Suppression of Wolbachia-mediated male-killing in the butterfly Hypolimnas bolina involves a single genomic region

Background Sex ratio distorting agents (maternally inherited symbionts and meiotically-driving sex chromosomes) are common in insects. When these agents rise to high frequencies they create strong population sex ratio bias and selection then favours mutations that act to restore the rare sex. Despite this strong selection pressure, the evolution of mutations that suppress sex ratio distorting elements appears to be constrained in many cases, where sex-biased populations persist for many generations. This scenario has been observed in the butterfly Hypolimnas bolina, where Wolbachia-mediated male killing endured for 800–1,000 generations across multiple populations before the evolution of suppression. Here we test the hypothesis that this evolutionary lag is the result of suppression being a multilocus trait requiring multiple mutations. Methods We developed genetic markers, based on conservation of synteny, for each H. bolina chromosome and verified coverage using recombinational mapping. We then used a Wolbachia-infected mapping family to assess each chromosome for the presence of loci required for male survival, as determined by the presence of markers in all surviving sons. Results Informative markers were obtained for each of the 31 chromosomes in H. bolina. The only marker that cosegregated with suppression was located on chromosome 25. A genomic region necessary for suppression has previously been located on this chromosome. We therefore conclude that a single genomic region of the H. bolina genome is necessary for male-killing suppression. Discussion The evolutionary lag observed in our system is not caused by a need for changes at multiple genomic locations. The findings favour hypotheses in which either multiple mutations are required within a single genomic region, or the suppressor mutation is a singularly rare event.

FRACTALS FROM NONLINEAR IFSs OF THE COMPLEX MAPPING FAMILY f(z) = zn + c

To generate exotic fractals, we investigate the construction of nonlinear iterated function system (IFS) using the complex mapping family [Formula: see text] ([Formula: see text]). A set of [Formula: see text]-values is chosen from the period-1 bulb of the Mandelbrot set, so that each mapping has an attracting fixed point in the dynamic plane. Computer experiments show that a set of arbitrarily chosen [Formula: see text]-values may not be able to generate a fractal. We prove a sufficient condition that if the [Formula: see text]-values are chosen from a specific region related to a circle in the period-1 bulb, the nonlinear IFS with such complex mappings is able to generate exotic fractal. Furthermore, if the set of [Formula: see text]-values possesses a specific symmetry in the Mandelbrot set, then the fractal also exhibits the same symmetry. We present a method of generating aesthetic fractals with [Formula: see text] or [Formula: see text] symmetry for [Formula: see text] and with [Formula: see text] or [Formula: see text] symmetry for [Formula: see text].