Ordinal Pattern Dependence in the Context of Long-Range Dependence.

Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the dependence between the two processes. This article deals with ordinal pattern dependence for a long-range dependent time series including mixed cases of short- and long-range dependence. We investigate the limit distributions for estimators of ordinal pattern dependence. In doing so, we point out the differences that arise for the underlying time series having different dependence structures. Depending on these assumptions, central and non-central limit theorems are proven. The limit distributions for the latter ones can be included in the class of multivariate Rosenblatt processes. Finally, a simulation study is provided to illustrate our theoretical findings.

Results of 2-Year Ring Testing of a Semifield Study Design to Investigate Potential Impacts of Plant Protection Products on the Solitary Bees Osmia Bicornis and Osmia Cornuta and a Proposal for a Suitable Test Design.

There are various differences in size, behavior, and life history traits of non-Apis bee species compared with honey bees (Apis mellifera; Linnaeus, 1758). Currently, the risk assessment for bees in the international and national process of authorizing plant protection products has been based on honey bee data as a surrogate organism for non-Apis bees. To evaluate the feasibility of a semifield tunnel test for Osmia bicornis (Linnaeus, 1758) and Osmia cornuta (Latreille, 1805), a protocol was developed by the non-Apis working group of the International Commission for Plant-Pollinator Relationships, consisting of experts from authorities, academia, and industry. A total of 25 studies were performed over a 2-yr period testing a replicated control against a replicated positive control using either a dimethoate or diflubenzuron treatment. Studies were regarded to be valid, if ≥30% of released females were found to occupy the nesting units in the night/morning before the application (establishment). Thirteen studies were regarded to be valid and were analyzed further. Parameters analyzed were nest occupation, flight activity, cell production (total and per female), cocoon production (total and per female), emergence success, sex ratio, and mean weight of females and males. Dimethoate was a reliable positive control at the tested rate of 75 g a.i./ha, once >30% females had established, displaying acute effects such as reduction in flight activity, increase in adult mortality (shown by nest occupation), and reproduction ability of the females (total cell and cocoon production). On the other hand, no effects on larval and pupal development were observed. The growth regulator diflubenzuron had statistically significant effects on brood development, causing mortality of eggs and larvae at a rate of approximately 200 g a.i./ha, whereas fenoxycarb did not cause any significant effects at the tested rates of 300 and 600 g a.i./ha. In conclusion, the ring-test protocol proved to be adequate once the study comprised a well-established population of female Osmia bees, and the results improved in the second year as the laboratories increased their experience with the test organism. It is noted that the success of a study strongly depends on the experience of the experimenter, the crop quality, the quality of the cocoons, and the weather conditions. Based on these finding, recommendations for a semifield study design with Osmia spp. are proposed. Environ Toxicol Chem 2021;40:236-250. © 2020 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.