We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energyconstrained (e.g. battery-operated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a static assignment, the power levels of the nodes are set at the beginning and remain unchanged until the nodes are depleted of energy. In a dynamic assignment, the powers can be adjusted during operation.We show that lifetime-maximizing static power assignments can be found in polynomial time, whereas for dynamic assignments, a quantized-time version of the problem is NP-hard. We then study the approximability of the quantized dynamic case and conclude that no polynomial time approximation scheme (PTAS) exists for the problem unless P = NP. Finally, by considering two approximation heuristics for the dynamic case, we show experimentally that the lifetime of a dynamically maintained multicast connection can be made several times longer than what can be achieved by the best possible static assignment. * Research supported by the Academy of Finland, Grants 202203 (J. Kohonen and P. Floréen) and 202205 (P. Kaski and P. Orponen); and by the Foundation of Technology, Helsinki, Finland (Tekniikan Edistämissäätiö) (P. Kaski).

We characterize allelic and gene expression variation between populations of the Glanville fritillary butterfly (Melitaea cinxia) from two fragmented and two continuous landscapes in northern Europe. The populations exhibit significant differences in their life history traits, e.g. butterflies from fragmented landscapes have higher flight metabolic rate and dispersal rate in the field, and higher larval growth rate, than butterflies from continuous landscapes. In fragmented landscapes, local populations are small and have a high risk of local extinction, and hence the long-term persistence at the landscape level is based on frequent re-colonization of vacant habitat patches, which is predicted to select for increased dispersal rate. Using RNA-seq data and a common garden experiment, we found that a large number of genes (1,841) were differentially expressed between the landscape types. Hexamerin genes, the expression of which has previously been shown to have high heritability and which correlate strongly with larval development time in the Glanville fritillary, had higher expression in fragmented than continuous landscapes. Genes that were more highly expressed in butterflies from newly-established than old local populations within a fragmented landscape were also more highly expressed, at the landscape level, in fragmented than continuous landscapes. This result suggests that recurrent extinctions and re-colonizations in fragmented landscapes select a for specific expression profile. Genes that were significantly up-regulated following an experimental flight treatment had higher basal expression in fragmented landscapes, indicating that these butterflies are genetically primed for frequent flight. Active flight causes oxidative stress, but butterflies from fragmented landscapes were more tolerant of hypoxia. We conclude that differences in gene expression between the landscape types reflect genomic adaptations to landscape fragmentation.

No abstract

No abstract