Geographical range margins of many taxonomic groups continue to shift polewards

Many species are extending their leading-edge (cool) range margins polewards in response to recent climate change. In the present study, we investigated range margin changes at the northern (cool) range margins of 1573 southerly-distributed species from 21 animal groups in Great Britain over the past four decades of climate change, updating previous work. Depending on data availability, range margin changes were examined over two time intervals during the past four decades. For four groups (birds, butterflies, macromoths, and dragonflies and damselflies), there were sufficient data available to examine range margin changes over both time intervals. We found that most taxa shifted their northern range margins polewards and this finding was not greatly influenced by changes in recorder effort. The mean northwards range margin change in the first time interval was 23 km per decade (N = 13 taxonomic groups) and, in the second interval, was 18 km per decade (N = 16 taxonomic groups) during periods when the British climate warmed by 0.21 and 0.28 °C per decade, respectively. For the four taxa examined over both intervals, there was evidence for higher rate of range margin change in the more recent time interval in the two Lepidoptera groups. Our analyses confirm a continued range margin shift polewards in a wide range of taxonomic groups.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Overcoming your child’s fears and worries: guided self-help manual for therapists working with groups

This manual for therapists accompanies ‘Overcoming your child’s fears and worries’ (Creswell & Willetts, 2007), a guide for parents to help their children overcome difficulties with anxiety