The central limit theorem for the number of mutations in the genealogy of a sample from a large population
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| Publicado en: | bioRxiv (Jan 26, 2025) |
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| Autor principal: | |
| Publicado: |
Cold Spring Harbor Laboratory Press
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| Acceso en línea: | Citation/Abstract Full Text - PDF Full text outside of ProQuest |
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| 001 | 3159906389 | ||
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| 022 | |a 2692-8205 | ||
| 024 | 7 | |a 10.1101/2025.01.23.634620 |2 doi | |
| 035 | |a 3159906389 | ||
| 045 | 0 | |b d20250126 | |
| 100 | 1 | |a Yun-Xin, Fu | |
| 245 | 1 | |a The central limit theorem for the number of mutations in the genealogy of a sample from a large population | |
| 260 | |b Cold Spring Harbor Laboratory Press |c Jan 26, 2025 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a The number K of mutations identifiable in a sample of n sequences from a large population is one of the most important summary statistics in population genetics and is ubiquitous in the analysis of DNA sequence data. K can be expressed as the sum of n-1 independent geometric random variables. Consequently, its probability generating function was established long ago, yielding its well-known expectation and variance. However, the statistical properties of K is much less understood than those of the number of distinct alleles in a sample. This paper demonstrates that the central limit theorem holds for K, implying that K follows approximately a normal distribution when a large sample is drawn from a population evolving according to the Wright-Fisher model with a constant effective size, or according to the constant-in-state model, which allows population sizes to vary independently but bounded uniformly across different states of the coalescent process. Additionally, the skewness and kurtosis of K are derived, confirming that K has asymptotically the same skewness and kurtosis as a normal distribution. Furthermore, skewness converges at speed $1/\sqrt{\ln(n)}$ and while kurtosis at speed $1/\ln(n)$. Despite the overall convergence speed to normality is relatively slow, the distribution of K for a modest sample size is already not too far from normality, therefore the asymptotic normality may be sufficient for certain applications when the sample size is large enough.Competing Interest StatementThe authors have declared no competing interest. | |
| 653 | |a Skewness | ||
| 653 | |a Kurtosis | ||
| 653 | |a Genealogy | ||
| 653 | |a DNA sequencing | ||
| 653 | |a Random variables | ||
| 653 | |a Statistical analysis | ||
| 653 | |a Nucleotide sequence | ||
| 653 | |a Population genetics | ||
| 653 | |a Mutation | ||
| 653 | |a Normal distribution | ||
| 653 | |a Central limit theorem | ||
| 653 | |a Statistical models | ||
| 773 | 0 | |t bioRxiv |g (Jan 26, 2025) | |
| 786 | 0 | |d ProQuest |t Biological Science Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3159906389/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3159906389/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u https://www.biorxiv.org/content/10.1101/2025.01.23.634620v1 |