Barriers to the spread of neutral alleles in the cytonuclear system

Neutral alleles can eventually pass a hybrid zone and their initial clines generated by a pure diffusion process dissipate with time, irrespective of the presence or absence of physical barriers. However, the transient neutral clines at the nuclear or organelle sites can be reinforced by the cytonuclear disequilibrium generated by diploid seed and haploid pollen dispersal. In this study, the spread of a neutral allele in an ecological zone of hermaphrodite plants is examined under three cytonuclear systems for genomes with contrasting modes of inheritance (paternal, maternal, and biparental inheritance). The results show that the transient neutral clines can exhibit the spatial pattern similar to the selective clines from separate genomes although discordance between them exists. The spread of a neutral allele is not only related to the vectors of seed and pollen dispersal but also to the mode of its inheritance. Pollen dispersal facilitates the direct effects of the selective organelle sites with paternal inheritance on the spread of a neutral nuclear allele. It also enhances its indirect effects on the spread of a neutral organelle allele with maternal inheritance via modifying the cytonuclear disequilibrium. A positive relationship exists between the barriers to the spread of selective nuclear (or organelle) and neutral organelle (or nuclear) alleles. An asymmetric barrier to the spread of the neutral alleles exists on the two sides of the physical barrier, given the presence of symmetric barrier to the spread of the selective alleles. These theoretical predictions highlight the effects of cytonuclear disequilibrium on the spread of a neutral allele and draw attention to our empirical cline analysis with neutral markers.