Matching Split distance for unrooted binary phylogenetic trees

(By Damian Bogdanowicz and Krzysztof Giaro)

Supplemental Material

During the computation we analyzed 10000 pairs of trees that were chosen at random from among all possible unrooted binary trees with a particular number of leaves (n) under two the most popular models: the uniform model and the Yule model. In the case of the uniform model, an edge is added uniformly and randomly to any edge of the base tree. In this model, all phylogenetic trees have the same probability to be drawn. In the case of the Yule model, an edge is added uniformly and randomly to a pendant edge only, and the corresponding label is uniformly and randomly drawn as well.

The uniform model

• n=10

  

• n=50

  

• n=100

  

• The detailed statistical results

  n	Quantile													avg	sd
  	0.02	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.95	0.97
  5	0	0	2	2	2	3	3	3	3	3	4	4	4	2.665	0.946
  10	12	14	15	17	18	18	19	20	20	21	22	23	23	18.780	2.767
  15	34	36	38	40	42	43	45	46	47	49	51	52	53	44.443	5.012
  20	63	66	69	72	75	77	79	81	83	86	89	92	94	78.798	7.902
  25	97	102	106	110	114	117	120	122	126	129	134	139	142	119.902	11.254
  30	138	144	149	155	159	163	167	171	176	181	188	194	198	167.910	15.460
  35	183	190	196	204	210	215	220	226	231	238	248	255	261	221.227	20.030
  40	233	242	249	259	266	273	279	286	293	301	313	324	332	280.585	25.259
  45	287	297	306	318	327	335	343	351	359	369	384	398	407	344.408	30.554
  50	345	357	368	382	393	402	411	421	431	444	462	479	489	413.662	36.970
  55	406	420	433	450	463	474	485	496	509	523	543	560	573	487.047	43.103
  60	470	487	503	522	537	550	563	576	589	607	631	652	664	565.196	50.315
  65	542	559	577	598	615	630	644	659	676	695	724	749	764	647.839	57.558
  70	609	631	651	676	696	713	730	747	765	787	819	848	865	733.168	65.801
  75	685	709	733	761	782	800	818	837	859	884	919	949	969	822.935	72.881
  80	767	794	816	847	872	892	911	932	957	986	1029	1063	1088	918.048	82.411
  85	847	878	903	937	964	987	1010	1034	1060	1093	1138	1177	1203	1016.300	92.055
  90	933	964	994	1032	1061	1087	1112	1138	1165	1199	1249	1289	1317	1117.540	99.619
  95	1021	1053	1085	1126	1157	1187	1214	1243	1277	1315	1369	1415	1445	1221.913	110.882
  100	1108	1144	1181	1226	1263	1294	1322	1352	1386	1429	1487	1537	1572	1329.663	119.696
  105	1201	1242	1281	1330	1369	1401	1434	1467	1503	1549	1612	1665	1705	1441.605	129.920
  110	1300	1347	1385	1437	1478	1512	1547	1585	1623	1673	1742	1797	1838	1557.035	139.339
  115	1394	1442	1487	1545	1589	1627	1664	1701	1747	1802	1877	1939	1981	1674.368	151.655
  120	1494	1546	1592	1654	1702	1743	1784	1824	1871	1928	2013	2086	2133	1794.614	163.616
  125	1597	1653	1705	1770	1820	1864	1911	1954	2005	2062	2152	2225	2275	1920.300	174.237
  130	1705	1765	1820	1891	1945	1992	2039	2087	2140	2203	2293	2373	2425	2050.487	185.638
  135	1811	1868	1933	2010	2067	2118	2164	2212	2268	2334	2431	2521	2578	2175.958	196.473
  140	1924	1991	2050	2127	2188	2242	2298	2351	2409	2480	2587	2681	2740	2309.193	210.883
  145	2043	2108	2170	2249	2316	2374	2430	2489	2552	2630	2734	2831	2890	2444.072	221.186
  150	2153	2225	2295	2381	2452	2511	2570	2630	2696	2776	2894	2994	3060	2584.101	234.292
  155	2265	2345	2420	2514	2585	2649	2707	2770	2841	2923	3051	3158	3225	2723.293	246.155
  160	2385	2464	2541	2643	2724	2790	2856	2923	2996	3088	3213	3330	3405	2870.498	263.739
  165	2505	2589	2673	2778	2862	2931	2998	3070	3151	3244	3387	3498	3574	3016.353	277.285
  170	2641	2726	2807	2918	2998	3072	3145	3216	3297	3399	3545	3673	3758	3163.300	288.636
  175	2748	2852	2944	3054	3143	3223	3298	3377	3461	3566	3721	3850	3936	3317.020	305.045
  180	2894	2996	3091	3206	3292	3372	3448	3529	3618	3727	3894	4022	4111	3472.936	313.904
  185	3007	3117	3214	3337	3434	3518	3602	3686	3783	3900	4066	4210	4298	3623.939	333.090
  190	3154	3261	3360	3490	3590	3676	3760	3855	3957	4070	4245	4404	4512	3788.776	348.902
  195	3276	3395	3499	3640	3747	3840	3929	4018	4124	4250	4430	4588	4694	3951.299	362.682
  200	3427	3534	3648	3784	3889	3991	4090	4188	4301	4429	4614	4775	4879	4114.372	381.242

The Yule model

• n=10

  

• n=50

  

• n=100

  

• The detailed statistical results

  n	Quantile													avg	sd
  	0.02	0.05	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	0.95	0.97
  5	0	0	2	2	2	3	3	3	3	3	4	4	4	2.663	0.952
  10	12	13	14	16	17	17	18	19	20	20	21	22	22	17.885	2.725
  15	31	33	35	37	38	39	40	42	43	44	46	47	48	40.298	4.245
  20	56	59	61	64	65	67	68	70	71	73	76	78	79	68.330	5.911
  25	84	88	91	94	97	99	100	102	104	107	110	113	115	100.389	7.614
  30	117	121	124	128	131	133	136	138	141	144	148	152	154	135.985	9.412
  35	152	156	160	165	168	171	174	177	180	183	188	193	196	174.281	11.061
  40	190	195	199	205	209	212	215	218	221	226	232	237	241	215.389	12.733
  45	230	235	241	246	251	254	258	262	266	271	277	283	286	258.561	14.467
  50	273	279	284	290	295	300	304	308	313	318	326	332	337	304.401	16.433
  55	316	323	329	336	342	346	351	355	360	366	375	382	387	351.449	18.059
  60	362	370	376	384	390	395	400	405	410	417	427	435	441	400.712	19.904
  65	409	417	424	432	439	444	450	455	461	469	479	488	494	450.578	21.772
  70	458	467	474	483	490	496	502	508	514	522	534	544	550	502.957	23.414
  75	507	517	525	535	542	549	555	562	569	578	590	601	609	556.401	25.853
  80	560	569	577	588	595	602	609	616	624	633	646	658	665	610.732	27.134
  85	612	622	631	642	651	658	665	673	681	690	704	717	726	666.877	28.943
  90	666	677	686	698	707	716	723	730	739	749	764	777	785	724.167	30.677
  95	720	731	742	755	764	773	781	790	798	809	825	840	849	782.455	32.832
  100	776	787	798	813	823	831	840	848	858	869	885	901	911	841.263	34.432
  105	832	845	856	870	880	890	899	909	920	932	950	965	975	901.423	36.664
  110	891	904	915	929	940	950	960	970	980	993	1012	1028	1039	962.037	38.322
  115	948	961	974	990	1002	1012	1022	1032	1044	1057	1078	1094	1105	1024.203	40.416
  120	1007	1022	1035	1051	1064	1074	1085	1095	1107	1122	1143	1160	1172	1086.994	42.447
  125	1067	1083	1097	1114	1126	1137	1148	1159	1171	1185	1206	1223	1237	1149.935	43.059
  130	1129	1145	1159	1176	1189	1201	1212	1225	1237	1254	1276	1295	1308	1215.330	46.016
  135	1190	1206	1220	1238	1253	1264	1276	1288	1301	1317	1340	1361	1374	1278.579	47.465
  140	1250	1269	1284	1304	1318	1331	1343	1356	1370	1387	1409	1429	1443	1345.578	49.548
  145	1316	1333	1349	1369	1384	1397	1410	1423	1437	1454	1479	1501	1516	1412.441	51.273
  150	1380	1399	1414	1435	1450	1464	1477	1490	1505	1523	1549	1572	1588	1479.903	53.139
  155	1443	1461	1479	1500	1516	1529	1543	1557	1572	1591	1620	1643	1658	1546.603	55.315
  160	1507	1526	1545	1567	1584	1598	1611	1625	1641	1662	1690	1713	1731	1614.852	57.004
  165	1573	1592	1612	1635	1653	1668	1681	1696	1712	1733	1762	1788	1806	1684.823	59.348
  170	1637	1658	1678	1701	1719	1735	1751	1767	1784	1806	1835	1860	1877	1754.206	61.867
  175	1706	1727	1747	1772	1791	1807	1823	1839	1856	1879	1909	1936	1955	1826.160	63.832
  180	1772	1792	1813	1839	1859	1875	1892	1909	1927	1948	1981	2009	2028	1895.470	66.023
  185	1842	1864	1884	1910	1929	1945	1962	1980	1998	2020	2052	2079	2097	1965.972	66.329
  190	1909	1931	1953	1981	2000	2018	2035	2053	2073	2096	2130	2160	2180	2039.212	69.580
  195	1978	2002	2023	2051	2071	2090	2107	2126	2146	2169	2204	2233	2253	2111.102	70.547
  200	2048	2072	2095	2122	2143	2162	2180	2198	2218	2243	2279	2310	2332	2184.096	72.650

The average value of the MS distance for 10000 pairs of trees under the two considered models

The solid lines show the average values, dashed lines represent double standard deviation intervals (avg�2*sd).