Hint Observe the use of the type = "s" argument of the plot() function to draw
steps between values.
Can you identify the richness hotspots along the river?
More elaborate measures of diversity will be presented in Chap. 8.
2.2.4 Ecological Data Transformation
There are instances where one needs to transform the data prior to analysis. The main
reasons are given below with examples of transformations:
• Make descriptors that have been measured in different units comparable. Standardization to z-scores (i.e., centring and reduction) and ranging (to a [0,1]
interval) make variables dimensionless. Following that, their variances can be
added, e.g. in principal component analysis (see Chap. 5);
• Transform the variables to have a normal (or at least a symmetric) distribution and
stabilize their variances (through square root, fourth root, log transformations,
etc.);
• Make the relationships among variables linear (e.g., log-transform the response
variable if the relationship is exponential);
• Modify the weights of the variables or objects prior to a multivariate analysis,
e.g., give the same variance to all variables, or the same length, (or norm) to all
object vectors;
• Code categorical variables into dummy binary variables or Helmert contrasts.
Species abundances are dimensionally homogenous (expressed in the same
physical units), quantitative (count, density, cover, biovolume, biomass, frequency,
etc.) or semi-quantitative (two or more ordered classes) variables, and restricted to
positive or null values (zero meaning absence). For these, simple transformations
can be used to reduce the importance of observations with very high values; sqrt
() (square root), ^0.25 (fourth root), or log1p() (log(y + 1) to keep absences as
zeros) are commonly applied R functions (see also Chap. 3). In extreme cases, to
give the same weight to all positive abundances irrespective of their values, the data
can be transformed to binary 1–0 form (presence-absence).
The decostand() function of the vegan package provides many options for
common standardization of ecological data. In this function, standardization refers
to transformations that have the objective to make the rows or columns of the data
table comparable to one another because they will have acquired some property. In
contrast to simple transformations such as square root, log or presence-absence, the
values are not transformed individually but relative to other values in the data table.
Standardizations can be done relative to sites (e.g. relative abundances per site) or
2.2 Data Exploration
21
steps between values.
Can you identify the richness hotspots along the river?
More elaborate measures of diversity will be presented in Chap. 8.
2.2.4 Ecological Data Transformation
There are instances where one needs to transform the data prior to analysis. The main
reasons are given below with examples of transformations:
• Make descriptors that have been measured in different units comparable. Standardization to z-scores (i.e., centring and reduction) and ranging (to a [0,1]
interval) make variables dimensionless. Following that, their variances can be
added, e.g. in principal component analysis (see Chap. 5);
• Transform the variables to have a normal (or at least a symmetric) distribution and
stabilize their variances (through square root, fourth root, log transformations,
etc.);
• Make the relationships among variables linear (e.g., log-transform the response
variable if the relationship is exponential);
• Modify the weights of the variables or objects prior to a multivariate analysis,
e.g., give the same variance to all variables, or the same length, (or norm) to all
object vectors;
• Code categorical variables into dummy binary variables or Helmert contrasts.
Species abundances are dimensionally homogenous (expressed in the same
physical units), quantitative (count, density, cover, biovolume, biomass, frequency,
etc.) or semi-quantitative (two or more ordered classes) variables, and restricted to
positive or null values (zero meaning absence). For these, simple transformations
can be used to reduce the importance of observations with very high values; sqrt
() (square root), ^0.25 (fourth root), or log1p() (log(y + 1) to keep absences as
zeros) are commonly applied R functions (see also Chap. 3). In extreme cases, to
give the same weight to all positive abundances irrespective of their values, the data
can be transformed to binary 1–0 form (presence-absence).
The decostand() function of the vegan package provides many options for
common standardization of ecological data. In this function, standardization refers
to transformations that have the objective to make the rows or columns of the data
table comparable to one another because they will have acquired some property. In
contrast to simple transformations such as square root, log or presence-absence, the
values are not transformed individually but relative to other values in the data table.
Standardizations can be done relative to sites (e.g. relative abundances per site) or
2.2 Data Exploration
21