BackgroundThe castor bean (Ricinus communis L.), a monotypic species in the spurge family (Euphorbiaceae, 2n = 20), is an important non-edible oilseed crop widely cultivated in tropical, sub-tropical and temperate countries for its high economic value. Because of the high level of ricinoleic acid (over 85%) in its seed oil, the castor bean seed derivatives are often used in aviation oil, lubricants, nylon, dyes, inks, soaps, adhesive and biodiesel. Due to lack of efficient molecular markers, little is known about the population genetic diversity and the genetic relationships among castor bean germplasm. Efficient and robust molecular markers are increasingly needed for breeding and improving varieties in castor bean. The advent of modern genomics has produced large amounts of publicly available DNA sequence data. In particular, expressed sequence tags (ESTs) provide valuable resources to develop gene-associated SSR markers.ResultsIn total, 18,928 publicly available non-redundant castor bean EST sequences, representing approximately 17.03 Mb, were evaluated and 7732 SSR sites in 5,122 ESTs were identified by data mining. Castor bean exhibited considerably high frequency of EST-SSRs. We developed and characterized 118 polymorphic EST-SSR markers from 379 primer pairs flanking repeats by screening 24 castor bean samples collected from different countries. A total of 350 alleles were identified from 118 polymorphic SSR loci, ranging from 2-6 per locus (A) with an average of 2.97. The EST-SSR markers developed displayed moderate gene diversity (He) with an average of 0.41. Genetic relationships among 24 germplasms were investigated using the genotypes of 350 alleles, showing geographic pattern of genotypes across genetic diversity centers of castor bean.ConclusionCastor bean EST sequences exhibited considerably high frequency of SSR sites, and were rich resources for developing EST-SSR markers. These EST-SSR markers would be particularly useful for both genetic mapping and population structure analysis, facilitating breeding and crop improvement of castor bean.

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Abstract. Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms. The impossibilities show that the properties satisfied by CCEA and MEA are maximal subsets of properties that can be satisfied by any algorithm for piecewise constant valuation profiles.

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