Hybrid Speciation and Introgression Both Underlie the Genetic Structures and Evolutionary Relationships of Three Morphologically Distinct Species of Lilium (Liliaceae) Forming a Hybrid Zone Along an Elevational Gradient

We studied hybrid interactions of Lilium meleagrinum, Lilium gongshanense, and Lilium saluenense using an integrative approach combining population genetics, fieldwork, and phenological research. These three species occur along an elevational gradient, with L. meleagrinum occurring at lower elevations, L. saluenense at higher elevations, and L. gongshanense between them. The species show strong morphological differentiation despite there being no clear environmental barriers to gene flow among them. Lilium gongshanense is likely to have a hybrid origin based on our prior work, but its progenitors remain uncertain. We sought to determine whether gene flow occurs among these three parapatric species, and, if so, whether L. gongshanense is a hybrid of L. meleagrinum and/or L. saluenense. We analyzed data from multiple chloroplast genes and spacers, nuclear internal transcribed spacer (ITS), and 18 nuclear Expressed Sequence Tag-Simple Sequence Repeat (EST-SSR) microsatellites for accessions of the three species representing dense population-level sampling. We also inferred phenology by examining species in the field and using herbarium specimens. We found that there are only two types of chloroplast genomes shared among the three species and that L. gongshanense forms two distinct groups with closest links to other species of Lilium based on ITS. Taken together, L. gongshanense is unlikely to be a hybrid species resulting from a cross between L. meleagrinum and L. saluenense, but gene flow is occurring among the three species. The gene flow is likely to be rare according to evidence from all molecular datasets, and this is corroborated by detection of only one putative hybrid individual in the field and asynchronous phenology. We suspect that the rarity of hybridization events among the species facilitates their continued genetic separation

Smoothing the Nonsmoothness

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is established and an illustration of its application is then provided

Ailanthone targets p23 to overcome MDV3100 resistance in castration-resistant prostate cancer

Androgen receptor (AR) antagonist MDV3100 is the first therapeutic approach in treating castration-resistant prostate cancer (CRPC), but tumours frequently become drug resistant via multiple mechanisms including AR amplification and mutation. Here we identify the small molecule Ailanthone (AIL) as a potent inhibitor of both full-length AR (AR-FL) and constitutively active truncated AR splice variants (AR-Vs). AIL binds to the co-chaperone protein p23 and prevents AR's interaction with HSP90, thus resulting in the disruption of the AR-chaperone complex followed by ubiquitin/proteasome-mediated degradation of AR as well as other p23 clients including AKT and Cdk4, and downregulates AR and its target genes in PCa cell lines and orthotopic animal tumours. In addition, AIL blocks tumour growth and metastasis of CRPC. Finally, AIL possesses favourable drug-like properties such as good bioavailability, high solubility, lack of CYP inhibition and low hepatotoxicity. In general, AIL is a potential candidate for the treatment of CRPC

Lilium liangiae, a new species in the genus Lilium (Liliaceae) that reveals parallel evolution within morphology

The former genus Nomocharis, which has been merged as a clade within the genus Lilium (Liliaceae), represents one of the most complicated and unclear groups included in the latter. Research on members of the Nomocharis clade has been quite limited due to the sampling difficulties caused by its selective environmental preferences. In this study, we propose a new species within this clade, Lilium liangiae, as a further bridge connecting the former genus Nomocharis with other members of the genus Lilium. We conducted morphological clustering, phylogenetic, and comparative genomics analyses of nuclear internal spacers and the newly generated complete chloroplast genome, in conjunction with previously published sequences, and performed ancestral state reconstruction to clarify the evolutionary pattern of important traits in Lilium. The clustering results of 38 morphological traits indicated that the new species is allied to Nomocharis, further increasing the morphological polymorphism in the latter. The phylogenetic results and morphological clustering both supported L. liangiae belonging to the subclade Ecristata in Nomocharis, its closest affinity being Lilium gongshanense. Inconsistencies in phylogenetic relationships were detected between nuclear and plastid datasets, possibly due to ancient hybridization and ongoing introgression. Comparative genomics revealed the conservation and similarity of their chloroplast genomes, with variations observed in the expansion and contraction of the IR regions. A/T and palindromic repeat sequences were the most abundant. Seven highly variable regions (Pi≥0.015) were identified as potential molecular markers based on the chloroplast genomes of 47 species within Lilium. Both nuclear and plastid genes exhibited very low variability within the Nomocharis clade, contrasting with their highly variable morphological appearance. The ancestral state reconstruction analysis suggests that the campanulate flower form, as in L. liangiae, arose at least three times within the genus Lilium, revealing parallel evolution in the latter. Overall, this study adds important genetic and morphological evidence for understanding the phylogenetic relationships and parallel evolution patterns of species within the genus Lilium

Almost first-degree stochastic dominance for transformations and its application in insurance strategy

Almost stochastic dominance is a relaxation of stochastic dominance, which allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. The authors first discuss the relations between almost first-degree stochastic dominance (AFSD) and the second-degree stochastic dominance (SSD), and demonstrate that the AFSD criterion is helpful to narrow down the SSD efficient set. Since the existing AFSD criterion is not convenient to rank transformations of random variables due to its relying heavily on cumulative distribution functions, the authors propose the AFSD criterion for transformations of random variables by means of transformation functions and the probability function of the original random variable. Moreover, they employ this method to analyze the transformations resulting from insurance and option strategy

Sufficient conditions of stochastic dominance for general transformations and its application in option strategy

A counterexample is presented to show that the sufficient condition for one transformation dominating another by the second degree stochastic dominance, proposed by Theorem 5 of Levy (Stochastic dominance and expected utility: Survey and analysis, 1992), does not hold. Then, by restricting the monotone property of the dominating transformation, a revised exact sufficient condition for one transformation dominating another is given. Next, the stochastic dominance criteria, proposed by Meyer (Stochastic dominance and transformations of random variables, 1989) and developed by Levy (1992), are extended to the most general transformations. Moreover, such criteria are further generalized to transformations on discrete random variables. Finally, the authors employ this method to analyze the transformations resulting from holding a stock with the corresponding call option