Extended Data Fig. 1: Intuition of the dependence of community diversity on partitioning level.

a. Local community behaviors for one-directional negative interaction. Low partitioning allows the interaction between the two populations, leading to the collapse of the green population. High partitioning separates the two populations and enables the growth of the green population. b. Local community behaviors for one-directional positive interaction. Low partitioning levels enable the growth of the green population, whereas the green population cannot grow well at high partitioning levels in absence of the other population. c. The same principle applies to 12-member communities with all negative interactions (red) or all positive interactions (blue). Increasing partitioning increases the diversity of communities with negative interactions but decreases the diversity of communities with positive interactions. Data are represented as mean values + /- SD, with n = 10, error bar represents standard deviation. d. Steady state is not required to generate biphasic response. The simulation results of a fully connected 15-member community at different t_f values: 50 (dark grey), 100 (grey), and 200 (light grey). The community has 50% of negative interactions and 50% of positive interactions, with a maximum δ of 1.5, a maximum γ value of 1, and a maximum β of 5. e. Biphasic dependence of diversity of local communities, which is quantified as the count of local communities that have unique combinations of members. The plot is generated with a 10-member community; each dot represents one randomization of the initial seeding. The solid trace represents the average number + /- SD (error bars) and n = 10 and the same as panel f. f. Biphasic dependence of diversity of local communities containing a population. The plot is generated with the same 10-member community in panel e, with one set of initial seeding. Each dot represents the diversity of local communities containing a population at a partitioning level. The solid trace represents the average number across 10 members. g. More unique types of local communities lead to higher diversity. For communities with both positive and negative interactions, types of local communities correlate with final community diversity. The lighter the trace, the more members there are in a community.