This version of the Mantel test supports asymmetric matrices and multiple partial-Mantel controls, a combination of features that is not possible using other widely available Mantel functions such as mantel.partial.
Usage
mantel_test(
x,
y,
z = NULL,
nperm = 999,
method = "pearson",
alternative = c("two.sided", "less", "greater")
)Arguments
- x, y
Square matrices (can be asymmetric).
- z
Optional list of one or more square control matrices if partial Mantel is desired.
- nperm
Number of random permutations to perform (positive integer).
- method
Correlation method (see cor for details).
- alternative
A character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
Value
A list with the following components:
stat: The correlation coefficient betweenxandy, measured on the data provided. This will be a partial correlation ifzis specified.quantile: The quantile of the observed stat in the null distribution.p.value: Significance, derived from the combination ofquantileandalternative.perm: A vector of null correlations based on permuted data.
Examples
# A convenience function to generate symmetric matrices:
sym_matrix <- function(x){
n <- which(cumsum(1:100) == length(x)) + 1
m <- matrix(0, n, n)
m[lower.tri(m)] <- x
m[upper.tri(m)] <- t(m)[upper.tri(t(m))]
m
}
# Simulate some example data:
g <- runif(45)
w <- runif(45)
d <- runif(45)
e <- sample(0:1, 45, TRUE)
G <- sym_matrix(g) # e.g. a genetic matrix
W <- sym_matrix(w) # e.g. a wind matrix
D <- sym_matrix(d) # e.g. a distance matrix
E <- sym_matrix(e) # e.g. an environment matrix
# Basic function usage:
mantel_test(G, W) # simple first-order Mantel
#> $stat
#> [1] 0.0272882
#>
#> $quantile
#> [1] 0.5635636
#>
#> $p.value
#> [1] 0.8728729
#>
#> $perm
#> [1] -0.1865725074 0.1761820611 0.0362366523 0.0911598003 -0.0739177689
#> [6] 0.0387884507 0.2475624596 -0.2242966534 -0.0253397801 -0.1908994086
#> [11] -0.2940769864 0.1150562086 0.1659640473 0.0877595223 -0.0317238039
#> [16] -0.0888211198 -0.0554553550 -0.0613410656 0.0056396132 0.1708803545
#> [21] -0.0225939577 -0.3283440113 -0.0371157129 -0.0485453653 -0.0915717792
#> [26] 0.0896048675 0.0742514758 -0.0851645775 0.0532770892 -0.0777374140
#> [31] 0.1912610586 0.0055342975 -0.1101132960 0.0440266601 -0.2551266399
#> [36] 0.1023160761 0.2985966470 0.2928431814 0.2407033570 0.0238776637
#> [41] -0.0722518100 0.2991020240 0.0869591262 -0.0637540099 0.1054032449
#> [46] 0.0182289505 0.1673964388 0.2134098820 -0.0889908800 0.0588053874
#> [51] -0.0220407225 0.1069836704 0.1421369238 0.0309195001 -0.1709877752
#> [56] -0.1143874561 0.2907055110 0.1228193346 0.0882146420 0.0851713245
#> [61] 0.2883606802 -0.0279623292 -0.0723140556 -0.1581855475 0.2562124289
#> [66] -0.1783656539 0.1470331087 0.0793438251 0.1620788345 0.0177812762
#> [71] 0.0060265667 -0.2474528837 -0.0560835269 -0.0122239688 -0.2573519631
#> [76] -0.0661664261 -0.1922769259 -0.0998907728 -0.0730191807 -0.1645932279
#> [81] 0.1701552653 -0.1482710534 -0.0712394774 -0.0026516959 -0.1523454169
#> [86] -0.2142426853 -0.2961096973 -0.3392635973 0.3779854961 0.1278284895
#> [91] -0.1354742266 0.0382827616 0.2085082825 0.2111880632 0.1593491321
#> [96] 0.0838014105 0.2210599790 0.0254945391 0.1271883183 0.0686146862
#> [101] 0.0429233861 -0.0343547309 -0.0046613387 -0.2165780700 0.1174766458
#> [106] 0.4542105121 -0.0024860606 -0.1222627360 -0.0952627240 0.2478441334
#> [111] -0.0119988446 -0.0185943441 0.2438420501 0.0540951068 0.1461182771
#> [116] -0.0996709852 -0.0133295537 0.0277581364 0.0309475775 0.0440938010
#> [121] -0.1301410511 0.4475123973 0.0606544986 0.2095956489 -0.0497075208
#> [126] -0.2096050455 0.1709946723 -0.0401052863 -0.0277458302 0.0101433431
#> [131] -0.1301659709 0.1685057184 0.0788382084 -0.2445510769 -0.0351682727
#> [136] 0.1610149391 0.1377443324 0.1691368610 -0.1318733270 -0.2374763155
#> [141] 0.0373632018 0.3588927821 0.0471568145 0.2273479064 0.0692619464
#> [146] -0.1747464104 -0.1188559297 0.1867111324 0.0504978960 -0.0975394337
#> [151] -0.1058613632 -0.0398243562 0.1288154361 -0.1029604248 0.1657644843
#> [156] 0.0260942399 -0.2904424027 -0.1276397274 0.0332282867 -0.0278668421
#> [161] -0.0739215869 -0.1116892091 -0.1740162859 0.0024039799 -0.0789233908
#> [166] -0.0684513176 0.1018682536 0.0030035935 -0.3223792711 0.0358123554
#> [171] 0.1000629339 -0.0312838040 -0.1257912580 0.0617969190 -0.1189353550
#> [176] -0.1020974782 -0.1491665776 0.0528912981 -0.0698485433 0.0104606064
#> [181] -0.0568043615 0.1317301404 0.0927306945 -0.3374642097 0.1228285782
#> [186] -0.0081990393 0.0647827101 -0.1484710877 -0.1363458243 -0.2098801877
#> [191] -0.0710469588 0.0029064339 -0.0446979837 -0.0712808479 -0.3019180563
#> [196] 0.2887293172 -0.0740308538 0.0430190886 -0.3221011780 0.2064721931
#> [201] 0.1186906310 0.1038025014 0.0715427706 -0.2031906855 -0.0241442862
#> [206] -0.2754340989 -0.1740046803 0.0174010765 0.0700514426 -0.1322676579
#> [211] 0.0310534781 -0.1953838804 0.0746946537 -0.0474378907 0.0073412903
#> [216] -0.2555238831 0.1348971822 -0.0246998847 0.1829803921 0.0576225149
#> [221] 0.1602573652 0.0401787123 0.0946558974 0.1758009100 0.1600060119
#> [226] -0.1929477757 -0.0681450001 0.2175884179 0.1326895719 -0.1877485660
#> [231] -0.0614310666 0.0764832224 0.0043301489 0.1385465673 0.0716847051
#> [236] 0.0110287571 -0.1993207603 -0.1502757015 0.1306758912 -0.0619723075
#> [241] -0.0870716317 0.0326582316 0.1679382294 0.2085348070 -0.0325295484
#> [246] -0.0689548323 0.0124097109 0.2151764731 -0.1043348893 -0.0579093609
#> [251] 0.0749688967 0.0441065792 0.1730007273 -0.1644525677 0.1392534568
#> [256] -0.1470979337 -0.0529718938 0.2354108118 0.1850808426 0.1860318810
#> [261] -0.2993681980 0.1856559107 -0.0346060926 0.1879401384 -0.0954549505
#> [266] -0.1293431678 0.0080085890 -0.1801472313 0.3139057526 -0.4228306075
#> [271] -0.0171057470 0.2791875954 0.0864946708 -0.0798482511 -0.3339375638
#> [276] 0.0748123239 0.1263142305 0.0438806942 -0.0042851698 0.0104033954
#> [281] -0.0726440857 0.1742569828 0.1195369984 0.1100356604 -0.0292495660
#> [286] -0.2134943318 -0.3311630908 0.1986931500 0.1270022216 -0.1480814858
#> [291] -0.0776197016 0.0682716377 0.2475375770 0.1844444983 0.0219745467
#> [296] 0.2738934169 -0.1572301525 -0.1751514220 0.0976193267 0.0608579974
#> [301] 0.0745020672 0.0553279496 0.2089145679 -0.1958511236 0.0336280860
#> [306] -0.3086466124 0.2648096095 0.0747921615 -0.3411417673 -0.0728856536
#> [311] -0.0784788873 -0.0632837587 -0.0821865024 -0.3430982110 -0.1062579558
#> [316] -0.0226897430 -0.0991866569 -0.0074648600 0.0721003178 0.4133604295
#> [321] -0.0921810924 -0.0851371782 -0.3959969556 0.1217357609 -0.0264805829
#> [326] 0.1363933648 0.0986651549 -0.0145435676 -0.0002564778 -0.0324341231
#> [331] 0.0351383054 -0.0017336513 -0.4271124432 -0.0749329848 0.1870264386
#> [336] -0.2224941025 0.1125557771 0.0938466735 0.1234682587 0.1131403885
#> [341] -0.0437687914 -0.0236292464 -0.0693882108 0.3347738812 0.0161095833
#> [346] -0.0042062329 -0.0611656745 0.1734648686 -0.0831019456 0.0807729707
#> [351] 0.1251269493 0.1217856187 -0.1863214718 -0.0616199765 0.0728145003
#> [356] -0.0462916012 0.1240425790 0.0032790159 0.0227398001 0.1356655512
#> [361] -0.1646568668 0.2127350498 -0.1489345915 0.1638582486 -0.0047266958
#> [366] 0.0657051276 -0.3362641415 0.0459817968 -0.1759379672 0.1322233290
#> [371] -0.0436269795 -0.3610896603 -0.1256885047 -0.0938417355 -0.0270128069
#> [376] 0.0941849583 -0.1194238876 0.2056656605 0.0850296644 -0.1440928146
#> [381] -0.2680924199 -0.0079137295 -0.1964912997 -0.2227543301 -0.0199086637
#> [386] 0.0857332572 -0.0042561801 0.0373220477 0.1964566792 -0.2469491673
#> [391] 0.0751727692 -0.0187338256 0.0118288852 -0.1644419064 0.1289229704
#> [396] 0.0154452938 -0.0962544902 0.1742010642 -0.1229835692 -0.1635887995
#> [401] 0.0629438360 -0.1847901049 -0.0046843060 0.1079735229 0.0714136147
#> [406] -0.0963222121 0.0686974852 -0.0613870411 -0.1179637839 0.3056572518
#> [411] 0.0178521117 -0.0724377860 0.0813940732 -0.1539778768 -0.0321261377
#> [416] 0.0664236888 0.1881890248 -0.2273843817 -0.1512129331 0.0291500492
#> [421] 0.3214397547 -0.2203955622 0.3215941464 0.2005271569 0.1128004496
#> [426] 0.1084926981 0.0179695578 -0.0946571251 -0.2237354595 0.0433462197
#> [431] -0.1032451076 0.2540579270 -0.0318173379 -0.0878527632 -0.1086764706
#> [436] 0.0638766643 -0.1129877221 0.1181813326 0.1496077831 -0.3150069272
#> [441] -0.1723440159 0.0165219546 -0.0445413162 0.0247860343 0.0628684568
#> [446] -0.0228068479 0.1532500855 0.1573107029 -0.0847058984 -0.0747972482
#> [451] 0.0222571140 0.0932736310 0.1384423069 -0.0345767602 0.1522142624
#> [456] 0.1444511977 -0.0329804029 0.2397941046 -0.0150310447 -0.1640162629
#> [461] 0.0738727943 0.1344956391 -0.1490444566 -0.0577469828 0.0492601339
#> [466] 0.3196146591 0.0139597263 0.3957809928 0.0259791544 0.1578795933
#> [471] -0.1509007152 -0.1444154582 -0.0725893555 0.1110593163 0.1645697167
#> [476] 0.0694343893 0.1071313555 0.2247599056 0.1137175653 -0.2429990255
#> [481] -0.0104029875 -0.0394695714 0.0447501127 0.0262715926 -0.0489031465
#> [486] -0.1716490443 0.1758752565 -0.3642385806 -0.2631643239 0.1053370851
#> [491] 0.0283576162 0.0086355938 -0.2220763482 -0.0482611947 -0.0177850842
#> [496] 0.1022681565 -0.1296535739 -0.1770199991 -0.2199701874 -0.0910185598
#> [501] 0.0833444281 0.0137239210 0.3115439346 0.1053335928 -0.1265294359
#> [506] 0.0191899666 0.1330767388 -0.0317069215 0.0205284619 0.2998232998
#> [511] 0.2638795122 0.1801255614 0.0519902532 0.1002855669 0.1110916958
#> [516] 0.0671512750 -0.0559149722 -0.1339900017 -0.1174939726 -0.0167714148
#> [521] 0.1528288603 -0.0956433168 -0.0380041742 -0.1122481440 -0.1218374539
#> [526] -0.3435201611 -0.1936745368 -0.1214250686 0.2121066747 0.2456337020
#> [531] 0.0183837924 0.0940953053 -0.0560515349 0.1485184034 0.0751213723
#> [536] 0.2323291341 0.0076135205 -0.0625341028 0.0374237812 -0.1074635243
#> [541] 0.0624177232 0.1269849718 -0.0541276386 -0.0472392435 0.0264884681
#> [546] 0.2106737910 -0.2762832542 -0.1563513415 -0.0835424242 0.1305399385
#> [551] 0.0287970074 0.1225549344 -0.0857348621 0.2508242752 -0.0403056221
#> [556] 0.0652757535 -0.0597268933 0.2041303028 -0.0881447495 0.1515115404
#> [561] 0.0062259433 0.0317010071 -0.3326515252 0.0017044694 -0.0989714533
#> [566] 0.3771058531 -0.0882538709 -0.0783725894 -0.0609587479 0.0940087420
#> [571] 0.0811910085 0.0155787886 -0.0609630087 -0.0330013215 -0.2115646605
#> [576] -0.0743477609 -0.2867297942 -0.0135923884 -0.0028416097 0.0858124092
#> [581] 0.1486572873 -0.2261018620 -0.0633632177 -0.0546709047 -0.1018284920
#> [586] 0.0777976297 -0.1413698894 0.2476068865 0.0417643088 -0.2413392694
#> [591] 0.2286553267 0.0889657059 0.1226457187 -0.1126730133 0.3369565538
#> [596] -0.0228159833 -0.0792391578 -0.0066087740 -0.1176003042 0.1334521075
#> [601] 0.0086264019 0.1703220925 -0.1630993344 -0.0386069520 -0.1159898493
#> [606] 0.1945657068 0.0175743091 0.0702384666 -0.1110599289 -0.0325709691
#> [611] -0.1041598858 -0.0711538757 0.0695188001 0.1697359312 -0.1700811108
#> [616] -0.1719427074 -0.0154952665 0.0908804271 0.0209919983 0.0224809790
#> [621] 0.0133985475 0.1135488975 -0.0294394312 0.0342594053 -0.0084787095
#> [626] 0.1806576635 0.2439732678 -0.1173466238 0.0196960097 0.2529726380
#> [631] 0.1054984215 -0.0491991158 0.2079812145 -0.3533008055 -0.2369794801
#> [636] -0.0718318181 0.0596122703 -0.2097733961 0.0254684628 -0.0459764535
#> [641] -0.1391444913 0.1555736653 0.1673489414 -0.0572932022 0.0014300345
#> [646] 0.2099597311 -0.1424306913 -0.1156832794 -0.0628386961 -0.1779772096
#> [651] -0.0547684207 -0.1017183300 -0.2675900888 -0.0528141462 0.3328581043
#> [656] 0.0677453195 0.1348179046 0.0427038701 0.1212457576 -0.1399903296
#> [661] 0.0944378464 -0.1014617073 0.1182548707 -0.0569509513 0.0874718304
#> [666] 0.3399398472 0.3794273335 0.0045743629 -0.0692629815 -0.1766611966
#> [671] 0.0865460948 -0.1677850562 -0.0225675914 0.1738074304 0.0824020467
#> [676] -0.1105518318 0.0088440885 0.1312802935 0.1061180576 -0.0513606908
#> [681] -0.1728108576 0.0855908296 -0.0104473322 -0.0535860216 -0.0274754465
#> [686] -0.1541384104 0.2748126430 -0.0440555357 -0.0661731951 0.1819539699
#> [691] -0.0133878011 0.0890773928 0.0694925152 -0.1275219718 -0.0624038737
#> [696] 0.1924218917 -0.0748350347 0.0340087352 -0.0649969383 -0.1648063077
#> [701] -0.0412475617 -0.3090325984 -0.0181001825 -0.2279564387 -0.2894544545
#> [706] -0.0107198224 0.1579466876 0.0162065340 0.0400707835 0.1332215672
#> [711] 0.1679002496 0.2217037352 -0.0049070558 0.2461280736 0.1717789003
#> [716] 0.0344286829 -0.3589168461 -0.0711877913 0.1273006098 -0.0684648144
#> [721] 0.1440450824 0.0797724835 -0.1554493771 -0.0955286803 -0.1071621675
#> [726] -0.2445768377 -0.2829632107 0.2612193852 0.1831942529 -0.0886578205
#> [731] 0.0642574497 0.0956420921 -0.0884821342 0.1577859191 -0.1301819294
#> [736] -0.1572351001 0.1223562359 -0.1947469545 0.0965530889 0.0948272485
#> [741] -0.1013846349 0.2109348781 -0.1684074635 0.0186205421 0.1601987237
#> [746] 0.0707585231 0.2737052548 -0.0737984616 0.2057990078 -0.0691786255
#> [751] -0.0187394201 0.0345303155 -0.0087286851 0.0380510529 -0.1932071893
#> [756] 0.0661710314 0.0164874654 -0.2463682464 0.0936361447 -0.2139858863
#> [761] 0.2014781898 -0.1996303038 0.2025103004 0.0137953798 -0.0639103626
#> [766] -0.2690643119 -0.2303180493 0.1730204248 -0.2340123434 -0.2271873184
#> [771] 0.0532049383 -0.0590119016 0.1860584059 -0.0174442727 0.1377097585
#> [776] -0.2199621066 0.0909092962 0.0532321146 -0.1258490856 0.0606362840
#> [781] 0.0330123483 0.1060852552 0.2369773001 -0.0891724454 0.3015398214
#> [786] 0.3010514902 -0.0347955504 -0.1159044004 -0.2802927227 0.0013640841
#> [791] -0.2919264324 0.0247090510 0.1103093114 -0.0212261761 -0.1956757787
#> [796] -0.1261972881 0.0005140898 -0.3691707852 0.0629342642 0.0238545949
#> [801] 0.0592171109 -0.0791102157 -0.1696333060 -0.0527300663 -0.3212008066
#> [806] 0.1699683500 -0.0753518371 0.0598573117 0.0456051443 0.0912086016
#> [811] -0.1883318304 0.0788037877 0.1746486996 0.0607179413 -0.0907674708
#> [816] -0.1432737977 -0.1696241215 0.0583587316 -0.1013593921 -0.0770222680
#> [821] -0.0278709652 -0.1008595761 0.1380201756 0.0684767664 -0.0727641796
#> [826] -0.1339364513 0.1625365388 0.0661749735 0.0129217305 -0.0171597032
#> [831] 0.1345287141 -0.1465161909 0.1013110466 0.0064068097 -0.2053153702
#> [836] -0.2073686232 0.0922798366 0.0729066821 -0.0397437372 0.0767407651
#> [841] -0.1823516290 0.2341956459 -0.1329876882 -0.0193816012 -0.0975174856
#> [846] -0.1353335905 0.1397503298 0.0070884248 -0.1493635469 0.1235511340
#> [851] -0.0366321266 0.0195815507 -0.0813349176 0.1244931223 -0.0167883408
#> [856] -0.0664081210 0.1524534216 0.0553966089 -0.0856996209 0.3155331131
#> [861] 0.0277855049 0.0511540549 -0.1329896749 0.2456583935 0.0197983370
#> [866] 0.0859744900 -0.0860641006 -0.2386345764 0.0150583180 -0.2333340611
#> [871] -0.1029412248 -0.2226944068 -0.0093761665 -0.0295043908 0.0403772081
#> [876] -0.0783728832 -0.0551987558 0.1919033230 0.2908392770 -0.1363342798
#> [881] 0.0118748535 0.1541025706 0.2456468889 -0.0586398829 -0.0245455397
#> [886] 0.0908283553 0.0289025455 0.2220186435 0.0985893263 -0.0200592157
#> [891] 0.1381415236 -0.1272474797 0.2376146261 0.1351480681 0.1142723060
#> [896] 0.2706482229 -0.1183057395 -0.1265784382 0.1681630688 -0.1490137780
#> [901] -0.0057549138 -0.0722833892 -0.2885638344 0.0408583638 0.0777948128
#> [906] 0.2070345062 -0.0339536836 0.0529755524 -0.2220901079 0.3039726589
#> [911] 0.1196824411 0.1035162851 -0.1515371413 -0.1742173371 0.1588234222
#> [916] -0.0633274321 -0.1233541617 -0.0645472540 -0.1640523640 0.1353409885
#> [921] 0.1469318212 -0.0546743908 -0.1944746139 0.0965290325 -0.0510103543
#> [926] -0.2066777617 -0.0108960586 -0.1151441859 0.3815852778 -0.1364007783
#> [931] 0.0497175050 -0.0252920481 -0.1194792612 0.0287997802 0.1427271279
#> [936] -0.2503184609 -0.0323964430 0.0378882332 0.2326433956 0.1791083434
#> [941] -0.0332047385 0.1868089806 0.0447489699 -0.0894775193 0.1222437397
#> [946] -0.2100984649 0.1250896506 0.2060644380 -0.0674442099 0.2202350943
#> [951] 0.2317814319 -0.3207058869 0.0588415206 0.0905284024 0.1338914327
#> [956] 0.0633797918 -0.0095718912 -0.0962181210 0.1474700193 -0.0821848742
#> [961] -0.1067285889 -0.0133128946 -0.1695146922 0.1815978491 0.1160663455
#> [966] 0.1478657544 0.0902598628 -0.0331297439 0.1016099141 -0.1007078184
#> [971] -0.0460681805 -0.1743560438 -0.2349466543 -0.0996211596 -0.0384982974
#> [976] -0.2198101318 -0.0739392860 -0.1737590431 -0.0711765549 -0.0191394925
#> [981] 0.1993737619 -0.2027265263 0.1546040648 -0.0189230190 0.1090508028
#> [986] 0.0258476877 -0.1224378879 -0.0936236480 -0.2806405344 0.1402236350
#> [991] 0.2246038779 0.1982402778 0.1683738019 -0.1274991104 0.2394320438
#> [996] 0.0762834705 -0.3561151330 -0.0115248489 0.1806209317
#>
mantel_test(G, W, list(D, E)) # partial Mantel
#> $stat
#> [1] 0.04108519
#>
#> $quantile
#> [1] 0.6096096
#>
#> $p.value
#> [1] 0.7807808
#>
#> $perm
#> [1] -0.0720114845 -0.0978154320 0.1817440074 0.1215062285 0.2032167794
#> [6] -0.0095620510 -0.2805865001 0.0967892236 -0.0639166614 -0.0461997145
#> [11] -0.1169549966 0.2286642685 -0.0355859664 0.1581913349 0.2017044002
#> [16] -0.1020485305 -0.0357039096 -0.0023997097 -0.0223625844 0.2214787391
#> [21] -0.1690243736 0.1771730083 0.0428291631 0.2370608570 -0.0735306836
#> [26] 0.1594271224 -0.0897060514 0.0096573662 0.2835189831 0.0933452383
#> [31] 0.1720765397 0.0303331185 -0.1419700991 0.1769960457 -0.2325913036
#> [36] -0.0033967450 0.2203640027 -0.1215631156 -0.0715292315 -0.0306081037
#> [41] 0.1707833167 -0.2315460749 0.2878790259 -0.0680635162 0.1229523433
#> [46] 0.1265853163 -0.1510529463 0.0963029915 -0.1054043164 0.0806979553
#> [51] 0.0830584840 0.0376658982 -0.3485698595 -0.1134026092 -0.1231411312
#> [56] 0.1880771371 -0.1793829057 0.0447423390 -0.0391904405 -0.0893023147
#> [61] -0.0603674562 -0.0940510781 0.2351579736 -0.2026664063 0.1526175774
#> [66] -0.0305328916 0.1194231904 -0.0996611349 0.0730403213 0.1261923354
#> [71] -0.3371632462 0.2378134056 -0.0494266540 -0.0424394598 -0.1638409015
#> [76] 0.0252972515 -0.0705935152 0.0167186066 0.2098043143 0.0546589496
#> [81] 0.1272754280 0.0424347858 -0.0604372345 -0.1703324083 -0.1490537225
#> [86] -0.0627343567 0.2003132710 -0.0541461389 -0.2382390057 -0.0301710598
#> [91] 0.1019445495 0.1653949103 -0.0705854496 0.1020669263 0.0637580076
#> [96] -0.0748913097 -0.1706830191 0.0899523987 0.0849549443 0.0500964675
#> [101] 0.1722113722 -0.2235690892 0.1573483036 -0.1261412703 0.1217192501
#> [106] 0.1265451283 -0.0716967927 0.1358281402 -0.0499346214 0.0220225058
#> [111] 0.0469781885 0.1149608102 -0.1132401953 -0.2401593252 -0.1483669731
#> [116] -0.1302412780 -0.0800636096 0.0030412975 -0.1541837625 0.1283316804
#> [121] 0.0920876171 -0.1451554944 -0.0812463467 -0.1037823175 -0.1279862472
#> [126] 0.1470824886 -0.0352045797 0.0929599768 0.1173645316 0.1041147578
#> [131] -0.2191926846 0.1966285797 -0.1156282748 0.1213518250 -0.0429401330
#> [136] 0.0293594616 -0.1824567992 0.0131779971 0.0676092772 0.0440088245
#> [141] 0.3165219831 -0.1175743048 0.1818746599 0.0529115619 -0.1342985500
#> [146] -0.2914951773 0.2471846468 -0.1657029612 -0.0940323432 0.0234966423
#> [151] -0.0466066158 0.0097216437 0.2560255359 -0.0805969365 -0.1123837643
#> [156] -0.1736723634 -0.0315838005 0.0136703074 -0.0706537837 0.2015189666
#> [161] -0.0550612844 -0.1407943143 0.0306288937 -0.0754104975 0.0691389509
#> [166] -0.1907638912 -0.0771122532 0.0056758726 -0.3413275431 0.2061797823
#> [171] -0.3854176755 0.1753812375 0.1677292307 0.4750414091 0.3140273723
#> [176] -0.2564154568 0.0270312670 0.0643942894 0.0628354076 0.1873687136
#> [181] 0.1628552513 0.1079834242 0.0019587857 0.0401389662 -0.0838796000
#> [186] 0.0596018217 -0.0267608441 0.0966269298 -0.2290983789 -0.1078291457
#> [191] -0.0608858511 0.0934581233 0.0617944321 0.2685083221 -0.3282076312
#> [196] 0.1222784491 -0.1621281831 0.1727770643 0.0405358590 0.2444502402
#> [201] -0.1679335809 -0.1560664216 -0.1825857429 -0.0324773460 0.0175899354
#> [206] 0.0576933267 0.1648576797 -0.0964945004 -0.0554289391 0.1778993205
#> [211] -0.1139152559 -0.2073825090 0.0330913402 -0.1903494088 -0.0639548997
#> [216] 0.1329986305 0.0214381387 -0.4291098840 -0.0892288553 0.3892070517
#> [221] -0.2665650618 0.3132612373 -0.1405547267 -0.0096686881 0.0679013254
#> [226] -0.0831349423 0.3833481340 0.1075080265 -0.0237796210 -0.1250134476
#> [231] -0.0934044053 0.0792072910 0.0345785574 0.2433379709 -0.0063339392
#> [236] 0.0657016401 -0.2320545637 -0.0385566417 -0.0011263722 0.0316257228
#> [241] 0.0217251271 0.1368904892 -0.0271725704 0.0997910254 -0.1206436119
#> [246] -0.0997464829 0.0298758604 0.1699774035 -0.0640062468 -0.0540721456
#> [251] -0.1482951613 -0.2095806969 0.1119855614 -0.0860554957 -0.1934205594
#> [256] 0.0452462380 -0.0899852564 0.0460958908 0.0122916087 0.1264128592
#> [261] 0.1313453871 -0.1551098870 -0.0625048975 -0.0239876082 0.2116289250
#> [266] 0.0691184507 0.3174334897 -0.1326311560 -0.1840453114 0.0928070377
#> [271] -0.0092659836 0.2431864003 -0.3152921731 -0.1135321504 -0.1323303437
#> [276] -0.3182349141 0.0600239864 -0.1030674328 0.1027069528 -0.0276536687
#> [281] -0.1810559284 -0.1886982968 0.0787497948 -0.0657430444 -0.2404595224
#> [286] -0.0865565056 -0.0471573072 0.0613511639 -0.0999079679 -0.2818018021
#> [291] -0.0442723145 0.0891976304 0.0751979858 0.1040331496 0.0220023356
#> [296] 0.0235315182 0.0285487291 -0.0316641593 -0.0895204279 0.2007698928
#> [301] -0.0155904164 -0.1829885597 -0.1238572856 0.1081255130 0.2682829969
#> [306] -0.1122761622 0.0827849038 -0.2057422666 0.0117932059 -0.1858770552
#> [311] 0.0482826847 0.0541096726 -0.1653076037 -0.3112511717 -0.0472943857
#> [316] -0.2339606689 -0.1476056014 -0.2111074499 0.2680141676 0.0382606803
#> [321] -0.1905502487 0.1232286530 0.0305676943 -0.0303441317 0.2194242336
#> [326] -0.0934246167 -0.0964947897 0.0599945466 0.0097744028 -0.1233614547
#> [331] 0.1397548721 -0.1864649775 -0.0132862803 -0.1631059348 0.2012046829
#> [336] -0.2137128430 0.0482949440 -0.0931087058 0.0084583162 0.2526576840
#> [341] 0.2901431160 -0.0317316706 0.0640989928 0.0424809160 0.0429083011
#> [346] -0.0751343192 -0.1636091991 0.1069248818 0.1503598776 0.1079327361
#> [351] -0.0423151822 0.1020294660 -0.0948752290 -0.1756744531 0.1734697036
#> [356] -0.2017766929 0.1057856812 -0.1182409872 0.0341355381 0.0185815752
#> [361] -0.0295818874 0.0824067862 0.2014678892 0.0479455707 -0.0969341075
#> [366] 0.3005632802 -0.1295459561 0.0121499463 -0.0617995405 0.1260984050
#> [371] -0.0882132172 -0.2037085869 -0.1587693544 0.0463232043 -0.0538628069
#> [376] -0.0633888354 -0.0497564714 -0.0213684836 0.0340537274 0.0848439658
#> [381] -0.0542664186 -0.0051140611 0.0475625445 0.2062204214 0.1987332457
#> [386] 0.0555401752 -0.1123690080 0.1275199132 0.1569128727 -0.1834188546
#> [391] 0.1521004038 -0.3240919926 0.0768563201 -0.1023058628 0.1000509769
#> [396] 0.0759662179 0.0161626319 0.0730624245 0.0415505063 0.1342673723
#> [401] -0.1875485322 -0.0055424400 0.0147965531 -0.0562244263 0.0278579997
#> [406] 0.1724046847 0.3510056528 0.4343357181 -0.1758344059 0.0557723133
#> [411] -0.0114169695 0.2429392409 0.2372523999 -0.0519432788 -0.0118540268
#> [416] -0.0913023396 0.0406268803 -0.1862875618 0.0403799048 -0.0851092951
#> [421] -0.1151636926 -0.2361100612 0.0124439336 -0.1243744591 -0.0621407588
#> [426] 0.0878662806 0.1385481396 -0.0119558188 -0.0625088007 -0.0532719073
#> [431] -0.0013379676 0.1598859843 -0.0764428376 -0.1254178601 -0.2298039163
#> [436] 0.2521697123 0.3358460795 -0.0504899956 -0.2710032506 -0.0300113882
#> [441] -0.0173991876 -0.1512402122 -0.0923089181 -0.0497080448 -0.0608731900
#> [446] 0.1981689523 0.0655701226 0.1278420250 -0.1467586552 0.2634975352
#> [451] -0.1872093732 -0.0828933133 -0.1842211999 -0.1708661465 -0.2606099090
#> [456] 0.1698849980 0.1862633712 0.0684394486 -0.3639741539 -0.0628476108
#> [461] -0.1495314820 -0.1813484200 0.0048007364 -0.1027754965 0.1336270102
#> [466] 0.0939531458 0.1933918919 0.1109868974 -0.0618336404 -0.0912513598
#> [471] -0.0578923077 -0.0119484252 0.0117394832 -0.0083477188 0.1151025277
#> [476] 0.0781987981 -0.0624603040 -0.1629752482 0.0537779890 -0.0819131533
#> [481] 0.1642242720 0.1017726614 -0.1366983078 0.2330815433 -0.0899095006
#> [486] -0.2242324130 0.1577292866 0.1617655922 0.0682602470 -0.1710111620
#> [491] 0.0268223703 0.0099450161 0.2196992509 -0.2983512074 0.1063512347
#> [496] 0.0513292983 -0.3291468807 -0.1748924305 -0.0569738485 0.0522397892
#> [501] -0.1427115480 0.4144500756 -0.2087938321 0.3390529693 -0.2719873225
#> [506] -0.2873427644 0.1476785490 -0.1370318899 -0.0287296928 0.0040195750
#> [511] 0.0199023010 0.1064973885 -0.0685793104 -0.3642090351 0.0970521438
#> [516] -0.0088153427 -0.1189828199 -0.0383988293 -0.0320378416 0.0524591590
#> [521] 0.2539644228 0.1746863231 0.1898155547 0.1523504015 -0.0336327863
#> [526] 0.1924139471 -0.0109297568 0.0730436540 -0.0565499713 0.0048440531
#> [531] 0.0973733664 -0.0592515106 0.1605637238 0.0154758682 -0.1810787409
#> [536] 0.1166242472 0.0636059660 -0.1673445713 0.3309324168 -0.2625035030
#> [541] 0.3419258346 -0.1804182490 -0.2095788238 -0.0467869900 0.0718738793
#> [546] 0.1892941196 0.1322611620 -0.3811398549 -0.0379008475 -0.0043896556
#> [551] -0.1559814069 -0.0234275926 0.0035518300 -0.0362537210 0.2099642178
#> [556] 0.1028282763 0.0887242576 0.0872483139 0.0767859261 -0.1996589417
#> [561] 0.0777836828 -0.1693851571 -0.1725283548 0.1073478018 -0.3195715534
#> [566] 0.2094077738 -0.0187960371 0.0383788867 -0.0714880663 0.1047870573
#> [571] -0.0557190297 -0.0986109751 -0.1517674358 -0.0451045197 -0.1852659041
#> [576] 0.0812767782 0.1650602658 0.0219596675 0.1321822847 0.1562299456
#> [581] 0.1629855180 0.0239379668 -0.2060780158 0.1476298261 0.0409370525
#> [586] 0.2609200993 -0.1646178316 0.1181538874 -0.0791342853 0.1958781545
#> [591] 0.0728809413 0.1181279560 0.0047948536 -0.1144966122 0.1162731345
#> [596] -0.0725300029 -0.1120074552 -0.1441840449 -0.2911872768 -0.0367948876
#> [601] 0.1570682287 0.0105531083 -0.0257726610 -0.1332894097 -0.2150934826
#> [606] 0.0346993571 0.1365586302 -0.0849798892 0.0134155746 -0.0534053145
#> [611] -0.1333601657 -0.1642224519 -0.0379186047 0.1198927399 -0.0022658460
#> [616] 0.0161072655 0.0898843695 0.0698495033 -0.0472002686 0.0399533507
#> [621] 0.1532110858 0.0302459890 -0.1273540794 0.1778215602 0.0973945512
#> [626] 0.0297186390 0.3028071684 -0.0748414142 -0.1298010301 0.0488328565
#> [631] -0.0235443964 0.0204459958 0.1902006531 0.2497275595 0.0001264883
#> [636] -0.0023881900 -0.0854310675 -0.1061799228 0.0463195974 0.3506446040
#> [641] -0.0779527879 0.0142852854 -0.2620205215 -0.0269392812 -0.0187311913
#> [646] -0.0220865405 0.0756664313 0.1130348104 -0.1123329264 0.1105275854
#> [651] -0.1153042158 -0.1127024923 -0.0442904311 0.0214602494 -0.0346204217
#> [656] 0.1179460648 -0.1099485019 -0.0411225753 -0.3682290497 -0.1237639674
#> [661] -0.0503448843 0.1881249083 0.0682841969 0.1493684363 0.1184692589
#> [666] -0.0421691396 0.1051551022 -0.0885545211 0.3682153828 -0.0542102638
#> [671] 0.0306572538 0.0278862768 0.1230431972 0.1322359794 0.0049552623
#> [676] -0.2126544397 0.0965758795 0.0700137223 -0.0771765969 -0.0754156987
#> [681] 0.2314994019 -0.1109860803 0.1779600654 -0.1327624070 -0.0367183726
#> [686] 0.1857551575 -0.0731959938 -0.1304854178 -0.1262911158 -0.2682988267
#> [691] 0.0375998626 0.0422450792 -0.0564476685 0.0438129194 0.0403574826
#> [696] 0.0583017986 -0.0439731862 0.2240660515 0.0661118953 -0.1561077959
#> [701] 0.1043137170 -0.0600542008 -0.0865837440 -0.1264735067 0.2099392677
#> [706] -0.2186563075 0.1041315419 -0.0880774744 -0.2813472652 -0.0425487442
#> [711] 0.0642005073 0.0753521077 0.1021830112 -0.0118121896 -0.1718996086
#> [716] -0.0412375206 -0.0067440066 0.2129315596 0.1349510690 -0.1190423786
#> [721] -0.1118276530 0.0538337815 -0.1825811776 0.1638277585 0.1424970839
#> [726] 0.1374481232 0.0905036677 -0.1447286232 0.1395014806 -0.0543208682
#> [731] 0.1639504921 -0.1782942236 -0.2406659218 0.1510395746 -0.0597234581
#> [736] 0.0328299029 0.3140805978 -0.1243193440 -0.0370583251 0.1910029126
#> [741] 0.0048072023 -0.0518566624 -0.0603608951 0.2814697413 -0.1575202951
#> [746] -0.0021182715 0.1003444469 -0.1517669263 0.0531479194 -0.0254452800
#> [751] -0.0949771637 0.0552657129 -0.1360147008 0.0039751529 -0.0124919021
#> [756] -0.1507432307 0.1632702367 0.1197951881 -0.3201253591 -0.0044128993
#> [761] 0.0384080108 -0.2196791610 0.0724621846 -0.2154391467 -0.3551507940
#> [766] 0.0540231783 -0.0257219959 -0.0310546262 -0.0065530655 0.2420266202
#> [771] 0.0433343143 0.0249337533 -0.0030768205 0.2616075356 -0.2034210256
#> [776] 0.0984694693 -0.1427473344 0.0358651495 0.0159088245 -0.2119958558
#> [781] -0.1359896292 0.2555519611 0.1815617364 0.2360397141 0.1318488136
#> [786] -0.0811956760 -0.0055971714 -0.1110171828 0.0675340075 0.0771727390
#> [791] 0.1331084662 -0.2251141592 0.0824973660 -0.1492476964 0.1299766820
#> [796] -0.0407740551 0.1900232411 -0.1656252125 -0.0154279124 0.1429599118
#> [801] 0.0798248297 0.0621507477 0.0950039206 -0.2063742657 0.3149837258
#> [806] 0.1748415452 -0.2656502475 0.1403408703 -0.0684223760 -0.3010588773
#> [811] 0.1259931976 -0.1645169331 0.1115392551 0.1912482751 0.0270066700
#> [816] -0.0241098687 -0.1718704167 -0.1874084130 -0.0192477465 -0.1598113658
#> [821] -0.1227618351 -0.0876584739 -0.0746881138 -0.1555759850 -0.4341084815
#> [826] -0.1426241681 0.2048242135 -0.0925986398 -0.0307432095 0.2285401953
#> [831] -0.0221304922 0.0971854294 0.0367450259 -0.0390898279 0.2100708116
#> [836] -0.2435014121 -0.1480091112 0.0808665562 -0.0017246648 0.1371053254
#> [841] 0.0180083703 0.1386388188 0.1525811761 -0.1568087570 0.1048257447
#> [846] 0.2360468306 0.0670457401 0.0179799142 -0.0311369091 0.1023791762
#> [851] 0.0424214438 0.1892956681 -0.0743178638 -0.0567450416 0.2064460707
#> [856] 0.1085074388 -0.0261886968 -0.1844991071 0.0680486054 0.0142891025
#> [861] 0.0180162545 -0.2557733429 0.0110885371 0.0478384417 -0.2333479946
#> [866] 0.0901236344 0.0036761755 -0.1136056109 -0.0483787257 0.0803637999
#> [871] -0.1540924064 -0.2884544531 -0.0808763843 -0.1547849521 -0.0991758271
#> [876] -0.1505915717 -0.1371534246 -0.1299176710 0.1958809024 0.1175911868
#> [881] -0.5205492080 -0.2123399740 0.1486976389 -0.0841996510 -0.1129486073
#> [886] 0.1322874189 -0.1069095766 -0.0824928431 -0.0353857254 0.0808021079
#> [891] -0.0308439087 -0.1117025481 -0.1033804278 0.0065826881 -0.0953071054
#> [896] -0.0133052502 0.0069616022 0.0521054635 -0.0252983422 -0.2316776743
#> [901] 0.0456794789 0.0318204613 -0.0084840939 -0.1077095940 -0.0014354622
#> [906] -0.0717450071 0.1073793575 0.1621269344 -0.0717876040 -0.3415592953
#> [911] -0.0337487667 -0.2600319005 -0.0989263191 -0.0181474582 -0.0873560932
#> [916] 0.2404724806 0.1788770175 0.2177977235 0.0723254952 0.1085071631
#> [921] -0.2255846608 -0.0709775368 -0.2000190136 0.3176013251 -0.0052267201
#> [926] 0.1390713438 0.0279773664 0.1775998231 -0.0246940721 0.0611700394
#> [931] -0.0698090851 -0.2570942101 -0.0800591301 0.0485347157 0.0006717066
#> [936] -0.2945416062 -0.2192613858 -0.1315992194 0.0396837672 -0.1833431751
#> [941] 0.1275100281 -0.1096040258 -0.1531059323 -0.1969587278 0.1956228281
#> [946] 0.1210873882 0.2844036913 0.2712857026 -0.0125685907 -0.1258770780
#> [951] -0.0069178159 0.3202360067 -0.0908832363 0.0413500343 0.1295436897
#> [956] -0.0723203119 -0.1690895659 0.1629513997 0.0978899519 -0.0585914273
#> [961] -0.0683073599 -0.2011760180 0.1602810708 0.0279853146 0.1092307088
#> [966] -0.0118609913 -0.0847651286 0.0085064500 -0.1956153895 0.2670697960
#> [971] 0.0296238653 -0.0566374687 -0.0355548448 0.0334744900 0.2136469328
#> [976] -0.2568335148 0.0652873854 -0.0041542667 0.1299098874 0.1704002657
#> [981] -0.1539353004 0.1761691216 -0.1726126738 -0.2722543865 0.0249404847
#> [986] -0.1406384271 0.0893540437 -0.0654371494 0.0960738561 0.0704588783
#> [991] -0.1435887775 0.1840633523 0.1238326665 0.0564036200 0.0188716450
#> [996] -0.0212356030 0.1440478833 -0.1888979500 0.1246486183
#>
mantel_test(G, W, method = "kendall") # use of alternative test statistic
#> $stat
#> [1] 0.03232323
#>
#> $quantile
#> [1] 0.6186186
#>
#> $p.value
#> [1] 0.7627628
#>
#> $perm
#> [1] -0.044444444 -0.153535354 -0.080808081 0.109090909 -0.101010101
#> [6] -0.153535354 0.048484848 -0.064646465 -0.080808081 0.113131313
#> [11] -0.109090909 0.056565657 0.052525253 -0.036363636 0.072727273
#> [16] -0.141414141 -0.145454545 0.129292929 0.068686869 0.068686869
#> [21] 0.032323232 -0.133333333 0.036363636 0.096969697 -0.016161616
#> [26] -0.056565657 0.004040404 -0.076767677 0.101010101 -0.169696970
#> [31] 0.202020202 0.056565657 -0.113131313 -0.044444444 0.012121212
#> [36] 0.165656566 -0.068686869 0.117171717 -0.165656566 0.056565657
#> [41] 0.052525253 0.105050505 -0.008080808 -0.101010101 0.036363636
#> [46] -0.032323232 0.008080808 0.141414141 -0.016161616 0.072727273
#> [51] 0.113131313 -0.040404040 0.092929293 -0.117171717 0.129292929
#> [56] 0.088888889 0.088888889 0.032323232 -0.052525253 0.004040404
#> [61] -0.068686869 0.105050505 0.048484848 0.068686869 -0.101010101
#> [66] 0.000000000 0.008080808 0.036363636 -0.109090909 -0.105050505
#> [71] -0.012121212 -0.149494949 -0.189898990 -0.084848485 0.096969697
#> [76] -0.044444444 -0.121212121 -0.117171717 0.060606061 0.068686869
#> [81] 0.080808081 -0.020202020 -0.028282828 0.060606061 0.028282828
#> [86] 0.044444444 0.084848485 0.020202020 -0.020202020 0.008080808
#> [91] 0.036363636 -0.117171717 -0.072727273 -0.064646465 -0.096969697
#> [96] 0.012121212 0.000000000 -0.092929293 -0.012121212 0.060606061
#> [101] 0.048484848 0.040404040 -0.088888889 -0.149494949 -0.032323232
#> [106] 0.282828283 0.169696970 -0.060606061 0.048484848 0.137373737
#> [111] 0.036363636 -0.125252525 -0.032323232 -0.088888889 0.141414141
#> [116] 0.181818182 -0.012121212 0.096969697 0.044444444 -0.036363636
#> [121] -0.153535354 0.028282828 0.020202020 0.060606061 -0.060606061
#> [126] 0.133333333 0.024242424 0.036363636 0.040404040 -0.008080808
#> [131] 0.109090909 -0.032323232 0.012121212 0.125252525 -0.068686869
#> [136] -0.044444444 0.105050505 -0.012121212 0.020202020 -0.121212121
#> [141] 0.024242424 -0.121212121 -0.109090909 -0.024242424 0.040404040
#> [146] 0.218181818 -0.048484848 -0.004040404 -0.024242424 0.064646465
#> [151] -0.161616162 -0.096969697 -0.036363636 -0.145454545 0.060606061
#> [156] 0.008080808 -0.004040404 -0.016161616 0.052525253 -0.145454545
#> [161] -0.052525253 0.032323232 0.068686869 0.020202020 0.060606061
#> [166] -0.096969697 -0.072727273 0.020202020 0.109090909 0.016161616
#> [171] -0.064646465 0.080808081 0.000000000 0.064646465 0.076767677
#> [176] -0.113131313 0.052525253 -0.076767677 -0.117171717 -0.157575758
#> [181] -0.052525253 -0.282828283 -0.133333333 0.020202020 0.084848485
#> [186] -0.084848485 -0.064646465 -0.004040404 -0.165656566 0.105050505
#> [191] -0.012121212 -0.036363636 0.024242424 0.020202020 0.129292929
#> [196] 0.056565657 0.024242424 -0.072727273 -0.056565657 0.040404040
#> [201] -0.036363636 -0.080808081 -0.084848485 -0.040404040 -0.088888889
#> [206] 0.113131313 -0.121212121 -0.072727273 -0.185858586 -0.056565657
#> [211] -0.040404040 0.024242424 -0.206060606 0.056565657 -0.008080808
#> [216] 0.008080808 0.092929293 -0.113131313 -0.096969697 -0.004040404
#> [221] -0.028282828 0.080808081 0.109090909 -0.032323232 0.242424242
#> [226] 0.036363636 0.044444444 -0.012121212 -0.076767677 -0.048484848
#> [231] 0.105050505 0.020202020 -0.145454545 0.117171717 0.076767677
#> [236] -0.004040404 0.024242424 -0.173737374 0.024242424 0.101010101
#> [241] -0.008080808 0.020202020 -0.169696970 0.056565657 -0.052525253
#> [246] 0.036363636 0.016161616 -0.117171717 -0.133333333 -0.040404040
#> [251] 0.008080808 -0.080808081 0.105050505 -0.185858586 0.117171717
#> [256] 0.036363636 -0.064646465 -0.008080808 0.044444444 0.012121212
#> [261] 0.113131313 0.185858586 -0.076767677 -0.008080808 0.008080808
#> [266] -0.109090909 -0.084848485 0.076767677 -0.060606061 -0.125252525
#> [271] 0.004040404 -0.064646465 -0.096969697 -0.153535354 -0.101010101
#> [276] -0.036363636 0.024242424 -0.125252525 0.141414141 0.052525253
#> [281] -0.040404040 0.096969697 0.189898990 0.169696970 0.084848485
#> [286] 0.177777778 -0.137373737 -0.121212121 -0.016161616 0.181818182
#> [291] -0.105050505 -0.121212121 0.068686869 -0.153535354 0.032323232
#> [296] 0.113131313 -0.113131313 0.000000000 -0.068686869 0.109090909
#> [301] -0.032323232 -0.044444444 -0.020202020 -0.040404040 -0.084848485
#> [306] 0.032323232 0.008080808 -0.032323232 -0.072727273 -0.080808081
#> [311] 0.056565657 0.193939394 0.064646465 0.161616162 0.109090909
#> [316] -0.113131313 0.012121212 -0.084848485 -0.076767677 0.096969697
#> [321] -0.125252525 0.028282828 0.238383838 -0.177777778 -0.056565657
#> [326] 0.173737374 -0.222222222 0.117171717 -0.004040404 -0.181818182
#> [331] -0.092929293 0.084848485 -0.092929293 0.084848485 0.028282828
#> [336] 0.032323232 0.214141414 0.052525253 -0.028282828 0.088888889
#> [341] -0.092929293 -0.129292929 0.056565657 0.048484848 0.028282828
#> [346] 0.024242424 -0.016161616 -0.024242424 -0.012121212 -0.185858586
#> [351] 0.000000000 0.129292929 -0.230303030 -0.088888889 -0.060606061
#> [356] 0.064646465 -0.068686869 -0.024242424 0.068686869 -0.052525253
#> [361] 0.064646465 -0.266666667 0.036363636 -0.028282828 -0.068686869
#> [366] 0.206060606 -0.084848485 -0.052525253 0.278787879 0.109090909
#> [371] 0.141414141 -0.125252525 -0.080808081 -0.088888889 -0.028282828
#> [376] -0.141414141 0.020202020 -0.096969697 -0.165656566 0.064646465
#> [381] -0.064646465 -0.068686869 -0.004040404 0.012121212 0.161616162
#> [386] -0.004040404 0.012121212 0.060606061 -0.254545455 0.044444444
#> [391] 0.028282828 0.068686869 -0.056565657 0.105050505 -0.032323232
#> [396] -0.189898990 0.024242424 -0.044444444 0.052525253 0.028282828
#> [401] 0.044444444 -0.020202020 0.004040404 -0.004040404 -0.016161616
#> [406] -0.101010101 -0.129292929 0.129292929 0.125252525 0.008080808
#> [411] -0.096969697 -0.113131313 -0.064646465 0.024242424 -0.092929293
#> [416] 0.044444444 0.032323232 -0.141414141 0.036363636 -0.092929293
#> [421] 0.028282828 -0.068686869 0.088888889 0.068686869 -0.161616162
#> [426] 0.117171717 0.056565657 0.044444444 0.004040404 0.056565657
#> [431] 0.169696970 -0.020202020 0.129292929 0.052525253 0.052525253
#> [436] -0.101010101 0.113131313 0.117171717 -0.177777778 0.064646465
#> [441] -0.012121212 0.044444444 0.153535354 -0.008080808 -0.125252525
#> [446] -0.177777778 0.028282828 -0.044444444 0.060606061 0.133333333
#> [451] -0.169696970 -0.173737374 0.044444444 0.189898990 0.052525253
#> [456] 0.072727273 0.016161616 0.000000000 -0.109090909 0.210101010
#> [461] -0.016161616 0.020202020 0.024242424 0.080808081 0.404040404
#> [466] 0.092929293 -0.137373737 0.088888889 -0.177777778 0.048484848
#> [471] 0.133333333 -0.052525253 0.157575758 0.000000000 -0.064646465
#> [476] 0.133333333 -0.020202020 0.117171717 0.064646465 -0.101010101
#> [481] 0.052525253 -0.274747475 0.117171717 0.000000000 0.072727273
#> [486] 0.125252525 0.101010101 0.016161616 -0.076767677 0.004040404
#> [491] 0.125252525 0.028282828 0.181818182 0.056565657 -0.048484848
#> [496] 0.214141414 0.068686869 0.012121212 0.024242424 0.088888889
#> [501] -0.064646465 -0.113131313 0.000000000 0.020202020 0.004040404
#> [506] 0.036363636 0.137373737 -0.040404040 0.092929293 -0.121212121
#> [511] -0.016161616 0.048484848 -0.032323232 -0.016161616 -0.056565657
#> [516] -0.161616162 -0.012121212 -0.088888889 -0.056565657 0.000000000
#> [521] -0.113131313 -0.004040404 -0.020202020 -0.012121212 0.072727273
#> [526] 0.020202020 0.032323232 -0.096969697 0.016161616 0.117171717
#> [531] 0.000000000 -0.121212121 -0.036363636 0.012121212 0.056565657
#> [536] 0.109090909 0.096969697 0.024242424 -0.052525253 0.016161616
#> [541] -0.270707071 0.076767677 0.044444444 0.202020202 -0.315151515
#> [546] -0.084848485 -0.060606061 -0.129292929 0.024242424 -0.032323232
#> [551] 0.012121212 -0.109090909 -0.020202020 0.008080808 0.173737374
#> [556] 0.052525253 0.145454545 -0.165656566 -0.173737374 0.000000000
#> [561] -0.068686869 -0.109090909 0.137373737 -0.028282828 0.109090909
#> [566] -0.088888889 -0.145454545 -0.040404040 -0.246464646 0.008080808
#> [571] -0.056565657 0.016161616 0.016161616 -0.036363636 0.036363636
#> [576] 0.012121212 -0.032323232 0.072727273 0.068686869 0.060606061
#> [581] 0.004040404 0.076767677 -0.125252525 0.101010101 -0.088888889
#> [586] 0.056565657 -0.133333333 -0.113131313 0.080808081 -0.193939394
#> [591] -0.012121212 0.004040404 -0.092929293 0.177777778 -0.020202020
#> [596] 0.076767677 -0.072727273 -0.080808081 -0.020202020 0.105050505
#> [601] -0.121212121 -0.048484848 0.008080808 0.206060606 0.064646465
#> [606] 0.157575758 0.197979798 0.076767677 0.008080808 0.032323232
#> [611] -0.004040404 -0.064646465 0.068686869 0.000000000 0.076767677
#> [616] -0.036363636 0.133333333 0.024242424 0.076767677 -0.133333333
#> [621] -0.060606061 -0.177777778 -0.080808081 -0.084848485 0.032323232
#> [626] -0.036363636 0.028282828 -0.282828283 -0.185858586 0.048484848
#> [631] -0.024242424 -0.072727273 0.084848485 0.282828283 0.327272727
#> [636] -0.052525253 0.068686869 0.024242424 0.068686869 -0.056565657
#> [641] 0.068686869 -0.036363636 -0.109090909 -0.068686869 -0.125252525
#> [646] -0.024242424 0.040404040 -0.072727273 0.044444444 0.129292929
#> [651] 0.060606061 -0.157575758 0.044444444 0.189898990 -0.024242424
#> [656] 0.012121212 -0.056565657 0.080808081 0.080808081 0.169696970
#> [661] -0.068686869 0.294949495 0.072727273 -0.092929293 -0.076767677
#> [666] 0.036363636 -0.084848485 -0.064646465 -0.044444444 0.020202020
#> [671] 0.068686869 -0.109090909 0.125252525 0.036363636 -0.092929293
#> [676] 0.254545455 0.076767677 -0.157575758 0.206060606 -0.024242424
#> [681] -0.020202020 -0.092929293 -0.064646465 -0.080808081 0.056565657
#> [686] -0.024242424 -0.145454545 0.125252525 0.096969697 -0.032323232
#> [691] -0.060606061 -0.016161616 0.036363636 -0.056565657 0.024242424
#> [696] 0.004040404 0.145454545 -0.185858586 0.076767677 -0.072727273
#> [701] -0.048484848 -0.068686869 -0.084848485 0.008080808 -0.040404040
#> [706] 0.105050505 -0.206060606 0.004040404 0.072727273 0.036363636
#> [711] -0.048484848 0.060606061 0.028282828 0.145454545 0.105050505
#> [716] -0.137373737 -0.028282828 0.105050505 0.181818182 0.012121212
#> [721] -0.056565657 -0.028282828 -0.032323232 -0.072727273 -0.153535354
#> [726] -0.068686869 0.076767677 0.153535354 -0.105050505 -0.101010101
#> [731] 0.109090909 0.121212121 -0.020202020 -0.056565657 0.016161616
#> [736] 0.068686869 -0.008080808 0.080808081 0.141414141 0.044444444
#> [741] 0.113131313 -0.076767677 0.109090909 0.202020202 -0.105050505
#> [746] 0.133333333 -0.040404040 -0.238383838 -0.004040404 -0.008080808
#> [751] -0.117171717 -0.016161616 0.129292929 -0.020202020 0.210101010
#> [756] -0.028282828 0.020202020 -0.096969697 0.036363636 0.214141414
#> [761] -0.129292929 -0.117171717 -0.117171717 -0.117171717 -0.072727273
#> [766] 0.161616162 0.080808081 0.024242424 -0.012121212 -0.153535354
#> [771] -0.056565657 -0.193939394 -0.101010101 0.092929293 -0.024242424
#> [776] 0.133333333 -0.012121212 0.048484848 0.165656566 0.068686869
#> [781] 0.048484848 0.000000000 0.068686869 0.064646465 0.060606061
#> [786] 0.064646465 -0.040404040 0.125252525 -0.080808081 -0.008080808
#> [791] -0.149494949 0.040404040 0.153535354 0.137373737 -0.109090909
#> [796] -0.024242424 -0.052525253 -0.092929293 0.008080808 0.052525253
#> [801] -0.040404040 -0.044444444 0.092929293 -0.068686869 0.028282828
#> [806] 0.096969697 -0.064646465 0.036363636 0.008080808 0.210101010
#> [811] -0.153535354 0.169696970 0.092929293 0.185858586 0.080808081
#> [816] 0.177777778 -0.092929293 0.177777778 -0.105050505 -0.149494949
#> [821] -0.024242424 -0.020202020 -0.197979798 -0.096969697 0.016161616
#> [826] 0.157575758 0.000000000 0.129292929 0.101010101 0.028282828
#> [831] 0.052525253 -0.149494949 -0.008080808 0.076767677 0.016161616
#> [836] 0.016161616 0.060606061 -0.129292929 0.040404040 -0.129292929
#> [841] -0.040404040 -0.238383838 -0.044444444 0.008080808 -0.072727273
#> [846] 0.282828283 0.137373737 0.040404040 -0.056565657 0.020202020
#> [851] 0.064646465 0.016161616 -0.088888889 0.092929293 0.080808081
#> [856] -0.024242424 0.012121212 0.076767677 0.028282828 -0.092929293
#> [861] -0.274747475 -0.157575758 0.024242424 -0.028282828 -0.072727273
#> [866] -0.036363636 0.048484848 -0.024242424 -0.056565657 0.169696970
#> [871] -0.008080808 0.036363636 0.052525253 -0.238383838 0.004040404
#> [876] -0.157575758 -0.008080808 0.060606061 -0.282828283 0.169696970
#> [881] -0.193939394 -0.044444444 0.096969697 0.028282828 -0.137373737
#> [886] 0.036363636 -0.088888889 -0.084848485 0.270707071 -0.286868687
#> [891] -0.024242424 -0.032323232 0.096969697 0.000000000 0.052525253
#> [896] 0.004040404 -0.092929293 -0.125252525 0.056565657 0.040404040
#> [901] 0.149494949 -0.101010101 -0.040404040 -0.133333333 -0.072727273
#> [906] 0.040404040 0.064646465 -0.117171717 0.149494949 0.133333333
#> [911] -0.020202020 -0.028282828 -0.024242424 0.149494949 0.036363636
#> [916] 0.032323232 0.024242424 0.032323232 0.092929293 0.092929293
#> [921] 0.101010101 -0.060606061 -0.048484848 0.020202020 0.092929293
#> [926] 0.153535354 -0.048484848 -0.068686869 0.084848485 0.230303030
#> [931] -0.117171717 0.000000000 -0.197979798 0.101010101 -0.145454545
#> [936] 0.024242424 0.177777778 -0.060606061 0.084848485 -0.072727273
#> [941] -0.052525253 0.109090909 -0.230303030 -0.028282828 0.117171717
#> [946] 0.197979798 0.125252525 -0.092929293 -0.133333333 0.040404040
#> [951] 0.004040404 0.060606061 -0.052525253 0.060606061 0.076767677
#> [956] -0.020202020 0.084848485 -0.181818182 0.032323232 0.028282828
#> [961] 0.036363636 -0.036363636 0.008080808 -0.064646465 0.024242424
#> [966] -0.024242424 -0.076767677 -0.117171717 -0.080808081 -0.084848485
#> [971] 0.016161616 -0.137373737 -0.048484848 0.036363636 0.080808081
#> [976] -0.141414141 -0.092929293 -0.165656566 -0.028282828 -0.008080808
#> [981] -0.101010101 -0.149494949 -0.121212121 0.056565657 0.044444444
#> [986] -0.032323232 0.088888889 -0.016161616 0.012121212 0.008080808
#> [991] -0.028282828 0.141414141 0.020202020 0.084848485 0.088888889
#> [996] -0.109090909 -0.052525253 -0.165656566 -0.008080808
#>
# Demonstrate that the function matches vegan::mantel.partial output:
# (using only symmetric matrices, and just one control variable, since
# vegan does not work with asymmetric matrices or multiple controls)
if(requireNamespace("vegan", quietly = TRUE)){
a <- mantel_test(G, W, list(D), nperm = 999)
b <- vegan::mantel.partial(G, W, D, permutations = 999)
c(a$stat, b$statistic)
c(1 - a$quantile, b$signif) # will differ slightly due to randomization
}
#> [1] 0.4054054 0.4070000