Wetland vegetation distribution modelling for the identification of constraining environmental variables

Abstract

Wetland ecosystems are of primary concern for nature conservation and restoration. Adequate conservation and restoration strategies emerge from a scientific comprehension of wetland properties and processes. Hereby, the understanding of plant species and vegetation patterns in relation to environmental gradients is an important issue. The modelling approaches in this study statistically relate vegetation patterns to measured environmental gradients in a lowland wetland ecosystem. Measured environmental gradients included groundwater quantity and quality aspects, soil properties and vegetation management. Among this variety, the objective was to identify the key environmental gradients constraining the vegetation, using recently developed methodologies within the modelling approaches. Comparison of results indicated that different environmental gradients were considered to be important by different methodologies.

Appendix A: Variable importance measure

Algorithm for estimating the variable importance of each predictive variable within random forests is given by:

• (i) For i = 1 to k do (grow a random forest consisting of k classification trees):

  • (1) apply tree i to the n oob elements and count the number of correct classifications over the n oob elements (C _i,untouched);

  • (2) for j = 1 to p (with p the total number of variables) do:

    • (a) take the n untouched oob elements;

    • (b) randomly permute the values of variable j in the n oob elements;

    • (c) apply tree i to all the j permuted oob elements;

    • (d) count the number of correct classifications (C _i,j-permuted);

    • (e) subtract the number of correct classifications of the variable-j-permuted oob elements from the number of correct classifications of the untouched oob elements and divide by the number of oob elements (ΔC _i,j = (C _i,untouched − C _i,j-permuted)/n);

The results from these iterations are p (number of variables, j = 1 to p) groups of k (number of trees, i = 1 to k) ΔC _i,j values. Since trees are independent, correlations among the ΔC _i,j values within the p groups are generally low. Finally:

• (ii) For each of the j = 1 to p groups, the mean ΔC _i,j over all i = 1 to k trees is calculated $(\overline{\Updelta C_j}=\sum^{k}_{i=1}{C_{i,j}/{k}}).$ The value $\overline{\Updelta C_j}\times 100$ is referred to as the ‘mean importance score’ of variable j. The value is positive when C _i,untouched >  C _i,j-permuted and negative when C _i,untouched <  C _i,j-permuted. Mean importance scores have high values when the classification error increases by permuting the values of variable p.

• (iii) Since correlations of the ΔC _i,j scores are generally low within the j = 1 to p groups, standard errors can be calculated for each of the j groups of i = 1 to k ΔC _i,j scores. Divide $\overline{\Updelta C_j}$ by the standard error (se) to obtain a z-score for variable j, and assign a significance level assuming normality.