Table 1.
Details and hypotheses of the 12 modelling experiments designed to substantiate the empirical relationship observed in Fig. 1.
| Model name | Model type | Parameter varied (experiment num.) | Parameter range | Repeats per parameter value | Number of runs (n) | Hypothesis |
|---|---|---|---|---|---|---|
| Wolf-Sheep Predation (WSP) | Agent-based | (1.1) Model total area |
World height: [0–100] World width: [0–100]. |
100 | 260,100 | Larger system areas should exhibit longer shift durations |
| (1.2) Module size (divide constant 100 × 100 area into sub-worlds) | [2, 5, 10, 20, 50, 100]a | 100 | 60,600 | More modular systems should exhibit longer shift durations | ||
| (1.3) Maximum distance wolves and sheep can move per time step | [1–100 cells] | 100 | 10,000 | More fluid systems should exhibit shorter shift durations | ||
| Game of Life (GoL) | Cellular automata | (2.1) Model total area |
World height: [0–100] World width: [0–100]. |
100 | 260,100 | Larger system areas should exhibit longer shift durations |
| (2.2) Module size (divide constant 100 ×100 area into discrete sub-worlds) | [2, 5, 10, 20, 50, 100] | 100 | 600 | More modular systems should exhibit longer shift durations | ||
| (2.3) Number of neighbouring cells any one cell can interact with | 4 or 8 | 100 | 200 | More fluid systems should exhibit shorter shift durations | ||
| Language Change (LC) | Network-structured | (3.1) Number of network nodes | [3–1000] | 100 | 99,800 | Networks with more nodes should exhibit longer shifts |
| (3.2) Number of inter-nodal connections | [99–4500] | 100 | 440,200 | Networks with more connections should exhibit longer shifts | ||
| (3.3) Standard deviation of connections measured from experiment 3.2. | [99–4500] | 100 | 440,200 | Networks with more homogenous connections should exhibit longer shifts | ||
| Lake Chilika (CHL) | System dynamics model | (4) Model total area | [500–10,000 km2] | 5000 areas randomly sampled between limits | 5000 | Larger system areas should exhibit longer shift durations |
| Spatial Heterogeneity (SH) | Ordinary differential equation | (5.1) Carrying capacity for phytoplankton (i.e. model size) | [1–100] | 1 (model does not have stochasticity) | 101 | Large systems should exhibit longer shift durations |
| (5.2) Fraction of volume exchanged between model parts (i.e. diffusion of stress) | [1–100] | 1 (model does not have stochasticity) | 101 | More fluid systems should exhibit shorter shift durations |