Experiments evaluated using multivariate methods

Separating the effect of (correlated) environmental variables Variation partitioning A B A in addition to B B in addition to A A or B In fact, more often used in observational studies - in experiments, we try to avoid correlated predictor (however, in ecology, we are not able to control everything

Effect of nitrogen fertilization on weed community Dose of fertilizer Cover of barley Weed community Pysek P. & Leps J. (1991):Response of a weed community to nitrogen fertilizer: a multivariate analysis. J. Veget. Sci. 2:

Effect of nitrogen fertilization on weed community Dose of fertilizer Cover of barley Weed community

Basic questions: * Is there an effect of fertilization on the structure of the weed community? (either direct, or mediated through cover of the crop) Problem of correlated predictors: * Is there a direct effect of fertilization (i.e., which could not be explained as mediated through the cover of the crop)? * Is there an effect of the crop that can not be explained by the direct effect of fertilizer?

Multiple regression: test of the complete model & test of partial effects [plus possible test of marginal effects]

Variation partitioning Dose Dose in addition to Cover Cover in addition Dose A Cover or Dose Cover

Variation partitioning - n.b. In linear methods, trace (all the eigenvalues together) sum up to 1, so the eigenvalue corresponds to the proportion of explained variability In unimodal methods, trace is higher than one, so the eigenvalue has to be divided by trace to get the proportion of explained variability

Variation partitioning - n.b. The variation could be partitioned among more than 2 variables (however, for more than 3 variables, the clarity of the result is lost) More useful: partitioning between groups of variables The amount of explained variability is positively dependent on number of explanatory variables is a group

Effect of dominant species, moss and litter on seedling germination Randomized complete blocks Spacková I., Kotorová I. & Leps J. (1998): Sensitivity of seedling recruitment to moss, litter and dominant removal in an oligotrophic wet meadow. Folia Geobot. Phytotax. 33:

Just of historical interest (the FORTRAN format etc.)

Standardization by samples Grubb theory of regeneration niche: importance of standardization - the standardization fundamentally changes the ecological interpretation of results

When there are very different eigenvalues, the “Focus scaling on” really plays a role! on interspecies correlation on intersample distances

Hierarchical structure each whole-plot is subdivided into 25 split-plots

Seedlings - nested design [seme96su.spe, seme96su.env]

Permutations of the whole-plots

Repeated observations from a factorial experiment fertilization, mowing, dominant removal] 3 replications, i.e. 24 plots together

Further use of ordination scores Do we need PIC here?