PMC

Inverse effectiveness in a single SC neuron. Top: Impulse rasters and histograms for of the response of an SC neuron to auditory (A) and visual stimuli of 5 intensities (V1–V5) presented alone. Middle: Impulse rasters and histograms showing the response of the neuron to co-presentation of an auditory stimulus (which alone generated no substantial response) with each of the visual stimuli. As intensity is increased, the multisensory response becomes more robust. Bottom: Larger unisensory visual responses correlate with larger multisensory responses. Note that the multisensory and unisensory responses appear to saturate at different maximum levels and that there is a significant amount of overlap in the ranges of the unisensory and multisensory response magnitudes. MSI (%) is shown by the gray histograms, and decreases as the unisensory response magnitude increases. Taken from .

A schematic of the standard method for identifying and evaluating the computations underlying multisensory integration. First, the mean multisensory response magnitude is compared, using a statistical criterion, to the largest of the mean unisensory responses (gray diamond). If the multisensory response is significantly larger, multisensory enhancement is identified (green, top). If the multisensory response is significantly smaller, multisensory depression is identified (yellow, bottom). If multisensory enhancement is identified, the computation can be further subdivided into superadditive, additive, or subadditive enhancement by comparing the multisensory response to the predicted sum of the unisensory responses. Bar graphs provide examples of the response magnitudes evoked by cross-modal stimuli presented individually (S₁, S₂) and in combination (S₁S₂) for each computational mode. If multisensory depression is identified, the computation engaged can be further subdivided into superminimal, minimal, or subminimal depression by comparing the multisensory response to the smallest of the unisensory responses. Bar graph conventions are the same as above.

Three response relationships among populations of SC neurons that are relevant to the principle of inverse effectiveness. The data were taken from (), and each dot represents a sample from a different stimulus or neuron. Left: A correlation exists between the estimated response variance and the response magnitude across the population, with the line of unity (solid black) providing the predicted relationship for a Poisson process. Although the data are roughly consistent with this model, the Poisson model does more poorly at high response magnitudes where the model’s assumptions become less well justified. Center: There is a tight correlation (r²=0.87) between the magnitudes of the multisensory and the best unisensory responses and the inset shows a log-log plot of this trend. Right: A characteristic example of “inverse effectiveness” showing a negative trend between MSI and the magnitude of the best unisensory response (inset shows the log-log plot). MSI = multisensory index; Imp. = impulses.

Identifying significantly negative trend lines between MSI and maximum unisensory magnitude in a single SC neuron in which a large range of unisensory response magnitudes were collected (from ). Top: In order to model the error associated with the estimates of the mean unisensory and multisensory responses, an empirical bootstrapping procedure is performed in which 20 samples of trial-by-trial impulse counts are selected (with replacement) for the purposes of averaging. The concordance of the selected trial-by-trial impulse counts with the actual data can be seen by the close match between then dotted and dashed lines for each of the unisensory (left) and multisensory (right) cumulative frequency distributions for this neuron. Bottom: The left figure illustrates the good correlation between mean unisensory and multisensory response magnitudes. Error bars indicate the standard error of the mean computed from the actual impulse counts. The right figure illustrates the relationship between median MSI (the MSI distribution rarely approximates a normal distribution) and the maximum unisensory response magnitude, showing a clearly negative trend. The error bars indicate the range accounting for 68% of the distribution of the data.

Inverse effectiveness is not a ubiquitous feature of datasets. Three randomized datasets are presented, each showing similar effects. For each case, the panel on top shows a scatter plot of multisensory responses and the maximum unisensory response to observe correlations, and in the bottom panel, MSI is plotted against the maximum unisensory response to examine any relationship between MSI and unisensory efficacy. Note that the bottom plots use a quasi-log scale for the ordinate: logarithmic (base 10) in the range above 10 and below −10, but linear between −10 and 10, to emphasize the area of interest. Left: Results of a simulation in which two unisensory responses and one multisensory response are generated from identical distributions. This procedure is repeated 20,000 times. Note the absence of a correlation between the two variables, a consequence of their randomness. Grey symbols represent MSI calculated from each sample in the top panel. Black dots show the mean MSI within each 0.1 wide bin of the abscissa. Note that though the trend of black points has a negative slope, it a) crosses MSI=0 halfway through the range and b) continues to become more negative with increasing values of the maximum unisensory response. This means that by increasing unisensory effectiveness, the multisensory interaction transitions from enhancement to depression, which is inconsistent with inverse effectiveness, and, in the negative range, shows the opposite of the predicted trend for inverse effectiveness. Center: Results of a simulation in which the mean values of unisensory and multisensory responses from a real dataset (same as ) are “scrambled”. This procedure is repeated 20,000 times. Note that statistics are possible in this dataset (the standard deviations associated with the means are used), and multisensory responses that are significantly different from maximum “unisensory” responses (top), and the associated MSI (bottom) are depicted in red and the others in green (two-tailed t-test, alpha= <0.05). All other conventions are the same as in the left figure. This dataset shows the same trend as the purely random numbers, with one additional caveat: most (approximately 95%) of the multisensory response values are not significant; that is, they show neither multisensory enhancement nor depression. As before, the trend line of means crosses MSI=0 about halfway through the range and continue to become even more negative, which is inconsistent with inverse effectiveness. Right: Results of a simulation in which the trial-by-trial impulse counts from the a real dataset (same as ) are randomly sampled 30 times each to simulate two unisensory responses and one multisensory response. This is repeated 202,000 times. All other conventions are the same as the center plot. The outcome is that there is no correlation and almost no significant differences between the maximum unisensory and multisensory responses (top). In addition, almost no data points show significant enhancement (bottom), a few show significant multisensory depression (bottom), and the negative trend line relating MSI to unisensory response efficacy again crosses zero. These plots illustrate that the results of random numbers or randomizing real datasets yields products inconsistent with the principle of inverse effectiveness.