Web-Spider Ecological Community: Redundancy Analysis (RDA)
1 Redundancy Analysis
Redundancy Analysis (RDA) is a method to extract the variation in a set of response variables that explained by a set of non-numerical explanatory variables with a direct gradient analysis technique. Gradient Analysis technique can be constructed by a linear model setting with a set of significant explanatory variables, which can be further extended with multiple linear regression (MLR) version. A matrix of the fitted values of all response variables generated through MLR is also subject to principal components analysis (PCA).
Simply speakingly, Redundancy Analysis (RDA) is a constrained version of principal components analysis (PCA), where canonical axes is the linear combinations of the explanatory variables fitted by MLR. The RDA approach can generate ordinations in the space for the matrix of non-numerical response variables and for explanatory non-numerical response variables. Ordination methods is a transformation of non-numerical variables to numerical values which are either based on Euclidean distances (RDA) or Hellinger-chord (tb-RDA) distances. Ordination approach is commonly used in numerical ecological modeling. Details can refer to
- Legendre and Gallagher (2001)
- Zuur, Ieno, and Smith (2007)
- Legendre and Legendre (2012)
- Borcard, Gillet, and Legendre (2018)
1.1 Hellinger-Chord Distances
Figure 1.1: sourced from Legendre and Gallagher (2001)
1.2 Unconstrainted Ordination
Figure 1.2: sourced from Legendre and Gallagher (2001)
1.3 Constrainted Ordination
Figure 1.3: sourced from Legendre and Gallagher (2001)
1.4 Hellinger Distances
Figure 1.4: sourced from Legendre and Gallagher (2001)
1.5 Chord Distances
Figure 1.5: sourced from Legendre and Gallagher (2001)
2 Load Spider Dataset
2.1 Spider Metacommunity
2.2 Environmental Dataset
2.3 Spider Dataset
2.4 census.comm
2.5 census.env
2.6 Hellinger-transformed community dataset
3 RDA Modeling of Web-Spiders
3.1 Environmental variables Setting
CA.full <- rda(comm.Hellinger ~ log10(tangle.vol.cm3) + Host + cld.num + sociality +
Year, scale = FALSE, data = data.env)
CA.fullCall: rda(formula = comm.Hellinger ~ log10(tangle.vol.cm3) + Host +
cld.num + sociality + Year, data = data.env, scale = FALSE)
Inertia Proportion Rank
Total 0.4035 1.0000
Constrained 0.1139 0.2823 6
Unconstrained 0.2896 0.7177 18
Inertia is variance
Some constraints were aliased because they were collinear (redundant)
Eigenvalues for constrained axes:
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6
0.04434 0.03326 0.02478 0.00519 0.00478 0.00155
Eigenvalues for unconstrained axes:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
0.06552 0.04400 0.04270 0.02975 0.01933 0.01760 0.01263 0.01000
(Showing 8 of 18 unconstrained eigenvalues)step.forward <- ordistep(rda(comm.Hellinger ~ 1, scale = FALSE, data = data.env),
scope = formula(CA.full), direction = "forward", pstep = 1000)
Start: comm.Hellinger ~ 1
Df AIC F Pr(>F)
+ Host 3 -166.82 13.9008 0.005 **
+ sociality 1 -148.50 15.9602 0.005 **
+ cld.num 1 -143.28 10.3537 0.005 **
+ Year 1 -136.95 3.8149 0.005 **
+ log10(tangle.vol.cm3) 1 -136.51 3.3741 0.005 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Step: comm.Hellinger ~ Host
Df AIC F Pr(>F)
+ log10(tangle.vol.cm3) 1 -169.86 4.9548 0.005 **
+ Year 1 -169.68 4.7698 0.005 **
+ cld.num 1 -165.80 0.9477 0.420
+ sociality 0 -166.82
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Step: comm.Hellinger ~ Host + log10(tangle.vol.cm3)
Df AIC F Pr(>F)
+ Year 1 -173.82 5.8359 0.005 **
+ cld.num 1 -168.84 0.9442 0.520
+ sociality 0 -169.86
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Step: comm.Hellinger ~ Host + log10(tangle.vol.cm3) + Year
Df AIC F Pr(>F)
+ cld.num 1 -172.88 1.0154 0.485
+ sociality 0 -173.82 step.forward$termscomm.Hellinger ~ Host + log10(tangle.vol.cm3) + Year
attr(,"variables")
list(comm.Hellinger, Host, log10(tangle.vol.cm3), Year)
attr(,"factors")
Host log10(tangle.vol.cm3) Year
comm.Hellinger 0 0 0
Host 1 0 0
log10(tangle.vol.cm3) 0 1 0
Year 0 0 1
attr(,"term.labels")
[1] "Host" "log10(tangle.vol.cm3)" "Year"
attr(,"order")
[1] 1 1 1
attr(,"intercept")
[1] 1
attr(,"response")
[1] 1
attr(,".Environment")
<environment: R_GlobalEnv>3.2 Variation Partitioning
3.2.1 Environmental variables Setting
data.env1 <- data.env[data.env$Year == 2015 & !is.na(data.env$longitude), ]
row.names(data.env1) <- data.env1$Nest
data.env1 Nest Host Collect.Date Year long.diam short.diam
2015age01 2015age01 Aglaoctenus 29-May 2015 30 25
2015age02 2015age02 Aglaoctenus 30-May 2015 96 44
2015age03 2015age03 Aglaoctenus 31-May 2015 73 38
2015age04 2015age04 Aglaoctenus 31-May 2015 73 42
h.from.ground basket.height Tangle.height CLD Quality P.Cover AS
2015age01 170 7 34 sparse excellent NA NA
2015age02 70 5 69 some good NA NA
2015age03 22 6 152 some good NA NA
2015age04 17 8 81 many good NA NA
Host.Pop tangle.vol.cm3 Spider.size.mm Orb.diam.1 Orb.diam.2
2015age01 1 6676 10 NA NA
2015age02 1 76303 20 NA NA
2015age03 1 110387 23 NA NA
2015age04 1 65017 20 NA NA
Orb.Area.cm2 Notes Simpson Shannon abundance richness density.m3
2015age01 NA 0.6000000 1.227529 10 5 14.979029
2015age02 NA 0.6224490 1.034601 14 3 1.834790
2015age03 NA 0.6159334 1.075604 29 4 2.627121
2015age04 NA 0.6875000 1.467205 32 7 4.921790
sociality cld.num latitude longitude prop.aggressive
2015age01 solitary 1 -1.066854 -77.61592 0.00000000
2015age02 solitary 2 -1.068090 -77.61607 0.00000000
2015age03 solitary 2 -1.074708 -77.61272 0.03448276
2015age04 solitary 3 -1.070106 -77.61587 0.12500000
[ reached 'max' / getOption("max.print") -- omitted 80 rows ]3.2.2 Space Setting
data.space <- geoXY(latitude = data.env1$latitude, longitude = data.env1$longitude,
unit = 1)
row.names(data.space) <- row.names(data.env1)
data.space X Y
2015age01 1718.71320 2365.149035
2015age02 1702.10730 2228.469908
2015age03 2075.18450 1496.639235
2015age04 1724.33827 2005.540331
2015age05 2229.34661 1535.232005
2015age06 1800.45381 2331.977743
2015age07 1896.79470 1754.657476
2015age08 1991.87567 1623.855388
2015age09 1828.47792 2151.237930
2015age11 1609.21782 2342.015711
2015age12 1530.01483 2270.863128
2015age13 2159.11771 1293.478187
2015age14 2346.15437 1402.677306
2015age15 225.23021 2638.450894
2015age16 225.28586 2650.593097
2015age17 1827.16236 2432.927985
2015age18 1850.76566 2196.596762
2015age19 1515.18194 2286.841166
2015age20 1446.16509 2243.150906
2015age21 1365.31042 2213.158635
2015dom01 1685.18421 2171.071707
2015dom02 1684.96940 2171.061755
2015dom03 1269.40806 2052.187359
2015dom05 1479.47927 1625.180072
2015dom06 1933.32655 1340.422662
2015dom08 1754.04190 2435.986480
2015dom09 1727.09962 2373.175650
2015dom10 1783.19459 2453.290309
2015dom11 1783.19459 2453.290309
2015dom12 1896.68228 1948.364385
2015dom14 222.98196 2679.881007
2015dom15 222.98196 2679.881007
2015dom19 1803.53235 2295.952518
2015dom20 1282.14295 2058.202620
2015dom21 1634.23907 1900.604976
2015dom22 1204.31118 939.533095
2015dom23 1205.99959 944.184971
2015dom24 1296.81668 269.075732
2015dom25 1202.95778 0.000000
2015dom28 1884.57401 1968.282199
2015dom30 1196.99657 3.911026
2015dom31 261.40813 2538.354289
2015ex01 1839.07586 1865.775062
2015ex02 1640.09676 2027.321329
2015ex03 2257.43528 1263.754611
2015ex04 1779.68754 2398.153360
2015ex05 1623.21151 2399.432709
2015ex06 1812.24600 1950.756115
2015ex07 1817.14318 1954.453731
2015ex08 332.40166 2459.722437
2015ex09 1248.02630 830.167006
2015ex10 1203.31282 1089.038894
2015ex11 1215.83179 2.001402
2015ex12 363.18712 526.187281
2015ex13 0.00000 1621.908168
2015ex15 1818.67354 1962.730245
2015ex16 372.92694 320.533869
2015ex17 229.13905 764.724492
2015ex18 218.25173 804.484933
2015ex19 208.18580 813.474653
2015ex21 41.54144 1685.099378
2015ex22 303.77987 2429.062295
[ reached getOption("max.print") -- omitted 22 rows ]3.2.3 Modified Hellinger-transformed dataset
comm.Hellinger1 <- comm.Hellinger[data.env$Year == 2015 & !is.na(data.env$longitude),
]
comm.Hellinger1 Neospintharus.sp1 Mimetus Faiditus.sp6 Faiditus.sp5 Faiditus.sp4
2015age01 0 0.0000000 0 0 0.3333333
2015age02 0 0.0000000 0 0 0.0000000
2015age03 0 0.1856953 0 0 0.0000000
2015age04 0 0.0000000 0 0 0.0000000
2015age05 0 0.1561738 0 0 0.0000000
2015age06 0 0.0000000 0 0 0.0000000
Paratenetus Tetramorium Rhomphaea Hypaeus Faiditus.sp1 Faiditus.sp3
2015age01 0 0 0 0.0000000 0.0000000 0.3333333
2015age02 0 0 0 0.0000000 0.0000000 0.5345225
2015age03 0 0 0 0.0000000 0.0000000 0.3216338
2015age04 0 0 0 0.1796053 0.3110855 0.3592106
2015age05 0 0 0 0.0000000 0.0000000 0.4938648
2015age06 0 0 0 0.0000000 0.0000000 0.2208631
Faiditus.sp2 Mysmenopsis.sp1 Mysmenopsis.sp2 Philoponella Ranzovius
2015age01 0 0.3333333 0.0000000 0.8164966 0
2015age02 0 0.4629100 0.0000000 0.7071068 0
2015age03 0 0.6432675 0.0000000 0.6695341 0
2015age04 0 0.7184212 0.1796053 0.4399413 0
2015age05 0 0.5630925 0.0000000 0.6439209 0
2015age06 0 0.5843487 0.0000000 0.6807456 0
Crematogaster Wasmannia
2015age01 0 0.000000
2015age02 0 0.000000
2015age03 0 0.000000
2015age04 0 0.000000
2015age05 0 0.000000
2015age06 0 0.382546
[ reached 'max' / getOption("max.print") -- omitted 78 rows ]3.2.4 PCNM
dis <- dist(data.space)
pcnm1 <- pcnm(dis)
data.pcnm <- as.data.frame(pcnm1$vectors)
data.pcnm PCNM1 PCNM2 PCNM3 PCNM4 PCNM5
2015age01 -0.10453685 0.07995080 0.005846451 -0.004912035 0.0067131818
2015age02 -0.10289196 0.04888911 0.002403331 -0.003996766 -0.0004820712
2015age03 0.03450754 -0.22415983 -0.016118035 0.006087890 -0.0202161608
PCNM6 PCNM7 PCNM8 PCNM9 PCNM10
2015age01 0.01852436 -0.1220186 -0.0001752782 -0.03750271 0.04048969
2015age02 -0.15178856 0.0641160 -0.0277964950 0.12798573 -0.08703467
2015age03 -0.25382015 0.2748703 -0.0260439927 0.12724939 -0.05263026
PCNM11 PCNM12 PCNM13 PCNM14 PCNM15
2015age01 0.003248005 0.01458943 0.028883551 0.02335808 -0.00403877
2015age02 -0.034927048 -0.07292320 0.008058058 0.14549377 0.02307526
2015age03 0.012089473 0.08425490 0.168102783 0.49526861 0.04343828
PCNM16 PCNM17 PCNM18 PCNM19 PCNM20
2015age01 0.003842022 -0.01159065 0.002989703 0.006258723 -0.01684925
2015age02 0.013035828 0.07623023 0.019503505 0.017344819 -0.15059109
2015age03 0.011556071 0.06118256 0.015940168 0.014535729 -0.07721144
PCNM21 PCNM22 PCNM23 PCNM24 PCNM25
2015age01 0.25677120 0.132344787 -1.567495e-02 9.39863e-02 5.653319e-04
2015age02 0.02467783 -0.075618278 2.320557e-03 1.47286e-03 9.012748e-04
2015age03 0.01428798 -0.002566293 -7.837802e-06 9.04672e-05 8.071059e-06
PCNM26 PCNM27 PCNM28 PCNM29 PCNM30
2015age01 3.787990e-02 -8.467772e-02 7.145196e-02 1.934414e-03 1.128389e-03
2015age02 1.763101e-03 -1.236150e-02 -1.398783e-01 -4.094078e-03 1.682418e-02
2015age03 8.975190e-06 -1.610407e-05 -3.627543e-05 -8.702016e-07 3.627073e-07
PCNM31 PCNM32
2015age01 -1.223683e-02 5.838803e-04
2015age02 1.096075e-02 -1.004268e-03
2015age03 1.773275e-07 -7.610650e-10
[ reached 'max' / getOption("max.print") -- omitted 81 rows ]3.2.5 Selection based on AdjR2
rda.space <- rda(comm.Hellinger1 ~ ., data = data.pcnm) #RDA of all PCNM vectors
rda.spaceCall: rda(formula = comm.Hellinger1 ~ PCNM1 + PCNM2 + PCNM3 + PCNM4 +
PCNM5 + PCNM6 + PCNM7 + PCNM8 + PCNM9 + PCNM10 + PCNM11 + PCNM12 +
PCNM13 + PCNM14 + PCNM15 + PCNM16 + PCNM17 + PCNM18 + PCNM19 + PCNM20 +
PCNM21 + PCNM22 + PCNM23 + PCNM24 + PCNM25 + PCNM26 + PCNM27 + PCNM28 +
PCNM29 + PCNM30 + PCNM31 + PCNM32, data = data.pcnm)
Inertia Proportion Rank
Total 0.4085 1.0000
Constrained 0.1696 0.4150 18
Unconstrained 0.2390 0.5850 18
Inertia is variance
Eigenvalues for constrained axes:
RDA1 RDA2 RDA3 RDA4 RDA5 RDA6 RDA7 RDA8 RDA9 RDA10
0.04437 0.02989 0.02781 0.01249 0.01237 0.00925 0.00804 0.00680 0.00553 0.00396
RDA11 RDA12 RDA13 RDA14 RDA15 RDA16 RDA17 RDA18
0.00274 0.00190 0.00156 0.00104 0.00074 0.00056 0.00040 0.00012
Eigenvalues for unconstrained axes:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
0.05708 0.04608 0.03852 0.02642 0.01580 0.01274 0.01004 0.00758
(Showing 8 of 18 unconstrained eigenvalues)3.2.6 Optimal RDA Component Selection
fsel.space <- ordiR2step(rda(comm.Hellinger1 ~ 1, data = data.pcnm), scope = formula(rda.space),
direction = "forward")Step: R2.adj= 0
Call: comm.Hellinger1 ~ 1
R2.adjusted
<All variables> 4.799459e-02
+ PCNM21 1.576868e-02
+ PCNM4 1.385148e-02
+ PCNM7 1.154958e-02
+ PCNM28 9.345271e-03
+ PCNM24 8.144699e-03
+ PCNM1 7.204080e-03
+ PCNM5 6.782931e-03
+ PCNM2 6.023598e-03
+ PCNM16 5.686736e-03
+ PCNM3 5.546793e-03
+ PCNM23 4.234051e-03
+ PCNM26 4.143214e-03
+ PCNM25 3.555229e-03
+ PCNM31 4.248328e-04
+ PCNM8 2.492437e-06
<none> 0.000000e+00
+ PCNM6 -7.999742e-04
+ PCNM15 -1.710880e-03
+ PCNM10 -1.832157e-03
+ PCNM11 -2.083595e-03
+ PCNM12 -2.356127e-03
+ PCNM32 -2.372807e-03
+ PCNM17 -3.345881e-03
+ PCNM27 -3.572893e-03
+ PCNM9 -3.898333e-03
+ PCNM19 -4.061810e-03
+ PCNM13 -4.111699e-03
+ PCNM30 -5.043622e-03
+ PCNM22 -5.313731e-03
+ PCNM14 -6.071884e-03
+ PCNM29 -7.189820e-03
+ PCNM20 -8.541832e-03
+ PCNM18 -1.010633e-02
Df AIC F Pr(>F)
+ PCNM21 1 -74.556 2.3298 0.028 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Step: R2.adj= 0.01576868
Call: comm.Hellinger1 ~ PCNM21
R2.adjusted
<All variables> 0.047994585
+ PCNM4 0.029985835
+ PCNM7 0.027655520
+ PCNM28 0.025423997
+ PCNM24 0.024208603
+ PCNM1 0.023256371
+ PCNM5 0.022830023
+ PCNM2 0.022061316
+ PCNM16 0.021720294
+ PCNM3 0.021578624
+ PCNM23 0.020249675
+ PCNM26 0.020157716
+ PCNM25 0.019562473
+ PCNM31 0.016393429
+ PCNM8 0.015965875
<none> 0.015768677
+ PCNM6 0.015153501
+ PCNM15 0.014231350
+ PCNM10 0.014108576
+ PCNM11 0.013854033
+ PCNM12 0.013578137
+ PCNM32 0.013561251
+ PCNM17 0.012576163
+ PCNM27 0.012346349
+ PCNM9 0.012016891
+ PCNM19 0.011851396
+ PCNM13 0.011800892
+ PCNM30 0.010857463
+ PCNM22 0.010584019
+ PCNM14 0.009816506
+ PCNM29 0.008684769
+ PCNM20 0.007316065
+ PCNM18 0.005732257
Df AIC F Pr(>F)
+ PCNM4 1 -74.809 2.2018 0.032 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Step: R2.adj= 0.02998583
Call: comm.Hellinger1 ~ PCNM21 + PCNM4
R2.adjusted
<All variables> 0.04799459
+ PCNM7 0.04219898
+ PCNM28 0.03993956
+ PCNM24 0.03870897
+ PCNM1 0.03774484
+ PCNM5 0.03731316
+ PCNM2 0.03653485
+ PCNM16 0.03618956
+ PCNM3 0.03604612
+ PCNM23 0.03470056
+ PCNM26 0.03460745
+ PCNM25 0.03400477
+ PCNM31 0.03079611
+ PCNM8 0.03036321
<none> 0.02998583
+ PCNM6 0.02954068
+ PCNM15 0.02860701
+ PCNM10 0.02848270
+ PCNM11 0.02822497
+ PCNM12 0.02794563
+ PCNM32 0.02792853
+ PCNM17 0.02693113
+ PCNM27 0.02669844
+ PCNM9 0.02636487
+ PCNM19 0.02619730
+ PCNM13 0.02614617
+ PCNM30 0.02519095
+ PCNM22 0.02491408
+ PCNM14 0.02413698
+ PCNM29 0.02299109
+ PCNM20 0.02160528
+ PCNM18 0.02000167
Df AIC F Pr(>F)
+ PCNM7 1 -74.916 2.0328 0.032 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Step: R2.adj= 0.04219898
Call: comm.Hellinger1 ~ PCNM21 + PCNM4 + PCNM7
R2.adjusted
+ PCNM28 0.05243330
+ PCNM24 0.05118713
+ PCNM1 0.05021079
+ PCNM5 0.04977365
+ PCNM2 0.04898548
+ PCNM16 0.04863583
+ PCNM3 0.04849057
<All variables> 0.04799459
+ PCNM23 0.04712798
+ PCNM26 0.04703369
+ PCNM25 0.04642338
+ PCNM31 0.04317411
+ PCNM8 0.04273573
<none> 0.04219898
+ PCNM6 0.04190279
+ PCNM15 0.04095729
+ PCNM10 0.04083141
+ PCNM11 0.04057042
+ PCNM12 0.04028754
+ PCNM32 0.04027023
+ PCNM17 0.03926020
+ PCNM27 0.03902457
+ PCNM9 0.03868677
+ PCNM19 0.03851709
+ PCNM13 0.03846530
+ PCNM30 0.03749799
+ PCNM22 0.03721762
+ PCNM14 0.03643068
+ PCNM29 0.03527029
+ PCNM20 0.03386694
+ PCNM18 0.03224303fsel.space$terms[[3]]PCNM21 + PCNM4 + PCNM74 COMMUNITY ANALYSES
4.1 Constrained ordination Approach
CA <- rda(comm.Hellinger ~ Host + log10(tangle.vol.cm3) + Condition(Year), data = data.env)
CACall: rda(formula = comm.Hellinger ~ Host + log10(tangle.vol.cm3) +
Condition(Year), data = data.env)
Inertia Proportion Rank
Total 0.40352 1.00000
Conditional 0.01014 0.02513 1
Constrained 0.10170 0.25204 4
Unconstrained 0.29168 0.72283 18
Inertia is variance
Eigenvalues for constrained axes:
RDA1 RDA2 RDA3 RDA4
0.04407 0.03177 0.02076 0.00510
Eigenvalues for unconstrained axes:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
0.06613 0.04402 0.04292 0.02975 0.01942 0.01763 0.01264 0.01029
(Showing 8 of 18 unconstrained eigenvalues)anova(CA)Permutation test for rda under reduced model
Permutation: free
Number of permutations: 999
Model: rda(formula = comm.Hellinger ~ Host + log10(tangle.vol.cm3) + Condition(Year), data = data.env)
Df Variance F Pr(>F)
Model 4 0.10170 12.553 0.001 ***
Residual 144 0.29168
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(CA, type = "t", display = c("sp", "bp"))
rda.plot <- ordination_plot(ordi = CA, group = data.env$Host, species = data.species,
polygons = T, plot.species = F, sp.bold = TRUE)
4.2 Summary of ordination
CA.sum <- summary(CA)
CA.sum
Call:
rda(formula = comm.Hellinger ~ Host + log10(tangle.vol.cm3) + Condition(Year), data = data.env)
Partitioning of variance:
Inertia Proportion
Total 0.40352 1.00000
Conditioned 0.01014 0.02513
Constrained 0.10170 0.25204
Unconstrained 0.29168 0.72283
Eigenvalues, and their contribution to the variance
after removing the contribution of conditiniong variables
Importance of components:
RDA1 RDA2 RDA3 RDA4 PC1 PC2 PC3
Eigenvalue 0.04407 0.03177 0.02076 0.005104 0.06613 0.04402 0.04292
Proportion Explained 0.11203 0.08077 0.05276 0.012976 0.16812 0.11189 0.10912
Cumulative Proportion 0.11203 0.19280 0.24556 0.258537 0.42665 0.53855 0.64766
PC4 PC5 PC6 PC7 PC8 PC9 PC10
Eigenvalue 0.02975 0.01942 0.01763 0.01264 0.01029 0.009754 0.008077
Proportion Explained 0.07563 0.04936 0.04482 0.03212 0.02616 0.024797 0.020533
Cumulative Proportion 0.72330 0.77266 0.81748 0.84960 0.87576 0.900556 0.921089
PC11 PC12 PC13 PC14 PC15 PC16
Eigenvalue 0.006665 0.006122 0.004165 0.003927 0.003508 0.002417
Proportion Explained 0.016942 0.015561 0.010587 0.009984 0.008917 0.006144
Cumulative Proportion 0.938031 0.953593 0.964180 0.974164 0.983080 0.989225
PC17 PC18
Eigenvalue 0.002321 0.001918
Proportion Explained 0.005899 0.004876
Cumulative Proportion 0.995124 1.000000
Accumulated constrained eigenvalues
Importance of components:
RDA1 RDA2 RDA3 RDA4
Eigenvalue 0.04407 0.03177 0.02076 0.005104
Proportion Explained 0.43333 0.31240 0.20409 0.050189
Cumulative Proportion 0.43333 0.74573 0.94981 1.000000
Scaling 2 for species and site scores
* Species are scaled proportional to eigenvalues
* Sites are unscaled: weighted dispersion equal on all dimensions
* General scaling constant of scores: 2.784598
Species scores
RDA1 RDA2 RDA3 RDA4 PC1 PC2
Neospintharus.sp1 0.027325 -0.0127020 -0.002715 0.029871 0.0220024 -0.032575
Mimetus -0.005103 -0.0309416 -0.043009 0.097087 0.1130095 0.068887
Faiditus.sp6 0.265151 -0.2270618 0.218172 -0.007540 0.0245121 -0.118131
Faiditus.sp5 -0.005842 -0.0168149 -0.036356 -0.029179 -0.0001956 0.003591
Faiditus.sp4 -0.032102 -0.0402920 -0.016337 0.046450 -0.0138207 -0.123495
Paratenetus -0.001792 0.0240305 0.018241 -0.009506 0.0264985 -0.003477
Tetramorium -0.004065 0.0003468 -0.008940 0.041389 -0.0008997 0.011024
Rhomphaea 0.087963 -0.0356823 0.029360 -0.002244 0.0422725 0.009445
Hypaeus -0.002774 0.0374285 -0.039248 -0.005926 -0.0088238 -0.017417
Faiditus.sp1 0.154217 -0.4100405 0.150375 -0.108011 0.2396292 -0.064169
Faiditus.sp3 0.165830 0.2660983 0.010059 -0.085846 -0.1968059 0.819422
Faiditus.sp2 0.308556 0.3249924 -0.121547 -0.157587 -0.0799760 -0.037802
Mysmenopsis.sp1 -0.406413 0.2929902 0.478765 -0.054526 0.1742522 0.092473
Mysmenopsis.sp2 -0.089672 -0.1408991 -0.113365 -0.147308 0.0227674 -0.024558
Philoponella -0.504471 -0.2312294 -0.144286 -0.115086 -0.7568105 -0.326167
Ranzovius 0.248234 -0.2112300 0.207447 -0.015567 0.0586507 -0.043723
Crematogaster 0.362055 0.0647372 0.030833 -0.018982 0.7379057 -0.125308
Wasmannia 0.007323 -0.0126200 0.025061 0.021645 0.0079707 -0.010069
Site scores (weighted sums of species scores)
RDA1 RDA2 RDA3 RDA4 PC1 PC2
2014age01 -0.403645 0.200227 0.330567 0.0830079 -0.016250 0.0184384
2014age03 -0.178653 0.087730 -0.180359 -0.0184466 -0.161113 0.1720758
2014age05 -0.192297 0.069627 -0.185807 -0.0071355 -0.133308 0.1628826
2014age06 -0.310498 -0.123204 -0.222174 0.2366257 -0.122475 -0.2347727
2014age07 -0.372473 0.192776 0.244200 -0.0630120 -0.069554 0.0714156
2014age08 -0.223072 -0.091807 -0.179440 0.7253468 -0.004651 -0.2362199
2014age09 -0.247560 -0.009802 -0.206037 0.0633948 -0.146656 0.0008070
2014age10 -0.310498 -0.123204 -0.222174 0.2366257 -0.137582 -0.2470926
2014age11 -0.310498 -0.123204 -0.222174 0.2366257 -0.083347 -0.2028634
2014age12 -0.310498 -0.123204 -0.222174 0.2366257 -0.155879 -0.2620136
2014age13 -0.230788 0.015538 -0.200269 0.0369901 -0.196169 0.0107857
2014age14 -0.437227 0.215618 0.409383 0.0123083 -0.012295 -0.0181473
2014age15 -0.327896 0.169360 0.398168 -0.1587261 -0.021858 0.1207198
2014dom01 -0.091997 0.035486 -0.075757 0.0738613 -0.323095 0.0156212
2014dom02 0.140193 0.135835 -0.081521 0.1968821 0.116931 -0.1763794
2014dom03 0.563972 0.237085 0.212889 0.0744676 0.554256 0.3439287
2014dom04 0.291210 0.589141 -0.287402 -0.7558195 -0.190293 0.0340648
2014dom05 0.101158 0.392740 -0.048685 0.0179248 -0.166202 0.5890575
2014dom06 0.533991 0.709265 -0.226401 -0.3847895 0.114034 -0.1094258
2014dom07 0.400957 0.679413 -0.266955 -0.7243821 -0.097940 0.0713172
[ reached getOption("max.print") -- omitted 130 rows ]
Site constraints (linear combinations of constraining variables)
RDA1 RDA2 RDA3 RDA4 PC1 PC2
2014age01 -0.368561 0.1426 0.20496 0.1716030 -0.016250 0.0184384
2014age03 -0.320510 0.1587 0.25731 0.0515765 -0.161113 0.1720758
2014age05 -0.375129 0.1404 0.19780 0.1880091 -0.133308 0.1628826
2014age06 -0.368883 0.1425 0.20460 0.1724084 -0.122475 -0.2347727
2014age07 -0.341301 0.1517 0.23466 0.1035096 -0.069554 0.0714156
2014age08 -0.395144 0.1337 0.17599 0.2380048 -0.004651 -0.2362199
2014age09 -0.360985 0.1451 0.21321 0.1526793 -0.146656 0.0008070
2014age10 -0.342117 0.1515 0.23377 0.1055484 -0.137582 -0.2470926
2014age11 -0.438210 0.1192 0.12906 0.3455807 -0.083347 -0.2028634
2014age12 -0.309699 0.1623 0.26909 0.0245722 -0.155879 -0.2620136
2014age13 -0.272835 0.1747 0.30926 -0.0675108 -0.196169 0.0107857
2014age14 -0.340806 0.1519 0.23520 0.1022729 -0.012295 -0.0181473
2014age15 -0.302585 0.1647 0.27685 0.0068014 -0.021858 0.1207198
2014dom01 0.278927 0.2846 -0.03314 -0.2920701 -0.323095 0.0156212
2014dom02 0.270634 0.2818 -0.04217 -0.2713560 0.116931 -0.1763794
2014dom03 0.082978 0.2188 -0.24665 0.1973912 0.554256 0.3439287
2014dom04 0.286194 0.2870 -0.02522 -0.3102227 -0.190293 0.0340648
2014dom05 0.177087 0.2504 -0.14411 -0.0376837 -0.166202 0.5890575
2014dom06 0.210468 0.2616 -0.10773 -0.1210668 0.114034 -0.1094258
2014dom07 0.261633 0.2788 -0.05198 -0.2488724 -0.097940 0.0713172
[ reached getOption("max.print") -- omitted 130 rows ]
Biplot scores for constraining variables
RDA1 RDA2 RDA3 RDA4 PC1 PC2
HostKapogea -0.45201 -0.4854 -0.5619 -0.49132 0 0
HostA.domingo 0.48697 0.7118 -0.4944 0.07495 0 0
HostA.eximius 0.52839 -0.6584 0.4350 0.31281 0 0
log10(tangle.vol.cm3) 0.06591 -0.3324 0.1802 -0.90910 0 0
Centroids for factor constraints
RDA1 RDA2 RDA3 RDA4 PC1 PC2
HostAglaoctenus -0.2852 0.1737 0.2659 0.02518 0 0
HostKapogea -0.2014 -0.2162 -0.2503 -0.21886 0 0
HostA.domingo 0.1718 0.2512 -0.1745 0.02645 0 0
HostA.eximius 0.1926 -0.2400 0.1586 0.11405 0 04.3 Optimal factors contributed to web-spider community
mv.comm <- mvabund(data.comm)
mv.fit <- manyglm(mv.comm ~ log10(tangle.vol.cm3) + Host, data = data.env, family = "negative.binomial")
plot(mv.fit)
mv.glm.M01 <- anova.manyglm(mv.fit, p.uni = "unadjusted")Time elapsed: 0 hr 2 min 4 seccolnames(mv.glm.M01$uni.p)[which(mv.glm.M01$uni.p[3, ] < 0.05)] [1] "Faiditus.sp6" "Faiditus.sp5" "Rhomphaea" "Faiditus.sp1"
[5] "Faiditus.sp2" "Mysmenopsis.sp1" "Mysmenopsis.sp2" "Philoponella"
[9] "Ranzovius" "Crematogaster" References
Borcard, Daniel, François Gillet, and Pierre Legendre. 2018. Numerical Ecology with r. Springer.
Legendre, Pierre, and Eugene Gallagher. 2001. “Ecologically Meaningful Transformations for Ordination of Species Data.” Oecologia 129 (October): 271–80.
Legendre, Pierre, and Louis Legendre. 2012. Numerical Ecology. Elsevier.
Zuur, Alain F., Elena N. Ieno, and Graham M. Smith. 2007. “Principal Component Analysis and Redundancy Analysis.” In Analysing Ecological Data, 193–224. New York, NY: Springer New York. https://doi.org/10.1007/978-0-387-45972-1_12.