Contrast response functions in the visual wulst of the alert burrowing owl: a single-unit study

In this article, we provide the first detailed quantitative description of how neurons within a postretinal area of the visual system of a bird respond to achromatic contrast. Using the owl visual wulst as experimental model, we show that the nonlinearities of neuronal contrast responses are not so pronounced as they are in V1 of mammals. Arguably, this may be taken as an indicator of a neural correlate of poor contrast sensitivity.

Abstract

The neuronal representation of luminance contrast has not been thoroughly studied in birds. Here we present a detailed quantitative analysis of the contrast response of 120 individual neurons recorded from the visual wulst of awake burrowing owls (Athene cunicularia). Stimuli were sine-wave gratings presented within the cell classical receptive field and optimized in terms of eye preference, direction of drift, and spatiotemporal frequency. As contrast intensity was increased from zero to near 100%, most cells exhibited a monotonic response profile with a compressive, at times saturating, nonlinearity at higher contrasts. However, contrast response functions were found to have a highly variable shape across cells. With the view to capture a systematic trend in the data, we assessed the performance of four plausible models (linear, power, logarithmic, and hyperbolic ratio) using classical goodness-of-fit measures and more rigorous statistical tools for multimodel inferences based on the Akaike information criterion. From this analysis, we conclude that a high degree of model uncertainty is present in our data, meaning that no single descriptor is able on its own to capture the heterogeneous nature of single-unit contrast responses in the wulst. We further show that the generalizability of the hyperbolic ratio model established, for example, in the primary visual cortex of cats and monkeys is not tenable in the owl wulst mainly because most neurons in this area have a much wider dynamic range that starts at low contrast. The challenge for future research will be to understand the functional implications of these findings.

NEW & NOTEWORTHY

In this article, we provide the first detailed quantitative description of how neurons within a postretinal area of the visual system of a bird respond to achromatic contrast. Using the owl visual wulst as experimental model, we show that the nonlinearities of neuronal contrast responses are not so pronounced as they are in V1 of mammals. Arguably, this may be taken as an indicator of a neural correlate of poor contrast sensitivity.

the visual wulst is the part of the avian telencephalon that receives its major input from the retinothalamofugal pathway. In the owl, this area presumably plays an important role in mediating a number of visual skills such as stereopsis (Nieder and Wagner 2000, 2001a), spatial frequency-dependent detection of low-contrast oriented periodic patterns (Harmening et al. 2009; Orlowski et al. 2012), surface extraction from motion (van der Willigen et al. 2002, 2003), perception of illusory contours (Nieder and Wagner 2001b), and exogenously driven spatial attention (Harmening et al. 2011; Ohayon et al. 2008). Essentially, two lines of indirect evidence support this hypothesis: first, compared with most other birds, the visual wulst of owls is atypically large, a trait thought to be related to the large amount of binocular signals that get integrated in this structure (Iwaniuk et al. 2008; Iwaniuk and Hurd 2005; Iwaniuk and Wylie 2006; Karten et al. 1973); second, neurons in this area display a rich repertoire of response properties that seem ideally suited to extract basic attributes of a visual scene. They have small retinotopically organized receptive fields, tuned to spatial as well as temporal frequencies and selective for orientation, direction of motion, and binocular disparity (Baron et al. 2007; Nieder and Wagner 2000, 2001a, 2001b; Pettigrew 1979; Pettigrew and Konishi 1976a; Pinto and Baron 2009, 2010; Wagner and Frost 1993, 1994). In this respect, the owl wulst is strikingly similar to the early visual cortex of mammals, which is interesting from a comparative perspective, since this similarity is thought to be essentially due to a process of convergent evolution (Medina and Reiner 2000; Pettigrew 1979; Shimizu and Bowers 1999). Thus, as well as contributing to a better understanding of a neural substrate putatively important for the visual performance of owls, the functional characterization of wulst neurons in this bird is likely to provide important insights concerning the evolutionary principles governing early vision.

In line with this long-term research perspective, the present study addresses an important and yet unexplored issue of how individual neurons in the owl wulst encode luminance contrast. A neuronal representation of this physical dimension is undoubtedly the most basic requirement for extracting information about objects and surfaces in the world. It is also intrinsically linked to, and interferes with, the elaboration of receptive field properties important for encoding other spatial and motion cues. In birds, including the barn owl, contrast processing has been mainly investigated by measuring, either behaviorally or by pattern electroretinogram, contrast response thresholds as a function of spatial frequency (barn owl, Harmening et al. 2009; for other species, see Ghim and Hodos 2006 and references therein). A common and intriguing result revealed by these studies is that, despite their highly developed visual capabilities, birds have much lower contrast sensitivities than mammals. As yet, there is no obvious and satisfactory explanation for this important functional difference between birds and mammals (see Ghim and Hodos 2006). Presumably, single-unit investigations of contrast response conducted in key postretinal areas of the visual system should provide valuable information about this issue. Unfortunately, this type of investigation is critically missing in birds. As far as we know, only two studies in the pigeon, one in the optic tectum (Jassik-Gerschenfeld and Hardy 1979) and the other in the nucleus of the basal optic root (Wolf-Oberhollenzer and Kirschfeld 1994), have reported data on the relationship between response amplitude of individual neurons and achromatic contrast. However, because this characterization was not the main objective of the aforementioned studies, only a few cells were analyzed, such that it is difficult to make solid inferences about these data.

The situation is strikingly different with regard to the mammalian retinothalamocortical pathway, for which a considerable amount of information about the contrast response properties of neurons at all stages of this pathway is available. Following the pioneering work of Kuffler (1953), the antagonistic center-surround organization of retinal ganglion cell receptive fields is thought to provide an explicit representation of local contrast, which then gets relayed by lateral geniculate nucleus (LGN) cells (reviewed in Shapley and Lam 1993). At this early processing level, neuronal contrast response functions (CRFs) typically show a monotonic increase over a relatively wide dynamic range, thereby closely matching the cumulative distribution of contrasts encountered in natural scenes (Tadmor and Tolhurst 2000). However, in visual cortex, a different representation of contrast has been shown to emerge: CRFs get steeper, with more prominent response expansion and saturation at low and high contrast, respectively. This transformation is already visible at the level of the striate cortex (Albrecht and Hamilton 1982; Contreras and Palmer 2003; Dean 1981; Sclar et al. 1990) and becomes progressively more pronounced further downstream toward extrastriate cortical areas (Gegenfurtner et al. 1997; Levitt et al. 1994; Palmer et al. 2007; Sclar et al. 1990). Over the past several decades, there has been a great deal of interest in discovering the factors and biophysical mechanisms accounting for the nonlinearities that reduce the dynamic range of cortical neuron CRFs (for review see, for example, Albrecht et al. 2003; Carandini et al. 1999). This research goal is important given that several lines of evidence suggest that such nonlinearities have an overall impact on the efficiency of information processing. For example, it has been shown that the expansive response profile at low contrast, also referred as “half-squaring,” may influence the tuning precision of other stimulus dimensions such as orientation, direction of motion, and spatial frequency (Albrecht and Geisler 1991, 1994; Heeger 1992a). On the other hand, saturation at high contrast, which is thought to depend on a relatively fast-acting adaptation mechanism often referred to as “contrast gain control,” allows the maintenance of stimulus selectivity over a wide range of contrast (Albrecht and Hamilton 1982; Bonds 1991; Ferster and Miller 2000; Frazor et al. 2004; Geisler and Albrecht 1992; Heeger 1992b).

Taken together, the above considerations motivated us to undertake a detailed characterization of CRFs based on the steady-state responses of visual wulst neurons in the burrowing owl. To this end, we used sine-wave gratings, presented within the cell classical receptive field and optimized in terms of eye preference, direction of drift, and spatiotemporal frequency. The contrast-dependent responses that we find are highly variable across cells but usually monotonic and nonlinear. Here the extent to which such responses can be adequately described by a simple general model is assessed and contrasted with results typically encountered in the mammalian primary visual cortex (V1). Parts of these results have been reported in abstract form (Vieira et al. 2008).

MATERIALS AND METHODS

Animal care and recording preparation.

Single-unit recordings were obtained from the visual wulst of 10 adult burrowing owls (Athene cunicularia). The number of animals used in this study is large because some of the data for this study were collected sporadically during experiments performed for other, yet unpublished studies.

All experimental procedures were carried out following a method that allows us to study visual response properties of neurons in awake, nonbehaving burrowing owls. This method has been previously described in detail (Baron et al. 2007) and takes advantage of the fact that eye movements are extremely limited in owls (Knudsen 1982; Pettigrew and Konishi 1976b; Steinbach et al. 1974), reaching a maximum estimated amplitude of 0.5° in the burrowing owl (Cooper and Pettigrew 1979). Consequently, once the head of the animal is fixed, stable receptive field properties can be obtained without the necessity to control eye movements. Head fixation, a condition that is well accepted by burrowing owls after a positively reinforced habituation period of ∼3 wk, is achieved by a device that secures a lightweight recording chamber (∼0.7% of animal total weight) and supports our multielectrode holder.

The chamber was surgically implanted under general anesthesia, induced and maintained with Zoletil 50 (1:1 mixture of tiletamine and zolazepam; Virbac, Carros, France). In owls, the visual wulst forms a prominent elevation covering a large part of the dorsal telencephalon (see, for example, Fig. 1a in Karten et al. 1973). The chamber was centered over a region known to represent the central portion of the contralateral visual field (Pettigrew 1979). Anatomically, this region is located about halfway along the anterior-posterior axis of the wulst, close to the shallow groove delimiting its lateral extent, namely, the vallecula. Implantation was performed under stereotaxic guidance, thereby maximizing the precision and reproducibility of target localization. A craniotomy (∼5 mm in diameter) was made at the center of the recording chamber to provide brain access. The surgery lasted ∼1 h, after which a broad-spectrum antibiotic (50 mg/kg Terramycin; Pfizer Laboratories, São Paulo, SP, Brazil) and an analgesic/anti-inflammatory (2 mg/kg Ketofen 1%; Merial, São Paulo, SP, Brazil) were administered intramuscularly. The animals were allowed to recover for a minimum of 4 days before the beginning of the recordings.

Fig. 1.

Responses of a simple and a complex cell to 4 s of stimulation with sinusoidal gratings of various contrast levels. On left are the 11 stimulus contrast levels used to elicit the neuronal responses shown on right. A: peristimulus time histograms for the simple cell. This cell class tends to increase its response throughout the whole contrast range. For this particular neuron, a minimum contrast level of 9.9% was required to evoke a significant response (1-tailed Wilcoxon matched-pairs signed-rank test, P = 0.001). B: peristimulus time histograms for the complex cell. The cell class tends to increase its firing rate over a more limited contrast range, generally with little response change associated with high contrasts. For this cell, a 2.5% stimulus contrast value was sufficient to elicit a significant response (1-tailed Wilcoxon matched-pairs signed-rank test, P = 0.003).

The animal protocols used in this study were approved by the Ethics Committee for Animal Experimentation (CETEA, license no. 2004/01) of the Federal University of Minas Gerais and were conducted in conformance with the guidelines established by the European Communities Council Directive of 24 November 1986 (86/609/EEC). The owls were maintained in an outdoor aviary under a license from the Brazilian Institute for the Environment and Natural Renewable Resources (IBAMA, license no. 3076223).

Extracellular recording.

Spiking activity was recorded from individual neurons with quartz-isolated platinum-tungsten electrodes (Thomas Recording, Giessen, Germany) with an impedance of 0.3–0.9 MΩ at 1 kHz. A custom-built device (see Baron et al. 2007 for more details) allowed us to lower two or three electrodes independently into the brain with precision hydraulic microdrives (MO95; Narishige Scientific Instrument Lab, Tokyo, Japan). Readings from the latter were used to provide estimates of recording depth. The insertion point of the electrode into the brain, which was indicated by a characteristic noise in the recorded signal, provided the reference point for the coordinates of the penetration. To confirm the reliability of these coordinates, we checked whether the electrode tip exited the surface of the brain at a depth of zero when withdrawing the electrode at the end of a penetration. The search for visually responsive neurons was carried out through the entire thickness of the wulst (∼3 mm in the burrowing owl). Cells isolated along the same track were spaced at 200-μm intervals or greater. In some penetrations, the first 1,000 μm were ignored so that sampling biases along the dorsal-ventral axis of the wulst could be minimized.

Extracellular potentials were amplified (×1,000) and band-pass filtered between 300 Hz and 7 kHz (HST/16o25 headset, 32-channel Preamplifier box; Plexon, Dallas, TX) before being digitized at 32 kHz by a high-speed, 16-bit resolution A/D card with onboard trigger and timer capabilities (PCI-6259; National Instruments, Austin, TX). The A/D board was also programmed to provide a second amplification stage of ×10. Signal display, acquisition, and storage were controlled through custom software written in LabVIEW (National Instruments) by Dr. Sergio Neuenschwander. Spike waveforms were detected and recorded only if they crossed a threshold of 3–4 standard deviations of the voltage trace. Unit isolation and discrimination was performed online by selecting clusters formed by plotting the maximum vs. minimum amplitude of action potentials. It was further refined offline with software developed by Dr. Nan-Hui Chen at the Max Planck Institute. The semiautomatic clustering algorithm implemented in this software uses a dynamic template matching procedure (for more details see Baron et al. 2007). Quality of spike sorting was verified by several indicators, including 1) good clustering of principal component analysis scores; 2) nonviolation of an absolute refractory period of 2 ms as verified from interspike interval histograms; and 3) stability of spike amplitude and width across time.

Stimulus presentation.

Stimuli used for quantitative tests were sine-wave gratings displayed on a 19-in. CRT monitor (Samsung SyncMaster 955DF) at a resolution of 1,024 × 768 pixels and a noninterlaced frame rate of 100 Hz. The monitor was placed 66 cm from the owl's eyes, such that all grating stimuli had spatial frequencies below the Nyquist limit of the monitor at this resolution. An 8-bit RGB mode was used and gamma correction applied to produce a linear behavior of the displayed luminance. All gratings had a mean luminance (56.1 cd/m²) that equaled that of the background and were presented within a circular patch of 2–6° diameter. Photometric measurements were made with a ColorCal colorimeter (Cambridge Research Systems) and were routinely performed to verify the stability of the monitor calibration. Stimuli were prepared as sequences of bitmap images, which were then presented with timing accuracy as movies by ActiveSTIM software.

Receptive field characterization and experimental protocol.

We initially assessed the responses of each isolated unit by listening to its discharges on a loudspeaker and by monitoring its stability over time on our data-recording computer display. The location and extent of receptive fields were plotted as minimum response fields (Barlow et al. 1967), defined here as the area in visual space from which handheld and mouse-controlled stimuli, such as spots and bars of varying orientation, evoked neuronal discharges at a rate exceeding that of the unit spontaneous activity. This mapping procedure was carried out separately for the ipsilateral and contralateral eyes, allowing the determination of the receptive field ocular dominance. The majority of cells we encountered were binocular, and all of them could be driven by monocular stimuli presented to either eye alone. After this preliminary assessment, receptive field measurements were then made through the eye that more effectively activated the cell (the nondominant or nonresponsive eye was covered) and with the center of the receptive field roughly at the center of the monitor screen.

Orientation, direction of motion, spatial frequency, and temporal frequency preferences were evaluated with full-contrast sinusoidal gratings varying along these dimensions while listening to the firing rate of the cell and/or by offline quantitative analysis. Subjective and quantitative estimation procedures were generally in good agreement. We systematically began with a protocol consisting of eight stimulus orientations, each presented in two motion directions (16 stimuli in total, 22.5° steps). For the large majority of cells (109/120; ∼90% of our sample), best direction estimates were derived by fitting responses with the sum of two von Mises functions (Baron et al. 2007). All subsequent tests employed gratings that drifted in the best direction. Optimal spatiotemporal frequency tuning parameters were then estimated by measuring responses to six spatial frequencies (0.25, 0.5, 1, 2, 4, 8 cycles/°) and six temporal frequencies (0.25, 0.5, 1, 2, 4, 8 cycles/s). Roughly a quarter of our cell population had spatiotemporal tuning profile characterized quantitatively and form part of the data set analyzed in Pinto and Baron (2009). For 70% of our cell sample, we also reevaluated receptive field extent by expanding the size of an optimal drifting sine-wave grating until the response of the neuron stopped increasing. The stimulus-size value at peak spatial summation derived from this protocol was used thereafter.

We then proceeded to a quantitative assessment of the CRF while all other parameters were held constant, in agreement with the cell preferences. Contrast was defined by the Michelson formula (%): 100 × (Lum_max − Lum_min)/(Lum_max + Lum_min), where Lum_max and Lum_min are the maximum and minimum luminance levels of the sinusoidal grating. The majority of neurons were tested with 13 values of contrast (0%, 2.6%, 3.7%, 5.0%, 7.0%, 9.0%, 13.7%, 19.0%, 26.4%, 36.7%, 50.9%, 70.0%, and 98.0%). For a subset of neurons (34/120 cells; 28% of the sample) 11 steps of contrast were used (0%, 1.6%, 2.5%, 4.0%, 6.2%, 9.9%, 15.8%, 25.0%, 39.6%, 62.6%, and 98%). Each trial started with a 1-s presentation of a uniform field of the same mean luminance as the grating test stimuli. The latter were then shown for 4 s, so that at least one full cycle of the grating was completed even at the lowest temporal frequency. An interval of 3 s between stimuli was chosen to minimize possible effects of stimulation history. Each stimulus condition was presented 10 times in a pseudorandom blockwise order.

Data analysis.

Our study builds upon previous research showing a close functional analogy between V1 and the owl visual wulst. According to Pettigrew (1979), this analogy also extends to two prominent cell types extensively studied in the striate cortex, namely, simple cells, characterized by their approximately linear spatial selectivity to the contrast polarity of a stimulus, and a much more diverse population of so-called complex cells, which do not exhibit this response property. The above functional classification has provided and continues to provide an important, albeit still debated, framework to understand neuronal mechanisms in V1. Therefore, to enable a more insightful visual wulst/V1 comparison, we decided to classify neurons as simple and complex. To do so, we relied on a linearity index of spatial summation commonly used in V1 studies (De Valois et al. 1982; Skottun et al. 1991). Accordingly, the index was computed by examining how a cell responded to a moving sinusoidal grating presented at the highest contrast and optimized in terms of spatial frequency, temporal frequency, and direction of motion. More specifically, the responses of each isolated unit were converted into poststimulus time histograms (PSTHs) with a 20-ms bin width. After removal of spontaneous activity, each histogram was then Fourier transformed to estimate responses at DC (F₀) and at the fundamental stimulus frequency (F₁) across the entire stimulus presentation period. Cells with a modulation index (F₁/F₀) > 1 for the most optimal stimulus condition were classified as simple, and their response rate was calculated as the amplitude of F₁. All other cells were classified as complex and had their responses calculated as mean firing rate. Spontaneous activity was calculated from the mean firing rate during two “blank-screen” periods: the 1,000 ms before stimulus onset (for all trials and conditions) and the 4,000 ms of zero-contrast stimulation.

Directional selectivity was assessed by means of the standard directional index, DI = 1 − (R_anti − R_spont)/(R_pref − R_spont), where R_pref and R_anti represent the responses to motion in the preferred and antipreferred directions, respectively, relative to the spontaneous activity R_spont. Based on this index, cells were classified as directional (DI ≥ 0.5) or bidirectional (DI < 0.5).

Two exclusion criteria were adopted to guarantee reliable descriptions of the effect of contrast on wulst neuronal responses. We used the Kruskal-Wallis test to discard cells whose responses were not significantly modulated by the contrast intensity of the gratings. We also excluded cells for which robust evoked responses were not verified for at least two contrast conditions. This was assessed by comparing, for each contrast condition, the firing rate in a 1,000-ms window immediately before and after stimulus onset with the one-tailed Wilcoxon matched-pairs signed-rank test (P < 0.05).

Following the lead of Ledgeway et al. (2005), we quantified the degree to which neuronal responses increase monotonically as a function of contrast, using a monotonicity index (MI) defined as

$$\text{MI}=1.0-\left(R_{\max }-R_{\text{Cmax}}\right)/\left(R_{\max }-R_{\text{spont}}\right)$$

where R_max is the maximum response of the neuron, R_Cmax is the firing rate at the maximal contrast tested (typically 98%), and R_spont is the spontaneous activity of the cell. This index is inversely proportional to the degree of nonmonotonic behavior (supersaturation) displayed by a cell in response to contrast, varying from unity, for cells with perfectly monotonic responses, to zero, for cells that return to baseline level at the maximal contrast.

We also made use of another scalar index tailored to capture the level of response saturation at high contrast. Following Ledgeway et al. (2005), this saturation index is defined as

$$\text{SI}=\left(R_{\text{Cmax}}-R_{\text{C50}}\right)/R_{\max }$$

where R_C50 represents the response to a grating of 50% contrast. SI takes positive values for a monotonically rising, nonsaturating response and negative values for a nonmonotonic response. For cells showing an asymptotic saturation, SI is zero.

Model fitting.

An important objective of our study was to seek out a simple general descriptive model of neuronal contrast responses in the visual wulst of the burrowing owl. Inspired by previous similar studies in the mammalian V1 (Albrecht and Hamilton 1982; Contreras and Palmer 2003) and encouraged by the largely monotonic response behavior of our cell sample, we decided to consider four different models defined as

$$\text{Linear}:R\left(C\right)=a+b^{\ast }C$$

$$\text{Logarithmic}:R\left(C\right)=a+b^{*}{\log }_{10}(C)$$

$$\text{Power}:R\left(C\right)=a^{*}{C}^b$$

$$\text{Hyperbolic}\text{ratio}:R\left(C\right)=R_{\max }{}^{*}{C}^n/\left(C_{50}^n+C^n\right)$$

where R(C) refers to response as a function of luminance contrast. More detailed information about these models can be found in results. Note that the hyperbolic ratio model is also known as the Naka-Rushton function.

Models were fitted to the data from each neuron by means of a nonlinear least-squares minimization procedure using the trust region algorithm, implemented in the MATLAB Curve Fitting Toolbox (MathWorks, Natick, MA). Curve fitting was carried out on median values, computed over all trials associated with each condition. This choice was motivated by the fact that the majority of cells showed significant positive correlation between spike count variance and mean contrast response (data not shown), thereby violating an important condition for regression analysis, namely, the homogeneity of variance (heteroscedasticity). In addition, normal distribution of trial responses across all conditions was satisfied for only 33% of our cell sample. For the rest of the data set, departure from normality was typically due to one or two outliers associated with a maximum of three conditions per cell (except for 1 instance of 5 conditions). Although the removal of these outliers caused very mild effects on the overall shape of trial-based fits, their inclusion would contravene the assumption of independent, Gaussian-distributed residuals and would therefore weaken, at least in principle, the robustness of our nonlinear regression analysis. Given the above, and under the reasonable assumption that central tendency in our data set is overall better captured by the medians, our approach can be viewed as more conservative. Moreover, for most cells in our sample this approach yielded residuals with zero-mean, normally distributed residuals, which is a prerequisite for the model selection analysis we employed subsequently (see below).

Fitting started with a specific set of initial parameter values for each tested model. These values were estimated on the basis of pilot analysis and data reported in the literature and were maintained unchanged for all cells. After an initial run of successive interactions (600 maximum) of the fitting algorithm, fits were checked to ensure that they had converged and their adjusted parameter values lay within acceptable bounds. In the rare cases when either of these conditions was not satisfied, we refitted the data with other starting parameter values until satisfactory convergence solutions representing global minima were obtained. To gain an accessible assessment of the quality of the fits provided by a model, we computed the percentage of the variance across conditions explained by this model:

$$R^2=100\left(1-\frac{{\text{SS}}_{\text{fit}}}{{\text{SS}}_{\text{total}}}\right)$$

where SS_fit is the sum of squares extracted from the fit and SS_total is the sum of squares obtained from a flat line formed by the mean of the fitted residuals. The F-test was also used to evaluate the statistical reliability of R² values obtained for each fitted curves. This statistic served as rejection criterion only when the null hypothesis could not be rejected for the four models under investigation.

Model selection.

A shortcoming of relying solely on goodness-of-fit measures as a means to compare multimodel performance is that such measures do not establish a trade-off between fitting accuracy and model complexity (i.e., number of free parameters). This trade-off is especially important when the models that are being compared have different numbers of parameters, as is the case in our study (n = 2 for the linear, power, and logarithmic models; n = 3 for the hyperbolic model). While adding parameters to a model tends to improve its data-fitting abilities, it may also diminish its predictive power (generalizability). This is because instead of approximating the true underlying process an overlying complex model exaggerates the representation of sampling errors (noise) that are specific to one data set and not necessarily reproducible across data sets, a classical statistical problem known as overfitting.

To circumvent this potential pitfall, we assessed the relative performance of each fitted model by using a model selection approach based on the Akaike information criterion (AIC; Akaike 1974). Detailed information about the theoretical concepts and mathematical formalisms underlying this information criterion are provided in Burnham and Anderson (2002). In essence, AIC implements a form of complexity penalization to balance the trade-off between model complexity and fitting accuracy, thereby incorporating the statistical principle of parsimony according to which the best model is the one with the highest information content but the least complexity. Given the number of data points being modeled N and the number of estimated parameters K included in a model, AIC is defined as

$$\text{AIC}=N\ln \left(\frac{{\text{SS}}_{\text{fit}}}{N}\right)+2K$$

where SS_fit is the root-mean-square error of the model fit. The first term rewards descriptive accuracy, while the second term penalizes the lack of model parsimony. Although this equation is very simple, it is important to emphasize that its derivation is founded on solid information-theoretic concepts according to which the smaller the AIC value the better the model has performed. This is because the model with the lowest AIC value is asymptotically equivalent to choosing that with the lowest expected information loss as estimated by the Kullback-Leibler discrepancy. In the present study, we used a derivate of AIC for small-sized sample, which is recommended whenever N/K < 40 (see Burnham and Anderson 2002). This derivate takes the form

$${\text{AIC}}_{\text{c}}=\text{AIC}+\frac{2K\left(K+1\right)}{N-K-1}$$

AIC or AIC_c values, on their own, have no meaning: they vary on a relative scale and are much affected by sample size. By taking the differences to the minimal value min(AIC_c) within the model set M = {M_i, i = 1, 2, …, m} under consideration:

$$\Delta {\text{AIC}}_{\text{c}}^i={\text{AIC}}_{\text{c}}^i-\min \left({\text{AIC}}_{\text{c}}\right)$$

we therefore ranked the models according to their Akaike weights (w_i), which is a normalized measure of relative model likelihoods and is defined as

$$w_i=\frac{\exp (-\Delta {\text{AIC}}_{\text{c}}^i/2)}{{\displaystyle \sum _{m=1}^M\exp (-\Delta {\text{AIC}}_{\text{c}}^i/2)}}$$

In other words, w_i can be interpreted as the relative probability of each model be the best one among the whole set of candidate models (the sum of w_i of all models is equal to 1). The above procedure was carried out on a cell-by-cell basis.

General statistical analysis.

Several standard statistical tests were also computed. We used the Lilliefors modification of the Kolmogorov-Smirnov test to check normality of data sets. If normality was verified, we applied a t-test to compare the means of two populations or an ANOVA test if comparisons were made between more than two populations. Otherwise, the Wilcoxon rank sum and Kruskal-Wallis tests were used, as nonparametric equivalents of the t- and ANOVA tests, respectively. Significance of differences in categorical properties was assessed with either the Fisher's exact test (for sample size < 5) or the χ²-test (for sample size > 5). Spearman's rank correlation test was used to evaluate the relationship between groups. The significance level used for all tests was P < 0.05.

RESULTS

The results presented in this study are based on quantitative data obtained from 120 well-isolated neurons recorded from a total of 97 sites and 63 vertical penetrations in the visual wulst of 10 burrowing owls. The number of cells for each animal is 21, 11, 17, 5, 5, 9, 3, 22, 14, and 8. The responses of 156 neurons were initially screened, but 36 of these neurons were eliminated after application of our exclusion criteria (see materials and methods). Reliable estimates of recording depths were obtained for 78% of the remaining neurons (94/120). The distribution of these estimates ranged from 60 to 2,850 μm but was not uniform, yielding a median value of 870 μm (25th and 75th percentiles = 350 and 1,714 μm). Recording site locations were not confirmed histologically and cannot therefore be accurately assigned to specific regions of the wulst. Nevertheless, what we can safely infer from the above result is that more neurons (∼70%) were sampled from the superficial layer, namely, the hyperpallium apicale, than from the three other layers altogether, namely, the nucleus interstitialis hyperpallii apicale, the hyperpallium intercalatum, and the hyperpallium densocellulare.

Neuronal response properties were studied quantitatively with patches of sine-wave drifting gratings carefully centered on the cell's receptive field. This spatial coregistration was stable throughout the recording period, as revealed by systematic verifications of receptive field position before and after each quantitative protocol. Minimum response field size estimates ranged from ∼1° to 5°, confirming that the area of the wulst devoted to the central visual field had been effectively targeted by our electrode penetrations. In line with this finding, the median peak value of area summation curves obtained for 70% of the 120 cells filtered out for further contrast response analysis was 3.0° (25th and 75th percentiles: 2.0° and 3.6°). Given the foregoing description, the small and sporadic eye movements seen in the burrowing owl (Cooper and Pettigrew 1979) are unlikely to have a significant impact on the physiological measurements we report in the rest of this article.

Cells were classified according to their level of response modulation (simple or complex) and directional selectivity (directional, bidirectional, and omnidirectional), thereby allowing the investigation of possible differences in contrast response profiles with respect to these cell categories. Seventeen percent of the neurons (20/120) were classified as simple on the basis of the F₁/F₀ modulation index (mean F₁/F₀: 1.66, SD 0.53), while the large majority (100/120, 83%) was classified as complex (mean F₁/F₀: 0.51, SD 0.22). Bimodality of F₁/F₀ value distribution was not supported by Hartigan's dip test (P > 0.05; Hartigan and Hartigan 1985). With respect to directional selectivity, the proportion of directional, bidirectional and omnidirectional cells in our sample was 59%, 36% and 2%, respectively. Only 4 of 120 cells were not significantly modulated by the grating direction of motion and were therefore left unclassified. Overall, these classification results are similar to those encountered in our two previous studies (Baron et al. 2007; Pinto and Baron 2009).

To assess the CRF of each cell, we typically used 13, at times 11, contrast intensity values that increased in an exponential rather than linear fashion, so that the majority of values fell within the lower half of the contrast range (see materials and methods). As will become apparent further below, this stimulation protocol allowed us to define more accurately the part of the CRFs that changed most dynamically while covering the whole range of contrast intensities.

Figure 1 displays typical response profiles of simple (Fig. 1A) and complex (Fig. 1B) cells as a function of contrast. Responses are presented in the form of PSTHs, binned at 20-ms resolution and averaged across 10 repetitions of the same contrast. Visual inspection of these PSTHs reveals several key features of neuronal response dependence on contrast in the wulst. To start with, clear evoked sustained responses can be observed even at relatively low contrast levels. The complex cells in Fig. 1 are a good example of this feature. For these cells, a grating contrast of 2.5% (Fig. 1B) was actually sufficient to elicit a significant increase in firing rate (1-tailed Wilcoxon matched-pairs signed-rank test, P < 0.003). In the case of the simple cells, a higher contrast was actually necessary to evoke a response above baseline (9.9%) according to our statistical analysis (P = 0.001), notwithstanding the fact that this difference between simple and complex cells was not a general trend in our data set. A more robust difference between these two cell classes, exemplified in Fig. 1, is that simple cells tended to increase their firing rate throughout the whole contrast range whereas complex cells tended to show response increments over a more limited contrast range, usually showing little or no change in firing at higher contrast values. This characteristic is readily noticeable when looking at the steady-state response component of complex cells, which largely contributes to the results presented in this study as our quantitative analysis is based on spike frequency averaged over the whole stimulation period. However, it is important to mention that contrast-specific changes in the temporal evolution of neuronal activity, like the appearance of onset transients in the response at higher contrast of the complex cell in Fig. 1B, may represent important coding strategies and would therefore be interesting to evaluate in the future.

As a preliminary quantitative assessment of the contrast response behavior of our cell sample, we calculated two scalar indexes (see materials and methods): one designed to capture the degree of response monotonicity (MI) and another tailored to estimate the level of response saturation (SI). As shown in Fig. 2A, the population histogram of MI has a pronounced negative skewness with a median value of 1, indicating that the large majority of cells (72%, 86/120) respond monotonically to increasing contrast intensities. The nonmonotonic behavior observed in the remaining cell subset was weak, with MI values concentrated around 0.8. Note that MI was calculated on median raw data and therefore does not consider the statistical reliability of the difference in amplitude between the two quantities from which it is derived, namely the maximum response (R_max) and the response at the maximum contrast level (R_Cmax). Such difference was actually confirmed for only 2 of the 34 cells that had an MI below 1, reinforcing the notion that single-unit contrast responses in the owl wulst are largely monotonic.

Fig. 2.

Distribution of monotonicity and saturation indexes for our population of wulst neurons. A: for the monotonic index, a value of 1 indicates a monotonic response behavior; a value of 0 indicates a nonmonotonic profile, for which the response at maximum contrast is the same as that of the baseline. In general, the majority of wulst neurons are monotonic. B: neurons with a saturation index above 0 have a monotonic response profile and a progressively lower degree of response saturation as the values of this index increase. Values equal to 0 indicate an asymptotic saturation response. Negative values signal a nonmonotonic profile. The mean (not the median) of the saturation index distribution (arrowhead) was used as an indicator of central tendency because normality was verified for this distribution.

The population histogram of SI plotted in Fig. 2B was normally distributed around a mean of 0.18 (SD: 0.19), indicating that most of our sampled neurons also exhibit some degree of response compression or even saturation at higher contrast levels. The mean SI of simple cells was 0.26 (SD: 0.19) and that of complex cells was 0.16 (SD: 0.19). The difference between these two means was, however, not statistically significant (t-test, P = 0.052). Similarly, no difference in SI between directional (mean: 0.17, SD 0.22) and bidirectional (mean: 0.20, SD 0.18) cells was observed (t-test, P = 0.396). Negative SI values, indicative of supersaturation (nonmonotonic) behavior, characterized 14% of our cell population. However, when statistically comparing the two terms that render this index negative (R_Cmax and R_C50), significance was reached for only two cells. This argues that supersaturation in our data is mainly due to small inherent trial-to-trial variability in our measurements and does not represent a robust behavior.

Contrast response functions.

Although the above analysis indicates that single-unit CRFs in the owl wulst are mostly nonlinear and monotonic, a great deal of cell-to-cell variability was observed with respect to the shape of CRFs. This is exemplified for eight representative neurons in Fig. 3. To account for this variability, we chose four simple mathematically defined shape descriptors (linear, power, logarithmic, and hyperbolic ratio) that emphasize different contrast-response profiles. Albrecht and Hamilton (1982) as well as Contreras and Palmer (2003) performed a detailed comparison of those four functions within V1 of cats and monkeys and concluded that the hyperbolic ratio function was the most adequate and general model to describe the CRF of cells at this level of cortical processing. Testing whether this would also apply to the owl wulst is sound given the functional analogy between this area and early visual cortex. Interest in considering the logarithmic and power models also stems from the fact that they formalize two long-standing psychophysical laws (Weber-Fechner law and Stevens' law, respectively) of how subjective intensity covaries with stimulus strength. Thus their adequacy in fitting our data may offer the possibility to connect neural observables to classic theories in psychophysics.

Fig. 3.

Contrast response function of 8 representative neurons recorded from the visual wulst. Responses are plotted against a linear scale of contrast. Each data point indicates the cell's median firing rate over trials, with 1st and 3rd quartiles represented by error bars. The smooth curve through the responses of each cell is the best fit of 4 candidate models. It may be linear (A and B), logarithmic (C and D), power (E and F), or hyperbolic ratio (H-ratio; G and H). Here, fitting performance was assessed on the basis of % of the variance explained by a given model (R²). For each selected model, the values of its free parameters are specified at bottom right of its respective plot. Dotted lines in G and H (cells with hyperbolic ratio as best fit) indicate C₅₀, that is, the contrast required to produce 50% of the cell's maximum response. The difference between the 2 cells with respect to this parameter is illustrative of the large variation in the dynamic range of the responses along the contrast axis that is present across our cell sample. Cells shown in A, B, and E are simple cells; the other 5 are complex cells. SF, spatial frequency; TF, temporal frequency; DI, directional index; SI, saturation index.

For each cell, we assessed the fitting quality provided by the four models using a least-squares optimization approach and computed the percentage of the variance explained by each model (R²) as an initial estimate of the goodness of fit. For the two cells shown in Fig. 3, A and B, the linear fit yielded a higher R². However, according to this criterion, most cells in our sample were better described by a logarithmic (Fig. 3, C and D), power (Fig. 3, E and F), or hyperbolic ratio (Fig. 3, G and H) function. An important point illustrated in Fig. 3 is that a substantial degree of variability in fitting parameter values was observed across cells sharing the same model as “best” fit. Take, for example, the threefold difference in C₅₀ between the two cells shown in Fig. 3, G and H, which is indicative of a marked shift in the dynamic range of the response along the contrast axis. A more detailed analysis of parameter values is provided in Analysis of hyperbolic ratio model parameter values.

For the four models under investigation, the distribution of R² values departed from normality with a prominent skew toward higher values. We therefore used medians (together with 25th and 75th percentiles) as a measure of central tendency and obtained, for each model, the following results: linear 79% (65% and 88%), logarithmic 83% (73% and 0.90%), power 88% (78% and 92%), and hyperbolic ratio 91% (84% and 95%). From these results, it can be inferred that although the hyperbolic model seems to provide an overall better description of the CRF, considerable overlap in distribution of R² values also exists among models. To test for the statistical reliability of the R² values obtained for each model, we performed an F-test, which essentially tests the null hypothesis that all regression coefficient values are equal to zero vs. the alternative that at least one of them is not. For only one cell in our sample, the null hypothesis could not be rejected at a 5% significance level for all the models tested. This cell was, therefore, excluded from further analysis. Model-specific nonvalidation of the F-test was detected for only seven cells. It occurred mainly for the linear (4 cells) and hyperbolic (2 cells) models, except for one instance in which this nonvalidation occurred for a family of models (power, log, and hyperbolic). To verify whether a given cell class was more likely to be better fitted by a particular function, we applied a Fisher's exact test on a 2 (cell category) × 4 (models) contingency table. According to this analysis, the linear model was found to be more adequate for simple cells, whereas all three nonlinear models accounted equally better for complex cells (Fisher's exact test, DoF = 3, P < 0.001). Dependence for nonlinear models was also verified for the population of directional selective neurons (Fisher's exact test, DoF = 3, P = 0.013).

To get a better appreciation of the difference in fitting quality between the hyperbolic model and the three other models, we constructed scatterplots where each point represents a pair of R² values, one obtained from the hyperbolic model and the other from one of the three other models. Figure 4 shows the results of this analysis.

Fig. 4.

Comparison of fitting quality between the hyperbolic model and the linear (A), logarithmic (B), or power (C) model as estimated by R² statistics. Each circle represents a pair of R² values, one obtained from the hyperbolic and the other from the other function under comparison. A circle below the straight line of the scatterplots (y = x) indicates that a better fit was obtained with the hyperbolic function. Although the latter displayed an overall better performance than the linear model, a substantial improvement of fitting quality, with an increased overlap, may be seen with respect to the logarithmic and power models.

As predicted by our preliminary analysis, which indicates that the response for the vast majority of the cells in our sample tends to compress to some extent at higher contrast values, the performance of the linear model was overall substantially worse than that exhibited by the hyperbolic model. The extent of this difference in performance can be appreciated by noting that the majority of data points in Fig. 4A fall below the straight line of the scatterplot. R² statistics indeed favored the linear model for only 21 of 119 cells considered in this analysis, and often did so in a markedly fashion. However, it is worth mentioning that 30% of the data set displayed reasonable and approximately similar fitting qualities (R² > 80%, R² model differences < 5%) for both linear and hyperbolic models. This reflects the fact that compressive nonlinearity is fairly mild for a sizable fraction of wulst neurons.

Figure 4, B and C, make it clear that, compared with the linear model, the logarithmic and power models not only allow a substantial improvement in fitting quality but also show an increased overlap with the hyperbolic model. The proportion of logarithmic and power fits with R² > 80% and that differed from the hyperbolic model by only 5% was 49% and 56%, respectively. This result is not surprising given that logarithmic, power, and hyperbolic models are all able to account for a wide range of response compression and inflexion points where such compression begins to occur along the contrast axis. These models also predict the relatively linear contrast-response relationship before compression. The small improvement in performance of the power model over the logarithmic model is likely due to the fact that the former accommodates a wider range of response profiles than the latter. Indeed, depending on the value of its exponent, a power function may describe a strictly linear response profile (exponent ∼ 1), a linear followed by a compressive/saturating profile (0 < exponent < 1), or an expansive nonlinear profile followed by a linear increase (exponent > 1), although this last type of profile was encountered for only two cells in our sample.

Why is the fitting quality obtained with the hyperbolic model overall superior to that of other models, and can we infer from this that the hyperbolic model provides a general and ideal description of single-unit CRF in the owl wulst?

Model selection uncertainty.

As a first step toward addressing the aforementioned related issues, it is important to bear in mind that because of its additional parameter the hyperbolic model has an inherent predisposition to yield better fits than other competing models. Is this extra flexibility truly necessary to characterize a large proportion of our cell sample or is it prone to overfit the data? This question is particularly important given that the generalizability of a model depends intimately on its parsimony. We therefore decided to reestimate the performance of our model set on the basis of AIC_c scores that implement a principled trade-off between model descriptive accuracy and model complexity (see materials and methods).

Table 1 compares the proportion of cells, broken down according to their respective classes, for which a particular model scored best according to R² or AIC_c measurements. Remember that for AIC_c scoring the model yielding the lowest value was selected as it provides the minimum Kullback-Leibler information loss and adequately filters out noise (or entropy) in the data from the information provided by the model parameters. The most striking result evident in Table 1 is that the performance of the hyperbolic model drops substantially when assessed by the AIC method, which implies that the extra variance explained by this model reflects a certain degree of overfitting and therefore has poor predictive power. Table 1 also indicates that this conclusion applies indiscriminately to all cell categories. It is also interesting to note that the vast majority of cells no longer supported by the hyperbolic model on the basis of AIC_c scores instead admit the logarithmic model as best fit. We initially found this result curious, as we expected this transfer in model support to impact the logarithmic and power models equally. Visual inspection of our data set revealed that in fact this did not occur because the CRFs in these particular instances had a rather rapidly accelerating compression that was more accurately described by both logarithmic and hyperbolic models.

Table 1.

Proportion of cells “best fitted” by one of the four candidate models according to R² and AIC_c measurements and cell classes

Models	Classes	R2	Total R2	AICc	Total AICc
Linear	Simple	9%	16%	9%	16%
	Complex	7%		7%
	Directional	6%		7%
	Bidirectional	10%		9%
Power	Simple	4%	24%	4%	30%
	Complex	20%		26%
	Directional	15%		19%
	Bidirectional	9%		11%
Logarithmic	Simple		11%	5%	35%
	Complex	11%		30%
	Directional	9%		23%
	Bidirectional	2%		12%
Hyperbolic ratio	Simple	4%	49%	1%	19%
	Complex	45%		18%
	Directional	31%		13%
	Bidirectional	18%		6%

The preceding analysis relied on selecting the model with the lowest raw AIC_c value as an indication of its performance, making it impossible to intuit the extent to which this particular model differs from the other three models. Note, however, that when AIC_c differences among models are small for a given cell, the acceptance of a single model may lead to a false sense of confidence. Although classical statistical reasoning based on hypothesis testing induces one to believe that valid inference implies, at best, the rejection of all but one candidate model (and is formally limited to do so for nested models only), the AIC-based approach pursues a radically different philosophy. It emphasizes multimodel inferences and provides a practical and mathematically well-founded methodology to do so. The latter essentially relies on Akaike weights (see materials and methods). These are computed by ranking the fitted models from best to worst, based on the differences in AIC_c values, and then deriving the relative probability of each model to be the best one, which in the AIC sense means that it minimizes the Kullback-Leibler discrepancy, given the data and the set of candidate models.

The frequency histogram plotted in Fig. 5 compiles the Akaike weights obtained for each cell and each model considered in our study. Probability values were largely concentrated between 0 and 0.1, indicating that, for most cells, no strong evidence exists in favor of one particular model. Using a 95% confidence interval (as recommended by Burnham and Anderson 2002), satisfactory inferential properties (i.e., small bias and good precision) were embodied by a single model for only 19% of our cell sample. Most often (43%), three models (usually, the 3 nonlinear models) were necessary to make up a confidence set; the inclusion of two and four models was necessary for 25% and 13% of the cells, respectively. In agreement with what we have already shown, the linear model had less inferential coverage across cells (42%) than the nonlinear models, whose coverage ranged between 65% and 76%.

Fig. 5.

Model comparison for each cell of our sample using the Akaike information criterion (AIC). Probability values between 0.9 and 1.0 indicate, for a given cell, relatively strong evidence in favor of a particular model. Probability values between 0 and 0.1 mean that no strong evidence exists in favor of a single model. Clearly, single model support was not frequent in our data set.

The main conclusion we draw from the above analysis is that there is a substantial degree of model uncertainty in our data set, implying that the notion of a single general descriptor of neuronal contrast response profiles may not be applicable to the owl wulst, at least with respect to the models we chose to compare. To fully understand why the hyperbolic function does not serve as a general model in the wulst, as reported in V1 (e.g., Albrecht and Hamilton 1982; Contreras and Palmer 2003; Sclar et al. 1990), we proceeded with an analysis of its parameter values.

Analysis of hyperbolic ratio model parameter values.

The hyperbolic ratio model derives its nonlinear properties through the interaction of three parameters: C₅₀, which is the contrast necessary to reach 50% of the maximum response, also called semisaturation contrast; n, the exponent, which determines the slope of the curve as well as the sharpness of the nonlinearities at low and high contrasts; and R_max, which is the spike rate at which the response saturates.

Starting with the distribution of C₅₀ (Fig. 6A), it is important to emphasize that a considerable number of cells (49/119, 41%) assumed incompatible values for this parameter, being higher than the maximum theoretically possible contrast (i.e., with C₅₀ > 100%). This occurred when a cell exhibited very little or no sign of response saturation at high contrast, as exemplified in Fig. 3, A, B, E, and F. Thus, for these cells, the hyperbolic function had good fitting capabilities (median R² = 0.89) but loses its descriptive relevance, and data for this cell group are therefore shown separately as a figure inset. The high incidence of incompatible hyperbolic ratio fits is a key piece of evidence for rejecting the hyperbolic function as a general contrast response descriptor of the owl wulst and constitutes a major difference between this model system and the striate (as well as extrastriate) cortex of cats and monkeys in which such incompatible fits are rare. This notwithstanding, the distribution of semisaturation contrast values of wulst neurons with compatible hyperbolic ratio fits (i.e., with C₅₀ < 100%) resembled that reported for the striate cortex: both were rather broad, indicating a great deal of variability in contrast sensitivity, and peaked below 1.3 log contrast unit. However, the central tendency of our C₅₀ distribution was lower than that reported for mammals. Note that, for this analysis, simple and complex cells were grouped together because only very few simple cells (5/70) had compatible hyperbolic fits and their C₅₀ values were not statistically different from those of complex cells. We interpret this result as being consistent with the overall tendency of simple cells to respond more linearly to contrast than complex cells.

Fig. 6.

Distribution of the hyperbolic ratio model parameter values. A: C₅₀, which is the semisaturation contrast. B: the exponent n, responsible for the steepness of the CRF as well as the nonlinearities at low (expansion; for n > 1) and high (compression/saturation) contrasts. C: C_i is derived from the hyperbolic model (see text) and corresponds to the contrast at which the expansion ends and gives way to a linear response increase. D: R_max, which indicates the firing rate at the saturation point. The main histograms show the distribution of parameter values for cells whose hyperbolic fits were compatible (n = 70); insets show the distribution of values for incompatible hyperbolic ratio fits (n = 49; see text). Note the broad distribution of C₅₀ indicative of the relatively high degree of variability in contrast sensitivity of wulst neurons. The small number of cells with higher n values indicates that an expansive profile is rare in the CRF. Arrowheads indicate the median of the distributions.

Examining Fig. 6B, we observe that the large majority of cells yielding compatible hyperbolic ratio fits have estimated exponent n values between 1 and 2. This is characteristic of contrast-response curves, which have a gentle, close-to-linear incline until approaching their C₅₀. In fact, only a small proportion of cells (17%, 12/70) have a rather steep slope (n > 2) as typically encountered in the striate cortex, where the average value of n is ∼2.5 (Sclar et al. 1990). The parameter n of the hyperbolic model also captures a nonlinear property that the other models considered here do not, namely, the ability to predict an expansive nonlinearity at low contrast at the same time as a compressive profile at high contrasts. For n > 1, this property is evidenced; for n ≤ 1, it is not. The latter scenario was found for 57% of our sampled neurons. Most of these had incompatible hyperbolic ratio fits (Fig. 6B, inset). However, a lack of expansive nonlinearity was also found in 30% of the population of cells with compatible fits (Fig. 6B, main histogram). Moreover, for the remaining 70% of this population, the contrast range over which an expansive power-law profile occurred was fairly restricted. This is evident when looking at the distribution of inflexion points c_i (Fig. 6C) that determine the contrast at which the power-law profile ends and gives way to a linear increase. Analytically, it is calculated as follows (see Duong and Freeman 2008):

$$c_i=c_{50}^n\sqrt{\frac{n-1}{n+1}}n>1$$

If one considers the total cell sample, only a minority of cells (20/119, 17%) had a marked response expansion over 1.0 log unit contrast when stimulated with low-contrast gratings. The opposite is true in the mammalian V1 (Albrecht and Hamilton 1982; Sclar et al. 1990) and in part explains the superiority of the hyperbolic ratio function over the linear, logarithmic, and power models in this area.

The distribution of R_max values is presented in Fig. 6D but provides little explanatory power for understanding the lack of generalizability of the hyperbolic function in the wulst. We note, however, that this distribution approximates that reported for single units in the striate cortex of cats (Contreras and Palmer 2003) and monkeys (Sclar et al. 1990).

Limiting the contrast range.

Many studies that have characterized contrast-response relationships in the mammalian visual system have either undersampled or ignored the top half of the contrast scale. For example, Albrecht and Hamilton (1982) considered contrast values up to 56%. This methodological bias may be justified by the fact that although local contrast in the natural world varies considerably, its distribution is highly skewed toward lower values (Balboa and Grzywacz 2003; Brady and Field 2000; Clatworthy et al. 2003; Frazor and Geisler 2006; Laughlin 1981; Tadmor and Tolhurst 2000). Thus finding a good match between this distribution and neuronal responses is presumably a strong indicator of an efficient coding scheme for luminance contrast under photopic conditions (see, for example, Laughlin 1981; Tadmor and Tolhurst 2000).

Considering the above, we decided to examine whether our CRF characterization established over the full contrast range (98%) would be altered by restricting our analysis to 50% and 70% contrast. For this, we considered only the 84 cells that had been probed with 13 contrast levels (see materials and methods). All the quantitative assessments described above were repeated for the reduced-contrast-range groups, and the results obtained for the three groups (50%, 70%, and 98% contrast range) were compared with Kruskal-Wallis and χ²-tests. No statistical differences were found in the number of cells better adjusted by a given model, despite small variations in the percentage of cells better fitted by the hyperbolic ratio and power functions. This result was confirmed both in terms of model fitting accuracy (R² analysis) and model predictive power (AIC analysis). From this finding, we conclude that the neuronal representation of contrast in the wulst is fully specified within the lower half of the contrast scale, which is compatible with the aforementioned notion of a contrast coding efficiency scheme in this area.

Stability of CRF over time.

Our recordings were performed in nonanesthetized owls trained to accept head restriction while being presented with a battery of test stimuli. Visual monitoring inclines us to believe that the owls remained in a steady state of active wakefulness during the experimental sessions, which presumably contributed to the good recording stability that we obtained here and in previous studies (Baron et al. 2007; Pinto and Baron 2009). Nonetheless, a drawback of our preparation is that it does not permit us to control possible nonobservable fluctuations in internal behavioral states such as attention, arousal, and motivation. A question therefore arises concerning the extent to which the receptive field characteristics reported in this study correspond to intrinsic properties of wulst cells and are independent of other factors, such as uncontrolled behavioral variables.

To investigate this issue, we used an approach similar to that described by Nieder and Wagner (2000), which basically consists of cross-correlating tuning profiles obtained from two consecutive recording periods in order to evaluate the stability of these profiles over time. Our stimulation protocols lasted ∼15 min, during which the entire set of contrast levels was repeated 10 times in an internally randomized block design. For each cell, we computed two CRFs, one derived from the first five blocks of trials and the other derived from the remaining five blocks. The mean temporal difference between trials from the first and second evaluation periods was therefore ∼7 min.

Figure 7, A–C, show examples of these bipartite CRFs for three cells together with their respective Spearman's rank correlation coefficients. Clearly, a relatively high degree of similarity in the contrast response between the first and second evaluation periods was found for most cells independently of their response profile. The distribution of correlation coefficients for all 120 analyzed CRF pairs was skewed toward higher values (Kolmogorov-Smirnov test, P ≪ 0.001), with a median coefficient of 0.85 (Fig. 7D). Only 17% of pairs (20/120) yielded correlation coefficients below statistical significance (ρ < 0.61), as is the case for the cell shown in Fig. 7C. For this subset of pairs, there was no obvious trend in the data indicative of consistent effects over time, which inclines us to believe that lower correlation coefficients were mostly due to inherent noise in the measurements.

Fig. 7.

Reproducibility of contrast responses over time. A–C: examples of unit contrast response profiles obtained during the early (tuning part 1) and late (tuning part 2) periods of stimulation. Total stimulation time was ∼15 min, resulting in a mean temporal difference between the 2 evaluation periods of 7 min. Correlation coefficients of the curves are shown at bottom right of each panel. D: distribution of correlation coefficients computed for the whole population of wulst neurons (n = 120). Coefficients to right of vertical dotted line are statistically significant (Spearman's rank correlation, P = 0.05). Arrowhead indicates median of the distribution.

DISCUSSION

The primary goal of this study was to characterize the steady-state responses of neurons in the owl visual wulst as a function of contrast intensity. The originality of this work may be appreciated by considering the fact that, to our knowledge, this is the first detailed study on the relationship between neuronal response and contrast ever done in birds (see introduction). Our findings and the inferences drawn from them may be summarized as follows: 1) As contrast intensity was increased from 0 to near 100%, most cells exhibited a monotonic response profile with a compressive, at times saturating, nonlinearity at higher contrasts. 2) Despite this general trend, the shape of CRFs was highly variable across cells. 3) With the view to capture a systematic trend in the data, we initially applied conventional goodness-of-fit measures to assess the performance of four plausible models—linear, power, logarithmic, and hyperbolic ratio—and found that the latter provided an overall improvement, albeit weak, in fitting quality over the other candidate models. 4) Nonetheless, using a more rigorous statistical method for multimodel inferences based on the AIC, we demonstrated that a high degree of model uncertainty is present in our data, meaning that no single descriptor is able on its own to capture the heterogeneous nature of single-unit contrast representation in the wulst. 5) We further showed that the generalizability of the hyperbolic ratio model is not tenable in the owl wulst, as it may be in V1 of cats and monkeys, essentially because most neurons in this area have a much wider dynamic range that starts at low contrast. 6) Finally, the fact that CRF profiles were found to be quite stable over the entire recording session of a cell suggests that such profiles are shaped, to a large extent, by hardwired circuit properties of the system.

In the remainder of this section, we start by addressing some methodological issues that are inherent to our animal recording preparation and that may have influenced our results. We then discuss the benefit of considering multimodel selection methods such as the one we used here in order to compare the support provided by each model within a set of promising candidates. Finally, we compare our results with those reported in the mammalian retinothalamocortical pathway and consider their functional implications with respect to the owl wulst.

Awake vs. anesthetized recording preparation.

Current understanding of contrast coding in the mammalian visual system is primarily based on experimental studies performed on animals that have been anesthetized and immobilized with a variety of pharmacological agents. Here, single-cell data were obtained in alert owls, leaving open the possibility that some discrepancies between our study and others are in fact due to differences in recording preparation. Though meager, available evidence is indeed consistent with this hypothesis. In the mammalian visual cortex, several basic receptive field properties have been shown to alter depending on whether the animal is awake or anesthetized (Guo et al. 2004; Lamme et al. 1998; Pack et al. 2001) and what kind or dose of anesthesia is used (Ikeda and Wright 1974; Solomon et al. 1999; Villeneuve and Casanova 2003). More specifically with respect to contrast, there is evidence that anesthesia can lead to a reduction in sensitivity threshold as well as a decrease in neuronal response levels for high values of contrast (Ikeda and Wright 1974; Solomon et al. 1999). In line with such findings, the C₅₀ parameter of the hyperbolic ratio function, which is inversely related to contrast sensitivity, is typically lower in awake behaving monkeys (7% in Palmer et al. 2007; between 11% and 17% in Thiele et al. 2009) than in anesthetized monkeys (24% in Albrecht and Hamilton 1982; 33% in Sclar et al. 1990). It is interesting to note, however, that a more recent study by Alitto et al. (2011) in the primate LGN found a reduction in neuronal firing rate associated with anesthesia but no significant difference in contrast sensitivity between anesthetized and alert animals. Altogether, the above evidence thus indicates that caution needs to be exercised before assuming a straightforward correspondence between data obtained from different recording preparations, even when basic receptive field properties such as luminance contrast are being considered. To clarify this complex issue, studies such as that reported by Leopold et al. (2002) and Greenberg et al. (2008), in which neuronal responses are compared as the same animal is pharmacologically brought in and out of consciousness, would certainly be useful.

It is also important to bear in mind that our awake recordings were carried out in head-restrained burrowing owls that were not required to perform any particular behavioral task. It was possible to do this because eye movements are negligible in this owl species (Cooper and Pettigrew 1979). However, a limitation of this approach is that it provides no direct means of controlling for potential influences of covert behavioral states on neuronal activity. Single-unit recordings in awake behaving macaque monkey have shown that attention, for example, can significantly modulate CRFs in at least three different ways: it may increase the overall contrast sensitivity of the curve (contrast-gain model, Martinez-Trujillo and Treue 2002; Reynolds et al. 2000), amplify neuronal responses as contrast is increased (response-gain model, Williford and Maunsell 2006), or add a fixed amount to the response for all visible contrast values (additive gain model, Thiele et al. 2009). Our analysis of CRF stability (see Fig. 7) suggests that attention-dependent effects, if any, remained stable throughout a recording protocol. However, it does not allow us to discard the presence of such effects in our experiments, especially if these were exerted in a stimulus-dependent manner. For example, the appearance of high-contrast gratings may have systematically attracted the owl's attention to that location and increased firing as a result, thereby reducing the degree of saturation of CRFs. Clearly, the foregoing discussion highlights the need for further work to investigate the extent to which attention and other related brain states such as alertness exert an influence in the wulst, an issue that has not been addressed yet.

Consideration of stimulus luminance.

We assessed the dependence of wulst neuronal responses on contrast using sine-wave gratings as test stimuli. Contrast was varied from 0 to 98%, thereby practically covering the entire Michelson contrast scale. As conventionally done in single-unit studies with a similar goal, all grating parameters other than contrast were maintained at a constant value defined according to the preference of each cell, except for mean luminance, which was always fixed at 56 cd/m² across all recording sessions. Three reasons motivated us to choose this level of luminance. First, the latter is comparable to luminance values most frequently used in neurophysiological (e.g., Albrecht and Hamilton 1982; Alitto and Usrey 2004; Busse et al. 2011; Contreras and Palmer 2003) and bird psychophysical (e.g., Harmening et al. 2009; Hirsch 1982; Jarvis et al. 2009) studies on contrast sensitivity. Second, according to measurements from Frazor and Geisler (2006), 56 cd/m² is well within the range of luminance typically encountered in natural photopic environments. Third, given the cathemerality of burrowing owls (Berger and Walker 1972; Haug and Oliphant 1990; Levey et al. 2004; Sissons et al. 2001; Thomsen 1971), it is most probable that most visually guided tasks performed by these birds will occur at luminance levels around or below the one we used in this study. Note that testing the influence of mean luminance levels on contrast-response profiles was beyond the scope of this study. Therefore, we cannot discard the possibility that our choice of luminance intensity was suboptimal for some cells in our sample to reach saturation at higher contrasts. However, current evidence suggests that this hypothesis is unlikely. In V1, CRFs are known to be largely independent of photopic luminance levels (Dai and Wang 2012; Geisler et al. 2007). That is, luminance scales CRFs without changing their overall profile. Given that this coding strategy is presumably adapted to the statistical properties of natural images (Mante et al. 2005), it is thus reasonable to expect that such a strategy is also operational in the owl wulst.

Model uncertainty.

The present study was motivated by the tantalizing attempt to find a simple mathematical function capable on its own of describing the response profiles of all the cells in our data set. As discussed by Albrecht et al. (2002, 2003), this research objective is critical for further quantitative elaborations of functional or mechanistic models. In this context, the need for appropriate methods for model selection is clearly mandatory. Naively, it may be argued that choosing the “best” model among competing candidates consists in identifying the model that fits the data at hand more tightly according to some indexes of goodness-of-fit (e.g., R², root mean square). This is in fact the approach taken by the vast majority of electrophysiological studies in visual neuroscience. In this report, we tried to overcome some of the drawbacks associated with this rather conventional approach by using a sample-size-corrected version of the AIC (Burnham and Anderson 2002). This well-established and simple statistical procedure formalizes the importance of choosing a model according to its predictive power by weighting the fitting performance of each model against its respective complexity (i.e., number of free parameters). In contrast to goodness-of-fit measures for which no formal standards exist for comparison, the AIC-based method determines the strength of evidence for each evaluated model according to an objective, mathematically well-grounded framework. In addition, as exemplified in the present study, this method can be applied to nonnested models and considers all models at once without the need to perform pairwise comparisons and significant tests with arbitrarily chosen critical values for rejecting or accepting the null hypothesis. Despite their considerable advantages over hypothesis-testing methods, AIC and other information criterion approaches (see Burnham and Anderson 2002; Zucchini 2000) have been used in only a limited number of neurophysiological studies (Averbeck and Lee 2003; Schall et al. 2004; Vladusich et al. 2006).

In our work, the application of the AIC method revealed two important and related features. The first was that the improvement in fitting quality provided by the hyperbolic function is not sufficient to justify the use of this three-parameter model for describing the response pattern of most cells in our sample. A subsequent analysis of the fitted model parameter values showed that this is mainly related to the fact that little expansive nonlinearity at low contrast is present in our data, thereby making the hyperbolic fit somehow redundant with the other two-parameter models we evaluated. Second, by calculating the evidence ratio of Akaike weights for one model to be preferred over its competitors, we were able to demonstrate that none of the models examined here was overwhelmingly better than the others. We interpret this finding as indicating that a great deal of contrast response heterogeneity exists in the visual wulst of the burrowing owl at the single-cell level (see Fig. 8). This characteristic has also been often reported by V1 contrast-response studies (see, for example, Albrecht and Hamilton 1982; Girman et al. 1999; Niell and Stryker 2008; Van den Bergh et al. 2010) but never rigorously quantified as we did here. Interestingly, it has been shown that the combined output of a population of neurons heterogeneously encoding a particular stimulus attribute improves the accuracy with which such attribute is being represented (Chelaru and Dragoi 2008; Shamir and Sompolinsky 2006; Tripathy et al. 2013). Therefore, rather than conceptualizing neuronal response heterogeneity as an epiphenomenon of biological variability, its existence should be more thoroughly investigated. In our view, the holistic approach implemented by AIC-like strategies provides an ideal way to do this.

Fig. 8.

Contrast response functions of all data set, highlighting response heterogeneity. Each gray line represents the best-fitted model normalized for each isolated cell in our sample. Black line corresponds to the mean curve. n = 119.

Comparison with V1.

Over the last few decades, comparative neurobiologists have provided a large body of evidence suggesting that homologous relationships exist between different pallial domains of birds and reptiles and specific sectors of the mammalian neocortex (Butler et al. 2011; Jarvis et al. 2005; Karten 1969; Reiner et al. 2005). In particular, it is now of consensual acceptance that the visual wulst, the major subdivision of the avian dorsal pallium, is in many ways homologically related to the striate cortex of mammals. A central argument in favor of this hypothesis is that both structures are primary telencephalic projection areas of the retinothalamofugal pathway (Karten et al. 1973; Medina and Reiner 2000; Shimizu and Bowers 1999). Additional support for this hypothesis comes from morphological, neurochemical, developmental, genetic, and physiological data (reviewed in Butler et al. 2011 and Medina 2009). At this point, it is perhaps worth emphasizing that most of what we know about the functional organization of the visual wulst is derived from electrophysiological studies done in the owl. Ever since the pioneering work of Pettigrew and colleagues in the late 1970s (Pettigrew 1979; Pettigrew and Konishi 1976a, 1976b), the response properties of visual wulst neurons in this bird have indeed been the subject of several complementary investigations (Baron et al. 2007; Liu and Pettigrew 2003; Nieder and Wagner 1999, 2000, 2001a, 2001b; Pinto and Baron 2009, 2010). The general consensus emerging from all this work is that the owl visual wulst bears astonishing functional similarities with the early visual cortex of mammals, especially V1 and, to a lesser extent, V2.

Our study reveals a quite distinct pattern of results with regard to contrast. Under steady-state stimulation using optimal drifting gratings, V1 neurons typically respond in a sigmoidal fashion over a relatively limited range of contrast. This overall response profile appears to be present in a wide variety of mammalian species. When one analyzes the parameters of the best-fitting hyperbolic function, which, following the lead of Albrecht and Hamilton (1982), has been standardly applied in V1 studies, notable differences with the owl wulst can be readily identified. These differences are rendered visually more explicit in Fig. 9, where the average CRF of all our hyperbolic ratio fits is compared with similar data reported in key mammalian studies. Note that, in V1, contrast-response relationships do not seem to vary significantly across layers. Their mean profiles were therefore computed using the reported mean values of the hyperbolic ratio fit parameters (C₅₀ and n). Note also that a large proportion of cells (41%) in our study yielded C₅₀ values higher than 100% contrast, meaning that these cells did not show response saturation at high contrast levels. Therefore, Fig. 9, A and B, contain two distinct mean curves derived from our study: 1) one resulting from compatible hyperbolic ratio curves, i.e., those with C₅₀ lower than the maximal theoretical value, and 2) one obtained from the incompatible hyperbolic ratio fits (C₅₀ > 100%). The number of incompatible fits already indicates a striking difference with V1, where nonsaturating cells are rare (e.g., 9% in cats and monkeys, Albrecht and Hamilton 1982). With respect to compatible fits, we find a median C₅₀ of 12.6%, which is lower than the central tendency typically reported for this parameter in the striate cortex of mammals, including cats (Albrecht and Hamilton 1982, mean C₅₀ = 15.5%; Contreras and Palmer 2003, mean C₅₀ = 25.9%), macaque monkeys (Albrecht and Hamilton 1982, mean C₅₀ = 24.0%; Sclar et al. 1990, median C₅₀ = 33.0%; Van den Bergh et al. 2010, mean C₅₀ = 24.6%), marmoset monkeys (Persi et al. 2011, median C₅₀ = 25.5%), owl monkeys (O'Keefe et al. 1998, median C₅₀ = 42.0%), ferrets (Alitto and Usrey 2004, median C₅₀ = 16.7%); squirrels (Heimel et al. 2005, median C₅₀ = 35.0%); rats (Girman et al. 1999, mean C₅₀ ∼50%, see Fig. 7D), and mice (Busse et al. 2011, median C₅₀ = 35.0%; Niell and Stryker 2008, median C₅₀ = 19.8%; Van den Bergh et al. 2010, mean C₅₀ = 42.5%).

Fig. 9.

Comparison between contrast responses derived from burrowing owl and mammals. A: mean CRF estimated for cells in owl wulst and mammalian primary visual cortex. Graph shows 2 curves related to owl wulst: black solid line is the mean curve from compatible hyperbolic ratio (Hr) fits (n = 70), while gray solid line is the mean curve from incompatible hyperbolic ratio fits (n = 49). B: same as A, but with contrast values plotted in logarithm scale to highlight the small response expansion at low contrast values and the gentle slope of the owl CRF, compared with mammals. C and D: comparison between owl CRF curves (black and gray solid lines are the same as in A and B) and CRF derived from monkey parvo- and magnocellular streams, both plotted in a linear-linear scale (C) and with contrast values in logarithm scale (D). Note the similarity between owl wulst and monkey LGN. Mammalian curves were derived from cat (Contreras and Palmer 2003), macaque monkey (Sclar et al. 1990), marmoset (Persi et al. 2011), mouse (Van den Bergh et al. 2010), and squirrel (Heimel et al. 2005).

The slope of CRFs that we estimated on the basis of the hyperbolic model exponent is also different from that usually reported in V1 studies. In the cortex, exponent values are typically higher than 2.5 (Albrecht and Hamilton 1982; Contreras and Palmer 2003; Heimel et al. 2005; Niell and Stryker 2008; Sclar et al. 1990; Van der Bergh et al. 2010; Zheng et al. 2007). In the visual wulst of burrowing owls, considering compatible fits, we obtained a central tendency of ∼1.2. The exponent values for incompatible fits were even lower, ranging from 0.13 to 1.0 (median = 0.47). Altogether, these results indicate that the response expansion at low contrast values is much less pronounced in the wulst than in V1. To better visualize this difference, we replotted in Fig. 9B the same data as shown in Fig. 9A but on a logarithmic contrast scale.

It is also interesting to note that smoothly graded responses over an extended range of contrast were a prominent feature of cells we classified as simple on the basis of F₁/F₀. In fact, our analysis reveals that, on the whole, simple cells (F₁/F₀ > 1) tend to be better fitted by a strictly linear model, whereas complex cells (F₁/F₀ < 1) are better described by the nonlinear models. This behavior constitutes another major difference with mammalian V1 wherein simple cells, although quasi-linear in many aspects, exhibit a clear sigmoidally shaped contrast response, much like complex cells (for review see Carandini et al. 1999). It may be that in the wulst simple and complex cells contribute differently to contrast sensitivity and, as a result, to the enhancement of neuronal selectivity. In V1, this distinction does not seem to be tenable (Albrecht and Hamilton 1982; Contreras and Palmer 2003). But, for now, it is unclear whether the aforementioned hypothesis is plausible, in view of the fact that the small proportion of simple cells together with the nonbimodal distribution of F₁/F₀ values we encountered in this study argue against the notion that simple and complex cells represent two distinct functional classes in the owl wulst.

Another notable difference between wulst and striate cortex neurons refers to the monotonicity of CRFs. In V1 of monkeys and cats, several studies have reported that, at high contrast, the firing rate of a nonnegligible proportion of cells drops instead of plateauing, a phenomenon also referred to as supersaturation (Albrecht and Hamilton 1982; Bonds 1991; Ledgeway et al. 2005; Li and Creutzfeldt 1984; Peirce 2007; Somers et al. 1998). As discussed by Peirce (2007), the existence of this phenomenon has not been widely recognized in the cortical literature, in part because most studies have dedicated little or no attention to probing high contrast values. This is not the case in the present study, since our stimulation protocol included at least two and most often three points falling within the top half of the contrast scale. Yet we found no robust evidence of supersaturation in the owl's wulst. For now, it would be premature to speculate on the functional implications of this finding, especially so because, even in V1, supersaturation is not at all well understood, neither with regard to its potential contribution for visual perception (although see Peirce 2007, 2011 and May and Zhaoping 2011, 2013 for interesting hypothesis) nor in terms of how it may be mediated by neuronal circuits (on this point, see Li and Creutzfeldt 1984; Somers et al. 1998).

Evidence for LGN-like response profiles?

Standing back and looking at our results from a broad phylogenetic perspective, it may be argued that contrast-dependent steady-state responses of wulst neurons resemble more closely those reported for the mammalian LGN. Even though there are clear species differences in this area (see, for example, Van Hooser et al. 2003), geniculate CRFs are overall more linear and less steep than in V1. This feature is often quantified in the LGN by the ratio between R_max and C₅₀, also referred to as contrast gain (Croner and Kaplan 1995; Kremers et al. 1997; Solomon et al. 1999; Van Hooser et al. 2003). Calculating this ratio, we found that 61% (73/119) of our cells yielded values equal to or smaller than 1 Hz/%contrast, very much like, for example, primate parvocellular cells (Croner and Kaplan 1995; Kremers et al. 1997; Solomon et al. 1999) and gray squirrel X/Y cells (Van Hooser et al. 2003). Only 25% (30/119) of cells we sampled showed contrast gain higher than 2 Hz/%contrast and, in this respect, are more similar to feline geniculate X and Y cells as well as primate magnocellular cells (typical range: from 2 to 10 Hz/%contrast; Benardete et al. 1992; Croner and Kaplan 1995; Kaplan and Shapley 1986; Shapley and Perry 1986; Solomon et al. 1999). Interestingly, direct comparison of our data with those from Sclar et al. (1990), who reported C₅₀ and n values for both P and M cells, suggests a bipartite trend for contrast processing in the owl remarkably similar to that found in monkey LGN. This correspondence can be verified in Fig. 9, C and D, where we compare our average CRF derived from compatible hyperbolic fits with the contrast response of monkey M cells as well as our average incompatible hyperbolic fit curve with monkey P cells. Moreover, the absence of response supersaturation we found in the wulst, which also typifies mammalian LGN neurons, again reinforces the functional resemblance of these two areas with respect to contrast processing.

Implications for spatial contrast sensitivity measured psychophysically.

Although no psychophysical assessment of contrast sensitivity has been performed in the burrowing owl, it is most unlikely that this bird species would stray away from what has been consistently found in birds when behaviorally evaluating their contrast sensitivity as a function of spatial frequency with stationary gratings at photopic light levels. That is, an inverted U-shaped curve peaking at average values below 20 (barn owl: 13, Harmening et al. 2009; budgerigars: 10, Lind and Kelber 2011; chicken: 12, Jarvis et al. 2009; pigeon: 12, Hodos et al. 2002; wedge-tailed eagle: 14, Reymond and Wolfe 1981). To date, the American kestrel is the only avian species known to have a contrast sensitivity maximum of ∼30 (Hirsch 1982). However, this exceptional case does not fundamentally modify the general observation that birds perform on the whole much worse than many mammals, especially primates, on contrast-discrimination tasks (see Ghim and Hodos 2006; Souza et al. 2011; Uhlrich et al. 1981 and references therein). This difference in performance is surprising given that birds rely heavily on vision for their survival success, although it is possible that in the case of nocturnal birds such a discrepancy may not be so pronounced under scotopic conditions, as shown recently in the barn owl (Orlowski et al. 2012).

To date, the neuronal mechanisms underlying the poor photopic contrast sensitivity of birds remain without explanation. Several theoretical models have demonstrated the importance of considering the combined contribution of the optical properties of the eye, receptor sampling, and retinal lateral inhibition in order to explain the overall band-pass profile of contrast sensitivity functions (Barten 1999; Rovamo et al. 1993, 1994, 1999). More recently, an expanded version of these earlier models has been successfully applied to predict the behavioral results obtained experimentally in a wide range of vertebrate species, including birds (Jarvis et al. 2009; Jarvis and Wathes 2007, 2008). However, the fact that these models are not explicitly constrained by postretinal mechanisms makes them difficult to reconcile with a bunch of evidence obtained in mammals, which suggests an important role of early visual cortex, especially V1, in mediating frequency-dependent contrast discrimination. For example, using optogenetic manipulations in mice, a recent study by Glickfeld et al. (2013) has elegantly demonstrated a causal link between neuronal activity in V1 and behavioral performance. This study is actually consistent with a previous lesion study performed in the same species (Prusky and Douglas 2004). In monkeys, chemical lesions in V1 seem to generate even more severe impairments of contrast sensitivity (Merigan et al. 1993). Furthermore, response properties in V1 are compatible with the idea that the latter plays a key role for this perceptual function. The evidence backing up this claim comes not only from numerous single-unit studies (Busse et al. 2011; Geisler and Albrecht 1997; Hawken and Parker 1990; Hua et al. 2010; Meng et al. 2013; Tolhurst et al. 1983) but also from investigations based on visual evoked potential (Berkley and Watkins 1973; Campbell et al. 1973; Souza et al. 2007) and fMRI BOLD signals (Boynton et al. 1999; Leguire et al. 2011).

On the basis of our results and in light of the foregoing discussion, we think it is reasonable to hypothesize that behavioral contrast sensitivity in birds is also compromised, at least in part, by central mechanisms that limit the emergence of marked neuronal contrast-response nonlinearities (exponentiation at low contrast and saturation at higher contrast) in visual areas of critical importance for perceptual discrimination. Presumably, candidate areas need to contain neurons with relatively small receptive fields tuned to orientation and spatial frequency (Blakemore and Campbell 1969; Campbell and Robson 1968; De Valois and De Valois 1988; Graham 1989; Graham and Nachmias 1971). In owls, visual wulst neurons are known to possess such properties (Baron et al. 2007; Pettigrew 1979; Pettigrew and Konishi 1976a; Pinto and Baron 2009, 2010). It is therefore an ideal model system to evaluate our hypothesis further. To do so, it will be important to assess whether the neuronal representation of contrast is significantly transformed as it ascends the owl retinothalamofugal pathway. Our null hypothesis is that no such transformation occurs, at least not in the same pronounced manner as in mammals (Sclar et al. 1990). Clearly, another important set of actions to validate our hypothesis will be to demonstrate that behavioral contrast sensitivity deteriorates as neuronal activity in the owl visual wulst is reversibly or permanently silenced.

Concluding remarks.

The overwhelming majority of neurons in the early visual cortex of mammals exhibit a clear sigmoidal response curve as stimulus contrast is increased. It would have been reasonable to expect a similar result in the owl visual wulst given available evidence indicating a close functional resemblance of this area with V1. Yet, interestingly, the data reported in this study do not support this conjecture. Though monotonic, CRFs are highly variable across visual wulst neurons and often lack a pronounced exponentiation and saturation at low and high contrasts, respectively. A direct consequence of this overall trend toward more linear, gradual contrast responses is that the hyperbolic ratio (Naka-Rushton) model, conventionally used in the cortex, proved to be inappropriate as a single overarching CRF descriptor in the wulst. These results are especially significant because they provide the groundwork for future studies seeking to understand how seemingly different neural encoding schemes of contrast information have emerged in visual telencephalic areas that are evolutionarily distant but presumably homologous. The present work also lends support to the untapped idea that the visual wulst may have an important role in mediating the low contrast sensitivity typically observed in birds at the psychophysical level.

GRANTS

This work was supported by the Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG) and Science Without Borders Program/Special Visiting Researcher (MEC/MCTI/CAPES/CNPq/FAPs, grant no. 88881.030407/2013-01). This article was produced as part of the activities of FAPESP Research, Innovation and Dissemination Center for Neuromathematics (grant no. 2013/07699-0, S. Paulo Research Foundation). P. G. Vieira received a scholarship from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

P.G.V. and J.B. conception and design of research; P.G.V., J.P.M.d.S., and J.B. performed experiments; P.G.V. and J.P.M.d.S. analyzed data; P.G.V., J.P.M.d.S., and J.B. interpreted results of experiments; P.G.V. and J.P.M.d.S. prepared figures; P.G.V. and J.B. drafted manuscript; P.G.V., J.P.M.d.S., and J.B. edited and revised manuscript; P.G.V., J.P.M.d.S., and J.B. approved final version of manuscript.