Decomposition of functional beta, but not alpha, diversity detects deviations from the “host-diversity-begets-parasite-diversity” rule in flea-mammal associations

The "host-diversity-begets-parasite-diversity" (HDBPD) pattern has been demonstrated for traditional metrics of functional diversity. We applied the decomposition of functional alpha (functional diversity structure; FDS) and beta (functional resemblance; FR) diversity into (a) Simpson's dominance, functional redundancy, and functional diversity and (b) taxonomic similarity, functional dissimilarity, and beta redundancy, respectively, coupled with ternary diagrams, to test whether the HDBPD rule also holds for FDS and FR and their separate components for communities of fleas and small mammals from different biomes of the Palearctic. We compared patterns of FDS and FR and their components within and between fleas and hosts within and between biomes and tested for correlation of separate components of functional alpha and beta diversities between fleas and hosts. Differences in FR between biomes were detected for both fleas and hosts (due to differences in each FR component), but not in FDS. Within biomes, fleas and hosts demonstrated marginally significant differences in FDS in steppes and temperate forests due to differences in the functional diversity component. Differences in FR between fleas and hosts were found in four of five biomes (due to differences in one or two FR components). Values of each of the three separate components of the flea FDS correlated positively with values of the respective components of the host FDS suggesting the effect of functional alpha diversity of hosts on that of fleas. No correlation between separate components of the flea and host FR was found implying no link between host and flea functional beta diversity. We conclude that the HDBPD rule, when applied to functional beta diversity, is not as universal as it was previously thought to be.