Quantitative Trait Evolution when Mutations have Large Effects

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" summary

Develops a coalescent model for quantitative traits with loci drawing mutational effects from arbitrary kernels, computes joint distributions via characteristic functions, and takes large-locus limits. When effects have thin tails the limit is multivariate Gaussian and simulations show rapid convergence as loci increase; when effects follow power laws the limit is alpha-stable but extra pairwise correlations appear and simulations do not converge cleanly. Applies tests to ~300 RNA‑seq genes, finding 54 significant fits with inferred alpha ~1.4–1.8.

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" chapters (23)

1. 0:00Intro
2. 0:27Quantitative traits
3. 1:07Fisher's quantitative trait model
4. 2:46Neutral genetic variance
5. 4:40Evidence for non-Brownian evolution
6. 6:26A coalescent model
7. 10:54Characteristic functions
8. 12:06Characteristic function of a compound Poisson process
9. 13:40Phenotype at the root
10. 15:28Sending the number of loci off to infinity
11. 16:25Decreasing mutation rate
12. 17:10Small effect mutations
13. 19:24A guess in the normal case
14. 20:18Tempting interpretation and conjecture
15. 21:23Testing the Gaussian conjecture
16. 22:05Conjecture for the stable limit
17. 22:18Testing the stable conjecture
18. 23:36Stable limit for sample of size 4
19. 24:25Extremely weak conjecture for large effect mutations
20. 24:58Empirical data
21. 26:13Distribution of p-values
22. 27:49Conclusions
23. 36:17One locus, sample of size 2 (CF)

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