Invasion outcomes and the diversity-stability relationship
The effects of invasion on community stability and diversity observed in our simulations depend on the outcome of the invasion. Invasion-induced destabilisation occurs primarily under vulnerability, where it almost always leads to community collapse (regime states E→N andO→N ; Figs. 4 and S8, Tables S9–S11). More than half of the invasions leading to integration and some leading to substitutions also trigger a loss of stability, with invasion-induced cycles replacing equilibrium (E→O ). We do not observe invasion-induced destabilisation under resistance, occupancy and rescue mechanisms. An invasion-triggered increase in stability, which would prevent a complete collapse of the resident community and is characteristic of the rescue (N→E ), occurs less frequently under occupancy (N→E andN→O ) and integration (N→O ). An invasion-triggered increase in stability associated with a shift from oscillations to stable equilibria (O→E ) is rare and occurs only under substitution and vulnerability (Fig. S1a).
As a result, we find that invasion-induced changes in diversity and stability are interrelated, but one cannot be predicted from the other alone (Fig. 4b). Diversity loss (ΔD < 0) is almost always associated with invasion-induced loss of stability (ΔS < 0). No net change in diversity (ΔD = 0) is mostly associated with no change in stability as expected, but loss of stability (invasion-induced cycles in EC) or increased stability (dampen cycles induced by invasion through species substitution in IGPP) also occur as a result of invasion. Interestingly, invasions leading to increased diversity (ΔD > 0) have the most evenly distributed effects on stability. About one third of the simulations each lead to reduced, increased or unchanged stability across species mass ratios, food web topologies and environmental conditions (Fig. 4b).