Decompositions of finite projective planes

We consider decompositions of finite projective planes into copies of a particular structure. Our main theorem provides a connection between the existence of a proper projective subplane and the existence of a decomposition into sets of collinear points. Based on this result, we develop a connection between the existence of a projective subplane in a plane II and that of a hitting set in the dual of II.

Blue sky thinking : using projective techniques to stimulate discussion, reflection and insight

The prime purpose of this session is to share a new use of projective techniques to stimulate discussion, reflection and insight with students. The session will provide an introduction to the nature and use of projective techniques and an explanation why images of the sky were chosen as the stimuli. Then, the majority of the session will consist of an opportunity to experience this new technique in a simulated session. The session will end with a plenary discussion and a review of the effectiveness and applicability of the technique.

The influence of non-climate predictors at local and landscape resolutions depends on the autecology of the species

Species distribution models have come under criticism for being too simplistic for making robust future forecasts, partly because they assume that climate is the main determinant of geographical range at large spatial extents and coarse resolutions, with non-climate predictors being important only at finer scales. We suggest that this paradigm might be obscured by species movement patterns. To explore this we used contrasting kangaroo (family Macropodidae) case studies: two species with relatively small, stable home ranges (Macropus giganteus and M.robustus) and three species with more extensive, adaptive ranging behaviour (M.antilopinus, M.fuliginosus and M.rufus). We predicted that non-climate predictors will be most influential to model fit and predictive performance at local spatial resolution for the former species and at landscape resolution for the latter species. We compared residuals autocovariate - boosted regression tree (RAC-BRT) model statistics with and without species-specific non-climate predictors (habitat, soil, fire, water and topography), at local- and landscape-level spatial resolutions (5 and 50km). As predicted, the influence of non-climate predictors on model fit and predictive performance (compared with climate-only models) was greater at 50 compared with 5km resolution for M.rufus and M.fuliginosus and the opposite trend was observed for M.giganteus. The results for M.robustus and M.antilopinus were inconclusive. Also notable was the difference in inter-scale importance of climate predictors in the presence of non-climate predictors. In conclusion, differences in autecology, particularly relating to space use, may contribute to the importance of non-climate predictors at a given scale, not model scale per se. Further exploration of this concept across a range of species is encouraged and findings may contribute to more effective conservation and management of species at ecologically meaningful scales. © 2014 Ecological Society of Australia.