Description: Increasing air temperatures are changing the arctic tundra biome. Permafrost is thawing, snow duration is decreasing, shrub vegetation is proliferating, and boreal wildlife is encroaching. Here we present evidence of the recent range expansion of North American beaver (Castor canadensis) into the Arctic, and consider how this ecosystem engineer might reshape the landscape, biodiversity, and ecosystem processes. We developed a remote sensing approach that maps formation and disappearance of ponds associated with beaver activity. Since 1999, 56 new beaver pond complexes were identified, indicating that beavers are colonizing a predominantly tundra region (18,293 km2) of northwest Alaska. It is unclear how improved tundra stream habitat, population rebound following overtrapping for furs, or other factors are contributing to beaver range expansion. We discuss rates and likely routes of tundra beaver colonization, as well as effects on permafrost, stream ice regimes, and freshwater and riparian habitat. Beaver ponds and associated hydrologic changes are thawing permafrost. Pond formation increases winter water temperatures in the pond and downstream, likely creating new and more varied aquatic habitat, but specific biological implications are unknown. Beavers create dynamic wetlands and are agents of disturbance that may enhance ecosystem responses to warming in the Arctic.

Description: In many spatial resource models, it is assumed that an agent is able to harvest the resource over the complete spatial domain. However, agents frequently only have access to a resource at particular locations at which a moving biomass, such as fish or game, may be caught or hunted. Here, we analyze an infinite time‐horizon optimal control problem with boundary harvesting and (systems of) parabolic partial differential equations as state dynamics. We formally derive the associated canonical system, consisting of a forward–backward diffusion system with boundary controls, and numerically compute the canonical steady states and the optimal time‐dependent paths, and their dependence on parameters. We start with some one‐species fishing models, and then extend the analysis to a predator–prey model of the Lotka–Volterra type. The models are rather generic, and our methods are quite general, and thus should be applicable to large classes of structurally similar bioeconomic problems with boundary controls. Recommedations for Resource Managers Just like ordinary differential equation‐constrained (optimal) control problems and distributed partial differential equation (PDE) constrained control problems, boundary control problems with PDE state dynamics may be formally treated by the Pontryagin's maximum principle or canonical system formalism (state and adjoint PDEs). These problems may have multiple (locally) optimal solutions; a first overview of suitable choices can be obtained by identifying canonical steady states. The computation of canonical paths toward some optimal steady state yields temporal information about the optimal harvesting, possibly including waiting time behavior for the stock to recover from a low‐stock initial state, and nonmonotonic (in time) harvesting efforts. Multispecies fishery models may lead to asymmetric effects; for instance, it may be optimal to capture a predator species to protect the prey, even for high costs and low market values of the predators.