THE EVOLUTION OF COMPLEXITY AND ROBUSTNESS IN SMALL POPULATIONS

By

Thomas LaBar

A DISSERTATION

Michigan State University

in partial fulfillment of the requirements

Submitted to

for the degree of

Microbiology and Molecular Genetics – Doctor of Philosophy
Ecology, Evolutionary Biology, and Behavior – Dual Major

2018

ABSTRACT

THE EVOLUTION OF COMPLEXITY AND ROBUSTNESS IN SMALL POPULATIONS

By

Thomas LaBar

A central goal of evolutionary biology is to understand a population’s evolutionary trajectory from
fundamental population-level characteristics. The mathematical framework of population genetics
provides the tools to make these predictions. And while population genetics provides a well-studied
framework to understand how adaptation and neutral evolution quantitatively alter population
fitness, less attention has been paid to using population genetics to predict qualitative evolutionary
outcomes. For instance, do different populations evolve alternative genetic mechanisms to encode
similar phenotypic traits, and if so, which processes lead to these differences? This dissertation
investigates the role of population size in altering the qualitative outcome of evolution.

It is difficult to experimentally investigate qualitative evolutionary outcomes, especially in
small populations, due to the time required for novel evolutionary features to appear. To get around
this constraint, I use digital experimental evolution. While digital evolution experiments lack
aspects of biological realism, in some regards they are the only methodology that can approach the
complexity of biological systems while maintaining the ease of analysis present in mathematical
models. Digital evolution experiments can never prove that certain evolutionary trajectories occur
in biological populations, but they can suggest hypotheses to test in more realistic model systems.
First, I explore the role of population size in determining the evolution of both genomic and
phenotypic complexity. Previous hypotheses have argued that small population size may lead to
increases in complexity and I test aspects of those hypotheses here. Second, I introduce the novel
concept of “drift robustness” and argue that drift robustness is a strong factor in the evolution
of small populations. Finally, I end with a project on the role of genome size in enhancing the
extinction risk of small populations. I conclude with a broader discussion of the consequences of
this research, some limitations of the results, and some ideas for future research.

Copyright by
THOMAS LABAR
2018

ACKNOWLEDGEMENTS

As with any large body of work, this dissertation was not solely due to the efforts of one person. I
have many people to thank for assisting me during my Ph.D.

First, I thank my advisor, Chris Adami, for his support over my five years as his student. During
my Ph.D., Chris was always available to provide feedback and advice on my work. He gave me
the independence to develop my own projects, while also supporting those same projects as they
progressed. Chris and I co-wrote many manuscripts during my Ph.D., only a fraction of which are
reproduced here. I am not convinced that I would have been this productive without Chris as my
mentor. I also must thank the past and current members of the Adami lab, for creating a productive
and multidisciplinary intellectual atmosphere.

Second, I thank Rich Lenski and the Lenski lab for providing me with a second academic
home at Michigan State. The Lenski lab took me in and taught me how to perform microbial
evolution experiments, an invaluable novel tool for myself that unfortunately is not apparent from
the work present here. I am grateful to the members of the Lenski lab for their invaluable discussions
concerning the field of microbial experimental evolution and evolutionary biology. I must especially
thank Kyle Card for his willingness to incorporate myself into his Ph.D. project and mentor me in
the ways of microbial evolution studies.

I thank my committee members, Yann Dufour, Charles Ofria, and Chris Waters, for their guid-
ance and comments during what was perhaps an atypical dissertation project for the Microbiology
and Molecular Genetics program.

I thank all of my collaborators, including Arend Hintze, Michael Miyagi, Aditi Gupta, Nitash
C.G., Ali Tehrani-Saleh, Kyle Card, Jasper Gomez, and Minako Izutsu, for the opportunity to work
with them on a variety of projects during graduate school.

I thank the BioMolecular Sciences Gateway Ph.D. program, the Microbiology and Molecular
Genetics Department, the Ecology, Evolutionary Biology, and Behavior program, and the BEACON
Center for the Study of Evolution in Action for providing me with the opportunity to receive my

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PhD and establishing departments and programs with an interdisciplinary focus such that a student
with a mathematics background would fit in. A special thanks goes out to all the support staff that
bring these programs into existence.

I thank Michigan State’s College of Natural Sciences for a recruiting fellowship and Michigan
State’s Graduate School for a University Distinguished Fellowship. I thank the BEACON Center
for the Study of Evolution in Action for a Top-Up Fellowship, for travel support, and for project
funding. I thank the Michigan State Microbiology and Molecular Genetics Department and the
relevant sponsors for the Russell B. DuVall award and the Rudolph Hugh Fellowship. I also thank
the Society for Molecular Biology and Evolution for travel support.

No PhD is done in isolation. I owe a debt of gratitude to my friends for helping me during my
time as a PhD student, especially the following: Anna Huff, Cara Weisman, Kyle Card, Meredith
Zettlemoyer, Katie Minnix, Josh Franklin, and Tanush Jagdish. I thank all of you for your friendship.
Finally, I must thank my parents for providing me with the upbringing to make all of this
possible. They always encouraged me to follow my own interests, both intellectual and otherwise,
and allowed me the opportunity to choose my own path in life. For that, I am eternally grateful.

v

TABLE OF CONTENTS

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CHAPTER 1

LIST OF TABLES .
LIST OF FIGURES .

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INTRODUCTION .

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1.1 Population Genetics and Evolutionary Dynamics of Small Asexual Populations
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1.2 Molecular Mechanisms of Evolution in Small Populations . . . . . . . . . . . . . .
1.3 Overview of Digital Experimental Evolution . . . . . . . . . . . . . . . . . . . . .
1.4 Outline .

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CHAPTER 2 DIFFERENT EVOLUTIONARY PATHS TO COMPLEXITY FOR SMALL

Introduction .

2.7 Acknowledgments .

2.5 Discussion .
2.6 Methods .
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2.1 Abstract
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2.2 Author Summary .
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2.4 Results .

AND LARGE POPULATIONS OF DIGITAL ORGANISMS . . . . . . . . 13
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2.4.1 Genome Size Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.2 Evolution of Phenotypic Complexity . . . . . . . . . . . . . . . . . . . . . 21
2.4.3 Non-Functional Insertions
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2.4.4 Deletion Bias .
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2.6.1 Avida .
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2.6.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6.3 Data Analysis .
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CHAPTER 3 EVOLUTION OF DRIFT ROBUSTNESS IN SMALL POPULATIONS . . 39
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3.3.1 A mathematical model of drift robustness . . . . . . . . . . . . . . . . . . 42
3.3.2 Drift robustness in digital organisms . . . . . . . . . . . . . . . . . . . . . 45
Small populations evolve an altered DFE . . . . . . . . . . . . . . . . . . . 46
3.3.3
3.3.4
Small population genotypes are drift-robust
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3.3.5 Drift robustness is not due to fitness differences . . . . . . . . . . . . . . . 49
3.3.6 Epistatic mutations lead to drift robustness . . . . . . . . . . . . . . . . . . 50
3.3.7 Deleterious mutations drive the evolution of drift robustness
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3.5.1 Mathematical model of drift robustness

3.1 Abstract
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3.5.3 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.5.4 Data Analysis .
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3.5.5 Data Availability .
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CHAPTER 4 GENOME SIZE AND THE EXTINCTION OF SMALL POPULATIONS . 66
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4.3.1 Large genome size increases the extinction risk of small populations . . . . 69
4.3.2 Extinction and large genome size is associated with increases in the lethal

4.1 Abstract
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mutational load .

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4.3.3 Lethal mutation rates and stochastic viability drive population extinction . . 73
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4.5.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
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4.5.3 Data Analysis .

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4.6 Acknowledgments .

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CHAPTER 5 CONCLUSION .
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5.1 Further Conclusions .

changes in the lethal mutation rate . . . . . . . . . . . . . . . .

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4.5.3.2 Analysis of stochastic viability . . . . . . . . . . . . . . . . . . . 82
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5.1.1 Absence of mutational hazards in altering small population evolution . . . . 85
5.1.2 The differences between mutational robustness and drift robustness . . . . . 86
5.1.3 Drift robustness and bacterial endosymbionts . . . . . . . . . . . . . . . . 87
5.1.4 Drift robustness and the role of epistasis in small-population adaptation . . 88
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5.2 Limitations

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5.2.1 Avida as an intermediate between mathematical modeling and biological

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Populations in Avida are much smaller than relevant biological populations
5.2.3 Results apply to asexual haploid species evolving in a constant environment

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5.3.1 What is the genetic mechanism behind drift robustness? . . . . . . . . . . . 92
5.3.2 Drift robustness and sexual reproduction . . . . . . . . . . . . . . . . . . . 93
5.3.3 Drift robustness and its interaction with other robustness mechanisms
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Small population size and the evolution of functional complexity . . . . . . 95
5.3.4
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BIBLIOGRAPHY .

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LIST OF TABLES

Table 2.1: Merit rewards for the evolution of phenotypic traits. . . . . . . . . . . . . . . 35

Table 4.1: Notable Avida parameters changed from default value.

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viii

LIST OF FIGURES

Figure 2.1: Final genome size as a function of population size. Red lines are the
median values for each population size. The upper and lower limits of each
box denote the third and first quartile, respectively. Whiskers are 1.5 times
the relevant quartile value. Plus signs denote those data points beyond the
whiskers. Data represent only those populations that did not go extinct. . . . . . 18

Figure 2.2: Evolution of complexity for small population sizes. Statistics shown in
the main text for population sizes ranging from 10 to 100 individuals. Data
for populations with 10 and 100 individuals are the same as in Figure 2.1.
A) Evolution of genome size. B) Proportion of fixed insertions that were
slightly-deleterious. C) Proportion of fixed insertions that were under positive
selection. D) Number of evolved novel phenotypic traits. Red lines are the
median values for each population size. The upper and lower limits of each
box denote the third and first quartile, respectively. Whiskers are 1.5 times
the relevant quartile value. Plus signs denote those data points beyond the
whiskers. Data represent only those populations that did not go extinct. . . . . . 19

Figure 2.3: The number of insertions fixed as a function of population size. Red lines
are the median values for each population size. The upper and lower limits
of each box denote the third and first quartile, respectively. Whiskers are 1.5
times the relevant quartile value. Plus signs denote those data points beyond
the whiskers. Data represent only those populations that did not go extinct. . .

. 20

Figure 2.4: Proportion of slightly-deleterious insertions as a function of population
size. Red lines are the median values for each population size. The upper
and lower limits of each box denote the third and first quartile, respectively.
Whiskers are 1.5 times the relevant quartile value. Plus signs denote those
data points beyond the whiskers. Data represent only those populations that
did not go extinct.

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Figure 2.5: Proportion of insertions under positive selection as a function of popula-
tion size. Red lines are the median values for each population size. The upper
and lower limits of each box denote the third and first quartile, respectively.
Whiskers are 1.5 times the relevant quartile value. Plus signs denote those
data points beyond the whiskers. Data represent only those populations that
did not go extinct.

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Figure 2.6: Final number of evolved phenotypic traits as a function of population
size. Red lines are the median values for each population size. The upper
and lower limits of each box denote the third and first quartile, respectively.
Whiskers are 1.5 times the relevant quartile value. Plus signs denote those
data points beyond the whiskers. Data represent only those populations that
did not go extinct.

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Figure 2.7: The evolved fitness relative to the ancestor genotype. Red lines are the
median values for each population size. The upper and lower limits of each
box denote the third and first quartile, respectively. Whiskers are 1.5 times
the relevant quartile value. Plus signs denote those data points beyond the
whiskers. Data represent only those populations that did not go extinct. . . . . . 22

Figure 2.8: Correlation between the final genome size and the final number of evolved
traits. Black circles represent the combined data from populations with 10,
100, 1000, and 10000 individuals. Only replicates that survived all 2.5×105
generations were included.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 2.9: The effect of a fixed mutation rate on the evolution of phenotypic com-
plexity. The variable genomic mutation rate treatment represents the data
from when the genomic point mutation rate is 10−1× L, were L is the genome
size. The fixed genomic mutation rate treatment represents the data from
when the genomic point mutation rate was fixed at 1.5 × 10−1, independent
of the genome size. Red lines are the median values for each population size.
The upper and lower limits of each box denote the third and first quartile,
respectively. Whiskers are 1.5 times the relevant quartile value. Plus signs
denote those data points beyond the whiskers. Data represent only those
populations that did not go extinct.

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Figure 2.10: The evolution of complexity in the non-functional insertion treatment.
All subplots are a function of the population size. A) The final genome
size. B) The final number of evolved phenotypic traits. Populations with
20 individuals are shown instead of those with ten individuals due to the
high extinction rates of populations with ten individuals. Red lines are the
median values for each population size. The upper and lower limits of each
box denote the third and first quartile, respectively. Whiskers are 1.5 times
the relevant quartile value. Plus signs denote those data points beyond the
whiskers. Data represent only those populations that did not go extinct. . . . .

. 25

x

Figure 2.11: The proportion of fixed insertions that were under positive selection in the
non-functional insertion treatment compared to the original treatment
for populations with 104 individuals. Red lines are the median values for
each population size. The upper and lower limits of each box denote the
third and first quartile, respectively. Whiskers are 1.5 times the relevant
quartile value. Plus signs denote those data points beyond the whiskers. Data
represent only those populations that did not go extinct.

. . . . . . . . . . . . . 26

Figure 2.12: The evolution of complexity in the deletion bias treatment. All subplots
are a function of the population size. A) The final genome size. B) The final
number of evolved phenotypic traits. Red lines are the median values for each
population size. The upper and lower limits of each box denote the third and
first quartile, respectively. Whiskers are 1.5 times the relevant quartile value.
Plus signs denote those data points beyond the whiskers. Data represent only
those populations that did not go extinct.

. . . . . . . . . . . . . . . . . . . .

. 27

Figure 3.1: Conceptual diagram of drift robustness. a) A single-peak fitness landscape.
In this landscape, the large population (red circles) can climb to the top of
the fitness peak, while the small population (black circles) can only maintain
fitness on an intermediate part of the peak. b) A multi-peak fitness landscape.
The large population evolves to the same fitness peak as in panel a. The small
population evolves to the steeper, drift-robust peak. While this peak is still
lower than the drift-fragile peak, the small population attains greater fitness
than it would have on the drift-fragile peak in the single-peak fitness landscape . 41

Figure 3.2: The fitness landscapes for the Markov model to test for the evolution of
drift robustness. Each circle represents one genotype and is labeled with
its fitness. Each arrow represents the transition between one genotype to
another (including the identical genotype) and is labeled with the transition
probability. a) The fitness landscape for the minimal model. s represents the
selection coefficient of the drift-fragile peak and 
 represents the small fitness
difference between the drift-fragile peak and the drift-robust peak. ui j and
πi j represent the mutation rate between genotypes and probability of fixation
from one genotype to another, respectively. b) The fitness landscape for the
extended model. Variables as in panel a. Transition probabilities omitted for
clarity .

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Figure 3.3: Critical population size for shift between robust and fragile peaks. a)
Results for various n values with κ = 0.01. b) Results for various κ values
with n = 2. .

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Figure 3.4: Differences in mutational effects between small-population genotypes and
large-population genotypes. Black and red represent small-population and
large-population genotypes, respectively. a) The combined distribution of
fitness effects (DFE) across all 100 small-population genotypes and 100 large-
population genotypes. b) Same data as in panel a, but grouped into different
classes of mutations, where a small-effect deleterious mutation is defined as
having an effect less than 5%. Here, and throughout, deleterious mutation
refers to viable deleterious mutations, while lethal mutation refers to non-
viable deleterious mutations. c) The likelihood of a small-effect deleterious
mutation for small-population and large-population genotypes. Red lines are
medians, edges of the box are first and third quartile, whiskers are at most
1.5 times the interquartile range, and the plus signs are outliers. d) The mean
relative fitness of every possible point mutation (1250 mutations) for each
genotype. .

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Figure 3.5: Small-population genotypes are drift-robust due to a decreased likelihood
of small-effect deleterious mutations. Black and red data points represent
small-population genotypes and large-population genotypes, respectively. a)
Relative fitness of the most-abundant genotype from every population during
the drift robustness test. Each circle represents the relative fitness of one
genotype from one replicate. b) Relationship between relative fitness in the
drift robustness test (panel a) and the likelihood of small-effect deleterious
mutations (Fig. 3.4c) .

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Figure 3.6: Fraction of small-effect deleterious mutations for genotypes from small
populations and large populations with equal fitness. Each area separated
by a dashed line shows genotypes with equal fitness (w). S and L represent
small-population and large-population genotypes, respectively. Differences
for each fitness value are significant.
(Mann-Whitney U-test; Bonferroni-
corrected p < 3 × 10−3). Box plots as described for Fig. 3.4c. . . . . . . . . . . 50

Figure 3.7: Evidence of small-population adaptation to drift-robust fitness peaks.
a) Distribution of maintained beneficial mutational effects for (effects for
mutations whose fitness gain was at-least partially maintained during sub-
sequent evolution) small-population genotypes (black) and large-population
genotypes (red). b) Spearman correlation coefficients between fitness and the
likelihood of a deleterious mutation for each maintained beneficial mutation
from each population. c) The likelihood of (viable) deleterious and lethal
mutations, shown in magenta and green, respectively, in a representative
small population’s lineage. The strong decrease in the likelihood of a (viable)
deleterious mutation early in the population’s history is evidence of epistatic
mutations resulting in drift robustness. d) Number of populations that fixed
a maintained beneficial mutation that decreased the likelihood of a (viable)
deleterious mutation by at least a specified amount. Colors as in panel a.

. . . . 51

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Figure 3.8: The evolution of drift robustness in small populations with or without
deleterious mutations in the initial adaptation experiments. Black and
blue data points represent small-population genotypes adapted with delete-
rious mutations and small-population genotypes adapted without deleterious
mutations, respectively. a) Relative fitness to the ancestral genotype after 105
generations of adaptation. Box plots as described for Fig. 3.4c. b) Likelihood
of small-effect deleterious mutations. c) Relative fitness of the most-abundant
genotype from every population during the drift robustness test. Each circle
represents the relative fitness of one genotype from one replicate. d) Rela-
tionship between relative fitness in the drift robustness test (panel c) and the
likelihood of small-effect deleterious mutations (panel b).

. . . . . . . . . . . . 54

Figure 4.1: Possibility of genome expansions increase extinction in low mutation rate
populations. A) Number of extinct populations as a function of population
size. Solid (dashed) lines represent variable (fixed) genome size populations.
Black (white) circles represent low (high) mutation rate populations. Error
bars are bootstrapped 95% confidence intervals (104 samples). B) Time to
extinction for population size and mutation rate combinations. Lines and
colors same as in panel A. Error bars represent two times the standard error
of the mean. Data only shown for those treatments that resulted in at least ten
extinct populations.

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Figure 4.2: Extinct populations evolved larger genomes. A) Final genome size for the
low mutation rate populations as a function of population size. Populations
that survived are shown with gray boxplots; populations that went extinct
are shown with white boxplots. Red bars are the median value, boxes are
the first and third quartile, upper/lower whiskers extend up to the 1.5 times
the interquartile range, and circles are outliers. ** indicates p < 10−4, *
indicates p < 10−2, and N.S. indicates p > 0.05 for the Mann-Whitney U-test.
Population sizes where fewer than ten populations went extinct (or survived)
not shown. B) Final genome size for the high mutation rate populations as a
function of population size. Description same as in panel A. Population sizes
where fewer than ten populations went extinct (or survived) not shown.

. . . . . 70

Figure 4.3: Lethal mutation rate correlates with genome size and population extinc-
tion. A) The lethal mutation rate as a function of genome size for the final
genotypes from each evolved low mutation rate population. White circles
are extinct populations; gray circles are surviving populations. B) The lethal
mutation rate for extinct and surviving populations across population sizes.
Boxplots as previously described. Colors and significance symbols same as
Figure 4.2. Population sizes where fewer than ten populations went extinct
(or survived) not shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

xiii

Figure 4.4: Insertions and deletions directly change the lethal mutation rate. A)
Change in the lethal mutation rate as a function of a mutation’s effect on
genome size. Boxplots as previously described. Each data point represents
a genotype from a reduced evolutionary lineage of a population with 20
individuals. B) Relationship between a mutation’s change in genome size and
the change in the lethal mutation rate. Data same as in panel A. Dashed lines
represent no change. Data points comparing genotypes with equal genome
size were excluded.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Figure 4.5: Evolution of stochastic viability contributes to extinction risk. A) Number
of population extinctions (out of 100 replicates) as a function of population
size for the deleterious-reversion (squares) and no-reversion (circles) treat-
ments. Dashed and solid lines represent populations from fixed genome
size and variable genome size treatments, respectively. Error bars are 95%
confidence intervals generated using bootstrap sampling (104 samples). No-
reversion treatment data same as in Fig. 4.1A. B) Number of population
extinctions (out of 100 replicates) as a function of population size for the
lethal-reversion (triangles) and no-reversion (circles) treatments. Other sym-
bols same as in panel A. C) Percent of viability trials (out of 1000) for which a
given genotype was not viable. Values between 0 and 1 indicate stochastic via-
bility. “Original” refers to the 100 genotypes from the N = 8 populations that
evolved with lethal mutations. “Revert-lethal” refers the 100 genotypes from
the N = 5 lethal-reversion populations. Boxplots as previously described.
D) Genome sizes for always-viable and stochastically-viable genotypes from
both the N = 8 no-reversion populations and the N = 5 lethal reversion
populations.

. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

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CHAPTER 1

INTRODUCTION

This dissertation deals with questions of the following nature: how does small population size
and strong genetic drift (or weakened natural selection) alter the long-term evolutionary outcome
of a population? In other words, how does population size alter what evolves, not just how a
population evolves. The role of population size on the evolutionary dynamics of a population has
been a topic of interest to evolutionary biologists dating back to Sewall Wright and his Shifting
Balance theory [223]. However, the consequences of population size for the molecular and genetic
mechanisms of evolution has been less well-studied, although the rise of comparative genomics has
started to fill this gap (e.g., [121]).

More precisely, the research presented here focuses on the role of genetic drift and weakened
I
selection in altering the evolution of genetic and genomic architecture in small populations.
define genetic and genomic architecture as the loci (or genes) encoding a given phenotypic trait
and any relevant characteristics concerning these loci. Much of my work has focused on how
population size can alter the evolution of genome architecture complexity. While there are perhaps
an overabundance of definitions of “complexity” across many fields, I use an intuitive definition:
the complexity of some feature is simply the number of parts that compose that feature. For
example, Chapter 2 focuses on the role of population size in driving the evolution of genetic and
phenotypic complexity. In this chapter, I defined genetic complexity as genome size (i.e., number
of loci in the genome) and phenotypic complexity as the number of phenotypic traits. Another
measure of genetic complexity, say for a given phenotypic trait instead of the whole genome, could
be the number of loci encoding said trait.

One reason why studies on how population size alters the molecular mechanisms of evolution are
less abundant than studies on the population genetics of small populations is due to their difficulty.
Small populations have a slower rate of adaptation than large populations due to decreases in
the generation and effect size of beneficial mutations [37, 39, 215] and thus any experiments to

1

measure evolutionary change in small populations will take longer than experiments with large
populations. This evolutionary slowness is further compounded if one wants to study changes in
any complexity measure, as changes in complexity often require multiple mutations and thus occur
over long experimental timescales [109]. To avoid these constraints, I use the digital evolution
systems Avida [154] to experimentally study how population size alters the evolution of genetic
architecture and complexity.

Due to the previously-published or submitted nature of many of the chapters, specific in-
troductory text will be present on a per-chapter basis.
In this Introduction, I will review the
population-genetic basis of how population size can alter evolutionary dynamics and may influ-
ence the evolution of biological complexity. I will also provide an overview of digital evolution
studies and their role in experimentally-testing theories concerning the evolution of complexity and
robustness in small populations. I will end with an outline of the rest of the dissertation.

1.1 Population Genetics and Evolutionary Dynamics of Small Asexual Populations

Here, I will review the relevant literature on the population genetics and evolutionary dynamics
of small populations. For my purposes here, I will focus on evolution in small asexual haploid
populations. While most biological populations are sexual and experience some recombination,
most of the work in my subfield of experimental evolution uses asexual populations due to their
ease of analysis, including the results I present here. While it is likely that some of the results
from this research also apply to populations with recombination, these scenarios are not tested here
(see Chapter 5 for discussions on the interplay between genetic drift and recombination and their
possible relationship to the results presented here).

There are two main factors that constrain adaptation in small asexual populations: 1) limited
beneficial genetic variation, and 2) limited maintenance of weakly-beneficial mutations. Limited
genetic variation in small populations results simply from the limited number of individuals. If
a population has N individuals and each individual offspring receives a novel beneficial mutation
with probability Ub, then the population receives N × Ub beneficial mutations per generation.

2

It follows that populations with a smaller N receive fewer beneficial mutations per generation.
Furthermore, small populations are expected to experience beneficial mutations of smaller effect
size, as large-effect beneficial mutations are likely rarer than small-effect beneficial mutations [111].
This stochasticity in mutation supply leads to decreased repeatability across populations due to
increased stochasticity in which beneficial mutations appear [103]. Finally, small populations
should have a decreased supply of standing genetic variation that may become beneficial upon
environmental change, although evidence for this prediction is mixed in natural populations [221].
Thus, small populations have a decreased rate of adaptation in a constant environment [37, 39],
increased stochasticity in adaptation across populations in complex environments [103, 175, 190],
and a decreased capability to respond to environmental change [15, 103, 221].

The second evolutionary constraint faced by small populations is that purifying selection is
weaker, and genetic drift stronger, in small populations. More precisely, if a mutation alters a
genotype’s fitness by s, it will be effectively neutral if:
|s| (cid:28) 1
Ne

(1.1)

,

where Ne is the effective population size [155]. As a result, if a mutation is deleterious (i.e.,
s < 0) and the absolute value of its size is much less than the reciprocal of the effective population
size, its fixation probability is approximately that of a neutral mutation.
In other words, small
populations have a greater likelihood of fixing a deleterious mutation with a small effect size than
do large populations. Conversely then, small populations have a lesser likelihood of maintaining
the fixation of small-effect beneficial mutations.

Given that small populations lack the ability to purge small-effect deleterious mutations, what
are the consequences for adaptation? When discussing the effect of deleterious mutations on
population mean fitness, the concept of a mutational load is often introduced [150]. The mutational
load is often defined as the (deterministic) reduction in mean fitness from some optimal value due
to segregating deleterious variation and mutation-selection balance [7, 167]. A similar concept
exists for fitness reductions in populations due to weakened selection in small populations:
the
drift load [7, 167, 212]. The drift load is often incorporated into the mutational load [7] and can

3

be defined as variations to the deterministic predictions from mutational load calculations due to
stochastic, drift-induced, fluctuations in mutation frequency [91]. Here, I will define a population’s
drift load as the reduction in fitness due to the fixation of slightly-deleterious mutations [7]; this
has been referred to previously as the “fixed drift load” to separate fitness reductions due to
fixation from fitness reductions due to increased frequency of slightly-deleterious mutations in
small populations [167].

Over time, the continual fixation of slightly-deleterious mutations increases a population’s drift
load. If one assumes beneficial mutations are sufficiently rare and fitness loss is irreversible, this
leads to large fitness declines in a process known as Muller’s ratchet [72, 151].
If selection is
hard, and reductions in fitness reduce the number of offspring produced each generation, fixation
of slightly-deleterious mutations will cause population size to decrease [123]. This results in
a positive feedback loop between the fixation of slightly-deleterious mutations and population
size decreases known as a mutational meltdown and may explain why asexual species go extinct
at high rates [125]. Experimental evidence of both Muller’s ratchet [9, 26, 41] and mutational
meltdowns [233] in laboratory microbial populations suggests both phenomena may be relevant to
natural populations.

While both theory and experiments suggest that fitness declines due to genetic drift occur, the
assumption that small populations will continually decline in fitness has been repeatedly challenged.
One proposed mechanism that could halt Muller’s ratchet is synergistic/negative epistasis between
slightly-deleterious mutations [92]. If mutations become more deleterious as fitness decreases, then
the fitness decline will halt as the strength of purifying selection increases [93]. While there are
studies that show that deleterious mutations interact in a negatively-epistatic manner (e.g., [185]),
the overall evidence is mixed [73]. Some theoretical evidence suggests that small populations
should evolve positive epistasis, not negative epistasis [69]. It should also be noted that this effect is
dependent on the exact distribution of deleterious fitness effects [25]. Another assumption behind
Muller’s ratchet is that beneficial mutations are sufficiently rare such that small populations cannot
fix compensatory mutations that reverse their decline in fitness. There is abundant evidence that

4

populations can easily fix compensatory mutations in response to fitness declines [18, 23, 49,
147, 166, 189]. Furthermore, theory predicts that small populations should be able fix beneficial
mutations to halt fitness declines [66, 167]. Laboratory experiments with small viral populations
have shown that the rate of beneficial mutations increases as fitness decreases [183]; this relationship
halts the fitness decline of small populations. These pieces of evidence, both theoretical and
experimental, suggest that while small populations do face a drift load, fitness will not decline
continuously. Instead, small populations reach an equilibrium fitness where the fixation of slightly-
deleterious mutations is balanced by the fixation of compensatory beneficial mutations [66].

While most of the research concerning the evolutionary dynamics of small populations is
focused on fitness reduction, some have suggested that small populations may actually possess an
adaptive advantage over large populations [81]. This idea is as follows. Because large populations
face strong natural selection, they can quickly adapt to the nearest fitness peak. However, while
this fitness peak may be a local optimum, it may not be a global optimum (i.e., the highest possible
fitness peak in the fitness landscape). Thus large populations may adapt to locally optimal, but
globally suboptimal, areas of the fitness landscapes. Small populations do not face such strong
selective constraints. While they may climb locally-optimal fitness peaks, they may also fall-
down locally-optimal peaks. While this results in a short-term fitness decline, it also allows small
populations to locate other, potentially higher, fitness peaks and possibly evolve greater fitness than
large populations in a process known as valley-crossing. This scenario is the basic idea behind
Wright’s Shifting Balance theory for adaptation in small sexual populations [223].

Experimental evidence from experimental evolution suggests that it is possible for small popula-
tions to achieve greater fitness than large populations, at least in the short term. The maximum fitness
of an ensemble of small (or intermediate-sized) populations is often greater than the maximum
fitness of an ensemble of large populations, although the average fitness of the large populations
will be greater than the average fitness of the smaller populations [175, 178]. It has been shown
that this requires a complex, multi-peak, fitness landscape [74, 81]. However, additional theory
suggests that any small-population advantage may be limited. In asexual populations, large pop-

5

ulations valley cross faster than small populations [210]. In sexual populations, the relationship
between valley crossing and population size depends on the recombination rate: high recombina-
tion rates leads to faster valley crossing in small populations, while low recombination rates lead
to faster valley crossing in large populations [211]. This positive relationship between the rate
of valley crossing and population size is due to large populations having a greater likelihood of
stochastic tunneling, or receiving a beneficial mutation on a segregating, but not fixed, deleterious
genetic background [79, 208]. This advantage towards stochastic tunneling in large populations
overwhelms any advantage small populations may have in valley-crossing due to their increased
fixation of deleterious mutations. There is also some theoretical evidence that intermediate-sized
populations, and not large populations, get stuck on locally-optimal fitness peaks, while both
small and large populations valley-cross to globally-optimal peaks [153]. Under these conditions,
large populations should have an evolutionary advantage towards adaptation, as they avoid getting
stuck on local fitness peaks, but can valley-cross faster than small populations. Overall, previous
studies support the conclusion that while small populations do have an adaptive advantage over
large populations under certain conditions, small population size tends to lead to reduced adaptation.

1.2 Molecular Mechanisms of Evolution in Small Populations

While the population genetics and evolutionary dynamics of small populations have been
explored in some detail for many years, only recently have researchers begun to study how population
size alters the molecular mechanisms of evolution. In this section, I will focus on previous research
that seeks to explain how small populations should evolve differently from large populations not
in terms of fitness (as previously discussed), but in terms of specific phenotypic traits and genetic
architecture. Why should it be assumed that small population size may result in alternative
evolutionary “strategies” compared to large populations? The loss of fitness that small populations
experience due to genetic drift may allow them to climb fitness peaks otherwise inaccessible to
large populations. Fitness differences result from alternative phenotypes and alternative genetic
systems and the ability to access alternative areas of the fitness landscape suggests that small

6

populations should be able to access alternative genetic architectures. An example of how non-
adaptive evolutionary forces can alter genetic architecture comes from populations that have evolved
under strong mutational pressure, i.e., the “Survival of the Flattest” effect [220].

One of the most prominent theories concerning the differential evolution of genome architecture
and complexity in small populations is Michael Lynch’s Mutational Hazard hypothesis (MH hy-
pothesis; see [119] for an overview). The MH hypothesis starts from the assumption that one should
expect a species’s genome architecture to be influenced by its population-genetic environment [119].
While many theories try to explain differences in genome architecture across species by invoking
adaptive explanations, non-adaptive evolutionary processes, such as drift and mutation, can also al-
ter genome architecture [119]. The MH hypothesis argues that many of the features that distinguish
prokaryotic genomes from eukaryotic genomes, particularly multicellular eukaryotic genomes, are
due to the small effective population sizes of both current-day eukaryotic populations [95] and
possibly the ancestral eukaryote population [115]. The hypothesis argues that weakened selection
in small populations prevents the removal of excess genomic content [118]. This excess genome
space is slightly-deleterious due to its ability to potentially receive deleterious mutations in future
generations [121]. In other words, excess genome content is mutationally-hazardous [128]. This
evolutionary mechanisms of weakened selection against mutational hazards in small populations
has been invoked to explain the evolution of large genomes composed of primarily non-coding
DNA [121], the abundance of introns [114, 121], the presence of complex gene regulatory net-
works [117], the origins of complex gene structure and organization [10, 115], and the maintenance
of gene duplicates and subfunctionalization [121, 122] in multiceulluar eukaryotes. Meanwhile,
prokaryotes, due to strong selection pressure, maintain small, compact genomes with modular
operons and comparatively little non-coding content [116]. Later on in evolutionary time, this
increased genetic complexity may then give rise to increased phenotypic complexity [94, 118, 121].
It should also be noted that small-population prokaryotes, such as bacterial endosymbionts, have
reduced genome size compared to their free-living relatives [13, 100] due to a strong deletion bias
in prokaryoties [99]. The MH hypothesis has been controversial and some follow-up empirical

7

studies have resulted in conflicting evidence (e.g., [8, 67, 214, 230]).

In recent years, the metaphorical concept of “drift barriers” has been introduced into the evo-
lutionary biology literature [35, 124, 135, 188, 224]. This concept, similar to those previously
mentioned for the role of population size in evolution, argues that there is some theoretical bio-
physical optimum “value" for phenotypic traits and it is population size that determines how close
to that optimum a population can evolve [129]. This idea is of course similar to those proposed
in population genetics, with fitness as the stand-in phenotypic trait. The concept of a drift barrier
has been most often applied to the evolution of certain error rates, such as the mutation rate [188]
and the transcriptional error rate [135], although some experimental data contradicts the concept
of drift barriers [193]. For example, one expects the per-nucleotide mutation rate to be negatively
correlated with population size, a prediction supported by mutation accumulation experiments and
estimates from natural populations [188]. However, it can in theory be applied to any phenotypic
trait of interest. And while the concept of drift barriers does not provide any specific predictions
for how population size should alter genetic architecture, it does provide a conceptual framework
for thinking about how population size alters evolutionary outcomes beyond changes in fitness.

A third proposed mechanism underlying adaptation in small populations, and one relevant to
results presented here, is the evolution of mutational robustness [38, 198, 218, 220]. The evolution
of mutational robustness occurs when a population evolves genomic architecture that reduces
the deleterious effect of mutations. The concept has often been argued to shape the genomes
of species with high mutation rates and large population sizes, such as RNA virus [19, 106].
However, theoretical results have demonstrated that in fact small populations should be favored to
evolve mutational robustness and large populations should evolve mutational fragility [48, 68, 97].
Further theory suggests that both small and large populations should evolve robustness to mutations,
but through different evolutionary paths [169, 224]. Small population should evolve costly global
robustness solutions (such as improved DNA repair machinery that reduces the mutation across the
whole genome) while large populations should evolve local robustness solutions (such as reducing
It should also be noted that the
the deleteriousness of mutations at each locus individually).

8

evolution of mutational robustness in small populations is likely tied to the exact fitness landscape.
Most of the fitness landscapes used contain only small-effect deleterious mutations and neutral
mutations [97, 169], a fact I will return to in Chapter 3.

None of these (related) theories concerning the evolution of mutational robustness in small
populations have been extensively tested due to the difficulty of evolving novel traits in small popu-
lations in the time at which evolution experiments are performed. However, there is evidence from
obligate bacterial endosymbionts that small populations do evolve mutational robustness in nature.
These bacteria overexpress genes encoding heat-shock molecular chaperones and chaperonins, such
as DnaK and GroEL, compared to their free-living relatives [137]. This overexpression phenotype
is thought to have evolved in response to deleterious mutation accumulation due to small popula-
tion size and genetic drift [148]; overexpressing groEL in both Escherichia coli and Salmonella
typhimurium subjected to mutation accumulation greatly restores fitness [52, 130]. Furthermore,
endosymbiotic bacteria accumulate mutations at greater rates than free-living bacteria, suggesting
these mutations are less deleterious in endosymbionts [137, 148]. Laboratory evolution experi-
ments have shown that overexpression of groEL prevents the extinction of small populations, but
is deleterious in large populations and thus removed by purifying selection [176]. This result does
support the predictions for the global and local robustness theory for small and large populations,
respectively [169]. Small bacterial populations also possess other phenotypes that may be related
to mutational robustness, such as increased protein multi-functionality [86, 231] and lack of genes
encoding parts of the DNA repair machinery [137, 149], but the relevance of these phenotypes to
robustness remains to be explored.

1.3 Overview of Digital Experimental Evolution

In order to overcome some of the difficulties with evolving small populations with alternative
genetic architectures, I performed digital evolution experiments. Digital experimental evolution [1,
3, 12] is the computational equivalent of microbial experimental evolution [6, 45, 83]. Instead of
a population of microbes evolving in a flask, one has a population of computer programs (“digital

9

organisms”) evolving in some digital world. Digital evolution serves as an intermediate step in
model-system complexity between the mathematical models used in theoretical population genetics
and the microbial systems used in typical evolution experiments.

Digital evolution experiments are more complex than mathematical models and allow for the
spontaneous discovery of new evolutionary phenomena that may be missed in simpler models.
This ability for discovery, though, is a trade-off with the opaqueness and occasional arbitrariness
of many digital evolution systems; the large number of parameters in digital evolution system can
make it difficult to tease apart which parameters cause a given outcome. Sometimes, it is better to
have a simpler model in order to aid in understanding; digital evolution experiments often lead to
the development of these models (see Chapter 3). The advantage of digital evolution experiments
over microbial evolution experiments is that one can perform experiments for a longer time at
greater replication, one can perform experimental manipulations not yet possible in biological
systems, and digital systems can test hypotheses not yet reachable for biological models. Digital
evolution experiments can allow for the development of hypotheses in a more efficient manner than
in biological systems, and these hypotheses can then be tested in biological systems. Of course,
digital systems are not biological systems, and the relative simplicity of digital systems to biological
systems means important details will always be missed. Furthermore, digital evolution studies
cannot answer some questions of strong interest to evolutionary biologists, such as what genetic
variation occurs in biological populations (as opposed to how evolution shapes genetic variation).
While the trade-offs are not such that they eliminate the effectiveness of digital experimental
evolution, they must be remembered when performing these studies.

The digital evolution system used here is the Avida system [154]. In Avida, self-replicating
computer programs compete within a population for limited memory space and limited CPU time.
Each program (“avidian”) consists of a circular genome; each loci in the genome consists of one of
the twenty-six possible instructions in the Avida genetic alphabet. Each (viable) avidian genome
encodes the ability for reproduction and can also encode the ability to perform Boolean logic
calculations that serve as phenotypic traits in Avida [109]. Avida populations evolve these traits,

10

and other general alterations to their replication machinery. During reproduction, mutations may
be introduced into the offspring’s genome and these mutations may alter their bearer’s replication
speed. Faster replicators produce more offspring per unit time, and thus will out-compete slower
replicators. This results in selection for replication speed, not due to some selection algorithm
as in most evolutionary simulations, but due to faster growth. Because avidian populations have
phenotypic variation (in replication speed), individuals pass this variation to their offspring (due to
self-replication) and there are differences in reproductive output due to this phenotypic variation,
they undergo Darwinian evolution by natural selection [164].

Each chapter goes into the relevant details behind Avida for their contained experiments, so I
will avoid repeating any further description. Instead, I will now review some of the results from
previous Avida experiments relevant to evolution in small populations. Lenski et al. studied the
interplay between genome complexity, robustness and epistasis and found that complex genotypes
(i.e., large genome size) were more robust to deleterious mutations than simple genotypes (i.e., small
genome size) due to a lesser likelihood of lethal mutations [108]. Later, Wilke et al. demonstrated
that populations with high mutation rates evolve “flat” genomic architecture with a high likelihood
of neutral mutations and populations with low mutation rates evolve “fit” genomic architecture
with a high likelihood of deleterious mutations; they named this phenomenon the “survival of the
flattest” effect [216]. In a follow-up study, Edlund and Adami showed that flat genotypes evolved
robustness by evolving increased negative epistasis, although mutational effects were, on average,
multiplicative for flat genotypes [44]. Further work demonstrated that this relationship between
robustness and epistasis was prevalent in many computational evolution systems [216]. Misevic et
al. showed that sexual reproduction protected against extinction due to the mutational load in small
populations [144]. Avida experiments supported the hypothesis [68, 97] that small populations
evolve mutational robustness while large populations evolve mutational fragility [48]. Additional
survival of the flattest experiments have shown that population size does not alter the critical
mutation rate at which the transition from fit genotypes to flat genotypes occur (although they only
tested populations as small as 250 individuals [32]). Altogether, these Avida results show that: 1)

11

populations can evolve alternative genetic architectures under differing environmental conditions,
2) different avidian genetic architectures differ in mutational robustness, and 3) population size
interacts with robustness in a non-trivial manner.

While Avida has been often used to study the evolution of genomic architecture in regards to
robustness, it was also developed to study the evolution of biological complexity. Avida has been
used to test the development of a new metric for complexity, physical complexity [2, 4], and show
that biological complexity tends to increase in populations under selection [5]. Lenski et al. 2003
demonstrated how traits of great complexity require the intermediate evolution of simpler traits
to act as a “structure” on which to construct greater complexity [109]. This study also showed
that deleterious mutations often precede the evolution of novel traits in a lineage’s evolutionary
trajectory [109], a result later confirmed in Avida for general adaptation for populations evolving
with a high mutation rate [33]. In recent years, Avida has been used to explore many topics in
the evolution of complexity, such as the origin of somatic cells [63], the origins of division of
labor [62], and the role of host-parasite interactions [56, 232] and other ecologies [29, 205] in
driving the evolution of complexity. Together, the prior results demonstrate that Avida is a suitable
model system to study the evolution of robustness and complexity in small populations.

1.4 Outline

In Chapter 2, I present previously-published [101] results on the role of population size and
genetic drift in driving the evolution of genetic complexity (measured as genome size) and pheno-
typic complexity (measured as the number of phenotypic traits). In Chapter 3, I present previously-
published results [102] on a phenomenon I call “drift robustness” and discuss how that shapes
the evolution of small populations. In Chapter 4, I present results on how greater genome size
can enhance the likelihood of extinction of small populations by altering their likelihood of lethal
mutations. Finally, I conclude by discussing some further conclusions I missed in the original
published versions of each chapter, by discussing some limitations of these research projects, and
by discussing what I see are likely productive areas of future research.

12

CHAPTER 2

DIFFERENT EVOLUTIONARY PATHS TO COMPLEXITY FOR SMALL AND LARGE

POPULATIONS OF DIGITAL ORGANISMS

Thomas LaBar, Christoph Adami
Originally published: PLoS Computational Biology, 12(12): e1005066.
Figures have been renumbered from the published version.
Reproduced with permission from the publisher:
http://journals.plos.org/ploscompbiol/s/licenses-and-copyright

2.1 Abstract

A major aim of evolutionary biology is to explain the respective roles of adaptive versus non-
adaptive changes in the evolution of complexity. While selection is certainly responsible for the
spread and maintenance of complex phenotypes, this does not automatically imply that strong se-
lection enhances the chance for the emergence of novel traits, that is, the origination of complexity.
Population size is one parameter that alters the relative importance of adaptive and non-adaptive
processes: as population size decreases, selection weakens and genetic drift grows in importance.
Because of this relationship, many theories invoke a role for population size in the evolution of
complexity. Such theories are difficult to test empirically because of the time required for the
evolution of complexity in biological populations. Here, we used digital experimental evolution to
test whether large or small asexual populations tend to evolve greater complexity. We find that both
small and large—but not intermediate-sized—populations are favored to evolve larger genomes,
which provides the opportunity for subsequent increases in phenotypic complexity. However, small
and large populations followed different evolutionary paths towards these novel traits. Small pop-
ulations evolved larger genomes by fixing slightly deleterious insertions, while large populations
fixed rare beneficial insertions that increased genome size. These results demonstrate that genetic
drift can lead to the evolution of complexity in small populations and that purifying selection is not

13

powerful enough to prevent the evolution of complexity in large populations.

2.2 Author Summary

Since the early days of theoretical population genetics, scientists have debated the role of population
size in shaping evolutionary dynamics. Do large populations possess an evolutionary advantage
towards complexity due to the strength of natural selection in these populations? Or do small
populations have the advantage, as genetic drift allows small populations to cross fitness valleys
that large populations are unlikely to traverse? There are many theories that predict whether large or
small populations–those with strong selection or those with strong drift–should evolve the greatest
complexity. Here, we use digital experimental evolution to examine the interplay between popu-
lation size and the evolution of complexity. We found that genetic drift could lead to increased
genome size and phenotypic complexity in very small populations. However, large populations
also evolved large genomes and phenotypic complexity. Small populations evolved larger genomes
through the fixation of slightly deleterious insertions, while large populations used rare beneficial
insertions. Our results suggest that both strong drift and strong selection can allow populations to
evolve similar complexity, but through different evolutionary trajectories.

2.3

Introduction

The relative importance of adaptive (i.e., selection) versus non-adaptive (i.e., drift) mechanisms in
shaping the evolution of complexity is still a matter of contention among evolutionary biologists [5,
22, 94, 118, 140, 191]. In molecular evolution, the role of non-adaptive evolutionary processes such
as genetic drift and genetic draft are well-established [61, 89, 155]. Theoretical population-genetic
principles argue that neutral evolution, not natural selection, drove the evolution of large, primarily
non-functional, genomes [43, 128, 161]. Meanwhile, there exists abundant experimental evidence
that natural selection is the main cause of evolutionary change [103, 194, 202], including the spread
of novel adaptive phenotypes [20, 142] in experimental populations. However, it is still possible

14

that non-adaptive processes play a significant role in the evolution of complexity. For instance,
genetic drift (or relaxed selection) may allow for the accumulation of mutations that can later lead to
the evolution of novel complexity [118, 204]. Much of the work demonstrating the role of selection
in driving the evolution of novel complex traits is based on experiments with large populations and
strong selection [84]. In much smaller populations (i.e., those with fewer than 104 individuals),
selection is weaker, and genetic drift begins to alter evolutionary dynamics [103, 131]. Therefore,
to explain the role of adaptive vs. non-adaptive process in the evolution of complexity, one must
explore the role of population size in the evolution of complexity.

Both theoretical modeling and experiments suggest many possibilities for the relationship
between population size and the evolution of complexity. There are two classes of evolutionary
trajectories that would favor large populations in the evolution of complexity. First, populations
could perform an adaptive walk (the fixation of a sequence of beneficial mutations) towards the
evolution of a novel complex trait [181]. If this was the case, then larger populations would follow
this trajectory faster than small populations due to their larger mutation supply. Experiments with
microorganisms support the possible existence of adaptive trajectories towards complexity, as there
is strong evidence that the mutations leading up to a phenotypic innovation in both Escherichia
coli [168] and phage λ [24] were under positive selection. However, it is unclear whether adaptive
mutations generally precede the evolution of complex traits or whether these large microbial
populations can only take adaptive walks due to the intensity of selection in large populations.
The second type of trajectory that favors large populations is the neutral walk (the fixation of a
sequence of neutral mutations). While any individual neutral mutation has a low probability of
fixation, a large population would be able to accumulate many neutral mutations at any given time
allowing for the exploration of its fitness landscape. Work by Wagner and colleagues suggests
that many phenotypic traits are connected to each other by sequences of phenotypically neutral
mutations [203, 204].

If the evolution of complexity requires the fixation of deleterious mutations (for example,
via valley-crossing), then the elimination of deleterious mutations by purifying selection may

15

limit the evolutionary advantage large populations may have. Wright was the first to propose an
evolutionary advantage of small populations due to valley-crossing [223]. More recently, scientists
have explored under which conditions small populations have an evolutionary advantage over large
populations [81, 175]. A prominent theory that predicts that small (but not large) populations should
evolve the greatest genomic complexity (and subsequently organismal complexity) is the Mutational
Burden (or Mutational Hazard) hypothesis, proposed by Lynch and colleagues [118, 119, 121]. This
hypothesis argues that genome size should be inversely correlated with the product of the effective
population size and the mutation rate [94, 121]. Strong purifying selection against excessive genome
size streamlines the genomes in large populations [13, 116, 235]. Meanwhile, weakened purifying
selection and increased genetic drift in small populations results in the accumulation of slightly
deleterious excess genome content [94, 119]. At a later time, this slightly deleterious genome content
may be mutated into novel beneficial traits [96, 118]. However, recent work on valley-crossing in
asexual populations (and sexual populations with a low recombination rate) showed that both small
and large populations cross valleys more than intermediate-sized populations [153, 210, 211].
Therefore, it is not clear whether large or small populations are expected to evolve the greatest
complexity when deleterious mutations are required.

The long timescales required to observe the emergence of novelty and evolution of complexity
make biological experiments to distinguish between these theories difficult to perform. To overcome
this difficulty, we used digital experimental evolution [3] to test the role of population size on the
evolution of genome size and phenotypic complexity in asexual organisms. Digital evolution
has a long history of addressing macroevolutionary questions (such as the evolution of novel
traits) experimentally [14, 226]. Digital populations can be manipulated in ways that biochemical
organisms can not, making it possible to study aspects of the evolutionary process that are ordinarily
too difficult to test [12]. In this regard, digital experimental evolution has the same goals as microbial
experimental evolution:
to use a well-controlled model system that is as simple as possible, to
study “evolution in action” [45]. And while digital evolution studies cannot test hypotheses that
depend on particular biochemical processes involved in cellular life, digital populations do undergo

16

selection, drift, and mutation, allowing for their use in testing hypotheses derived from theoretical
population genetics. Thus, digital experimental evolution represents a well-suited model system to
test the population genetics-based theories concerning the role of population size in the evolution
of complexity.

Here, we evolved populations ranging in size from 10 to 104 individuals, starting with a
minimal-genome ancestor. We found that small populations do evolve greater genome sizes and
phenotypic complexity (number of phenotypic traits) than intermediate-sized populations. These
small populations evolve larger genomes primarily through increased fixation of slightly deleterious
insertions. However, the small population sizes that enhance the evolution of phenotypic complex-
ity also enhance the likelihood of population extinction. We also found that the largest populations
evolved similar complexity to the smallest populations. Large populations evolved longer genomes
and greater phenotypic complexity through the fixation of rare beneficial insertions instead. Large
populations were able to discover these rare beneficial mutations due to an increased mutation
supply. Finally, we found that a strong deletion bias can prevent the evolution of greater complexity
in small, but not in large, populations.

2.4 Results

To explore the effect of population size on the evolution of genome size and phenotypic complexity,
we used the Avida digital evolution system [154]. Avida is a platform that allows researchers to
perform evolution experiments inside of a computer, as the genetic code that evolves are actual
computer programs of variable length. It has been used extensively in research in evolutionary
biology [1, 3, 217], and is described in detail in Methods.

We evolved one hundred replicate populations across a range of population sizes (10 − 104
individuals) for 2.5 × 105 generations. Many of the smallest populations (those with ten indi-
viduals) did not survive the entire experiment. Therefore, we evolved one hundred additional
small populations ranging from twenty individuals to ninety individuals in order to examine how
the probability of extinction was related to the evolution of complexity. All populations with at

17

least thirty individuals survived for the entire experiment. Forty-seven of the populations with
ten individuals went extinct, while only one of one hundred populations underwent extinction in
the populations with twenty individuals. Extinction was a consequence of populations evolving
large genomes that accumulated deleterious mutations and led to the production of only non-viable
offspring. These extinct populations were not included in the statistics described below.

2.4.1 Genome Size Evolution

Of the surviving populations, we first examined how genome size changes from the ancestral value
of fifteen instructions. The size of the genome from every population size increased, on average (see
Fig. 2.1 and panel A in Fig. 2.2). However, both the smallest and the largest populations evolved the
largest genomes. Populations with ten individuals evolved a median genome size of 35 instructions,
while populations with ten thousand individuals evolved a median genome size of 36 instructions.
The median final genome size decreased as population size increased for populations with between
ten and fifty individuals. However, from populations with fifty individuals to populations with ten
thousand individuals, the median final genome size increased as population size increased.

Figure 2.1: Final genome size as a function of population size. Red lines are the median values
for each population size. The upper and lower limits of each box denote the third and first quartile,
respectively. Whiskers are 1.5 times the relevant quartile value. Plus signs denote those data
points beyond the whiskers. Data represent only those populations that did not go extinct.

Next, we examined the dynamics of fixation of insertion mutations (insertions, for short) to

18

10100100010000Population Size101102103Genome SizeFigure 2.2: Evolution of complexity for small population sizes. Statistics shown in the main
text for population sizes ranging from 10 to 100 individuals. Data for populations with 10 and 100
individuals are the same as in Figure 2.1. A) Evolution of genome size. B) Proportion of fixed
insertions that were slightly-deleterious. C) Proportion of fixed insertions that were under positive
selection. D) Number of evolved novel phenotypic traits. Red lines are the median values for each
population size. The upper and lower limits of each box denote the third and first quartile,
respectively. Whiskers are 1.5 times the relevant quartile value. Plus signs denote those data
points beyond the whiskers. Data represent only those populations that did not go extinct.

explain why both the smallest and the largest populations evolved the largest genomes. For each
experimental population, we counted every insertion that occurred on the fittest genotype’s ancestral
lineage that went back to the ancestral genotype (the “line of descent", see Methods). The median
number of insertions fixed follows the same trend as the evolution of genome size (Fig. 2.3). A
large fraction of these fixed insertions are slightly deleterious in populations with fewer than one
hundred individuals (see Fig. 2.4 and panel B in Fig. 2.2). However, no insertions are slightly
deleterious, on average, in large populations with more than one hundred individuals. The opposite
trend holds for beneficial insertions. The fraction of insertions that are under positive selection

19

ABCDincreases with increasing population size, with the largest populations usually fixing only beneficial
insertions (Fig. 2.5 and panel C in Fig. 2.2). These data demonstrate that small populations evolve
larger genomes through the fixation of slightly deleterious insertions. However, large populations
can evolve similarly large genomes through the fixation of rare beneficial insertions.

Figure 2.3: The number of insertions fixed as a function of population size. Red lines are the
median values for each population size. The upper and lower limits of each box denote the third
and first quartile, respectively. Whiskers are 1.5 times the relevant quartile value. Plus signs
denote those data points beyond the whiskers. Data represent only those populations that did not
go extinct.

Figure 2.4: Proportion of slightly-deleterious insertions as a function of population size. Red
lines are the median values for each population size. The upper and lower limits of each box
denote the third and first quartile, respectively. Whiskers are 1.5 times the relevant quartile value.
Plus signs denote those data points beyond the whiskers. Data represent only those populations
that did not go extinct.

20

10100100010000Population Size050100150200250300350400450Insertions Fixed10100100010000Population Size0.00.20.40.60.81.0Proportion of Fixed InsertionsFigure 2.5: Proportion of insertions under positive selection as a function of population size.
Red lines are the median values for each population size. The upper and lower limits of each box
denote the third and first quartile, respectively. Whiskers are 1.5 times the relevant quartile value.
Plus signs denote those data points beyond the whiskers. Data represent only those populations
that did not go extinct.

2.4.2 Evolution of Phenotypic Complexity

Next, we focus on the role of population size in the evolution of phenotypic complexity (defined
as the number of phenotypic traits). In Avida, a phenotypic trait is a program’s ability to perform
a certain mathematical operation on binary numbers (see Methods). The evolution of phenotypic
complexity follows the same trend as the evolution of genome size (see Fig. 2.6 and panel D in
Fig. 2.2). Populations with ten individuals evolved a median of four traits, while populations
with one thousand and ten thousand individuals evolved a median of one trait. The rest of the
population sizes evolved a median of zero traits. As an avidian’s fitness is primarily determined by
its phenotypic traits in the Avida environment used here, the evolution of fitness showed a similar
trend to the evolution of phenotypic complexity (Fig. 2.7).

That the trend in genome size evolution and in phenotypic complexity evolution are mirrored
suggests that the evolution of larger genomes enables the evolution of increased phenotypic com-
plexity. To establish a link between the two, we performed two tests. First, we examined the
correlation between genome size and phenotypic complexity across all populations. Phenotypic
complexity is positively correlated with genome size (Fig. 2.8, Spearman’s ρ ≈ 0.72; p < 2.3 x
10−57 ), suggesting that it was the increased genome size that allowed for the evolution of increased

21

10100100010000Population Size0.00.20.40.60.81.0Proportion of Fixed InsertionsFigure 2.6: Final number of evolved phenotypic traits as a function of population size. Red
lines are the median values for each population size. The upper and lower limits of each box
denote the third and first quartile, respectively. Whiskers are 1.5 times the relevant quartile value.
Plus signs denote those data points beyond the whiskers. Data represent only those populations
that did not go extinct.

Figure 2.7: The evolved fitness relative to the ancestor genotype. Red lines are the median
values for each population size. The upper and lower limits of each box denote the third and first
quartile, respectively. Whiskers are 1.5 times the relevant quartile value. Plus signs denote those
data points beyond the whiskers. Data represent only those populations that did not go extinct.

22

10100100010000Population Size0246810Evolved Traits10100100010000Population Size100101102103104105106107108Relative Fitnessphenotypic complexity. However, there are two potential mechanisms that could cause an increased
genome size to result in increased phenotypic complexity. On the one hand an increased genome
size could simply allow more “room” for novel functional content. On the other hand, it could be
that the increased genome size leads to a faster rate of evolution due to the increased genomic mu-
tation rate. To examine the role of an increased mutation rate in driving the evolution of phenotypic
complexity, we evolved a further one hundred populations of ten individuals with a fixed genomic
mutation rate of 1.5 × 10−1 (i.e., the ancestral genomic mutation rate). Under this condition, no
population went extinct (as opposed to forty-seven in the variable mutation rate treatment). The
fixed genomic mutation rate populations evolved a median of 2 phenotypic traits compared to
the variable genomic mutation rate populations that had evolved a median of 4 phenotypic traits
(Fig. 2.9). These data demonstrate that the increased genomic mutation rate that follows from
larger genomes does increase the evolution of phenotypic complexity. However, even with a fixed
genomic mutation rate, the smallest populations still evolved a greater median number of traits (on
average 2 traits) than every other population size. Thus, while an increased genomic mutation rate
(due to increased sequence length) indeed enhances the evolution of phenotypic complexity, small
populations still possess an evolutionary advantage due to drift-driven increases in genome size
only.

Figure 2.8: Correlation between the final genome size and the final number of evolved traits.
Black circles represent the combined data from populations with 10, 100, 1000, and 10000
individuals. Only replicates that survived all 2.5×105 generations were included.

23

101102103Genome Size0246810Evolved TraitsFigure 2.9: The effect of a fixed mutation rate on the evolution of phenotypic complexity. The
variable genomic mutation rate treatment represents the data from when the genomic point
mutation rate is 10−1 × L, were L is the genome size. The fixed genomic mutation rate treatment
represents the data from when the genomic point mutation rate was fixed at 1.5 × 10−1,
independent of the genome size. Red lines are the median values for each population size. The
upper and lower limits of each box denote the third and first quartile, respectively. Whiskers are
1.5 times the relevant quartile value. Plus signs denote those data points beyond the whiskers.
Data represent only those populations that did not go extinct.

2.4.3 Non-Functional Insertions

In the previous experiments, large populations evolved larger genomes and greater phenotypic
complexity because they fixed rare beneficial insertions. Next, we more closely examine the finding
that beneficial insertions are necessary for the evolution of complexity in large populations. We
repeated the experiments with the same population sizes and mutation rates, except we changed how
insertions worked. Instead of inserting one of the twenty-six instructions that compose the Avida
instruction set, we inserted “blank” instructions into the genome (see Methods for details). These
blank instructions cannot be beneficial (on their own or in combination with existing instructions)
and would have to be further mutated to lead to the evolution of phenotypic complexity. In this
treatment, greater phenotypic complexity in large populations would require a two-step mutational
process, as opposed to the single step in a beneficial insertion.

We saw no qualitative difference in the trend between these experiments and the original
experiments (Fig. 2.10). Very small and large populations still both evolved the largest genomes
and the greatest phenotypic complexity. Populations of all sizes evolved longer genomes and more

24

Variable GenomicMutation RateFixed GenomicMutation Rate0246810Evolved Traitsphenotypic traits in this treatment (Fig. 2.10) than in the original treatment (Fig. 2.1 and Fig. 2.6).
The fraction of fixed insertions that were under positive selection decreased for every population size
compared to the original experiments, as expected from the insertion of non-functional instructions
(Fig. 2.11). We observed an increased rate of extinction in the very small populations, with
only 2 populations with ten individuals and 25 populations with twenty individuals surviving the
experiment. Population extinction was likely enhanced by the increased growth in genome size in
these experiments as compared to the original experiments.

Figure 2.10: The evolution of complexity in the non-functional insertion treatment. All
subplots are a function of the population size. A) The final genome size. B) The final number of
evolved phenotypic traits. Populations with 20 individuals are shown instead of those with ten
individuals due to the high extinction rates of populations with ten individuals. Red lines are the
median values for each population size. The upper and lower limits of each box denote the third
and first quartile, respectively. Whiskers are 1.5 times the relevant quartile value. Plus signs
denote those data points beyond the whiskers. Data represent only those populations that did not
go extinct.

25

ABFigure 2.11: The proportion of fixed insertions that were under positive selection in the
non-functional insertion treatment compared to the original treatment for populations with
104 individuals. Red lines are the median values for each population size. The upper and lower
limits of each box denote the third and first quartile, respectively. Whiskers are 1.5 times the
relevant quartile value. Plus signs denote those data points beyond the whiskers. Data represent
only those populations that did not go extinct.

2.4.4 Deletion Bias

Finally, we performed experiments to test whether the effect of a deletion bias (a higher fraction
of deletions among all indels) alters the relationship between population size and the evolution of
complexity. A biased ratio of deletion to insertion mutations is found in biological organisms across
the tree of life, especially in bacteria [99, 143]. In these experiments we set the ratio of deletions
to insertions as 9:1, but kept the total indel mutation rate as in the original experiments. In this
treatment, only one population with ten individuals went extinct, as opposed to 47 populations in
the original treatment. However, the advantage towards evolving complexity previously enjoyed by
small populations vanished (Fig. 2.12). The median genome size increased as the population size
increased for all populations sizes. Only the largest populations evolved a median number of novel
phenotypic traits greater than zero. These results suggest that it is not only the role of genetic drift,
but the equal frequency of insertions and deletions that results in the increased genome size and
phenotypic complexity in small populations.

26

OriginalTreatmentNon-Functional InsertionTreatment0.00.20.40.60.81.0Proportion of Fixed InsertionsFigure 2.12: The evolution of complexity in the deletion bias treatment. All subplots are a
function of the population size. A) The final genome size. B) The final number of evolved
phenotypic traits. Red lines are the median values for each population size. The upper and lower
limits of each box denote the third and first quartile, respectively. Whiskers are 1.5 times the
relevant quartile value. Plus signs denote those data points beyond the whiskers. Data represent
only those populations that did not go extinct.

2.5 Discussion

The idea that small populations could have an evolutionary advantage over large populations
dates back to Wright and his Shifting Balance theory [223]. More recently, a potential small-
population advantage has been demonstrated both theoretically [81] and experimentally [175], but
only in regard to short-term increases in fitness. The Mutational Burden hypothesis provides an
evolutionary mechanism that gives small populations an advantage towards increased phenotypic
complexity [96, 118]. However, an experimental demonstration of this advantage is lacking. Our
study provides further insight into the conditions that give small populations such an evolutionary
advantage. We confirmed that small populations do evolve larger genomes due to the increased

27

ABfixation of slightly deleterious mutations, as predicted [121]. We also showed how small populations
have an increased potential to later evolve increased phenotypic complexity in small populations
through the larger genomes generated by increased genetic drift [94, 118]. As phenotypic traits
are strongly beneficial in the Avida environment used here, these small populations used slightly
deleterious genome expansions to cross fitness valleys and eventually reach novel fitness peaks.

Our work also shows that this evolutionary advantage of small populations is limited by an
increased rate of population extinction. Such a trend between the evolution of large genomes
and an increased rate of extinction is seen in some multicellular eukaryote clades [200, 201].
These small populations are still likely to have a larger risk of extinction beyond that caused
by population-genetic risks such as Muller’s ratchet [151] and mutational meltdowns [125, 233].
Ecological stressors increase extinction risk [134] and small populations are less able to adapt to
detrimental environmental changes [221]. Our results concerning extinction, combined with the
risk of other factors not examined here, suggest that the likelihood of a small population using
genetic drift to evolve greater complexity without an increased risk of extinction may be limited.
However, it is possible that multiple small populations could reduce the risk of extinction without
reducing the evolution of complexity; future work should consider the interplay between population
size and the evolution of complexity within a metapopulation of small populations.

Large populations also evolved greater genome sizes and phenotypic complexity. In our original
experiments, genome evolution in large populations was driven by the fixation of rare beneficial
insertions (Fig. 2.6). While it is likely that many gene duplications are not under positive selection
and lost due to genetic drift and mutation accumulation [120], some, especially those resulting
in the amplification of gene expression, can be immediately beneficial and later lead to increased
phenotypic complexity [17, 21, 77, 152]. Due to the increased mutation supply, these events would
occur at a greater frequency in large populations [207] and possibly lead to an increased probability
of the evolution of complexity there. However, we also found that large populations did not require
this large supply of beneficial insertions. Even when insertion mutations added non-functional
instructions and further point mutations were required to evolve functional traits, large populations

28

still evolved complexity similar to that evolved in small populations. These results suggest that
purifying selection may not limit the evolution of complexity in large populations. Finally, we
found that when deletions occur at a much greater frequency than insertions, only large populations
have an evolutionary advantage towards complexity. As many bacteria do have a bias towards
deletions [36, 100], this result suggests that large microbial populations can have an evolutionary
advantage over small microbial populations for evolving novel traits after all.

Such a trend where both large and small, but not intermediate-sized populations have an
evolutionary advantage has already been theoretically proposed elsewhere. Weissman et al. showed
that both small and large populations cross fitness valleys more easily than intermediate-sized
populations [210]. Small populations valley-crossed due to genetic drift and large populations did
so due to an increased supply of double mutants. Ochs and Desai also showed that intermediate-
sized populations evolved to a lower fitness peak compared to small or large populations when
valley-crossing was required for reaching a higher peak [153]. We found similar results, but
from different evolutionary mechanisms. Here, populations needed to increase in genome size in
order to evolve phenotypic complexity. Additionally, our populations evolved in a complex fitness
landscape with many different possible paths to phenotypic complexity. While small populations
did fix deleterious insertions to increase genome size, large populations evolved on a different path,
either through beneficial insertions (Fig. 2.5) or neutral insertions (Fig. 2.9). It is possible that even
larger populations than those evolved here would fix more deleterious insertions, as the likelihood
of a further, beneficial mutation arising on the background of a segregating deleterious mutation
increases as population size increases. However, our results emphasize that large populations
may not be dependent on valley-crossing in some fitness landscapes if alternative evolutionary
trajectories exist, even if these trajectories are rare. While the first maps of fitness landscapes
suggested mutational paths are small in number [209], more recent work suggests that many
indirect evolutionary trajectories exist in larger fitness landscapes [162].

The small population sizes that led to the evolution of greater phenotypic complexity via
drift are very small (10 individuals). As biological populations of that size are unrealistic, we

29

may wonder whether small biological populations can actually evolve greater complexity due to
increased genetic drift. However, there are reasons to believe that these results would generally
hold for biological systems. The limited range of small population sizes that led to complexity
is an Avida-specific result due to the severe fitness effect of insertion mutations in avidians with
small sequence length. We found that for those sequences, most insertions are lethal (about 80%),
and the rest are significantly detrimental, of the order 10% to 90%. To overcome a detrimental
effect of 20% via drift, populations must be as small as N = 10. Insertion mutations in biological
genomes are not nearly as detrimental, and therefore the critical population size to see evolution of
complexity via drift is much larger. In E. coli, for example, the deleterious effect of insertions is
between 1 and 3% [46]. We can therefore expect to see the effect of increased complexity due to
drift in biological populations that are small, but not unreasonably small.

Another possible avenue for future work suggested by this study is to use a simpler population
genetics model to explore the same questions we attempted to answer here. Many previous
theoretical studies have examined the relevance of valley-crossing to the evolution of complex traits
in simple fitness landscapes [153, 210, 211]. One benefit of a simpler model is that it allows for a
broader exploration of the relevant parameters involved in the interplay between population size,
genome size, and the evolution of phenotypic complexity. While we were not able to perform
large parameter searches using the Avida system, our work here establishes a possible relationship
between the factors that influence the evolution of complexity in a fitness landscape with many
possible mutational trajectories to novel traits [109]. These results should drive future theoretical
studies on the evolution of genome size and phenotypic complexity using population genetics
models with simpler fitness landscapes.

Here we studied the evolution of complexity in haploid asexual digital organisms with an
ancestral minimal genome on a frequency-independent fitness landscape. While beyond the scope
of this work, it is worth considering how adjusting these genotype characteristics would alter our
results. It is likely that the ancestral minimal genomes are a requirement for small populations to
evolve the same number of novel traits as large populations. If the ancestor organism had a significant

30

amount of non-functional genome content, the mutation supply advantage that large populations
have should result in an accelerated rate of phenotypic evolution in large populations [48]. The
organisms used here, as in all Avida experiments, are haploid. It is possible that polyploidy would
alter the results found here. However, the implementation of a ploidy cycle in Avida is non-trivial
due to the mechanistic style of replication, and so presently other experimental systems would have
to be used to explore the role of ploidy in the evolution of phenotypic complexity.

It is unclear how sexual, instead of asexual, reproduction would change the results. While sex-
ual reproduction can enhance adaptation by combining beneficial mutations that arise in different
background, it can also break up beneficial combinations of mutations [157]. One result that may
be altered by sexual reproduction is the rate of extinction in small populations, as sex has been found
to reduce the rate of mutational meltdowns [127]. Weissman et al. also demonstrate that the large
population advantage towards valley-crossing does not exist under high recombination rates [211].
Sexual reproduction has previously been studied using Avida, but it is more akin to homologous
recombination in bacteria [145] (as there is no ploidy cycle). Future work should address the role
of sexual recombination on the results shown here. Finally, the experiments performed here had
no frequency-dependent fitness effects. Previous Avida studies showed that frequency-dependent
interactions enhanced the evolution of complexity for a given population size [205, 232]. It is worth
exploring how the presence of frequency-dependent selection alters the evolution of complexity,
especially in small populations. The benefits of the diversity seen in frequency-dependent fitness
landscapes may be reduced in small populations. The extensions to the experiments performed here
would provide a more complete understanding of the role of adaptive and non-adaptive evolutionary
processes in the origins of complexity.

31

2.6 Methods

2.6.1 Avida

In order to experimentally test the role of population size and genetic drift in the evolution of
complexity, we used the digital evolution system Avida version 2.14 [154]. In Avida, self-replicating
computer programs (avidians) compete in a population for a limited supply of CPU (Central
Processing Unit) time needed to successfully reproduce. Each avidian consists of a circular haploid
genome of computer instructions. During its lifespan, an avidian executes the instructions that
compose its genome. After executing certain instructions, it begins to copy its genome. This new
copy will eventually be divided off from its mother (reproduction in most Avida experiments is
asexual). Because an avidian passes on its genome to its descendants, there is heredity in Avida.
As an avidian copies its genome, mutations may occur, resulting in imperfect transmission of
hereditary information. This error-prone replication introduces variation into Avida populations.
Finally, avidians that differ in instructions (their genetic code) also likely differ in their ability to
self-replicate; this results in differential fitness. Therefore, because there is differential fitness,
variation, and heredity, an Avida population undergoes evolution by natural selection [164]. This
allows researchers to perform experimental evolution in Avida as in microbial systems [75, 84].
Avida has been successfully used as a model system to explore many topics concerning the evolution
of complexity [5, 63, 108, 109, 232].

Twenty-six different instructions compose the Avida instruction set (see [154] for a more
complete overview). These include instructions for genome replication, such as an instruction to
allocate memory for a new daughter genome, an instruction to copy instructions from the mother
genome into the daughter genome, and an instruction to divide off the new avidian. There are
instructions that allow for the input, output, and manipulation of random numbers that are used
in the performance of certain Boolean logic calculations (see below). There are also instructions
for altering instruction execution, including conditional instructions and instructions for changing
the next instruction location in the genome to be executed. It is important to note that the Avida

32

instruction set was not designed to mimic any biological organism. Instead, it was created in order
to have an organism with mechanistic reproduction in a non-specified fitness landscape that allows
for studies of evolutionary dynamics.

The Avida world consists of a toroidal grid of N cells, where N is the (maximum) population
size. When an avidian successfully divides, its offspring is placed into a cell in the population.
While the default setting places the offspring into one of nine neighboring cells of the parent,
here the offspring is placed into any cell in the entire population. This simulates a well-mixed
environment without spatial structure. When there are empty cells in the population, new offspring
are preferentially placed in an empty cell. However, if the population is at its carrying capacity,
the individual who is currently occupying the selected cell is replaced by the new offspring (a new
individual can also eliminate its parent if that cell is selected). This adds an element of genetic
drift into the population as the individual to be removed is selected without regard to fitness. A
population can also decrease in size by the death of individuals. An avidian will die without
producing offspring if it executes 20L instructions without successfully undergoing division, where
L is the avidian’s genome size. This can lead to population extinction in very small populations.

Time in Avida is divided into updates, not generations. This method of keeping time was
implemented in order to allow individuals to execute their genomes in parallel. During one
update, a fixed number of instructions is executed across the entire population. The resource that
is necessary to execute instructions (the CPU “energy”) is measured in SIPs (single instruction
processing) units. By default, there are 30N SIPs available to the entire population per update,
where N is the population size. SIPs are distributed among the individual genotypes within a
population in proportion to the trait or traits displayed by an individual. The total amount of
SIPs garnered by an individual from traits is called the “merit”.
In a homogeneous population
of one genotype (clones) where each individual has the same merit, each individual will obtain
approximately 30 SIPs per update. However, in a heterogeneous population where merit differs
between individuals, SIPs will be distributed in an uneven manner. That way, individuals with
a greater merit will execute and/or replicate a larger proportion of their genome per update and

33

replicate faster, thus having a greater fitness. This places a strong selection pressure on evolving a
greater merit. One generation has passed when the population has produced N offspring. Typically
(depending on the complexity of an avidian) between 5 and 10 updates pass in one generation.

A genotype’s merit is increased through the evolution of certain phenotypic traits that form
a “digital metabolism” [3]. These phenotypic traits are the ability (or lack there-of) to perform
certain Boolean logic calculations on random binary numbers that the environment provides. To do
this, an avidian must have the right “genes”–in this case, the right sequence of instructions. First,
during an avidian’s lifespan, instructions that allow for the input and output of these random binary
numbers must be executed. Further instructions should manipulate those numbers so as to perform
the rewarded computations. When a number is then written to the output, the Avida program
checks to see whether a logic operation was successfully performed. If so, the the individual that
performed the computation consumes a resource tied to the performance of that trait (there are
many different codes, that is, combinations of instructions, that will trigger the reward). Resource
consumption causes the offspring of that individual to have their merit modified by a factor set by the
experimenter. Here, we use the “Logic-9” environment to reward the performance of nine one- and
two-input logic functions [109]; see Table 2.1 for the names and specific rewards of each function.
Each individual only gains a benefit from performing each function once per generation. There is an
infinite supply of resources for the performance of each logic function in the present experiments,
making fitness frequency-independent. Because the performance of these logic functions increases
merit, they also increase fitness and are under strong positive selection.

While increases in an individual’s merit increase replication speed and thus the individual’s
fitness, fitness in Avida is implicit and not directly calculated. Unlike simulations of evolutionary
dynamics, a genotype’s fitness is thus not set a priori by the experimenter. The only way to measure
the fitness of an avidian is to run it through its lifecycle and examine its phenotype. This is similar
in principle to how bacterial fitness cannot be calculated by examining an individual bacterium’s
genome, but must be measured through a number of different experiments, such as competition
assays [107]. A genotype’s fitness is determined by how many offspring it can produce per unit

34

Table 2.1: Merit rewards for the evolution of phenotypic traits.

Boolean Logic Calculaton Merit Multiplier

2
2
4
4
8
8
16
16
32

NOT
NAND
ORNOT
AND

ANDNOT

OR
NOR
XOR

XNOR (Equals)

time. Genotypes that can reproduce faster will out-compete other genotypes, all else being equal.
Therefore, evolution will increase a population’s fitness through two means. The first is that the
population will evolve individuals with a greater number of phenotypic traits and thus with a
greater merit, as explained above. The second way to increase replication speed is by optimizing
(shortening) the replication time. This occurs either by shrinking the genome, which results in
fewer instructions that need to be copied and replicated, or by optimizing genome architecture for
faster replication. Fitness w in Avida can be estimated by the following equation:

w ≈

merit

replication time

(2.1)

For an avidian to be able to successfully reproduce, it must first allocate memory for the new
individual, copy its genome into the allocated memory space, and then divide off the daughter
organism. As instructions are copied, the avidian may inaccurately copy some instructions into the
newly allocated memory at a rate set by the experimenter. Additionally, upon division, insertions
and deletions of a single instructions occur at (possibly different) rates set by the experimenter.
Finally, larger insertions or deletions (indels) can occur when an avidian divides into two daughter
genomes if the division occurs unevenly. In most cases, this results in the creation of one larger
and one smaller genome and both of these are non-viable. However, in rare cases, one of these
new genotypes is able to reproduce, resulting in a large change in genome size in that individual’s
descendants. Because this mutation through inaccurate division is a characteristic of a genome and

35

thus emergent, the rate at which it occurs is not set by the experimenter.

2.6.2 Experimental Design

We used four experimental designs (treatments) to explore how population size determines the
evolution of complexity: the original experiments, the non-functional insertion experiments, the
fixed genomic mutation rate experiments, and the deletion bias experiments. For all experiments,
we evolved populations of size N={10, 100, 1000, 10000} for 2.5× 105 generations under 100-fold
replication. For the original treatment, we also performed experiments with population sizes of
N={20, 30, 40, 50, 60, 70, 80, 90}. All populations were initiated at full size N with an altered
version of the standard length-100 Avida start organism [154]. The alteration was the removal of
all non-essential genome content (85 nop-c instructions). This reduced the genome size of the
ancestor organisms from 100 instructions to only 15 instructions.

For the original experiments, point mutations occurred at a rate of 0.01 mutations per instruction
copied, and insertions and deletions at 0.005 events per division. Insertions and deletions occur at
most once per division. The ancestor thus started with a genomic mutation rate of 0.15 mutations
per generation (0.01 mutations/instruction copied × fifteen instructions copied per generation), but
this changes over the course of the experiment as genome size evolves. These experiments are
similar to most standard Avida experiments, with the exception of a smaller genome size (fifteen
instructions) for the ancestral organism.

For the remainder of the experimental settings, one of the above settings was changed to examine
a specific effect. For the experiments where the genomic mutation rate was fixed, point mutations
occurred at a rate of 0.15 mutations per division, independently of genome size, which fixes the
mutation rate at 0.15 mutations/genome/generation. For the non-functional insertion experiments,
the mutation rates were the same as in the original experiments. However, instead of inserting one
of the twenty-six instructions from the Avida instruction set (see [154] for the Avida instruction
set), “blank" instructions called nop-x were inserted. These instructions have no function on
their own or in combination with any other instruction. Finally, for the deletion bias experiments,

36

point mutations occurred at the same rate as in the standard experiments. However, insertions and
deletions did not occur at the same rate. Insertions occurred at a rate of 0.001 per division and
deletions occurred at a rate of 0.009 per division. This kept the total mutation rate equal to the
other experimental treatments, while altering the ratio of insertions to deletions.

2.6.3 Data Analysis

In order to analyze the evolution of complexity in each population, we extracted the individual
with the greatest fitness at the end of each experiment (the “dominant” type). We then calculated
relevant statistics for each of these genotypes by running them through Avida’s analyze mode. This
mode allows us to run each genotype through its lifecycle in isolation, and calculate its fitness, its
genome size, whether it performs any logic functions, and whether it produces viable offspring,
among other characteristics. To measure the evolution of phenotypic complexity, we determined
how many unique logic calculations each genotype could perform. Such a measure of complexity
is similar to a measure of phenotypic complexity used previously [191] in population genetics.
The relative fitness was calculated by dividing the analyzed fitness value by the ancestor’s fitness
(0.244898).

To examine why certain population sizes evolved larger genomes, we examined the “line of
descent” (LOD) of the fittest type [109]. An LOD contains every intermediate genotype between
the final individual with the greatest fitness and the ancestral genotype that initialized each popu-
lation. This line provides a perfect “fossil record” to examine all of the mutations, insertions, and
deletions that led to the final fittest genotype for each population. We also calculated the selection
coefficient s for each mutation, defined as the ratio of the offspring’s fitness to the parent’s fitness
minus one. We defined beneficial mutations as those with s > 0 and deleterious mutations as
those with s < 0 (this ignores classifying slightly beneficial and slightly deleterious mutations as
neutral.) We determined the number of beneficial insertion mutations by counting those insertions
on the LOD with s > 1
N , where N is the population size. These are beneficial mutations that are not
nearly-neutral and hence should be under positive selection. We note that using s > 1
N is only an

37

approximation, as the equation for a nearly neutral mutation is |s| (cid:28) 1
Ne , where Ne is the effective
population size [156]. We also examined those mutations that had a slightly deleterious effect on
fitness, i.e., those whose selection coefficient was − 1

N < s < 0.

2.7 Acknowledgments

We thank members of the Adami lab for discussions. This work was supported in part by Michigan
State University through computational resources provided by the Institute for Cyber-Enabled
Research.

38

CHAPTER 3

EVOLUTION OF DRIFT ROBUSTNESS IN SMALL POPULATIONS

Thomas LaBar, Christoph Adami
Originally published: Nature Communications, 8:1012, 2017.
Chapter (with minor corrections) reused with permission from the publisher:
https://www.nature.com/reprints/permission-requests.html

3.1 Abstract

Most mutations are deleterious and cause a reduction in population fitness known as the mutational
load. In small populations, weakened selection against slightly-deleterious mutations results in an
additional fitness reduction. Many studies have established that populations can evolve a reduced
mutational load by evolving mutational robustness, but it is uncertain whether small populations
can evolve a reduced susceptibility to drift-related fitness declines. Here, using mathematical
modeling and digital experimental evolution, we show that small populations do evolve a reduced
vulnerability to drift, or “drift robustness”. We find that, compared to genotypes from large popu-
lations, genotypes from small populations have a decreased likelihood of small-effect deleterious
mutations, thus causing small-population genotypes to be drift-robust. We further show that drift
robustness is not adaptive, but instead arises because small populations can only maintain fitness
on drift-robust fitness peaks. These results have implications for genome evolution in organisms
with small effective population sizes.

3.2

Introduction

One consequence of the power of adaptation is that the majority of mutations reduce their bearer’s
fitness [51]. The recurring nature of these deleterious mutations results in an equilibrium reduc-
tion of population fitness at mutation-selection balance. At the population level, this reduction

39

in fitness is known as the genetic or mutational load [7, 34, 90, 91]. As selection generally
acts to increase a population’s mean fitness, one avenue for selection to increase mean fitness is
to reduce the mutational load by altering mutation-selection balance and increasing mutational
robustness [38, 218]. The evolution of mutational robustness has been demonstrated using the-
oretical modeling [68, 97, 169, 198], digital experimental evolution [44, 48, 220], and microbial
experimental evolution [146, 176, 179].

Recurring deleterious mutations are not the only strain on fitness.

In small populations,
genetic drift leads to the fixation of slightly-deleterious mutations that bring about a reduction in
fitness [167, 212]. Over time, genetic drift can lead to continual fitness declines and ultimately
population extinction [72, 125].
In asexual populations, this phenomenon of fitness decline is
known as Muller’s ratchet [151] and is thought to play a role in the evolution of mitochondria [113],
bacterial endosymbionts [148], the Y chromosome [65], and other obligate asexual lineages.
Muller’s ratchet may explain why there are few long-lived obligate asexual species and may provide
a selection pressure for the evolution of sexual recombination [54]. However, it was recently
proposed that small populations do not continuously decline in fitness, but only do so until they
reach drift-selection balance when the fixation of beneficial mutations counteracts the fixation of
slightly-deleterious mutations [66, 167, 183, 212]. Furthermore, Muller’s ratchet may be limited in
strength if small populations can alter drift-selection balance and evolve drift robustness. However, it
is unknown if populations can evolve drift robustness, or what genetic and evolutionary mechanisms
could cause drift robustness.

Here, we propose a hypothesis concerning the evolution of drift robustness in small populations.
Consider evolution on a single-peak fitness landscape (Fig. 3.1a). In a large population (defined
here such that its effective population size is larger than the inverse of every selection coefficient
in the landscape), natural selection will ultimately lead to the fixation of all beneficial mutations.
In a small population, while selection may also lead to the fixation of these beneficial mutations,
weakened purifying selection inherent to small populations will result in the subsequent loss of
these beneficial mutations. Thus, while a large population can maintain itself at the top of the

40

fitness peak, a small population is unable to maintain fitness due to an increased rate of fixation
of slightly-deleterious mutations. Therefore, this small population will not occupy the top of the
fitness peak, but some lower area where the fixation of slightly-beneficial mutations and the fixation
of slightly-deleterious mutations balance out [66].

Figure 3.1: Conceptual diagram of drift robustness. a) A single-peak fitness landscape. In this
landscape, the large population (red circles) can climb to the top of the fitness peak, while the
small population (black circles) can only maintain fitness on an intermediate part of the peak. b)
A multi-peak fitness landscape. The large population evolves to the same fitness peak as in panel
a. The small population evolves to the steeper, drift-robust peak. While this peak is still lower
than the drift-fragile peak, the small population attains greater fitness than it would have on the
drift-fragile peak in the single-peak fitness landscape

Now, consider a fitness landscape with two fitness peaks, with one peak slightly higher than
the other peak (Fig. 3.1b). We will denote the higher peak as the “drift-fragile” fitness peak. A
population evolves towards this peak by fixing a sequence of small-effect beneficial mutations.
As a consequence, the genotype at the top of the peak will have many small-effect deleterious
mutations in its mutational neighborhood. We will denote the lower peak as the “drift-robust”
fitness peak. A population evolves to this peak by fixing a sequence of large-effect beneficial
mutations and the genotype at the top of the peak will have many large-effect deleterious mutations
in its mutational neighborhood. The question is: how will small and large populations evolve on
this fitness landscape?

According to our hypothesis, large populations will evolve towards the drift-fragile fitness
peak and small populations will evolve towards the drift-robust fitness peak. This hypothesis is

41

0.00.20.40.60.81.0Fitness0.00.20.40.60.81.0Fitnessabsimilar to the idea of the “Survival of the Flattest” effect, where mutationally-robust genotypes
will out-compete fitter, but more mutationally-fragile genotypes at high mutation rates [220].
However, we stress that the evolutionary mechanism behind this trend is not the out-competition
of drift-fragile genotypes by drift-robust genotypes in small populations. Instead, we propose that
small populations evolve to drift-robust fitness peaks because these populations can only maintain
themselves on drift-robust areas of the fitness landscape. If a small population would evolve towards
a drift-fragile part of the fitness landscape, it would subsequently fix deleterious mutations and
decrease in fitness until it evolved back to a drift-robust area. Large populations can easily maintain
fitness in drift-fragile areas, and thus we expect them to evolve to the higher fitness peak.

Here, we demonstrate that small populations should evolve drift robustness in accordance with
our hypothesis. We first confirm the logic behind this hypothesis with a two-peak fitness landscape
mathematical model and show that drift robustness will evolve in small, but not large, populations
in a fitness landscape with a drift-fragile fitness peak and a lower-fitness drift-robust fitness peak.
Then, we use digital experimental evolution with the Avida system [154] to test this hypothesis in
a complex fitness landscape. We find that small populations of digital organisms evolve towards
fitness peaks with a low likelihood of slightly-deleterious mutations, while large populations evolve
towards fitness peaks with a high likelihood of slightly-deleterious mutations. We end by discussing
the implications of these results for organisms exposed to strong genetic drift, including bacterial
endosymbionts and RNA viruses.

3.3 Results

3.3.1 A mathematical model of drift robustness

To test our drift robustness hypothesis, we designed a minimal mathematical model in order to test
the conditions under which drift robustness will evolve in small populations, while drift fragility
will evolve in large populations (see Methods). We designed a fitness landscape with a wild-type
genotype with fitness w1 = 1 and two fitness peaks with w3 = 1 + s and w4 = 1 + s− 
, respectively

42

(Fig. 3.2a), where s is a fitness advantage (in percent), and 
 quantifies how much lower the fitness
of the peak w4 is compared to w3. The lower of these peaks is the drift-robust fitness peak, as
it can be reached from the wild-type genotype by fixing a strongly-beneficial mutation of size
s − 
. As a consequence, this peak’s mutational neighborhood only consists of strongly-deleterious
mutations. The drift-fragile peak is, in contrast, reached by first fixing an intermediate genotype
with fitness w2 = 1 + s
2 and then fixing another mutation with the same fitness effect. Both these
mutants are slightly-beneficial and thus the drift-fragile peak will have a mutational neighborhood
of slightly-deleterious mutations. In an extended model (Fig. 3.2b), the drift-fragile peak has n − 1
intermediate steps that are reached with mutations of step size s/n, so that choosing n allows us to
vary the steepness of the slope of the drift-fragile peak.

When disregarding landscape structure, population genetics arguments imply that large popu-
lations will fix on the higher of the two peaks, while if the population size is small, the difference
in fitness between peaks is irrelevant and a population should fix on either peak with approximately
equal probability. Instead, our model predicts that when deleterious mutations are more abundant
than beneficial mutations, there is a broad range of parameter values where the small populations
evolve to predominantly fix at the drift-robust fitness peak (even though it is of lower fitness) and
the large populations evolve to the drift-fragile fitness peak (Fig. 3.3). For the minimal model, we
derive a critical population size at which the small population shifts from fixing at the higher peak to
the lower one instead, with the assumption that beneficial mutations are exponentially-distributed,
(see Methods)

Ncrit = 1 +

(3.1)

log κ−1

2


where κ = ub
fitness effect ¯s .

¯s < 1 is the ratio between the beneficial mutation rate ub and the mean beneficial

In the extended model, where n (and thus the slope of the drift-fragile peak) can vary, we find

the critical population size to be:

Ncrit = 1 + (n − 1)log κ−1

2


43

(3.2)

Figure 3.2: The fitness landscapes for the Markov model to test for the evolution of drift
robustness. Each circle represents one genotype and is labeled with its fitness. Each arrow
represents the transition between one genotype to another (including the identical genotype) and is
labeled with the transition probability. a) The fitness landscape for the minimal model. s
represents the selection coefficient of the drift-fragile peak and 
 represents the small fitness
difference between the drift-fragile peak and the drift-robust peak. ui j and πi j represent the
mutation rate between genotypes and probability of fixation from one genotype to another,
respectively. b) The fitness landscape for the extended model. Variables as in panel a. Transition
probabilities omitted for clarity

where n is the number of mutations required to reach the top of the drift fragile peak. This general
equation makes the following predictions concerning how populations should shift from drift-
fragile peaks to drift-robust peaks. As the fitness deficit of the drift-robust fitness peak increases
(
), the critical population size, and thus range of population sizes that lead to the evolution of
drift robustness, also decrease (Fig. 3.3). In other words, small populations will only preferentially
evolve towards the drift-robust fitness peak if the trade-off between drift robustness and fitness
is not too severe. If the drift-robust peak results in extremely low fitness, the small population
will evolve as far up the drift-fragile peak as it can while maintaining fitness. As the shallowness

44

1+s✏1+s2u41⇡4111+su14⇡141u41⇡41u21⇡21u12⇡12u23⇡23u32⇡321u32⇡321+s1+s✏11+ksn1+(n1)sn1+snab......1u21⇡21u23⇡231u12⇡12u14⇡14Figure 3.3: Critical population size for shift between robust and fragile peaks. a) Results for
various n values with κ = 0.01. b) Results for various κ values with n = 2.

of the slope of the drift-fragile peak increases (i.e., n, or the number of mutations to reach the
drift-fragile peak, increases), the critical population size also increases. This result argues that the
range of population sizes leading to the evolution of drift robustness is greater as the mutations that
lead to the drift-fragile peak are more frequent, with a decreased beneficial effect. Finally, as κ
decreases [either by a decrease in the beneficial mutation rate (ub) or an increase in the height of the
fitness peaks (s)] the critical population size increases, demonstrating that the larger the differential
between the flux of beneficial mutations towards the peaks, the larger the critical population size.
We should note here that κ has a weaker influence on Ncrit than 
 or n. This lesser influence, due
to the equation containing log κ−1, exists because there is only a slight difference in the fixation
probability of beneficial mutations between small and large populations. The relevant difference
comes down to the lack of maintainability of these beneficial mutations in small populations, an
effect captured by n, the number of beneficial mutations required to reach the drift-fragile peak.

3.3.2 Drift robustness in digital organisms

The mathematical model supports our hypothesis for the evolution of drift robustness in small
populations, but it rests on a number of assumptions that may alter the evolution of drift robustness
in complex fitness landscapes. For instance, we assumed that populations can be viewed as
monomorphic and evolution proceeds as transitions from one genotype to another (these models

45

00.020.040.060.080.10ǫ101102103104Critical Population Sizeκ = 0.01n = 2n = 3n = 500.020.040.060.080.10ǫ101102103104Critical Population Sizen = 2κ = 0.001κ = 0.01κ = 0.1abare broadly known as origin-fixation models [136]). We also used a fitness landscape with only
two fitness peaks, while biological fitness landscapes certainly contain many fitness peaks.

To test if small populations evolve drift robustness in a complex fitness landscape, we used
the digital evolution system Avida [154].
In Avida, a population of self-replicating computer
programs (“avidians”) compete for the memory space and CPU time necessary for reproduction.
During self-replication, random mutations occur, potentially altering the new avidian’s reproduction
speed. When an avidian successfully reproduces, its offspring replaces a random individual in the
population, resulting in genetic drift. As avidians that replicate faster will produce more offspring
per unit time than avidians with slower replication speeds, faster replicators are selected for and
spread mutations that enable faster replication. Because Avida populations undergo selection,
mutation, and drift, they represent a digital model system to study fundamental questions concerning
evolutionary dynamics.

To test for the evolution of drift robustness in small avidian populations, we evolved 100 replicate
populations at small (102 individuals) and 100 populations at large (104 individuals) population
sizes for 105 generations. From each population, we isolated the most abundant genotype at the
end of the experiment; we will refer to these genotypes as the 100 small-population genotypes
and the 100 large-population genotypes. Small populations evolved a lower relative fitness than
large populations (median = 1.85 vs. median = 2.05, Mann Whitney U = 2237.0, n = 100,
p = 7.31 × 10−12 one-tailed), as expected for populations that experience a smaller beneficial
mutation supply over the course of the experiment.

3.3.3 Small populations evolve an altered DFE

To look for signs of drift robustness, we studied differences in the Distribution of Fitness Effects
(DFE) of de-novo mutations for small-population genotypes and large-population genotypes. First,
we generated every possible point mutation for all genotypes and combined these data into one
DFE (Fig. 3.4a). Both show the typical properties of DFE’s found in biological organisms: most
mutations are either lethal or have little effect [51]. However, there are some differences. Small-

46

population genotypes have an excess of neutral, beneficial, and strongly deleterious mutations
(defined as viable deleterious mutations with a fitness effect greater than or equal to 5%; Fig. 3.4b),
while large-population genotypes have an excess of small-effect deleterious mutations (defined as
viable deleterious mutations with a fitness effect less than 5%; Fig. 3.4b). We confirmed that these
trends hold when we calculated a DFE for each genotype (rather than one DFE for all genotypes
from a given population size) as follows. Small population genotypes had a greater likelihood of
beneficial mutations (median=0.0256 vs. median=0.0008, Mann Whitney U = 413.5, n = 100,
p = 6.26 × 10−30 one-tailed), neutral mutations (median = 0.40 vs. median = 0.26, Mann Whitney
U = 321.0, n = 100, p = 1.45 × 10−30 one-tailed), large-effect deleterious mutations (median =
0.084 vs. median = 0.054, Mann Whitney U = 2854.0, n = 100, p = 7.90 × 10−8 one-tailed),
and a lesser likelihood of lethal mutations (median = 0.33 vs. median = 0.37, Mann Whitney
U = 4031.5, n = 100, p = 9.00 × 10−3 one-tailed) and small-effect deleterious mutations (median
= 0.11 vs. median = 0.31, Mann Whitney U = 124.5, n = 100, p = 5.13 × 10−33 one-tailed;
Fig. 3.4c). Additionally, there was no difference in the average single-mutant relative fitness
for small-population genotypes and large-population genotypes, even though there were fitness
differences between the population-size treatments (median w = 0.612 vs. median w = 0.611,
Mann Whitney U = 4890.0, n = 100, p = 0.39 one-tailed; Fig. 3.4d).

3.3.4 Small population genotypes are drift-robust

The lack of small-effect deleterious mutations in small populations suggests that these populations
adapted to drift-robust fitness peaks and that the large populations adapted to drift-fragile peaks.
To test if these small-population genotypes are drift-robust, we took the 100 small-population
genotypes and 100 large-population genotypes and measured these genotypes’ change in fitness
when placed in an environment with strong genetic drift (i.e., low population size). We evolved 10
populations of 50 individuals for each genotype for 103 generations and measured their change in
fitness. Small-population genotypes clearly declined less in fitness than large-population genotypes
(median decline = 1% vs. median decline = 6%; Mann-Whitney U = 43959.5, n = 1000,

47

Figure 3.4: Differences in mutational effects between small-population genotypes and
large-population genotypes. Black and red represent small-population and large-population
genotypes, respectively. a) The combined distribution of fitness effects (DFE) across all 100
small-population genotypes and 100 large-population genotypes. b) Same data as in panel a, but
grouped into different classes of mutations, where a small-effect deleterious mutation is defined as
having an effect less than 5%. Here, and throughout, deleterious mutation refers to viable
deleterious mutations, while lethal mutation refers to non-viable deleterious mutations. c) The
likelihood of a small-effect deleterious mutation for small-population and large-population
genotypes. Red lines are medians, edges of the box are first and third quartile, whiskers are at
most 1.5 times the interquartile range, and the plus signs are outliers. d) The mean relative fitness
of every possible point mutation (1250 mutations) for each genotype.

48

−1.0−0.8−0.6−0.4−0.20.0Selection Coefficient0.00.10.20.30.40.5Frequency of MutationsLethalLargeDel.SmallDel.NeutralBeneficial0.00.10.20.30.40.5Frequency of MutationsSmall-PopulationGenotypesLarge-PopulationGenotypes0.000.050.100.150.200.250.300.350.400.45Fraction Small-effect Deleterious MutationsSmall-PopulationGenotypesLarge-PopulationGenotypes0.10.20.30.40.50.60.70.8Mean Relative Mutant Fitnessabcdp = 1.44 × 10−273 one-tailed; Fig. 3.5a). Furthermore, a genotype’s decline in fitness is correlated
with its likelihood of a small-effect deleterious mutation, supporting the idea that small populations
have evolved to fitness peaks with a low likelihood of small-effect deleterious mutations due to the
peak’s drift robustness (Spearman’s ρ = 0.80, p ≈ 0; Fig. 3.5b).

Figure 3.5: Small-population genotypes are drift-robust due to a decreased likelihood of
small-effect deleterious mutations. Black and red data points represent small-population
genotypes and large-population genotypes, respectively. a) Relative fitness of the most-abundant
genotype from every population during the drift robustness test. Each circle represents the relative
fitness of one genotype from one replicate. b) Relationship between relative fitness in the drift
robustness test (panel a) and the likelihood of small-effect deleterious mutations (Fig. 3.4c)

3.3.5 Drift robustness is not due to fitness differences

The above results are consistent with the hypothesis that small populations evolve to drift-robust
fitness peaks and large populations evolve to drift-fragile fitness peaks. However, one could argue
the results are also consistent with evolution on a single-peaked fitness landscape (Fig. 3.1a). The
small populations we examined have lower fitness than the large populations and thus could have a
decreased likelihood of small-effect deleterious mutations and more robustness to drift because they
are further down on the fitness peak and cannot climb the rest of the peak. To test if our results were
due to the lower fitness of the small-population genotypes, we isolated genotypes of the same fitness
from the evolutionary lineages of the small and large populations (see Methods for details). We
then compared these genotypes’ likelihood of small-effect deleterious mutations. Genotypes from

49

Small-PopulationGenotypesLarge-PopulationGenotypes0.850.900.951.001.051.10Relative Fitness after Drift Test0.000.050.100.150.200.250.300.350.400.45Fraction Small-effect Deleterious Mutations0.850.900.951.001.051.10Relative Fitness after Drift Testabthe small populations had a decreased likelihood of small-effect deleterious mutations compared to
genotypes from large populations for every examined fitness value (Fig. 3.6). These results support
the hypothesis that small populations have evolved to different fitness peaks than large populations
and are not merely occupying a lower region of the same fitness peak.

Figure 3.6: Fraction of small-effect deleterious mutations for genotypes from small
populations and large populations with equal fitness. Each area separated by a dashed line
shows genotypes with equal fitness (w). S and L represent small-population and large-population
genotypes, respectively. Differences for each fitness value are significant. (Mann-Whitney U-test;
Bonferroni-corrected p < 3 × 10−3). Box plots as described for Fig. 3.4c.

3.3.6 Epistatic mutations lead to drift robustness

Next, we examined the mutations that enabled small populations to evolve towards drift-robust
peaks. Our mathematical model has a drift-robust peak accessible by strongly-beneficial mutations
and a drift-fragile peak accessible by slightly-beneficial mutations. Therefore, we first examined the
distribution of fitness effects for maintained beneficial mutations (beneficial mutations whose fitness
gain was at-least partially maintained during subsequent evolution) to see if small populations fixed
more strongly-beneficial mutations (Fig. 3.7a). While small populations did fix a significantly large
proportion of maintained strongly-beneficial (s > 0.05) mutations (median = 0.06 vs. median =
0.05, Mann Whitney U = 4067.5, n = 100, p = 0.01 one-tailed), the difference was slight.

The fixation of strongly-beneficial mutations is not the only way small populations could
climb drift-robust peaks. Small populations could also climb drift-robust fitness peaks through

50

SLSLSLSLSLSLSLSLSLSL0.00.10.20.30.40.5Fraction Small-effect Deleterious Mutationsw = 0.3721w = 0.375w = 0.378w = 0.381w = 0.384w = 0.3871w = 0.4w = 0.4848w = 0.4851w = 0.5Figure 3.7: Evidence of small-population adaptation to drift-robust fitness peaks. a)
Distribution of maintained beneficial mutational effects for (effects for mutations whose fitness
gain was at-least partially maintained during subsequent evolution) small-population genotypes
(black) and large-population genotypes (red). b) Spearman correlation coefficients between fitness
and the likelihood of a deleterious mutation for each maintained beneficial mutation from each
population. c) The likelihood of (viable) deleterious and lethal mutations, shown in magenta and
green, respectively, in a representative small population’s lineage. The strong decrease in the
likelihood of a (viable) deleterious mutation early in the population’s history is evidence of
epistatic mutations resulting in drift robustness. d) Number of populations that fixed a maintained
beneficial mutation that decreased the likelihood of a (viable) deleterious mutation by at least a
specified amount. Colors as in panel a.

51

0.000.050.100.150.200.25Fitness Effect0.00.10.20.30.40.5FrequencySmall-PopulationGenotypesLarge-PopulationGenotypes−0.6.0.4.0.20.00.20.40.60.81.0Spearman Correlation Coefficient0500100015002000Mutation Number0.00.10.20.30.40.50.60.70.8Likeli ood of Mutational Effect(Viable) Delete)iousLet al−0.40.0.35.0.30.0.25.0.20.0.15.0.10.0.050.000.05Change in Deleterious Mutational Likelihood020406080100Number of Populationsabcdepistatic beneficial mutations that decreased the likelihood of small-effect deleterious mutations. By
decreasing the likelihood of small-effect deleterious mutations, the likelihood that a future small-
effect deleterious mutation will arise and fix is also decreased. Thus, these epistatic beneficial
mutations can be maintained by small populations.

To see if these types of mutations were fixed in the small populations, we first looked at the
correlation between the fitness of maintained beneficial mutations and their genotypes’ likelihood
of deleterious mutations for each population. In a non-epistatic fitness landscape, we would expect
the likelihood of deleterious mutations to increase as fitness increases due to the fixation of, and the
subsequent decrease in the likelihood of, beneficial mutations. However, in some epistatic fitness
landscapes, this correlation is not guaranteed to exist, as the fixation of beneficial mutations may
alter the fitness effects of mutations at other loci. In fact, small populations showed a significant
decrease in the correlation between fitness and deleterious mutational likelihood when compared to
large populations (median Spearman’s ρ = 0.24 vs. median Spearman’s ρ = 0.73, Mann Whitney
U = 2082.0, n = 100, p = 5.07 × 10−13 one-tailed; Fig. 3.7b). This result is consistent with small
populations evolving towards fitness peaks with a decreased likelihood of deleterious mutations
through the fixation of epistatic mutations.

Next, we looked for specific mutational signatures of the fixation of epistatic beneficial mutations
in small populations. We found that 22 small populations had fixed beneficial mutations that
reduced the likelihood of a deleterious mutation by 50%, while only 4 large populations did so.
All of these mutations increased the likelihood of lethal mutations (mean increase = 72%, 2× S.E.
= 11%; Fig. 3.7c). We then studied the magnitude of the decrease in the likelihood of deleterious
mutations. Forty-five small populations fixed mutations that decreased this deleterious likelihood
by at least 0.1, while only 13 large populations did so (Fig. 3.7d). All of these mutations also
increased the likelihood of lethal mutations. Finally, we confirmed that these epistatic mutations
specifically decreased the likelihood of small-effect deleterious mutations. Most of the decrease in
the likelihood of deleterious mutations consisted of a decrease in small-effect deleterious mutations
(median percentage of decrease = 83.9%, interquartile range = 20.6-97.1%), further suggesting that

52

small populations evolve drift robustness by fixing beneficial mutations that decrease the likelihood
of small-effect deleterious mutations and increase the likelihood of lethal mutations.

3.3.7 Deleterious mutations drive the evolution of drift robustness

Finally, to test whether drift robustness evolves in small populations because these populations can
only maintain fitness in drift-robust areas of the fitness landscape, we performed further evolution
experiments where deleterious mutations were prevented from occurring (see Methods for further
details). In this environment, populations cannot decline in fitness, so small populations do not
maintain fitness differently on drift-robust and drift-fragile fitness peaks. We evolved 100 small
populations without deleterious mutations under the main experimental conditions. Small popula-
tion genotypes evolved greater relative fitness without deleterious mutations than in the treatment
with deleterious mutations (median = 2.05 vs. median = 1.85, Mann Whitney U = 2464.6, n = 100,
p = 2.92 × 10−10 one-tailed; Fig. 3.8a). As expected in an environment where fitness maintenance
was not a factor, small-population genotypes had a greater likelihood of small-effect deleterious mu-
tations (median = 0.19 vs. median = 0.11, Mann Whitney U = 1769.0, n = 100, p = 1.47 × 10−15
one-tailed; Fig. 3.8b). These small-population genotypes were less robust to genetic drift (median
fitness decline of 5% vs. median fitness decline of 1%, Mann Whitney U = 118333.0, n = 100,
p = 2.25 × 10−192 one-tailed; Fig. 3.8c) and this decreased robustness correlates with their in-
creased frequency of small-effect deleterious mutations (Spearman’s ρ = −0.43, p = 2.07× 10−45;
Fig. 3.8d). These results suggest that small populations evolve to alternative areas of the fitness
landscape if they can maintain small-effect beneficial mutations.

3.4 Discussion

Our results suggest the following explanation for the evolution of drift robustness in small
populations. Small populations cannot adapt to fitness peaks with a high likelihood of small-effect
If small populations climb these peaks, genetic drift will cause them to
deleterious mutations.

53

Figure 3.8: The evolution of drift robustness in small populations with or without deleterious
mutations in the initial adaptation experiments. Black and blue data points represent
small-population genotypes adapted with deleterious mutations and small-population genotypes
adapted without deleterious mutations, respectively. a) Relative fitness to the ancestral genotype
after 105 generations of adaptation. Box plots as described for Fig. 3.4c. b) Likelihood of
small-effect deleterious mutations. c) Relative fitness of the most-abundant genotype from every
population during the drift robustness test. Each circle represents the relative fitness of one
genotype from one replicate. d) Relationship between relative fitness in the drift robustness test
(panel c) and the likelihood of small-effect deleterious mutations (panel b).

lose previously-fixed beneficial mutations, leading to a decrease in fitness. In other words, small
populations cannot maintain themselves on drift-fragile fitness peaks. Thus, small populations, if
they do adapt, must adapt to drift-robust fitness peaks. Due to the relative increased strength of
selection, large populations do not face this constraint and adapt to drift-fragile peaks. Therefore,
our results argue that small populations and large populations should evolve to different areas of
the fitness landscape and evolve qualitatively-different genetic architecture.

We should emphasize here that there are certain requirements for the evolution of drift robustness
in small populations. First, the fitness landscape must contain multiple peaks; some peaks must

54

Small-PopulationGenotypesSmall-PopulationGenotypesNo Deleterious1.21.41.61.82.02.22.42.62.8Relative FitnessSmall-PopulationGenotypesSmall-PopulationGenotypesNo Deleterious0.000.050.100.150.200.250.300.350.400.45Fraction Small-effect Deleterious MutationsSmall-PopulationGenotypesSmall-PopulationGenotypesNo Deleterious0.800.850.900.951.001.051.10Relative Fitness after Drift Test0.000.050.100.150.200.250.300.350.400.45Fraction Small-effect Deleterious Mutations0.800.850.900.951.001.051.10Relative Fitness after Drift Testabcdbe drift-robust with few small-effect deleterious mutations and some must be drift-fragile with
many small-effect deleterious mutations.
If there is only one fitness peak, small populations
would still likely have a decreased likelihood of small-effect deleterious mutations. However, this
would occur because these populations have failed to maintain small-effect beneficial mutations,
not because they have evolved to drift-robust peaks. Second, the requirement of multiple fitness
peaks further implies that this effect will only be seen in fitness landscapes with strong epistasis
in parts of the landscape, as (sign) epistasis leads to multiple fitness peaks [165]. Third, there
must be evolutionary trajectories between drift-robust fitness peaks and drift-fragile fitness peaks.
Otherwise, small populations would only evolve downwards on a drift-fragile fitness peak. Finally,
there must be more trajectories to drift-fragile fitness peaks than drift-robust fitness peaks.

We are not the first to propose that small populations will evolve robustness mechanisms in
response to their deleterious mutational burden. However, these mechanisms are usually discussed
in terms of mutational robustness, not robustness to drift. Previous studies provided two charac-
teristics of the evolution of mutational robustness in small populations. First, small populations
should preferentially evolve to lower fitness peaks with more “redundancy,” defined as a decreased
average deleterious mutational effect and large populations should evolve to fitness peaks with
a high average deleterious mutational effect [48, 97]. Our results suggest opposite evolutionary
trajectories for small and large populations. While our results concerning the evolution of drift
robustness do suggest that small populations evolve to lower fitness peaks, and small populations
do evolve more redundancy in terms of exactly-neutral mutations, these small populations do not
evolve towards fitness peaks with a decreased deleterious mutational effect (Fig. 3.4d). In fact, they
evolve towards fitness peaks with a minimal likelihood of small-effect deleterious mutations. This
discrepancy likely exists due to the fitness landscape used to study the evolution of redundancy
in small populations: the mutations in that fitness landscape were all small-effect deleterious mu-
tations [97]. Thus, small populations could not maintain fitness except on the flattest of fitness
landscapes [97]. In a version of this model with multiple fitness peaks (e.g., one with small-effect
deleterious mutations and one with large-effect deleterious mutations), we expect that small pop-

55

ulations would evolve to the peak with large-effect deleterious mutations. Such an outcome was
recently predicted for populations evolving at very high mutation rates [104], although a different
model predicts that small populations should evolve to areas that minimize the deleterious effect of
mutations [69], in accordance with Krakauer and Plotkin’s model [97].

The second characteristic of mutational robustness in small populations is that these populations
should evolve “global” robustness mechanisms, such as error-correction mechanisms, that affect
many loci [68, 169, 224]. There are no global error-correction mechanisms available to the avidian
genomes here (although one could allow the evolution of mutation rates, e.g., [31]). However, we did
find that small populations preferentially fixed epistatic mutations that strongly altered the likelihood
of deleterious mutations (Fig. 3.6c, d). These mutations are global in the sense that they alter the
fitness effects of mutations at multiple loci. However, unlike previous work that suggested small
populations should fix global solutions that reduce the effect of deleterious mutations [68, 169, 224],
we found that these mutations increased the likelihood of lethal mutations. We do not have strong
evidence that this increased lethality is essential and expect that small populations could also
fix mutations that increased the likelihood of neutral mutations while reducing the likelihood of
deleterious mutations if they exist in the Avida fitness landscape. Generally, our results emphasize
that the evolutionary process behind drift robustness is the trend to reduce the likelihood of small-
effect deleterious mutations, which can be achieved in multiple ways.

As the evolution of drift robustness relies on a number of conditions, we may ask which em-
pirical fitness landscapes, or which organisms, meet these criteria? Candidates for organisms with
drift-robust genomes include those that undergo severe bottlenecks during their lifecycle, includ-
ing bacterial endosymbionts [148] and RNA viruses [234]. There is evidence that both bacterial
endosymbionts [52, 86, 100, 176] and RNA viruses [47, 76] have evolved alternate genome archi-
tectures in response to their population-genetic environment. In endosymbionts, drift robustness
could be achieved by choosing rare codons in such a way that substitutions are highly deleteri-
ous, and indeed proteins in Buchnera have been found to be exceptionally resistant to drift [192].
However, there has been to date no systematic study of how different organisms respond to strong

56

genetic drift. Future work with biological organisms should establish the circumstances that cause
organisms to vary in their robustness to genetic drift. Furthermore, experimental evolution may be
able to produce organisms with drift-robust genomes whose architecture can be studied directly.

3.5 Methods

3.5.1 Mathematical model of drift robustness

We describe a model to study the minimal conditions required for the evolution of drift robustness.
Based on our hypothesis, we need to study evolution on a fitness landscape with at least two fitness
peaks: one drift-robust peak with few small-effect deleterious mutations and one drift-fragile peak
with many small-effect deleterious mutations. We assume that deleterious mutations are more
frequent than beneficial mutations and that beneficial mutations of large-effect are less frequent
than beneficial mutations of small-effect. Finally, there must also be a mutational path between the
drift-fragile peak and the drift-robust peak. Drift robustness on such a landscape would manifest
itself when a population that predominantly occupies a high (drift-fragile) fitness peak when under
selection at large population sizes, switches instead to the lower (drift-robust) fitness peak when
the population is small. Below we will calculate the critical population size at which this switch
occurs.

We design a fitness landscape with four genotypes, represented by four nodes (Fig. 3.2a).
Genotype 1 (the wild-type) has fitness w1 = 1 and is the ancestral genotype for our populations.
Genotypes 2 and 3, with fitness w2 = 1 + s
2 and w3 = 1 + s, respectively represent the genotypes
on the drift-fragile fitness peak (s is the size of the fitness benefit). Genotype 4, with fitness
w4 = 1 + s − 
, illustrates the drift-robust fitness peak at lower fitness (lower by 
 > 0). In the
extended version of this model that we present later, we discuss the case where an arbitrary number
of mutations lie “on the path” towards the drift-fragile peak (thus increasing the peak’s fragility).
The likelihood that a mutation on the genetic background of genotype i leads to genotype j is
denoted by ui j and the probability of fixation of that mutation is denoted by πi j, with 0 < ui j, πi j ≤ 1.

57

the probability the population will not change is 1 −


Therefore, the probability the population will evolve from genotype i to genotype j is ui j πi j and
ui j πi j. Mutations cannot occur from the
drift-fragile peak to the drift-robust peak and vice-versa, but an indirect path between them exists.
To allow for this dynamic, back-mutations can occur.

j

We assume that evolution occurs in a mutation-limited environment (weak mutation, strong
selection limit), where the population is almost always monoclonal. When a mutation arises, it
will either go extinct or takeover the population. This assumption allows us to treat evolution as a
Markov chain [50]. We then solve for the stationary distribution of mutants in the population, to
calculate the likelihood a population with defined characteristics will evolve to either one fitness
peak or the other.

To solve the Markov chain, we first write down the transition matrix T as :



T =

1 − u12π12 − u14π14

u21π21

0

u41π41



.

u12π12

1 − u21π21 − u23π23

u32π32

0

u14π14

u23π23
1 − u32π32

0
0

The stationary distribution (cid:174)x∗ = (x∗

1, x∗

2, x∗

with eigenvalue 1, i.e. (cid:174)xT = (cid:174)x. We are interested in the relative fraction R = x∗
fraction of occupation between the drift-robust and drift-fragile peaks and turns out to be

1 − u41π41

0

0
3, x∗
4) is the left eigenvector of the transition matrix
4, which is the

3/x∗

R =

u41π41u12π12u23π23
u14π14u21π21u32π32
πi j
πji

.

(3.3)

We first calculate the fractions Pi j =

. Using Kimura’s probability of fixation [88] (a small
s approximation of the exact formula of Sella and Hirsh [182, 219]) for an asexual Wright-Fisher
process (N is the population size) we find

so that

P14 = e2(s−
)(N−1)
P12 = P23 = es(N−1)

,

,

R =

u41
u14

u12
u21

u23
u32

P12P23/P14 ≡ Me2
(N−1)

,

58

(3.4)

(3.5)

(3.6)

where we introduced M = u41
u14

u12
u21

u23
u32

, which we now estimate.

For simplicity, we assume that a deleterious mutation rate (for example, the “back mutation rate"
u41) is given by µ, the overall mutation rate (thus assuming that most mutations are deleterious).
We also assume that the mutation rate up the drift-fragile peak (u12 = u23 = ufragile) is greater
than the mutation rate up the drift-robust peak (u14 = urobust); this is equivalent to assuming that
small-effect mutations are more frequent than large-effect mutations. Then, one gets

M =

u41
u14

u23
u32
ufragileufragile

u12
u21

µ

Therefore, if urobust >

=

µ

ufragile

ufragile

urobust

µ

µ

=

ufragile
urobust

ufragile

µ

, we find that

M < 1 ,

(3.7)

(3.8)

thus allowing for a transition between the two peaks determined by the population size N.

If we assume beneficial mutations follow a certain distribution, we can derive a precise critical
population size at which this transition between fitness peaks occurs. Assume the beneficial
mutation rate is pb(s) = ub µρ(s), where ρ(s) is the distribution function of mutations with benefit
s, and ub is the likelihood that a mutation is beneficial.
If mutations with larger benefit s are
exponentially more unlikely (see, e.g., [55, 60, 64]), we can use the distribution function ρ(s) =
¯s e−s/¯s (here ¯s is the average beneficial effect) to show that
1

b(s/2)
p2
pb(s) =

ub
¯s .

= pb(s − 
) ≈ pb(s), while u12
= u23
u21
u32
≡ κ < 1 .
M = p2

b(s/2)/pb(s) =

ub
¯s

Then, for 
 small we find u14
u41

= pb(s/2), so that

(3.9)

(3.10)

This result is expected to be general, as it simply states that the flux of beneficial mutations towards
the peak with a shallower slope (smaller s, here 1 + s/2) is larger than the flux into the branch with
steeper slope (larger s, here 1 + s − 
).

The critical point at which both the drift-fragile and the drift-robust peak are equally populated

is determined from setting R = 1 in Eq. (3.6), which gives
log κ−1

Ncrit = 1 +

2


.

(3.11)

59

We show the critical population size as a function of the fitness deficit of the drift robust peak 

in Figure 3.3. We see that, depending on the fitness deficit, the evolutionary dynamics prefer the
drift-robust peak at small population sizes even though its peak height is inferior to the drift-fragile
peak. These results do not depend on the explicit function we used to describe the distribution of
beneficial mutations as long as that function is decreasing, nor does it depend on the specifics of
the construction of the fitness landscape.

Next, we created an extended version of our fitness-landscape model. Drift-fragility could be
exacerbated by subdividing the height w3 = 1 + s into n increments (Fig. 3.2b, in the previous
model n = 2). In this case,

b(s/n)
pn
pb(s) = (ub

¯s

)n−1 ,

(3.12)

(3.13)

and the critical population size becomes

Ncrit = 1 + (n − 1)log κ−1

2


.

The simple result Eq. (3.13) relies on an exact cancellation of the fixation probabilities of the
intermediate n − 1 steps, and occurs for both the Kimura approximation as well as the exact
Sella-Hirsh formula.

3.5.2 Avida

Experimental evolution was carried out using the digital evolution system Avida version 2.14.
Avida has previously been used to study many concepts that are difficult to test with biological
systems [5, 62, 63, 101, 108, 232]. In Avida, a population of self-replicating computer programs
undergoes Darwinian evolution. Each of the programs (“avidians”) consists of a genome of
sequential computer instructions, drawn from an alphabet of twenty-six possible instructions.
Together, these instructions encode the ability for an avidian to create a new daughter avidian, copy
its genome into the new avidian, and divide off the offspring. During this process, mutations can be
introduced into the offspring’s genome at a controlled rate, introducing genetic variation into the
population. When a new offspring is placed into the population (and the population is at carrying

60

capacity), a random individual is replaced by the new avidian, a process that introduces genetic
drift into Avida populations. Avidians differ in their replication speed due to different genomic
sequences, so avidians that can replicate faster will out-compete slower-replicating types. Therefore,
because variation is heritable, and because this variation leads to differential reproduction, an Avida
population undergoes Darwinian evolution by natural selection.

The Avida world consists of a toroidal grid of N cells, where N is the maximum population
size. Each cell can be occupied by at most one avidian, although a cell may be empty. Upon
reproduction, the offspring avidian is placed into an empty cell (if the population is below capacity)
or into a random cell, where it replaces the already-present avidian. Although the default Avida
setting places offspring into one of nine neighboring cells (including the parent) so as to emulate
growth on a surface, in the present experiments any cell may be selected for replacement to simulate
a well-mixed environment. Reproduction is asexual in all of the experiments performed here.

Time in Avida is set according to “updates” (the time it takes for an avidian population to
execute a give number of instructions). During each update, 30N instructions are executed across
the population, where N is again the population size. In order to be able to execute its code, an
avidian must have a resource, measured as “Single Instruction Processing” units (SIPs). At the
beginning of each update, SIPs are distributed to programs in the population in proportion to a
quantity called “merit”, which is related to a genotype’s ability to exploit the environment (see [154]
for details). In the experiments performed here, merit was held constant across all individuals, so
on average 30 SIPs were distributed to each individual every update.

It should be noted that in most Avida experiments, populations can evolve the ability to perform
certain Boolean logic calculations that can improve their merit and hence their fitness [109]. In
the experiments performed here, the evolution of these logic calculations was set to be neutral
and not under positive selection.
Instead, the route for an avidian to improve its fitness was
solely by reducing the number of instruction executions needed to copy its genome. A population
will typically evolve a faster replication speed by increasing the number of instructions that copy
instructions from the parent genome to the offspring genome. When this copy number increase

61

occurs, more instructions are copied per update, resulting in faster replication and greater fitness.
This fitness landscape was used because the fitness landscape where logic calculations are under
selection lack small-effect deleterious mutations, which would preclude the observation of drift
robustness. This lack of small-effect deleterious mutations occurs due to antagonistic pleiotropy and
trade-offs between the logic functions and genome replication. Because there are a fixed number of
loci in the genome, the more loci dedicated to the logic functions, the fewer loci dedicated to genome
replication. Therefore, because most loci are dedicated to logic functions, and mutations to these
loci are strongly-deleterious, there are few small-effect deleterious mutations in the logic-function
fitness landscape.

Although Avida uses the update as its unit of time, experiments such as those performed here
are often run for a given number of generations (the time it takes for the entire population to
be replaced). The experiment ends when the average generation across all of the individuals in
the population reaches a pre-specified number. Each individual’s generation counter is equal to
its parent’s generation plus one. Therefore, while Avida experiments occur for a set number of
generations, the population does not evolve with discrete generations. If fitness differs between
individuals and lineages in the population, there can be variation in the individuals’ generations in
the population.

3.5.3 Experimental Design

We performed three sets of experiments here. First, initial adaptation experiments were performed to
generate genotypes adapted to small and large population-size environments. We evolved 100 small
populations (102 individuals) and 100 large populations (104 individuals) for 105 generations. The
genomic mutation rate was set to 10−1 mutations/generation/genome and these mutations occurred
upon division; offspring could differ by at most one mutation from their parent. The ancestor
organism for the initial adaptation treatments was the default Avida ancestor, but with an altered
genome length of 50 instructions. This alteration was performed by removing 50 nop-C instructions
from the default genome (these instructions are inert).

62

The second experimental step was to perform a test to measure the drift robustness of individuals
evolved at a small population size vs. individuals evolved at a large population size. From each small
and large population, we used the most abundant individual to form a set of 100 small-population
genotypes and 100 large-population genotypes per treatment. For each of these genotypes, we
evolved 10 populations (2000 replicates in total) at a population size of 50 individuals for 103
generations. All other treatment parameters were the same as the initial adaptation experiments.

The final set of experiments tested whether deleterious mutations were responsible for the
evolution of drift robustness in small populations. We repeated the initial adaptation experiment
and the drift robustness test under the same parameter settings as for the original treatment. However,
during the initial adaptation experiment, we reverted any deleterious mutations that appeared in
the population [33]. In this setup, the Avida world examines the fitness cost of every new point
mutation. If this new mutant has decreased fitness relative to its parent, the mutant is prevented
from entering into the population.

3.5.4 Data Analysis

We calculated statistics for the evolved avidians using Avida’s Analyze Mode [154]. In Analyze
Mode, the experimenter can run an avidian through its life-cycle (until reproduction) and calculate
several genotype characteristics. Fitness was calculated as the ratio between the number of instruc-
tions in the genome (the sequence length) to the number of instruction executions needed to copy
the genome and reproduce (this is an unbiased predictor of the actual number of offspring).

In order to calculate the distribution of fitness effects for each genotype and other related
mutational measures, each point mutation was generated for each genotype (25 × L mutations,
where L is the number of instructions in the genome). The fitness effect of each mutation was
− 1, where wm is the fitness of the mutant and w0 was the fitness of the
calculated as s = wm
w0
genotype. The average mutational effect of each genotype is the arithmetic mean of these fitness
effects. The fraction of mutations of a given fitness effect was calculated as the number of mutations
with that fitness effect divided by 25L.

63

To estimate the distribution of fitness effects of fixed mutations for each genotype, we analyzed
the line-of-descent (LOD) of these genotypes. The LOD of a genotype contains every genotype
that led from the ancestral genotype to the genotype of interest; it represents a fossil record of that
lineage [109]. We calculated the fitness effect of each mutation along the LOD as above. For
calculating the change in the frequency of lethal and deleterious mutations along the LOD as in
(Fig. 3.7c), we performed the calculations detailed above for each LOD genotype.

In order to examine possible differences in the distribution of beneficial fixed effects between
small populations and large populations, we had to identify the beneficial mutations that contributed
to adaptation. This is non-trivial, as small populations fix more beneficial mutations than large
populations due to their oscillations in fitness. In order to not include these transient fixed beneficial
mutations, we selected the beneficial mutations from each population whose fitness gain was at
least partially maintained during the future evolution of the population. We labeled a beneficial
mutation on a population’s LOD as maintained if 1) it resulted in the lineage attaining a new fitness
maximum, and 2) fitness never decreased below the previous fitness value on the LOD except for
a transient amount of time. We defined a transient amount of time as less than five consecutive
genotypes on the LOD having a lower fitness. This transient fitness decrease allowance is necessary
due to the possibility of valley-crossing in Avida fitness landscapes [33].

To compare the fraction of small-effect deleterious mutations between genotypes from small
populations and genotypes from large populations (Fig. 3.6), we first selected one genotype from
each lineage for a given fitness value. If a lineage had multiple genotypes with the same fitness, as
was often the case, we took the last genotype that appeared. Then, for each fitness value with more
than 20 genotypes from both small and large populations, we calculated the fitness effect of every
possible point mutation and the fraction of these mutations that were deleterious with a small effect
size as described above.

Statistical analyses were performed using the NumPy [197], SciPy [82], and Pandas [139]
Python modules. Figures were created with the Matplotlib [78] Python module. The stationary
distribution for the mathematical model was solved using Mathematica version 11.0.1.0 [222].

64

3.5.5 Data Availability

The Avida software is available for free use ( https://github.com/devosoft/avida). Avida configura-
tion scripts, data from Avida experiments, statistical analysis and figure-generating scripts, as well
as the Mathematica code, are available at the Dryad data repository (DOI:10.5061/dryad.nr780).

3.6 Acknowledgements

T.L. acknowledges a Michigan State University Distinguished Fellowship, a BEACON fellow-
ship, and the Russell B. Duvall award for support. This work was supported in part by Michigan
State University through computational resources provided by the Institute for Cyber-Enabled Re-
search. This material is based in part upon work supported by the National Science Foundation
under Cooperative Agreement No. DBI-0939454. Any opinions, findings, and conclusions or
recommendations expressed in this material are those of the authors and do not necessarily reflect
the views of the National Science Foundation.

65

CHAPTER 4

GENOME SIZE AND THE EXTINCTION OF SMALL POPULATIONS

Thomas LaBar, Christoph Adami

4.1 Abstract

Although extinction is ubiquitous throughout the history of life, the factors that drive extinction
events are often difficult to decipher. Most studies of extinction focus on inferring causal factors
from past extinction events, but these studies are constrained by our inability to observe extinction
events as they occur. Here, we use digital evolution to avoid these constraints and study “extinction
in action”. We focus on the role of genome size in driving population extinction and examine the
genetic mechanisms behind the relationship between genome size and extinction. We find that
the relationship between genome size and extinction is driven by two genetic mechanisms that in-
crease a population’s lethal mutational burden: large genome size leads to both an increased lethal
mutation rate and an increased likelihood of stochastic reproduction errors and non-viability. We
further show that this increased lethal mutational burden is directly due to genome expansions, as
opposed to subsequent adaptation after genome expansion. This result, contrary to the expectation
that genome expansions should increase the neutrality of mutations, not their lethality, suggests a
role for epistasis in driving extinction. These findings suggest that large genome size can enhance
the extinction likelihood of small populations and may inform which natural populations are at an
increased risk of extinction.

4.2

Introduction

The ubiquity of extinction events throughout the history of life [80], and the increasing real-
ization that Earth’s biosphere may be experiencing a sixth mass extinction [11] drives interest in
determining the factors that cause certain species, but not others, to go extinct [134]. It is accepted

66

that a combination of genetic [160, 186], demographic [132, 141], environmental [112, 196], and
ecological [30, 42, 163] factors contribute to species extinctions. Beyond those deterministic fac-
tors, chance events also likely influence some extinction events [170, 195]. Here, we focus on
the genetic factors influencing extinction, specifically the role of small population size and genetic
drift [123].

In small populations, weakened purifying selection leads to increased fixation of small-effect
deleterious mutations [213]. As multiple deleterious mutations fix, the absolute fitness of the
population may decrease, resulting in a decrease in population size. This decreased population size
further weakens selection, leading to the fixation of additional deleterious mutations and a further
decrease in population size. This process continues until population extinction. This positive
feedback loop between decreased population size and deleterious mutation fixation is known as
a mutational meltdown [125]. Mathematical models of mutational meltdowns suggest that even
intermediate-sized asexual populations can quickly go extinct [58, 126]. Likewise, small sexual
populations are also vulnerable to fast meltdowns [105].

The concept of a mutational meltdown provides a population-genetic mechanism for extinction.
However, it is still uncertain what factors beyond population size influence the likelihood of a
meltdown. If deleterious mutation accumulation drives mutational meltdowns, then species with
a greater genomic mutation rate should be at a greater risk of extinction [184, 233]. Another
proposed genetic mechanism that could lead to population extinction are genome expansions (i.e.,
mutations that increase genome size). Indeed, there is some evidence that genome size positively
correlates with extinction risk in certain clades of multicellular organisms [200, 201].

While the relationship between high mutation rates and extinction suggests that larger genome
size heightens extinction risk solely by increasing mutation rates, the connection between genome
size and extinction can be complicated.
If genome expansions lead to increased neutrality, the
overall genomic mutation rate may increase, but the deleterious mutation rate will remain constant.
Species with larger genomes should only face an increased mutational burden if genome expansions
lead to increased genome content under purifying selection. For example, potential detrimental

67

molecular interactions between an original genomic region and its duplicate may result in an
increased mutational burden [40]. As genome expansions are likely to lead to many alterations
in the distribution of mutational effects, it is still unclear which genetic mechanisms lead genome
expansions to drive population extinction.

It is difficult to test the role of genome size in extinction in both natural and laboratory model
systems. Here, we use digital experimental evolution [3, 12, 75, 84, 164] to test whether genome
expansions can drive population extinction. In a previous study with the digital evolution system
Avida [154] on the role of population size in the evolution of complexity, we found that the smallest
populations evolved the largest genomes and the most novel traits, but also had the greatest extinction
rates [101]. Now, we use Avida to test explicitly the mechanisms behind the role of genome size in
the extinction of small populations.

Avida differs from previous models of extinction in small populations in the mode of selection.
Unlike mutational meltdown models [123], where selection is hard and the accumulation of dele-
terious mutations directly leads to population extinction, selection is primarily soft in Avida and
deleterious mutations alter relative fitness (i.e., competitive differences between genotypes), not
absolute fitness (i.e., differences in the number of viable offspring between genotypes). Extinction
occurs in Avida through the accumulation of “lethal” mutations, or more precisely, “non-viable”
mutations that prevent their bearer from reproducing. These non-viable avidians occupy a portion
of the limited space allocated to an avidian population, thus reducing the effective population size
and potentially causing extinction over time.

We find multiple genetic mechanisms lead genome expansions to drive the extinction of small
populations. Increased genome size not only leads to an increase in the genomic mutation rate, but
specifically to an increase in the lethal mutation rate. Elevated lethal mutation rates in large-genome
genotypes are likely due to detrimental interactions between ancestral genome regions and dupli-
cated genome content. Additionally, we show that genotypes with large genomes have an elevated
probability of stochastic replication errors during reproduction (i.e., stochastic viability), further
elevating the likelihood of offspring non-viability and extinction. These results suggest that large

68

genome size does elevate the risk of population extinction due to an increased lethal mutational
burden from multiple genetic mechanisms.

4.3 Results

4.3.1 Large genome size increases the extinction risk of small populations

To test if genome expansions and large genome size enhanced the probability of population
extinction, we evolved populations across a range of population sizes at both high (1.5 muta-
tions/genome/generation) and low (0.15 mutations/genome/generation) mutation rates with either
a fixed genome size or a variable genome size. Under the low mutation rate regime, populations
with variable genome sizes had greater rates of extinction than those with fixed small genomes
(Fig. 4.1A). Under the high mutation rate regime, there was no significant difference between
populations with a variable genome size and populations with a constant genome size (Fig. 4.1A).
Estimations of the time to extinction further support these trends:
in the low mutation regime,
populations where genome size could evolve went extinct in fewer generations than those where
genome size was constant. There were no differences in the high mutation rate regime (Fig. 4.1B).
Next, we compared the final evolved genome size between genotypes from extinct populations
and surviving populations. Across the range of population sizes for which at least 10 populations
both survived and went extinct, “extinct” genotypes evolved larger genomes than those “surviving”
genotypes in the low mutation rate regime (Fig. 4.2A). In the high mutation rate regime, one
population size (N = 15 individuals) led to surviving populations evolving larger genomes, while
there was no statistically-significant difference for the other population sizes (Fig. 4.2B). Together,
these results suggest that genome expansions and large genome size can enhance the risk of small
population extinction if the initial mutation rate is too low for extinction to otherwise occur. We next
focus on examining the mechanism behind the relationship between genome size and extinction in
the low mutation rate populations.

69

Figure 4.1: Possibility of genome expansions increase extinction in low mutation rate
populations. A) Number of extinct populations as a function of population size. Solid (dashed)
lines represent variable (fixed) genome size populations. Black (white) circles represent low
(high) mutation rate populations. Error bars are bootstrapped 95% confidence intervals (104
samples). B) Time to extinction for population size and mutation rate combinations. Lines and
colors same as in panel A. Error bars represent two times the standard error of the mean. Data
only shown for those treatments that resulted in at least ten extinct populations.

Figure 4.2: Extinct populations evolved larger genomes. A) Final genome size for the low
mutation rate populations as a function of population size. Populations that survived are shown
with gray boxplots; populations that went extinct are shown with white boxplots. Red bars are the
median value, boxes are the first and third quartile, upper/lower whiskers extend up to the 1.5
times the interquartile range, and circles are outliers. ** indicates p < 10−4, * indicates p < 10−2,
and N.S. indicates p > 0.05 for the Mann-Whitney U-test. Population sizes where fewer than ten
populations went extinct (or survived) not shown. B) Final genome size for the high mutation rate
populations as a function of population size. Description same as in panel A. Population sizes
where fewer than ten populations went extinct (or survived) not shown.

70

510152025Population Size020406080100Extinct Populations5101520Population Size02468Generations to Extinction (x104)AB5678101520Population Size02004006008001000Genome Size10121516172025Population Size02004006008001000AB*******N.S.N.S.4.3.2 Extinction and large genome size is associated with increases in the lethal mutational

load

Avidian populations only face population-size reductions through one mechanism: parent avidians
produce non-viable (or infertile) offspring that replace viable avidians. In other words, the lethal
mutational load should drive population extinction.
It is therefore possible that the increased
genomic mutation rate that co-occurs with genome expansions specifically increased the genomic
lethal mutation rate. The elevated lethal mutation rate then leads to increased rates of population
extinction. We first tested whether larger genomes had an increased lethal mutation rate. Genome
size was correlated with the lethal mutation rate across genotypes from all population sizes,
supporting the hypothesis that increases in genome size result in increased lethal mutational load
and eventually population extinction (Fig. 4.3A; Spearman’s ρ ≈ 0.75, p = 1.77 × 10−148). Next,
we examined whether populations that went extinct had previously evolved greater lethal mutation
rates than surviving populations. As with the trend for genome size, extinct populations evolved
greater lethal mutations rates than surviving populations (Fig. 4.3B).

Figure 4.3: Lethal mutation rate correlates with genome size and population extinction. A)
The lethal mutation rate as a function of genome size for the final genotypes from each evolved
low mutation rate population. White circles are extinct populations; gray circles are surviving
populations. B) The lethal mutation rate for extinct and surviving populations across population
sizes. Boxplots as previously described. Colors and significance symbols same as Figure 4.2.
Population sizes where fewer than ten populations went extinct (or survived) not shown.

The previous data support the hypothesis that genome expansions drive population extinction
by increases in the lethal mutation rate and thus the lethal mutational load. However, it is unclear

71

02004006008001000Genome Size0.51.01.5Lethal Mutation Rate5678101520Population Size0.51.01.5AB******whether genome expansions themselves increase the likelihood of lethal mutations (suggesting
epistasis between genome expansions and the ancestral genome) or whether genome expansions
merely potentiate future increases in the lethal mutation rate (due to subsequent adaptation). To test
these two scenarios, we examined the evolutionary histories (i.e., lines-of-descent) for all N = 20
low mutation-rate populations. We then examined the relationship between changes in genome
size and changes in the lethal mutation rate (Fig. 4.4A). When genome size was constant, the lethal
mutation rate did not change on average (mean change = 7×10−4 mutations/genome/generation, 95%
Confidence Interval (CI) = ±2 × 10−3 mutations/genome/generation). Genome size increases on
average increased the lethal mutation rate (mean change = 0.024 mutations/genome/generation, 95%
CI = ±0.0023 mutations/genome/generation), while genome size decreases on average decreased
the lethal mutation rate (mean change = -0.033 mutations/genome/generation, 95% CI = ±0.0040
mutations/genome/generation). Additionally, the change in genome size positively correlates with
the change in the lethal mutation rate (Fig. 4.4B; Spearman’s ρ = 0.67, p ≈ 0.0), suggesting that
genome expansions directly lead to increases in the genomic lethal mutation rate.

Figure 4.4: Insertions and deletions directly change the lethal mutation rate. A) Change in
the lethal mutation rate as a function of a mutation’s effect on genome size. Boxplots as
previously described. Each data point represents a genotype from a reduced evolutionary lineage
of a population with 20 individuals. B) Relationship between a mutation’s change in genome size
and the change in the lethal mutation rate. Data same as in panel A. Dashed lines represent no
change. Data points comparing genotypes with equal genome size were excluded.

72

GenomeSizeConstantGenomeSizeIncreasedGenomeSizeDecreased-0.50.00.5Change in Lethal Mutation Rate-750-500-2500250Change in Genome Size-0.50.00.5AB4.3.3 Lethal mutation rates and stochastic viability drive population extinction

Finally, to establish the role of the lethal mutation rate in driving population extinction, we performed
additional evolution experiments to test whether the prevention of lethal mutations would prevent
population extinction. We repeated our initial experiments (Fig. 4.1), except offspring with lethal
mutations were reverted to their parental genome (lethal-reversion treatment; see Methods for
details). We also did the same experiment where deleterious, but non-lethal, mutations were
reverted in order to test if deleterious mutations contributed to extinction. When populations
evolved without deleterious mutations, extinction rates were similar to, if not greater than, those
for populations that evolved with deleterious mutations (Fig. 4.5A). Populations that evolved with
fixed-size genomes and without lethal mutations never went extinct, demonstrating how the lack of
lethal mutations can prevent extinction (Fig. 4.5B). However, when these populations evolved with
variable genome sizes, extinction still occurred, although at a lower rate than when lethal mutations
were present (Fig. 4.5B).

While these data demonstrate that lethal mutations do primarily drive extinction risk, the fact
that extinction can still occur presumably without lethal mutations is unexpected and indicates
that there is a second factor that relates genome size to extinction. This is surprising, as lethal
mutations are the only direct mechanism to cause extinction in Avida. One possible explanation
for extinction in the lethal-reversion populations is that mutants arise in these populations that are
initially viable, but later become non-viable. In other words, these populations evolve stochastic
viability, where characteristics of the random numbers the avidians input during their life-cycle
affect their ability to reproduce. These genotypes with stochastic viability would, on occasion,
not be detected as lethal mutants, and thus enter the population even when lethal mutations are
reverted. As they reproduce, these stochastically-viable genotypes will input other numbers and
thus become, in effect, non-viable and subsequently lead to population extinction. To check if the
populations that went extinct without lethal mutations did evolve stochastic viability, we tested the
viability of all 100 genotypes from the lethal-reversion, variable genome size N = 5 populations.
We also performed the same tests with the 100 genotypes from the N = 8 populations that evolved

73

Figure 4.5: Evolution of stochastic viability contributes to extinction risk. A) Number of
population extinctions (out of 100 replicates) as a function of population size for the
deleterious-reversion (squares) and no-reversion (circles) treatments. Dashed and solid lines
represent populations from fixed genome size and variable genome size treatments, respectively.
Error bars are 95% confidence intervals generated using bootstrap sampling (104 samples).
No-reversion treatment data same as in Fig. 4.1A. B) Number of population extinctions (out of
100 replicates) as a function of population size for the lethal-reversion (triangles) and no-reversion
(circles) treatments. Other symbols same as in panel A. C) Percent of viability trials (out of 1000)
for which a given genotype was not viable. Values between 0 and 1 indicate stochastic viability.
“Original” refers to the 100 genotypes from the N = 8 populations that evolved with lethal
mutations. “Revert-lethal” refers the 100 genotypes from the N = 5 lethal-reversion populations.
Boxplots as previously described. D) Genome sizes for always-viable and stochastically-viable
genotypes from both the N = 8 no-reversion populations and the N = 5 lethal reversion
populations.

74

5101520Population Size020406080100Extinct Populations5101520Population Size020406080100Extinct PopulationsRevert-LethalSurvivedRevert-LethalExtinctOriginalSurvivedOriginalExtinct0.00.20.40.60.81.0Non-viable Trials (%)AllViableStochasticViable0246810Genome Size (x102)ABCDwith lethal mutations to see if these mutants arose in our original populations.

For both sets of genotypes, we found that some genotypes were stochastically viable (Fig. 4.5C).
In fact, of the 23 genotypes from populations that went extinct in the lethal-reversion treatment, 19
displayed stochastic viability. No genotypes from surviving populations were stochastically-viable.
Of the 42 genotypes from populations that went extinct among our original treatment genotypes, 8
displayed stochastic viability. Two genotypes from surviving populations were stochastically-viable,
suggesting these populations would have an enhanced likelihood of extinction if the experiment had
continued. Finally, we compared the genome sizes between genotypes from the lethal-reversion
genotypes that were always measured as viable and those that measured as stochastic-viable.
Stochastic-viable genotypes evolved larger genomes than deterministic-viable genotypes (Mann-
Whitney U-test, median = 128 instructions versus median = 191 instructions, p < 2 × 10−4;
Fig. 4.5D), further suggesting that increased genome size can lead to the evolution of stochastic
viability and eventual population extinction. We comment on the relevance of stochastic viability
in biological populations in the Discussion below.

4.4 Discussion

We explored potential genetic mechanisms behind the relationship between genome size and
the extinction of small populations. Genome expansions drive extinction because they increase the
lethal mutation rate of small populations. Elevated lethal mutation rates arise through two genetic
mechanisms. First, genome expansions directly increase the lethal mutation rate, suggesting
that epistatic interactions between ancestral genome content and novel duplicated content lead
to more lethal mutations. Second, genotypes with larger genomes have a greater likelihood of
evolving stochastic viability. Both mechanisms contribute to the lethal mutational burden of small
populations and together heightened the risk of population extinction.

The relationship between genome expansions and increases in the lethal mutation rate is at first
counterintuitive. It is classically thought that gene/genome duplications should lead to an increase
in the rate of neutral mutations, not lethal mutations, due to increases in mutational robustness [70].

75

Increases in the lethal mutation rate (and not the neutral mutation rate) should only occur if there
are genetic interactions (i.e., epistasis) between the ancestral genome section and the duplicated
genome section. Is there evidence for gene/genome duplications leading to increased mutational
load, as opposed to increased robustness? Recently, it was argued that gene duplication can also
result in increased mutational fragility, not just mutational robustness, if a duplicate gene evolves to
interact with its ancestor [40]. However, more empirical studies are needed to determine whether
genome expansions can elevate the mutational burden of a population to such a level that population
extinction becomes a possibility.

Our second proposed mechanism underlying the connection between genome size and extinction
is the evolution of stochastic-viable genotypes that could only reproduce under some environmental
conditions (here, random number inputs). The connection behind stochastic viability and extinction
in small populations is intuitive. Mutations causing stochastic viability likely have a weak effect
(due to their stochastic nature) and can fix in small populations due to weakened selection. After
fixation, the lethality of these mutation may be stochastically revealed, and extinction occurs.
However, studies on the functional consequences of mutations responsible for extinction are rare
(although see [57, 174]) and it is uncertain whether these mutations arise in populations at
high extinction risk. One suggestion that mutations with stochastic effects might be relevant to
population extinction comes from microbial experimental evolution. It has been shown that small
populations have reduced extinction risk if they overexpress genes encoding molecular chaperones
that assist with protein folding [176]. These overexpressed chaperones presumably compensate for
other mutations that cause increased rates of stochastic protein misfolding. Therefore, mutations
responsible for an increased likelihood of protein misfolding may be an example of a class of
mutations with a stochastic effect that enhance extinction risk. However, this is only speculation
and further work is needed to determine if stochastic viability is a possible mechanism behind
extinction risk.

The most prominent model of small population extinction is the mutational meltdown model
[123, 125, 126], which argues that even intermediate-sized asexual and sexual populations (i.e.,

76

103 individuals) can go extinct on the order of thousands of generations. In contrast to mutational
meltdown models, only very small populations go extinct in Avida, and extinction occurs on a longer
timescale. The difference between our results and previous results from mutational meltdown
models are likely due to differences in the character of selection between the two models. Selection
is hard in mutational meltdown models, and the accumulation of deleterious mutations directly
increases the probability that offspring will be non-viable [123]. In Avida, selection on deleterious
mutations is soft and the accumulation of deleterious mutations is unrelated to the likelihood of
non-viable offspring. The lethal mutation rate will only increase indirectly in Avida with genome
expansions. Without the positive feedback loop between deleterious mutation accumulation and
population size, avidian populations only evolve a high rate of non-viable mutants if they evolve
large genomes, thus explaining the trends we saw here.

These differences between extinction in hard selection models and the Avida selection model
emphasizes the need to consider whether selection in biological populations is primarily hard or soft.
Unfortunately, there has been little resolution on this question [172, 206]. There is some evidence
that soft selection may be more prevalent than hard selection. For instance, soft selection has been
invoked as an explanation for why humans are able to experience high rates of deleterious mutations
per generation [27, 110]. Moreover, the persistence of small, isolated populations [16, 173, 225]
suggests that not only is selection primarily soft in nature, but that the extinction dynamics we study
here are relevant to a subset of biological populations. While large genome size may not be the
factor that causes populations to decline, it could drive an already-reduced population to extinction.
In a previous study, we observed that small populations evolved the largest genomes, the greatest
phenotypic complexity, and the greatest rates of extinction [101]. This result raised the question
of whether greater biological complexity itself could increase a population’s rate of extinction. Al-
though we did not test whether increased phenotypic complexity had a role in extinction, we have
shown that genome complexity, measured in terms of genome size, did drive small-population ex-
tinction. While it is possible that phenotypic complexity also enhanced the likelihood of extinction,
the Avida phenotypic traits likely do not increase the lethal mutation rate. Thus, both high extinction

77

rates and increased phenotypic complexity arise due to the same mechanism: greater genome size.
This result illustrates an evolutionary constraint for small populations. While weakened selection
and stronger genetic drift can lead to increases in biological complexity, small populations must also
evolve genetic architectures that reduce the risk of extinction [176, 199]. Otherwise, small popu-
lations cannot maintain greater complexity and their lethal mutational load drives them to extinction.

4.5 Methods

4.5.1 Avida

Here we review those aspects of Avida (version 2.14; available at https://github.com/devosoft/avida)
relevant to the current study (see [154] for a complete overview). In Avida, simple computer pro-
grams (“avidians") compete for the resources required to undergo self-replication and reproduction.
Each avidian consists of a genome of computer instructions drawn from a set of twenty-six avail-
able instructions in the Avida genetic code. A viable asexual avidian genome must contain the
instructions to allocate a new (offspring) avidian genome, copy the instructions from the parent
genome to the offspring genome, and divide off the offspring genome into a new avidian. During
this copying process, mutations may occur, introducing variation into the population. These novel
mutations can then be passed onto future generations, resulting in heritable variation. This genetic
variation causes phenotypic variation: avidians with different genomes may self-replicate at differ-
ent speeds. As faster self-replicators will outcompete slower self-replicators, there is differential
fitness between avidians. Therefore, given there is heritable variation and differential fitness, an
Avida population undergoes Darwinian evolution [1, 164]. Avida has previously been used to
test hypotheses concerning the evolution of genome size [71, 101], the role of population size in
evolution [48, 101, 102, 144], and the consequences of population extinction [187, 227, 228, 229].
The Avida world consists of a grid of N cells; each cell can be occupied by at most one avidian.
Thus, N is the maximum population size for the Avida environment. While avidian populations are
usually at carrying capacity, the presence of lethal mutations can reduce their effective population

78

size below this maximum size. Here, offspring can be placed into any cell in the environment,
simulating a well-mixed environment (i.e., no spatial structure). If a cell is occupied by another
avidian, the new offspring will overwrite the occupant. The random placement of offspring avidians
adds genetic drift to Avida populations, as avidians are overwritten without regard to fitness.

Fitness for an avidian genotype is estimated as the ratio of the number of instructions a genotype
executes per unit time to the number of instructions it needs to execute to reproduce. Therefore, there
are two avenues for a population of avidians to increase fitness: increase their number of instructions
executed per unit time or decrease the number of instruction executions needed for self-replication.
Avidian populations can increase the number of instructions executed by evolving the ability to
input random numbers and perform Boolean calculations on these numbers (a “computational
metabolism”) [109]. They can also decrease the number of instruction executions necessary for
reproduction by optimizing their replication machinery.

There are a variety of different implementations of mutations in Avida. Here, we used settings
that differed from the default in order to improve our ability to analyze the causes of population
extinction (see Table 4.1 for a listing of changes to the default settings). Point mutations change
one locus from one of the twenty-six Avida instructions to another random, uniformly chosen,
instruction, occur upon division between parent and offspring, after replication. There is an equal
probability that each instruction in the genome will receive a point mutation; thus, genome size
determines the total genomic mutation rate. To model indels, we used so-called “slip” mutations.
This mutational type will randomly select two loci in the genome and then, with equal probability,
either duplicate or delete the instructions in the genome between those two loci. While the rate
of indel mutations remains constant, the chance of large indel mutations increases as genome size
grows. Finally, to ease our analysis, we required every offspring genotype to be identical to its
parent’s genotype before the above mutations were applied at division.

One aspect of Avida mutations that differs from traditional models of population extinction is the
presence of lethal, or non-viable, mutations in addition to deleterious, and non-lethal, mutations.
Instead, they prevent their bearer from successfully
These mutations do not kill their bearer.

79

Table 4.1: Notable Avida parameters changed from default value.

Parameter
WORLD_ X
WORLD_ Y
BIRTH_ METHOD
COPY_ MUT_ PROB
DIV_ MUT_ PROB
DIVIDE_ INS_ PROB
DIVIDE_ DEL_ PROB
DIVIDE_ SLIP_ PROB
REQUIRE_ EXACT_ COPY 0
REVERT_ FATAL
0.0
REVERT_ DETRIMENTAL 0.0

N
1
4
0.0
µ
0.0
0.0
0.01
1
1.0
1.0

Default Value Changed Value Treatment
60
60
0
0.0075
0.0
0.05
0.05
0.0

All
All
All
All
All
All
All
Variable Genome Size
All
Lethal-reversion
Deleterious-reversion

reproducing within the maximum allowed lifespan (i.e., they are non-viable). Here, we used the
default maximum lifespan of 20 × L instruction executions, where L is the genome size. In other
words, this setting limits the number of times an avidian can cycle through their genome in an
attempt to reproduce. Such a setting must exist in order to allow avidian genomes to be analyzed.
Otherwise, non-reproducing avidians could be analyzed forever, as the only way to decide if an
avidian can reproduce is to actually execute the code in its genome.

In Avida, it is possible to perform experiments where the appearance of mutations with certain
effects is prevented [33]. For example, it is possible to revert a mutation of a particular predetermined
effect after it has appeared. To enable this, the Avida program analyzes the fitness of every novel
genotype that enters the population and, if the fitness is of the pre-set effect, the mutation is reverted.
This system allows experimenters the ability to determine the relevance of certain mutational effects
to evolution. However, mutations of certain effects can still enter the population if their fitness effects
are stochastic. An avidian has stochastic fitness if its replication speed depends on characteristics
of the random numbers it inputs in order to do its Boolean calculations. Some stored numbers may
alter the order in which certain instructions are executed or copied into an offspring’s genome, thus
altering fitness.

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4.5.2 Experimental Design

To study the role of genome size in the extinction of small populations, we first evolved populations
across a range of per-site mutation rates (µ = 0.01 and µ = 0.1) and population sizes (N =
{5, 6, 7, 8, 10, 15, 20} for µ = 0.01 and N = {10, 12, 15, 16, 17, 20, 25} for µ = 0.1). For each
combination of population size and mutation rate we evolved 100 populations for at most 105
generations. Each population was initialized at carrying capacity with N copies of the default
Avida ancestor (which has 100 instructions) with all excess instructions removed; this resulted
in an ancestor with a genome of 15 instructions (only those needed for replication). Ancestral
genotypes with per-site mutation rates of µ = 0.01 and µ = 0.1 thus have genomic mutation rates of
U = 0.15 and U = 1.5 mutations/genome/generation, respectively. Genome size mutations (indels)
occur at a fixed rate of 0.01 mutations/genome/generation for all treatments. Additionally, for each
mutation rate and population size combination, an additional 100 populations were evolved in an
environment where genome size was fixed. To directly test for the role of lethal and deleterious
mutations in driving extinction, we evolved 100 populations at the low mutation rate population
sizes under conditions where either lethal mutations or deleterious, but non-lethal, mutations were
reverted (the “lethal-reversion” and “deleterious-reversion treatments”, respectively).

4.5.3 Data Analysis

For all evolution experiments, we saved data on the most abundant (dominant) genotype every ten
generations. The final saved dominant genotype was used in all analyses here. All data represents
either genotypes at most ten generations before extinction (in the case of extinct populations) or
genotypes from the end of the experiment (in the case of surviving populations).
In order to
calculate the lethal mutation rate and other relevant statistics for a genotype, we generated every
single point mutation for that genotype and measured these mutants’ fitness using Avida’s Analyze
mode. The lethal mutation rate was estimated as Ulethal = µ × L × plethal, where µ is the per-site
mutation rate, L is the genome size, and plethal is the probability that a random mutation will be
lethal.

81

4.5.3.1 Analysis of the relationship between genome expansions and changes in the lethal

mutation rate

To test whether genome expansions themselves were directly responsible for the increase in the
lethal mutation rate or whether the lethal mutation rate increased after evolution in response
to a genome expansion, we first reconstructed the line-of-descents (LODs) for each of the one
hundred genotypes evolved in a population of 20 individuals with a per-site mutation rate of 0.01
mutations/site/generation (the low mutation rate). An LOD contains every intermediate genotype
from the ancestral genotype to an evolved genotype and allows us to trace how genome size evolved
over the course of the experiment [109]. We reduced these LOD to only contain the ancestral
genotype, the genotypes that changed genome size, the genotype immediately preceding a change
in genome size, and the final genotype. We measured the genome size and the lethal mutation rate
for each of these remaining genotypes. Then, we measured the relationship between the change in
genome size and the change in the lethal mutation rate for genome expansions, genome reductions,
and the segments of evolutionary time where genome size was constant.

4.5.3.2 Analysis of stochastic viability

In order to test the possibility that some of our populations had evolved stochastic viability, we
analyzed each genotype from the N = 5 lethal-reversion populations and each genotype from
the N = 8, µ = 0.01, original populations. These population sizes were chosen because they
had the greatest equality between the number of extinct populations and the number of surviving
populations. We performed 1000 viability trials, where a genotype was declared non-viable if it
could not reproduce. A genotype was declared stochastically-viable if the number of non-viable
trials was greater than 0 and less than 1000. Otherwise, it was defined as deterministically-viable.
All data analysis beyond that using Avida’s Analyze Mode was performed using the Python
packages NumPy version 1.12.1 [197], SciPy version 0.19.0 [82], and Pandas version 0.20.1 [139];
figures were generated using the Python package Matplotlib version 2.0.2 [78]. All Avida scripts
and data analysis scripts used here are available at https://github.com/thomaslabar/

82

LaBarAdami_GenomeSizeExtinction.

4.6 Acknowledgments

We thank M. Zettlemoyer and C. Weisman for comments on drafts of the manuscript. This work
was supported in part by Michigan State University through computational resources provided by
the Institute for Cyber-Enabled Research.

83

CHAPTER 5

CONCLUSION

This conclusion will consist of three sections. First, I will make some broad conclusions con-
cerning the work I presented here that did not fit with any specific chapter. I will also address
some chapter-specific conclusions that did not make the published version. Then, I will address
limitations of this research and speculate on how these limitations may affect the results. Finally, I
will end by discussing potential future work.

5.1 Further Conclusions

If the main conclusions of the research present here could be summarized in one sentence, it
would be the following. Population size qualitatively, and not just quantitatively, alters the outcome
of the evolutionary process. Historically, the focus on the role of population size has been on
how it alters a population’s evolutionary dynamics.
In other words, small population size may
limit adaptation [221], it may prevent the fixation of small-effect beneficial mutations [66], or it
may increase the fixation of deleterious mutations [151], among other potential consequences of
weak selection and strong drift. All of these effects are quantitative in the sense that while they
may mathematically affect a population’s adaptive state by reducing fitness, small populations are
still qualitatively similar to their large population size relatives. This view assumes that small
populations are just less-adapted versions of large populations. They evolve similar phenotypes in
similar environments compared to large populations, but in a less-optimal state.

The results presented here argue for a larger difference between small and large populations.
Instead of there solely being quantitative (i.e., fitness) differences between small and large pop-
ulations, there are qualitative differences: small and large populations evolve towards alternative
genetic architectures. These findings support other studies that have also showed qualitative differ-
ences in the evolutionary trajectories of small and large populations (e.g., [94, 97, 119, 169, 171]).

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However, previous attempts either are purely theoretical simulations (e.g., [97, 131], but see [171])
or rely on comparative genomics evidence (e.g., [121]), where it is difficult to control for every
possible factor [214]. By using Avida, one can both control for only the role of population size in
altering evolutionary outcomes and perfectly reconstruct the evolutionary trajectories that led to al-
ternative genomic architectures. And while Avida populations likely possess different possibilities
for genetic architecture than biological populations, the possible levels of control in Avida allowed
for the discovery of a novel population-genetic principle (drift robustness) that should factor into
some biological systems. The extent to which this general principle of small populations evolving
qualitatively different from large populations applies across life remains to be explored.

5.1.1 Absence of mutational hazards in altering small population evolution

In Chapter 2, I tested the role of population size in driving the evolution of genome complexity
(measured as genome size) and the evolution of phenotypic complexity (measured as number
of phenotypic traits). This study was inspired by Lynch’s Mutational Hazard (MH) hypothesis,
which argues that genetic drift and mutational pressure should drive the evolution of genome
complexity (one measure of which is genome size [121]) and potentiate the evolution of functional
complexity [94, 118, 121]. Due to the differences in avidian genomes (asexual haploids) and the
genomes of multicellular eukaryotes (primarily obligate sexual reproducers with ploidy greater than
one), one must be cautious when claiming this work as a test of the Mutational Hazard hypothesis.
However, one can speculate on how the conclusions from this work inform on the validity of the
MH hypothesis.

I did find evidence that genetic drift in small populations leads to greater genome complexity
and phenotypic complexity (Chapter 2) as the MH hypothesis would predict. However, the MH
hypothesis does not just predict evolutionary outcomes, but also the mechanism behind those
outcomes. The MH hypothesis predicts it is the cost of excess DNA that drives selection against
unneeded genome content. This cost originates from the potential of any section of the genome
I did not find any evidence that this
to be mutated in a manner deleterious to the organism.

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selective pressure existed in my experiments. It is certainly the case that the reduction in fitness
from deleterious mutations alters genomic architecture under some Avida conditions [220], but
this occurs at much greater mutation rates than those used here. Why did I not see evidence of
selection against mutational hazards? One possibility is the range of population sizes used in Avida,
a possible limitation I discuss below.

What these results suggest is that there are other parameters that alter the conclusions of the
MH hypothesis beyond population size and mutational pressure. It is likely dependent on the exact
structure of the fitness landscape and thus the distribution of fitness effects of de-novo mutations. I
would speculate that all of these small-population evolution hypotheses: the MH hypothesis [119],
global/local mechanisms of mutational robustness [169], the drift-barrier hypothesis [188], and drift
robustness [102] are all aspects of the same overarching theory for evolution in small populations.
However, this speculation remains for future theoretical work, both in terms of mathematical
modeling and in terms of digital evolution.

5.1.2 The differences between mutational robustness and drift robustness

A main conclusion from the discovery of drift robustness in small populations is that evolving
robustness to the deleterious consequences of genetic drift is different from evolving robustness to
the deleterious consequences of mutations, or mutational robustness. Drift robustness is caused by
genetic architectures that limit the fixation of small-effect deleterious mutations. Drift robustness
evolves by a small population either not fixing small-effect beneficial mutations (thus not increas-
ing the likelihood of small-effect deleterious mutations and furthermore not adapting) or fixing
adaptive mutations that increase the likelihood of large-effect deleterious mutations. This scenario
does assume that a population cannot simultaneous adapt and increase the supply of neutral muta-
tions. Mutational robustness theory argues that small populations should reduce either the rate of
deleterious mutations or the effect size of said mutations [48, 68, 97, 131]. It is worth asking how
previous work missed the distinction between drift robustness and mutational robustness.

In some of the studies that demonstrated the evolution of mutational robustness in small popula-

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tions [97, 169], all deleterious mutations were slightly-deleterious. In this scenario, these mutations
fixed due to drift and lead to the evolution of increased neutrality (i.e., mutational robustness). This
also occurred in a study using Fisher’s Geometric Model, where there is likely a significant density
of slightly-deleterious mutations in the model’s distribution of fitness effects [68]. One of the re-
quirements for drift robustness is the existence of multi-peak fitness landscapes, something absent
in many of these models [68, 97]. Rajon and Masel’s model did include multiple fitness peaks
and they did find that small and large populations evolved alternative robustness “solutions” [169].
However, their “robust” fitness peaks only led to a reduction in slightly-deleterious “molecular
errors”, as all errors in this model were slightly-deleterious. My results emphasize the need to
consider evolution on complex fitness landscapes with non-trivial distribution of fitness effects and
to consider that the distribution of fitness effects is itself evolvable.

5.1.3 Drift robustness and bacterial endosymbionts

The classic model systems for the study of mutational robustness in small populations are obligate
bacterial endosymbionts [52]. Some pieces of evidence supporting mutational robustness include
the overexpression of genes encoding molecular chaperones [52, 53, 176] and increased rates of gene
evolution [148, 149, 177]. In light of the evidence presented here suggesting that small populations
should be expected to evolve drift robustness, not mutational robustness, it is worth asking whether
bacterial endosymbionts have really evolved drift robustness, not mutational robustness.

Proponents of mutational robustness in bacterial endosymbionts argue that overexpression of
molecular chaperones, or heat-shock proteins, epistatically alters the fitness landscape and reduces
the deleterious effects of mutations [53]. In other words, the overexpression of molecular chap-
erones decreases the phenotypic variation of mutations. However, recent work in Saccharomyces
cerevisiae demonstrates that molecular chaperone overexpression increases, not decreases, pheno-
typic variation on average [59]. This result suggests that this overexpression phenotype increases
the average deleterious effect of de-novo mutations, if one assumes that most phenotypic varia-
tion is deleterious. This consequence of overexpression is more aligned with the concept of drift

87

robustness, not mutational robustness, but rigorous tests are still needed for confirmation.

There is evidence that endosymbionts have faster rates of evolution than their free-living rel-
atives [148, 149], suggesting that mutations are more tolerable, or less deleterious; this trend is
another sign of mutational robustness. However, recent work has shown that, for some endosym-
bionts, while some genes do show faster rates of evolution, other genes show reduced rates of
evolution [177]. This result is consistent with increased purifying selection in some genes, and
thus an increased deleterious mutational load (either by increasing the prevalence of deleterious
mutations or increasing their deleterious effect). Furthermore, these genes are not host-related,
demonstrating that this increased purifying selection is not due to interactions with the host [177].
This result is also more consistent with drift robustness than mutational robustness.

Finally, evidence now exists that some endosymbionts have evolved increased protein multi-
functionality, compared to their free-living relatives [86, 231]. Increased protein multifunctionality,
or increased pleiotropy, may be evidence of drift-robust adaptation. If a mutation hits a gene that
encodes a multifunctional protein, multiple traits may face a loss of function. It stands to reason
that these mutations on pleiotropic genes will be more deleterious than mutations in non-pleiotropic
genes that affect only one function. Small populations may evolve increased pleiotropy because
beneficial mutations may be more maintainable if they occur in, or lead to, pleiotropic genes. As
with the other two pieces of evidence, its connection to drift robustness is speculative, but worthy
of future exploration.

5.1.4 Drift robustness and the role of epistasis in small-population adaptation

A prominent hypothesis suggest that epistasis, particularly negative (synergistic) epistasis between
slightly-deleterious mutations, could limit drift-related fitness declines [92] (although see [25, 69]).
I did not test directly for the presence of epistasis between slightly-deleterious mutations. Instead, I
argued that it is the absence of small-effect deleterious mutations that causes drift robustness [102].
However, epistasis does play a large role in allowing small populations to adapt past their previ-
ous drift barrier while maintaining drift-robust genomic architecture by increasing the severity of

88

previously small-effect deleterious mutations. Recent studies on the role of epistasis during adap-
tation has shown that negative epistasis between beneficial mutations is present across a variety of
species [28, 87, 98, 180]. My results provide an alternative example for how epistasis may shape
the adaptive trajectories of populations, particularly those evolving in strong-drift environments.

5.2 Limitations

5.2.1 Avida as an intermediate between mathematical modeling and biological experiments

One of the benefits of Avida, and digital evolution more broadly, is that it acts as a model system
in-between simpler, but conceptually-clearer, mathematical modeling, and the complexities of
biological systems. Thus, Avida can be used to discover novel phenomena that may be lacking in
simple mathematical models, but obscured or difficult to decipher in biological systems. However,
Avida’s intermediate position in model complexity can also be a drawback. While Avida allows
for the discovery of novel phenomena lacking in many mathematical models, there is a benefit to
simplicity unreachable in Avida experiments. Mathematical models allow one to narrow down
possible causes of some evolutionary pattern until one understands the minimal requirements to
reproduce the pattern. For example, the evidence for the evolution of drift robustness was better-
supported by demonstrating its existence in a mathematical model (Chapter 3). And while not
every problem can be modeled in such fashion, mathematical models do in many cases illustrate
evolutionary dynamics in a clearer fashion than many Avida experiments.

On the other end of the model-complexity spectrum, Avida lacks certain relevant characteristics
of biological systems and is inferior in many ways to biological model systems. One of the
assumptions behind using Avida to model biological evolution is that evolutionary dynamics are
equivalent no matter the evolving substrate (computer code versus DNA). While I believe this is
true, this assumption of similarity between Avida and biology may weaken when one begins to
consider questions concerning the evolution of genetic architecture and how genotype-phenotype
maps evolve. Put another way, Avida is an excellent system to study how evolution shapes genetic

89

variation. However, there is no guarantee that the characteristics of genetic variation in Avida, such
as the possible distribution of mutational effects, are similar to that in biology. And while Avida
can inform biologists of how evolution proceeds assuming the production of the specific variation
in Avida, one must always keep in mind that if variation is different in biological systems than in
Avida, the outcomes of the evolutionary process will also be different. While these limitations do
not eliminate the usefulness of Avida as a model system to study the evolutionary process, they
must be remembered during interpretation of the results.

5.2.2 Populations in Avida are much smaller than relevant biological populations

When discussing my results from Chapter 2 and their implications for the Mutational Hazard
hypothesis [119], I stated that I did not observe selection against mutational hazards in these
experiments. One possible explanation for this result is that, compared to biological populations,
all of my Avida experiments really use “small” populations. In the Mutational Hazard hypothesis,
it was estimated that the effective population sizes of multicellular eukaryotes is approximately
104 individuals, which is the absolute population size of my largest populations.
It is possible
that evidence for selection against mutational hazards would be seen in larger Avidian populations.
However, it is difficult to run Avida (or most agent-based models) at larger population sizes due
to current computational limitations. One argument against the idea that a population size of 104
individuals is too small to see selection against mutational hazards in Avida is that even smaller
avidian populations can fix anti-mutator (or mutation-decreasing) mutations if the deleterious
mutational load is large [31], suggesting the selective capacity should still have existed at the
population sizes I used in my experiment.

It is also worth discussing whether this limitation in terms of Avida population sizes affected
the conclusions of my drift robustness research. There are two consequences of small population
size that are relevant for this consideration: weak selection in small populations and limited
production of genetic variation in small populations. As far as weakened selection is concerned,
In the fitness landscape
the experiments did accurately represent small and large populations.

90

used to study drift robustness, the selection coefficient (s) of deleterious mutations did not appear
to go below 10−3. Thus, populations of 104 individuals were large enough (i.e., N > 1|s|) that
selection should have limited the frequency of every deleterious mutation. However, in regards to
limited genetic variation in small populations, the implications are less clear. It is possible that
differences in mutation supply altered the evolutionary outcomes between small populations and
large populations in addition to the inability to fix small-effect beneficial mutations. The respective
roles of weakened selection and limited mutation supply remain to be tested with both mathematical
models and computational evolution studies.

5.2.3 Results apply to asexual haploid species evolving in a constant environment

The final limitation of the experiments presented here is the limited experimental conditions used
throughout. All experiments used asexual haploid genotypes evolving in a constant environment,
as do most experimental evolution studies [83, 84]. While not a large issue for many studies of
evolutionary dynamics, this limitation is relevant here. Other than obligate-host bacterial endosym-
bionts, many, if not most, small populations are multicellular eukaryotes, which are obligate sexual
species and often diploid [121]. These are also the small populations that are expected to evolve
greater genetic complexity due to weakened selection and genetic drift [121]. By only performing
experiments with asexual haploid organisms, it is not possible to test if elements of recombina-
tion or ploidy alter evolutionary dynamics and lead to the evolution of greater/lesser complexity.
Likewise, given that diploidy and recombination can alter the dynamics of deleterious mutations
(e.g., [138, 159]), it is uncertain how multiple copies of each locus may alter the evolution of drift
robustness in small populations. Furthermore, all experiments here were performed in constant
environments. Given that one expects populations to evolve greater complexity in environments
of greater complexity (if only to evolve regulatory machinery to handle environmental changes),
the lack of environmental variability may be responsible for some of the results within. However,
variable environments appears to increase the fixation of stochastically-deleterious mutations [35],
and thus fluctuating environments may increase the range of population sizes that would lead to

91

drift-robust genetic architecture. An exploration of these additional factors remains for future
studies.

5.3 Future Work

The most impactful result of this dissertation is the discovery of drift robustness and its evolution
in small populations. Therefore, the most productive future work would be spent developing a
better understanding of how, and under which conditions, drift robustness would evolve in natural
populations. The obvious first choice for extending the idea of drift robustness is to test whether
drift robustness will still evolve under some of the conditions highlighted above as limitations, such
as diploidy, sexual reproduction, and realistic population sizes. Testing the predictions of drift
robustness using both bioinformatic approaches and experimental systems is also needed. In this
section, I will discuss a few possibilities in greater detail.

5.3.1 What is the genetic mechanism behind drift robustness?

In Chapter 3, when I proposed the concept of drift robustness, the idea was tested with both a
mathematical model and digital evolution experiments. Both methods showed that the evolution
of drift robustness was possible in small populations. However, I did not test whether the exact
mechanism that led to drift robustness in the mathematical model was the same mechanism that
led to drift robustness in the Avida populations.
I only showed that the results from the Avida
experiments were consistent with the mathematical model. The exact genetic mechanism behind
the evolution of drift robustness in Avida remains to be explored.

While there is no guarantee that an understanding of the genetic mechanisms of drift robustness
in Avida will provide valuable insights about biological systems, it will likely lead to some testable
hypotheses and insight into possible mechanisms. As I wrote in the Limitations section of this
chapter, the role of limited mutation supply was not explored in either the mathematical model (in
which variation in mutation supply does not exist by design) or the Avida experiments (in which

92

variation in mutation supply exists but was not tested). A study of the genetic mechanisms of
drift robustness may reveal a role for genetic variation in addition to weakened selection. Fur-
thermore, such a study may provide insight regarding the consequences of drift robustness beyond
the distribution of fitness effects. For example, in order to maintain drift-robust genetic architec-
ture, small populations may have to evolve altered epistasis, pleiotropy, modularity, complexity,
or other genetic characteristics. Future work should use Avida to further explore the mechanisms
and consequences of drift-robust adaptation in small populations. Such studies will also drive the
production of more-sophisticated mathematical models of drift robustness, improvement of which
is needed given the simplicity of the original model.

5.3.2 Drift robustness and sexual reproduction

The connection between population size, genetic drift, and sexual reproduction has been a topic
of discussion for a long time. Muller discussed the concept of a ratchet in asexual populations to
argue that sexual populations suffer a lesser mutational load [151]. Others have argued that sex
evolved in order to facilitate the combination of beneficial mutations that would otherwise be lost
due to clonal interference [60]. This mechanism would only exist in large populations, as it requires
multiple segregating beneficial mutations [133]. Otto and Barton argued that decreased variation
in small populations will drive increases in recombination [158]. This decreased variation provides
a role for recombination to combine alleles together in beneficial combinations not present in small
populations. In large populations, the rate of recombination does not increase, as individuals with
the optimal combination of alleles are likely already present. Sex can also evolve in finite large
populations as a method of disassociating deleterious mutations from beneficial mutations [85, 138].
Given previous connections between small population size and the evolution of sexual recom-
bination, it is worth asking if and how the requirement for drift robustness in small populations
influences the evolution of sex.
If the mutation rate is low enough so that mutations either fix
or drift way, as in my model of drift robustness (Chapter 3), than it is unlikely the evolution of
sex would occur, as detailed above. However, if there are multiple segregating mutations in both

93

the small and large populations, as in the Avida simulations, then there could be an interaction
between the requirement for drift robustness and the evolution of sex. For example, one could
hypothesize that the evolution of sexual reproduction would alleviate the need to evolve drift-robust
genomic architecture, for similar reasons as Muller argued that sex would prevent a ratchet-like loss
of fitness. Drift-robust genotypes and drift-fragile genotypes may also differ in their capabilities
to evolve sexual reproduction due to their differences in mutational effects. All of these research
directions will likely be fruitful for future work.

5.3.3 Drift robustness and its interaction with other robustness mechanisms

Potential model systems in which drift robustness may evolve are bacterial endoymbionts, as these
species already evolved one robustness trait: overexpression of molecular chaperones [52, 53].
However, in other ways, many obligate endosymbionts appear less robust. For example, many
endosymbionts have lost many genes encoding DNA repair enzymes, suggesting they have evolved
higher mutation rates than their free-living relatives [149]. Such an outcome is predicted for
small populations [129] (although see [169, 171] for alternative predictions). It is unknown why
small populations would evolve robustness through one mechanisms, but fragility through another
mechanism.

One possible explanation is that it is mutationally “easier” to evolve overexpression of a molec-
ular chaperone than it is to maintain a set of DNA repair enzymes. Overexpression of a gene likely
can occur through a single mutation. However, the DNA repair machinery is a large mutational
target, and thus it may prove more evolutionarily-difficult to maintain. In other words, the most
probable evolutionary outcome is to evolve the simple genetic mechanism (overexpression of molec-
ular chaperones), which then allows for the loss of the complex genetic mechanism (DNA repair
machinery). Such an evolutionary scenario could easily be modeled, either mathematically or com-
putationally. Likewise, it may be not too difficult to test this hypothesis through experiments. One
could subject microbial populations to mutation accumulation, and then perform small-population
evolution experiments with clones from these populations. Then, one could examine the evolved

94

fitness recovery strategies to test this hypothesis.

5.3.4 Small population size and the evolution of functional complexity

Here, I only focused on the role of population size in shaping the characteristics of genetic archi-
tecture. However, it is conceivable that the same evolutionary factors that result in the evolution of
alternative genomic architectures in small populations could also lead to the evolution of alternative
phenotypic traits in these populations. For example, it has been proposed that small populations
evolve alternative phenotypic characteristics because only small populations with these character-
istics do not go extinct [199]. It has also been proposed that there is a relationship between large
body size and small population size, as large body size drives increased resource consumption and
thus a lower population size [119].

One of the proposals of the Mutational Hazard hypothesis and similar theories is that the
absence of strong selection potentiates the future evolution of complexity, not only in terms of
genome complexity [121], but also in terms of functional complexity [94, 118]. In other words,
one should expect small populations to not only evolve alternative genetic architectures, but also
alternative phenotypic traits, as different phenotypic traits likely have different selective strengths in
different environments. An understanding of how a fundamental parameter, population size, leads to
qualitatively-different evolutionary outcomes will lead to a more predictive theory of evolutionary
dynamics. And while this dissertation only tested the role of population size in the evolution
of genetic architecture, the success of population-genetic principles to explain the evolution of
complexity and robustness suggests that such a theory of phenotypic evolution is within reach.

95

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