Summary1. Perennial woody invaders often form persistent patches that significantly alter the structure and composition of native plant communities. Given their long generation times compared with ruderal invaders, these species may experience prolonged establishment phases between successful introduction and spread. Gap dynamics of shade-tolerant invaders could lead to multiple lag phases during the invasion process. 2. In order to investigate the potential for long or multiple lag phases, we reconstructed the invasion of Acer platanoides (a shade-tolerant, invasive, exotic tree) on an 1130-ha temperate forested island in Lake Huron, USA. We measured and mapped the spatial location of every A. platanoides ≥ 0·5 m in height that had successfully established within a 728-ha forested park on the island. A simple age-diameter relationship, developed from a randomly selected subsample of the population, was used to assign an establishment date to each individual. 3. Following a 34-year establishment phase, the area occupied by ≥ 1 A. platanoides ha − 1 increased linearly at a rate of 5·6 ha year − 1 for 35 years, after which range expansion slowed. Population growth lagged behind range expansion, with rapid population growth associated with infill between parents. During the expansion phase, numerous satellite populations established but contributed little to population growth and spatial expansion because of the long time required for them to become reproductive. These satellite populations will most probably accelerate population growth and spread once they reach reproductive age. 4. Roads and trails provided important corridors for propagule movement away from developed areas over the course of the invasion. They also appeared to facilitate longer distance dispersals than would be expected given the biology of the species. 5. Synthesis and application . Our results suggest that shade-tolerant invaders with long generation times may undergo long establishment phases as well as periodic lags during the expansion phase. These lags may provide windows of opportunity for control but could easily be misinterpreted as signs that the population has reached an equilibrium density or the geographical extent of its spread. Additionally, roads and trails may provide important corridors for movement of propagules via non-standard means of dispersal.

The extent to which plant populations are seed vs. establishment limited can be understood by quantifying the recruitment function, describing the number of seedlings that establish as a function of the number of seeds added. Here, we derive a general equation for the recruitment function based on a mechanistic model describing how the availability of safe sites (sites suitable for germination and establishment) interacts with the number and distribution of seeds added to a plot to determine the number of recruits. The parameters of this recruitment function have a direct biological interpretation that can provide insight into the processes limiting recruitment in plant populations.

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Controlling invasive species is critical for conservation but can have unintended consequences for native species and divert resources away from other efforts. This dilemma occurs on a grand scale in the North American Great Lakes, where dams and culverts block tributary access to habitat of desirable fish species and are a lynchpin of long-standing efforts to limit ecological damage inflicted by the invasive, parasitic sea lamprey (Petromyzon marinus). Habitat restoration and sea-lamprey control create conflicting goals for managing aging infrastructure. We used optimization to minimize opportunity costs of habitat gains for 37 desirable migratory fishes that arose from restricting sea lamprey access (0-25% increase) when selecting barriers for removal under a limited budget (US$1-105 million). Imposing limits on sea lamprey habitat reduced gains in tributary access for desirable species by 15-50% relative to an unconstrained scenario. Additional investment to offset the effect of limiting sea-lamprey access resulted in high opportunity costs for 30 of 37 species (e.g., an additional US$20-80 million for lake sturgeon [Acipenser fulvescens]) and often required ≥5% increase in sea-lamprey access to identify barrier-removal solutions adhering to the budget and limiting access. Narrowly distributed species exhibited the highest opportunity costs but benefited more at less cost when small increases in sea-lamprey access were allowed. Our results illustrate the value of optimization in limiting opportunity costs when balancing invasion control against restoration benefits for diverse desirable species. Such trade-off analyses are essential to the restoration of connectivity within fragmented rivers without unleashing invaders.