Abstract
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.
Highlights
Sequence space is explored through evolution by mutation, recombination and selection in accordance with the fitness landscape
Ochoa et al [50,51] derived a reformulation of the Nowak and Schuster analytical expression (Equation 4), in which they make explicit the reduction in the error threshold when moving from infinite populations to those of size N
Using a population of haploid individuals and a genetic algorithm with a simple two-peak fitness landscape (Figure 1), we find that the mutation rates at which the high, narrow peak and the lower, flatter peak are lost for increasing population sizes can be approximated by an exponential function (Figure 3)
Summary
Some animal species can exist in populations of only hundreds, while those nearing extinction may be found in populations of only a few individuals. The latter case is of particular concern. Understanding the effect of population size on the critical parameters of evolution (mutation, recombination, selection, and genetic drift) is essential in making accurate predictions regarding the likely fate of a small population if left to persist in its current environment. Inbreeding resulting from genetic drift in small populations can depress population fitness and increase the risk of extinction [1]. Population decline can lead to loss of fit genetic material that may be difficult to recover in very small populations due to mutational meltdown [3]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
