Hi Listers,
I am trying to better understand how spatial autocorrelation is determined.
I have attached 2 txt files one is a fish species x sites abundance table
and the other is a distance file with the lat and longs for each site
(converted to cartesian coords). I have run the tests for spatial
correlation using the methodology from the Borcard et al. Use R! book.
The result was no significant spatial correlation. However an nmds
ordination of the fish data shows 3 very strongly clustered groups of sites
which corresponds to 3 oceanic islands. A permutation analysis of the fish
resemblance matrix with a distance matrix was also highly significant with
a rho=0.646 spearmans rank correlation. To my mind I would have thought
that with such strong groupings in the data that spatial correlation would
be present at the scale of islands? Can someone help me explain this result?
My analysis below
fish_hellinger <- decostand (fish,"hellinger")
fish.xy # spatial dataset space_ed.txt
#test for overall trend
lineartest <- anova(rda(fish_hellinger,fish.xy))
Permutation test for rda under reduced model
Model: rda(X = fish_hellinger, Y = fish.xy)
Df Var F N.Perm Pr(>F)
Model 2 0.17148 8.6098 199 0.005 ** ##significant linear trend
Residual 14 0.13942
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# fit linear trend to the fish data and then extract residuals for
subsequent use in spatial analysis
> fish_hellinger_detrended <- resid(lm(as.matrix(fish_hellinger)~
.,data=fish.xy))
# make a distance matrix from the residuals data for input to the
correlogram call
> fish_hellinger_D1 <- dist(fish_hellinger_detrended)
# perform the mantel-based test for spatial correlation
> (fish_correlogram <-
mantel.correlog(fish_hellinger_D1,XY=fish.xy,nperm=99))
Mantel Correlogram Analysis
Call:
mantel.correlog(D.eco = fish_hellinger_D1, XY = fish.xy, nperm = 99)
class.index n.dist Mantel.cor Pr(Mantel) Pr(corrected)
D.cl.1 118.013676 462.000000 -0.042424 0.11 0.11
D.cl.2 352.037024 0.000000 NA NA NA
D.cl.3 586.060371 0.000000 NA NA NA
D.cl.4 820.083719 0.000000 NA NA NA
D.cl.5 1054.107067 384.000000 0.033639 0.30 NA
D.cl.6 1288.130414 0.000000 NA NA NA
D.cl.7 1522.153762 0.000000 NA NA NA
D.cl.8 1756.177109 320.000000 NA NA NA
D.cl.9 1990.200457 0.000000 NA NA NA
D.cl.10 2224.223804 0.000000 NA NA NA
D.cl.11 2458.247152 240.000000 NA NA NA
--
cheers
Andy
Andrew Halford Ph.D
Research Scientist (Kimberley Marine Parks)
Dept. Parks and Wildlife
Western Australia
Ph: +61 8 9219 9795
Mobile: +61 (0) 468 419 473
LUT_GIBB LUT_FULV CHL_STRO SCA_PRAS NAS_LITU
KYP_VAIG LUT_BOHA SCA_RUBR NAS_UNIC HIP_HARI
APH_FURC NAS_ELEG CHL_ENNE KYP_CINE NAS_BREV
CEP_ARGU BOL_MURI LUT_KASM CHL_MICR LET_OBSE
LUT_DECU VAR_LOUT CET_BICO LUT_MONO NAS_VLAM
HIP_LONG CHE_UNDU GRA_ALBO NAS_CAES ACA_XANT
LUT_RIVU CEP_MINI COR_AYGU COR_GAIM LET_XANT
TRI_OBES NAS_FAGE PMS_LAEV LET_ERUS LET_OLIV
CAC_MELA CAC_AMBL EPI_FUSC NAS_HEXA PMS_AREO
APR_VIRE SCA_GHOB SCA_XANT EPI_TAUV EPI_POLY
EPI_MACR LET_EHUS AET_ROGA NAS_TONG VAR_ALBI
LET_HARA SYM_NEMA
Coc1 1 6 16 5 9 0 6 1 20
17 0 9 0 14 3 0 0 0 0
10 0 1 0 3 0 0 0 0 1
0 0 0 0 0 0 0 0 0 1
0 1 0 1 0 0 0 1 0 0
0 0 0 0 0 0 0 0
Coc4 0 0 1 24 12 0 0 7 4
24 0 15 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0
1 2 1 0 0 0 1 1 0 0
0 0 0 0 0 0 0 0
Coc8 5 21 22 19 15 6 4 6 8
11 0 28 0 3 7 0 0 0 0
5 0 1 0 2 0 0 2 0 0
0 0 0 2 2 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0
Coc12 0 0 40 20 6 0 0 5 6
19 0 16 4 0 0 0 0 0 0
2 0 3 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
Coc13 13 43 31 2 7 59 4 7 8
44 0 9 43 49 0 0 0 0 0
0 0 0 0 0 0 0 3 0 0
6 0 0 2 0 0 1 0 0 0
0 2 0 1 0 0 0 1 0 0
0 0 0 0 0 0 0 0
Coc16 96 89 34 30 4 4 0 3 3
20 0 5 8 5 0 0 0 0 0
6 0 0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 1 0 0
0 0 0 0 0 0 4 0
Coc18 3 3 20 26 13 0 1 0 0
15 0 8 0 0 0 1 0 0 0
0 0 1 0 3 8 0 1 1 0
0 0 0 1 0 0 2 0 0 0
0 0 5 3 0 0 0 1 0 0
0 1 0 0 0 0 0 0
Coc23 45 10 47 210 8 18 5 4 1
14 0 9 94 14 0 0 1 0 0
0 0 0 0 6 0 0 1 0 0
0 0 0 2 0 1 5 0 0 0
0 2 1 0 0 0 0 0 0 1
0 2 0 0 0 0 0 0
Coc25 0 186 22 15 5 0 0 5 8
16 0 3 11 0 0 0 2 0 0
0 0 2 0 0 0 0 5 0 0
0 0 0 0 0 1 0 0 0 0
0 2 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0
Coc28 44 452 78 30 10 0 1 4 9
20 0 16 12 0 0 0 0 0 0
0 0 2 0 2 0 0 2 0 0
0 0 0 0 0 5 0 0 0 0
0 2 0 2 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Coc34 5 13 21 17 6 0 7 2 5
29 0 15 10 0 0 1 0 0 0
14 0 0 0 0 0 0 0 0 0
0 0 0 3 0 0 0 0 0 1
0 1 0 0 0 0 0 1 0 0
0 1 0 0 0 0 0 0
Coc35 0 2 17 21 12 0 3 3 38
9 0 17 0 0 14 2 2 2 0
8 0 1 0 0 2 0 1 1 1
0 0 0 0 0 1 0 0 0 0
0 2 2 2 0 0 0 1 0 0
0 0 0 0 0 0 0 0
X1 0 0 1 0 0 38 13 11 0
0 14 0 1 17 6 4 0 0 0
0 0 1 0 0 3 0 0 12 15
0 0 5 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0
X2 0 0 0 0 7 12 11 12 0
0 13 0 0 6 0 5 0 0 0
0 0 3 0 0 0 0 0 0 3
0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
X4 0 0 0 0 8 16 3 16 1
0 22 1 0 1 0 5 0 13 0
0 0 3 0 0 0 0 0 2 0
1 0 10 0 3 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0
X7 0 0 2 0 2 0 5 21 0
0 21 0 0 0 8 11 0 0 2
0 0 6 0 0 0 0 0 0 0
0 1 0 1 2 0 0 0 0 0
0 0 0 0 2 0 0 0 1 0
0 0 0 0 0 0 0 0
X9 0 0 8 0 7 1 3 29 0
0 29 0 5 0 1 5 0 0 0
0 0 9 0 0 0 0 0 0 26
0 0 0 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
X10 2 0 3 3 5 6 10 15 0
0 20 0 0 0 2 10 0 0 0
0 0 5 1 0 3 0 1 4 3
0 0 5 0 0 0 0 0 0 0
0 0 0 0 2 0 0 0 0 0
0 0 0 0 0 1 0 0
X11 1 0 7 3 10 8 17 13 0
0 24 0 0 2 2 0 0 0 0
0 0 4 0 0 0 0 0 10 5
0 0 10 0 4 0 0 0 0 0
0 0 0 0 1 0 0 0 6 0
0 0 0 0 0 0 0 0
X12 0 0 2 0 9 0 6 16 0
0 21 0 0 0 0 5 0 0 0
0 0 5 1 0 0 0 0 5 2
0 0 6 2 0 0 0 0 0 0
0 0 0 0 6 0 0 0 0 0
0 0 0 0 0 1 0 0
X14 0 0 0 1 19 36 4 101 4
0 20 0 0 0 2 1 0 0 0
0 0 3 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0
0 0 0 0 4 0 0 0
X16 0 0 0 0 8 16 8 16 2
0 26 0 0 8 8 4 0 0 0
0 0 3 0 0 2 0 0 5 4
0 0 5 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0
X18 0 0 4 0 8 5 10 31 4
0 45 0 0 0 2 0 0 0 0
0 0 1 0 0 0 0 0 0 2
0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 1 0 3 0
0 0 0 0 0 0 0 0
X19 1 0 0 0 7 3 9 29 0
0 10 0 0 0 1 3 0 0 0
0 0 7 0 1 0 0 0 0 1
0 0 0 0 2 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 2 0 0
X20 0 0 0 0 11 52 18 29 2
0 19 0 0 0 4 0 0 2 0
0 0 7 0 0 0 0 0 2 0
0 0 0 0 3 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
X21 16 0 0 0 14 40 14 15 1
0 21 2 0 2 3 6 0 1 0
0 0 14 0 0 0 0 0 3 2
0 0 0 0 2 0 1 0 0 0
0 0 2 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0
X22 0 0 0 0 14 48 18 17 1
0 30 0 0 0 0 7 0 12 0
0 0 2 0 0 0 0 0 0 0
2 0 3 0 6 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
X24 0 0 2 5 6 12 8 7 0
0 26 0 0 2 0 7 0 0 0
0 0 5 0 0 0 0 0 4 2
0 0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 2 0 0 0
0 0 0 1 0 0 0 0
Cl1 11 0 0 4 9 0 22 0 21
0 3 0 0 0 4 11 12 23 10
0 8 0 10 0 15 9 1 0 0
41 0 0 1 0 4 0 13 6 3
1 0 1 0 8 1 3 0 0 0
0 0 0 0 0 0 0 0
Cl2 2 0 0 2 19 0 6 0 7
0 3 0 0 0 0 12 10 70 4
1 8 1 7 0 6 2 4 2 0
0 0 0 1 2 1 1 1 1 4
0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0
Cl3 3 0 0 0 21 0 1 0 1
0 7 0 0 0 41 4 0 0 6
0 9 2 25 0 3 0 2 0 0
0 0 0 1 2 2 0 0 0 8
4 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0
Cl5 83 0 0 1 19 0 18 5 10
0 7 0 0 0 19 15 0 1 29
0 41 0 7 0 0 9 6 0 0
0 0 0 0 2 1 1 0 5 0
1 0 0 0 0 1 0 0 0 0
0 0 1 0 1 0 0 0
Cl6 70 0 0 1 46 0 46 4 0
0 4 0 0 0 12 7 0 0 12
0 21 1 12 0 6 7 9 0 0
0 4 0 2 1 1 3 2 2 2
1 0 2 0 1 1 0 0 1 0
0 0 0 0 0 0 0 2
Imp1 61 0 0 0 2 3 13 0 15
0 4 0 0 0 5 12 7 7 6
1 13 3 10 0 3 2 5 0 0
18 6 0 5 1 0 1 0 1 0
3 0 1 0 0 0 2 0 0 0
0 0 0 0 0 0 0 0
Imp2 9 0 0 2 18 2 9 4 1
0 6 0 0 1 0 2 1 0 31
0 13 0 3 1 0 18 6 0 0
0 1 0 2 0 2 0 0 3 0
2 0 0 1 0 2 3 0 0 0
0 0 0 1 0 0 0 0
Imp4 6 0 0 2 22 0 9 0 20
0 7 0 0 0 9 12 0 0 24
0 13 4 16 0 0 0 3 0 0
0 0 0 2 3 0 0 0 0 1
6 0 0 0 0 6 0 0 0 0
5 0 0 0 0 0 0 0
Imp7 15 0 0 0 6 0 11 1 47
0 4 0 0 4 13 10 0 0 16
0 15 0 10 0 6 2 5 0 0
3 14 0 0 0 2 2 0 7 1
2 0 2 0 1 0 1 0 0 2
0 0 5 1 0 0 0 0
Imp9 195 0 0 0 16 6 13 6 32
0 1 0 0 6 16 10 11 0 5
0 5 2 11 0 0 7 4 0 0
3 0 0 2 0 0 3 8 3 0
3 0 3 0 0 1 1 0 0 0
0 0 0 0 0 0 0 0
LAT LONG
Coc1 10780.76 -1335.326
Coc4 10779.5 -1335.06
Coc8 10785.59 -1337.317
Coc12 10780.08 -1336.277
Coc13 10777.29 -1342.804
Coc16 10777.62 -1345.016
Coc18 10778.98 -1339.375
Coc23 10780.52 -1337.295
Coc25 10778.78 -1348.324
Coc28 10780.47 -1350.227
Coc34 10784.83 -1336.664
Coc35 10785.78 -1338.755
X1 11750.95 -1155.076
X2 11754.07 -1156.99
X4 11750.57 -1158.306
X7 11747.88 -1162.078
X9 11749.43 -1155.939
X10 11763.62 -1151.669
X11 11764.79 -1151.835
X12 11766.23 -1151.47
X14 11767.03 -1153.384
X16 11767.1 -1155.994
X18 11766.98 -1158.239
X19 11765.28 -1159.777
X20 11763.99 -1162.885
X21 11762.99 -1166.181
X22 11759.46 -1156.282
X24 11762.2 -1153.782
Cl1 13287.19 -1908.418
Cl2 13286.38 -1907.632
Cl3 13288.95 -1911.594
Cl5 13283.59 -1909.513
Cl6 13282.85 -1911.118
Imp1 13241.55 -1935.344
Imp2 13242.79 -1935.809
Imp4 13243.45 -1937.547
Imp7 13237.1 -1941.398
Imp9 13235.16 -1944.386
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