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).