Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit

Global data on earthworm abundance, biomass, diversity and corresponding environmental properties

Publisher Copyright: © 2021, The Author(s).Earthworms are an important soil taxon as ecosystem engineers, providing a variety of crucial ecosystem functions and services. Little is known about their diversity and distribution at large spatial scales, despite the availability of considerable amounts of local-scale data. Earthworm diversity data, obtained from the primary literature or provided directly by authors, were collated with information on site locations, including coordinates, habitat cover, and soil properties. Datasets were required, at a minimum, to include abundance or biomass of earthworms at a site. Where possible, site-level species lists were included, as well as the abundance and biomass of individual species and ecological groups. This global dataset contains 10,840 sites, with 184 species, from 60 countries and all continents except Antarctica. The data were obtained from 182 published articles, published between 1973 and 2017, and 17 unpublished datasets. Amalgamating data into a single global database will assist researchers in investigating and answering a wide variety of pressing questions, for example, jointly assessing aboveground and belowground biodiversity distributions and drivers of biodiversity change.Peer reviewe

Global data on earthworm abundance, biomass, diversity and corresponding environmental properties

Earthworms are an important soil taxon as ecosystem engineers, providing a variety of crucial ecosystem functions and services. Little is known about their diversity and distribution at large spatial scales, despite the availability of considerable amounts of local-scale data. Earthworm diversity data, obtained from the primary literature or provided directly by authors, were collated with information on site locations, including coordinates, habitat cover, and soil properties. Datasets were required, at a minimum, to include abundance or biomass of earthworms at a site. Where possible, site-level species lists were included, as well as the abundance and biomass of individual species and ecological groups. This global dataset contains 10,840 sites, with 184 species, from 60 countries and all continents except Antarctica. The data were obtained from 182 published articles, published between 1973 and 2017, and 17 unpublished datasets. Amalgamating data into a single global database will assist researchers in investigating and answering a wide variety of pressing questions, for example, jointly assessing aboveground and belowground biodiversity distributions and drivers of biodiversity change

Is the meiofauna a good indicator for climate change and anthropogenic impacts?

Our planet is changing, and one of the most pressing challenges facing the scientific community revolves around understanding how ecological communities respond to global changes. From coastal to deep-sea ecosystems, ecologists are exploring new areas of research to find model organisms that help predict the future of life on our planet. Among the different categories of organisms, meiofauna offer several advantages for the study of marine benthic ecosystems. This paper reviews the advances in the study of meiofauna with regard to climate change and anthropogenic impacts. Four taxonomic groups are valuable for predicting global changes: foraminifers (especially calcareous forms), nematodes, copepods and ostracods. Environmental variables are fundamental in the interpretation of meiofaunal patterns and multistressor experiments are more informative than single stressor ones, revealing complex ecological and biological interactions. Global change has a general negative effect on meiofauna, with important consequences on benthic food webs. However, some meiofaunal species can be favoured by the extreme conditions induced by global change, as they can exhibit remarkable physiological adaptations. This review highlights the need to incorporate studies on taxonomy, genetics and function of meiofaunal taxa into global change impact research