Sexually Antagonistic “Zygotic Drive” of the Sex Chromosomes

Genomic conflict is perplexing because it causes the fitness of a species to decline rather than improve. Many diverse forms of genomic conflict have been identified, but this extant tally may be incomplete. Here, we show that the unusual characteristics of the sex chromosomes can, in principle, lead to a previously unappreciated form of sexual genomic conflict. The phenomenon occurs because there is selection in the heterogametic sex for sex-linked mutations that harm the sex of offspring that does not carry them, whenever there is competition among siblings. This harmful phenotype can be expressed as an antagonistic green-beard effect that is mediated by epigenetic parental effects, parental investment, and/or interactions among siblings. We call this form of genomic conflict sexually antagonistic “zygotic drive”, because it is functionally equivalent to meiotic drive, except that it operates during the zygotic and postzygotic stages of the life cycle rather than the meiotic and gametic stages. A combination of mathematical modeling and a survey of empirical studies is used to show that sexually antagonistic zygotic drive is feasible, likely to be widespread in nature, and that it can promote a genetic “arms race” between the homo- and heteromorphic sex chromosomes. This new category of genomic conflict has the potential to strongly influence other fundamental evolutionary processes, such as speciation and the degeneration of the Y and W sex chromosomes. It also fosters a new genetic hypothesis for the evolution of enigmatic fitness-reducing traits like the high frequency of spontaneous abortion, sterility, and homosexuality observed in humans

The Role of Transfer Operators and Shifts in the Study of Fractals: Encoding-Models, Analysis and Geometry, Commutative and Non-commutative

We study a class of dynamical systems in L2 spaces of infinite products X. Fix a compact Hausdorff space B. Our setting encompasses such cases when the dynamics on X = Bℕ is determined by the one-sided shift in X, and by a given transition-operator R. Our results apply to any positive operator R in C(B) such that R1 = 1. From this we obtain induced measures Σ on X, and we study spectral theory in the associated L2(X,Σ). For the second class of dynamics, we introduce a fixed endomorphism r in the base space B, and specialize to the induced solenoid Sol(r). The solenoid Sol(r) is then naturally embedded in X = Bℕ, and r induces an automorphism in Sol(r). The induced systems will then live in L2(Sol(r),Σ). The applications include wavelet analysis, both in the classical setting of ℝn, and Cantor-wavelets in the setting of fractals induced by affine iterated function systems (IFS). But our solenoid analysis includes such hyperbolic systems as the Smale- Williams attractor, with the endomorphism r there prescribed to preserve a foliation by meridional disks. And our setting includes the study of Julia set-attractors in complex dynamics. © Springer-Verlag Berlin Heidelberg 2014