Positive selection on an acrosomal sperm protein, M7 lysin, in three species of the mussel genus Mytilus

Marine invertebrate sperm proteins are particularly interesting because they are characterized by positive selection and are likely to be involved in prezyogotic isolation and, thus, speciation. Here, we present the first survey of inter and intraspecific variation of a bivalve sperm protein among a group of species that regularly hybridize in nature. M7 lysin is found in sperm acrosomes of mussels and dissolves the egg vitelline coat, permitting fertilization. We sequenced multiple alleles of the mature protein-coding region of M7 lysin from allopatric populations of mussels in the Mytilus edulis species group (M. edulis, M. galloprovincialis, and M. trossulus). A significant McDonald-Kreitman test showed an excess of fixed amino acid replacing substitutions between species, consistent with positive selection. In addition, Kolmogorov-Smirnov tests showed significant heterogeneity in polymorphism to divergence ratios for both synonymous variation and combined synonymous and non-synonymous variation within M. galloprovincialis. These results indicate that there has been adaptive evolution at M7 lysin and, furthermore, shows that positive selection on sperm proteins can occur even when post-zygotic reproductive isolation is incomplete.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.