Individuality emerging in cap making by 1 sponge crab 2

11 Successful camouﬂage requires an animal to be integrated into the environment. When an individual grows, the camouﬂage is usually modiﬁed to maintain the integrated state. How does the animal maintain the whole body-camouﬂage system as an individual? We studied the cap making behavior of the sponge crab, Lauridromia dehaani that can carry an artiﬁcial sponge as a cap. We obtained the behavioral data, including repeated samples, from the same individual crab. Multilevel or hierarchical models are often used to deal with the clustered data. However, the evaluation of the appropriateness of the hierarchical model is a challenge in statistical modeling. This is because it is a statistically non-regular model. Here, we for the ﬁrst time applied marginal-level WAIC (Widely Applicable Information Criterion) to the behavioral data and found that the hierarchical models remarkably outperformed non-hierarchical ones in decision making of material size and cap making by the crab. Our new modeling approach successfully detected the integrated ’individuality’ revealed as probabilistic distribution structures in the real world behavioral data.

propodus of the fourth and fifth pairs of the pereiopods and the dactylus can move opposite direction, so 47 they can use the legs just like chelae to grasp and stretch the cap (Fig. 1A) (Guinot et al., 2013;Guinot 48 and Wicksten, 2015). 49 In order to measure the appropriateness of the assumption of the 'individual' in the cap making 50 behavior, we propose a novel statistical formulation of how to capture the individuality from the be-51 havioral data. To capture the structure in the clustered data so far, the class of statistical models with 52 hierarchical structure is often used (Galbraith et al., 2010). Data is sometimes called 'pseudo-replicated' 53 because of the violation of the assumption of independent and identically distributed samples under 54 the non-hierarchical models (Reinhart, 2015). Pseudo-replication can be dealt with appropriately if we 55 explicitly introduce a hierarchical structure into the model such as linear mixed or generalized linear 56 mixed models (Zuur et al., 2009;Kagaya and Patek, 2016). However, it has been a challenge to assess 57 the appropriateness of these models because they are statistically non-regular models (Watanabe, 2018; 58 Millar, 2018). In order to infer the true probability distribution using regular models, the maximum 59 likelihood-based framework of the model selection using AIC (Akaike Information Criterion) has tradi-60 tionally been used (Akaike, 1974;Sakamoto et al., 1986). However, for the non-regular models, one can 61 not approximate the posterior distribution by any normal distribution, so one needs a fully Bayesian ap-62 proach and WAIC (Widely Applicable Information Criterion) (Watanabe, 2010b,a). WAIC can be used 63 for non-regular, non-identifiable, non-realizable models under the identical and independent distribution 64 (Watanabe, 2018). Additionally, not only we need the approach, but also we must be careful about how to 65 compute WAIC. It is strongly recommended to compute the marginal-level WAIC which is consistently 66 applicable to the hierarchical and non-hierarchical models instead of typically used conditioned-level 67 WAIC (Millar, 2018). We took the approach to examine whether the 'individual' specified as hierar-68 chical structure exists in the cap making behavior of marine sponge crabs who make caps or hats for 69 'concealment strategy' (Guinot and Wicksten, 2015).

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There has been several researches implying the individual differences in the material preference. In 71 the field research, one study dealt with the preference of dromids to materials for caps and the correspon-72 dence between the size of cap to the size of the crab (McLay, 1983). It is reported that Cryptodromia 73 hilgendorfi use the caps made from many species of sponges, but they particularly prefer the sponge 74 Suberites carnosus, and the crabs make sponge caps twice as large as the carapace area. In the experi-75 mental research, the preference for the size of material and the suitability between the size of crabs and 76 the caps are scarcely investigated. Dromia personata mainly uses sponges and ascidians (Bedini et al.,77 2003), while they can also make caps with paper (Dembowska, 1926). Dembowska (1926) reported 78 qualitatively that the size of caps made by Dromia personata (reported as D. vulgaris) with paper is as 79 large as the size of those that the crabs originally carried. However, it should be noted that these stud-80 ies have not dealt with the problem raised in this study, because the samples for analyses are datasets 81 consisting of one observation from one individual.

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In this study, we investigated a species of the sponge crab: Lauridromia dehaani and examined the 83 individuality of their cap making behavior. To sample repeated observations from one individual, we 84 repeatedly gave three different sizes of artificial sponges. We modeled the four variates, (1) choice of 85 sponge size, (2) removed size, (3) cap hole size, and (4) time for making, as random variables with 86 hierarchical structures. We introduced hierarchical structures into statistical models, and assessed the 87 appropriateness of the assumption by comparing non-hierarchical competing alternative models using 88 marginal-level WAIC (Millar, 2018). When these models were compared with their non-hierarchical 89 versions of the models, WAIC values favored hierarchical models in all of the four variates. Therefore, 90 our assumption of individuals for the behavioral data is considered to be appropriate in terms of the 91 model predictability. We added the carapace width as an explanatory variable to the model. Therefore, it 92 should be noted that our novel detection of behavioral individuality as probabilistic distribution structure 93 does not mean the individual difference explained by the carapace width or other correlative variables to 94 the width. We propose that the individuality would be acquired through the unique reciprocal interaction   (19.5-23.8 • C) of the aquarium for more than two days for acclimation. We measured their carapace 105 width (Fig. 1B), and divided them into five classes depending on whether they lacked any of the fourth 106 and fifth pereiopods: (A) only one of them was absent, (B) either of both sides were absent, (C) both of 107 the fourth and fifth of each side were absent, (D) more than three were absent, (O) none of the fourth and 108 fifth pereiopods were absent. In this study, the specimens that classed B or D were not collected so that 109 we just used the categories, A, C, and O.  We checked whether the crab carried any sponge once a day in the morning. If it did, we collected 118 the sponge, otherwise, the crab and the three sponges remained in the cage. When the crab did not carry 119 any sponge for five days, we stopped the experiment. First, we performed one trial for one individual 120 (n = 30), but five trials for one individual after February 2017 (n = 8) to examine the individuality of 121 the behavior. We thoroughly desiccated all the sponges that the crabs processed, measured their whole 122 area of them, and the area of the concave part dug by the crab from the pictures taken 46 cm above the 123 sponges.

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To confirm that the cap making behavior is similar to the behavior in the detailed report (Dembowska,125 1926; McLay, 1983), We video recorded the behavior from the two crabs. They were used only for this 126 recording in the aquarium (310 mm × 180 mm × 240 mm). The recording lasted more than three hours 127 after they were put into the aquarium with the sponge. We repeated the recording 5 times for each crab.  (Gelman et al., 1992). All of the draws were judged to converge when R hat < 1.10. 140 We compared the predictive performances of the models using WAIC (Watanabe, 2018(Watanabe, , 2010b. To 141 provide an overview of the models, we will explain only the best-performing models in terms of WAIC 142 in this section. The other models were, for example, without the explanatory variables or without the 143 individuality (Table 1). It should be emphasized that WAIC must be computed with the marginalization  The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/330787 doi: bioRxiv preprint behavioral choice of material size (model 1 1) 154 The crabs did not choose S size sponges and unexpectedly abandoned the choice itself. Therefore, we N act is the total number of behavioral acts ID represents animal identity. It should be noted that we The prior of d cut s is subjected to the half t distribution, d cut s ∼ Student t + (4, 0, 10).
Altogether, the measured quantity of how much of the sponge was removed as the response vari- The copyright holder for this preprint (which was not peer-reviewed) is the author/funder.  189 We assumed that the time for making lasted until the animal carries the sponge, Days[n], fits the ZIP

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Cap making using an artificial sponge 195 The behavior of the two crabs was video recorded to confirm the behavioral sequence of cap making us-196 ing an artificial sponge. They usually grasped either side of the sponge by the second and third pereiopods 197 (Fig. 1A), and tore off small pieces of the sponge by chelae ( Fig. 2A upper   Finally, the crabs released the second and third pereiopods from the cap and began to carry it (Fig. 2B,   205 C). In the digging behavior, it often happened that they rotated their body forward and dug with it to 206 make the hole larger. They repeated this process up to eleven times per night and it took up to five hours.

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When the crabs rotated their body, the direction of the rotation was maintained along with the sponge.

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While the crabs cut the sponge, they actively moved around the sponge. In contrast, they persistently 209 stayed under the sponge during digging to make a hole. In the next sections, We will describe the results  The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/330787 doi: bioRxiv preprint Cap choice 213 None of the 38 animals choose the S size sponge, and 7 animals abandoned the cap making behavior 214 altogether (Fig. 3A). Therefore, we defined the choice as the random variable taking three behavioral  Table. 1). The posterior probability of the behavioral choices was more widely variable in the model 1 1 218 than in model 1 6 depending on the individual difference specified as a choice L (Fig. 3B). The probability 219 of choice sampled from the posterior distribution is visualized in white lines (Fig. 3A,C). For example, 220 although the animal indicated with the white arrowhead (Fig. 3A) is small, it preferably selected the 221 size L. In either case of hierarchical or non-hierarchical model, the behavioral choice of the sponges 222 was better explained by the carapace width (Fig. 3A,C), suggesting larger crabs tended to choose L size 223 sponge rather than M size. However, the crabs larger than about 9 cm carapace width did not choose the 224 sponges.

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Cutting and removing behavior 226 After the choice of M or L size sponge, the crabs decided whether to remove the extra part of the sponge 227 (Fig. 4). Here, we modeled how much of the sponge was removed by the crabs (N animal = 30). The

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The removing behavior showed two paths. One path was that the crabs decided to remove the sponge 232 and then decided how much of the sponge they remove. The other path was that they skipped removing,  (Fig. 4C). 236 The WAIC score of the hierarchical model 2 1 was -2.08 and the score of counterpart non-hierarchical 237 model 2 6 was 7.40 (Fig. 4D, Table 1). The decrease of removed size can be recognized when the choice 238 is fixed to L size in the predictive density of both of the models (Fig. 4C,D).  Time for making process 247 We modeled the time for making (from the choice of sponge to carrying) by 32 crabs as a random 248 variable subjected to zero-inflated distribution (Fig. 6). No obvious relation was found between the 249 carapace width and the number of days until the crabs carried the first cap, and a number of crabs had The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/330787 doi: bioRxiv preprint fifth pereiopods of the right side even carried the cap once during five trials. The crabs may prefer toxic 264 materials, but there were no materials with the toxic chemicals available in this study. 265 Several similarities were observed in L. dehaani cap making behavior compared with other crabs 266 such as D. personata and C. hilgendorfi (Dembowska, 1926;McLay, 1983). From the video recordings, 267 we described the complete cap making behavioral sequence, and the sponge crabs were found to process between the size of crabs and the days to make caps (Fig. 8, Table 1). Dembowska (Dembowska, 1926) 273 qualitatively reported that younger D. personata make caps faster than older individuals. We counted 274 the days the crabs took to make caps, but the time resolution would be too small to detect a correlation. Woodin, 2008a). In this experiment, crabs that did not carry caps was larger than those that carried caps.

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When they grow up to some extent, their number of predators would be limited and the energetic cost to 285 make caps might increase, so larger individual 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 287 experiment were smaller than those of necessary size for the crabs. Dembowska (Dembowska, 1926) 288 reported that the proportion of caps to the size of D. personata tended to decrease with the size of the 289 crabs, and considered that this was because there were few sponges that fit the large crabs. Similarly, To make the living or non-living materials suitable to the animal body design, animals choose and some-296 times customize the material. Hermit crabs are well known to prefer specific shells (Bertness, 1980;297 Hazlett, 1981;Wilber, 1990). Although hermit crabs cannot modify the shells by themselves, for exam-298 ple, the terrestrial hermit crabs, Coenobita rugosus, are suggested to recognize and learn the shape of  The cap making and carrying behavior can be considered a tool making and using behavior (Guinot 309 and Wicksten, 2015). When considering the tight reciprocal coupling of the nervous system, body and   The bright area mismatches the data points except for the non-removing points. Note that the WAIC of 355 the hierarchical model (-2.08) is remarkably smaller than the non-hierarchical one (7.40).

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We wish thank the Shirahama aquarium for use of the aquarium tanks, and the Sakai fishing port for 368 the offers of the crabs. We wish to acknowledge Dr. Michael Rosario for his advice in improving the 369 manuscript. We would like to thank Editage (www.editage.com) for English language editing.       . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/330787 doi: bioRxiv preprint