.242)
1.845 (0.061)
0.694 (0.073)

0.761 (0.080)

0.827 (0.183)

0.828 (0.107)

0.112

< 0.001

0.021

0.356

0.004

< 0.001

 

Table 14. Comparisons of properties between sexual and asexual evolved populations

with genome doublings prevented. The P values are based on two-tailed t-tests.

77

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