2208:
population size and/or balancing selection. However, calculating a conventional "p-value" associated with any Tajima's D value that is obtained from a sample is impossible. Briefly, this is because there is no way to describe the distribution of the statistic that is independent of the true, and unknown, theta parameter (no pivot quantity exists). To circumvent this issue, several options have been proposed.
53:. A randomly evolving DNA sequence contains mutations with no effect on the fitness and survival of an organism. The randomly evolving mutations are called "neutral", while mutations under selection are "non-neutral". For example, a mutation that causes prenatal death or severe disease would be expected to be under selection. In the population as a whole, the
136:
estimates of the population genetic parameter theta, and so are expected to equal the same value. If these two numbers only differ by as much as one could reasonably expect by chance, then the null hypothesis of neutrality cannot be rejected. Otherwise, the null hypothesis of neutrality is rejected.
2310:
Finally, genome wide scans of Tajima's D in sliding windows along a chromosomal segment are often performed. With this approach, those regions that have a value of D that greatly deviates from the bulk of the empirical distribution of all such windows are reported as significant. This method does
2302:
A more nuanced approach was presented in a paper by
Simonsen et al. These authors advocated constructing a confidence interval for the true theta value, and then performing a grid search over this interval to obtain the critical values at which the statistic is significant below a particular alpha
1947:
Suppose you are a geneticist studying an unknown gene. As part of your research you get DNA samples from four random people (plus yourself). For simplicity, you label your sequence as a string of zeroes, and for the other four people you put a zero when their DNA is the same as yours and a one when
2207:
A negative Tajima's D signifies an excess of low frequency polymorphisms relative to expectation, indicating population size expansion (e.g., after a bottleneck or a selective sweep). A positive Tajima's D signifies low levels of both low and high frequency polymorphisms, indicating a decrease in
2306:
A very rough rule of thumb to significance is that values greater than +2 or less than -2 are likely to be significant. This rule is based on an appeal to asymptotic properties of some statistics, and thus +/- 2 does not actually represent a critical value for a significance test.
30:. Tajima's D is computed as the difference between two measures of genetic diversity: the mean number of pairwise differences and the number of segregating sites, each scaled so that they are expected to be the same in a neutrally evolving population of constant size.
2303:
value. An alternative approach is for the investigator to perform the grid search over the values of theta which they believe to be plausible based on their knowledge of the organism under study. Bayesian approaches are a natural extension of this method.
65:
The strength of genetic drift depends on population size. If a population is at a constant size with constant mutation rate, the population will reach an equilibrium of gene frequencies. This equilibrium has important properties, including the number of
890:
2311:
not assess significance in the traditional statistical sense, but is quite powerful given a large genomic region, and is unlikely to falsely identify interesting regions of a chromosome if only the greatest outliers are reported.
1792:
1198:
57:
of a neutral mutation fluctuates randomly (i.e. the percentage of individuals in the population with the mutation changes from one generation to the next, and this percentage is equally likely to go up or down) through
1953:
1 2 Position 12345 67890 12345 67890 Person Y 00000 00000 00000 00000 Person A 00100 00000 00100 00010 Person B 00000 00000 00100 00010 Person C 00000 01000 00000 00010 Person D 00000 01000 00100 00010
93:). To standardize the pairwise differences, the mean or 'average' number of pairwise differences is used. This is simply the sum of the pairwise differences divided by the number of pairs, and is often symbolized by
2298:
and dividing it by the number of samples. Simulations have shown this distribution to be conservative, and now that the computing power is more readily available this approximation is not frequently used.
1502:
1029:
1427:
1357:
647:
2123:
1092:
954:
1266:
2389:
Elgvin, Tore O.; Trier, Cassandra N.; Tørresen, Ole K.; Hagen, Ingerid J.; Lien, Sigbjørn; Nederbragt, Alexander J.; Ravinet, Mark; Jensen, Henrik; Sætre, Glenn-Peter (2 June 2017).
587:
366:
253:
2291:, the magnitude of the statistic is expected to increase the more the data deviates from a pattern expected under a population evolving according to the standard coalescent model.
2294:
Tajima (1989) found an empirical similarity between the distribution of the test statistic and a beta distribution with mean zero and variance one. He estimated theta by taking
1572:
1937:
749:
2194:
1870:
1538:
1664:
454:, so that they are no longer expected to be equal. The difference in the expectations for these two variables (which can be positive or negative) is the crux of Tajima's
500:
1905:
1696:
452:
404:
111:
2603:
1601:
736:
699:
674:
542:
521:
479:
1819:
1624:
432:
87:
2659:
128:
DNA for at least 3 individuals. Tajima's statistic computes a standardized measure of the total number of segregating sites (these are DNA sites that are
414:, demographic fluctuations and other violations of the neutral model (including rate heterogeneity and introgression) will change the expected values of
1958:
Notice the four polymorphic sites (positions where someone differs from you, at 3, 7, 13 and 19 above). Now compare each pair of sequences and get the
1704:
1098:
2699:
132:) in the sampled DNA and the average number of mutations between pairs in the sample. The two quantities whose values are compared are both
2199:
Since this is a statistical test, you need to assess the significance of this value. A discussion of how to do this is provided below.
2565:
2730:
2652:
2259:
Theta-Pi greater than Theta-k (Observed>Expected). More haplotypes (more average heterozygosity)than # of segregating sites.
2245:
Theta-Pi less than Theta-k (Observed<Expected). Fewer haplotypes (lower average heterozygosity) than # of segregating sites.
1433:
1575:
133:
960:
1365:
1272:
713:
for the sequence in question. However, in real world uses, one must be careful as past population changes (for instance, a
2817:
599:
2812:
116:
The purpose of Tajima's test is to identify sequences which do not fit the neutral theory model at equilibrium between
2645:
2039:
1037:
2822:
2786:
2283:
such as Tajima's D, the critical question is whether the value calculated for the statistic is unexpected under a
905:
1604:
1206:
550:
264:
151:
2781:
2725:
129:
2704:
2689:
1543:
714:
38:
885:{\displaystyle D={\frac {d}{\sqrt {{\hat {V}}(d)}}}={\frac {{\hat {k}}-{\frac {S}{a_{1}}}}{\sqrt {}}}}
481:
is calculated by taking the difference between the two estimates of the population genetics parameter
2694:
2402:
2271:
However, this interpretation should be made only if the D-value is deemed statistically significant.
90:
2231:
Theta-Pi equivalent to Theta-k (Observed=Expected). Average
Heterozygosity= # of Segregating sites.
1910:
2684:
2668:
2295:
702:
46:
42:
2161:
1827:
1513:
2418:
1632:
590:
125:
2251:
Recent selective sweep, population expansion after a recent bottleneck, linkage to a swept gene
484:
2750:
2676:
2561:
2534:
2485:
2436:
2371:
2320:
1878:
677:
411:
2771:
2735:
2524:
2516:
2475:
2467:
2426:
2410:
2361:
2353:
2284:
2280:
1579:
710:
67:
1669:
2776:
2766:
2709:
706:
437:
389:
96:
1585:
720:
683:
658:
526:
505:
463:
2406:
2529:
2504:
2480:
2455:
2431:
2390:
2366:
2341:
1804:
1798:
1609:
417:
72:
37:
evolving randomly ("neutrally") and one evolving under a non-random process, including
1948:
it is different. (For this example, the specific type of difference is not important.)
2801:
121:
59:
50:
2342:"Statistical method for testing the neutral mutation hypothesis by DNA polymorphism"
2807:
2618:
652:
89:, and the number of nucleotide differences between pairs sampled (these are called
34:
27:
145:
Under the neutral theory model, for a population at constant size at equilibrium:
2520:
2471:
2357:
2740:
2237:
Population evolving as per mutation-drift equilibrium. No evidence of selection
1963:
1907:, whereas Hartl & Clark use a different symbol to define the same parameter
124:. In order to perform the test on a DNA sequence or gene, you need to sequence
2631:
1787:{\displaystyle {\hat {k}}={\frac {\sum \sum _{i<j}k_{ij}}{\binom {n}{2}}}.}
2422:
1193:{\displaystyle c_{2}=b_{2}-{\frac {n+2}{a_{1}n}}+{\frac {a_{2}}{a_{1}^{2}}}}
54:
23:
2597:
2440:
2414:
2538:
2489:
2375:
2505:"Properties of statistical tests of neutrality for DNA polymorphism data"
2031:
Person C 00000 01000 00000 00010 Person D 00000 01000 00100 00010
2025:
Person B 00000 00000 00100 00010 Person D 00000 01000 00100 00010
2019:
Person B 00000 00000 00100 00010 Person C 00000 01000 00000 00010
2013:
Person A 00100 00000 00100 00010 Person D 00000 01000 00100 00010
2007:
Person A 00100 00000 00100 00010 Person C 00000 01000 00000 00010
2001:
Person A 00100 00000 00100 00010 Person B 00000 00000 00100 00010
1995:
Person Y 00000 00000 00000 00000 Person D 00000 01000 00100 00010
1989:
Person Y 00000 00000 00000 00000 Person C 00000 01000 00000 00010
1982:
Person Y 00000 00000 00000 00000 Person B 00000 00000 00100 00010
1976:
Person Y 00000 00000 00000 00000 Person A 00100 00000 00100 00010
545:
117:
2622:
1959:
2637:
2608:
2591:
2150:
described above is the difference between these two numbers—the
2641:
2613:
1962:
number of polymorphisms between two sequences. There are "five
2154:
number of polymorphisms found in pairwise comparison (2) and
2634:, and its application to DNA sequences, is available online.
2134:
Since there were n=5 individuals and S=4 segregating sites
33:
The purpose of Tajima's D test is to distinguish between a
2586:
1629:
The first estimate is the average number of SNPs found in
1497:{\displaystyle a_{2}=\sum _{i=1}^{n-1}{\frac {1}{i^{2}}}}
2503:
Simonsen, KL.; Churchill, GA.; Aquadro, CF. (Sep 1995).
406:
is the mutation rate at the examined genomic locus, and
1024:{\displaystyle e_{2}={\frac {c_{2}}{a_{1}^{2}+a_{2}}}}
2164:
2042:
1913:
1881:
1830:
1807:
1707:
1672:
1642:
1612:
1588:
1546:
1516:
1436:
1422:{\displaystyle a_{1}=\sum _{i=1}^{n-1}{\frac {1}{i}}}
1368:
1352:{\displaystyle b_{2}={\frac {2(n^{2}+n+3)}{9n(n-1)}}}
1275:
1209:
1101:
1040:
963:
908:
752:
723:
686:
661:
602:
553:
529:
508:
487:
466:
440:
420:
392:
267:
154:
99:
75:
642:{\displaystyle D={\frac {d}{\sqrt {{\hat {V}}(d)}}}}
2759:
2718:
2675:
2265:Balancing selection, sudden population contraction
899:
676:statistic described above could be modeled using a
26:created by and named after the Japanese researcher
2188:
2117:
1931:
1899:
1864:
1821:, the total number of polymorphisms in the sample
1813:
1786:
1690:
1658:
1618:
1595:
1566:
1532:
1496:
1421:
1351:
1260:
1192:
1086:
1023:
948:
884:
730:
693:
668:
641:
581:
536:
515:
494:
473:
446:
426:
398:
360:
247:
105:
81:
2234:Observed variation similar to expected variation
1652:
1637:
2604:Online view of Tajima's D values in human genome
2118:{\displaystyle {3+2+2+3+1+3+2+2+1+1 \over 10}=2}
2248:Rare alleles abundant (excess of rare alleles)
701:value for a sample of sequences is outside the
2456:"Statistical tests of neutrality of mutations"
1087:{\displaystyle c_{1}=b_{1}-{\frac {1}{a_{1}}}}
2653:
2609:Python3 package for computation of Tajima's D
1774:
1761:
655:demonstrated by computer simulation that the
8:
2391:"The genomic mosaicism of hybrid speciation"
1966:two" (ten) comparisons that need to be done.
1574:are two estimates of the expected number of
949:{\displaystyle e_{1}={\frac {c_{1}}{a_{1}}}}
2556:Hartl, Daniel L.; Clark, Andrew G. (2007).
2262:Rare alleles scarce (lack of rare alleles)
1578:(SNPs) between two DNA sequences under the
1261:{\displaystyle b_{1}={\frac {n+1}{3(n-1)}}}
2660:
2646:
2638:
2128:The second estimate of the equilibrium is
2528:
2479:
2430:
2365:
2163:
2043:
2041:
1912:
1880:
1850:
1829:
1806:
1773:
1760:
1749:
1733:
1723:
1709:
1708:
1706:
1671:
1651:
1636:
1634:
1611:
1592:
1587:
1556:
1547:
1545:
1529:
1518:
1517:
1515:
1486:
1477:
1465:
1454:
1441:
1435:
1409:
1397:
1386:
1373:
1367:
1302:
1289:
1280:
1274:
1223:
1214:
1208:
1182:
1177:
1167:
1161:
1146:
1128:
1119:
1106:
1100:
1076:
1067:
1058:
1045:
1039:
1012:
999:
994:
983:
977:
968:
962:
938:
928:
922:
913:
907:
852:
836:
819:
810:
796:
795:
792:
766:
765:
759:
751:
727:
722:
690:
685:
665:
660:
616:
615:
609:
601:
557:
556:
554:
552:
533:
528:
512:
507:
491:
486:
470:
465:
439:
419:
391:
329:
317:
306:
296:
266:
216:
204:
193:
183:
153:
98:
74:
2210:
1797:The second estimate is derived from the
45:, demographic expansion or contraction,
2332:
2036:The average number of polymorphisms is
582:{\displaystyle {\sqrt {{\hat {V}}(d)}}}
361:{\displaystyle E=\theta =E\left=2N\mu }
248:{\displaystyle E=\theta =E\left=4N\mu }
7:
2560:(4th ed.). Sinauer Associates.
378:is the number of segregating sites,
1765:
1666:pairwise comparisons of sequences
1641:
1567:{\displaystyle {\frac {S}{a_{1}}}}
523:, and D is calculated by dividing
386:is the effective population size,
14:
2731:Models of nucleotide substitution
2632:A video explanation of Tajima's D
2558:Principles of Population Genetics
16:Population genetic test statistic
1576:single nucleotide polymorphisms
410:is the index of summation. But
1932:{\displaystyle \theta =4N\mu }
1840:
1834:
1714:
1685:
1673:
1523:
1343:
1331:
1320:
1295:
1252:
1240:
876:
873:
861:
829:
801:
783:
777:
771:
633:
627:
621:
574:
568:
562:
277:
271:
164:
158:
1:
2454:Fu, YX.; Li, WH. (Mar 1993).
22:is a population genetic test
2223:Biological interpretation 2
2189:{\displaystyle d=2-1.92=.08}
1865:{\displaystyle E(S)=a_{1}M.}
1533:{\displaystyle {\hat {k}}\,}
717:) can bias the value of the
502:. This difference is called
2220:Biological interpretation 1
1659:{\displaystyle n \choose 2}
2839:
2787:Nonsynonymous substitution
2594:(Mac OS X, Linux, Windows)
2521:10.1093/genetics/141.1.413
2472:10.1093/genetics/133.3.693
2358:10.1093/genetics/123.3.585
544:by the square root of its
382:is the number of samples,
1992:You vs D: 3 polymorphisms
1985:You vs C: 2 polymorphisms
1979:You vs B: 2 polymorphisms
1973:You vs A: 3 polymorphisms
1605:effective population size
495:{\displaystyle \theta \,}
2275:Determining significance
2137:a1=1/1+1/2+1/3+1/4=2.08
1900:{\displaystyle M=4N\mu }
705:then one can reject the
2782:Synonymous substitution
2726:Models of DNA evolution
2619:Bio::PopGen::Statistics
2340:Tajima, F. (Nov 1989).
2203:Interpreting Tajima's D
2016:B vs C: 2 polymorphisms
2010:A vs D: 2 polymorphisms
2004:A vs C: 3 polymorphisms
1582:model in a sample size
374:In the above formulas,
2415:10.1126/sciadv.1602996
2190:
2119:
2033:
2028:C vs D: 1 polymorphism
2022:B vs D: 1 polymorphism
1998:A vs B: 1 polymorphism
1956:
1933:
1901:
1866:
1815:
1788:
1692:
1660:
1620:
1597:
1568:
1534:
1498:
1476:
1423:
1408:
1353:
1262:
1194:
1088:
1025:
950:
886:
732:
695:
670:
643:
583:
538:
517:
496:
475:
448:
428:
400:
362:
328:
249:
215:
141:Scientific explanation
107:
83:
2705:Stabilizing selection
2690:Directional selection
2580:Computational tools:
2296:Watterson's estimator
2191:
2120:
1971:
1951:
1934:
1902:
1867:
1816:
1789:
1693:
1691:{\displaystyle (i,j)}
1661:
1621:
1598:
1569:
1535:
1499:
1450:
1424:
1382:
1354:
1263:
1195:
1089:
1026:
951:
887:
733:
715:population bottleneck
696:
671:
644:
584:
539:
518:
497:
476:
449:
429:
401:
363:
302:
258:for diploid DNA, and
250:
189:
108:
84:
39:directional selection
2818:Statistical genetics
2695:Disruptive selection
2162:
2040:
1911:
1879:
1828:
1805:
1705:
1670:
1633:
1610:
1586:
1544:
1514:
1434:
1366:
1273:
1207:
1099:
1038:
961:
906:
750:
742:Mathematical details
721:
684:
659:
600:
551:
527:
506:
485:
464:
447:{\displaystyle \pi }
438:
418:
399:{\displaystyle \mu }
390:
265:
152:
106:{\displaystyle \pi }
97:
91:pairwise differences
73:
2813:Molecular evolution
2760:Molecular processes
2685:Balancing selection
2669:Molecular evolution
2407:2017SciA....3E2996E
2217:Mathematical reason
2214:Value of Tajima's D
1596:{\displaystyle n\,}
1187:
1004:
731:{\displaystyle D\,}
703:confidence interval
694:{\displaystyle D\,}
669:{\displaystyle D\,}
537:{\displaystyle d\,}
516:{\displaystyle d\,}
474:{\displaystyle D\,}
47:genetic hitchhiking
43:balancing selection
2700:Negative selection
2279:When performing a
2186:
2115:
1929:
1897:
1862:
1811:
1784:
1744:
1688:
1646:
1616:
1593:
1564:
1530:
1494:
1419:
1349:
1258:
1190:
1173:
1084:
1021:
990:
946:
882:
728:
691:
666:
639:
593:, by definition).
591:standard deviation
579:
534:
513:
492:
471:
444:
424:
396:
358:
245:
103:
79:
2823:Statistical tests
2795:
2794:
2677:Natural selection
2269:
2268:
2202:
2107:
1969:Person Y is you!
1814:{\displaystyle S}
1779:
1772:
1729:
1717:
1650:
1619:{\displaystyle N}
1562:
1526:
1507:
1506:
1492:
1417:
1347:
1256:
1188:
1156:
1082:
1019:
944:
880:
879:
825:
804:
787:
786:
774:
678:beta distribution
637:
636:
624:
577:
565:
427:{\displaystyle S}
340:
337:
227:
224:
134:method of moments
82:{\displaystyle S}
68:segregating sites
2830:
2772:Gene duplication
2736:Allele frequency
2662:
2655:
2648:
2639:
2571:
2543:
2542:
2532:
2500:
2494:
2493:
2483:
2451:
2445:
2444:
2434:
2395:Science Advances
2386:
2380:
2379:
2369:
2337:
2287:. For Tajima's
2281:statistical test
2256:Tajima's D>0
2242:Tajima's D<0
2211:
2195:
2193:
2192:
2187:
2124:
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2121:
2116:
2108:
2103:
2044:
1938:
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1594:
1580:neutral mutation
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828:
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806:
805:
797:
793:
788:
776:
775:
767:
764:
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735:
734:
729:
711:neutral mutation
700:
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555:
543:
541:
540:
535:
522:
520:
519:
514:
501:
499:
498:
493:
480:
478:
477:
472:
458:test statistic.
453:
451:
450:
445:
433:
431:
430:
425:
405:
403:
402:
397:
367:
365:
364:
359:
345:
341:
339:
338:
330:
327:
316:
297:
254:
252:
251:
246:
232:
228:
226:
225:
217:
214:
203:
184:
112:
110:
109:
104:
88:
86:
85:
80:
2838:
2837:
2833:
2832:
2831:
2829:
2828:
2827:
2798:
2797:
2796:
2791:
2777:Silent mutation
2767:Gene conversion
2755:
2714:
2710:Selective sweep
2671:
2666:
2587:DNAsp (Windows)
2578:
2568:
2555:
2552:
2547:
2546:
2502:
2501:
2497:
2453:
2452:
2448:
2401:(6): e1602996.
2388:
2387:
2383:
2339:
2338:
2334:
2329:
2317:
2277:
2205:
2160:
2159:
2146:The lower-case
2045:
2038:
2037:
2035:
2032:
2026:
2020:
2014:
2008:
2002:
1996:
1990:
1986:
1983:
1977:
1968:
1967:
1955:
1949:
1945:
1909:
1908:
1877:
1876:
1875:Tajima defines
1846:
1826:
1825:
1803:
1802:
1759:
1745:
1725:
1703:
1702:
1698:in the sample,
1668:
1667:
1635:
1631:
1630:
1608:
1607:
1584:
1583:
1552:
1542:
1541:
1512:
1511:
1482:
1437:
1432:
1431:
1369:
1364:
1363:
1324:
1298:
1291:
1276:
1271:
1270:
1236:
1225:
1210:
1205:
1204:
1163:
1142:
1141:
1130:
1115:
1102:
1097:
1096:
1072:
1054:
1041:
1036:
1035:
1008:
989:
979:
964:
959:
958:
934:
924:
909:
904:
903:
848:
832:
815:
794:
748:
747:
744:
719:
718:
707:null hypothesis
682:
681:
657:
656:
598:
597:
549:
548:
525:
524:
504:
503:
483:
482:
462:
461:
436:
435:
416:
415:
388:
387:
301:
292:
263:
262:
188:
179:
150:
149:
143:
95:
94:
71:
70:
17:
12:
11:
5:
2836:
2834:
2826:
2825:
2820:
2815:
2810:
2800:
2799:
2793:
2792:
2790:
2789:
2784:
2779:
2774:
2769:
2763:
2761:
2757:
2756:
2754:
2753:
2751:Fay and Wu's H
2748:
2743:
2738:
2733:
2728:
2722:
2720:
2716:
2715:
2713:
2712:
2707:
2702:
2697:
2692:
2687:
2681:
2679:
2673:
2672:
2667:
2665:
2664:
2657:
2650:
2642:
2636:
2635:
2628:
2627:
2626:
2625:
2616:
2614:MEGA4 or MEGA5
2611:
2606:
2601:
2595:
2589:
2577:
2576:External links
2574:
2573:
2572:
2567:978-0878933082
2566:
2551:
2548:
2545:
2544:
2495:
2466:(3): 693–709.
2446:
2381:
2331:
2330:
2328:
2325:
2324:
2323:
2321:Fay and Wu's H
2316:
2313:
2276:
2273:
2267:
2266:
2263:
2260:
2257:
2253:
2252:
2249:
2246:
2243:
2239:
2238:
2235:
2232:
2229:
2225:
2224:
2221:
2218:
2215:
2204:
2201:
2185:
2182:
2179:
2176:
2173:
2170:
2167:
2114:
2111:
2106:
2102:
2099:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2075:
2072:
2069:
2066:
2063:
2060:
2057:
2054:
2051:
2048:
2030:
2024:
2018:
2012:
2006:
2000:
1994:
1988:
1981:
1975:
1952:
1944:
1941:
1928:
1925:
1922:
1919:
1916:
1896:
1893:
1890:
1887:
1884:
1873:
1872:
1861:
1858:
1853:
1849:
1845:
1842:
1839:
1836:
1833:
1810:
1799:expected value
1795:
1794:
1783:
1776:
1771:
1768:
1763:
1755:
1752:
1748:
1742:
1739:
1736:
1732:
1728:
1722:
1716:
1713:
1687:
1684:
1681:
1678:
1675:
1654:
1649:
1645:
1639:
1615:
1591:
1559:
1555:
1551:
1525:
1522:
1509:
1508:
1505:
1504:
1489:
1485:
1481:
1474:
1471:
1468:
1463:
1460:
1457:
1453:
1449:
1444:
1440:
1429:
1416:
1413:
1406:
1403:
1400:
1395:
1392:
1389:
1385:
1381:
1376:
1372:
1360:
1359:
1345:
1342:
1339:
1336:
1333:
1330:
1327:
1322:
1319:
1316:
1313:
1310:
1305:
1301:
1297:
1294:
1288:
1283:
1279:
1268:
1254:
1251:
1248:
1245:
1242:
1239:
1234:
1231:
1228:
1222:
1217:
1213:
1201:
1200:
1185:
1180:
1176:
1170:
1166:
1160:
1154:
1149:
1145:
1139:
1136:
1133:
1127:
1122:
1118:
1114:
1109:
1105:
1094:
1079:
1075:
1071:
1066:
1061:
1057:
1053:
1048:
1044:
1032:
1031:
1015:
1011:
1007:
1002:
997:
993:
986:
982:
976:
971:
967:
956:
941:
937:
931:
927:
921:
916:
912:
893:
892:
878:
875:
872:
869:
866:
863:
860:
855:
851:
847:
844:
839:
835:
831:
822:
818:
814:
809:
803:
800:
791:
785:
782:
779:
773:
770:
763:
758:
755:
743:
740:
726:
689:
664:
650:
649:
635:
632:
629:
623:
620:
613:
608:
605:
576:
573:
570:
564:
561:
532:
511:
490:
469:
443:
423:
395:
369:
368:
357:
354:
351:
348:
344:
336:
333:
326:
323:
320:
315:
312:
309:
305:
300:
295:
291:
288:
285:
282:
279:
276:
273:
270:
256:
255:
244:
241:
238:
235:
231:
223:
220:
213:
210:
207:
202:
199:
196:
192:
187:
182:
178:
175:
172:
169:
166:
163:
160:
157:
142:
139:
102:
78:
15:
13:
10:
9:
6:
4:
3:
2:
2835:
2824:
2821:
2819:
2816:
2814:
2811:
2809:
2806:
2805:
2803:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2764:
2762:
2758:
2752:
2749:
2747:
2744:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2723:
2721:
2717:
2711:
2708:
2706:
2703:
2701:
2698:
2696:
2693:
2691:
2688:
2686:
2683:
2682:
2680:
2678:
2674:
2670:
2663:
2658:
2656:
2651:
2649:
2644:
2643:
2640:
2633:
2630:
2629:
2624:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2599:
2596:
2593:
2590:
2588:
2585:
2584:
2583:
2582:
2581:
2575:
2569:
2563:
2559:
2554:
2553:
2549:
2540:
2536:
2531:
2526:
2522:
2518:
2515:(1): 413–29.
2514:
2510:
2506:
2499:
2496:
2491:
2487:
2482:
2477:
2473:
2469:
2465:
2461:
2457:
2450:
2447:
2442:
2438:
2433:
2428:
2424:
2420:
2416:
2412:
2408:
2404:
2400:
2396:
2392:
2385:
2382:
2377:
2373:
2368:
2363:
2359:
2355:
2352:(3): 585–95.
2351:
2347:
2343:
2336:
2333:
2326:
2322:
2319:
2318:
2314:
2312:
2308:
2304:
2300:
2297:
2292:
2290:
2286:
2282:
2274:
2272:
2264:
2261:
2258:
2255:
2254:
2250:
2247:
2244:
2241:
2240:
2236:
2233:
2230:
2228:Tajima's D=0
2227:
2226:
2222:
2219:
2216:
2213:
2212:
2209:
2200:
2197:
2183:
2180:
2177:
2174:
2171:
2168:
2165:
2157:
2153:
2149:
2144:
2143:=4/2.08=1.92
2142:
2138:
2135:
2132:
2131:
2126:
2112:
2109:
2104:
2100:
2097:
2094:
2091:
2088:
2085:
2082:
2079:
2076:
2073:
2070:
2067:
2064:
2061:
2058:
2055:
2052:
2049:
2046:
2029:
2023:
2017:
2011:
2005:
1999:
1993:
1987:
1980:
1974:
1970:
1965:
1961:
1950:
1942:
1940:
1926:
1923:
1920:
1917:
1914:
1894:
1891:
1888:
1885:
1882:
1859:
1856:
1851:
1847:
1843:
1837:
1831:
1824:
1823:
1822:
1808:
1800:
1781:
1769:
1766:
1753:
1750:
1746:
1740:
1737:
1734:
1730:
1726:
1720:
1711:
1701:
1700:
1699:
1682:
1679:
1676:
1647:
1643:
1627:
1613:
1606:
1589:
1581:
1577:
1557:
1553:
1549:
1520:
1487:
1483:
1479:
1472:
1469:
1466:
1461:
1458:
1455:
1451:
1447:
1442:
1438:
1430:
1414:
1411:
1404:
1401:
1398:
1393:
1390:
1387:
1383:
1379:
1374:
1370:
1362:
1361:
1340:
1337:
1334:
1328:
1325:
1317:
1314:
1311:
1308:
1303:
1299:
1292:
1286:
1281:
1277:
1269:
1249:
1246:
1243:
1237:
1232:
1229:
1226:
1220:
1215:
1211:
1203:
1202:
1183:
1178:
1174:
1168:
1164:
1158:
1152:
1147:
1143:
1137:
1134:
1131:
1125:
1120:
1116:
1112:
1107:
1103:
1095:
1077:
1073:
1069:
1064:
1059:
1055:
1051:
1046:
1042:
1034:
1033:
1013:
1009:
1005:
1000:
995:
991:
984:
980:
974:
969:
965:
957:
939:
935:
929:
925:
919:
914:
910:
902:
901:
898:
897:
896:
870:
867:
864:
858:
853:
849:
845:
842:
837:
833:
820:
816:
812:
807:
798:
789:
780:
768:
761:
756:
753:
746:
745:
741:
739:
724:
716:
712:
708:
704:
687:
679:
662:
654:
630:
618:
611:
606:
603:
596:
595:
594:
592:
571:
559:
547:
530:
509:
488:
467:
459:
457:
441:
421:
413:
409:
393:
385:
381:
377:
372:
371:for haploid.
355:
352:
349:
346:
342:
334:
331:
324:
321:
318:
313:
310:
307:
303:
298:
293:
289:
286:
283:
280:
274:
268:
261:
260:
259:
242:
239:
236:
233:
229:
221:
218:
211:
208:
205:
200:
197:
194:
190:
185:
180:
176:
173:
170:
167:
161:
155:
148:
147:
146:
140:
138:
135:
131:
127:
123:
122:genetic drift
119:
114:
100:
92:
76:
69:
63:
61:
60:genetic drift
56:
52:
51:introgression
48:
44:
40:
36:
31:
29:
25:
21:
2745:
2579:
2557:
2512:
2508:
2498:
2463:
2459:
2449:
2398:
2394:
2384:
2349:
2345:
2335:
2309:
2305:
2301:
2293:
2288:
2285:null process
2278:
2270:
2206:
2198:
2155:
2151:
2147:
2145:
2140:
2139:
2136:
2133:
2129:
2127:
2034:
2027:
2021:
2015:
2009:
2003:
1997:
1991:
1984:
1978:
1972:
1957:
1946:
1874:
1796:
1628:
1510:
894:
653:Fumio Tajima
651:
460:
455:
407:
383:
379:
375:
373:
370:
257:
144:
115:
64:
35:DNA sequence
32:
28:Fumio Tajima
19:
18:
2741:Ka/Ks ratio
738:statistic.
130:polymorphic
2802:Categories
2746:Tajima's D
2327:References
126:homologous
20:Tajima's D
2600:(Windows)
2592:Variscan
2423:2375-2548
2175:−
1927:μ
1915:θ
1895:μ
1731:∑
1727:∑
1715:^
1524:^
1470:−
1452:∑
1402:−
1384:∑
1338:−
1247:−
1126:−
1065:−
868:−
808:−
802:^
772:^
680:. If the
622:^
563:^
489:θ
442:π
412:selection
394:μ
356:μ
322:−
304:∑
284:θ
275:π
243:μ
209:−
191:∑
171:θ
162:π
101:π
55:frequency
24:statistic
2598:Arlequin
2509:Genetics
2460:Genetics
2441:28630911
2346:Genetics
2315:See also
1603:from an
546:variance
118:mutation
2623:BioPerl
2539:8536987
2530:1206737
2490:8454210
2481:1205353
2432:5470830
2403:Bibcode
2376:2513255
2367:1203831
2158:. Thus
2152:average
1960:average
1943:Example
2719:Models
2564:
2537:
2527:
2488:
2478:
2439:
2429:
2421:
2374:
2364:
2130:M=S/a1
1964:choose
895:where
2550:Notes
2419:eISSN
589:(its
49:, or
2562:ISBN
2535:PMID
2486:PMID
2437:PMID
2372:PMID
2178:1.92
1738:<
1540:and
434:and
120:and
2808:DNA
2621:in
2525:PMC
2517:doi
2513:141
2476:PMC
2468:doi
2464:133
2427:PMC
2411:doi
2362:PMC
2354:doi
2350:123
2184:.08
1801:of
709:of
41:or
2804::
2533:.
2523:.
2511:.
2507:.
2484:.
2474:.
2462:.
2458:.
2435:.
2425:.
2417:.
2409:.
2397:.
2393:.
2370:.
2360:.
2348:.
2344:.
2196:.
2125:.
2105:10
1939:.
1626:.
113:.
62:.
2661:e
2654:t
2647:v
2570:.
2541:.
2519::
2492:.
2470::
2443:.
2413::
2405::
2399:3
2378:.
2356::
2289:D
2181:=
2172:2
2169:=
2166:d
2156:M
2148:d
2141:M
2113:2
2110:=
2101:1
2098:+
2095:1
2092:+
2089:2
2086:+
2083:2
2080:+
2077:3
2074:+
2071:1
2068:+
2065:3
2062:+
2059:2
2056:+
2053:2
2050:+
2047:3
1924:N
1921:4
1918:=
1892:N
1889:4
1886:=
1883:M
1860:.
1857:M
1852:1
1848:a
1844:=
1841:)
1838:S
1835:(
1832:E
1809:S
1782:.
1775:)
1770:2
1767:n
1762:(
1754:j
1751:i
1747:k
1741:j
1735:i
1721:=
1712:k
1686:)
1683:j
1680:,
1677:i
1674:(
1653:)
1648:2
1644:n
1638:(
1614:N
1590:n
1558:1
1554:a
1550:S
1521:k
1488:2
1484:i
1480:1
1473:1
1467:n
1462:1
1459:=
1456:i
1448:=
1443:2
1439:a
1415:i
1412:1
1405:1
1399:n
1394:1
1391:=
1388:i
1380:=
1375:1
1371:a
1344:)
1341:1
1335:n
1332:(
1329:n
1326:9
1321:)
1318:3
1315:+
1312:n
1309:+
1304:2
1300:n
1296:(
1293:2
1287:=
1282:2
1278:b
1253:)
1250:1
1244:n
1241:(
1238:3
1233:1
1230:+
1227:n
1221:=
1216:1
1212:b
1184:2
1179:1
1175:a
1169:2
1165:a
1159:+
1153:n
1148:1
1144:a
1138:2
1135:+
1132:n
1121:2
1117:b
1113:=
1108:2
1104:c
1078:1
1074:a
1070:1
1060:1
1056:b
1052:=
1047:1
1043:c
1014:2
1010:a
1006:+
1001:2
996:1
992:a
985:2
981:c
975:=
970:2
966:e
940:1
936:a
930:1
926:c
920:=
915:1
911:e
877:]
874:)
871:1
865:S
862:(
859:S
854:2
850:e
846:+
843:S
838:1
834:e
830:[
821:1
817:a
813:S
799:k
790:=
784:)
781:d
778:(
769:V
762:d
757:=
754:D
725:D
688:D
663:D
634:)
631:d
628:(
619:V
612:d
607:=
604:D
575:)
572:d
569:(
560:V
531:d
510:d
468:D
456:D
422:S
408:i
384:N
380:n
376:S
353:N
350:2
347:=
343:]
335:i
332:1
325:1
319:n
314:1
311:=
308:i
299:S
294:[
290:E
287:=
281:=
278:]
272:[
269:E
240:N
237:4
234:=
230:]
222:i
219:1
212:1
206:n
201:1
198:=
195:i
186:S
181:[
177:E
174:=
168:=
165:]
159:[
156:E
77:S
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