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Eradication and maintenance management of island invasive species have long histories, and incremental improvements of existing technologies plus occasional novel approaches have led to more challenging targets and increased success rates in certain categories. Many nonnative mammals have been eradicated from islands, as have several nonnative birds, insects, and plants. Hundreds of rat populations have been eliminated, with a success rate over 80%, and islands over 10,000 ha are now feasible targets. Mouse eradication has proven more challenging, but aerial broadcast of anticoagulant toxins has led to increased success. Carnivore eradication—especially of feral housecats and foxes—has been frequently attempted with a recent success rate over 90%. Eradication of herbivores—primarily goats, rabbits, wild boar, and boar/pig hybrids—has been attempted almost 200 times, with a success rate over 90%. Trends in mammal eradication include more frequent attempts and higher success rates on larger islands and inhabited islands, as well as attempts targeting multiple invasive species. Documented conservation gains from island mammal eradications are numerous. For insects, about two-thirds of some 50 island attempts have succeeded, and most targeted agricultural pests. No summary statistics exist on island plant eradications, but several small infestations have been eradicated. Several insect and plant island invaders have been maintained at low densities by biological control, and plants have been controlled short of eradication by herbicides, often combined with physical or mechanical means. Failures in both eradication and maintenance management on islands often result from insufficient long-term commitment of resources. Excitement and controversy abound over the prospect that new techniques relying on molecular genetic tools—especially RNA-guided gene drives—may permit eradication or maintenance management of nonnative invaders in situations that have previously appeared extremely difficult or infeasible. Island populations of invertebrates, small mammals, and some plants are particularly propitious targets.

Connectivity among populations and habitats is important for a wide range of ecological processes. Understanding, preserving, and restoring connectivity in complex landscapes requires connectivity models and metrics that are reliable, efficient, and process based. We introduce a new class of ecological connectivity models based in electrical circuit theory. Although they have been applied in other disciplines, circuit-theoretic connectivity models are new to ecology. They offer distinct advantages over common analytic connectivity models, including a theoretical basis in random walk theory and an ability to evaluate contributions of multiple dispersal pathways. Resistance, current, and voltage calculated across graphs or raster grids can be related to ecological processes (such as individual movement and gene flow) that occur across large population networks or landscapes. Efficient algorithms can quickly solve networks with millions of nodes, or landscapes with millions of raster cells. Here we review basic circuit theory, discuss relationships between circuit and random walk theories, and describe applications in ecology, evolution, and conservation. We provide examples of how circuit models can be used to predict movement patterns and fates of random walkers in complex landscapes and to identify important habitat patches and movement corridors for conservation planning.