terminology

• species data = the measured variables we want to explain (response or dependent variables)

• environmental data = the variables we use for explaining the species data (explanatory or independent variables)

• sites are rows• columns are variables

data transformation

• Usually applied to response variables only– Make the measurement scales similar or the same– Stabilize variance (log / sqrt)– recode into binary variables

association measures

• Q mode– distances, e.g., Euclidean

• R mode– correlations, e.g., Pearson's correlation

distances

• Q mode, quantitative– Bray-Curtis• gives the same weight to same differences in

abundances irrespective of the scales• 1 ... 2 -> 1 and 1001 ... 1002 -> 1• Usually at least square root transformation before

distances are calculated

– Hellinger• abundances are divided by the site's total abundance

and then square root transformed

distances

• Q mode, presence / absence– Jaccard