Analyses of community structure and stability before and after invasion
We distinguish six mechanisms of invasion-induced change in the community based on the observed changes in local composition and diversity (hereafter invasion outcomes , Box 1). The invasion-induced change in diversity\(\Delta D=N_{\text{INV}}-\ N_{\text{RES}}\) is calculated as the difference between the number of species in the invaded and resident community NINV and NRESpresent after 5000 years (end of simulation) under the same environmental conditions and species masses.
To assess how invaders affect the stability of the resident system, we first calculate the Jacobian matrix at the equilibrium with the species present after 5000 years (Eqs 10–13, Table S8) and use its dominant eigenvalue to determine the stability of the resulting community. We distinguish three stability regimes for the invaded community (hereafterSINV ) and the resident system (hereafterSRES ): stable equilibrium (E ), population oscillations (O ), and a collapsed system with no remaining species (N ) (Binzer et al. 2012; Sentis et al. 2017), to which we arbitrarily assign values v (E ) = 2, v (O ) = 1 and v (N ) = 0. We then compare the stability regimes between the resident system and the invaded community under the same environmental conditions and species mass ratios. Nine outcomes (hereafter regime states ,SRES→SINV ) define all possible changes in stability caused by species invasion. Similar to\(\ \Delta D\), we calculate the invasion-induced change in stability as\(\Delta S=v\left(S_{\text{INV}}\right)\ -\ v\left(S_{\text{RES}}\right)\). Positive, zero and negative values of \(\Delta S\) correspond to stabilizing (O→E , N→O and N→E ), neutral (O→O , E→E and N→N ) and destabilising (O→N ,E→O , E→N ) effects of the invader on the local consumer-resource system, respectively.
To assess how the body mass of the invader affects the community responses across food web modules and abiotic conditions, we calculate the percentage of each invasion outcome (Box 1) and regime state for a given set of body mass ratios across all 80,200 combinations of temperature (0–40ºC) and nutrient levels (0.1–20 g.m-2) for each combination of body masses in each food web module (Tables S4–S7), and average these percentages across all combinations of body masses considered for each module.