Inheritance of distyly and homostyly in self-incompatible Primula forbesii.

The evolutionary transition from self-incompatible distyly to self-compatible homostyly frequently occurs in heterostylous taxa. Although the inheritance of distyly and homostyly has been deeply studied, our understanding on modifications of the classical simple Mendelian model is still lacking. Primula forbesii, a biennial herb native to southwest China, is a typical distylous species, but after about 20 years of cultivation with open pollination, self-compatible homostyly appeared, providing ideal material for the study of the inheritance of distyly and homostyly. In this study, exogenous homobrassinolide was used to break the heteromorphic incompatibility of P. forbesii. Furthermore, we performed artificial pollination and open-pollination experiments to observe the distribution of floral morphs in progeny produced by different crosses. The viability of seeds from self-pollination was always the lowest among all crosses, and the homozygous S-morph plants (S/S) occurred in artificial pollination experiments but may experience viability selection. The distyly of P. forbesii is governed by a single S-locus, with S-morph dominant hemizygotes (S/-) and L-morph recessive homozygotes (-/-). Homostylous plants have a genotype similar to L-morph plants, and homostyly may be caused by one or more unlinked modifier genes outside the S-locus. Open pollinations confirm that autonomous self-pollination occurs frequently in L-morphs and homostylous plants. This study deepens the understanding of the inheritance of distyly and details a case of homostyly that likely originated from one or more modifier genes.

Self-awareness control effect of cooperative epidemics on complex networks.

Coinfection mechanism is a common interacting mode between multiple diseases in real spreading processes, where the diseases mutually increase their susceptibility, and has aroused widespread studies in network science. We use the bond percolation theory to characterize the coinfection model under two self-awareness control strategies, including immunization strategy and quarantine strategy, and to study the impacts of the synergy effect and control strategies on cooperative epidemics. We find that strengthening the synergy effect can reduce the epidemic threshold and enhance the outbreak size of coinfected networks. On Erdos-Rényi networks, the synergy effect will induce a crossover phenomenon of phase transition, i.e., make the type of phase transition from being continuous to discontinuous. Self-awareness control strategies play a non-negligible role in suppressing cooperative epidemics. In particular, increasing immunization or the quarantine rate can enhance the epidemic threshold and reduce the outbreak size of cooperative epidemics, and lead to a crossover phenomenon of transition from being discontinuous to continuous. The impact of quarantine strategy on cooperative epidemics is more significant than the immunization strategy, which is verified on scale-free networks.

Group percolation in interdependent networks.

In many real network systems, nodes usually cooperate with each other and form groups to enhance their robustness to risks. This motivates us to study an alternative type of percolation, group percolation, in interdependent networks under attack. In this model, nodes belonging to the same group survive or fail together. We develop a theoretical framework for this group percolation and find that the formation of groups can improve the resilience of interdependent networks significantly. However, the percolation transition is always of first order, regardless of the distribution of group sizes. As an application, we map the interdependent networks with intersimilarity structures, which have attracted much attention recently, onto the group percolation and confirm the nonexistence of continuous phase transitions.