A population model modified from that of Carter (2019b) was used to estimate the half-life of neutral mutations in populations ranging from 10 to 100,000 individuals. Each of those models was run 1,000 times. This model was also adapted to track neutral mutations in mitochondria and Y chromosomes. Further modifications were made to include a Mendel-like model of probability selection. The main difference is that Mendel uses discrete generations, where all parents die and are replaced with their offspring at each iteration. To maintain the population size, surplus individuals are culled according to a probability selection method based on individual fitness scores (the sum of the effects of the specific mutations each individual carries). See Sanford et al. (2007) for additional details. Carter’s method uses overlapping generations, so selection had to be on the level of individual survival. To do this, the range of fitness within the population in each year was calculated. During the mortality loop, where individuals are assigned a risk of dying according to an actuarial table, the risk of dying was increased according to the individual’s rank within the fitness spectrum. The mutation rate and average mutation effect (controlled by a scaling factor) were adjusted to allow for long-term survival (e.g., 30,000 Mendel generations equates to approximately 300,000 years). Mendel also has settings for heritability and non-scaling noise. These were effectively treated as “1” and “0”, respectively. III. RESULTS The ending fitness for each full-genome population model in Mendel is presented in Table 1. As expected, small populations with a high rate of non-neutral mutations trended toward extinction. Unexpectedly, some populations lasted for the entire simulation run (10,000 generations, approximately 300,000 model years) yet were clearly trending toward extinction the entire time. This included even the largest populations when individuals were receiving more than 5 non-neutral mutations per generation (Fig. 3). Neutral mutations accumulated in a linear manner (Fig. 4). This was true in all populations. This was also expected, as was the fact that effectively neutral mutations behaved as purely neutral ones. Also, the presence of beneficial mutations in the population, which allowed for positive selection, did not slow the accumulation of neutral or deleterious alleles. Even the fixation of strongly beneficial mutations (e.g., selective sweeps) did nothing to slow the rate of mutation accumulation. In the end, the fixation of neutral mutations was directly proportional to the base mutation rate. In the largest populations, there was no guarantee that any alleles would be fixed. In the population with 10,000 individuals, there was no fixation of any neutral alleles in multiple runs. Surprisingly, there were more fixed neutral alleles in the model run with a lower neutral mutation rate. This is due to the removal of individuals with more deleterious alleles, even though the rate of fixation of deleterious mutations was also higher in general. The total number of mutations that appeared in a model run equals µNg, where g = the number of generations. The percentage of mutations remaining at the end of the run can be obtained from the Mendel output files. For purely neutral mutations, the loss of alleles was strong in the smallest populations but increased by two orders of magnitude (from 1.00% retention to 0.01% retention) as N increased Figure 5. The total number of neutral mutations appearing (orange) and the percent retained (blue) at the end of the model run vs population size. Strong drift (measured here as allele retention, which will eventually translate into allele fixation) is evident in the smallest population, but drift slows to a crawl after the population reaches a few thousand individuals. CARTER Genealogical vs. phylogenetic mutation rates 2023 ICC 174
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