There is a recent proposal to apply convex hulls to the measurement of habitat filtering, trophic diversity and functional richness. Although this approach has successful applications, some conceptual difficulties with the interpretation of results should not be overlooked. The basic assumption that trait convergence and the associated deflation of the convex hull is a result of environmental (habitat) filtering does not always hold, because 1) some traits may converge as a result of competition as well, and 2) environmental factors, such as disturbance, may lead to divergence, rather than convergence for certain characters. There is neither evidence nor theoretical proof that increasing correlations between traits and reduction in trait combinations are always caused by habitat filtering, especially when individual trait tranges are unchanged. Diversity measurements in terms of convex hull volumes may be misleading because zero or near zero values may results no matter how wide the individual trait ranges are. For these reasons, applications of convex hulls cannot be viewed uncritically, and considerable care must be taken even if the method is used in combination with other techniques.
Beta diversity, species replacement and nestedness are often examined through pairwise comparisons of sites based on presence-absence data, and the relative importance of these ecological phenomena is evaluated by operations with dissimilarity coefficients. An example is the nestedness resultant dissimilarity (NRD) procedure recently proposed by Baselga (2010, Global Ecology andBiogeography 19: 134–143) to disentangle the nestedness fraction of beta diversity from species replacement. In our view, the component terms in this measure are not scaled uniformly and the nestedness fraction cannot be quantified properly without giving clear definitions for its measurement. We suggest to distinguish among three additive fractions of the species set of two sites: number of species shared (overlap), species replacement (=spatial turnover) and richness difference. Then, absolute beta diversity is obtained as a composite of the second two fractions (known as βWB), while nestedness is derived from the first and the third. To express beta diversity and nestedness in a relativized form, the respective sums are divided by the total number of species. These allow defining a new index to measure the fraction of beta diversity which is shared by nestedness as well, and is calculated as relativized richness difference with the condition that the two sites being compared have at least one species in common. It is called diversity-nestedness intersection coefficient (F). Baselga’s nestedness resultant dissimilarity and the diversity-nestedness intersection coefficient are compared graphically using artificial and actual examples. These functions follow a mathematical relationship for perfectly nested data, otherwise their results are divergent. Discrepancy increases when beta diversity is large, especially if richness differences override species replacement effects in shaping presence-absence data structures. An advantage of F is its compatibility with a general theoretical and methodological framework for revealing pattern in presence-absence data matrices.
The paper evaluates spatial autocorrelation structure in grassland vegetation at the community level. We address the following main issues: 1) How quadrat size affects the measurement of spatial autocorrelation for presence/ absence and cover data? 2) What is the relationship between spatial autocorrelation and classification? 3) Is there a temporal change of spatial autocorrelation in the vegetation studied? We found that multivariate variogram shape, variance explained and the sill are different for presence/absence data and cover data, whereas quadrat size increases apparently introduce a stabilizing effect for both. Spatial stationarity is detected for species presence, and non-stationarity for cover. A new graphical tool, the clusterogram is introduced to examine spatial dependence of classification at various numbers of clusters. We found that spatial autocorrelation plays a crucial role in the classification of vegetation and therefore we suggest that its effect should not be removed from clustering. Mutual interpretation of variogram and clusterogram shape may be informative on the number of meaningful clusters present in the data. Spatial autocorrelation structure did not change markedly after 23 years for presence/absence data, indicating that the vegetation of the study area is stationary in time as well. The present study demonstrates that traditional quadrat data are suitable for evaluating spatial autocorrelation, even though field coordinates are recorded several years after sampling is completed.
The paper advocates a more extensive use of additive trees in community ecology. When the distance/dissimilarity coefficient is selected carefully, these trees can illuminate structural aspects that are not obvious otherwise. In particular, starting from squared distances based on presence/absence data, the resulting trees approximate relationships in species richness, a feature not available through other graphical techniques. The construction of additive trees is illustrated by three actual examples, representing different circumstances in the analysis of grassland community data.
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