[R-sig-eco] envfit and adonis restricted permutations
Gavin Simpson
gavin.simpson at ucl.ac.uk
Tue Jun 28 13:08:04 CEST 2011
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/
>
> --
> View this message in context: http://r-sig-ecology.471788.n2.nabble.com/envfit-and-adonis-restricted-permutations-tp6522883p6522883.html
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>
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Dr. Gavin Simpson [t] +44 (0)20 7679 0522
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