We consider the growth of an epitaxial thin film on a continuously supplied substrate using both the Burton-Cabrara-Frank (BCF) mean-field model and kinetic Monte-Carlo (KMC) simulation. Of particular interest are effects due to the finite size of the deposition zone, which is modeled by imposing an up-and downwind adatom density equal to the adatom density on an infinite terrace in equilibrium with a step. For the BCF model, we find this scenario admits a steady-state pattern with a specific number of steps separated by alternating widths. The specific spacing between the steps depends sensitively on the processing speed and on whether the number of steps is odd or even, with the range of velocities admitting an odd number of steps typically much narrower. These predictions are only partially confirmed by KMC simulations, however, with particularly poor agreement for an odd number of steps. To investigate further, we consider alternative KMC simulations with the interactions between random walkers on the terraces neglected so as to conform more closely with the mean field model. The latter simulations also more readily allow one to disable the step detachment mechanism, in which case they agree well with the predictions of the BCF model.

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The fitness effects associated with Wolbachia infection have wide-ranging ecological and evolutionary consequences for host species. How these effects are modulated by the relative influence of host and Wolbachia genomes has been described as a balancing act of genomic cooperation and conflict. For vertically transmitted symbionts, like cytoplasmic Wolbachia, concordant host–symbiont fitness interests would seem to select for genomic cooperation. However, Wolbachia’s ability to manipulate host reproductive systems and distort offspring sex ratios presents an evolutionary conflict of interest with infected hosts. In the parthenogenesis-inducing (PI) form of Wolbachia found in many haplodiploid insects, Wolbachia fitness is realized through females and is enhanced by their feminization of male embryos and subsequent parthenogenetic reproduction. In contrast, as long as Wolbachia is not fixed in a population and sexual reproduction persists, fitness for the host species is realized through both male and female offspring production. How these cooperating and competing interests interact and the relative influence of host and Wolbachia genomes were investigated in the egg parasitoid Trichogramma kaykai, where Wolbachia infection has remained at a low frequency in the field. A factorial design in which laboratory cultures of Wolbachia-infected T. kaykai were cured and re-infected with alternative Wolbachia strains was used to determine the relative influence of host and Wolbachia genomes on host fitness values. Our results suggest fitness variation is largely a function of host genetic background, except in the case of offspring sex ratio where a significant interaction between host and Wolbachia genomes was found. We also find a significant effect associated with the horizontal transfer of Wolbachia strains, which we discuss in terms of the potential for coadaptation in PI-Wolbachia symbioses.

Noninvertible circle maps may have a rotation interval instead of a unique rotation number. One may ask which of the numbers or sets of numbers within this rotation interval may be observed with positive probability in term of Lebesgue measure on the circle. We study this question numerically for families of circle maps. Both the interval and "observed" rotation numbers are computed for large numbers of initial conditions. The numerical evidence suggests that within the rotation interval only a very narrow band or even a unique rotation number is observed. These observed rotation numbers appear to be either locally constant or vary wildly as the parameter is changed. Closer examination reveals that intervals with wild variation contain many subintervals where the observed rotation numbers are locally constant. We discuss the formation of these intervals. We prove that such intervals occur whenever one of the endpoints of the rotation interval changes. We also examine the effects of various types of saddle-node bifurcations on the observed rotation numbers.