Fig. 4.

Lovebirds stabilize their head beat by beat in all directions except frontal. (A) Whereas motion in the frontal (x) direction is not stabilized (gain $\overline{a}\approx 1$), the neck stabilizes lateral (y), vertical (z), pitch, roll, and yaw motion for each bird (N = 3; separated by bird in SI Appendix, Fig. SF15). Head stabilization in each gust condition is similar across visual environments (underbars represent gust conditions). (B) A passive neck suspension model reveals ranges of natural frequency ratios $\left(f_{\text{n}}/f\right)$ and damping coefficients $\left(\zeta \right)$ corresponding to gains and phase lags observed in the head motion (circles, mean; contours, ±SD). (C) Smaller flying animals can maintain vertical image jitter less than eye diameter $\left({\Delta }_{z,\text{eye}}/d_{\text{eye}}<1\right)$ regardless of the head–body gain $\left(\overline{a}\right)$. Mean and SD by species group was derived from literature (58) for evaluating the scaling trend (light gray, insects; medium gray, hummingbirds; dark gray, other birds; SI Appendix, Fig. SF37 for all species). The Inset shows lovebird eye displacements are similar for each visual condition. See SI Appendix, section S2 for scaling details.