Contrast sensitivity, visual acuity and the effect of behavioural state on optokinetic gain in fiddler crabs

Animals have evolved a diversity of visual systems which reflect the varied visual tasks they face in the disparate environments in which they live (Land and Nilsson, 2012). Every visual system has its strengths and weaknesses in terms of performance. To understand why these have evolved, and to interpret the behavioural actions and decisions animals make in response to sensory cues, it is necessary to understand the information they receive via their sensory systems.

Two of the main characteristics of an eye that determine the information it can provide are its spatial resolving power (ability to see spatial detail) and its contrast sensitivity (ability to discriminate lighter from darker image elements) (Land, 1997; Land and Nilsson, 2012; Theobald et al., 2010). Spatial resolving power depends in part on photoreceptor diameter and the inter-receptor spacing of the retinal mosaic; smaller and more densely packed photoreceptors result in a higher spatial acuity. Larger ommatidia, on the other hand, capture more photons, and have a larger aperture which results in higher spatial cut-off frequency and diffraction limit. Consequently, larger receptors have higher contrast sensitivity (Warrant and McIntyre, 1993). A simultaneous improvement of both spatial acuity and contrast sensitivity is only possible if eye size increases (Land, 1981, 1985) and, as eye size essentially scales with animal size (Howard and Snyder, 1983; Land, 1997; Land and Nilsson, 2012), this leads to an unavoidable trade-off between spatial acuity and contrast sensitivity.

Spatial acuity and contrast sensitivity can be measured using many methods. In compound eyes (the most common eye type in arthropods) spatial acuity is often calculated from anatomical information such as the distribution and density of photoreceptors (particularly inter-ommatidial angle; Land, 1997; Snyder et al., 1977; Stavenga, 2003), using the pseudopupil analytical approach (Horridge, 1978; Land, 1997; Rigosi et al., 2021; Stavenga, 1979) or (more recently) by using micro-computed tomography (microCT)-based 3D reconstruction techniques (Bagheri et al., 2020; Taylor et al., 2019). Anatomical methods can provide a detailed estimation of visual acuity across the full visual field of animals. However, assumptions have to be made about how the structure of the eye translates into physiological performance (Land, 1997). While most anatomical estimates of spatial acuity closely match estimates made by behavioural measurements (e.g. Hemmi and Mark, 1998; Land, 1997; Wehner, 1981), there are some exceptions (Brokovich et al., 2010; Douglas and Hawryshyn, 1990). In contrast, anatomical methods do not provide an estimation of contrast sensitivity.

An integrated measure of visual performance that reveals both spatial resolution and contrast sensitivity is the contrast sensitivity function (CSF). This measures the eye's capacity to resolve spatial patterns as the size and contrast change. The contrast sensitivity function provides a means to examine the trade-off between contrast sensitivity and visual acuity across different species. It can be measured with behavioural (e.g. Chakravarthi et al., 2017; Currea et al., 2018; Lawson and Srinivasan, 2020; Nityananda et al., 2015) or electrophysiological techniques (e.g. Hardie, 1979; Ogawa et al., 2019; Palavalli-Nettimi et al., 2019; Ryan et al., 2020; Straw et al., 2006). Both approaches provide information about the way in which eyes work, but ocular neural responses do not necessarily reflect what the animal responds to behaviourally (e.g. Duistermars et al., 2007).

Behavioural experiments are essential to assess the overall capacity of an animal's visual system and the extent to which it uses the information available. Although behavioural choice paradigms may provide optimal results (e.g. Chakravarthi et al., 2016; Macuda et al., 2001), they generally rely on training and are very time-consuming. For many animals, training is not a feasible option, making optomotor responses a commonly used experimental alternative (Chakravarthi et al., 2017; Currea et al., 2018; Lawson and Srinivasan, 2020; Nityananda et al., 2015). Optomotor responses are innate compensatory eye, head or body movements that are performed to minimize optic flow (the movement of the image of the external world across the animal's retina) when an animal is exposed to a wide-field rotating stimulus. By altering the contrast, speed or angular speed, and spatial frequency of the stimuli, it is possible to measure the complete contrast sensitivity function.

One crucial factor that is often ignored in determining the contrast sensitivity of animals is their behavioural state, which may include factors such as whether the animal is actively moving or not, proximity to conspecifics or a refuge, etc. Recent studies have highlighted the importance of an animal's behavioural state on the strength of stimulus-induced responses at both neuronal and the behavioural levels (Gilbert and Bauer, 1998; Hengstenberg et al., 1986; Horn and Lang, 1978; Maimon et al., 2010; Nolen and Hoy, 1984; Ramirez and Pearson, 1993; Reichert et al., 1985; Rind et al., 2008; Rosner et al., 2009, 2010; Schmidt and Konishi, 1998; Sillar and Roberts, 1988; Staudacher and Schildberger, 1998; Treue and Maunsell, 1996). Optic flow is generated when an animal walks or flies around in its environment. Therefore, an animal's nervous system can be in a different state while the animal is actively moving. Indeed, Rosner et al. (2009) have shown that the ‘gain’ (i.e. the ratio of tracking velocity of eye or head movements to stimulus velocity) of optomotor head movements which counteract retinal image slip, increases with motor activity in insects.

Owing to their limited sensory capabilities and a relatively simple neural system, fiddler crabs can be used to investigate how the eye anatomy and physiology, including regional specialisations in retinae or visual fields, reflect the behavioural ecology of animals and affect their behavioural strategies. However, their contrast sensitivity function and whether fiddler crabs' behavioural state affects their ability to see contrast remains unknown.

The compound eyes of fiddler crabs are located on long stalks, which the crabs keep perpendicular to their visual horizon at all times, allowing for a full panoramic field of view (Nalbach, 1990; Zeil and Al-Mutairi, 1996; Zeil and Hemmi, 2006). The visual acuity of fiddler crabs across the visual field have been derived from anatomical measurements using both the pseudopupil method (Smolka and Hemmi, 2009) and microCT approaches (Bagheri et al., 2020). These studies have shown that each eye of fiddler crabs (Gelasimus dampieri and Gelasimus vomeris) contains more than 8000 ommatidia with a ‘visual streak’ of high vertical (elevational) sampling resolution along the visual horizon in which vertical resolution reaches 1.8 cycles per degree (cyc deg⁻¹) (Bagheri et al., 2020) when calculated from anatomical information. This streak of high vertical resolution is interpreted as an adaptation to the mudflat environment (Hughes, 1977) inhabited by fiddler crabs and is thought to help the animals detect conspecifics and terrestrial predators within the part of the visual field where they are most likely to occur (Zeil and Al-Mutairi, 1996; Zeil and Hemmi, 2006). In contrast, the anatomically inferred horizontal (azimuthal) sampling resolution is relatively uniform across the eye with a lower maximum close to 0.4 cyc deg⁻¹ (Bagheri et al., 2020). Although the detailed anatomical measurements provide a theoretical estimate of visual performance, these estimates have never been confirmed at a behavioural level in fiddler crabs.

Optomotor responses in crabs are mediated by both eye and body rotations. Compensatory eye movements consist of a slow tracking phase to stabilize the image on the retina and to reduce image blur, followed by a saccadic reset that brings the eyes back to their initial position (see Horridge and Burrows, 1968). Binocularly elicited optomotor responses in crabs are direction insensitive and significantly weaker than monocular responses (Barnatan et al., 2019). The movement of both eyes in optomotor responses are strongly coupled in crabs (Horridge and Sandeman, 1964) and the response is a function of the inputs to both eyes (Nalbach et al., 1985). Unlike many arthropods (e.g. Land et al., 1990; Rossel, 1980; Young, 1988), crabs only follow the motion of the stripes, but do not fixate or track objects of interest, i.e. there is no position dependent response (Sandeman, 1978).

In this study, we measured the vertical and horizontal behavioural contrast sensitivity function of the fiddler crab Gelasimus dampieri using an optomotor paradigm. We measured optokinetic responses (eye rotations in response to optic flow) to both vertical and horizontal moving, sine wave luminance gratings spanning a range of different spatial frequencies, velocities and contrasts. We explored the effect of behavioural state on optokinetic gain and contrast sensitivity by comparing restrained with tethered, but freely rotating, animals.

Fiddler crabs of species Gelasimus dampieri (formerly Uca dampieri Crane 1975) were collected from intertidal mudflats near Broome (–17.9°S, 122.2°E), Western Australia. The crabs were housed in an artificial mudflat at the University of Western Australia. The artificial mudflat had a periodic tidal inundation and a 12 h:12 h light:dark cycle in which artificial lighting included ultraviolet light. The animals were fed fish food pellets twice a week and water quality, temperature (27–29°C) and salinity (28–33 ppt) were checked regularly. During periods of active experimentation, animals were transferred to small compartments containing a small rock and a small PVC pipe in which the animals could seek refuge. The small compartments were maintained at the same tidal inundation, light cycle, diet, water quality and animal care routine as the artificial mudflat. Experiments were approved by the University of Western Australia's animal ethics committee under the UWA AEC permit RA3/400/1020.

The ‘horizontal’ contrast sensitivity function was measured in a virtual optomotor drum with crabs in two behavioural states: walking and non-walking. An individual was positioned on the top centre of a custom-made treadmill (Fig. 1) consisting of a 10 cm diameter polystyrene ball elevated by air flow from of a pressurized air reservoir, allowing the ball to rotate freely. The crabs were tethered using a hinged wire hanger which was fixed with cyanoacrylate glue (Loctite Super Glue gel, Loctite Belgium, Kontich, Belgium) to the animal's carapace. To elicit eye rotations rather than body rotations, the tethers were prevented from rotating, and the air supply was turned off making the ball immobile. This prevented the animals from rotating around the tether point and stopped them from walking, which helped with the automated eye tracking and allowed us to measure contrast sensitivity functions (CSFs) from immobile animals. In order to determine the effects of these physical restrictions, we also tested a walking condition, to explore the effects of behavioural state on the optokinetic gain. We turned on the air supply and allowed the tether to rotate, permitting the animals to walk freely and rotate around the vertical axis. For both behavioural states (immobile and walking), CSF measurements were derived from eye rotations relative to environment.

The optomotor stimulus was presented on four LCD computer monitors (Dell E2310H 1920×1080 resolution) surrounding the treadmill (Fig. 1). The monitors were calibrated for linearity in contrast using standard Gamma correction techniques with monitor luminance measured for different input pixel values using a radiometer (ILT1700, International Light Technologies) with a radiance detector. The resulting look-up table was used to ensure that the screen's luminance changed linearly with changes in the pixel value from 0 (black) to 255 (white), allowing accurate sinusoidal luminance gratings to be displayed. A digital video camera (SONY 4K FDR-AX100, 25 frames s⁻¹) with an accessory one dioptre lens, was placed directly above the crabs to record the animals' eye and body rotations during stimulus presentations. The apparatus was fully enclosed to prevent animals being distracted by external movements or external room lights. The exception was of a small opening, approximately 8 cm in diameter at the top of the apparatus, which provided access for the video camera. A small mirror reflecting part of the stimulus (i.e. the luminance grating) was positioned in the camera's field of view, allowing the stimulus and behaviour to be recorded simultaneously, and the behaviour of the crabs and the timing of the stimuli to be accurately synchronized. The mirror was placed next to the polystyrene ball outside the animal's field of view.

Presenting a virtual vertically rotating (pitch) optomotor drum ideally requires the axis of the drum to be changed according to the animal's orientation in the horizontal plane. As such apparatus was impractical, the ‘vertical’ contrast sensitivity function was measured in experimental apparatus in which the virtual optomotor drum comprised two LCD computer monitors rotated by 90 deg to present the visual stimuli. The crabs thus viewed horizontal gratings moving vertically in their forward and rear fields of view (±30 deg Azimuth).

The stimuli were created in MATLAB 2014a (Mathworks, Inc. Massachusetts, United States) and the Psychophysics Toolbox 3 (Brainard, 1997; Kleiner et al., 2007). The stimuli consisted of horizontally moving, vertically oriented sine-wave gratings covering from 0 to 50 deg elevation of the visual field of crabs. The gratings were corrected for perspective distortions such that the stimulus on the four monitors appeared as a circular drum to a crab positioned at the centre of the monitors. A typical optomotor response, in a restrained animal, consists of slow eye rotations in the direction of the stimulus followed by rapid rotations in the opposite direction which resets the eye to its default resting position (Movie 1). Previous studies with brief stimulation periods (1–5 s) have shown reliable optomotor responses (Currea et al., 2018; Nityananda et al., 2015). Therefore, to minimize the number of eye resets, to verify that eye rotations were caused by stimulus rotations (i.e. shown by the eye rotating in the direction of the stimulus) and to increase the robustness of our threshold estimates, we changed the direction of motion five times, resulting in six stimulus segments each lasting 4 s. The direction of the first movement, clockwise or anti-clockwise, was randomized. Since fiddler crabs visually align their eyes with the horizon (Zeil et al., 1986), a stationary black horizontal bar was presented at the bottom of the monitors such that it made a luminance step exactly at the height of the crab's eye (Fig. 1). This simulated horizon helped to ensure natural eye-stalk alignment and orientation. The height of the luminance step was individually adjusted for each crab to compensate for their eye height.

To measure the full contrast sensitivity function, we presented all 252 combinations of seven spatial frequencies (0.013, 0.025, 0.05, 0.1, 0.2, 0.4 and 0.8 cyc deg⁻¹, which correspond to a cycle width of 76.9, 40, 20, 10, 5, 2.5, 1.25 and 1 deg) and six contrasts (0.03, 0.06, 0.13, 0.25, 0.5 and 1) at six rotational speeds (0.625, 1.25, 2.5, 5, 10 and 20 deg s⁻¹). For a periodic sinusoidal grating of spatial frequency (f_s), moving at speed (S), the temporal frequency can simply be calculated as f_t=S×f_s. Stimulus contrasts were calculated using the Michelson contrast equation where L_max and L_min are the maximum and minimum luminance, respectively. The average luminance, measured at the centre of the monitor from the centre of treadmill, was 103 cd m⁻².

Stimulus presentation followed a randomised block design where spatial frequency was randomised and then all possible combinations of contrast and rotational speed were presented in random order within a spatial frequency block. A block therefore consisted of one spatial frequency and all 36 combinations of contrast and speed and lasted approximately 15 min.

In total six crabs, two males and four females were used in these experiments. Two of the females were presented with all possible stimulus combinations. The other two females had to be replaced halfway through the experiments. As these experiments are time-consuming and subject to limitations imposed by the UWA ethics committee's approval, we were unable to increase our sample size.

The visual stimuli were presented using the same method as for the horizontal contrast sensitivity curve except that the number of monitors was reduced to two. One monitor was inverted so that the stimuli on opposite monitors were moving in opposite directions (one up, and one down) creating from the crabs' perspective an illusion of seeing part of a vertically rotating (pitch) optomotor drum.

The stimuli consisted of full screen gratings at ten spatial frequencies (0.05, 0.1, 0.14, 0.2, 0.28, 0.4, 0.57, 0.8, 1.13 and 1.6 cyc deg⁻¹, which correspond to a cycle width of 20, 10, 7.14, 5, 3.57, 2.5, 1.75, 1.25, 0.88 and 0.625 deg), six contrasts (0.03, 0.06, 0.13, 0.25, 0.5 and 1) and one speed (2.5 deg s⁻¹) which was close to the optimal velocity range in the horizontal contrast sensitivity experiment. The stimuli covered from 0 to 64 deg elevation of the visual field of crabs. As none of the crabs responded at spatial frequencies above 0.4 cyc deg⁻¹ these frequencies were omitted from the analyses. Five crabs, three females and two males were used in this experiment.

An animal was secured into position at the centre of the apparatus using a wire hanger. To allow for automated tracking of eye rotations, small, thin (approximately 0.2×1 mm) pieces of plastic (blue and yellow in colour) were glued to each eyestalk, adjacent to the small hair found on the eye stalk cuticle (Movie 1), using cyanoacrylate glue. This position allowed the crabs to move their eyes freely without any restriction.

The apparatus was then fully covered, and the animal was monitored using the video camera. When the animal had both eyestalks in an upright, natural position, an experimental block of stimuli, consisting of all possible contrast and rotational speed combinations for a particular spatial frequency, was commenced. If the animal moved out of position, or both eye stalks were not in an upright, vertical position, the experiment was interrupted and the crab was placed into a small container with salt water for few minutes before restarting the experimental block from the beginning. Each block lasted about 15 min, after which the animal was removed from the apparatus and placed in a container with salt water for approximately 5 min before commencing the next block of stimuli. Stimulus presentation within each block was randomised (as explained above) and fully automated.

To assess whether behavioural state affects the crabs' contrast sensitivity thresholds, several additional trials were conducted in which the crabs were allowed to rotate their bodies as well as their eyes. The animals were shown a subset of the horizontally moving, vertical grating stimulus combinations used in the main experiment: one combination that was easy for the crabs to resolve (spatial frequency=0.05 cyc deg⁻¹; rotational speed=2.5 and 10 deg s⁻¹) and one combination that was expected to be more challenging (spatial frequency=0.2 cyc deg⁻¹; rotational speed=2.5 and 10 deg s⁻¹). Four crabs, three females and one male were used in these experiments.

The video recordings of the crab's responses were analysed frame by frame using a custom program (Jan Hemmi, UWA) written in MATLAB 2014a (Mathworks, Inc. Massachusetts, United States), using colour segmentation to track the blue and yellow eye stalk markers, and hence each crab's eye rotations. The crab's behaviour was synchronised with the stimuli and the angular rotation of the eye (around the yaw axis for horizontal contrast sensitivity measurements and around the roll axis for vertical contrast sensitivity measurements), for each of the six reversals of direction were calculated for each condition. This resulted in data consisting of eye orientations for both eyes relative to the start and end times of all stimulus movements across all combinations of spatial frequency, contrast, and grating speed. Eye resets were automatically removed from the data set based on threshold eye rotation speeds (15 deg s⁻¹).

Optokinetic gain, the ratio of angular eye tracking speed to grating speed, was used as a measure of how well the animal followed a stimulus. Optokinetic gain values range between 0 and 1, where 1 means that the animal's eyes followed the stimulus exactly (i.e. they rotated at the same speed as the stimulus) and a value of 0 means that the animal did not move its eyes at all. To calculate the optokinetic gain, slopes were fitted to the cleaned (eye resets removed, Fig. 2A,B) data of orientations in time using linear regression for all six stimulus reversals for each stimulus combination. The six slopes (one for each reversal direction), and the stimulus speed and direction, were used to calculate the average optokinetic gain for each of the experimental conditions, as described below. Having calculated the optokinetic gain, the contrast sensitivity function was constructed for each animal.

Contrast sensitivity is typically expressed as the inverse of the threshold contrast that allowed a crab to detect a given pattern. To estimate contrast thresholds, the optokinetic gain was plotted against contrast for all combinations of spatial frequencies and angular speeds. A threshold was set at 10% gain and gains below the threshold were taken to indicate that the animal was unable to track the stimulus (Fig. 2C). Contrast thresholds were calculated for each frequency and speed combination as the linear interpolations between the highest contrast that did not reach the threshold gain and the next higher contrast that exceeded the 0.1 gain threshold (the red data points in Fig. 2). This method was less sensitive to outliers and produced more robust results compared to fitting a sigmoidal curve. The contrast sensitivity of the left and right eyes for each animal were averaged to estimate the contrast sensitivity of the individual animal.

In the experiments with restrained crabs, contrast sensitivity was analysed using a linear mixed effects model analysis (LME, MATLAB R2017b). In the behavioural state experiments, optokinetic gains were logarithmically transformed, and logistic regressions were fitted to the gain versus contrast curves for individual animals for each condition to predict optokinetic gain for a contrast of 0.5 (see Table 2). This contrast level produced data from most animals and therefore allowed a statistical comparison of the largest dataset with a linear mixed effects model. The predicted optokinetic gains then were analysed using a linear mixed effect model (LME, MATLAB R2017b). We tested for spatial frequency, speed, the effect of behavioural state, and drum orientation (horizontal versus vertical) as categorical variables. The variance associated with individual crabs was taken into account by fitting a random offset to the model. Significance (P<0.05) was determined by comparing the fit of each model to a reduced model and all P-values presented were estimated by comparing the fit of each model against the final model (using likelihood ratio tests) that only contained significant terms. All significant terms were included in the final model. Model assumptions were checked by exploring the distribution of the residuals (using Q–Q plots) and examining plots of the standardized residuals against the fitted values.

All crabs stayed alert (eyestalks up) throughout most of the trials. Restrained animals showed different tendencies to try to move. Most animals remained still throughout a trial, while two tried, without success, to rotate their bodies.

Crabs that were tethered, but allowed to rotate, utilized both body and eye rotations to follow the grating. Three out of four crabs rotated for the majority of the trials. One crab in this experiment walked on the treadmill, but did not rotate its body at all, although it was free to do so, and responded with eye rotations only.

Both spatial frequency and rotational speed had a significant effect on contrast sensitivity (Table 1). The average contrast sensitivity to horizontally moving, vertical gratings peaked at an intermediate spatial frequency of 0.1 cyc deg⁻¹ for the majority of speeds tested. For all crabs, contrast sensitivity declined faster towards higher spatial frequencies than towards lower spatial frequencies (Fig. 3). The highest average contrast sensitivity (the reciprocal of contrast at threshold; see Fig. 2) was 17.3, measured at a speed of 5 deg s⁻¹ (Fig. 3D); however, peak contrast sensitivities for the middle of the speed range were all very similar (Fig. 3B–D). Contrast sensitivity reduced slightly at the slowest speed (0.625 cyc deg⁻¹; Fig. 3A) and more strongly at higher speeds (10 and 20 deg s⁻¹). Contrast sensitivity was significantly lower at 20 deg s⁻¹ compared with 5 deg s⁻¹ (LME, N=4, d.f.=30, P<0.01, Fig. 3D,F).

Visual acuity represents the highest spatial frequency to which an animal responded with a gain of 10% in any of the tested conditions and was 0.8 cyc deg⁻¹. It occurred at the lowest speed of 0.625 deg s⁻¹ (Fig. 3A). However, this spatial frequency was only detected by two animals and the traces were noisy (Fig. S1A). For most animals the (high) spatial frequency of 0.4 cyc deg⁻¹ was detectable at most rotational speeds and the eye rotations reliably followed the stimulus (e.g. Fig. S1B). In general, the highest detectable spatial frequency decreased as rotational speed increased.

The sensitivity of an animal to experienced rotational speeds can be calculated from the animal's sensitivity to different combinations of spatial and temporal frequencies. To test whether the contrast sensitivity function of the crabs is best described as a function of speed or as a separable function of spatial and temporal frequency, we combined the effect of spatial frequency and rotation speed on contrast sensitivity for horizontally moving, vertically orientated, stimulus gratings as a contour plot in Fig. 4. If the contrast sensitivity of crabs was speed-tuned, we would expect for any given spatial frequency crabs would respond best to an optimum speed and therefore an elongation of isolines along spatial frequency axis. However, this was not the case. The isolines were best described by a separate spatial and temporal tuning. However, their vertical elongation suggested a stronger preference towards particular spatial frequencies, with the spatial frequency response somewhat tuned to frequencies around 0.1cyc deg⁻¹.

To compare horizontal and vertical contrast sensitivity in restrained crabs, the vertical contrast sensitivity function was measured for a rotational speed of 2.5 deg s⁻¹ (Fig. 5). To account for the fact that the horizontal and vertical contrast sensitivity experiments were conducted at different times, we repeated the horizontal contrast sensitivity measurements for two spatial frequencies (N=5; group 2). Both groups of crabs had similar horizontal contrast sensitivities (LME, P=0.98) but the vertical contrast sensitivity was significantly lower than the horizontal contrast sensitivity [Fig. 5, black versus grey lines; LME for group 2 comparing two spatial frequencies (0.1 and 0.2 cyc deg⁻¹), N=5, d.f.=14, P=0.004; LME for both groups comparing three spatial frequencies (0.05, 0.1 and 0.2 cyc deg⁻¹), N=9, d.f.=29, P=0.019]. Out of 37 contrast sensitivity measurements, all except one measurement were lower for the vertically compared with the horizontally rotating stimuli. For group 2, the average maximum vertical contrast sensitivity (8.5) was less than half of the average maximum horizontal contrast sensitivity (20.6; Fig. 5). Vertical acuity, at 2.5 deg s⁻¹, was also lower than horizontal acuity (0.28 measured for group 2 versus 0.4 cyc deg⁻¹ measured for group 1, respectively).

During the experiments it appeared that the crabs that intended to move had higher optokinetic gains than non-moving crabs. We therefore conducted a comparison of optokinetic gain for tethered crabs that were allowed to move versus restrained crabs that were not able to move. With one exception, in all combinations of spatial frequencies and speeds tested, tethered crabs had a higher optokinetic gain (Fig. 6, P<0.01; Table 2). The exception was a spatial frequency of 0.05 cyc deg⁻¹ and speed of 2.5 deg s⁻¹ for which we found no apparent difference between tethered and restrained crabs (Fig. 6A). Although the contrast threshold was generally lower for tethered crabs than restrained crabs, this decrease in threshold was not significant (LME, N=4, d.f.=28, P=0.09).

To estimate the contrast sensitivity function of fiddler crabs, we measured their optokinetic responses to wide-field, moving gratings with different orientations, spatial frequencies, contrasts and speeds, from a small group of crabs (5–6 crabs). We measured an average maximum contrast sensitivity of 17.3, which is equivalent to a contrast threshold of approximately 6%. The highest sensitivity we measured was 32.26, which is equal to a minimum perceived contrast of approximately 3%. While their contrast sensitivity function is both spatially and temporally tuned, the shape of the contrast sensitivity contours suggests a stronger spatial than temporal tuning. Our optokinetic data suggests a higher horizontal rather than vertical acuity. The behavioural state of the crabs had a significant effect on the optokinetic gain, with walking crabs showing higher optokinetic gain than tethered crabs.

The measured contrast sensitivity did not exceed 32.6 for any measurement. Only 6 out of 168 measurements were above 20 and the average maximum contrast sensitivity observed was 17.3±1.7 (mean±s.e.m.), corresponding to 6% contrast. It is important to note that our sample size was relatively small (4–6 crabs), so this average value may vary slightly with a larger sample. Nevertheless, we anticipate that the maximum contrast sensitivity of fiddler crabs is higher than their optomotor contrast sensitivity. Optomotor sensitivity is not uniform across the visual field of fiddler crabs, and it is limited to the dorsal part of their eyes only; a narrow horizontal band in visual space with the peak located about 10–15 deg above the horizon (Kunze, 1963; Nalbach, 1990). In fiddler crabs, the largest facets, which are expected to support the highest contrast sensitivity, are located around the horizon, approximately 10 deg below this optomotor sensitive region (Fig. 7A, Bagheri et al., 2020; Smolka and Hemmi, 2009). Previous studies have shown task-dependant variations of contrast sensitivity in several species including bumble bees and fruit flies (Chakravarthi et al., 2017; Duistermars et al., 2007). We thus expect fiddler crabs to have a higher contrast sensitivity for tasks such as predator avoidance and mating as predators and conspecifics are often seen within approximately 10 deg of the horizon (Bagheri et al., 2020; Smolka and Hemmi, 2009; Zeil and Al-Mutairi, 1996). Other methods such as electrophysiological measurements should be employed to provide regional measurements from different locations on the eye of fiddler crab.

Our behavioural measurement of visual acuity in fiddler crabs suggests a maximum of 0.8 cyc deg⁻¹ horizontal acuity which is two times higher than previous measurements based on anatomical methods (Bagheri et al., 2020; Smolka and Hemmi, 2009). However, out of 120 measurements with a spatial frequency of 0.8 cyc deg⁻¹ there are only two apparent responses from two crabs (at a rotational speed of 0.625 deg s⁻¹; Fig. 3A) that reached our threshold. If we had used a slightly higher gain threshold (12% rather than 10%), those responses would not have reached our criterion. Hence, we conclude that these values reflect measurement noise (see Fig. S1A). After all, our measurements are attempting to estimate threshold values. In contrast, out of 120 measurements at spatial frequency of 0.4 cyc deg⁻¹, with different speeds and contrasts, we had 20 reliable responses (e.g. Fig. S1B). A visual acuity of 0.4 cyc deg⁻¹ agrees well with anatomical measurements (Fig. 7C and Bagheri et al., 2020; Smolka and Hemmi, 2009).

The crabs' vertical resolution (0.28 cyc deg⁻¹) is lower than their horizontal resolution (0.4 cyc deg⁻¹), even though previous studies using microCT (Bagheri et al., 2020) and pseudopupil methods (Smolka and Hemmi, 2009; Zeil and Al-Mutairi, 1996) have estimated the maximum vertical resolution to be 4–5 times higher than the horizontal resolution. We should note that unlike the horizontal contrast sensitivity experiments where we stimulated the entire visual field, in the experiments with the ‘vertical’ contrast sensitivity drum we only stimulated the crabs forward and rear fields of view (see Materials and Method section). Crab sensitivity to movement varies over azimuth, with stimulation of lateral region eliciting a stronger optokinetic reaction than stimulation of frontal region (Kunze, 1963; Nalbach and Nalbach, 1987; Sandeman, 1978). This could have resulted in an underestimation of vertical visual acuity. In addition, vertical resolution is not uniform across the eye of fiddler crabs (Fig. 7B, Bagheri et al., 2020; Smolka and Hemmi, 2009; Zeil and Al-Mutairi, 1996). Vertical resolution decreases sharply from a clear ‘streak’ along the visual horizon towards dorsal and ventral fields of view. While there is yet no data on the regional optomotor sensitivity of G. dampieri, the optomotor sensitivity peaks at about 10–15 deg above the horizon in other fiddler crabs (Kunze, 1963; Nalbach, 1990). This would provide anatomical estimates of vertical acuity (0.32–0.47 cyc deg⁻¹ in the front and 0.1–0.2 cyc deg⁻¹ in the rear) that are close to our behavioural measurements (Fig. 7B; Bagheri et al., 2020). Consequently, optomotor responses provide poor estimates of potential maximum vertical visual acuity in fiddler crabs and do not provide information about the variation of visual acuity across the visual field. However, the match between anatomical acuity and optomotor experiments at the same part of the eye lend support to the predicted anatomical acuities in other parts of the visual field. Electrophysiological measurements could provide information about local spatial acuity across the visual field in fiddler crabs.

The inverted U-profile of the contrast sensitivity function of the fiddler crab G. dampieri (Fig. 3), is consistent with contrast sensitivity functions measured in many other species (e.g. Chakravarthi et al., 2017; Currea et al., 2018; Lawson and Srinivasan, 2020; Nityananda et al., 2015). The decrease in contrast sensitivity at the low spatial frequency is most likely caused by lateral inhibition in early visual neural pathways (Barten, 1999; De Valois et al., 1974), whereas at higher spatial frequencies, the attenuation is likely to be due to optical blur (Land and Nilsson, 2012).

The contrast sensitivity function shows a peak at spatial frequency of 0.1 cyc deg⁻¹ and a slight elongation of the contrast sensitivity contours across speed, (perpendicularly to spatial frequency axis, Fig. 4) suggesting that the fiddler crabs' optomotor system is slightly spatial frequency tuned.

The crabs responded reliably to image rotational speeds in the range 0.6–20 deg s⁻¹, with an optimum at 2.5–5 deg s⁻¹ (Figs 3 and 4). This speed tuning is much lower than in flying insects such as the hawkmoth (1–200 deg s⁻¹; O'Carroll et al., 1996), bumblebees (5–2000 deg s⁻¹; O'Carroll et al., 1996), hoverfly (0.5–2000 deg s⁻¹; O'Carroll et al., 1996) and praying mantis (10–2000 deg s⁻¹; Nityananda et al., 2015). At 2.5–5 deg s⁻¹ fiddler crab speed tuning is closer to the range of human speed tuning which has an optimum speed of approximately 2 deg s⁻¹. However, the crabs' maximum contrast sensitivity lies at a lower spatial frequency (0.1 cyc deg⁻¹, Fig. 4) compared with that of humans (2 cyc deg⁻¹; O'Carroll et al., 1996). The sensitivity to high rotational velocities in flying insects reflects their need to resolve the high rotational image speeds generated by their flight (O'Carroll et al., 1996), whereas in praying mantis it is probably to spot fast-moving small prey (Nityananda et al., 2015). Fiddler crabs, like humans, move at low speeds and both have a similar critical flicker fusion frequency (32–74 Hz; Brodrick et al., 2022; Layne et al., 1997) and are therefore tuned to low retinal image speeds.

Our data show that the crabs' optokinetic gain increased when they were allowed to walk. Although our results provide some evidence that the higher optokinetic gain of moving crabs also increases their contrast sensitivity, this effect failed to be significant (P=0.09). However, this conclusion might simply be a consequence of the low number of measurements. Nevertheless, our results provide evidence for the effect of crabs' behavioural state on their visual performance, at least in terms of optokinetic gain if not in contrast sensitivity.

Our result is supported by a previous study, which showed that walking crabs respond more powerfully to optomotor stimulation (Nalbach and Nalbach, 1987). Other studies also have shown that the gain of motion sensitive neurons in locusts (Rind et al., 2008) and flies (de Haan et al., 2012; Maimon et al., 2010) is enhanced during locomotion. These studies also showed that the speed tuning of motion-sensitive neurons shifted towards higher velocities. Chiappe et al. (2010) hypothesized that such a shift towards higher velocities may enable the detection of the faster retinal image shifts while animals move through their environments. The mechanism underlying such a shift is as yet unknown, however, it could be due to a shorter time constant of the elementary motion detector's delay filter while an animal moves (Clifford et al., 1997; De Ruyter van Steveninck et al., 1986). This shift is clearly only adaptive in physically moving animals, since restrained animals do not generate optic flow. It remains to be seen whether the observed increase in response gain in the optomotor system is also associated with a simultaneous increase in the crabs' speed tuning to higher speeds. We found no evidence for this (P=0.18, Table 2); however, it was not the focus of our experimental design.

It will also be interesting to see whether the increase in gain transfers to the lobula giant (LG) neurons that underlie the crabs' escape responses (Medan et al., 2007). Increase in the gain of LG neurons and a shift towards higher temporal frequency tuning may help pick up the small visual signals provided by image of flying birds which feed on crabs that are foraging on the mudflat (Land and Layne, 1995).

We behaviourally measured the contrast sensitivity and visual acuity in five fiddler crabs of the species Gelasimus dampieri in optomotor experiments. The measurements showed good agreement with anatomical and pseudopupil estimates of resolving power for the retinal region of maximum optomotor sensitivity, with horizontal and vertical visual spatial acuities of approximately 0.4 cyc deg⁻¹ and 0.28 cyc deg⁻¹, respectively. The maximum contrast sensitivity was 6%. Our results show that tethered, but freely walking, crabs have a higher optokinetic gain than restrained crabs, highlighting the importance of the correct behavioural context when studying the performance of animals.