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Neural Mechanisms That Hide Individual Behavioral Differences: Evidence from Psychophysics and Neuroscience

Abstract

In both theory and practice, individual behavioral differences can reveal details of underlying neural mechanisms, and this has been widely exploited in experimental psychology. However, under some circumstances, individual differences are conspicuous by their absence. Three illuminating examples are treated in this theoretical review: (1) In color vision, there is a surprising lack of variation in red–green color opponency, especially as studied using unique hues, given the huge variation of L:M-cone ratios in normal observers. (2) Conversely, in achromatic vision, individual differences in L:M-cone ratios can be studied by measuring spectral sensitivity (luminance efficiency) functions. However, contrary to reasonable expectations, parvo and magno mechanisms can give rise to indistinguishable spectral sensitivity functions, so individual variations in parvo and magno activation often cannot be studied via spectral sensitivity. (3) Similar convergences occur in neuroscience: in simulated and actual neuronal networks and in electrophysiological/functional imaging studies of intact animals/humans. Neuronal systems trained or developed to do the same tasks need not wind up with the same wiring or the exact same behavior. However, under some circumstances, their behaviors can become functionally similar. Markedly different neural mechanisms somehow yield similar behaviors, a result found in systems as different as motor behaviors in crustaceans and sensory behaviors in humans. Theoretically, similar neural mechanisms can result from different neural combinations, a response convergence which limits our ability to infer the origins of some perceptual channels. When expected individual differences do not manifest, this is a clue that something interesting is happening and a goad to further investigation.

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Notes

  1. Some studies find that observers with really extreme cone ratios are carriers of protanopia or deuteranopia (Hofer et al. 2005; Miyahara et al. 1998; Neitz et al. 2002). One curiosity of postmortem retina RNA data is that it shows the same distribution of L:M derived from ERG data with most having more L-cones than M-cones, but almost no people with more M-cones than L-cones (Carroll et al. 2002). This might suggest that the sample of donor eyes included deuteranopia carriers but not protanopia carriers.

  2. Early unique hue studies typically used monochromatic (maximum saturation) lights. Monitor-based experiments cannot produce optimally saturated colors and show more unique hue variation. Webster et al. (2000b) computed the dominant wavelengths of their phosphor-mixture-generated colors and found that the variation of the unique hues all increases relative to the monochromatic experiments, but unique green still shows the largest variation. For example, unique yellow is centered at 574 nm and ranges from 570 to 580 nm in Webster et al.’s subjects. Unique green’s centroid is shifted to 545 nm and ranges from 491 to 562 nm in Webster et al.’s subjects. Therefore, when the present paper refers to the relative narrowness of unique hues, it is referring to perception of saturated spectral pure hues, not to desaturated “pastel” colors.

  3. There are limits to this Crick-inspired psychophysical-identity qualia-identity argument: a well-known philosopher I asked to critique this argument offered a counterexample—a rare mental condition in which a person becomes convinced that his/her spouse has been replaced with an exact duplicate (Capgras delusion). Since the stimulus is the same and there is no reason to suspect that the observer’s perceptual mechanisms have changed, the difference in spouse qualia is presumably due to emotional content bound to the perceptual qualia. This is not a major sticking point for color scientists.

  4. To see the possibilities of these models for invariance, imagine the competing terms, not as contending armies of neurons, but more like the ancient practice of single combat between the champions of their respective armies—numerosity is irrelevant and other qualities determine which competitor wins the day.

  5. This model was inspired by winner-take-all models in population dynamics. In population modeling, the neural responses RECT(LC)/a and RECT(MC)/d are called “carrying capacities” and correspond to the size the species population would grow to if its competitors became extinct. In neural terms, it corresponds roughly to the maximum response of a Naka–Rushton response function.

  6. Unfortunately, these rabbits are also so inbred that (if upset) they can kill themselves with a reflexive defensive arcing of their defective spines.

  7. Another area of experimental psychology that valued small-N designs is behavioral conditioning. B.F. Skinner thought it better to have 1000 h of conditioning on one rat, than 1 h each on a thousand rats.

  8. The term “phenotype” is used here in a loose, metaphorical way—as a goad to potentially useful lines of thought—and because the metaphor already has some currency among some neural theorists, though usually not in their formal works. No exact correspondence to formal meaning in genetics is implied, although see Dawkins’ (1989) for some other uses of an extended phenotype notion.

  9. It was also a surprise because of the nature of the receptive fields. For example, Lehky and Sejnowski (1988) found “bar detectors” in their network, despite the fact that the training set included no bar-like features. One lesson that one might take from this modeling is that although visual cortical responses are more superficially understandable than motor neuron responses, we should not delude ourselves into thinking that the obvious role for such a neuron is the only role the neuron is playing in the network.

  10. The likely predictability of test/retest correlations from single trial variance/covariance data is an amusing unnoticed bonus that has not yet (to my knowledge) been tested or exploited.

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Acknowledgements

This research was supported by the National Science Foundation #1456650 and benefited from old conversations with Viktor Jirsa, J.J. Vos, and the late Carl Ingling. I thank John Mollon and David Peterzell for reviewing the manuscript and Jack Werner for providing data from Werner and Wooten (1979a, b).

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Appendix: Background on the study of behavioral mechanisms in individual differences

Appendix: Background on the study of behavioral mechanisms in individual differences

Although this article addresses some particular cases where known structural individual differences do not lead to useable information about individual functional differences, those results are not interesting in a conceptual vacuum. There is a rich individual differences literature, and to put the exceptions in their proper place, it is useful to know something about cases where individual functional differences can be probed for useful structural information. Much of the development of this area can be traced to psychometric theory, where individual differences were used in a bootstrap fashion to both design better tests and to attempt to fathom their meaning (Nunnally and Bernstein 1994). Much work has also been done on attention, memory, intelligence, personality, reaction time, and various cognitive processes (Burt 1940; Eysenck and Eysenck 1987; Guttman 1954; John et al. 1977; Just and Carpenter 1992; Lu et al. 1992; MacCallum and Austin 2000; Schmiedek et al. 2007; Spearman 1927; Zinbardo and Boyd 1999). However, the focus of this Appendix is on individual differences in perception (and their uses), which are described briefly here. For a more comprehensive review of this topic, see Peterzell (2016).

The study of individual differences in perception dates back to Thurstone (1944), Pickford (1946), Jones (1948), and Cohen (1949). More recently, the discovery of multiple parallel visual channels raised the possibility that information about the underlying mechanisms might be encoded in the variance/covariance structure of human vision measured under conditions that differentially tap these channels. Thus, several studies attempt to infer the number and tuning of spatial and temporal frequency channels from contrast sensitivity data in many observers (Sekuler et al. 1983; Peterzell and Kelly 1997; Peterzell and Teller 1996, 2000; Peterzell et al. 1993, 1995, 1997, 2000; Mayer et al. 1995; Simpson and McFadden 2005). For an example of such data, see Table 2 (from Billock and Harding 1996). Table 2 shows a correlation matrix for temporal contrast sensitivity taken for a low spatial frequency stimulus viewed by 40 observers. The correlations on the first matrix diagonal, which are for temporal frequencies separated by 1 octave, are larger than correlations on the succeeding diagonals separated by multiple octaves of temporal frequency. This pattern of correlations at near and distant temporal frequencies is consistent with individual contrast sensitivity being mediated by multiple independent tuned temporal frequency-sensitive mechanisms. A convenient way to represent such data is to average along matrix diagonals, plotting the average correlation as a function of frequency separation (Fig. 4).

Table 2 Correlations for temporal contrast sensitivity measured at 0.5 cycles/deg (from Billock and Harding 1996)
Fig. 4
figure 4

Temporal correlation functions derived from spatiotemporal contrast sensitivity individual differences (Billock and Harding 1996). When a visual function is subserved by multiple quasi-independent channels, individual differences tend to show up as a pattern of correlations that is high for similar conditions and low for less similar conditions. Table 2 shows a matrix of such correlations for various temporal frequencies. The pattern of correlations can be surprisingly regular. The linear functions shown here are computed from the thresholds of 40 observers measured at 8 temporal frequencies and averaged over several spatial frequency conditions. The steep function is for low (0.5–5.7 cycles/deg) spatial frequencies. The shallow function is for higher (8–23 cycles/deg) spatial frequencies. Their common correlation, extrapolated to 0.77 at 0 octaves of separation, suggests that the test–retest correlation for this data set would be, if measured, about 0.77. Reprinted by permission

Figure 4 shows the correlation functions for temporal contrast sensitivity at low and high spatial frequencies. These functions are linear on an octave scale and are readily interpretable. The correlation intercepts of 0.77 at 0 octaves of separation can be taken as an estimate of test/retest correlation.Footnote 10 The slope is more interesting. We know from studies using other methods that human temporal contrast sensitivity appears to be subserved by two to four temporal frequency mechanisms (for a review, see Hess and Snowden 1992). The slope of the data taken at high spatial frequency conditions is − 0.029 ± 0.004, suggesting more than one temporal frequency mechanism subserving individual variation (because variation in the strength of a single channel should result in a slope of zero). For lower spatial frequencies the slope − 0.083 ± 0.003 is significantly steeper than the slope measured under high-frequency conditions, suggesting that more mechanisms mediate the detection of temporal contrast sensitivity for low spatial frequency than for high spatial frequency conditions. These results are consistent with other evidence that at least three channels mediate the detection of temporal modulation (Billock and Harding 1996).

Other models for correlation structure are available. An interesting special case—simplex correlational structure—was studied by Guttman (1954). For a simplex correlation matrix, only the matrix elements closest to the diagonal are independent, and lower elements in the matrix can be predicted from products of matrix elements above them, reminiscent of the behavior of a Markov-based model (in Markov models, a system’s behavior is dependent only on the system’s behavior on the previous time step; see Jöreskog 1970 and Peterzell et al. 1993.) Guttman notes that an n × n matrix of such correlations would support n − 1 factors; such a structure would be expected to arise from a Markov-like model. Alternately, in theory, the slope of the correlation function can be used to infer the natural image statistics to which observers are adapted (by evolution or development; Billock 2000; Billock et al. 2001a). For example, natural images generally have 1/fb spatial frequency (f) amplitude spectra. A meta-analysis of 11 studies of natural images found an average b of 1.08 for 1176 images (Billock 2000). The correlation structure of spatial contrast sensitivity measured by Billock and Harding (1996) predicts b values of 1.09–1.20, reasonably close to the structure of natural images. It is interesting to note that although Markov models are quite different from 1/f models, these two can be difficult to distinguish experimentally (Billock 2000). For example, multimechanism Markov models and 1/f continuous mechanism models yield indistinguishable results when applied to data on ion channel dynamics (Bassingwaighte et al. 1995; Liebovitch and Toth 1990).

For large numbers of observers, structural modeling and factor analysis can be used to create sensible multichannel models of visual modalities (e.g., Sekular et al. 1984; Peterzell 2016; Peterzell et al. 1993, 1995; Mayer et al. 1995; Scialfa et al. 2002). Similarly, several studies of individual variation in color vision or chromatic neural response yielded useful results (Bosten et al. 2014; Dobkins et al. 2000; Emery et al. 2016; Guth and Lodge 1973; Gunther and Dobkins 2002, 2003; Peterzell et al. 1996, 2000; Peterzell and Teller 2000; Read et al. 2016; Romney et al. 2005; Webster and MacLeod 1988; Webster et al. 2000a, b, 2002; Young 1986). Recently, these approaches have also found uses in the study of binocular vision, mental imagery, motion perception, face perception, synesthesia, and more (Cappe et al. 2014; de-Wit and Wagemans 2016; Kosslyn et al. 1990; Nefs et al. 2010; Rogowska 2015; Wang et al. 2012; Wilmer 2008; Wilmer et al. 2012; Yovel et al. 2014).

In general, individual data are used to produce an exploratory factor model, or an existing confirmatory model can be fit to individual data. When an exploratory approach is used, often the factors are rotated until a simpler structure emerges. These simple structures have factors that have compact dependence on the stimulus variables (for example, in spatial frequency experiments, each factor is tuned to a particular spatial frequency and the loadings drop-off smoothly away from that peak frequency). Such factors resemble the spatial frequency channels found in other kinds of psychophysical experiments. Beyond the consistency of simple structure with tuned channels, the assumption of tuned channels simplifies planning of experiments that will be analyzed by exploratory factor analysis (EFA). In general, EFA is most likely to succeed when each factor has loadings from several variables, when some of the selected variables are likely to be influenced by multiple factors and when variables’ measurements are reliable (Fabrigar et al. 1999). In this light, it is clear why factor analysis of sensory data often succeeds. Sensory researchers tend to sample along a single physical continuum that is known to produce consistent and sensible results in single observers, using psychophysical methods that are known to produce reliable data. For example, contrast perception is believed to be subserved by multiple overlapping spatial frequency channels, each with a preferred spatial frequency and a bandwidth (full width at half maximum of about 1 octave on average; range ca. 0.5–2.5 octaves). When a researcher studying contrast perception selects as variables spatial frequencies spaced say 0.5 octaves apart, each spatial frequency will produce a response from more than one spatial frequency channel. This situation is methodologically perfect for factor analysis (Fabrigar et al. 1999), and the simple structures it produces are highly consistent with the known properties of visual channels. By itself, this makes EFA a useful adjunct to other psychophysical methods of probing tuned neural channels. Actually producing a model, for say contrast sensitivity, requires some kind of combination rule for how contrast sensitivity depends on channel (factor) interactions. A common rule is the Quick–Minkowski sum (e.g., Eq. 5), which is (not coincidently) a convenient way to compute probability summation (Quick 1974). Linear sums and envelope rules are also employed.

A number of interesting confirmatory factor analyses (CFAs) have also been made. For example, Peterzell and Teller (1996, 2000) adapted Hugh Wilson’s six spatial frequency channel model for contrast sensitivity and applied it to predicting the correlation structure of contrast sensitivity data under some circumstances. Structural modeling, which combines factor analysis and regression techniques, has been useful for many such efforts (for an early example, see Sekular et al. 1984).

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Billock, V.A. Neural Mechanisms That Hide Individual Behavioral Differences: Evidence from Psychophysics and Neuroscience. Comput Brain Behav 3, 102–125 (2020). https://doi.org/10.1007/s42113-019-00030-5

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Keywords

  • Unique hue invariance
  • Spectral sensitivity
  • Response convergence
  • Stochastic resonance in neural networks
  • Neuronal network robustness
  • Variability quenching
  • Qualia problem