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.