Models of Causal Inference in the Elasmobranch Electrosensory System: How Sharks Find Food

We develop a theory of how the functional design of the electrosensory system in sharks reflects the inevitability of noise in high-precision measurements, and how the Central Nervous System may have developed an efficient solution to the problem of inferring parameters of stimulus sources, such as their location, via Bayesian neural computation. We use Finite Element Method to examine how the electrical properties of shark tissues and the geometrical configuration of both the shark body and the electrosensory array, act to focus weak electric fields in the aquatic environment, so that the majority of the voltage drop is signalled across the electrosensory cells. We analyse snapshots of two ethologically relevant stimuli: localized prey-like dipole electric sources, and uniform electric fields resembling motion-induced and other fields encountered in the ocean. We demonstrated that self movement (or self state) not only affects the measured field, by perturbing the self field, but also affects the external field. Electrosensory cells provide input to central brain regions via primary afferent nerves. Inspection of elasmobranch electrosensory afferent spike trains and inter-spike interval distributions indicates that they typically have fairly regular spontaneous inter-spike intervals with skewed Gaussian-like variability. However, because electrosensory afferent neurons converge onto secondary neurons, we consider the convergent input a "super afferent" with the pulse train received by a target neuron approaching a Poisson process with shorter mean intervals as the number of independent convergent spike trains increases. We implement a spiking neural particle filter which takes simulated electrosensory "super afferent" spike trains and can successfully infer the fixed Poisson parameter, or the equivalent real world state, distance to a source. The circuit obtained by converting the mathematical model to a network structure bears a striking resemblance to the cerebellar-like hindbrain circuits of the dorsal octavolateral nucleus. The elasmobranchs’ ability to sense electric fields down to a limit imposed by thermodynamics seems extraordinary. However we predict that the theories presented here generalize to other sensory systems, particularly the other octavolateralis senses which share cerebellar-like circuitry, suggesting that the cerebellum itself also plays a role in dynamic state estimation