Example using PERMANOVA with single and multiple covariates (a.k.a., independent variables).

adonis_output.txt

Call:
adonis(formula = GPfr_phylum_bray ~ SampleType, data = sampledf) 

Permutation: free
Number of permutations: 999

Terms added sequentially (first to last)

           Df SumsOfSqs MeanSqs F.Model     R2 Pr(>F)    
SampleType  8    8.2618 1.03272    5.81 0.7322  0.001 ***
Residuals  17    3.0218 0.17775         0.2678           
Total      25   11.2836                 1.0000           
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Call:
adonis(formula = GPfr_phylum_bray ~ Description, data = sampledf) 

Permutation: free
Number of permutations: 999

Terms added sequentially (first to last)

            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
Description 24   11.1949 0.46646  5.2634 0.99215  0.027 *
Residuals    1    0.0886 0.08862         0.00785         
Total       25   11.2836                 1.00000         
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Call:
adonis(formula = GPfr_phylum_bray ~ SampleType + Description,      data = sampledf) 

Permutation: free
Number of permutations: 999

Terms added sequentially (first to last)

            Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
SampleType   8    8.2618 1.03272 11.6530 0.73220  0.022 *
Description 16    2.9331 0.18332  2.0686 0.25995  0.060 .
Residuals    1    0.0886 0.08862         0.00785         
Total       25   11.2836                 1.00000         
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

permanova_demo.R

# Adjusted from http://deneflab.github.io/MicrobeMiseq/demos/mothur_2_phyloseq.html#permanova

library(phyloseq)
library(dplyr)
library(ggplot2)
library(vegan)
data(GlobalPatterns)
GPr  = transform_sample_counts(GlobalPatterns, function(x) x / sum(x) )
GPfr = filter_taxa(GPr, function(x) mean(x) > 1e-5, TRUE)
GPfr_phylum <- GPfr %>%
  tax_glom(taxrank = "Phylum") %>%                     # agglomerate at phylum level
  transform_sample_counts(function(x) {x/sum(x)} ) %>% # Transform to rel. abundance
  psmelt() %>%                                         # Melt to long format
  filter(Abundance > 0.02) %>%                         # Filter out low abundance taxa
  arrange(Phylum) 


###
# Plot #####
###
p.phyla <- ggplot(GPfr_phylum, aes(x = Sample, y = Abundance, fill = Phylum)) + 
  geom_bar(stat = "identity") +
  # Remove x axis title
  theme(axis.title.x = element_blank()) + 
  #
  guides(fill = guide_legend(reverse = TRUE, keywidth = 1, keyheight = 1)) +
  ylab("Relative Abundance (Phyla > 2%) \n") +
  ggtitle("Phylum Composition of GlobalPatterns Communities by Sample") 

print(p.phyla)

###
# PERMANOVA #####
###
set.seed(1)

# Calculate bray curtis distance matrix
GPfr_phylum_bray <- phyloseq::distance(GPfr, method = "bray")

# make a data frame from the sample_data
sampledf <- data.frame(sample_data(GPfr))

# Adonis test
adonis(GPfr_phylum_bray ~ SampleType, data = sampledf)
adonis(GPfr_phylum_bray ~ Description, data = sampledf)
adonis(GPfr_phylum_bray ~ SampleType + Description, data = sampledf)

Note that the order of the covariates (a.k.a., independent variables) MATTERS in this case, i.e., different results are obtained using SampleType + Description or Description + SampleType (results not shown). For more info, s. https://stats.stackexchange.com/questions/188519/adonis-in-vegan-order-of-variables-or-use-of-strata

[UPDATE] This is for ANOVA http://www.statmethods.net/stats/anova.html says:

In a nonorthogonal design with more than one term on the right hand side of the equation order will matter (i.e., A+B and B+A will produce different results)! We will need use the drop1( ) function to produce the familiar Type III results.

[UPDATE2] For the adonis function, and maybe related to aov, the testing is done sequentially, s. vegandevs/vegan#229. Hence, the effect of the ordering. Unsure what the "marginal" means, instead of "sequential".

[Update3] Note the comment in vegandevs/vegan#229:

I do not recommend using all possible orders. Either you do marginal tests and accept the statistics it can deliver, or you have an a priori meaningful order.

-> See the

a priori meaningful order

Not sure how to get this though.