(Fig. 5). The loss of alleles due to genetic drift was highly consistent within each size class, increasing only slightly as populations approached the extinction threshold (Fig. 6). In the model behind Fig. 3 and Fig. 4, the rate of neutral alleles was set to 0.25. Without selection, the expected final ratio of neutral to deleterious alleles would be 0.25/0.75, or 1:3. The final ratio was 124,950:343,677, or 1:2.75. Selection was able to remove only about 8% of the deleterious alleles. The average number of excess mutations in the runs where all mutations were neutral was 1,216 (+/- 558 SD). Given that individuals carried more neutral alleles than would be predicted by solely multiplying the number of generations by the neutral mutation rate, clearly one must account for the mutational half-life. A second population model (Carter 2019) was modified to track the lifespan of single mutations in human-like populations of various sizes (Fig. 7). N ranged from 10 to 100,000 and each model was run 1,000 times. There was a barely noticeable trend toward longer maximum and average lifetimes for neutral alleles (measured in generations) among the larger populations. Most new mutations were lost to drift within five generations. It took a little less time for this to happen in the smallest populations. This accounts for the slightly higher-than-expected mutation burden seen in the Mendel results. It takes a few generations to lose new mutations, so the total mutation count stands slightly above the long-term accumulation rate. When modeling mitochondrial DNA over evolutionary timescales in Mendel, a mutation rate of 0.05 created a fixation rate of approximately 1 mutation every 2,700 years for n = 1,000, 5,000, and 10,000. This is between the phylogenetic rates published by Rieux et al. (2014) and Soares et al. (2009). However, the rate was 40% lower in the smallest population (n = 500) and there was zero substitution in the largest population (n = 100,000). Figure 8 shows a clear separation between the accumulation of deleterious and neutral mutations in the largest population. It also shows a gradual leveling off in the deleterious mutation curve, similar to the predictions of Soares et al. (2009). Some of this leveling off would have been due to the fact that all individuals started with a perfect fitness score. As mutations built up and fitness declined, selection would have increased. Thus, in these models there is a ‘burn-in’ time before the effects of selection can truly be measured. Yet, as stated above, no fixation was occurring in this population, even after approximately 300,000 years of model time. The smaller populations had a deleterious-to-neutral fixation ratio ranging from 0.4 to 0.9. Thus, even in the best-case scenario, at most 60% of the deleterious mutations can be removed. Mendel is not actually set up to do the mitochondrial experiments described here. In its current configuration, there is no way to model asexual compartments. Thus, the individuals in these models carried two mitochondrial types and selection against the worst mitochondrial mutations would be mitigated by the second version carried by the individual. However, one might consider this a reasonable compromise after accounting for known interactions from the nuclear DNA, epigenetic effects, and environmental variability. Also, since there are upwards of 1,000 mitochondria per human cell, mitochondrial mutations start out in a hemizygous state by default. It takes several generations for any new mutation to go to fixation within an individFigure 8. The accumulation of mutations in a Mendel model designed to assess mutation accumulation over an evolutionary timescale. These are the results of a single run with a mutation rate of 0.05 and a population size of 100,000. Data were plotted every 1,000 generations. Note that Mendel cannot model haploid systems, so all individuals would carry two versions of the mtDNA, thus complicating the analysis. CARTER Genealogical vs. phylogenetic mutation rates 2023 ICC 176
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