Studies of vocalisations and gestures in primates, birds and fish show that signalling behaviour is flexibly adjusted depending on the presence, characteristics and behavioural states of others. Such flexibility is likely important in competitive social contexts such as sexual signalling, where attractiveness is directly affected by rival behaviour. Although sexual displays are often sensitive to the presence and proximity of rivals, less is known about the effect of changes in rival signalling. In this study, we used a biomimetic robot to manipulate rival morphology and waving behaviour in a wild population of fiddler crabs (Afruca tangeri) and investigated whether males responded flexibly by adjusting their own activity and waving. We found that males were less likely to enter their burrow when the robotic rival was waving, particularly if that rival had a small claw, spending less time in their burrow if they did enter. While outside, males produced more waves when the robotic rival was waving fast, not by changing their own rate but by prolonging their bouts. These results reveal the subtle ways in which an invertebrate flexibly adjusts behaviour to remain competitive in a dynamic environment, investing more in signalling when it is likely to be most profitable.

1 Study area and species

The study was carried out between May and July 2022 on a wild population of A. tangeri that inhabit the Ria Formosa Natural Park on the south-eastern coast of Portugal, between Manta Rota and Cacela Velha (37.16 N, 7.53 W). At low tide, this area consists mainly of mudflats, salt marshes and dry sandy banks.

2 Robotic stimulus male

To provide a standardised rival stimulus of different sizes, we used a 3D scan of a fiddler crab specimen from a museum collection [47]. The body and major claw of this scan were 3D-printed separately by FabLab Devon (fablabdevon.org). The major claws were printed in two sizes: one where the major claw was 5 cm from manus base to pollex tip (the approximate mean length of male A. tangeri major claws in our records; see supplementary materials), and one where the major claw measured 7 cm (the largest major claw length in our records; see supplementary materials). The body was 3D printed in one size: the size of the original scan when the major claw was scaled to the mean length (25.8 mm carapace width). After printing, the models were painted to closely resemble male A. tangeri colours to the human eye using acrylic paint (figure 1).

The printed major claw was glued to a mobile joint that allowed vertical movement. This joint was then fixed to a plastic base and a length of metal wire passed through the plastic base, allowing the printed claw to be joined to a Tower Pro Micro Servo SG90. This micro servo was attached to an Arduino Uno Rev3 microcontroller that controlled the timing of the micro servo movement and therefore the vertical movement of the printed claw, emulating the waving of a male A. tangeri. The Arduino microcontroller was also connected to an HC-05 Bluetooth serial transceiver, allowing the wave speed of the robot to be changed remotely via Bluetooth connection to a phone. The robotic stimulus male could wave at two speeds: a “Slow” speed of one wave every 2 s, simulating low-intensity waving; and a “Fast” speed of one wave every 1 s, simulating high-intensity waving (see video in supplementary materials). These wave speeds were estimated from videos of real males collected in previous field seasons (SKD unpubl.).

We assume focal male behaviour reflects responses to any rival male rather than being specific to the scanned specimen that formed the basis of our 3D-printed models. We observed multiple male A. tangeri aggressively challenging and physically attacking the robotic rival during test trials (see supplementary materials). Given that we have only observed A. tangeri fighting with conspecifics, we are confident that the focal males perceived the robotic rival as a conspecific rival male and our assumption of generalisability is justified.

3 Experimental set-up

All experimental trials were carried out during diurnal low-tide periods, between 8:00 and 17:00. Before the trial began, a male who was actively waving on the surface next to his burrow was selected as the focal male. All burrows within a 60 cm radius of the focal male’s burrow were plugged for the duration of the trial (~20 minutes) using bundles of locally collected samphire (Salicornia europaea). This prevented any crabs that occupied nearby burrows from emerging onto the surface during a trial and temporarily removed all but the focal male from the experimental area. Crabs are adapted to spending 4–6 hours in their burrow every high tide, so it is unlikely that the trapped individuals experienced any negative consequences, except for a 20-minute period where food availability was restricted. Other males could still walk through the experimental area, and this was recorded when it happened. The robotic stimulus male was placed on the substrate 30 cm away from the focal male’s burrow entrance (approximately the average distance to the nearest neighbouring burrow; JAW unpubl.) with either the “small” or “large” claw attached. Each focal male was only presented with one claw size (randomised across males) for the duration of their trial. Two GoPro Hero 4 cameras were then set up to record the behaviour of the focal male, one behind the robotic stimulus and one on the other side of the focal male’s burrow, facing the robotic stimulus. This camera setup ensured that the frontal view of the focal male was always visible.

Once all equipment was set up, the experimenter (JAW) retreated to a distance at which his presence would not affect focal male behaviour (>10 m), and a timer was started. If the focal male did not emerge from his burrow within 7.5 minutes, that trial was abandoned. If the focal male did emerge, the timer was reset to mark the beginning of the first condition of the trial and we moved through a sequence of four conditions with that male, each condition lasting for 5 minutes: (1) the robotic stimulus was present but not waving (“No wave” treatment); (2) the robotic stimulus started waving at one of the two wave speeds (either “Slow wave” or “Fast wave” treatment); (3) the robot waving was stopped and the focal male experienced another “No wave” condition; (4) the robot waved at the speed that the focal male had not experienced in condition 2. All changes to robot wave speed were done remotely to avoid disturbing the focal male.

The time at which the trial started was noted, as well as the substrate surface temperature (measured using a Magnusson KC-180A1 infrared thermometer, ±2°C). The claw size treatment and order of wave speed presentation were balanced across focal males using a randomised-blocks design: each ‘block’ consisted of four trials covering the four possible experimental conditions (large, Slow→Fast; small, Slow→Fast; large, Fast→Slow; small, Fast→Slow), with these applied to four different males in fully randomised order. The same “small” and “large” robot claws were used across all focal males in each claw size treatment and the same robot body was used for all focal males.

4 Focal male morphometrics

Once a trial had ended, all apparatus was removed from the area and a tube trap was placed in the entrance to the focal male’s burrow. If the focal male entered the trap (27 males out of 58 used for the final analysis), we measured the distance between the base of his manus and the tip of his pollex (claw length) and the widest point of the dorsal side of his carapace (carapace width; figure 1) using a Whitworth electronic calliper (± 0.01mm) and weighed him using Ohaus Traveller’s scales (±0.1g). The captured males were then marked with a non-toxic paint pen on the carapace to avoid using the same male twice across trials.
If the focal male did not enter the trap within 20 minutes (31 males out of 58 used for the final analysis), the trap was removed and his claw length and carapace size were estimated from the GoPro footage using the software ImageJ, with a measuring tape placed above his burrow in the video footage for scale. Because these males were not caught, they could not be marked to avoid reusing them. However, their burrows were avoided when selecting males for future trials. Given that individuals of this species occupy their burrows for 1–2 weeks and given the large population (many thousands of individuals) occupying the mud flats in the study area, the chances of accidentally using the same male twice for a trial are very low.

The experimental trials were carried out on 70 focal males, but only 58 were used for the final analysis as some trials were either interrupted by human passers-by (5 trials) or the focal male left the experimental area during the trial, usually after losing a fight with a wandering male (7 trials). Table 1 shows the focal male and trial information for each of the four experimental treatments, as well as information on the trials not included in the final analysis.

5 Ethical note

This study used biologically realistic interventions in a natural environment. Captured individuals were returned to their burrow after measurement and neighbouring burrows were unplugged after the trial had ended. All work was carried out with approval from the University of Exeter's Research Ethics Panel (application ID: 513844) and the Instituto da Conservação da Natureza e das Florestas (permit ID: 579 / 2022 / CAPT).

6 Behaviour coding and data

For each experimental trial, we extracted all time points at which the focal male entered or exited his burrow, or performed a wave with his major claw (the definitions for these behaviours are in Table 2). We then calculated the proportion of time the focal male spent in his burrow during each wave speed treatment. We also recorded the number of males in frame that were not the focal male, as well as the number of females in a frame (i.e. within a maximum of 60cm of the focal male), at each point in the videos.
Videos were coded once by one of the research team (JAW) who was not blind to the claw size or wave speed treatment. A second person, unaware of the aims of the study, independently coded 10 percent of the trial videos in which the robotic rival was not visible; this person was therefore blind to both the claw size and wave speed treatments. All behaviour coding was carried out using BORIS. The inter-rater correlation coefficient (also known as the intra-class correlation coefficient, ICC; calculated in R using Stan and Cmdstan [50-53]) for the total number of waves was 0.87 (89% highest density interval (HDI) [0.76, 0.97]), and the ICC for the time spent not waving was 0.89 (89% HDI [0.81, 0.98]). The ICC for time spent in the burrow was 0.87 (89% HDI [0.77, 0.97]). These values indicate ‘good’ to ‘excellent’ reliability for our behavioural measures.

7 Statistical analyses

7.1 Burrow use
We used a linear hurdle model to analyse whether males adjusted the time spent in their burrows in response to changes in the behaviour and claw size of the robotic rival. In this analysis, we asked how the signalling behaviour of the biomimetic rival male affected (1) the probability that a male entered his burrow and (2) how long he spent there. For each of the 5-minute wave speed conditions (“No wave”, “Slow wave” or “Fast wave”), the probability that the male entered his burrow at all was modelled using the Bernoulli distribution (binary outcome, the ‘hurdle’). For those cases where the male did enter his burrow, the proportion of the 5 minutes he spent there was modelled using the Beta distribution (ranging between 0 and 1). In both parts of the linear hurdle model, the experimentally manipulated predictors we included were the wave speed of the robot, the claw size of the robot, as well as the interaction between the two. We also included treatment order and the following uncontrolled predictor variables: the focal male’s carapace width; his claw-length-to-carapace-width ratio; the substrate surface temperature at the start of the trial; and the time the trial started relative to the lowest tide point. Previous studies have found that fiddler crab behaviour is statistically associated with each of these variables, so we included them as fixed effects to refine our tests of the experimental treatment effects. Occasional visits from females and rival males were ignored in these models as they happened on a much quicker timescale than the response variable, which is a summary of a 5-minute period. Random intercepts were included for focal male identity to account for non-independence among measurements and capture natural variation among males in their overall tendency to enter and spend time in the burrow.

7.2 Signalling behaviour
To analyse the male’s behaviour when he was outside his burrow, the data were divided into 5-second time intervals. Any 5-s intervals in which the focal male left the field of view of both video cameras at any point were discarded. In each of the remaining intervals, we recorded the number of times the focal male waved, the number of females in the frame, as well as the number of wandering rival males (in view of either of the two GoPro cameras). This gave a total of 10,400 5-s intervals across 58 individuals. We chose 5 s as the time interval for analysis to balance the amount of detail we retain in behavioural sequences (which is highest when the data are divided into small intervals) against the computational processing time required to analyse the data (which is also highest when the data are divided into many small intervals).

We analysed the resulting data using hidden Markov models (HMMs), a data-driven approach that identifies the bout structure of repetitive sexual displays such as claw waving, avoiding the pitfalls of researcher-defined bout criteria that have been used in the past (discussed in Perry et al, 2019). HMMs do this by assuming that an individual is in one of several states at any given time. The individual’s current state is ‘hidden’ in the sense that it is not directly observable, but the expression of observable behaviour is an indicator of that state. In this study, we modelled focal males as being in one of two hidden states: a signalling state (in which he is actively displaying) and a non-signalling state (in which he is visible above ground but is doing anything other than actively displaying). We used the number of waves per 5 s as a proxy from which to infer the underlying state of the male. By fitting HMMs to the full sequence of 5-s time intervals in a trial, we could simultaneously estimate the male’s waving rate in the signalling state and his probability of transitioning between states (from signalling to non-signalling, or vice versa) from one interval to the next. Explicitly modelling the rate of waving and the probability of continuing or ending a signalling bout allows us to disentangle multiple ways that a male can adjust his bout-structured waving behaviour and may reveal flexible changes in signalling that would be overlooked by coarser analytical techniques. This technique also allows us to treat each focal male’s behaviour as a time series, explicitly accounting for the temporal autocorrelation between behaviours in successive intervals. Figure 2 is a visual representation of how these models work. For more information on HMMs see Perry et al. (2019), McClintock et al. (2020), and Glennie et al. (2023).

The HMMs also allow us to estimate how the probabilities of transitioning between states and waving rates depend on predictor variables characterising the male and his social context. We estimated the effect each predictor variable has on (1) the probability a focal male stays in the signalling state, (2) the probability he stays in the non-signalling state, (3) the rate of waving when in the signalling state and (4) the (low) rate of waving when in the non-signalling state. The experimentally manipulated predictors we included were the wave speed of the robot, the claw size of the robot and their interaction. As before, to control for additional sources of variation and refine our tests of the experimental treatment effects, we also included the following uncontrolled predictor variables known to be associated with fiddler crab behaviour: the number of females in view (of either GoPro) in each 5-s interval; whether a wandering rival male was in view in each 5-s interval; the substrate surface temperature at the start of the trial; the focal male’s carapace width; his claw-length-to-carapace-width ratio; and the time of the 5-s interval relative to the lowest tide point. Random intercepts were included for focal male identity to account for non-independence among measurements and capture natural variation among males in their average transition probabilities and waving rates. A full outline of the models used can be found in equations 1 and 2 in the supplementary materials.

7.3 Model fitting
All models were written in Stan and compiled and run using CmdStanR version 0.5.3 and CmdStan version 2.30.1 in R version 4.1.2 on the UK Crop Diversity high-performance computing platform. Weakly informative priors were used for all parameters and checked using prior predictive checks (full model information including priors in supplementary materials). Model convergence was checked using trace plots, posterior predictive checks, and the potential scale reduction factor (R ̂). To increase the stability of the reported intervals, and following the convention laid out by McElreath (2018), the 89% HDI of effect sizes (unless otherwise stated) is reported throughout. We also report the proportion of posterior samples indicating an effect in the opposite direction from the reported effect, denoted either as Pr(β > 0) if the majority of the posterior density mass is negative, or as Pr(β < 0) if the majority of the posterior density mass is positive; thus small values of this proportion suggest that the reported effect is clearly distinguishable from zero. All continuous predictors (temperature, time, carapace width, claw:carapace ratio) were converted to z-scores prior to analysis to facilitate model convergence and aid interpretation. All effect sizes (β) are reported on the link scale. Therefore, effects on transition probabilities represent the change in log odds associated with a 1-unit increase in the predictor. Effects on wave rates represent the change in the logarithm of the wave rate associated with a 1-unit change in the predictor. Because we used a Bayesian mixed-modelling framework with weakly informative, regularising priors, the risk of Type I errors in these models is lower than in other frameworks. A simplified version of this analysis was run without non-experimental predictors to ensure the robustness of the full model. This simplified model found the same results and is outlined in the supplementary materials.