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 1 and panel A in S1 Fig). 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.

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Fig 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.

https://doi.org/10.1371/journal.pcbi.1005066.g001

Next, we examined the dynamics of fixation of insertion mutations (insertions, for short) to 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 (S2 Fig). A large fraction of these fixed insertions are slightly deleterious in populations with fewer than one hundred individuals (see Fig 2 and panel B in S1 Fig). 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 increases with increasing population size, with the largest populations usually fixing only beneficial insertions (Fig 3 and panel C in S1 Fig). 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.

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Fig 2. 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.

https://doi.org/10.1371/journal.pcbi.1005066.g002

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Fig 3. 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.

https://doi.org/10.1371/journal.pcbi.1005066.g003

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 4 and panel D in S1 Fig). 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 (S3 Fig).

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Fig 4. 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.

https://doi.org/10.1371/journal.pcbi.1005066.g004

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 complexity. 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 5, 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 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 mutation 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 (S4 Fig). 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.

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Fig 5. 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.

https://doi.org/10.1371/journal.pcbi.1005066.g005

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 (S5 Fig). 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 phenotypic traits in this treatment (S5 Fig) than in the original treatment (Figs 1 and 4). 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 (S6 Fig). 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.

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 [45, 46]. 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 (S7 Fig). 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.

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 [42]. 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 [72]. This allows researchers to perform experimental evolution in Avida as in microbial systems [19, 73]. Avida has been successfully used as a model system to explore many topics concerning the evolution of complexity [2, 65, 71, 74, 75].

Twenty-six different instructions compose the Avida instruction set (see [42] 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 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 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” [37]. 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 [65]; see S1 Table 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 [76]. A genotype’s fitness is determined by how many offspring it can produce per unit 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: (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 thus emergent, the rate at which it occurs is not set by the experimenter.

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 [42]. 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 [42] 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, 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.

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 [5] 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 [65]. An LOD contains every intermediate genotype between the final individual with the greatest fitness and the ancestral genotype that initialized each population. 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 , 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 is only an approximation, as the equation for a nearly neutral mutation is , where N_e is the effective population size [77]. We also examined those mutations that had a slightly deleterious effect on fitness, i.e., those whose selection coefficient was .