831baa1ac7b24d81491a5498dd72139c pmc_10531300.pdf b60cc124c1547690911bcb5aa76ed30b5daff9fc pmc_10531300.pdf f6023e972f33599507943257e45d852f5e3a24cf6fa269d76d03911cdd3222e2 pmc_10531300.pdf Title: A General Framework for Neutrality Tests Based on the Site Frequency Spectrum Subject: One of the main necessities for population geneticists is the availability of sensitive statistical tools that enable to accept or reject the standard Wright–Fisher model of neutral evolution. A number of statistical tests have been developed to detect specific deviations from the null frequency spectrum in different directions (e.g., Tajima's D, Fu and Li's F and D tests, Fay and Wu's H). A general framework exists to generate all neutrality tests that are linear functions of the frequency spectrum. In this framework, it is possible to develop a family of optimal tests with almost maximum power against a specific alternative evolutionary scenario. In this paper we provide a thorough discussion of the structure and properties of linear and nonlinear neutrality tests. First, we present the general framework for linear tests and emphasise the importance of the property of scalability with the sample size (that is, the interpretation of the tests should not depend on the sample size), which, if missing, can lead to errors in interpreting the data. After summarising the motivation and structure of linear optimal tests, we present a more general framework for the optimisation of linear tests, leading to a new family of tunable neutrality tests. In a further generalisation, we extend the framework to nonlinear neutrality tests and we derive nonlinear optimal tests for polynomials of any degree in the frequency spectrum. Keywords: coalescent theory; site frequency spectrum; neutrality test; statistical power; summary statistics Author: Sebastián E. Ramos-Onsins, Giacomo Marmorini, Guillaume Achaz, and Luca Ferretti Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Tue Aug 29 09:16:52 2023 CEST ModDate: Tue Aug 29 09:34:40 2023 CEST Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 32 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 582244 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- XHDUGC+URWPalladioL-Bold Type 1 Custom yes yes no 10 0 GXOXJP+URWPalladioL-Roma Type 1 Custom yes yes no 15 0 BPKMHP+URWPalladioL-Ital Type 1 Custom yes yes no 19 0 TERQLI+PazoMath-Italic Type 1 Builtin yes yes no 23 0 KONDUX+EuphemiaUCAS-Bold Type 1C WinAnsi yes yes no 41 0 HIZBRM+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 44 0 UUYISD+CMEX10 Type 1 Builtin yes yes no 66 0 QOHSNS+CMSY10 Type 1 Builtin yes yes no 70 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 74 0 GFCIOP+PazoMath Type 1 Builtin yes yes no 78 0 Helvetica Type 1 Custom no no no 95 0 DURHUM+CMMI10 Type 1 Builtin yes yes no 100 0 QIPYIM+MSAM10 Type 1 Builtin yes yes no 104 0 EZQIKX+MSBM10 Type 1 Builtin yes yes no 169 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2024-09-01 08:22:08 CEST RepresentationInformation: pmc_10531300.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2024-07-12 02:35:40 CEST Size: 582244 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 456 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: section.1 Item: Title: Material and Methods Destination: section.2 Children: Item: Title: Linear Neutrality Tests Destination: subsection.2.1 Item: Title: Sample Size Independent Tests Destination: subsection.2.2 Children: Item: Title: Scaling of Weights with Sample Size Destination: subsubsection.2.2.1 Item: Title: Divergent Weights Destination: subsubsection.2.2.2 Item: Title: Weights of Singletons Destination: subsubsection.2.2.3 Item: Title: Alternative Choices of Scaling Destination: subsubsection.2.2.4 Item: Title: Optimal Tests Destination: subsection.2.3 Children: Item: Title: On the Existence of Generic Tests Destination: subsubsection.2.3.1 Item: Title: Optimal Tests and Their Geometric Structure Destination: subsubsection.2.3.2 Item: Title: Beyond Linear Neutrality Tests Destination: subsection.2.4 Children: Item: Title: Quadratic and Nonlinear Tests Destination: subsubsection.2.4.1 Item: Title: Strongly Centred Optimal Tests Destination: subsubsection.2.4.2 Item: Title: Weakly Centred Optimal Tests Destination: subsubsection.2.4.3 Item: Title: Empirical Simulations and Code Used for Studying the Statistical Power of Neutrality Tests Destination: subsection.2.5 Item: Title: Results Destination: section.3 Children: Item: Title: General Optimisation of Linear Tests Destination: subsection.3.1 Children: Item: Title: Generalised Optimality Conditions Destination: subsubsection.3.1.1 Item: Title: Tunable Optimal Tests Destination: subsubsection.3.1.2 Item: Title: Simulations of the Power of Optimal Tests Destination: subsection.3.2 Item: Title: Discussion Destination: section.4 Item: Title: Appendix A Destination: section.A. Children: Item: Title: Appendix A.1 Destination: subsection.A.1 Item: Title: Appendix A.2 Destination: subsection.A.2 Item: Title: Appendix A.3 Destination: subsection.A.3 Item: Title: Appendix A.4 Destination: subsection.A.4 Item: Title: Appendix A.5 Destination: subsection.A.5 Item: Title: Appendix A.6 Destination: subsection.A.6 Item: Title: Appendix A.7 Destination: subsection.A.7 Item: Title: Appendix B Destination: section.B. Item: Title: References Destination: section.C. Info: Title: A General Framework for Neutrality Tests Based on the Site Frequency Spectrum Author: Sebastián E. Ramos-Onsins, Giacomo Marmorini, Guillaume Achaz, and Luca Ferretti Subject: One of the main necessities for population geneticists is the availability of sensitive statistical tools that enable to accept or reject the standard Wright Fisher model of neutral evolution. A number of statistical tests have been developed to detect specific deviations from the null frequency spectrum in different directions (e.g., Tajima's D, Fu and Li's F and D tests, Fay and Wu's H). A general framework exists to generate all neutrality tests that are linear functions of the frequency spectrum. In this framework, it is possible to develop a family of optimal tests with almost maximum power against a specific alternative evolutionary scenario. In this paper we provide a thorough discussion of the structure and properties of linear and nonlinear neutrality tests. First, we present the general framework for linear tests and emphasise the importance of the property of scalability with the sample size (that is, the interpretation of the tests should not depend on the sample size), which, if missing, can lead to errors in interpreting the data. After summarising the motivation and structure of linear optimal tests, we present a more general framework for the optimisation of linear tests, leading to a new family of tunable neutrality tests. In a further generalisation, we extend the framework to nonlinear neutrality tests and we derive nonlinear optimal tests for polynomials of any degree in the frequency spectrum. 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