Critical mutation rates in small populations

Mutation introduces change at the sequence level. There is a critical mutation rate above which changes occur too frequently for natural selection to maintain the population's genetic makeup. This thesis examines the relationship between this critical mutation rate and the number of individuals in the adapting population. It presents an algorithmic method capable of providing widely applicable results in haploid and diploid populations, and varies this method against analytical models for the error threshold.\ud \ud Use of the method led to the discovery of an exponential relationship between the critical mutation rate and population size, particularly strong in small populations with 100 individuals or less, contradicting the existing idea that critical mutation rate and population size are independent. The critical mutation rate (and error threshold) were found to be lower in diploids due to differences in recombination. Analysis of the survival-of-the-fittest to survival-of-the-flattest transition enabled improvement of existing definitions of the critical mutation rate.\ud \ud Development of a faster algorithm capable of running experiments with parameter values within the range found in nature began the process of bridging the gap between artificial and biological evolution. A link was established between the exponential model and natural mutation rates. Increasing the gene length by a factor of 10 was found to decrease both the critical mutation rate and error threshold by an order of magnitude. Natural mutation rates lie below these values, although further work is required to establish any trend. A potential link has been established between the critical mutation rate, error threshold, and optimal mutation rate control theory.\ud \ud Future work may develop the algorithmic method to include more complex features of biological populations, and go on to determine the effect the exponential model can have on population extinction, recovery, and conservation