PERMANOVA

Loading packages vegan multivariate analysis of ecological communities, and loading data.

Adavantage for using this method: Non-paramentric,no assumed distribution, based on dissimilarities.

library(vegan)
werra_sp    <- read.csv(file = "/Users/chengqiwang/Downloads/werra_sp.csv",
                        header = T,sep=",",stringsAsFactors=FALSE,row.names = 1)

werra_env   <- read.csv(file = "/Users/chengqiwang/Downloads/werra_env.csv",
                        header = T,sep=",",stringsAsFactors=FALSE)  

1. Transform or standardize data

Sequencing reads is a large number and significant different vary groups. We’d better reduce the range/scale of it to about 10.\(X^{(a)}\), \(a\in (0,1)\)

range(werra_sp^0.25)

## [1]  0.00000 10.98475

2. Calculate ecological resemblance

• Bray-Curtis dissimilarity (abundance weighted)
• Jaccard (presence/absence)
• Gower’s non-continuous variables) (Dissimilarity: 0 = sites are indentical, 1 = sites do not share any species)

dist_werra  <- vegdist(werra_sp^0.25,method = "bray")
##nmds        <- metaMDS(dist_werra)##global Multidimensional Scaling using monoMDS

3.PERMANOVA

“adonis” is a function for the analysis and partitioning sums of squares using semimetric and metric distance matrices.

Null hypotheie : There is no different between these two or more comparable groups.

R-square is the important statistic for interpreting Adonis as it gives you the effect size. (For example: an R-squared of 0.44 means that 44% of the variation in distances is explained by the grouping being tested. The p-value tells you whether or not this result was likely a result of chance. A p-value of 0.05 means that there is a 5% chance that you detected a difference between groups.)

Small p-value with small R-square : this situation normally because of large sample size. Actualy only small part can be explained, however large sample size make the p-value small.

pmv         <- adonis(werra_sp^0.25~position,data = werra_env,
                      permutations = 999,
                      method = "bray")
pmv

## 
## Call:
## adonis(formula = werra_sp^0.25 ~ position, data = werra_env,      permutations = 999, method = "bray") 
## 
## Permutation: free
## Number of permutations: 999
## 
## Terms added sequentially (first to last)
## 
##           Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)  
## position   1   0.72127 0.72127  3.9937 0.30736  0.015 *
## Residuals  9   1.62540 0.18060         0.69264         
## Total     10   2.34666                 1.00000         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4.Modify the effective size number

Omega-squared (\(\omega^2\)) provides a less biased measure of effect size for ANOVA-type analyses by accounting for the mean-squared error of the observed samples. \[R^2=1-\frac{SS_A}{SS_T}\] \[\omega^2=\frac{SS_A-(a-1)\frac{SS_W}{N-a}}{SS_T+\frac{SS_W}{N-a}}\]

df.rsd      <- pmv$aov.tab$Df[2]##degree of freedom of residual
df.dfd      <- pmv$aov.tab$Df[1]##degrees of freedom defined by the grouping factor
SS.A        <- pmv$aov.tab$SumsOfSqs[1]##between-group sum of squares
SS.W        <- pmv$aov.tab$SumsOfSqs[2]##sum of the squares of distances within groups
SS.T        <- pmv$aov.tab$SumsOfSqs[3]##total sum of squares 

omega.sq    <-(SS.A-(df.dfd-1)*(SS.W/df.rsd))/(SS.T+SS.W/df.rsd);omega.sq

## [1] 0.2853952

Display the density plot of all F-test.

densityplot(permustats(pmv))