Landscape structure affects metapopulation-scale tipping points

Even when environments deteriorate gradually, ecosystems may shift abruptly from one state to another. Such catastrophic shifts are difficult to predict and sometimes to reverse (so-called hysteresis). While well studied in simplified contexts, we lack a general understanding of how catastrophic shifts spread in realistically spatially structured landscapes. For different types of landscape structures, including typical terrestrial modular and riverine dendritic networks, we here investigate landscape-scale stability in metapopulations whose patches can locally exhibit catastrophic shifts. We find that such metapopulations usually exhibit large-scale catastrophic shifts and hysteresis and that the properties of these shifts depend strongly on the metapopulation spatial structure and on the population dispersal rate: an intermediate dispersal rate, a low average degree or a riverine spatial structure can largely reduce hysteresis size. Our study suggests that large-scale restoration is easier with spatially clustered restoration efforts and in populations characterized by an intermediate dispersal rate.