Community structure and dynamics
We consider a resident consumer-resource system and examine five scenarios that differ in the trophic position of the invader, including another basal resource, another consumer, a top predator, an intraguild predator feeding on both resident species, or an intraguild prey feeding on the (shared) resident resource while being consumed by the resident consumer (Fig. 1a-e). This corresponds to apparent competition (hereafter AC), exploitative competition (EC), tri-trophic chain (TC) and intraguild predation (IGP) (Tables S1–S3).
We simulate the dynamics of each module for each combination of temperature between 0°C and 40°C (step size 0.1°C) and nutrient levels (IK ) available to the basal resource species the between 0.1 g.m-2 and 20 g.m-2 (step size 0.1 g.m-2), yielding 80,200 combinations of temperature and nutrient levels as in Binzer et al. (2012) and Sentis et al. (2017). We also vary the body masses of species in each module, constraining consumers to be at least as large as their resources, which is true for most predator-prey pairs (McCauley et al. 2018). For simplicity, we set the body mass of the basal resource species to 1 mg and express the other masses in relative values (Fig. 1a-e).
We denote the body mass ratio between competing resourcesRINV:RRES (AC module) and the consumer:resource ratio C:R (TC and IGP modules) as α , the mass ratio between competing consumersCINV:CRES (EC and IGP modules) or between predators and intermediate consumers P:C (TC and IGP modules) as β , and the mass ratio between resident resource and consumer CRES:RRES (AC and EC modules) and between the top predator and resident basal resource (P:R ; TC and IGP modules) as γ = αβ. Furthermore, we quantify the asymmetry in size ratios between adjacent trophic levels with a ratio parameter δ = β /α (Table S4). We consider module-specific sets of mass ratios to reflect the different trophic positions of the invader: 4 or 15 consumer-resource body mass ratios for the resident system, and 16 or 25 combinations of species mass ratios (i.e., at least all pairwise combinations of α andβ = 1, 2, 5 and 10, Text S1) in each module (Tables S5–S7). All numerical simulations were run in the packages ‘deSolve’ and ‘rootSolve’ in the R software (Soetaert & Herman 2009; Soetaert et al. 2010).