envfit and adonis restricted permutations
On Mon, 2011-06-27 at 16:39 -0700, Steve Leonard wrote:
Hi all, I am using envfit and adonis to examine patterns in floristic composition amongst sites that vary with repect to fire history and fire severity (factors) and a number of environmental variables (mostly continuous). Within each site vegetation has been sampled in two environments (slope and gully, one sample in each). I have used the 'strata' argument to restrict permutations to within sites, as I believe this accounts for the lack of independence of samples within sites (like including site as a random factor in a mixed model). Results of envfit indicate that the variables 'easting' and 'northing' are not significantly correlated with the ordination of sites, despite having relatively high R2 values (see 'fit1' below). When I apply envfit with unrestricted permutations, results are significant for easting and northing (see 'fit2'). Similarly, easting and northing are significant when I analyse the same data using adonis (see 'mod1'). Can anyone explain this apparent discrepancy? Is there a problem with the way I am using 'strata'? Any advice gratefully received.
Yep; Notice that the r2 values don't change whether you use `strata = site` in the `envfit()` examples. What changes is the null distribution of r2 values against which the observed r2 is compared. Random permutation appears to produce results with far lower r2, in general than the observed, whilst permuting within `site` results in many r2 values larger than the observed (~51 and ~27% more respectively for easting and northing). The run without strata is not appropriate as the samples are not freely exchangeable /between/ sites under the null hypothesis if you have clustering at the site level. Using `strata` is the more appropriate null hypothesis as samples are only freely exchangeable **within** site. Depending on whether you have sufficient sites, 999 permutations might be too many (there are only two permutations within each level of `site`, so what is 2 * number of sites in your data set?), but as yet we don't have a facility for iterating over the full set of permutations. The general facility is available in the `permute` package on r-forge but won't get fully integrated into vegan until later in the summer. As for `adonis()`, AFAIUI, it is decomposing the **entire** dissimilarity matrix into "variance" explained by each covariate. In nMDS, you have reduced the entire dissimilarity matrix to three dimensions and then look for correlations in those three dimensions with covariates. The "discrepancy" is due to the two techniques working with different "data" and assessing different versions of "explanatory power". These results, at first blush, would suggests to me that easting and northing effects are in the parts of the dissimilarity matrix not represented well by the 3-d nMDS solution. Does this help? G
Thanks Steve PS Data files attached if anyone cares to delve into them
flora<-read.csv("C://r//flora_ord_cd_no_UBG.csv", header=T)
sv<-read.csv("C://r//flora_sv_no_UBG.csv", header=T)
attach(sv)
library(vegan)
This is vegan 1.18-33 Warning message: package 'vegan' was built under R version 2.13.0
mds1<-metaMDS(flora, distance="bray", k=3, trace=F, autotransform =F)
fit1<-envfit(mds1~environment+history+severity+asp_class+easting+northing+ann_rain+Num_fire+TSF+tpi+sr_100_mean+slope, choices=c(1:3), strata=site) fit1
***VECTORS
NMDS1 NMDS2 NMDS3 r2 Pr(>r)
easting -0.068611 -0.144025 -0.987193 0.2912 0.517
northing -0.015771 0.995731 -0.090943 0.2657 0.366
ann_rain -0.104761 -0.776971 -0.620758 0.3133 0.013 *
Num_fire 0.578255 0.802894 0.144850 0.0213 0.820
TSF -0.450387 -0.325620 -0.831338 0.0476 0.936
tpi -0.889913 0.139690 0.434213 0.0666 0.014 *
sr_100_mean -0.193648 0.585345 -0.787319 0.0390 0.698
slope -0.664790 0.506331 -0.549257 0.0809 0.004 **
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
P values based on 999 permutations, stratified within strata.
***FACTORS:
Centroids:
NMDS1 NMDS2 NMDS3
environmentg -0.3182 0.0604 0.0177
environments 0.3113 -0.0591 -0.0173
historyNR -0.0686 -0.0104 -0.0526
historyR 0.0702 0.0106 0.0538
severityCB 0.0141 -0.0273 0.3109
severityCS -0.0257 -0.0702 0.2188
severityGB -0.0086 -0.0421 -0.0386
severityRF 0.0199 -0.0132 -0.2918
severityUB 0.0058 0.0891 -0.0738
asp_classE -0.0753 0.0850 0.0162
asp_classN -0.0177 -0.1153 -0.0120
asp_classNE -0.1051 -0.1974 -0.0086
asp_classNW 0.1137 0.0589 -0.0183
asp_classS 0.0738 0.0454 0.0618
asp_classSE 0.0262 0.0909 -0.0408
asp_classSW -0.0778 0.1801 0.0694
asp_classW 0.0502 0.0374 -0.0369
Goodness of fit:
r2 Pr(>r)
environment 0.2354 0.001 ***
history 0.0177 0.001 ***
severity 0.0810 0.001 ***
asp_class 0.0444 0.689
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
P values based on 999 permutations, stratified within strata.
fit2<-envfit(mds1~environment+history+severity+asp_class+easting+northing+ann_rain+Num_fire+TSF+tpi+sr_100_mean+slope, choices=c(1:3)) fit2
***VECTORS
NMDS1 NMDS2 NMDS3 r2 Pr(>r)
easting -0.068611 -0.144025 -0.987193 0.2912 0.001 ***
northing -0.015771 0.995731 -0.090943 0.2657 0.001 ***
ann_rain -0.104761 -0.776971 -0.620758 0.3133 0.001 ***
Num_fire 0.578255 0.802894 0.144850 0.0213 0.267
TSF -0.450387 -0.325620 -0.831338 0.0476 0.041 *
tpi -0.889913 0.139690 0.434213 0.0666 0.010 **
sr_100_mean -0.193648 0.585345 -0.787319 0.0390 0.070 .
slope -0.664790 0.506331 -0.549257 0.0809 0.003 **
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
P values based on 999 permutations.
***FACTORS:
Centroids:
NMDS1 NMDS2 NMDS3
environmentg -0.3182 0.0604 0.0177
environments 0.3113 -0.0591 -0.0173
historyNR -0.0686 -0.0104 -0.0526
historyR 0.0702 0.0106 0.0538
severityCB 0.0141 -0.0273 0.3109
severityCS -0.0257 -0.0702 0.2188
severityGB -0.0086 -0.0421 -0.0386
severityRF 0.0199 -0.0132 -0.2918
severityUB 0.0058 0.0891 -0.0738
asp_classE -0.0753 0.0850 0.0162
asp_classN -0.0177 -0.1153 -0.0120
asp_classNE -0.1051 -0.1974 -0.0086
asp_classNW 0.1137 0.0589 -0.0183
asp_classS 0.0738 0.0454 0.0618
asp_classSE 0.0262 0.0909 -0.0408
asp_classSW -0.0778 0.1801 0.0694
asp_classW 0.0502 0.0374 -0.0369
Goodness of fit:
r2 Pr(>r)
environment 0.2354 0.001 ***
history 0.0177 0.029 *
severity 0.0810 0.001 ***
asp_class 0.0444 0.291
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
P values based on 999 permutations.
mod1<-adonis(flora~environment+history+severity+asp_class+easting+northing+ann_rain+Num_fire+TSF+tpi+sr_100_mean+slope, method="bray", strata=site) mod1
Call:
adonis(formula = flora ~ environment + history + severity + asp_class +
easting + northing + ann_rain + Num_fire + TSF + tpi + sr_100_mean + slope,
method = "bray", strata = site)
Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
environment 1 4.316 4.3155 19.3742 0.08508 0.001 ***
history 1 0.569 0.5687 2.5530 0.01121 0.001 ***
severity 4 2.801 0.7003 3.1440 0.05523 0.001 ***
asp_class 7 2.143 0.3061 1.3744 0.04225 0.295
easting 1 1.115 1.1151 5.0060 0.02198 0.001 ***
northing 1 1.860 1.8598 8.3493 0.03667 0.001 ***
ann_rain 1 0.797 0.7966 3.5762 0.01570 0.007 **
Num_fire 1 0.290 0.2896 1.2999 0.00571 0.158
TSF 1 0.159 0.1591 0.7144 0.00314 0.270
tpi 1 0.454 0.4541 2.0388 0.00895 0.486
sr_100_mean 1 0.369 0.3692 1.6576 0.00728 0.323
slope 1 0.211 0.2111 0.9476 0.00416 0.491
Residuals 160 35.639 0.2227 0.70264
Total 181 50.722 1.00000
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
http://r-sig-ecology.471788.n2.nabble.com/file/n6522883/flora_ord_cd_no_UBG.csv
flora_ord_cd_no_UBG.csv
http://r-sig-ecology.471788.n2.nabble.com/file/n6522883/flora_sv_no_UBG.csv
flora_sv_no_UBG.csv
-----
Dr Steve Leonard
Research Fellow
Department of Zoology| La Trobe University | Bundoora, 3086 Australia
T: +61 3 9479 2773 | M: +61 429 418 388 | F: +61 3 9479 1551 | W: www.latrobe.edu.au/zoology/
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