Weighted cue integration for straight-line orientation

Summary Animals commonly integrate multiple sources of information to guide their behavior. Among insects, previous studies have suggested that the relative reliability of cues affects their weighting in behavior, but have not systematically explored how well alternative integration strategies can account for the observed directional choices. Here, we characterize the directional reliability of an ersatz sun at different elevations and wind at different speeds as guiding cues for a species of ball-rolling dung beetle. The relative reliability is then shown to determine which cue dominates when the cues are put in conflict. We further show through modeling that the results are best explained by continuous integration of the cues as a vector-sum (rather than switching between them) but with non-optimal weighting and small individual biases. The neural circuitry in the insect central complex appears to provide an ideal substrate for this type of vector-sum-based integration mechanism.

While there is an abundance of evidence suggesting that insects integrate multiple cues when performing navigation behaviors, few propose concrete models which describe the integration process. Compass cue integration presents a direct case study for directional cue integration, and for this, the ball-rolling dung beetle Kheper lamarcki (MacLeay, 1821) provides an ideal model organism. Upon finding a dung pat, these beetles break off a piece of dung, shape it into a ball, climb on top of it, and rotate about their own vertical axis. During this ''orientation dance'', a snapshot of all available cues is taken and then used to support a directed and efficient escape from the competition at the dung pile (Baird et al., 2012;Byrne et al., 2003;el Jundi et al., 2016). The natural environment provides a plethora of cues that are used by the beetles to sustain this straight-line orientation. Known orientation cues include the position of the sun (Byrne et al., 2003), moon (Dacke et al., 2004), spectral gradients (Jundi et al., 2015), the intensity pattern of the milky way (Dacke et al., 2013;Foster et al., 2017), and wind direction (Dacke et al., 2019). Previous studies have also shown that the beetles will interpret an artificial green light spot as an ersatz sun and will use it to orient with equal accuracy as under natural conditions (El Jundi et al., 2015).
The beetles' ability to maintain their bearings remained stable until an elevation of 75 , beyond which it decreased rapidly with increasing elevation ( The mean precision at 60 + and 75 + elevation is highlighted to allow comparison to the wind (dashed lines). The mean precision at 60 + is close to that at 2.5 m=s wind speed, and similarly the mean precision at 75 + is less than that at 2.5 m= s wind speed but much greater than would be expected at , n = 20, see Figure 1). These results suggest that higher solar elevations provide a less reliable cue, which can be attributed to the decrease in directional information given by a visual cue as it approaches zenith. It should be noted that direct comparisons between the indoor setup and outdoor conditions may not be applicable as the light intensity is lower in the artificial setup. Despite this, a similar decrease in orientation precision at high solar elevations can also be observed outdoors for the same species of dung beetles , as well as for other animals (for example, equatorial sandhoppers and desert ants (Ugolini, 2001(Ugolini, , 2002Mü ller and Wehner, 2007)).
Under the conditions where menotaxis was observed, we found that as the speed increased, so did the beetles' ability to maintain their bearings ( , n = 20, see Figure 1). Taken together, the results suggest that higher wind speeds provide a more reliable cue for menotaxis (changing to anemotaxis beyond 3.0 m= s). Previous studies have demonstrated that the antennae of dung beetles are wind sensitive (Linsenmair, 1972), and Okubo et al. (2020) have shown that with increasing wind speed, the antennae of fruit flies are subject to larger displacements. Our results are therefore in line with previous research as one would expect greater deflections of the dung beetle antennae to provide a clearer perception of wind direction. Note the similarity in reliability between a wind cue of 2.5 m=s and an ersatz sun at a 60 elevation (see Figure 1).

Cue conflict between an ersatz sun and wind
The effect of reliability on the integration and weighting of a visual sun cue and a mechanosensory wind cue was studied in a cue conflict experiment. The reliability was manipulated by changing the elevation of the ersatz sun or the speed of the wind current and the conflict was introduced by shifting the azimuthal direction of the wind (see STAR Methods, Behavioural experiments -Cue conflict between an ersatz sun and wind). Changes in heading direction were calculated using the angular difference between two consecutive exits (see Figure 2). All beetles included in the analysis were able to recover their initial bearing following each cue conflict run (see STAR Methods, Quantification and statistical analysis -Cue conflict between an ersatz sun and wind).

Dung beetles perform a weighted integration of a wind cue and sun cue
As can be expected from previous studies outdoors (Dacke et al., 2019), when presented with a wind cue of 2.5 m=s and a simulated solar elevation of 45 + , 60 + , 75 + , or 86 + , beetles were able to maintain their bearing between two consecutive exits when the directional information from the two cues remained unchanged (mG SD: À 3 + G28 + (n = 30), À 11 + G28 + (n = 27), À 5 + G45 + (n = 26), and 3 + G47 + (n = 23); p < 0:001, Rayleigh tests, see Figure 2B). However, when the directional information from the sun and wind cues were put in conflict, by altering the wind direction between two consecutive exits, the behavior changed depending on solar elevation. At a solar elevation of 45 and the wind current set to 2.5 m=s, the beetles did not change their direction at either a 60 or a 120 cue conflict (mGSD: À 9 + G43 + and 16 + G68 + ; p < 0:001, Rayleigh tests, n = 30, see Figure 2B). This suggests that at this elevation, the ersatz sun has a greater weight compared to the wind cue. In contrast, for solar elevations of 75 + and 86 + , the beetles updated their bearing in accordance with the 60 or 120 azimuthal change of the wind current (mGSD: 78 + G56 + and 116 + G60 + ; p < 0:001 at 75 + elevation (n = 26), 74 + G80 + and 123 + G62 + ; p = 0:025 and p < 0:001 at 86 + elevation (n = 23), Rayleigh tests, see Figure 2B). At a 60 solar elevation, the beetles again responded to the 60 azimuthal shift of the wind (mG SD: 55 + G 76 + ; p < 0:01, Rayleigh test, n = 27); interestingly, when presented with a conflict of 120 + , the changes in bearing did not differ significantly from a uniform distribution (p = 0:837, Rayleigh test, n = 27). Thus, the beetles did not seem to keep their relative bearing to either the ersatz sun or the wind.
Together, our results suggest that the relative weight between the sun cue and the wind cue is affected by elevation and that the critical elevation (at which the ersatz sun becomes less reliable than a wind cue of 2.5 ll OPEN ACCESS iScience 25, 105207, October 21, 2022 3 iScience Article m=s) lies between 45 and 75 . This result matches previous observations in dung beetles (Dacke et al., 2019) and ants (Mü ller and Wehner, 2007); the higher the solar elevation, the lower the influence of the cue. From our results, it may appear as if the beetles are simply following the more reliable cue, which has previously been a suggested orientation strategy among dung beetles when presented with sun and wind (Dacke et al., 2019), sun and polarized light , or sun and other skylight cues . However, considering the uniform distribution found at a solar elevation of 60 together with a 120 cue conflict, the beetles are not always able to follow one cue over the other. This could indicate that at this elevation, the cue reliabilities intersect. Furthermore, the population spread increases with conflict; this effect is consistent across almost all test conditions when the wind speed is set to 2.5 m=s. This suggests that the beetles are not following a simple winner-take-all strategy, as under strict winner-take-all (see STAR Methods, Integration models) the population dispersion should be unaffected by cue conflict. The pseudo winner-take-all behavior and increasing variance that we observe at elevations of 45 , 75 , and 86 could be explained by a circular integration model (Murray and Morgenstern, 2010) with iScience Article non-optimal weights (see STAR Methods, Integration models), suggesting both cues are contributing to behavior, even when one appears to be followed and the other ignored.

Orientation behavior varies when cue weights are similar
Due to the random distribution of beetles' changes in heading when the 60 elevation sun cue and the 2.5 m/s wind cue were put in conflict by 120 , it appeared that the population failed to orient under this condition. However, an additional experiment that focused on individual precision, in which each beetle was permitted to exit the arena ten times in the presence of the cue conflict conditions, showed that the beetles did not fail to orient. Instead, we found that the beetles oriented along a new random bearing that they then successfully maintained ( Furthermore, when the two cues were returned to their original positions, the beetles recovered their initial bearing (see STAR Methods, Quantification and statistical analysis -Cue conflict between an ersatz sun and wind), suggesting that this new random bearing we see is actually an effect of the integration strategy and not a permanent re-set of the bearing. Similarly, Khaldy et al. (2021) showed that the ball-rolling dung beetles Garreta unicolor and Garreta nitens appeared disoriented when subjected to a conflict produced by simultaneous manipulation of a sun cue and the pattern of polarized light. However, upon returning the cues to their original positions, these animals recovered their initial bearings. Likewise, bogong moths fly in a seemingly disoriented manner when presented with a conflict between the magnetic field and visual landmarks; when the cues are returned to their original positions the moths, too, recover their initial bearings (Dreyer et al., 2018).
To explore these apparent new bearings taken by beetles at a 120 conflict, we tested whether the individual change in bearing was consistent over different days or if it was prone to change. We employed the previously described cue conflict assay, focusing on a 60 + solar elevation with a wind speed of 2.5 m= s and tested individual beetles over three consecutive days. Similar to our previous cue conflict experiments, the beetles were able to maintain their bearings each day when the cues were kept in their original positions (mGSD: À 1 + G23 + , 9 + G41 + , and À 4 + G44 + for day one, two, and three, respectively; p < 0:001, Rayleigh tests, n = 14, see Figure S3). However, upon changing the azimuthal position of the wind by 120 , the individual change in bearing differed across the three days (n = 14, see Figure 2D). This shows that the apparent new bearing taken by beetles at a 60 + solar elevation is not consistent over days.
The results from this three day experiment reinforce the idea that a weighted integration is taking place as both cues must be considered to generate the variability we see in the mean vector (see Figure 2D); if this were a winner-take-all (or biased winner-take-all), we would not expect to see any beetles in the lower lefthand quadrant. Furthermore, the inconsistency in population response suggests an additional source of noise in the integration process. A potential explanation for this noise would be individual variation or ''preference''. A very small (random) individual bias could cause an increase in spread in the population of responses where cue weights are near equal (see STAR Methods, Integration models; Results and Discussion, Modeling).
The weight given to a sun cue and a wind cue is dictated by their relative reliability In previous experiments, the reliability of the ersatz sun was altered. Here, the wind speed was reduced to 1.25 m=s to study the effect of decreased wind reliability on the relative weighting of the sun and wind cues. We again employed the previously described cue conflict assay at solar elevations 60 + , 75 + , and 86 + .

Behavior indicating a weighted integration strategy
In all, our behavioral results show that the dung beetle compass is dynamic and that relative cue reliability dictates which cue is favored; this occurs as a continuous integration process, rather than a winner-take-all. The cue which is perceived to be less noisy, and thus more reliable, is predominantly used to guide straightline orientation. This holds true until the relative reliabilities are similar and the beetles initially appear to be unable to utilize the provided cues for orientation. However, when investigating individual precision, we found that beetles were able to maintain their apparent new bearing, as well as recover their initial bearing when the cues were returned to their original positions. Furthermore, individual orientation behavior differed across three days. Together, these results suggest that the observed randomness is an effect of a weighted integration strategy, but the integration may be inconsistent across days. To attempt to characterize the integration strategy, we performed simulations to experiment with different strategies and weight relationships.

Modeling
Cue integration studies typically compare winner-take-all (WTA) to ''optimal'' cue integration, defined as the linear weighted arithmetic mean, WAM ( (Legge et al., 2014;Sun et al., 2018;Wystrach et al., 2015), but WAM is inappropriate for circular inputs. Instead, cue integration in the circular domain can be represented by a weighted vector sum (STAR Methods, Integration models), for which the optimal weights (which minimize the variance of the combined cue) are given by the concentrations of the von Mises noise distributions which characterize each cue. WVS has been used in a model of ant navigation (Hoinville and Wehner, 2018), and has the interesting property that it can resemble WAM at small conflicts and WTA at large conflicts (see Figure S6). This has inspired us to consider two further alternatives. The first is a ''non-optimal weighted'' vector sum (NVS) which exaggerates the pseudo-WTA region of the WVS, such that the stronger cue usually dominates the response but both contribute, unlike true WTA. The second is a biased (non-optimal weighted) vector sum (BVS), which simulates small individual biases toward one or the other cue, creating a variety of behavior when the cues are near-equally balanced. Illustrative model outputs for the same input distributions are given in Figure 3. For completeness, we compare all five models (WTA, WAM, WVS, NVS, and BVS, defined explicitly in STAR Methods, Integration models) to the behavioral data to calculate their relative likelihoods. The results are given in Table 1.
Our modeling results indicate that all circular models (WVS, NVS, and BVS) better account for our behavioral data than the classically considered WAM and WTA. The extremely similar outcomes between WTA and WVS were unexpected, but it is likely that these models both account for different portions of the data (i.e. they are equally bad at capturing the full range of behavior). The non-optimal circular model (NVS), which takes advantage of the pseudo-WTA property of a circular integration model (a vector sum, see STAR Methods, Integration models), performs substantially better than either optimal circular integration or a winner-take-all as this model should capture the small influence of the secondary cue. Finally, the inclusion of individual bias in BVS increases the population-level noise where cue weights are near equal, which should capture the behavioral variability at the critical elevation conditions (60 + elevation, 2.5 m= s wind speed), leading to the best overall fit.
The key take-away from our simulations is that a weighted circular model best accounts for the data.

OPEN ACCESS
To tie our results to physiology, the neural circuitry in the insect central complex appears to provide an ideal substrate for performing a vector sum calculation. In the insect brain, head direction is maintained by a ring-attractor circuit (Seelig and Jayaraman, 2015;Kim et al., 2017;Heinze, 2017). This circuit is fed by the ring neurons, which seem to cluster into groups which are sensitive to different orientation cues (Okubo et al., 2020;Hardcastle et al., 2021). The two layers are linked by plastic all-to-all connections-every ring neuron connects to every compass (head direction) neuron (Kim et al., 2019;Fisher et al., 2019)-which should allow the network to learn relationships between different cues, forming a single integrated snapshot for orientation. In beetles, the relationship between the different available cues could be learned during the dung beetle ''dance'' (Baird et al., 2012), which is thought to be the point at which their orientation snapshot is taken ( iScience Article ''switch'' between apparently optimal integration behavior and cue selection behavior and finally, Sjolund et al. (2018) note similar results for spatial (distance and direction) cue integration in humans. Not only is a weighted circular model a likely candidate for cue integration in our case and in ants (Hoinville and Wehner, 2018), but the orientation center of the insect brain would seem to be well suited to encode the underlying vector sum. Overall behavior is then governed by the weights used, which need not be consistent across different species.
In summary, our behavioral data point to a weighted integration of wind and solar cues. Subsequent computer modeling suggests that the integration is most likely a form of vector summation, which seems to be well encoded by the insect head direction circuit. Vector summation can produce a variety of different integration outcomes depending on the weights used; a neural circuit which supports vector summation could produce different behavior depending on how an agent computes these weights. Thus, a single core model (vector summation) with different peripheral processing stages (weight-adjustment and/or bias etc.) may explain a wide range of cue integration behaviors across different insect species, despite the highly conserved neuroanatomy.

Limitations of the study
To fully isolate the orientation cues in question (sun and wind cues), we performed our experiments in an indoor setup which allowed us to control all possible cue parameters. Consequently, the indoor setup is limited in its representation of the real world. One major constraint of our behavioral setup is motion parallax, which becomes more severe at higher solar elevations.
The modeling is based on beetle exit angles which do not fully characterize the strategy in use by the beetles (especially with the aforementioned motion parallax). Modeling based on full tracks for each individual would be more informative but these data are not practically available. This means that applications of the specific model instances presented are limited.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following: All circular models (WVS, NVS, and BVS) outperform the weighted arithmetic mean (WAM). Non-optimal weighted circular models (NVS and BVS) do better than both the statistically optimal WVS and previously hypothesized WTA. As parameter counts are small, the Akaike information criterion (AIC) and Bayesian information criterion (BIC) do not sufficiently penalize either BVS or NVS to affect the order of the results. Likelihoods are best at 0 and decrease as models become less likely. The AIC and BIC ratios are best at 1 and increase as goodness-of-fit decreases. iScience Article measured from the centre of the setup at a height of about 7 cm (corresponding to the height of a beetle on top of its dung ball) using a spectrometer (QE65000; Ocean Optics). Serving as wind cues, four wind generators were positioned on the floor 1.3 m from the centre of the setup. The first wind generator was aligned with one of the LED-lined arches and the remaining three were placed at an angle of 60 , 120 and 180 relative to the first. Each wind generator was constructed from three fans (PFR0912XHEE, 4.50A; Delta Electronics Inc., Taipei City, Taiwan) separated by 0.25 m and was powered by a Mean Well RSP-320-12, 26.7A power supply.
Measures of wind speeds were obtained by the use of a hot wire anemometer (HHF-SD1; Omega) placed 7 cm above the centre of the arena (see Figure S4). A sand-painted circular arena (0.3 m radius) was placed in the centre of the setup, with the arena perimeter labelled from 0 to 355 in 5 increments and with 0 aligned with magnetic north. To control solar elevation and wind speed, custom-built software was used with an Arduino Uno (experiments conducted in South Africa), or a Raspberry Pi 4 Model B (experiments conducted in Sweden). All experiments were filmed from above using a Sony camera (FDRAX53 Handycam) or a Raspberry Pi camera (Camera Module 2 NoIR), supported by infrared illumination (B07DDJ1YDB, 1A; eecoo, Shenzhen, China). To eliminate unwanted cues, the setup was placed inside a tent made out of blackout cloth (see Figure S1).

Behavioural experiments
Throughout each experimental day beetles were temporarily kept in shallow bins containing fresh dung and given time to construct dung balls. During behavioural experiments, each beetle was placed alongside its dung ball in the centre of the circular arena (semi-randomly in one of four cardinal directions). Following its characteristic orientation dance, the beetle was allowed to roll to the perimeter where its exit bearing was recorded. The beetle and its ball were then placed back into the centre of the arena and the procedure was repeated a number of times that depended on the experimental question (see below). In total, each beetle took between 5 and 15 min to complete an experimental series, after which it was put away for the day. The same beetle was never tested more than once for each experiment and if it performed another experimental series this was always carried out on a different day.

Reliability of sun and wind cues
We used orientation precision of ball rolling beetles as a proxy for reliability under different cue conditions with the assumption that more reliable cues would lead to greater precision and vice versa. Orientation precision under an ersatz sun was tested at elevations of 5 , 20 , 45 , 60 , 75 , 80 , 82 , 84 , 86 , 88 , or 90 . For every elevation, 20 beetles were tested. Each individual was marked to ensure that it was only used once per elevation. Each beetle was placed in the center of the arena and allowed to exit from it five times. Following this, the azimuth of the ersatz sun was shifted by 180 and the beetle exited the arena an additional five times.
The same procedure was used to test the beetles' ability to perform straight-line orientation at wind speeds of 0.5, 0.8, 1.0, 1.5, 1.9, 2.5, 3.0 and 4.0 m=s, with the direction of the wind current shifted by 180 after five exits. For every wind speed 20 beetles were tested and each individual was marked to ensure that it was only tested once per wind speed. To sustain the beetles' motivation in the presence of wind, this experiment was performed with an ersatz sun positioned in zenith.

Cue conflict between an ersatz sun and wind
Cue conflict experiments. Based on the results gathered from the reliability experiments described above, a cue conflict experiment was conducted using an ersatz sun at elevations of 45 , 60 , 75 , and 86 in the presence of a wind current of 2.5 m=s. In a separate cue conflict assay, solar elevations of 60 , 75 and 86 were presented together with a wind speed of 1.25 m=s. All conflicts were achieved by shifting the azimuthal direction of the wind current while keeping the ersatz sun stationary.
Each beetle exited the arena a total of eight times: three times with the directional information from the ersatz sun and wind current in congruence, once with a conflict of 60 + (or 120 + ), once with the cues in their original position (congruent), once with a conflict of 120 + (or 60 + , respectively), and finally two exits with the cues returned to their original positions (congruent). The purpose of the repeated congruent exits was to ensure that the beetles strived to adhere to the same bearing throughout its experimental series (see STAR Methods, Quantification and statistical analysis -Cue conflict between an ersatz sun and wind). The order in which the conflicts were presented was pseudo-randomised. Thus, each beetle performed both test conditions where the azimuthal directional information of the two cues were put in conflict by 60 or 120 ll OPEN ACCESS iScience 25, 105207, October 21, 2022 iScience Article between two consecutive rolls, as well as a control condition where the directional information remained unchanged (0 conflict).
Further cue conflicts at 60 elevation. The same cue conflict assay (congruent (33) -60 /120 conflictcongruent -120 /60 conflict -congruent (32)) was replicated in another experimental series. These spanned over three days with the ersatz sun at an elevation of 60 and the wind speed set to 2.5 m= s. Each day, data was collected from the same population of individually marked beetles.
Individual precision. Individual precision was studied at an elevation of 60 and a wind speed of 2.5 m= s.
In this experimental setting, the beetles exited the arena a total of 36 times: ten times with an ersatz sun and a wind current in congruence, ten times with a conflict of 60 + (or 120 + ), three times with the cues in their original positions, ten times with a conflict of 120 + (or 60 + , respectively), and finally three times with the cues returned to their original positions.

Simulation overview
The software performs a simplified simulation of the cue conflict paradigm above. We are interested in the change in the value of an integration of two angular inputs with von Mises noise. We define a von Mises distribution for each cue (using the precision data described in STAR Methods, Behavioural experiments -Reliability of sun and wind cues) and an angle is sampled from each. We then compute the integration of these angles when the cues are aligned (their distributions have the same mean), and when the cues are in conflict (the distributions have different means). The difference between the two integrations is the change in the integration, which can be interpreted as a change in bearing. We compared five different cue integration models and assessed their ability to produce our behavioral data by comparing how likely the data would be under any candidate model (see STAR Methods, Evaluation process).

Simulated cue representation
In order to capture sensory noise in a circular context, cues are treated as independent von Mises random variables (Murray and Morgenstern, 2010). The von Mises probability density function is given by: f VM ðx; m; kÞ = e kcosðx À mÞ 2pI 0 ðkÞ (Equation 1) where m is the mean angle of the distribution, k is the concentration (equivalent to s À 2 for the normal distribution, often called ''reliability' ' (Ernst and Bü lthoff, 2004;Murray and Morgenstern, 2010)), and I 0 ðaÞ is the modified Bessel function of the first kind of order zero (Batschelet, 1981;Murray and Morgenstern, 2010). This is analogous to using normal distributions to simulate Gaussian noise when working with linear data (e.g. time taken by an animal to exit an arena), rather than angular data (e.g. angle at which the animal exits the arena). To sample from these distributions we need to estimate parameters m Wind , k Wind , m Light , k Light , such that the distributions f Light ðx; m Light ; k Light Þ and f Wind ðx; m Wind ; k Wind Þ are those which can produce simulations which match the observed behavior under light (an ersatz sun) or wind respectively.
The estimates for the means are the input azimuths of each cue; it is reasonable to assume that the average perceived cue position is the true cue position. The concentration parameter estimates can be approximated from the mean vector length of a random sample from a parent distribution (Mardia and Jupp, 2009). The best available proxy for such a random sample is the data collected to examine the reliability of sun and wind cues (see Results and Discussion, Reliability of ersatz sun and wind cues). We tried to model the reliability data using linear and split-linear fits respectively (performed using SciPy curve-fitting utilities (Virtanen et al., 2020)); these fits can be seen in Figure 1. However, if we try to approximate the k-values from these directly the resultant populations are less precise than they should be; to fix this, we included small additive constants which augment the mean vector lengths, improving the final k approximation with respect to the observed data. The final estimators are: The quality of this approximation can be seen in Figure S7; the approximation is slightly faster to compute, saving some time when running larger simulations. We can test the k-values by simulating the precision experiments used to estimate them. Including the additive corrections, this method allows us to simulate beetle populations which approximately match real beetles under single-cue conditions.

Integration models
With the above cue representation, we compared five different simple models to evaluate how likely they are to have produced the experimental data. Each integration is computed twice per simulated individual; once for the initial condition and once for the conflict condition.

Winner-take-all (WTA)
Under winner-take-all, we compute weights for each cue and the integration is simply the cue azimuth of the cue with the greatest weight. Weights and integration are given by: ) Note we do not check the case where cues have equal weights because this never occurs. In such an instance you could break the tie randomly.

Weighted arithmetic mean (WAM)
WAM is the standard (statistically optimal) weighted average model which arises throughout cue integration literature (Ernst and Banks, 2002;Ernst and Bü lthoff, 2004;Knill and Pouget, 2004). A weighted arithmetic mean is not appropriate for angular or otherwise cyclic inputs (Batschelet, 1981;Murray and Morgenstern, 2010); a standard example in circular statistics is to consider the average of 0 + and 360 + . If we assume equal weights, then Equation 10 will give 180 + where we would expect 0 + . However, this method has previously been used in the context of directional cue integration in ants (Sun et al., 2018;Wystrach et al., 2015), humans (Alais and Burr, 2004), and monkeys (Fetsch et al., 2012). Furthermore, direction and distance can often be mixed and discussed generally as 'spatial' cues (Cheng et al., 2007;Nardini et al., 2008;Sjolund et al., 2018) which can lead to difficulty when interpreting integration across two different domains. Thus, due to its widespread application, we included WAM in our comparison. The weights and integration are given by: iScience Article in the results and discussion. The n-numbers indicate number of individual beetles tested at each experimental condition.

Reliability of sun and wind cues
To investigate (i) the beetles' orientation precision and, (ii) their directional preferences in the presence of a single cue, the ten exit bearings recorded for each beetle were normalised to the azimuthal position of the orientation cue. Beetles whose normalised exits were not significantly different from a uniform distribution (p % 0:05, Rayleigh test) were deemed unable to orient and thus excluded from analysis for tactic behavior. For each experimental group, i.e. elevation of the ersatz sun (except for 90 elevation) or wind speed, Rayleigh tests were conducted on the population of mean bearings. We define menotaxis as mean bearings taken at any angle with respect to the cue (uniform distribution), while a population showing a directional preference towards or away from a directional cue is defined as performing taxis. Orientation precision was then investigated for the experimental groups that performed menotaxis (i.e. beetles that were able to use the sun and wind stimuli as compass cues).
This was done by calculating the mean vector length (R) from the normalised bearings of each beetle, including the individuals that were previously excluded. The R-value extends from 0 to 1, where a higher value suggests greater precision.

Cue conflict between an ersatz sun and wind
To study the effect of cue reliability on the integration and weighting of directional information given by an ersatz sun and wind in conflict, an exclusion criterion was implemented. The criterion stated that, if the six headings were not significantly different from a uniform distribution when the two cues were in their original positions (congruent) (p R 0:1, Rayleigh test, see Figure S2 for justification), then the beetle was eliminated from further analysis. This ensured that the remaining beetles were able to return to their original heading consistently and thus able to orient.
Changes in heading direction were calculated using the angular difference between two consecutive exits (see Figure 2). For changes in heading at the 0 cue conflict, the angular difference was calculated between the first and second exit where the directional information of the two cues remained unchanged (congruent). For changes in heading at a 60 and 120 cue conflict the difference was calculated between an exit where the cues were in congruence and the following exit where the wind cue had been shifted. The population mean change in heading, together with Rayleigh tests (p R 0:05), were used to determine the behavioural response to the azimuthal shift of the wind. This was carried out for all conflict conditions.
To determine individual precision when presented with a conflict between an ersatz sun at a 60 elevation and a 2.5 m=s wind current, the ten bearings recorded at each conflict were tested for uniformity (p R 0:05, Rayleigh test).