Customizing material into embodied cap by sponge crab

Getting camouflaged with environmental material can improve survivability of animals. How animals select and customize the material to fit it to their body design remains unclear. To address the question, we examined the cap making behavior of the sponge crab, Lauridromia dehaani that carries sponge as a cap. We tested their preference to size of original material, the whole area size of cap that the crabs cut off, and its hole size of the caps that the crabs customize to make it suitable for their body. Three different sizes of artificial sponge were given to the crabs experimentally so that they could choose one sponge among them. We video recorded the process of cap making behavior, and measured the size of caps. Although a certain fixed behavioral pattern was observed in the cap making behavior, choice and size of cap hole considerably varied even in a single individual. To fully consider the individuality, we incorporated it into hierarchical statistical models. Estimating the parameters in the models by a Bayesian approach revealed that large individuals tended to choose large sponges with the variability specific to each individual. Furthermore, the individual-specific tendency was also observed in the relationship of the carapace width and the cap hole size. These results imply that the crabs update the cap making behavior by recalibration, given that they have to molt to become large. These findings might give a new insight into body extending capability of crustaceans.

Introduction also make caps with paper (Dembowska, 1926). 54 In this study, we focused on a species of sponge crab: Lauridromia dehaani. In order to experimentally control 55 the sponge size and its condition, we gave different sizes of artificial sponges to the crabs. We examined the 56 relationship of the carapace size with the size of sponge the animal select, the size of cap holes, and the time 57 they took for cap making. To explore and model these relationships with the individuality specific to each 58 animal, we constructed the statistical models implementing the individuality as hierarchical structure in the 59 parameters to be estimated. We applied the models to the data and estimated the posterior distribution

Statistical modeling
In order to quantify and extract the structure of the behavioral aspects including individuality, we explored 90 26 statistical models constructed for the four different aspects of the behavior: (1) choice of sponge size (6 91 models), (2) cutting behavior (8 models), (3) cap hole making behavior (6 models), (4) time until carrying the 92 sponge (6 models). In either case, we have constructed the models that explicitly includes individuality as the 93 hierarchical (or multi-level) models and estimated the posterior distribution of the parameters. We scripted 94 the models in a probabilistic programming language Stan (Matsuura, 2016;Stan Development Team, 2017). 95 We used non-informative uniform priors for the parameters in all of the models. The softwares performed 96 sampling from the posterior distributions using No-U-Tern Sampler (NUTS), which is implemented as a 97 Hamiltonian Monte Carlo (HMC) sampler. Whether the sampling was converged was diagnosed by trace 98 plots and quantitatively via the Gelman-Rubin convergence statistic, R hat (Gelman and Rubin, 1992). All of 99 the draws were judged to converge when R hat < 1.10. 100 We compared the predictability of the models using the widely applicable information criterion (WAIC, 101 Watanabe, 2010). To give the essense of the models, we will explain only the best performed models in terms 102 of WAIC in this section. The other models are, for example, without the explanatory variables or without 103 the individuality (Table 2). It should be noted that WAIC can be computed in different ways depending on 104 what we want to predict the data (Watanabe, 2018). In our case, we are interested in the prediction of when 105 we get a new individual and get a new behavioral act instead of the prediction of a new behavioral act from 106 the individuals sampled in this study. Therefore, for the multi-level models assuming the individuality, we 107 performed numerical integration of the local parameters defining the hierarchy to average out. The predictive 108 distributions based on the best models were constructed using the mode of the parameters, and visualized as 109 the density plots with the data points in the following figures.
As described above, we also considered the individuality so that the intercept term b day [ID[n]] was incorporated 156 into this model.

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Cap making behavior 159 The crabs usually made their caps at night. They usually grasped either side of the sponge by the second 160 and third pereiopods (Fig. 1A). They teared off small pieces of sponge by chelae ( Fig. 3A upper left, upper 161 right, S1). Sometimes they moved to another side of sponge. By repeating these behaviors, the crabs made 162 the groove to cut off the clod of sponge. After cutting, the crabs made a hole by tearing off small pieces of 163 sponge (Fig. 3A bottom, S2). It took 14 minutes to dig the hole on average (3 individuals, 7 trials). The 164 chelae of larger crabs tore off larger pieces of sponge. Then the crabs rotated their body backward in order to 165 catch it by fourth and fifth pereiopods while they kept the clod grasping by second and third pereiopods. 166 Finally, the crabs released second and third pereiopods from the cap, and began to carry it (Fig. 3B, C). The  The behavioral choice of the sponges was better explained by the carapace width (Fig. 5). The larger crabs 182 tended to choose L size sponge. However, the crabs whose carapace width becomes larger than 9 cm did not   Figure 5: The larger crabs selected larger sponges, but when the size becomes larger than about 9 cm, they abandoned the choice itself. The gray region represents the predictive distribution constructed by the 50 percentiles of the posterior distribution of the parameters on the best performed model 1_1 (Table 1, 2).  (Table 1, 2).

Cutting behavior 187
The cutting behavior showed two paths. One path was that the crabs decided to cut off the sponge and 188 then decided how much they cut off the sponge. The other path was that they skipped cutting off, then  Table 1), nor the selected sponge (c cut in Table 1). On the other hand, the 194 removed size was well explained. The smaller size of crabs tended to remove larger size of sponge to make 195 caps (e cut in Table 1). Additionally, the removed size was more remarkably explained by the chosen sponge 196 size, because the 2.5 percentile of the f cut was estimated to be larger than zero (Table 1) size increased with the carapace width (Fig. 7). Moreover, the model with the individuality best performed 202 in the predictability ( Table 2). The 2.5 percentile of the parameter b hole was even larger than zero (Table 1). 204 There were no obvious relation between the carapace width and the number of days until the crabs carried 205 the first cap, and a number of crabs had carried the cap by next day. The expected days to carrying was 206 0.611 on the best performed model (Fig. 8).   (Table 1, 2).  In particular, some homolid crabs are reported to carry not only sponges or ascidians but also sea anemones 212 (Chintiroglou et al., 1996), and they drive away their predators with these materials (Braga-Henriques et al., 223 personata and C. hilgendorfi (Dembowska, 1926;McLay, 1983). The crabs C. hilgendorfi make the caps 224 usually during the night, and McLay (1983) expected that this is because making caps at night is probably 225 less risky. It is likely that L. dehaani make caps at night for the same reason. From the video recordings we 226 described all of the cap making behavioral sequence (Fig. 3), and the sponge crabs were found to process positive correlation between the size of crabs and the days to make caps (Fig. 8, Table 1). Dembowska (1926) 232 qualitatively reported that the younger D. personata make caps earlier than old individuals. We counted the 233 days the crabs took to make caps, but the time resolution would be too large to detect the correlation. Further 234 study measuring the time with less time resolution such as minutes to hours might detect the correlation.

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Additionally, further controlled experiments for testing the time and the risk sensitivity will be required.

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Making cost and size choice: why the crab abandoned carrying sponge?
There are not so many marine animals showing the decorating behavior, because this behavior would compel 238 the animal to pay the energetic cost (Berke and Woodin, 2008). For example, the adult males of Oregonia 239 gracilis tended to decorate less than the juveniles or adult females, and this would be because the energetic 240 cost of the adult males to maintain their large claws increases and they could not pay the cost for decorating.

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In this experiment, the size of the crabs that did not carry caps was larger than that carried caps (Fig. 5).

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When they grow up to some extent, the number of predators for them would be limited and the energetic 243 cost to make caps might increase so that larger individuals would not make the caps.

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Another possibility for why the crabs abandoned carrying sponge is that the sponges used in this experiment 245 were smaller than those of necessary size for the crabs. Dembowska (1926)  In our study, we demonstrated that not only the crabs chose the size of sponges (Fig. 5), but also they cut 263 off the suitable size of sponge (Fig. 6) and made the suitable size of hole in the sponge (Fig. 7).

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Moreover, in either case of the statistical models, the models including the individuality outperformed the 265 other models without it in terms of the model predictability. In order to control the quality and size of the 266 sponges, we used artificial sponges in this experiment. Although the sponge was artificial, they have the great 267 potential of making caps fitting to their own body. We finished the trial when the crab carried the cap, but 268 sometimes observed the individuals showing modification by digging after they carry caps. Hence, it is likely 269 that if we continue recording, the animals will be able to obtain more suitable sponge caps.

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Among vertebrates, the primates such as chimpanzees and gorillas (e.g. Boesch and Boesch, 1990; Breuer 271 et al., 2005) and the birds such as new caledonian crows (Hunt, 1996) have been researched as tool users.

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On the other hand, among invertebrates, it is known that octopuses use coconuts as defensive tools (Finn 273 et al., 2009) and insects, for instance bumblebees, are able to perform the task in which they have to use 274 surrounding materials (Loukola, et al., 2017). Some crustacean, such as green crabs and American lobster 275 are able to perform instrumental conditioning (Abramson and Feinman, 1990;Tomina and Takahata, 2010). 276 Our findings demonstrated that the crabs update the cap size depending on the current body size during 277 inter-molt period. It is confirmed that the sponge crab repeatedly modified the cap to fit it to their body.

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Therefore, it is likely that certain learning processes subserve the cap making behavior. Additionally, it is 279 probable that the crabs also take advantages of the shape and the size of the body itself as a guide model.

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Almost all of the cutting behavior did not include the trial-and-error process, suggesting that some topdown