Physics · Dynamics
SpatioTemporalNullModel#3576
Simulate agents that move like the real ones but ignore each other, to test for social structure
Mechanism
A NullModelBaseline for trajectory data that keeps individual kinematics and removes coordination. From pooled tracking data estimate: (1) a two-state stationary/moving Markov chain, with an agent stationary when speed < v_min (1 px/frame) and persistence P_SS = N_SS/(N_SS+N_SM), P_SM = N_MM/(N_MM+N_MS); (2) a first-order speed-transition matrix over N_v = 30 speed bins with Laplace smoothing, P[m,n] = (T_mn + eps)/sum_l(T_ml + eps), eps = 0.01; (3) speed-conditioned turning angles, dtheta | v_i ~ N(mu_i, sigma_i^2), so slow agents turn more; (4) entry statistics (x0, y0, v0, theta0) from first appearances. Simulate agents independently: spawn at edges to match the empirical head-count timeline N_a(t), remove those that exit, switch motion state with probabilities 1-P_SS and 1-P_SM, update speed with momentum v_{t+1} = zeta v_t + (1-zeta) v_sampled (zeta = 0.6), give stationary agents U(0, 0.3) px/frame jitter to mimic tracking noise, wrap heading to [-pi, pi], and step x += v cos(theta), y += v sin(theta). Run many realisations (25 per experiment) through the same network construction. Differences that remain are evidence of interaction rules, memory or task allocation rather than motion statistics.
Invariants
- Each synthetic agent moves independently of every other agent
- Marginal speed distribution, speed autocorrelation, speed-dependent turning and entry/exit timeline match the data
- Synthetic trajectories pass through the identical interaction and network pipeline
Failure modes
- Pooling kinematics across behavioural regimes blurs regime-specific motion that is itself a product of coordination
- Unmodelled environmental drivers (pheromone fields, food, boundaries) let the null miss structure that is not social
- Too few realisations to estimate the null distribution of the measure
Where this came from
- Thesis Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026), Ch. 3.1.2 'Spatio-Temporal Null Model', Eqs. 3.11-3.21; Fig. 4.5
Builds on
Used by
Identity
The name is the hash of the definition. Change a word and it becomes a different pattern.
- Sema ID
sema:SpatioTemporalNullModel#mh:SHA-256:3576582815f7cac5bb54c54b13d3a0f7cdf0fab3d808480b18b96c12527ce6e5- Reference
SpatioTemporalNullModel#3576- Ring
- 2
- Tier
- 1