Species mobility and frequency dynamics in a Swiss limestone grassland

Community dynamics in a calcareous grassland (Mesobrometum) in Egerkingen (Jura mountains, Switzerland) were investigated for 53 non-woody species in 25 1-m2 plots over 6 years. 50 0.0 1-m2 subplots per plot were recorded. The derived variables were spatial frequency, temporal frequency, frequency fluctuation, turnover, and cumulative frequency (each species), and cumulative species richness (all species). Spectra for 53 species of all variables were different for the two investigated spatial scales (0.0 1 m2, 1 m2). The comparison with other investigations of similar grass lands showed that the behaviour of some species is specific for this type of vegetation in general (e.g. Achillea millefolium, Arrhenatherum elatius, Bromus erectus ), but most species behaved in a stand-specific way, i.e. they may play another (similar or completely different) role in another grassland stand. Six spatio-temporal patterns were defined across species. To understand community dynamics, not only the dynamics of mobility but also of frequency fluctuations and spatial distribution of the species are fundamental. In addition, the understanding of temporal behaviour of all species present should be included. Averages always hide important information of vegetation dynamics, as was shown by the present investigation.

Robust meta-analytic-predictive priors in clinical trials with historical control information.

Historical information is always relevant for clinical trial design. Additionally, if incorporated in the analysis of a new trial, historical data allow to reduce the number of subjects. This decreases costs and trial duration, facilitates recruitment, and may be more ethical. Yet, under prior-data conflict, a too optimistic use of historical data may be inappropriate. We address this challenge by deriving a Bayesian meta-analytic-predictive prior from historical data, which is then combined with the new data. This prospective approach is equivalent to a meta-analytic-combined analysis of historical and new data if parameters are exchangeable across trials. The prospective Bayesian version requires a good approximation of the meta-analytic-predictive prior, which is not available analytically. We propose two- or three-component mixtures of standard priors, which allow for good approximations and, for the one-parameter exponential family, straightforward posterior calculations. Moreover, since one of the mixture components is usually vague, mixture priors will often be heavy-tailed and therefore robust. Further robustness and a more rapid reaction to prior-data conflicts can be achieved by adding an extra weakly-informative mixture component. Use of historical prior information is particularly attractive for adaptive trials, as the randomization ratio can then be changed in case of prior-data conflict. Both frequentist operating characteristics and posterior summaries for various data scenarios show that these designs have desirable properties. We illustrate the methodology for a phase II proof-of-concept trial with historical controls from four studies. Robust meta-analytic-predictive priors alleviate prior-data conflicts ' they should encourage better and more frequent use of historical data in clinical trials.