Food Web Assembly Rules for Generalized Lotka-Volterra Equations
a, Consumer limited food web and its interaction matrix. The symbols “×” mark nonzero entries and circles a path through the matrix. Basic nutrient is shown as a gray hexagon, whereas species on subsequent trophic levels are shown with coloured circles. Small circles highlight limitations by consumers. Shaded ovals indicate possible pairing of species. b, Possible assembly of the food web in (a) with labels for No+Ne and No−Ne. We set all growth and coupling constants equal to unity, but consider fine-tuned decay coefficients α ≪ 1 (details: , in prep.). Note the transitions between biomass limiting states. Sizes of circles indicate approximate densities of species in the different states. Link shown in gray was set to zero in the numerical simulations in (c). c, Species added one-by-one as shown in (b) and granted small initial population density (10−4). After each addition the system is integrated until steady state is reached. In the plot, colors of curves denote species of similar colors in the panels of (b). Note the double-logarithmic axis-scaling in (c). Time in each panel is relative to the time of introduction of the new species.