The modified niche model
To introduce life-history stages into food webs, we developed additional algorithms that modified food webs from the niche model by Williams & Martinez (2000). Food web topologies generated by other food web structural models can also be used as long as they assign feeding hierarchies and ranges to every taxon, such as the variants of the niche model (generalized niche model ; the relaxed niche model ; the minimum potential niche model ). Our method utilized the concepts of ontogenetic diet shifts and niche overlap among ontogenetic stages (Werner & Gilliam 1984; Werner 1986) to identify life-history stages and heuristically assembled the specified number of taxa with a stage structure. It can be adapted to other situations where, for example, stage-structured taxa feed higher in the trophic level (e.g., set the minimum trophic level > 3 to become a fish or exclude consumers feeding on autotrophs from the pool of fish candidates) or feeding range overlaps are smaller or larger. The outputs can be fed into the ATN framework or other dynamical models that can accommodate biomass flow via growth and reproduction.
We grouped trophic species created by the niche model to assemble a stage-structured fish taxon, unlike the previous models where a trophic species was split into stages (Rudolf & Lafferty 2010; Bland et al. 2019). As a result, our method generated food webs that largely preserved topologies (i.e., besides removing rare within-stage and reverse cannibalism) produced by the niche model, which has been shown to reproduce empirically observed food web properties (Williams & Martinez 2000, 2008). The previous methods introduced new nodes and links, likely compromising the merit of using the niche model. Our approach also agrees with the method employed by Williams & Martinez (2000, 2008) to evaluate the niche model’s performance, where some of the empirical data they used distinguished different stages of the same species (e.g., larval/young-of-year and adult fish in Little Rock Lake, Ythan estuary, and Chesapeake data). Our approach hence followed from the definition of trophic species, a group of taxa sharing predators and prey, from the common phenomena of the ontogenetic diet shift, and from the fact that the niche model creates trophic species. What constitutes a trophic species should depend on the level of aggregation appropriate for a given study. Because we were interested in trophically distinct roles of ontogenetic stages on food web dynamics (Werner 1986), it was both convenient and reasonable to interpret trophic species as ontogenetic stages and group multiple trophic species into a stage structured species. It appears to be a great advantage to minimize alteration of food webs obtained from the niche model. As a by-product, we also eliminated the convoluted steps to assign niche values to newly created nodes in the method by Bland et al. (2019). We think that our approach improves and simplifies their method, making it more conceptually accessible to food web researchers.
In our results, a far greater number of food webs with unlinked stages persisted than those with linked stages. Linked stage-structured food webs were qualified with more stringent criteria (namely, higher stages cannot persist without lower stages for more than 10 generations vs. independent stages; at least one fish with 3 or more stages persisting vs. at least any 3 fish nodes persisting). Once the food webs were persisting, linked life-history stages stabilized food webs relative to when they were unlinked, as indicated by the lower variability of biomass dynamics (CV) and higher numbers of taxa (nodes) persisting in the food webs (Fig. 4). The relative frequency of food webs with oscillating biomass dynamics (i.e., higher CV) was higher when stages were unlinked. In contrast, the linked and unlinked food webs in Bland et al. (2019) behaved similarly in terms of these measures. Furthermore, the mean of the CVs of energy flow into fishes was modestly higher in the linked webs on average, mirrored by greater positive skewness, which indicated that the linked webs contained more weak links than the unlinked webs. A similar difference in CVs of energy influx resulted in approximately a 5% change (an increase in webs of 20 species, while a decrease in larger webs) in the proportion of stable webs in Gross et al. (2009). Having weak interactions is one of the key properties that can increase stability of food webs . Also, we observed that the linked webs had lower slopes of biomass spectra and hence exhibited more bottom-heavy biomass pyramids than did the unlinked webs. Bottom-heavy biomass pyramids tend to relate to dynamically stable consumer-resource dynamics, while top-heavy biomass pyramids tend to suggest unstable dynamics . Therefore, the stabilizing effects of life-history stages that we saw in our simulations appear in agreement with what current food web theories predict.
Our method and the method by Bland et al. (2019) also differed somewhat in modeling demographic shifts via growth and reproduction at the end of growing seasons. The differences were in how surplus energy were dealt with and in the proportion of the biomass of the terminal fish stage to be transferred to the first stage. Thus, the differences between our results and those of Bland et al. (2019) may not be attributable only to how life-history stages were constructed (grouping nodes vs. splitting a node). Further research should systematically explore how a life-stage structure can affect food web stability. Our method can serve as a tool to generate biologically justifiable stage-structured food web topologies to facilitate such explorations in future studies.
We noticed that the original niche model by Williams & Martinez (2000) produces many consumers that include autotrophs in their diets. In temperate and northern regions, fishes feeding on autotrophs are uncommon because of low activity levels of digesting enzymes . We added this realism through prey preferences in the dynamic model. In simulations, fishes consumed little autotrophic biomass as a consequence, despite including autotrophs in their diets. We also noticed that persisting webs often did not have a top predator based on their topologies (Fig. A4), which implied that food webs with top predators tended to be dynamically unstable. In natural systems, there may be no true top predators as even the adult stages of piscivorous fishes could be eaten by vertebrate and invertebrate predators (e.g., birds, octopuses) or parasitized (e.g., scale eaters, leeches, pathogens). Alternatively, we could have retained in the ATN filtered webs only interactions that were substantial enough to be observed in the fields. If we removed interactions that contributed a very small fraction to the consumers’ total energy intake (\(<10^{-4}\%\)) with the specified diet preference, 70% of persisting webs had at least one top predator (data not shown).