Multiple planar coincidences with N-fold symmetry

Planar coincidence site lattices and modules with N-fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results for spectral, combinatorial and asymptotic properties in terms of Dirichlet series generating functions.Comment: 13 pages, two figures. For previous related work see math.MG/0511147 and math.CO/0301021. Minor changes and references update

On right conjugacy closed loops of twice prime order

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl

Monarch butterflies do not place all of their eggs in one basket: oviposition on nine Midwestern milkweed species

Over the past two decades, the population of monarch butterflies east of the Rocky Mountains has experienced a significant decline in overwintering numbers. Habitat restoration that includes planting milkweeds is essential to boost monarch numbers within the breeding range. Milkweeds are the only host plants for larval monarch butterflies, but female oviposition preference for different milkweed species, especially those with overlapping ranges, is not well documented. We examined the relative inclination to lay eggs on nine milkweed species native to Iowa (no choice), and oviposition preference (choice) among the four most commonly occurring Iowa species (Asclepias incarnata, Asclepias syriaca, Asclepias tuberosa, and Asclepias verticillata). In both experiments, eggs were counted daily for four days. The milkweeds tested were Asclepias exaltata (poke milkweed), Asclepias hirtella (tall green milkweed), A. incarnata (swamp milkweed), Asclepias speciosa (showy milkweed), Asclepias sullivantii (prairie milkweed), A. syriaca (common milkweed), A. tuberosa (butterfly milkweed), A. verticillata (whorled milkweed), and Cynanchum laeve (honeyvine milkweed). When females were given only a single species on which to lay eggs, there were significant differences among milkweed species in the average number of eggs laid; A. incarnata had the highest average egg count. When females were given a choice among A. incarnata, A. syriaca, A. tuberosa, and A. verticillata, there were also differences among milkweed species in the number of eggs laid; again, A. incarnata had the highest average number of eggs laid. Additionally, females laid more total eggs when four plants of different milkweed species were available than when there were four plants of a single milkweed species. Our results show that monarch butterflies will lay eggs on all nine milkweeds, but that there are clear preferences for some milkweed species over others

Microgeographical, inter-individual, and intra-individual variation in the flower characters of Iberian pear Pyrus bourgaeana (Rosaceae)

Flower characteristics have been traditionally considered relatively constant within species. However, there are an increasing number of examples of variation in flower characteristics. In this study, we examined the variation in attracting and rewarding flower characters at several ecological levels in a metapopulation of Pyrus bourgaeana in the Doñana area (SW Spain). We answered the following questions: what are the variances of morphological and nectar characters of flowers? How important are intra-individual and inter-individual variance in flower characters? Are there microgeographical differences in flower characters? And if so, are they consistent between years? In 2008 and 2009, we sampled flowers of 72 trees from five localities. For six flower morphological and two nectar characteristics, we calculated coefficients of variation (CV). The partitioning of total variation among-localities, among-individuals, and within-individuals was estimated. To analyze differences among localities and their consistency between years, we conducted generalized linear mixed models. The CVs of nectar characters were always higher than those of morphological characters. As expected, inter-individual variation was the main source of variation of flower morphology, but nectar characters had significant variation at both intra- and inter-individual levels. For most floral traits, there were no differences among localities. Our study documents that variation is a scale-dependent phenomenon and that it is essential to consider intra- and inter-individual variance when investigating the causes and consequences of variation. It also shows that single year studies of floral characters should be viewed with caution