Horizontal gene transfer (HGT) enables segments of DNA to be transferred between individuals in a population in addition to from parent to child. It is a prominent process in bacterial reproduction. Existing in silico models have succeeded in predicting when HGT will occur in evolving bacterial populations, and have utilised the concept of HGT in evolutionary algorithms. Here we present a genetic algorithm designed to model the process of bacterial evolution in a fitness landscape in which individuals with greater mutational robustness can outcompete those with higher fitness when a critical mutation rate (CMR) is exceeded. We show that the CMR has an exponential dependence on population size and can be lowered by HGT in both clonal and non-clonal populations. A population reproducing clonally has a higher CMR than one in which individuals undergo crossover. Allowing HGT only from donors with a non-zero fitness prevents HGT from lowering the CMR. In all cases the change in CMR with population size is greater for populations with 100 individuals or less. This represents a significant stage in bacterial evolution; smaller populations will exist when a population is founded or near to extinction. This will also be the case if a subset of the population is considered as a population in its own right, for example, the sub population of resistant bacteria that emerges due to the introduction of antibiotic resistance genes. Understanding the effect of mutation at such a critical stage is key to predicting the likely fate of a population.

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and the survival of individuals with greater mutational robustness (the flattest). Small populations are more likely to exceed the CMR and become less well adapted; understanding the CMR is crucial to understanding the potential fate of small populations under threat of extinction. Here we present a simulation model capable of utilising input parameter values within a biologically relevant range. A previous study identified an exponential fall in CMR with decreasing population size, but the parameters and output were not directly relevant outside artificial systems. The first key contribution of this study is the identification of an inverse relationship between CMR and gene length when the gene length is comparable to that found in biological populations. The exponential relationship is maintained, and the CMR is lowered to between two to five orders of magnitude above existing estimates of per base mutation rate for a variety of organisms. The second key contribution of the study is the identification of an inverse relationship between CMR and the number of genes. Using a gene number in the range for Arabidopsis thaliana produces a CMR close to its known mutation rate; per base mutation rates for other organisms are also within one order of magnitude. This is the third key contribution of the study as it represents the first time such a simulation model has used input and produced output both within range for a given biological organism. This novel convergence of CMR model with biological reality is of particular relevance to populations undergoing a bottleneck, under stress, and subsequent conservation strategy for populations on the brink of extinction.