Under the UN-Decade of Ecosystem Restoration and Bonn Challenge, second-growth forest is promoted as a global solution to climate change, degradation and associated losses of biodiversity and ecosystem services. Second growth is often invaded by alien tree species and understanding how this impacts carbon stock and biodiversity recovery is key for restoration planning. We assessed carbon stock and tree diversity recovery in second growth invaded by two Acacia species and non-invaded second growth, with associated edge effects, in the Brazilian Atlantic Forest. Carbon stock recovery in non-invaded forests was threefold lower than in invaded forests. Increasingly isolated, fragmented and deforested areas had low carbon stocks when non-invaded, whereas the opposite was true when invaded. Non-invaded forests recovered threefold to sixfold higher taxonomic, phylogenetic and functional diversity than invaded forest. Higher species turnover and lower nestedness in non-invaded than invaded forests underpinned higher abundance of threatened and endemic species in non-invaded forest. Non-invaded forests presented positive relationships between carbon and biodiversity, whereas in the invaded forests we did not detect any relationship, indicating that more carbon does not equal more biodiversity in landscapes with high vulnerability to invasive acacias. To deliver on combined climate change and biodiversity goals, restoration planning and management must consider biological invasion risk. This article is part of the theme issue ‘Understanding forest landscape restoration: reinforcing scientific foundations for the UN Decade on Ecosystem Restoration’.

Context: The sandy‐savanna ecosystem “Mussununga”, a natural ecosystem that occurs as patches throughout the Atlantic Forest domain, is threatened by anthropogenic factors and biological invasions of Australian Acacia species. Habitat degradation in the Atlantic Forest domain and extensive road networks could facilitate Acacia invasion into Mussununga.Objectives: We investigated whether: (a) landscape permeability (measured by effective conductance) facilitates Acacia invasion; (b) forest fragments are barriers, and roads and highways are corridors for invasive spread of Acacia; and (c) size and shape of Mussununga patches play a role in biological invasion.Methods: Acacia invasion was investigated in 32 Mussununga sites within the Atlantic Forest domain. We tested the effect of a set of landscape permeability scenarios based on circuit analysis and nine other metrics of landscape structure on Acacia occurrence using three buffer‐zone sizes (0.5, 1, and 2 km).Results: The likelihood of Acacia invasion significantly increased with landscape permeability. The best‐fitting landscape permeability scenario designated road networks as corridors, intact forests and water surfaces as barriers, and degraded habitats as non‐barriers. We also found that Mussununga areas within a 0.5 km buffer negatively affected the biological invasion by Acacia.Conclusions: Extensive habitat degradation by deforestation and dense road networks facilitate Acacia invasion into sandy‐savanna Mussununga ecosystems. Landscape permeability may be used as a risk‐assessment tool for biological invasion by Acacia species. Mussununga patches can be protected from Acacia invasion through preserving or restoring forest belts around them and disconnecting them from the road network.