A depiction of our approach toward characterizing the neutral or selected evolution of phenotype based on mutation accumulation and quantitative trait locus data for a phenotype. (A) A constructed example of phenotypic change due to unbiased mutation within seven mutation accumulation lines. (B) A constructed example of phenotypic change due to downwardly biased mutation within seven mutation accumulation lines. (C and D) The distribution of mutational effects inferred from A. (E and F) The distribution of mutational effects inferred from B. (G and I) A depiction of a probability of fixation of novel mutations that is invariant across potential phenotypic values. (H and J) A depiction of probability of fixation of novel mutations that increases with the phenotypic value. (K) The product of the functions depicted in C and G: in this case, a symmetrical distribution of fixed mutations with a zero mode. (L) The product of D and H: in this case, an asymmetrical distribution of fixed mutations with a positive mode and positive skewness. (M) The product of the functions depicted in I and M: in this case, a symmetrical distribution with a negative mode. (N) The product of the functions depicted in F and J: in this case, an asymmetrical distribution with a zero mode and positive skewness. (O) An example of a single sample of mutations (outlines) drawn from the distribution depicted in K, compared to the experimentally observed positive and negative QTL (shaded bars): in this case, the sample matched the QTL well. (P) An example of a single sample of mutations (outlines) drawn from the distribution depicted in L, compared to the experimentally observed positive and negative QTL (shaded bars): in this case, the sample matched the positive QTL fairly well, but matched the negative QTL poorly. (Q) An example of a single sample of mutations (outlines) drawn from the distribution in M, compared to the experimentally observed positive and negative QTL (shaded bars): in this case, the sample matched the positive QTL poorly, but matched the negative QTL fairly well. (R) An example of a single sample of mutations (outlines) drawn from the distribution in N, compared to the experimentally observed positive and negative QTL (shaded bars): in this case, the sample matched the positive and negative QTL well. The mutations drawn here “happen” to exactly match the QTL effects depicted in O, but in fact sampling from the fixed mutation distribution is highly stochastic and requires numerically integrating over many samples to accurately yield the likelihood that the fixed mutation distribution underlies the experimentally observed QTL. (S) A plot of the likelihood across a range of values of the strength of selection: in this case, samples drawn from the distribution in K are identified as fitting better than samples drawn from the distribution in L, indicating neutral evolution of the phenotype. Parts of the plot that lie above the dashed line correspond to a 95% CI. The plot at the *y*-axis corresponds to neutrality and falls within the CI, so we cannot reject a hypothesis of selective neutrality for this phenotype. (T) A plot of the likelihood across a range of values of the strength of selection: in this case, samples drawn from the distribution in N are identified as fitting better than samples drawn from the distribution in M, indicating evolution of the phenotype driven by natural selection. The plot at the *y*-axis corresponds to neutrality and falls outside the CI, so we can reject a hypothesis of selective neutrality for this phenotype and estimate that the strength of selection corresponds to the level of selection identified by the peak of the plot.

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