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Bottom-up effects of plant diversity on multitrophic interactions in a biodiversity experiment
(2010)
In order to predict which ecosystem functions are most at risk from biodiversity loss, meta-analyses have generalised results from biodiversity experiments over different sites and ecosystem types. In contrast, comparing the strength of biodiversity effects across a large number of ecosystem processes measured in a single experiment permits more direct comparisons. Here, we present an analysis of 418 separate measures of 38 ecosystem processes. Overall, 45 % of processes were significantly affected by plant species richness, suggesting that, while diversity affects a large number of processes not all respond to biodiversity. We therefore compared the strength of plant diversity effects between different categories of ecosystem processes, grouping processes according to the year of measurement, their biogeochemical cycle, trophic level and compartment (above- or belowground) and according to whether they were measures of biodiversity or other ecosystem processes, biotic or abiotic and static or dynamic. Overall, and for several individual processes, we found that biodiversity effects became stronger over time. Measures of the carbon cycle were also affected more strongly by plant species richness than were the measures associated with the nitrogen cycle. Further, we found greater plant species richness effects on measures of biodiversity than on other processes. The differential effects of plant diversity on the various types of ecosystem processes indicate that future research and political effort should shift from a general debate about whether biodiversity loss impairs ecosystem functions to focussing on the specific functions of interest and ways to preserve them individually or in combination.
Although temporal heterogeneity is a well-accepted driver of biodiversity, effects of interannual variation in land-use intensity (LUI) have not been addressed yet. Additionally, responses to land use can differ greatly among different organisms; therefore, overall effects of land-use on total local biodiversity are hardly known. To test for effects of LUI (quantified as the combined intensity of fertilization, grazing, and mowing) and interannual variation in LUI (SD in LUI across time), we introduce a unique measure of whole-ecosystem biodiversity, multidiversity. This synthesizes individual diversity measures across up to 49 taxonomic groups of plants, animals, fungi, and bacteria from 150 grasslands. Multidiversity declined with increasing LUI among grasslands, particularly for rarer species and aboveground organisms, whereas common species and belowground groups were less sensitive. However, a high level of interannual variation in LUI increased overall multidiversity at low LUI and was even more beneficial for rarer species because it slowed the rate at which the multidiversity of rare species declined with increasing LUI. In more intensively managed grasslands, the diversity of rarer species was, on average, 18% of the maximum diversity across all grasslands when LUI was static over time but increased to 31% of the maximum when LUI changed maximally over time. In addition to decreasing overall LUI, we suggest varying LUI across years as a complementary strategy to promote biodiversity conservation.
Land-use intensification is a key driver of biodiversity change. However, little is known about how it alters relationships between the diversities of different taxonomic groups, which are often correlated due to shared environmental drivers and trophic interactions. Using data from 150 grassland sites, we examined how land-use intensification (increased fertilization, higher livestock densities, and increased mowing frequency) altered correlations between the species richness of 15 plant, invertebrate, and vertebrate taxa. We found that 54% of pairwise correlations between taxonomic groups were significant and positive among all grasslands, while only one was negative. Higher land-use intensity substantially weakened these correlations(35% decrease in rand 43% fewer significant pairwise correlations at high intensity), a pattern which may emerge as a result of biodiversity declines and the breakdown of specialized relationships in these conditions. Nevertheless, some groups (Coleoptera, Heteroptera, Hymenoptera and Orthoptera) were consistently correlated with multidiversity, an aggregate measure of total biodiversity comprised of the standardized diversities of multiple taxa, at both high and lowland-use intensity. The form of intensification was also important; increased fertilization and mowing frequency typically weakened plant-plant and plant-primary consumer correlations, whereas grazing intensification did not. This may reflect decreased habitat heterogeneity under mowing and fertilization and increased habitat heterogeneity under grazing. While these results urge caution in using certain taxonomic groups to monitor impacts of agricultural management on biodiversity, they also suggest that the diversities of some groups are reasonably robust indicators of total biodiversity across a range of conditions.
Land-use intensification is a major driver of biodiversity loss(1,2). Alongside reductions in local species diversity, biotic homogenization at larger spatial scales is of great concern for conservation. Biotic homogenization means a decrease in beta-diversity (the compositional dissimilarity between sites). Most studies have investigated losses in local (alpha)-diversity(1,3) and neglected biodiversity loss at larger spatial scales. Studies addressing beta-diversity have focused on single or a few organism groups (for example, ref. 4), and it is thus unknown whether land-use intensification homogenizes communities at different trophic levels, above-and belowground. Here we show that even moderate increases in local land-use intensity (LUI) cause biotic homogenization across microbial, plant and animal groups, both above- and belowground, and that this is largely independent of changes in alpha-diversity. We analysed a unique grassland biodiversity dataset, with abundances of more than 4,000 species belonging to 12 trophic groups. LUI, and, in particular, high mowing intensity, had consistent effects on beta-diversity across groups, causing a homogenization of soil microbial, fungal pathogen, plant and arthropod communities. These effects were nonlinear and the strongest declines in beta-diversity occurred in the transition from extensively managed to intermediate intensity grassland. LUI tended to reduce local alpha-diversity in aboveground groups, whereas the alpha-diversity increased in belowground groups. Correlations between the alpha-diversity of different groups, particularly between plants and their consumers, became weaker at high LUI. This suggests a loss of specialist species and is further evidence for biotic homogenization. The consistently negative effects of LUI on landscape-scale biodiversity underscore the high value of extensively managed grasslands for conserving multitrophic biodiversity and ecosystem service provision. Indeed, biotic homogenization rather than local diversity loss could prove to be the most substantial consequence of land-use intensification.
Species diversity promotes the delivery of multiple ecosystem functions (multifunctionality). However, the relative functional importance of rare and common species in driving the biodiversity multifunctionality relationship remains unknown. We studied the relationship between the diversity of rare and common species (according to their local abundances and across nine different trophic groups), and multifunctionality indices derived from 14 ecosystem functions on 150 grasslands across a land use intensity (LUI) gradient. The diversity of above- and below-ground rare species had opposite effects, with rare above-ground species being associated with high levels of multifunctionality, probably because their effects on different functions did not trade off against each other. Conversely, common species were only related to average, not high, levels of multifunctionality, and their functional effects declined with LUI. Apart from the community level effects of diversity, we found significant positive associations between the abundance of individual species and multifunctionality in 6% of the species tested. Species specific functional effects were best predicted by their response to LUI: species that declined in abundance with land use intensification were those associated with higher levels of multifunctionality. Our results highlight the importance of rare species for ecosystem multifunctionality and help guiding future conservation priorities.
We analyze a general class of self-adjoint difference operators H-epsilon = T-epsilon + V-epsilon on l(2)((epsilon Z)(d)), where V-epsilon is a multi-well potential and v(epsilon) is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]). Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H-epsilon is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H-epsilon, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H-epsilon converge to the first n eigenvalues of the direct sum of harmonic oscillators on R-d located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H-epsilon. These are obtained from eigenfunctions or quasimodes for the operator H-epsilon acting on L-2(R-d), via restriction to the lattice (epsilon Z)(d). Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrodinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted l(2)-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two "wells" (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrodinger operator in [22].
Metastability in reversible diffusion processes : II. Precise asymptotics for small eigenvalues
(2005)
We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form -epsilonDelta + delF(.) del on R-d or subsets of Rd, where F is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum is given, up to multiplicative errors tending to one, by the eigenvalues of the classical capacity matrix of the array of capacitors made of balls of radius epsilon centered at the positions of the local minima of F. We also get very precise uniform control on the corresponding eigenfunctions. Moreover, these eigenvalues can be identified with the same precision with the inverse mean metastable exit times from each minimum. In [BEGK3] it was proven that these mean times are given, again up to multiplicative errors that tend to one, by the classical Eyring- Kramers formula
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N --> infinity (where N, or N-d with d greater than or equal to 1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N-d and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types
Consider the operator T = -d(2)/dx(2) + x(2) + q(x) in L-2 (R), where q is a real function with q' and integral(0)(x) q(s) ds bounded. The spectrum of T is purely discrete and consists of simple eigenvalues. We determine their asymptotics mu(n) = (2n + 1) + (2 pi)(-1) integral(-pi)(pi) q(root 2n+1 sin theta)d theta + O(n(-1/3)) and we extend these results for complex q.