Simulation design
We generated 30,000 networks of 60 nodes and connectance equal to 0.15 containing between 2 and 6 stage-structured fishes with at least 3 and up to 5 stages (Table 1a). We generalized the fixed numbers used by Bland et al. (2019; three fish species with three stages). Food web studies on northern temperate systems typically include two to three species of fish, each of which has two to four stages (e.g., The minimum overlap between feeding ranges to be qualified as consecutive stages of the same stage-structured fish species was 20% . We then ran the ATN on each network from random initial biomasses uniformly distributed between 0.1 to 100 \(\mu gC/L\). We ran two sets of simulations on the same networks. In one set, stages were linked via growth and reproduction as described above (“linked”), while in the other set we removed the growth and reproduction links between stages (“unlinked”) to examine the effects of the additional biomass flow on the resulting food web dynamics and persistence. The simulations were otherwise identical (including the seed for the random number generator). Taxa were considered extinct when the biomasses became < 10-6\(\ \mu gC/L\), and if any of the taxon reached the biomass of 1012 \(\mu gC/L\) the simulation was terminated (Table 1b). These values were many orders of magnitudes smaller and larger, respectively, to the mean total fish biomass (101.1 \(\mu gC/L\) ). At the end of each generation, fishes that retained only older stages but not younger ones for more than 10 generations were removed as extinct. This happened in some simulations because the biomasses of older stages without younger ones lingered although they were to decay over time. Each year consisted of 90 time-steps, representing one growing season, followed by a non-growing season where reproduction and growth were accounted for. One time-step corresponded to the generation time of the autotrophic species the growth rates of other taxa were normalized to the time scale of the basal species, as typically done in the ATN models; Brose et al. 2006). Food webs were regarded as persistent if simulations lasted for 1000 growing seasons, which was sufficient for transient dynamics to die out, with all the nodes of persisting species connected in one network, no invertebrates without predators, no species without food (i.e., transients did not completely die out in a handful of webs), and at least one fish with 3 or more stages for the linked case or at least 3 fish taxa for the unlinked case. We note that we regarded food webs as persistent if they retained fishes and met other criteria we just stated (Fig. 3) to the end of the simulations, not by the proportions of taxa (nodes) persisted as typically reported by food web studies.