Evolutionary trees: an integer multicommodity max-flow-min-cut theorem

In biomathematics, the extensions of a leaf-colouration of a binary tree to the whole vertex set with minimum number of colour-changing edges are extensively studied. Our paper generalizes the problem for trees; algorithms and a Menger-type theorem are presented. The LP dual of the problem is a multicommodity flow problem, for which a max-flow-min-cut theorem holds. The problem that we solve is an instance of the NP-hard multiway cut problem

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

ECOLOGICAL IMPLICATIONS OF FORAGING AND LIFE-HISTORY IN THREE COLD-ADAPTED SPECIES

This research investigates the ecology of: ringed seals (Pusa hispida), moose (Alces alces), and bowhead whales (Balaena mysticetus). Each of these species draws upon specialized strategies to meet the physical demands of life in their extreme environments. However, they are currently experiencing unprecedented changes in their habitats. This work adds to what is known about the behavior, physiology, and population dynamics of cold-adapted species—providing insights of value for an improved understanding of foraging and life-history theory, and informing conservation and ecosystem monitoring efforts. Chapter 1 provides a brief introduction to the scope of work within this dissertation. Chapter 2 documents the seasonal movements of ringed seals in the Alaskan Arctic, along with their diving, foraging, and haul-out behaviors. Their behavior, including daily activity budgets and habitat use, is characterized and interpreted with respect to life-history and foraging theory. Demographic habitat partitioning is documented and is consistent with theoretical expectations. Results highlight the importance of benthic diving and suggest that reduced sea ice during critical periods may have energetic consequences for ringed seals. Chapter 3 compares the influences of top-down, bottom-up, and abiotic effects on moose body condition and per capita population growth at Isle Royale National Park. Body condition was quantified using the ratio of urea-nitrogen to creatinine (UN:C) during the late winter, when severe reductions of forage abundance and quality increase catabolic processes. Body condition responded to abiotic effects, including warm summer temperatures. Spatial heterogeneity also influenced body condition, likely due to different forest ecosystems. Per capita population growth responded most to top-down effects, but also to bottom-up effects. The substantial influence of predation rate upon per capita population growth is discussed with respect to “masking” other potentially complex interrelationships among energetics, body condition, and population dynamics. Chapter 4 improves understanding of the relationships among factors with life-history implications that are potentially informative on the status of bowhead whales and their ecosystem. In particular, factors that influence cyamid ectoparasite prevalence and abundance are examined. Also important are observed relationships between whale age, body condition, and ancillary data that have potential to influence ecological interpretations