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Appendix A. Movies of the lattice model depicting six-species competition, varying the localness of competition ("local" vs. "global"), and the level of intransitivity ("hierarchical" vs. "intransitive").
We generated four movies to track the early progression of one iteration of our lattice model for six-species competition (Fig. A1). Each cell in the 100 × 100 lattice is occupied by a competing individual. The six unique colors represent the six competing species. The competitive relationships between these six species are given at the top of Fig. A2. The first frame of each movie represents the state of the lattice immediately after initial seeding. Each subsequent frame represents the net change in the lattice from the previous frame over 250 time steps. The frames are displayed at a rate of 15 per second. The movies show local, hierarchical competition (Fig. A1a), local, intransitive competition (Fig. A1b), global, hierarchical competition (Fig. A1c), and global, intransitive competition (Fig. A1d). We initially set the movies to run for 20 model generations; however, in the two cases of hierarchical competition (Fig. A1a, c), the lattice became a monoculture in <20 generations, resulting in shorter movies.
Figure A2 shows the time-series results for the average of 5 complete model iterations for local, hierarchical competition (Fig. A2a), local, intransitive competition (Fig. A2b), global, hierarchical competition (Fig. A2c), and global, intransitive competition (Fig. A2d). In hierarchical six-species communities, most species rapidly became disaggregated (Fig. A2a, c). The fewer wins a species had against other competitors (i.e., fellow members of its interaction web), the more quickly it became disaggregated. The exception to this trend was that the strongest competitor (species A) became steadily more aggregated until it became a monoculture after about 10 generations (Fig. A2a, c). These patterns occurred whether hierarchical competition was local or global (Fig. A2a, c).
In contrast, in intransitive six-species communities, local and global competition had qualitatively different species aggregation patterns through time (Fig. A2b, d). In local intransitive competition, the stronger competitors (species A, B, and C) quickly became more aggregated, and eventually formed a highly stable triad (Fig. A2b). Meanwhile, the weaker competitors (species D, E, and F) also became slightly more aggregated, although this pattern eventually broke down during species extinctions (Fig. A2b). On the other hand, when competition was global, the aggregation values of the weaker competitors slowly but steadily decreased towards zero, accompanied by a corresponding upward drift in the aggregation values of the stronger competitors as they took over more and more cells in the lattice (Fig. A2d).
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| FIG. A1. (a) This movie shows the early progression of one iteration of the 100 × 100 cell lattice in local, hierarchical, six-species competition. The species identities and their competitive relationships are shown in the competitive outcomes diagram at the top left of Fig. A2. The movie starts at initial seeding and proceeds until shortly after the lattice reaches a monoculture (in the ninth generation). The movie corresponds to one of the five iterations whose averaged competitive outcomes (i.e., time series of species richness, species evenness, and spatial aggregation) are shown in Fig. A2a. Click on panel a to watch the movie. Click here to watch the same movie in mpg format. (b) This movie shows the early progression of one iteration of the 100 × 100 cell lattice in local, intransitive, six-species competition. The species identities and their competitive relationships are shown in the competitive outcomes diagram at the top right of Fig. A2. The movie starts at initial seeding and proceeds until the twentieth generation. The movie corresponds to one of the five iterations whose averaged competitive outcomes (i.e., time series of species richness, species evenness, and spatial aggregation) are shown in Fig. A2b. Click on panel b to watch the movie. Click here to watch the same movie in mpg format. (c) This movie shows the early progression of one iteration of the 100 × 100 cell lattice in global, hierarchical, six-species competition. The species identities and their competitive relationships are shown in the competitive outcomes diagram at the top left of Fig. A2. The movie starts at initial seeding and proceeds until shortly after the lattice reaches a monoculture (in the ninth generation). The movie corresponds to one of the five iterations whose averaged competitive outcomes (i.e., time series of species richness, species evenness, and spatial aggregation) are shown in Fig. A2c. Click on panel c to watch the movie. Click here to watch the same movie in mpg format. (d) This movie shows the early progression of one iteration of the 100 × 100 cell lattice in global, intransitive, six-species competition. The species identities and their competitive relationships are shown in the competitive outcomes diagram at the top right of Fig. A2. The movie starts at initial seeding and proceeds until the twentieth generation. The movie corresponds to one of the five iterations whose averaged competitive outcomes (i.e., time series of species richness, species evenness, and spatial aggregation) are shown in Fig. A2d. Click on panel d to watch the movie. Click here to watch the same movie in mpg format. |
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FIG. A2.
Mean species richness and species evenness, as well as mean aggregation (AIi)
for each of s = 6 species across 500 model generations. (a) and (b)
depict results for locally-competing communities with hierarchical (relative
intransitivity = 0), and intransitive (relative intransitivity = 1) competition,
respectively; (c) and (d) depict similar patterns for globally-competing
communities (N = 5 iterations per panel). Solid black lines
represent species richness, and dotted black lines represent species evenness (Evar;
Smith and Wilson 1996). Colored lines track mean species aggregation (AIi).
Each color corresponds to a species whose competitive relationships are
outlined in the associated interaction webs at the top of the figure (arrows
point from competitive dominant to subordinate, e.g., A B means species A outcompetes species B). Further, these colors correspond to those
in Fig. A1. |
LITERATURE CITED
Smith, B., and J. B. Wilson. 1996. A consumer's guide to evenness indices. Oikos 76:70–82.
