Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By an essential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur in many compositional situations, such as household budget patterns, time budgets, palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful in such situations. From consideration of such examples it seems sensible to build up a model in two stages, the first determining where the zeros will occur and the second how the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

A Comparative study of germination strategies of two species of genus Allium sect. Allium

Germination experiments were performed with seeds of two species of genus Allium section Allium, a rare and endangered species A. pyrenaicum and a common A. sphaerocephalon. Different pre-treatments and a photoperiod of 24 h darkness were applied in order to simulate different germination conditions. Both species showed a high percentage of viable seeds a part of which were dormant. An elevate percentage of dormant seeds could be caused by a later collection time. Low altitude populations had more mortality than the others, possibly caused by the hard summer conditions during flowering and fruiting time. Comparisons between dates of species coexistence localities only show inter-population variability and it could be caused by the detected dormancy. Darkness accelerates germination, possibly for elongation radicle stimulation. Heat-shock pre-treatments decreased germination time in seeds from localities where fire is a probable event. The rarity of A. Pyrenaicum not seems to be caused by restricted germination requirements but is attributable to distinct habitat preferences, related to his altitudinal range of distribution