[R-sig-eco] Permanova with nested data

[Beth Atkinson]

Hi,

Apologies if this has been asked before, I looked looked through the 
archives and couldn't find a solution.


I have plant community data from 32 woodland plots. Plots are grouped into 
sites (8 sites in total). Half the sites (4) are on one soil type, and half 
on another. At each site there are 4 plots, each under a different 
management regime .  I want to know if the plant communities under 
different management regimes and on different soil types differ.

My data is as follows:


veg <- a data frame containg the community data (abundances of each species 
at each plot)


environ<-read.csv(file.choose(),header=TRUE)

> str(environ)
'data.frame':   32 obs. of  4 variables:
 $ code: Factor w/ 32 levels "cf.1","cf.3",..: 1 9 17 25 2 10 18 26 3 11 ...
 $ site: Factor w/ 8 levels "eight","five",..: 5 5 5 5 8 8 8 8 3 3 ...
 $ type: Factor w/ 4 levels "clearfell","plantation",..: 1 2 3 4 1 2 3 4 1 
2 ...
 $ nvc : Factor w/ 2 levels "W10","W8": 2 2 2 2 2 2 2 2 1 1 ...

# site is the name of each site
# type refers to the management regime
# nvc refers to the soil type (actually the NVC classification)

Prior to PERMANOVA I used betadisper() to test for homogeneity of 
multivariate dispersion.  No difference in dispersion was found either 
between plots on different site types, or plots on different NVC types.


I carried out a PERMANOVA using adonis on this data as follows:

adon.mod1.bray<-adonis(veg~ type*nvc, data=environ,strata=environ$site,
	method = "bray", permutations=999)

I used strata=environ$site as management regime is nested within site.

> adon.mod1.bray

Call:
adonis(formula = veg ~ type * nvc, data = environ, permutations = 999,
	 method = "bray", strata = environ$site)

Terms added sequentially (first to last)

          Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)
type       3    2.2358 0.74528  3.5742 0.24662  0.001 ***
nvc        1    1.0905 1.09045  5.2296 0.12028  0.001 ***
type:nvc   3    0.7353 0.24509  1.1754 0.08110  0.208
Residuals 24    5.0044 0.20852         0.55200
Total     31    9.0659                 1.00000


Is this acceptable. Is the strata=environ$site part correct?

If data points are only being permutted within sites, and each site only 
occurs on one soil type, is there no permutation between NVC/soil types?

I've also heard that adonis does not give the correct p values when data is 
nested. Is this correct, and a problem in the above example? If so is there 
a more suitable analysis? Would a db-RDA as follows be ok?:


dbRDA<-capscale(veg~type*nvc+Condition(site), data=environ, 
distance="bray", add=TRUE)

anova.cca(dbRDA, stop=999)

anova.cca(dbRDA, by="terms", step=999)

> anova.cca(dbRDA, by="terms", step=999)
Permutation test for capscale under reduced model
Terms added sequentially (first to last)

Model: capscale(formula = veg ~ type + nvc + Condition(site) + type:nvc, 
data = environ, distance = "bray", add = TRUE)
         Df    Var      F N.Perm Pr(>F)
type      3 2.9615 3.3215    999 <2e-16 ***
type:nvc  3 1.1299 1.2673    999 0.1141
Residual 18 5.3496


However, this doesn't show a result for nvc. Why?

I've also been looking into the manyglm() function in mvabund, but I don't 
think this can accept random effects.

Any help would be greatly appreciated,

Thanks,

Beth

--------------------------------------------------------
Beth Atkinson

PhD student
Community Ecology Group
School of Biological Sciences
University of Bristol
Woodland Road
Bristol
BS8 1UG