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We study a version of public announcement logic with common knowledge based on the relevant logic |$\textsf {R}$|⁠. Public announcements, as represented in our framework, are not necessarily truthful and accepted by all agents, nor is it assumed that beliefs are preserved under announcements. We establish a completeness result with respect to a relational semantics, and we show that an alternative semantics based on information states is dual to the relational one. We add a question-forming inquisitive disjunction operator to the language and prove a completeness result with respect to the information semantics. [ABSTRACT FROM AUTHOR]

Rapid advances in short-read DNA sequencing technologies have revolutionized population genomic studies, but there are genomic regions where this technology reaches its limits. Limitations mostly arise due to the difficulties in assembly or alignment to genomic regions of high sequence divergence and high repeat content, which are typical characteristics for loci under strong long-term balancing selection. Studying genetic diversity at such loci therefore remains challenging. Here, we investigate the feasibility and error rates associated with targeted long-read sequencing of a locus under balancing selection. For this purpose, we generated bacterial artificial chromosomes (BACs) containing the Brassicaceae S-locus, a region under strong negative frequency-dependent selection which has previously proven difficult to assemble in its entirety using short reads. We sequence S-locus BACs with single-molecule long-read sequencing technology and conduct de novo assembly of these S-locus haplotypes. By comparing repeated assemblies resulting from independent long-read sequencing runs on the same BAC clone we do not detect any structural errors, suggesting that reliable assemblies are generated, but we estimate an indel error rate of 5.7×10-5. A similar error rate was estimated based on comparison of Illumina short-read sequences and BAC assemblies. Our results show that, until de novo assembly of multiple individuals using long-read sequencing becomes feasible, targeted long-read sequencing of loci under balancing selection is a viable option with low error rates for single nucleotide polymorphisms or structural variation. We further find that short-read sequencing is a valuable complement, allowing correction of the relatively high rate of indel errors that result from this approach. [ABSTRACT FROM AUTHOR]

• Background and Aims The coexistence of hermaphrodites and female-sterile individuals, or androdioecy, has been documented in only a handful of plants and animals. This study reports its existence in the plant species Cardamine amara (Brassicaceae), in which female-sterile individuals have shorter pistils than seed-producing hermaphrodites. • Methods Morphological analysis, in situ manual pollination, microsatellite genotyping and differential gene expression analysis using Arabidopsis microarrays were used to delimit variation between female-sterile individuals and hermaphrodites. • Key Results Female sterility in C. amara appears to be caused by disrupted ovule development. It was associated with a 2.4- to 2.9-fold increase in clonal propagation. This made the pollen number of female-sterile genets more than double that of hermaphrodite genets, which fulfils a condition of co-existence predicted by simple androdioecy theories. When female-sterile individuals were observed in wild androdioecious populations, their ramet frequencies ranged from 5 to 54 %; however, their genet frequencies ranged from 11 to 29 %, which is consistent with the theoretically predicted upper limit of 50 %. • Conclusions The results suggest that a combination of sexual reproduction and increased asexual proliferation by female-sterile individuals probably explains the invasion and maintenance of female sterility in otherwise hermaphroditic populations. To our knowledge, this is the first report of the coexistence of female sterility and hermaphrodites in the Brassicaceae. [ABSTRACT FROM AUTHOR]

Theoretical and empirical comparisons of molecular diversity in selfing and outcrossing plants have primarily focused on long-term consequences of differences in mating system (between species). However, improving our understanding of the causes of mating system evolution requires ecological and genetic studies of the early stages of mating system transition. Here, we examine nuclear and chloroplast DNA sequences and microsatellite variation in a large sample of populations of Arabidopsis lyrata from the Great Lakes region of Eastern North American that show intra- and interpopulation variation in the degree of self-incompatibility and realized outcrossing rates. Populations show strong geographic clustering irrespective of mating system, suggesting that selfing either evolved multiple times or has spread to multiple genetic backgrounds. Diversity is reduced in selfing populations, but not to the extent of the severe loss of variation expected if selfing evolved due to selection for reproductive assurance in connection with strong founder events. The spread of self-compatibility in this region may have been favored as colonization bottlenecks following glaciation or migration from Europe reduced standing levels of inbreeding depression. However, our results do not suggest a single transition to selfing in this system, as has been suggested for some other species in the Brassicaceae. [ABSTRACT FROM AUTHOR]