Neural representations of a moving object's distance and approach speed are essential for determining appropriate orienting responses, such as those observed in the localization behaviors of the weakly electric fish, Apteronotus leptorhynchus. We demonstrate that a power law form of spike rate adaptation transforms an electroreceptor afferent's response to "looming" object motion, effectively parsing information about distance and approach speed into distinct measures of the firing rate. Neurons with dynamics characterized by fixed time scales are shown to confound estimates of object distance and speed. Conversely, power law adaptation modifies an electroreceptor afferent's response according to the time scales present in the stimulus, generating a rate code for looming object distance that is invariant to speed and acceleration. Consequently, estimates of both object distance and approach speed can be uniquely determined from an electroreceptor afferent's firing rate, a multiplexed neural code operating over the extended time scales associated with behaviorally relevant stimuli.spike frequency adaptation | perceptual invariance | sensory transformations | neural coding D etermining how nervous systems maintain perceptual invariance in the face of multifeatured sensory input is a general problem when attempting to connect sensory physiology to highlevel perception. For instance, spatial parameters, such as an object's size, distance, and orientation, are inextricably confounded in sensory images projected onto the retina (1). This becomes an even more acute problem for the encoding of dynamic stimuli (1); when presented with a temporally modulated visual stimulus, retinal ganglion cells are sensitive to as many as six different features of the input (2). In its most reduced form, a generic neuron's conversion of input current into membrane potential is characterized by a membrane time constant (SI Text). A single response time constant endows a neuron with the ability to encode variations in stimulus intensity faithfully over one specific time scale. Because naturalistic stimuli can vary over a wide range of time scales, there will be inevitable mismatches between the rate at which the stimulus intensity changes and the temporal dynamics that define a neuron's response. Therefore, during sensation, neurons may be highly sensitive to both stimulus intensity and the time course over which it evolves. This introduces ambiguity into the estimation of stimulus features from a neuron's firing rate and presents a further challenge for understanding how neural systems maintain perceptual invariance.An object moving toward an animal provides a concrete example of such a problem because two variables of interest, the object's distance and approach speed, are both expected to influence the firing rate of a primary sensory neuron. These "looming" stimuli arise commonly in many sensory systems, including the electrosense, and appear to pose the same ratecoding dilemma for the electroreceptor afferents, whose firing rate has...