Novel Covariance-Based Neutrality Test of Time-Series Data Reveals Asymmetries in Ecological and Economic Systems
Fig 4
Investigating the competitive asymmetry (A-D).
Analyzing the non-neutrality of competitive systems (A) The negative relationship between νt vs. ft indicates mean reversion. Overlaying νt vs. ft scatter plot from a particular CVT from the male tongue data onto the results from 4,000 WFP trajectories with long sampling intervals, Δt, shows that mean reversion can be accounted for by sparse time-sampling of the data. (B) However, even when correcting for sparse time-sampling, the left-skewed P-value distribution in the male tongue indicates stronger signal of non-neutral volatility than 16,000 surrogate WFPs. (C) The parameter β2 from significantly (P < 0.001 for male tongue, P < 0.01 for surrogate data) heteroskedastic auxiliary regressions in eq 8 reveals significantly more β2 > 0 than β2 < 0 in the data. The different P-value cutoffs are for visualization—the same bias for β2 > 0 holds for a standard cutoff of P < 0.01 (D) Overlaying scatterplots of the residuals, , from all heteroskedastic cases (P < 0.01) of the male tongue data, reveals the empirical pattern of heteroskedasticity. Compared to surrogate neutral data, the male tongue is more volatile when the groupings are uneven, suggesting that either rare or abundant groups are more volatile—or equal groupings are relatively less volatile—than neutrality would predict. (E) All datasets have the same over-abundance of β2 > 0 for heteroskedastic (P < 0.05) CVTs.