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.