Similar threshold functions from contrasting neural signal models

Three neural signal models of increment threshold detection are compared. All assume that the criterion for threshold is the attainment of a critical, minimum neural signal (or difference between two neural signals), and that the signal due to a test flash of intensity λ in the absence of a background light is $\text{λ}\text{(λ + σ)}$ (where σ is the semi-saturation constant). The models differ in the manner in which a background light of intensity θ is assumed to affect the signal. One model (due to Alpern et al., 1970a, Alpern et al., 1970b, Alpern et al., 1970c) assumes that the test flash signal, $\text{λ}\text{(λ + σ)}$, is attenuated by the multiplicative factor $\text{θ}{}_{\mathrm{D}}\text{(θ + θ}{}_{\mathrm{D}}\text{)}$ (where θ_D is a constant interpreted as sensory noise); another model specifies that the test flash signal is simply reduced (by subtraction) by the amount $\text{θ}\text{(θ + K)}$ (K a constant). One main result of this paper is that in the absence of pigment bleaching, these two models imply indistinguishable increment threshold functions. Further, a necessary and sufficient condition for each model guaranteeing the absence of saturation with steady backgrounds is found to be empirically satisfied. A third model is considered where the background field is assumed both to contribute to the neural signal and simultaneously to attenuate it (via a gain change). These assumptions are closely related to theoretical accounts of color induction and color perception. Though this model needs further investigation, it appears to be in better accord with actual increment threshold data than the others.