Fig 5. Simple implementation of optimal decision making.

(A) Signalling variables p and q contain information about the helix orientation angle Ψ and distance R to the target. Contour levels for conditional probability densities $P(p,q|R,\Psi >\frac{\pi }{2})$ (red) and $P(p,q|R,\Psi \le \frac{\pi }{2})$ (black) (corresponding to 1%, 10%, 50%, 90% percentiles; R = 1.5mm). (B) Relative frequency of ‘high-gain’ steering predicted by the optimal decision strategy, for given combination of (p, q). We define a decision boundary Θ(p) (yellow) by a piecewise linear fit to the 50%-contour line (up to p = 5ms, corresponding to a limit of sufficiently reliable state estimation, see S1 Appendix). (C) Simulated swimming path using this decision rule with dynamic switching between ‘high-gain’ steering (red) and ‘low-gain’ steering (black); projected on xy-plane. The chemoattractant concentration in this plane is shown (blue gradient), together with the boundary of the noise zone. (D) Success probability P(R₀) for full simulations with simple decision making (red) as a function of initial distance R₀ to the egg. For comparison, success probabilities for ‘low-gain’ steering (white) and ‘high-gain’ steering (black) are shown. (E) The effective chemotactic range $\mathcal{R}$ with decision making (red) is larger than $\mathcal{R}$ for an optimal constant gain factor (black). Parameters, see S1 Appendix.