Introducing life-history stage-structured consumers to the food
webs generated by the niche model
We built on the original niche model by Williams & Martinez (2000; Box
1) and incorporated an additional algorithm to construct life-history
structured consumers by grouping trophic species based on the extent of
overlap between feeding ranges. As organisms grow in size during their
ontogeny, they experience changing competition, predation, and energetic
demands and may shift diets to maintain positive growth and minimize
mortality (Werner & Gilliam 1984). Ontogenetic diet shifts among
life-history stages within a species are widely observed in nature
(Werner & Gilliam 1984, Werner 1986), with diet ranges overlapping at
various degrees . Diet overlap is negligible in the case of diet shifts
associated with habitat shifts (e.g., riverine vs. marine) or
metamorphosis (e.g., aquatic vs. terrestrial), nested when organisms add
larger prey to the diet as they grow in size, or partially nested
because smaller prey are successively dropped from diet for energetic or
mechanical reasons . We applied this concept to construct food webs with
consumers with a life-history stage structure.
After obtaining food webs from the niche model (Box 1), we assigned two
measures of trophic position, the short-weighted trophic level (\(T\))
and the prey-averaged trophic level (\(T2\)), to each taxon . The
short-weighted trophic level is the average of shortest trophic level
(\(T1\)) and the prey-averaged trophic level (Williams & Martinez 2000,
2004). The shortest trophic level is equal to 1 + the shortest chain
length from a basal species to the consumer, and the prey-average
trophic level is equal to 1 + the mean trophic level of all the
consumer’s resources (Williams & Martinez 2004). An integer
(\(N_{\text{fishes}}\); Table 1) was uniformly randomly drawn from an
interval between the desired minimum and maximum numbers of
stage-structured taxa. We assumed that they were fishes (assume no stage
structure in autotrophs and invertebrates) and that fishes fed on at
least one non-basal taxon (i.e., \(T2>2\)). To create a
stage-structured fish taxon, we first selected a species with the
highest \(T2\) (a “focal taxon”) that was greater than 2
(\(\text{Th}_{\text{fish}}\)), indicating that this taxon ate at least
one non-basal taxon (Fig. 1 and Fig. A1 for an extended graphical
example). We then identified taxa whose feeding range maxima fell within
the range of the focal taxon with the overlap of the two feeding ranges
greater than a specified minimum overlap (\(\text{OL}_{\min}\)) of the
union of the two and whose niche value was smaller than and closest to
the focal taxon’s niche value, to become the next lower stage. This
stage became the next focal taxon, and we repeated the steps until
either the specified maximum number of stages (\(\text{Nstage}_{\max}\))
had been assigned or taxa whose range maxima fell in the range of the
focal taxon with sufficient overlap ran out. When a focal taxon did not
have any overlapping taxa to choose from to form the minimum number of
stages (\(\text{Nstage}_{\min}\)), this taxon was disqualified and
another taxon was chosen in the same way as the current focal taxon if
other choices for the previous focal taxon were available. If it was
impossible to find the minimum number of stages for the first focal
taxon, it (but not the other ones that had been subsequently considered)
was reclassified as a taxon without a stage structure and classified as
an invertebrate. This occurred when a focal taxon happened to have a
small feeding range so that no range optima fell in the range. The
multiple taxa (nodes) selected in this procedure collectively made up
one stage-structured fish taxon and were removed from the pool of
available taxa. We then chose another focal taxon with the next highest\(T2\) from the remaining taxa and repeated the steps. We repeated these
procedures until the chosen number of fishes had been created or taxa
with suitable range overlaps had run out. If the minimum number of
stage-structured taxa could not be created, the food web was discarded.
Predation of lower stages by higher stages within a stage-structured
taxon was interpreted as cannibalism. Cannibalism within a stage and
cannibalism of higher stages by lower stages (very rare) were removed
(cannibalism in non-structured taxa was kept). Taxa that were not
identified as autotrophs nor fishes were identified as invertebrates
(non-structured consumers). Therefore, nodes in the network represented
autotrophic trophic species, invertebrate trophic species, or
life-history stages of a fish. Hereafter, a node or a taxon refers to a
non-stage-structured species (invertebrates and autotrophs) or a fish
stage (Fig. 2). A species refers to an autotrophic species, an
invertebrate species, or a fish species that consists of three or more
life-history stages, while a stage refers to a fish life-history stage.