The interplay of directional information provided by unpolarised and polarised light in the heading direction network of the diurnal dung beetle Kheper lamarcki

ABSTRACT The sun is the most prominent source of directional information in the heading direction network of the diurnal, ball-rolling dung beetle Kheper lamarcki. If this celestial body is occluded from the beetle's field of view, the distribution of the relative weight between the directional cues that remain shifts in favour of the celestial pattern of polarised light. In this study, we continue to explore the interplay of the sun and polarisation pattern as directional cues in the heading direction network of K. lamarcki. By systematically altering the intensity and degree of the two cues, we effectively change the relative reliability as they appear to the dung beetle. The response of the beetle to these modifications allows us to closely examine how the weighting relationship of these two sources of directional information is influenced and altered in the heading direction network of the beetle. We conclude that the process by which K. lamarcki relies on directional information is very likely done based on Bayesian reasoning, where directional information conveying the highest certainty at a particular moment is afforded the greatest weight.


Introduction
Combining information from several different sensory cues can reduce the effect of noise in a system, allowing for greater accuracy of the behavioural output (Cheng et al., 2007;Deneve and Pouget, 2004). Within the realm of navigation, multisensory integration provides a robust navigational toolkit that lowers directional uncertainty; rock ants follow less tortuous routes when landmarks are visible (Hunt et al., 2018) and desert ants are better at localizing their nest when olfactory cues are present (Huber and Knaden, 2017). Depending on the context and conditions under which the animal finds its way, directional information from multiple sensory cues can often be integrated, operating in parallel (Buehlmann et al., 2020). Thus, navigational performance will not be compromised if directional information from one source is disrupted. At high solar elevations, when directional information from the sun is deemed unreliable (Dacke et al., 2014), dung beetles rely on directional information from wind to guide their straight-line orientation across the savanna (Dacke et al., 2019). Similarly, Myrmica ants, that predominantly depend on directional information from visual cues when negotiating a maze, resort to olfactory cues for directional information as the light intensity decreases and visual information becomes less reliable (Cammaerts, 2012).
information. Along the same line of reasoning, if two directional cues of equal weight are set in conflict, this should result in an intermediate direction between both sources of information. This outcome is observed in homing ants when the apparent e-vector direction of the celestial pattern of polarised light is set in conflict with the artificial panorama (Freas et al., 2017;Reid et al., 2011) or the artificial panorama is set in conflict with celestial cues (Legge et al., 2014;Wystrach et al., 2015).
For the dung beetle Kheper lamarcki, the sun is naturally the most prominent directional compass cue in its heading direction network (Dacke et al., 2013a;Dacke et al., 2014;el Jundi et al., 2015;Khaldy et al., 2019a;Khaldy et al., 2019b;Smolka et al., 2016). If the position of the sun is experimentally set in conflict with other celestial cues (with the aid of a mirror), K. lamarcki changes its bearing by 180° in response to this positional change (Dacke et al., 2014). Comparably, if the view of the sun is blocked (by a shading board), and the evector direction of the celestial polarised light is turned by 90° with a polariser, this beetle turns in accordance with the 90° positional change of the e-vector. Thus, when the sun is out of sight, the relative weight between the remaining directional cues shifts in favour of the celestial pattern of polarised light (el Jundi et al., 2014).
In this study, we explore in greater detail, the interplay of the sun and polarisation pattern as directional cues in the heading direction network of the beetle. Following the rather unusual finding reported in Dacke et al., 2002, where UV and green receptors were found in the dorsal rim area (DRA) of a closely related diurnal dung beetle Pachysoma striatum, we also set out to measure the spectral sensitivity of the DRA of K. lamarcki. By altering the intensity and degree of the presented cues, we effectively change the reliability of the cues as they appear to the dung beetle, allowing us to examine how the weighting relationship of these two sources is influenced and altered by their reliability in the heading direction network of the beetle.

Collection and Maintenance of Animals
Beetles of the diurnal species Kheper lamarcki were collected using dung-baited pit-fall traps at Stonehenge game farm (26°23'56"S, 24°19'36"S), South Africa, in November 2020 and temperature-controlled room, under a 12 h light/dark cycle, at a room temperature of 26°C and fed with fresh dung every third day.

Statistics
Circular data are reported as mean ± one circular standard deviation. Circular statistics on measured data were performed using Oriana 4.0 (Kovach Computing Services, Anglesey, UK). Distributions of exit angles were analysed using Rayleigh's uniformity test for circular data (Batschelet, 1981). Changes in direction between treatments were calculated by measuring the absolute mean angular difference of the five exits preceding and the five exits following the treatment. This applied for all treatments apart from the condition where a dim ersatz sun was presented in combination with a 64% polarised overhead light. Here, the distribution of exit angles was analysed by calculating the mean vector length (R) of the first five consecutive rolls. In conditions where the animal displayed bimodal distribution of exit angles, angles were projected back onto the semi-circle surrounding the direction of most exit angles. A Mann-Whitney rank-sum test was used to determine if absolute angular difference between a treatment was significantly higher in the test condition (position of stimulus is changed by 90° between treatments) compared to the control condition (position of stimulus remains unchanged between treatments). The Mann-Whitney test was thus used to test if the animal turned with the stimulus. To test for homogeneity on two or more samples, a Mardia-Watson-Wheeler test was used. Generalised linear model (RStudio Team (2019). RStudio: Integrated Development for R. RStudio, Inc., Boston, MA, USA, http://www.rstudio.com/) was used to assess the relationship between degree of polarisation and probability of a turn (>45°).

Physiology
In preparation for intracellular recordings from the photoreceptors of dark-adapted individuals, the beetles were immobilized with beeswax and resin at a room temperature (for details see Belušič et al., 1 ) and mounted on a goniometric XYZ-stage that carried a micromanipulator (Sensapex, Oulu, Finland). A 50 μm diameter Ag/AgCl wire (inserted into the head capsule next to the eye) served as a reference electrode. Microelectrodes (Sutter, Novato, CA, USA) filled with 3 mol l −1 KCl (resistance 100-15 MΩ) were inserted into the eye via a small triangular hole in the cornea, ventral of the (expected) dorsal rim area. The signal was amplified using an SEC 10 LX amplifier (Npi electronic, Tamm, Germany) and a Cyber Amp 320 (Axon Instruments, Union City, CA, USA) and finally digitized via Micro 14 1 CED, Cambridge, U ). Spectral stimulation was provided with an LED array "LED synth" Belušič et al., 1 ) ), and with light from a Xenon arc lamp (XBO, Cairn, UK) filtered with a monochromator (B&M, Limburg, Germany). The light sources were tuned to emit equal numbers of photons at every wavelength "isoquantal" mode). A UV transmissive polarisation filter (OUV2500, Knight Optical, UK) was mounted in a motorised rotator (Qioptiq, Germany) and inserted into the stimulation beam to facilitate measures of polarisation sensitivity. All cells were first quickly stimulated with the LED synth, to determine their spectral sensitivity within 2 s, after which their polarisation sensitivity was measured at their sensitivity peak (360 nm or 500 nm). This was followed by measuring the intensity-response function and a detailed spectral scan with a monochromator. The response amplitudes of single cells were transformed to sensitivities by means of an intensity-response function and a reverse Hill transformation Belušič et al., 1 ) . Polarization sensitivity was calculated as the ratio between the sensitivity maximum and minimum, i.e., PS = Smax/Smin (Bernard and Wehner, 1977). Some cells were lost during the spectral scan, hence N cells with measured polarisation sensitivity is higher than N cells with measured spectral sensitivity.

Light Measurements
Irradiance was measured by placing a cosine corrector coupled to a spectrometer via a calibrated light guide (cosine corrector: CC-3-UV-T; spectrometer: QE65000; light guide:

Experimental Setup
The experimental setup consisted of i) an overhead polarised light stimulus, raised 15 cm above a flat, circular, sand painted 60 cm diameter arena, and ii) a green light stimulus presented from the side, 30 cm from the arena centre, at a height of 10 cm (Fig. 1). below the 10 th sheet (100 % polarisation) (Fig. 1). As a result of the experimental design, the animal was no less than 7-12 cm away from the overhead stimulus (see Fig. 1). Thus, the overhead stimulus subtended a visual angle of approximately 136°-154° from the arena centre throughout all conditions. The combined polarised light stimulus had an irradiance of 1.26 x 10 15 photons cm -2 s -1 : cyan alone 2.39 x 10 14 photons cm -2 s -1 and UV alone 1.04 x 10 15 photons cm -2 s -1 . This applied to all conditions where the polarised light stimulus was used, except for the condition in which the intensity of the polarised light stimulus was lowered. In this condition, the irradiance for 365 nm was lowered to 3.18 x 10 13 photons cm -2 s -1 while 505 nm remained unchanged.

Green light stimulus
The beetles were also presented with a green unpolarised light source (a previously When evaluating the isolated response to the ersatz sun, the polariser was removed from the overhead light stimulus, resulting in an unpolarised overhead stimulus with the same spectrum. This applied to all conditions except for the condition where the response to the dim ersatz sun was evaluated in which no overhead light was presented.

Experimental method
A beetle was placed alongside its dung ball, in the centre of the circular arena and allowed to roll its ball to the perimeter where the exit bearing was noted. The beetle was then removed from its ball and placed back in the centre of the arena alongside its ball. This procedure was repeated five times. Beetles not successful in adhering to their bearing over their initial five exits (p < 0.1, Rayleigh uniformity test) were excluded from any further experiments.

Manipulation of directional input Polarised light
Once the beetle had exited the arena five times, the polarisation filter was either kept in place (control) or turned by 90° (test) before the beetle was allowed to roll five additional times.
The initial orientation of the filter alternated for each beetle, with every second beetle starting with the polarisation filter aligned to the 0°-180° direction of the circular arena, and every other beetle with the filter aligned perpendicular to this.

Ersatz sun
The initial position of the ersatz sun was placed in one of four positions around the arena (0°, 90°, 180° or 270°). Once the beetle had exited the arena five times with the ersatz sun in a fixed position, the apparent position of this light was either held stationary or changed by 90°, in relation to its previous position, before the beetle was allowed to roll five additional times.

Ball-rolling dung beetles can orient to a green light stimulus
When the position of the ersatz sun was changed by 90° between two trials (test), the beetles However, when the ersatz sun was lowered in intensity by tenfold (from 1.72 x 10 13 to 1.02 x 10 12 photons cm -2 s -1 ) the beetles failed to orient to the ersatz sun in the presence of an overhead unpolarised light (Fig. 4H). Only when no overhead light was present, did the beetle show a response to the turned stimulus (Fig. 4G). This indicates that when the overhead light is present, the light information provided by the dim ersatz sun cannot be distinguished from the background light, and the beetle fails to orient.

The weighting relationship between the ersatz sun and polarised light is highly dynamic
To investigate the weighting relationship of directional information from the sun (here represented by an ersatz sun) and the directional information from polarised skylight (here represented as an overhead polarised light source), the beetles were presented with both cues at the same time. When the ersatz sun was changed by 90° between trials (test), the beetles turned significantly in accordance with this change only when the degree of the polarised light presented from above (that remained in place) was set to its lowest setting of 11%

The light intensity of the directional cues influences their weighting relationship
Given that the beetles neither conclusively maintained their original bearing, nor turned in accordance with the 90° azimuthal change of the ersatz sun when the overhead light was 64% polarised, we next lowered the intensity of the UV light of the polarised light approximately hundredfold (from 1.04 x 10 15 to 3.18 x 10 13 photons cm -2 s -1 ). This allowed us to investigate if also the intensity of the polarised light would influence the weighting relationship between the two sources of directional information.
To confirm that the beetles were still able to respond to the e-vector rotation of this dimmer stimulus, we first presented the overhead light cue in isolation; either stationary (control; μ = 17.57° ± 13.64°, N = 15) or with a 90° rotation between trials (μ = 81.21° ± 14.98°, N = 15) (Fig. 4F). The beetles still turned in accordance with the turn of the polarisation axis of the overhead light (Mann-Whitney rank sum test, W = 345, p < 0.001, z = 4.65, N = 15). We further found that there was no significant difference in orientation performance between the groups of beetles orienting under the high and low intensity of the Correspondingly, when instead dimming the intensity of the ersatz sun and presenting this in combination with the full intensity polarisation stimulus of 64%, the beetles were unresponsive to the positional change of the dim ersatz sun (see Fig. 4H). Instead, the beetles adhered to their original direction (Fig. 4E), similar to when presented a full intensity ersatz sun in combination with 100% overhead polarised light (Mann-Whitney rank sum test, W =191, p < 0.59, z = -0.52, N = 15) (compare Fig. 4C). Thus, when the intensity of the overhead polarised light or the ersatz sun was lowered, the weighting relationship between the two sources shifted away from the directional information provided by the dimmed cue.

Evidence of UV and green polarisation sensitive photoreceptors in the dorsal rim area of Kheper lamarcki
Under a clear, sun-lit sky, the celestial polarised light pattern is highly distinguishable across all wavelengths of light. Under overcast skies or a tree canopy, the detection of this celestial pattern is most advantageous in the UV range ( Barta and Horváth, 2004;Hegedüs et al., 2007a;Seliger et al., 1994;Wang et al., 2014). Perhaps it is because of this stability that most Interestingly, for the diurnal dung beetle K. lamarcki, our findings show evidence for polarisation sensitive photoreceptors in UV as well as green sensitive cells (Fig. 3).
Furthermore, the rare finding of two spectrally distinct, highly polarisation-sensitive photoreceptor classes (UV and green) for polarisation detection has also been suggested in , and therefore no longer a reliable directional cue, the ability to maintain a straight rolling bearing is disrupted in diurnal and nocturnal dung beetles alike (Dacke et al., 2013b;Dacke et al., 2013a). A similar correlation is also found in the nocturnal ball rolling dung beetle, Scarabaeus satyrus (Foster et al., 2019); when allowed to roll underneath an overhead polarised light source (similar to the polarised light source presented in this paper; Fig. 1) of differing degrees of polarised light, the ability of the beetle to maintain its exit bearing over consecutive rolls (orientation precision) lowered in correspondence to each degree of overhead polarised light presented.

The intensity of the directional cue affects its reliability as a directional cue
In this study, we find that K. lamarcki can reliably extract and utilise directional information from polarised light of a degree as low as 11% (Fig. 2C), corresponding to the threshold limit  (Brines and Gould, 1979;Brines and Gould, 1982;Labhart, 1988;Labhart, 1996;Rossel and Wehner, 1984). Only when the noise of the visual signal outcompetes the difference between the orthogonally arranged groups of microvillar rhabdomeres, does the intensity of the polarisation cue become an important factor (el Jundi and Homberg, 2012). Thus, the inability of K. lamarcki to steer straight according to the polarisation pattern surrounding the moon is very likely due to the limitations of the animal's own sensory ecology; the eyes of K. lamarcki might just not be able to detect the polarised skylight pattern (or any other additional celestial cues) across the night sky.
Along similar lines, the integration of directional information from a point-light source is highly dependent on its intensity. When the position of the ersatz sun was changed by 90°, the beetles changed their headings accordingly ( Fig. 2A). This was expected, as this outcome for K. lamarcki has been shown in several previous studies (Khaldy et al., 2019a;el Jundi et al., 2015a;Smolka et al. 2016). However, if the same paradigm was presented to the beetle, but now with an ersatz sun of lowered intensity by tenfold, the beetles could not maintain a straight bearing. Only when no overhead light was present would the beetles respond to the turned stimulus (Fig. 4G). This outcome suggests that when an overhead unpolarised light is present, the light information provided by the dim ersatz sun cannot be distinguished from the background. In this scenario, no directional information can be provided by the surroundings, and the beetles fail to orient. On the contrary, when the same dim ersatz sun is presented in an otherwise darkened setup, the visual contrast between this light cue and the background is greater, thus providing enough visual directional information for orientation.

Varying the reliability of the presented cue influences the relative weighting relationship
When presented with an ersatz sun in combination with an overhead polarised light source at 11% polarisation, all beetles turned in response to the azimuthal displacement of the ersatz sun (Fig. 4C). However, when presented in isolation, K. lamarcki is fully able to extract directional information from the weakly polarised light (Fig. 2C). We interpret this relative weighting of directional information, now in favour for the ersatz sun, as if this single bright light generates a stronger and more reliable directional signal relative to the artificial band of polarised light. This weighting relationship is directly comparable to that observed outdoors; when the apparent position of the sun is changed by 180° with the aid of a mirror, while simultaneously blocking the real sun from view under a natural sky, K. lamarcki will turn in response to the mirrored sun (Dacke et al., 2014;Khaldy et al., 2019a;Khaldy et al., 2019b).
This means that the directional information from the sun dominates in its heading direction network, not only over the celestial polarisation information, but over all remaining skylight cues. However, with the apparent position of the sun shaded from view, which can occur naturally by cloud cover or experimentally using a shading board, these beetles instead follow the polarised light of the diurnal sky (el Jundi et al., 2014). Now, the distribution of the relative weight between the directional cues that remain, shift in favour of the polarised light input.
When instead presented with a fully (100%) polarised light source, in addition to the same laterally presented ersatz sun as above, the beetle no longer turned in response to a 90° azimuthal change of the ersatz sun. Their consistent orientation along the same bearing was now instead guided by the stable e-vector direction of the overhead polarised light (Fig. 4C).
In this paradigm, directional information from the ersatz sun no longer dominates the heading direction network of the beetle, and the relative weighting between the two cues presented has shifted towards directional information from the polarised light cue. Our result clearly demonstrates that this species alters its weighting of cues in a context-dependant manner.
Because polarised skylight does not exceed 80% in the natural sky (Brines & Gould, 1982;Hegedüs et al., 2007b;Foster et al., 2019), the beetle will never be exposed to a fully polarised sky in nature. However, natural factors, such as clouds or vegetation can reduce the reliability of the sun as a source of directional information, effectively shifting the weight attributed to this directional cue in the heading direction network of the beetle similar to our 100% polarised light condition.
When next presented 64% polarised overhead light in combination with the ersatz sun, When the intensity of the overhead polarised UV light is lowered, the beetles again turn with the ersatz sun (Fig. 4D). Interestingly, if presented with a dim ersatz sun in combination with the full intensity of 64% polarised overhead light, the beetles seemingly ignore the positional change of the dim ersatz sun and instead orient primarily according to the directional information from the overhead polarised light. Weakening the relative input of directional information from one cue thus effectively shifts the relative directional weighting between these two sources of information.

Journal of Experimental Biology • Accepted manuscript
From the behavioural outcomes of our experiments, we can safely conclude that K.
lamarcki integrates multiple sources of directional information in a Bayesian manner Cheng et al., r ding, r ding and Wolpert, 06), demonstrating clearly that directional information conveying the highest certainty at any given moment is afforded the greatest weight in the navigational network of the animal.  Journal of Experimental Biology • Accepted manuscript   Fig. S1. A logistic regression fitted to the probability of a turn larger than 45° when the stimulus was turned by 90°. There was a significant increase in the probability of a turn with increasing degree of polarization (11% polarisation: 10/15 individuals; 64% polarisation: 13/15 individuals; 100% polarisation: 15/15). We modelled this relationship as a linear increase in the log-odds of a turn with the base 10 logarithm of degree of polarization in percent (following Foster et al., 2019). The fitted model is shown as a red line with red shaded 95% confidence intervals, superimposed on the original turn angles.