Transient microgeographic clines during B chromosome invasion

The near-neutral model of B chromosome evolution predicts that the invasion of a new population should last some tens of generations, but the details on how it proceeds in real populations are mostly unknown. Trying to fill this gap, we analyze here a natural population of the grasshopper Eyprepocnemis plorans at three time points during the last 35 years. Our results show that B chromosome frequency increased significantly during this period, and that a cline observed in 1992 had disappeared in 2012 once B frequency reached an upper limit in all sites sampled. This indicates that, during B chromosome invasion, at microgeographic scale, transient clines for B frequency are formed at the invasion front. Computer simulation experiments showed that the pattern of change observed for genotypic frequencies is consistent with the existence of B chromosome drive through females and selection against individuals with high number of B chromosomes.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.