(A) Schematic of the apparatus (left), where animals crawl atop an agar substrate while exposed to a 1D linear temperature gradient. Sample thermotaxis trajectories (right) from 18 C. elegans crawling for 60 min and 25 Drosophila crawling for 15 min, where the red dots indicate the starting position for all trajectories. Worms start at 20°C and exhibit negative thermotaxis, moving toward their 15°C cultivation temperature, while larvae start at 17.5°C and crawl away from aversive cold temperatures. The wheel indicates labels for crawling direction ranges, with octant 1 parallel to the gradient heading toward warmer temperatures and octant 5 heading antiparallel towards cooler temperatures. (B) Diffusion over time (left) in the x- and y-directions for C. elegans. throughout the experiment, indicating diminished, but highly significant, diffusion along the navigation direction. The average turning rate (upper right) diminishes over time, as in the Figure 1B,B’ isotropic case; the turning rate ratio (lower right) remains below 1 and nearly constant throughout the experiment. (C) Equilibrium probability distributions in the x (top) and y (bottom) directions (both use the same scale), extrapolated from empirical trajectories using the Markov state model (MSM). The lag time used is 750 s. Red lines are smoothed traces to guide the eye. The free-energy picture of equilibrium conditions (right), to place the analysis in context with the protein folding analysis tools employed here. Lower-free energy corresponds to higher population as , where here . (B’) Diffusion, and turning rates for Drosophila larvae, also showing . The average turning rate stabilizes early, and the turning rate ratio , the primary behavioral modulation underlying thermotaxis, remains nearly constant. (C’) Equilibrium probability distributions for Drosophila larvae (left), and the corresponding free-energy landscape (right), determined from the MSM. Analysis is based on 30 experiments, 131 tracks, and 3061 turns for worms, and 20 experiments, 303 tracks, and 7771 turns for larvae. The directions of overall population drift for (A) are indicated by green arrows, with the numbers indicating the dimensionless drift velocity, approximately 10 times greater than for the isotropic navigation cases (see Materials and methods). Error bars are s.e.m. where shown; in the other cases the error bar size is smaller than the line thickness, and therefore not seen.