No abstract

Allopolyploids arise from the hybridization of two species concomitant to genome doubling. While established allopolyploids are common in nature and vigorous in growth, early generation allopolyploids are often less fertile than their progenitors and display frequent phenotypic instabilities. It is commonly assumed that new allopolyploid species must pass through a bottleneck from which only those lines emerge that have reconciled genomic incompatibilities inherited from their progenitors in their combined genome, yet little is known about the processes following allopolyploidization over evolutionary time. To address the question if a single allopolyploidization event leads to a single new homogeneous species or may result in diverse offspring lines, we have investigated 13 natural accessions of Arabidopsis suecica, a relatively recent allopolyploid derived from a single hybridization event. The studied accessions display low genetic diversity between lines, yet show evidence of heritable phenotypic diversity of traits, some of which may be adaptive. Furthermore, our data show that contrary to the notion that unstable phenotypes in neoallopolyploids are eliminated rapidly in the new species, some instabilities are carried along throughout the species' evolution, persisting in the established allopolyploid. In summary, our results suggest that a single allopolyploidization event may lay the foundation for diverse populations of the new allopolyploid species.

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We show there is an infinite number of knots whose unknotting numbers can only be realized through a sequence of crossing changes on a nonminimal projection, if ambient isotopies between crossing changes are not allowed. In this process, the question arises one crossing change at a time is made, always on a minimal projection, in order to obtain the unknotting number of a knot.

Given a pair of distinct points p and q in a metric space with distance d, the mediatrix is the set of points x such that d(x, p) = d(x, q). In this paper, we examine the topological structure of mediatrices in connected, compact, closed 2-manifolds whose distance function is inherited from a Riemannian metric. We determine that such mediatrices are, up to homeomorphism, finite, closed simplicial 1-complexes with an even number of incipient edges emanating from each vertex. Using this and results from [7], we give the classification up to homeomorphism of mediatrices on genus 1 tori (and on projective planes) and outline a method which may possibly be used to classify mediatrices on higher-genus surfaces.