Dynamic Dominating Set and Turbo-Charging Greedy Heuristics

The main purpose of this paper is to exposit two very different, but very general, motivational schemes in the art of parameterization and a concrete example connecting them. We introduce a dynamic version of the DOMINATING SET problem and prove that it is fixed-parameter tractable（FPT）. The problem is motivated by settings where problem instances evolve. It also arises in the quest to improve a natural greedy heuristic for the DOMINATING SET problem.     

Arboreality predicts Batrachochytrium dendrobatidis infection level in tropical direct-developing frogs

Pathogen-mediated changes in host behaviour can result from hosts altering their habitat preferences. Although infection risk with pathogenic fungus Batrachochytrium dendrobatidis in amphibians is associated with environments favouring its growth, the relationship with microhabitat use has not been examined. Here, we aim to determine if microhabitats used by frogs during their nocturnal activity predict B. dendrobatidis prevalence and infection intensity. Our focal host, Eleutherodactylus coqui, is a habitat generalist that uses multiple habitats from the forest floor to the canopy. We analysed data on B. dendrobatidis occurrence in 157 adults and 122 juveniles at El Yunque National forest in Puerto Rico. We categorized each individual’s nocturnal microhabitat as forest floor, curled palm fronds in the floor, arboreal bromeliads and foliage or tree trunks 50 cm to 2.5 m above ground. We found that frogs on the forest floor had the greatest B. dendrobatidis prevalence (73%), compared with those active in vegetation above ground (55%). Overall, the probability of B. dendrobatidis infection in frogs using microhabitats on the forest floor was twice as great as for those on arboreal substrates. Differences in B. dendrobatidis prevalence and intensity in E. coqui may be explained by specific abiotic conditions of microenvironments (temperature and humidity) affecting both pathogen and host, and by the age-specific ecological requirements of hosts. Adults were found to be most active in microhabitats where individuals had lower infection burdens, suggesting pathogen-modulated habitat choice. This work has important implications for the evolutionary dynamics of enzootic diseases and provides data that may inform potential mitigation strategies against a generalist amphibian pathogen.