Critical mutation rate has an exponential dependence on population size in haploid and diploid populations

Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has significant potential in aiding population management to prevent local (and global) extinction events

Critical mutation rate has an exponential dependence on population size for eukaryotic-length genomes with crossover

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and survival of individuals with greater mutational robustness (“flattest”). We identify an inverse relationship between CMR and sequence length in an in silico system with a two-peak fitness landscape; CMR decreases to no more than five orders of magnitude above estimates of eukaryotic per base mutation rate. We confirm the CMR reduces exponentially at low population sizes, irrespective of peak radius and distance, and increases with the number of genetic crossovers. We also identify an inverse relationship between CMR and the number of genes, confirming that, for a similar number of genes to that for the plant Arabidopsis thaliana (25,000), the CMR is close to its known wild-type mutation rate; mutation rates for additional organisms were also found to be within one order of magnitude of the CMR. This is the first time such a simulation model has been assigned input and produced output within range for a given biological organism. The decrease in CMR with population size previously observed is maintained; there is potential for the model to influence understanding of populations undergoing bottleneck, stress, and conservation strategy for populations near extinction

Critical mutation rate has an exponential dependence on population size for eukaryotic-length genomes with crossover

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and survival of individuals with greater mutational robustness (“flattest”). We identify an inverse relationship between CMR and sequence length in an in silico system with a two-peak fitness landscape; CMR decreases to no more than five orders of magnitude above estimates of eukaryotic per base mutation rate. We confirm the CMR reduces exponentially at low population sizes, irrespective of peak radius and distance, and increases with the number of genetic crossovers. We also identify an inverse relationship between CMR and the number of genes, confirming that, for a similar number of genes to that for the plant Arabidopsis thaliana (25,000), the CMR is close to its known wild-type mutation rate; mutation rates for additional organisms were also found to be within one order of magnitude of the CMR. This is the first time such a simulation model has been assigned input and produced output within range for a given biological organism. The decrease in CMR with population size previously observed is maintained; there is potential for the model to influence understanding of populations undergoing bottleneck, stress, and conservation strategy for populations near extinction

Critical Mutation Rate has an Exponential Dependence on Population Size for Eukaryotic-length Genomes with Crossover

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and survival of individuals with greater mutational robustness (“flattest”). We identify an inverse relationship between CMR and sequence length in an in silico system with a two-peak fitness landscape; CMR decreases to no more than five orders of magnitude above estimates of eukaryotic per base mutation rate. We confirm the CMR reduces exponentially at low population sizes, irrespective of peak radius and distance, and increases with the number of genetic crossovers. We also identify an inverse relationship between CMR and the number of genes, confirming that, for a similar number of genes to that for the plant Arabidopsis thaliana (25,000), the CMR is close to its known wild-type mutation rate; mutation rates for additional organisms were also found to be within one order of magnitude of the CMR. This is the first time such a simulation model has been assigned input and produced output within range for a given biological organism. The decrease in CMR with population size previously observed is maintained; there is potential for the model to influence understanding of populations undergoing bottleneck, stress, and conservation strategy for populations near extinction

Embodied Computational Evolution: Feedback Between Development and Evolution in Simulated Biorobots

Given that selection removes genetic variance from evolving populations, thereby reducing exploration opportunities, it is important to find mechanisms that create genetic variation without the disruption of adapted genes and genomes caused by random mutation. Just such an alternative is offered by random epigenetic error, a developmental process that acts on materials and parts expressed by the genome. In this system of embodied computational evolution, simulated within a physics engine, epigenetic error was instantiated in an explicit genotype-to-phenotype map as transcription error at the initiation of gene expression. The hypothesis was that transcription error would create genetic variance by shielding genes from the direct impact of selection, creating, in the process, masquerading genomes. To test this hypothesis, populations of simulated embodied biorobots and their developmental systems were evolved under steady directional selection as equivalent rates of random mutation and random transcriptional error were covaried systematically in an 11 × 11 fully factorial experimental design. In each of the 121 different experimental conditions (unique combinations of mutation and transcription error), the same set of 10 randomly created replicate populations of 60 individuals were evolved. Selection for the improved locomotor behavior of individuals led to increased mean fitness of populations over 100 generations at nearly all levels and combinations of mutation and transcription error. When the effects of both types of error were partitioned statistically, increasing transcription error was shown to increase the final genetic variance of populations, incurring a fitness cost but acting on variance independently and differently from genetic mutation. Thus, random epigenetic errors in development feed back through selection of individuals with masquerading genomes to the population’s genetic variance over generational time. Random developmental processes offer an additional mechanism for exploration by increasing genetic variation in the face of steady, directional selection

Critical mutation rate has an exponential dependence on population size

Populations of individuals exist in a wide range of sizes, from billions of microorganisms to fewer than ten individuals in some critically endangered species saved on the brink of extinction. In any evolutionary system, there is significant evolutionary pressure to evolve sequences that are both fit and robust; at high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness, a concept that has been referred to as survival-of-the-flattest. Previous studies have suggested that population size does not influence the size of mutation rate that can be tolerated before fitter individuals are outcompeted by those that have a greater mutational robustness. However, using a genetic algorithm with a simple two-peak fitness landscape, we show that the size of mutation rate at which the high, narrow peak and the lower, broader peak are lost for increasing population sizes can be approximated by an exponential function (where a peak was considered to be lost when there were no individuals present anywhere in its range). In addition, there is evidence for a continuum of mutation rates representing a transition from survival-of-the-fittest to survival-of-the- flattest. This identifies a critical mutation rate representing the start of the transition, which is defined as the highest mutation rate where survival-of-the-fittest is still the predominant outcome, but where the population is no longer able to maintain the fittest peak indefinitely. The effect of population size on the critical mutation rate is shown to be particularly noticeable in small populations with 100 individuals or less. This provides new insight into the factors that can affect survival-of-the-flattest in small populations, and has implications for populations under threat of local extinction

Critical Mutation Rate Has an Exponential Dependence on Population Size

Populations of individuals exist in a wide range of sizes, from billions of microorganisms to fewer than ten individuals in some critically endangered species saved on the brink of extinction. In any evolutionary system, there is significant evolutionary pressure to evolve sequences that are both fit and robust; at high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness, a concept that has been referred to as survival-of-the-flattest. Previous studies have suggested that population size does not influence the size of mutation rate that can be tolerated before fitter individuals are outcompeted by those that have a greater mutational robustness. However, using a genetic algorithm with a simple two-peak fitness landscape, we show that the size of mutation rate at which the high, narrow peak and the lower, broader peak are lost for increasing population sizes can be approximated by an exponential function (where a peak was considered to be lost when there were no individuals present anywhere in its range). In addition, there is evidence for a continuum of mutation rates representing a transition from survival-of-the-fittest to survival-of-theflattest. This identifies a critical mutation rate representing the start of the transition, which is defined as the highest mutation rate where survival-of-the-fittest is still the predominant outcome, but where the population is no longer able to maintain the fittest peak indefinitely. The effect of population size on the critical mutation rate is shown to be particularly noticeable in small populations with 100 individuals or less. This provides new insight into the factors that can affect survival-of-the-flattest in small populations, and has implications for populations under threat of local extinction