Unraveling the mating system of the burrowing shrimp Lepidophthalmus siriboia (Decapoda Callichiridae) based on life history traits

Natural history studies are important in helping to understand the origin and evolution of social organization as well as the evolution of specialized morphological structures linked to mating behavior of animals. Here we describe the burrow use pattern, sex ratio, and sexual dimorphism of the burrowing shrimp Lepidophthalmus siriboia to test a series of evolutionary hypotheses. To this end, a total of 259 individuals of L. siriboia were collected from the northeast region of Brazil. No shrimp pairs or burrows inhabited by more than one shrimp were detected during the study period. A solitary habit is a non-random behavior in this species because single shrimps were found with a greater frequency than expected by chance. All ovigerous females were found living solitarily, which suggests that males abandon these females shortly after insemination. Contrary to the expectations of an anisogamous species, L. siriboia produced a female-biased operational sex ratio (OSR), contradicting the hypothesis that only males compete for mates. The latter was supported by the existence of sexual dimorphism in cheliped size, a condition that argues in favor of female–female competition in this species. In the same line of reasoning, heterochely was present in adult males, although it was also present to a lesser degree in adult females. Female asymmetry of chelipeds suggests the evolution of an unconventional role in female major cheliped use. The major cheliped showed a positive allometric growth pattern through the ontogeny of both sexes. However, when growth patterns of the major and minor chelipeds were compared, the fitted regression lines for each sex had different slopes, indicating that the cheliped could be an appendage sexually selected by individuals of the opposite sex during mating.

Natural history studies are important in helping to understand the origin and evolution of social organization as well as the evolution of specialized morphological structures linked to mating behavior of animals.Here we describe the burrow use pattern, sex ratio, and sexual dimorphism of the burrowing shrimp Lepidophthalmus siriboia to test a series of evolutionary hypotheses.To this end, a total of 259 individuals of L. siriboia were collected from the northeast region of Brazil.No shrimp pairs or burrows inhabited by more than one shrimp were detected during the study period.A solitary habit is a nonrandom behavior in this species because single shrimps were found with a greater frequency than expected by chance.All ovigerous females were found living solitarily, which suggests that males abandon these females shortly after insemination.Contrary to the expectations of an anisogamous species, L. siriboia produced a female-biased operational sex ratio (OSR), contradicting the hypothesis that only males compete for mates.The latter was supported by the existence of sexual dimorphism in cheliped size, a condition that argues in favor of female-female competition in this species.In the same line of reasoning, heterochely was present in adult males, although it was also present to a lesser degree in adult females.Female asymmetry of chelipeds suggests the evolution of an unconventional role in female major cheliped use.The major cheliped showed a positive allometric growth pattern through the ontogeny of both sexes.However, when growth patterns of the major and minor chelipeds were compared, the fitted regression lines for each sex had different slopes, indicating that the cheliped could be an appendage sexually selected by individuals of the opposite sex during mating.

INTRODUCTION
Competition for sexual partners (often called intrasexual selection) is a powerful force for the evolutionary change and, together with the female choice (often called intersexual selection), constitute the two fundamental theoretical underpinnings of the sexual selection theory (Darwin 1871; Andersson 1994).Sexual selection theory suggests that males should try to mate with as many females as possible (Andersson 1994;Alcock 2001).As a result, males compete with each other for mates, so the development of specialized fighting body structures (such as ornaments, threat devices, and weapons) can be the difference between winning and losing when males compete for receptive females (O'Brien et al. 2018;Somjee 2021).
Specialists recognize that sexually selected traits are often disproportionately elaborate, colorful, and large in comparison with traits evolving under natural selection (Andersson 1994;Alcock 2001).Many sexually selected traits (such as ornaments, threat devices, and weapons) are very large relative to the overall size of the animal, that is, these features develop allometrically (Eberhard et al. 2018).Allometry has basic concepts that allow us to understand the association between size and morphology itself.One of these fundamental concepts is that allometric scaling is any change that deviates from isometry, that is, from no change in proportions (Huxley & Tessier 1936).Various forms or levels of allometry can be defined (such as ontogenetic allometry, static allometry and evolutionary allometry - Gould 1966Gould , 1974;;Cheverud 1982;Klingenberg & Zimmermann 1992;Pelabon et al. 2014); however, all these approaches are linked together by a central idea that tries to integrate aspects of developmental and evolutionary biology into a unified theory of morphological evolution (Klingenberg & Zimmermann 1992).In fact, allometric relationships generate functional hypotheses for understanding trait variation; for example, the difference between cheliped growth rate in male and female decapods can be used to explain the adaptation of each sex to their different reproductive roles (Correa & Thiel 2003;Bauer 2004;Hernáez 2018b).
The burrowing shrimps of the infraorder Axiidea (Decapoda), in which are included 11 families and about 507 species -the latter data obtained from a count made in the WoRMS database (https://www.marinespecies.org/)-is a clade that groups a series of fossorial forms of great ecological importance due to their role as ecosystem engineers (Ziebis et al. 1996;Bertics et al. 2010;Pillay 2019).Because the life habit of these species is mainly fossorial, the reproductive behavior and, consequently, the mating system are poorly documented in the species of this clade compared with other decapod groups (e.g.Caridea Brachyura) in which this issue has been widely studied (Bauer 2000(Bauer , 2004;;Correa & Thiel 2003;Shuster 2007;Subramoniam 2013).Despite the efforts made over recent years, instead of direct behavioral observations, mating systems of burrowing shrimps have been inferred by such characteristics as social organization within the burrow (i.e. group size and sex composition), adult sex ratio (i.e. the proportion of receptive females to sexually active males), and sexual dimorphism in body size and chelipeds (i.e.sexual selection) (e.g.Shimoda et al. 2005;Hernáez 2018b;Hernáez & João 2018;Hernáez et al. 2021; for an exception, see Somiya & Tamaki 2017).
Unraveling mating system in L. siriboia Many burrowing shrimps are characterized by solitary habits and a remarkable sexual dimorphism both in body size and chelipeds (Shimoda et al. 2005;Hernáez 2018b;Hernáez et al. 2021).That is the main reason why burrowing shrimps are expected to be mainly polygamous, since most monogamous species live in malefemale pairs and exhibit a low degree of sexual dimorphism (e.g.Baeza 1999;Correa & Thiel 2003;Bauer 2004;McDermott 2005;Baeza et al. 2016;Hernáez et al. 2022b).Also, such pattern of distribution differs from that of many crustacean taxa, in which monogamous species live as heterosexual pairs, with mates often sharing similar trait characteristics [i.e.assortative mating here defined sensu Schwartz (2013) as the nonrandom matching of individuals into relationships], such as size and ornamentation (see Jormalainen 1998;Correa & Thiel 2003;Bauer 2004;Shuster 2007).
Crustacean chelipeds fulfill multiple ecological roles, including prey capture and processing, agonistic interactions, and mate acquisition and handling (Hughes 2000).In burrowing shrimps, chelipeds are usually sexually dimorphic (Shimoda et al. 2005;Hernáez & Wehrtmann 2007;Hernáez & João 2018;Hernáez et al. 2021) and this sexual dimorphism alone could provide sufficient evidence for sexual selection mediated by male-male competition (Shine 1989;Eberhard et al. 1998;Temeles et al. 2000;Graham et al. 2020) or by social selection not directly related to mating opportunities (Tobias et al. 2012).Sexual selection is frequently associated with the hyperallometric growth of chelipeds that are used during combat or display mostly in males (Bauer 2004;Bonduriansky 2007;Hernáez 2018b;Hernáez et al. 2021).Thus, it is reasonable to expect that the study of allometric growth pattern (e.g.static allometry of adult secondary sexual traits) may help to understand the mechanisms associated with the evolution of mating systems (monogamous or polygamous), and offer a new perspective on the underlying mechanisms of sexual selection in burrowing shrimps.On the other hand, information on the development of hypertrophied major cheliped in burrowing shrimp females is non-existent, despite the fact that female heterochely is conspicuous in many of the studies available in the literature (e.g.Hernáez & João 2018;Hernáez et al. 2022aHernáez et al. , 2022c)).
In this study, we are particularly interested in examining a series of aspects related to the life history of the burrowing shrimp Lepidophthalmus siriboia Felder & Rodrigues 1993 (Callichiridae), the only representative of this genus along the Southwestern Atlantic (Hernáez 2018a).This species builds their galleries in coarse grained sand bars of estuarine areas, forming populations in hypohaline habitats with lower salinities below (Hernáez et al. 2022c).A previous study of the population dynamics of L. siriboia examined the growth pattern of this species and concluded that female L. siriboia live longer than males due to slower growth during the juvenile phase (Rosa Filho et al. 2013).Although an advance in general aspects of the growth pattern of L. siriboia, the aforementioned study did not address the morphological and ecological traits of these organisms that could help to understand the natural history of the species.Given the above, we tested the hypothesis that the life history traits of L. siriboia are associated with a polygamous mating system.To this end, we investigated the burrow use pattern, sex ratio, sexual dimorphism, and relative growth of L. siriboia from the South-western Atlantic.Furthermore, we examined in detail heterochely and handedness in males and females, as a potential indication of the sexual/social selection in this species.

Study area and shrimp sampling
Specimens of L. siriboia were collected during August 2021 in the intertidal zone of the Manguaba River mouth, Alagoas, northeastern region of Brazil (9°09ʹ28.83"S,35°17ʹ44.29"W;Fig. 1a-d).The study site is an estuarine area characterized by coarse sediment in which mangrove trees appear as the main biotic component of the habitat.Lepidophthalmus siriboia is the dominant macroinvertebrate in the intertidal zone of this area, where this species may reach a maximum density of two burrows per square metre (P.Hernáez unpubl.data).The entrances to the burrows constructed by L. siriboia are easy to identify at the surface of the sediment because of their typical volcano shape: 1-4 cm high and 3-14 cm in diameter at the base, with one opening in the surface.
Samples were collected at low tide during periods of lower daily temperature, when individuals are located near the surface, which facilitates shrimp capture (Hernáez & João 2018).Shrimps were collected from the burrows by using a handmade yabby pump (for details see Dworschak 2015) and using the collecting method proposed by Hernáez et al. (2021).Suction pumping of burrows with a yabby pump, like the one used during this study, is an efficient method for sampling organisms living in intertidal burrows (de Rodrigues 1966; see also Hernáez 2018a).In our study, this device was especially efficient due to the burrow morphology of L. siriboia; the burrow is a tube cylindrical throughout (diameter = 5-10 mm) running perpendicularly or slightly obliquely angles to the surface, with only one surface opening (chimney-like) after which the tube is divided into three main regions: the first portion about 10 cm long, the second about 20 cm long, and the third portion about 50 cm long.All above measurements were taken with a flexible rubber tubing.After shrimp collection, the specimen or specimens from each burrow were carefully rinsed with seawater, placed in individual plastic bags, and preserved in 70% ethanol until further examination in the laboratory.Part of the material analyzed in this study was deposited in the Museu de Oceanografia Prof. Petrônio Alves Coelho, Universidade Federal de Pernambuco (MOUFPE 20692).
In the laboratory, each specimen was sexed following the methodology proposed by Hernáez et al. (2022c).We also classified females as brooding or non-brooding, according to the presence or absence of embryos carried beneath the abdomen, respectively.Developing embryos of ovigerous females were classified into two stages: initial stage, characterized by rounded eggs with uniform yolk and no visible eye pigments, and final stage, characterized by ovoid eggs with elongated and barely visible eye pigments or fully developed eyes and free abdomens.We used a stereomicroscope (Zeiss Stemi SV-6, to the nearest 0.1 mm; Oberkochen, Germany) equipped with a digital analysis image system (Zeiss AxioCam MRc5) to measure the carapace length (CL), defined as the distance measured from the postorbital margin to the posterior margin of the carapace, and the major and minor cheliped area (ChA), defined as the surface included within carpus height and carpus length (Fig. 1c), measured in lateral view (for details, see the dataset in the supplementary material, available online).Cheliped area (ChA) was chosen as the dependent variable because this measure better represented the allometric change in cheliped growth than carpus length and height throughout the ontogeny of this species.
It is important to highlight the following.Unlike brachyuran crabs and caridean shrimps in which the propodus is usually much larger than the carpus, in many burrowing shrimp species (e.g.Biffarius delicatulus, Callichirus corruptus, C. garthi, C. seilacheri, Lepidophthalmus jamaicense) it is the opposite; the carpus is usually larger and more massive than the propodus (Schmitt 1935;Dworschak et al. 2012;Hernáez et al. 2015Hernáez et al. , 2020Hernáez et al. , 2022aHernáez et al. , 2022c)).In L. siriboia, the carpus is similar in size to the propodus, but the former has a more regular shape than the latter, which favors the measurement process.That is why we chose the carpus instead of the propodus to represent the allometry changes in growth pattern of L. siriboia.

Social structure and sex ratio
We explored whether ghost shrimps occurred solitarily, in pairs or in aggregations within burrows.For this purpose, we examined whether the distribution of L. siriboia in burrows differed significantly from a random distribution by comparing the observed distribution with the Poisson distribution (Elliott 1983).Significant differences between the distributions were tested using a Chi-square goodness of fit test (Zar 1996).
The sex ratio of the population was estimated as the number of males divided by the total number of males and females collected.The observed sex ratio was tested for deviations from an expected 1:1 sex ratio using a binomial test (Wilson & Hardy 2002).In parallel, sex ratio along ontogeny was analyzed for L. siriboia to verify the ratio between sexes and compare with natural ratio (1:1), as a function of size.For this analysis, we considered 10 or more shrimps in each size class as an adequate sample size to calculate accurate sex-ratios.In case this condition was not fulfilled, shrimps were pooled into a subsequent or preceding size class until attaining the minimal number of individuals to ensure meaningful statistical analysis.In the same way, we calculated the operational sex ratio (i.e. the proportion of receptive females to sexually active males), as an indirect way to determine the intensity and direction of competition for mates (Emlen & Oring 1977).Here we define as receptive all those females that at the time of sampling had mature dark orange ovaries following the criteria proposed by Hernáez et al. (2012) and used in other similar studies (e.g.Hernáez et al. 2021).

Sexual dimorphism, heterochely and handedness
We tested whether L. siriboia exhibited sexual dimorphism in body size and chelipeds by comparing the average carapace length (CL) and cheliped (the maximum ChA value between the left and right cheliped) between male and female shrimps using an unpaired t-test.Before conducting the test above, assumptions of normality and homogeneity of variances were checked and found to be satisfactory (Zar 1996).
Heterochely, that is, the presence of a first pair of specialized chelipeds of different shape and size, is a common attribute in most decapods (e.g.Aegla franca: Bueno & Shimizu 2009;Alpheus brasileiro: Pescinelli et al. 2018;Platyxanthus crenulatus: Laitano et al. 2013), including members of the different families of the burrowing shrimps (e.g.Callianassidae, Callichiridae, Ctenochelidae, among others; Shimoda et al. 2005;Hernáez 2018b).To study heterochely in L. siriboia, we examined the morphology and size of the major and minor cheliped in males and females.To do that, we paid special attention to the ornamentation pattern of the prehensile surface of the dactylus and fixed finger of the male and female major and minor cheliped to understand the functional aspects of these appendages.In parallel, the ChA of the major and minor chelipeds were compared separately in males and females using a paired t-test.We assumed that differences in shape and size of each cheliped in L. siriboia are associated with the social (e.g.territory defense) or sexual (e.g.male-male competition) function of these appendages (see Schenk & Wainwright 2001).
We explored whether the larger cheliped is carried at the right or left side of the body.To do this, we calculated the handedness index (HI) for each specimen using the formula [HI = (R -L)/(R + L)] proposed by Wang et al. (2022), where "R" and "L" are the ChA of the right and left cheliped, respectively.In other words, a positive value for HI indicates a tendency to the right and a negative value to the left.Next, the ChA average of the right and left chelipeds were compared separately for males and females using a paired t-test.Only adult shrimps were included in the above analysis of heterochely and handedness to certify that both procedures were conducted among individuals at similar developmental stages (i.e.static allometry; see Gould 1966;Cheverud 1982;Klingenberg & Zimmermann 1992).The classification of shrimps as juvenile or adult was conducted using the Torrejon-Magallanes's (2020) method, which is explained in detail in the section below.

Sexual selection and relative growth
We hypothesize that the male major cheliped under sexual selection will be proportionally larger when compared with the minor cheliped -because selective pressure for fighting for sexual partners (via male-male competition) favors the evolution of disproportionate traits under sexual selection theory (Eberhard et al. 2018).Furthermore, if female chelipeds are also under sexual selection for heterochely (via female aggressive behavior), we also expect a similar cheliped size difference to that seen in males.We predicted that if the major cheliped is sexually selected, the major cheliped would have a steeper scaling value (greater values of slope) when compared to the minor cheliped scaling value.To test this hypothesis, we conducted different analyses of covariance (ANCOVA) to test the effect of a categorical factor (i.e. the type of structure: minor and major cheliped) on a dependent variable (i.e. the area of the structure; ChA) while controlling for the effect of a continuous co-variable (i.e. the carapace length of the individual, CL).The slopes of the regression lines were compared by testing the interaction between the categorical variable (i.e. the morphological structure) with the continuous independent variable (CL).If the interaction is significant, the effect of the covariate on the response variable depends on the level of the categorical factor (i.e. the regression lines have different slopes).On the contrary, a significant treatment effect with no significant interaction shows that the covariate has the same effect for all levels of the categorical factor.Only adult shrimps were included in the above analysis to certify that the procedure was conducted among individuals at a similar developmental stage (static allometry; see Gould 1966;Cheverud 1982;Klingenberg & Zimmermann 1992).
The regression between cheliped area and body size may be different between males and females of decapods if they grow differently.To test that, we conducted an analysis of relative growth and subsequently an analysis of covariance (ANCOVA) to compare the growth pattern of males and females during the post larval phase (i.e. from juvenile to adult phase).We considered the morphological changes as ontogenetic allometry, because the growth was measured during the entire post larval phase (see Pelabon et al. 2014).For this purpose, we first examined the relationship between the cheliped carpus area by choosing the maximum ChA value between the left and right cheliped, and the carapace length (CL) of shrimps by using the allometric model Y = a × X b (Hartnoll 1978(Hartnoll , 1982)).The slope (b) of the log-log least-squares linear regression represents the rate of exponential increase (b > 1) or decrease (b < 1) of the carpus with a unit of increase in body size (CL) of shrimps.We used separate t-tests to examine whether the estimated slope of the relationship between ChA and CL for males and females deviated from the expected isometric ratio (b = 1) (Zar 1996).Next, we conducted an ANCOVA to test whether ChA differs between sexes, including CL as a covariate (Sokal & Rohlf 2011).If the ANCOVA detected a significant effect of the interaction between sex and CL in the different growth pattern herein studied, then we concluded that males and females of L. siriboia grow differently.
As mentioned, we classified the individuals as juvenile or adult using the library "sizeMat" proposed by Torrejon-Magallanes (2020), included in environment R (R Core Team 2022).This classification analysis is based on Principal Components Analysis (PCA) with two allometric variables (x: independent variable, y: dependent variable) in log base, allowing recognition of two groups that would represent juveniles and adults.Next, each shrimp was assigned to each group using a hierarchical classification procedure (hierarchical cluster with agglomeration method: "Ward.D" and the distance measure: "euclidean"; see Corgos & Freire 2006).Then, using the results of the classification, a discriminant analysis (linear) was conducted to obtain a discriminating function that permitted any individuals to be classified as a juvenile or an adult on the basis of the X and Y variables.Lastly, the "classify mature" function returned an object of class "classify", with the allometric variables "x" (independent) and "y" (dependent), and classification of shrimps as juvenile (code = 0) or adult (code = 1).

Social structure and sex ratio
Lepidophthalmus siriboia is characterized by solitary habits.Considering all shrimps collected from the 761 sampled burrows, the number of shrimps per burrow was either 0 or 1 (average ± SD = 0.34 ± 0.47 shrimp burrow −1 ); from which 65 and 34% of the sampled burrows were composed of empty burrows and burrows inhabited by only one individual, respectively.The distribution of L. siriboia within burrows differed significantly from a Poisson random distribution because of the presence of solitary shrimps with a frequency greater than expected by chance alone (Chi-square test of goodness of fit: χ 2 = 27.79,df = 4, P < 0.001).In particular, the number of burrows harboring solitary shrimps expected by chance was substantially lower than the observed frequency (104 vs 146 burrows).No shrimp pairs or burrows inhabited by more than one shrimp were detected during the study period.
A total of 101 males and 158 females (31 of which were brooding females with embryos in different developmental stages) were retrieved from the sampled burrows.The overall sex ratio of L. siriboia differed significantly from evenness (Chi-square test of goodness of fit: males:females = 0.64:1.00,χ 2 = 12.54, df = 1, P < 0.001).With the exception of only one size class (i.e.6.1-7.0 mm CL), females of L. siriboia were more abundant than males in all size classes; with a greater difference between the number of shrimps per sex in the size classes smaller than 6.0 mm CL and larger than 10 mm CL (Table S1 in Supplemental Data).Considering only the sexually mature individuals, the operational sex ratio was also female-biased (0.67:1.00, χ 2 = 5.24, df = 1, P = 0.022).
The chelipeds of L. siriboia are sexually dimorphic (Fig. 2a-d).These differences were primarily observed in the shape and the ornamentation of the major cheliped dactylus and fixed finger.Also, significant differences were observed in the shape and the size between the major and minor cheliped of males and females during adult phase; denoting heterochely in both sexes 3a).Compared to the minor cheliped, the major cheliped of the male is massive and strongly armed on the prehensile margin; with one triangular tooth at the proximal end of the fixed finger and four strong teeth separated by a deep U-shaped notch (Fig. 2a-b).The female major cheliped is also massive relative to the minor cheliped but less heavily armed than that of mature males; the teeth of the prehensile margin of the fixed finger and dactylus are of much lower profile than in males, most prehensile teeth being rudimentary or obsolesce (Fig. 2c-d).
In both sexes, there was a significant difference in the areas of the major and minor cheliped carpus (paired t-test, males: t 54 = 23.37,P < 0.0001; females: t 82 = 30.52,P < 0.0001) (Fig. 3a).We explored whether the larger cheliped is carried at the right or left side of the body (Chi-square goodness of fit test, χ 2 ).This analysis showed a similar proportion of shrimps carrying the larger cheliped on the right side and left side in both sexes (males: χ 2 = 0.16, df = 1, P = 0.686; females: χ 2 = 1.46, df = 1, P = 0.227).In addition, in both sexes there was no significant difference in the handedness index of the left and right chela (unpaired t-test, males: t 53 = 0.61, P = 0.542; females: t 81 = 0.61, P = 0.543) (Fig. 3b).This meant that for males and females, the size of the right and left cheliped was similar in both sexes, therefore, heterochely in this species is not associated with a specific side of the body.In both sexes, the interaction between the main factor (kind of cheliped) and the covariate (CL) was significant, indicating that the effect of the carapace length on the response variable (major or minor cheliped) depended on the level of the categorical factor (i.e.kind of cheliped; Table 1a-d).In other words, the fitted regression lines for Table 1.
Result of the analyses of covariance (ANCOVA) used to compare two regression lines by testing the effect of the major and minor kind of cheliped (categorical factor) on the relationship cheliped carpus area (ChA, dependent variable) and carapace length (CL, co-variable) in males (a) and females (c) of the intertidal burrowing shrimp Lepidophthalmus siriboia.The regression equations, correlation coefficients (r 2 ), standard errors of the slopes (SE), t-value plus degrees of freedom (t [df] ) and correspondent P-values of each studied variable are shown (b, d).Raw data attended ANCOVA assumptions.Significant P-values (P < 0.001) are marked by asterisks and non-significant values are marked by "ns".each sex had different slopes, indicating different growth rates for each cheliped kind (Fig. 4a-b).Although both traits increased disproportionately as body size increased, the minor cheliped exhibited a growth curve with a much shallower slope than the major cheliped (Table 1b, d; see also Fig. 4a-b).In males, for example, for every 1 mm of body increase, the area of the major cheliped increased by 8.6 mm 2 , while in the minor cheliped the area increased by 2.4 mm 2 ; the major cheliped, based on the area measured, grew at a rate 3.6 times that of the minor one.In females this growth difference was less notable, the major cheliped growing at a rate 2.4 times that of the minor one.

ANCOVA -with interaction
The classification of each shrimp as juvenile or adult allowed the determination of a CL size range for each of these growth phases.In males, juveniles and adults, respectively, they ranged from 4.6 to 8.5 mm CL and from 7.2 to 11.9 mm CL, showing a 28% overlap between prepubertal and postpubertal phases (Fig. 5a).Juvenile and adult females ranged from 3.0 to 10.5 mm CL and from 6.9 to 12.1 mm CL, respectively, and these ranges overlap considerably (69%) between ontogenetic phases (Fig. 5b).A positive correlation was detected between CL and ChA of the largest cheliped in shrimps through the two ontogenetic phases of the two sexes (Fig. 5a-b).In both sexes, the major cheliped showed a positive allometric growth pattern through the ontogeny, with a positive increase in the slope during the adult phase (Table 2a) thus confirming that major cheliped growth differs significantly between adult males and females of L. siriboia.

DISCUSSION
Burrowing shrimps are rarely or never seen outside their burrows once they have settled after the larval phase [Dworschak et al. 2012;Hernáez 2018b; for several exceptions,  2a.
Axiopsis serratifrons : Kensley 1981;Corallianassa coutierei, C. longiventris, Neaxius acanthus: Dworschak et al. 2006;Kneer 2006;Krausillichirus (Callianassa) kraussi: Forbes 1978; Thalassina anomala: Ng & Kang 1988].Due to this fossorial habit, knowledge about mating behavior of burrowing shrimps is limited and based on indirect lines of evidence.Here, we have brought to light information on the natural history of the burrowing shrimp L. siriboia with the purpose of unraveling the mating behavior of this species.Most aspects of the L. siriboia's life history studied here argue that this species is not monogamous.Monogamous species usually live in heterosexual pairs and exhibit a low degree of sexual Relative growth in the intertidal burrowing shrimp Lepidophthalmus siriboia at Manguaba River mouth, Alagoas, northeastern region of Brazil.(A) relationship between the major cheliped (ChA) and carapace length (CL) of juvenile (JU) and adult (AD) males (MA) and females (FE) of Lepidophthalmus siriboia.The regression equations (in the log 10 -form), correlation coefficients (R 2 ), standard errors of the slopes (SE), t-value plus degrees of freedom (t [df] ) and correspondent P-values are shown.(b) Summary results of the analysis of covariance (ANCOVA) testing the effects of shrimp sex and CL on the ChA of L. siriboia individuals.Raw data attended ANCOVA assumptions.The regression equations, correlation coefficients (r 2 ), standard errors of the slopes (SE s ), t-value (t), including between brackets the degree of freedom and the level of allometry of each studied variable are shown in "b".CL = carapace length; ChA = area of the major cheliped carpus; MA = males; FE = females; JU = juveniles; AD = adults.dimorphism (Andersson 1994;Correa & Thiel 2003;Bauer 2004), whereas our biological model exhibited completely the opposite.Below, we discuss in detail on the L. siriboia's mating system based on the empirical data obtained here and the theoretical information available in the literature about this clade and other groups of decapods.The distribution of L. siriboia differed significantly from random because of the predominance of solitary shrimps.This means that solitary habit in L. siriboia is a nonrandom process, that is, individuals choose to live solitarily within their respective burrows.No shrimp pairs or burrows inhabited by more than one shrimp were detected during the study period.Such behavior seems to be a phylogenetic trend within this clade, since most burrowing shrimp studied live individually, each inhabiting a burrow of its own (e.g.Audacallichirus mirim, Neocallichirus maryae, N. pinheiroi: Hernáez 2018a; Callichirus corruptus: Hernáez et al. 2022a; C. seilacheri: Hernáez & João 2018; Nihonotrypaea harmandi: Somiya & Tamaki 2017).Although some exceptions of burrowing shrimps forming complex social structures with burrows inhabited by more than two individuals have been described in literature (e.g.Callichirus islagrande: Bilodeau et al. 2005;C. garthi: Hernáez & Wehrtmann 2007;Lepidophthalmus bocourti: Hernáez et al. 2021), the general trend in most Axiidea species is a solitary life within its own burrow (see revision by Dworschak et al. 2012).
The consequences of a solitary lifestyle on the behavior of a species such as L. siriboia are not trivial, since individuals are forced at some point to leave their burrow in search of potential sexual partners.Our experience in the study of these shrimps suggests that the most plausible hypothesis that answers this question is that a shrimp, probably a male, digs a temporary connection from its burrow to another nearby burrow in search of receptive females (Hernáez & João 2018;Hernáez et al. 2021).This assumption is in line with that reported by Somiya and Tamaki (2017), who conducted one of the only experimental studies addressing the mating behavior of these organisms.In that study, the authors stated that mating in Neotrypaea harmandi, an intertidal burrowing shrimp with solitary habit from the Japanese waters, is short (around 30 min), and after copulation, the male moves back to its own burrow and promptly starts to close the connection between burrows.The existence of solitary females brooding embryos in different stages of development (27%) additionally suggests that the males in L. siriboia might be roaming among host burrows in search of mates and then abandoning females (once found) soon after insemination.Consequently, it is likely that sexually active males in L. siriboia are exposed to a high degree of agonistic interactions during search of receptive females.For this reason, sexual dimorphism in terms of body size and chelipeds might give comparative advantages during the movements between galleries and malemale competition for sexual partners (see below).
The overall population sex ratio and operational sex ratio (OSR) of L. siriboia had a biased sex ratio, with females outnumbering males in both cases.This outcome agrees with the general trend of female-biased sex ratios observed in many burrowing shrimp species (e.g. A. mirim : Pezzuto 1998;C. garthi: Hernáez & Wehrtmann 2007;Lepidophthalmus louisianensis: Felder & Lovett 1989;L. sinuensis: Nates & Felder 1999;Trypaea australiensis: Butler et al. 2009).The female-skewed sex ratio observed in L. siriboia additionally represents another line of reasoning indicating that this burrowing shrimp is not monogamous.Males and females are found in similar proportions in populations of burrowing shrimps of the family Axianassidae (Gebiidea: Hernáez et al. 2022b) and other families of decapods (i.e.Alpheidae, Hippolytidae, Palaemonidae, and Pinnotheridae) that exhibit a monogamous mating system (Baeza 1999;Correa & Thiel 2003;McDermott 2005;Baeza et al. 2016;Alves et al. 2021).
Several factors shape the sex ratio in anisogamous species, among them, sexlinked inheritance, sex ratio at conception, differential mortality during the lifespan, investment in parental care, and the particular mating system (Trivers 1972;Kokko & Jennions 2008).In our study, we speculate that the female-biased sex ratio observed in L. siriboia may be associated with the presence of sex-specific differences in mortality rates during the lifespan of individuals.The latter assumption is supported by the more detailed analysis of the sex ratio as a function of size revealed the predominance of females in the different size classes even the smaller ones (see Table S1 in Supplemental Data).This finding shows that the sex ratio at the initial post-larval stage (or, less precisely, at recruitment) differs from evenness (i.e.0.5 for each sex), thus implying, a high male mortality during the larval stage of L. siriboia.Similarly, the female-biased operational sex ratio (OSR) observed in this species reinforces the idea that males, but not females, might be leaving their burrows (at least temporarily) in search of new sexual partners.This is because in a femalebiased sex ratio population, the risk of encountering other males while searching is minimized by the high probability of finding a female rather than a male (Mathews 2002).Also, the idea that adult males abandon their burrows in search of receptive females seems to be a plausible hypothesis, since this behavior would increase the probability of fatal combats with other potential male competitors, thus explaining the bias towards females in larger size classes of L. siriboia, as well as in other burrowing shrimp species (see Hernáez & João 2018).In fact, the number of adult males was almost half that of adult females, suggesting that for some reason (e.g.aggressive encounters between adult males and/or differential predation with a bias towards males), there is a high mortality rate of males in adulthood.In L siriboia, the greater number of females than males additionally suggest the predominance of a mating system characterized by polygynous males (i.e.particular males may have multiple mates) and female-centred competition (Subramoniam 2013), where male mating success depends primarily on males' ability to find (and mate with) as many receptive females as possible.
Lepidophthalmus siriboia showed a female-biased operational sex ratio (OSR).This outcome contradicts the hypothesis that anisogamy produces a male-biased operational sex ratio (OSR) leading to males competing for mates (sensu Trivers 1972).Our results suggest that not only males compete for the monopolization of a resource.The latter was supported by the existence of an evident sexual dimorphism of cheliped size and heterochely, a condition that argues in favor of female-female competition in L. siriboia.While it is true that males have larger and more ornamented chelipeds than females, the latter develop weapons that might be used to defend burrows against invasion from other shrimps from the same or opposite sex.In this sense, carrying eggs and caring for them until they are released as larvae, as is the case of burrowing shrimps, is energetically costly.Therefore, the need to have an immediate refuge (i.e.her own burrow) to defend offspring seems to be particularly acute for L. siriboia females.Unfortunately, our observations do not allow further conclusions about female-female competition in L. siriboia.We argue in favor of additional experimental studies to reveal possible behavioral strategies displayed by female individuals of this species.
Despite the lack of statistically significant differences in body size, females in L. siriboia were, on average, larger than males (i.e. the P-value was marginally significant), which supports the findings reported in other populations of the same species (Rosa Filho et al. 2013) and for other species of burrowing shrimps in which natural selection favors a larger female body size compared to males (e.g.Filhollianassa filholi : Devine 1966;C. corruptus: Botter-Carvalho et al. 2007).This pattern is consistent with our idea that males, but not females, leave their own burrows in search of mates, since a smaller body size should make it easier for them to move between galleries.Conversely, sexual selection favors the development of larger female body sizes than males because females tend to invest more energy into somatic growth than males when their reproductive success (i.e.fecundity) depends on reaching a larger body size (Huber 2005).In decapods, such evolutionary trend is explained because fecundity increases with female body size (Corey & Reid 1991;Hines 1991;Reid & Corey 1991;Hernáez & Palma 2003;Hernáez et al. 2008, among others).
Most adult males and females in L. siriboia had one massive (i.e.larger and strong) cheliped, either on the right or left side.According to our observations, male cheliped ornamentation is more suitable for fighting than the female version.This assumption agrees with the idea that males from most burrowing shrimps (e.g.Devine 1966;Rodrigues 1985;Nates & Felder 1999;Shimoda et al. 2005;Hernáez et al. 2015) and other decapods (e.g.Hartnoll 1978Hartnoll , 1982;;Baeza & Asorey 2012), invest heavily in chelipeds that probably are used as weapons during the male-male sexual competition or during territory defense (Rodrigues & Höld 1990).
The absence of male-female shrimp pairs occupying the same burrow made it impossible to determine the size association between sexes in L. siriboia.Consequently, we cannot know if pair formation in this species is determined by the female choice or intrasexual competition or by a combination of both (Heuring & Hughes 2020).Nonetheless, our analysis of sexual selection on the basis of morphological traits (i.e.allometric scaling analysis of the major cheliped in both sexes) suggest that the major cheliped is sexually selected in both sexes, albeit fulfilling different roles during the postlarval stage of males and females.In males, the major cheliped is mainly used as a weapon during male-male sexual competition, whereas in females it is attributed to burrow defence during incubation of the embryos.In the case of males, sexually selected traits used in male-male competition are more likely to exhibit positive and marked allometry when compared to other non-sexually selected traits, because the information being signalled is many times the difference between winning and losing when males compete for receptive females (O'Brien et al. 2018;Somjee 2021).We assume that both the smaller body size and the development of a massive cheliped in males of L. siriboia are traits that favor on the one hand the movement of individuals between burrows and on the other hand the competition against other males during the search for receptive females.Taking this scenario into account, males would not need to achieve a large body size since a large and heavy body may discourage the search for more sexual partners.Thus, the information signalled as: "I am faster than you" might be more relevant than "I am bigger than you" (Eberhard et al. 2018).Taking into account this fact, in burrowing shrimps, males with larger chelipeds will have comparative advantages when competing against others with smaller chelipeds during male-male sexual competition or during territory defence (Shimoda et al. 2005;Hernáez & João 2018;Hernáez et al. 2021).
Overall, males in L. siriboia may compete in ways that maximize the rate they encounter females, but neither defend females nor resources (i.e.female burrows).Females, for their part, invest a part of their energy in weapons used in defence of their burrow which is crucial for embryo development.Based on all of the above, the mating system in L. siriboia may be classified as polygamous, with polygynous  and c) hypothetical scenarios; the right male having a larger body size than left.Male and female individuals occupy their respective burrows during the non-reproductive season (a); sexually active male (left burrow) invades the burrow of receptive female (centre burrow -note ovary development) after digging a temporary connection from its burrow to nearby female burrow during reproductive season (b); male returning to its own burrow (left burrow) after copulation with the receptive female, the latter carrying eggs (centre burrow -note eggs carried externally) and male (right burrow) digging a temporary connection from its burrow to another nearby burrow in search of receptive females (c).The right male being larger than left.
males.Behavior of this species could be modelled under three hypothetical scenarios (Fig. 6a-c).The first would be non-reproductive behavior, with each shrimp living alone within its own burrow and carrying out burrow maintenance activities (Fig. 6a).The second would be reproductive behavior in which the females produce pheromones that are detected by the sexually active males; males dig a temporary connection from their burrows to another nearby burrow in search of receptive females (Fig. 6b) and after copulation, each male moves back to its own burrow and promptly starts to close the connection between burrows (Fig. 6c).The third and last scenario would see the solitary female carrying her eggs until the larvae hatch while the males continue to search for other receptive females (Fig. 6c).Lastly, the conventional and old idea that sex roles involve caring females and competitive males takes on significant value in the L. siriboia burrowing shrimp (Trivers 1972).

Fig. 1 .
Fig. 1. -Dorsal view of male (a) and female (b) individuals of the intertidal burrowing Lepidophthalmus siriboia, scale bar = 1 cm.Schematic representation of a cheliped showing the appendicular measurements (i.e.carpus length and carpus height) used to calculate the area of the major and minor cheliped in males and females of L. siriboia; scale bar = 5 mm, setae omitted (c).Geographical position of the study area (d).

Fig. 4 .
Fig. 4. -Sexual selection in Lepidophthalmus siriboia.The scaling relationship between carapace length and major cheliped (white circles) and minor cheliped size (grey circles) in males (a) and females (b) of the burrowing shrimp Lepidophthalmus siriboia.In the corner, the slopes of the regression lines adjusted for each body trait relationship are provided.The equations that originated the regression lines plotted are shown inTable 1b, d.

Fig. 5 .
Fig. 5. -Allometric growth in Lepidophthalmus siriboia.Relative growth of the major cheliped as a function of carapace length in juvenile and adult male (a) and female (b) of the burrowing shrimp Lepidophthalmus siriboia.The equations that originated the regression lines plotted in each chart (a, b) are shown in the log 10 -form in Table2a.

Fig. 6 .
Fig. 6. -Behavior of the burrowing shrimp L. siriboia during one observed (a) and two (band c) hypothetical scenarios; the right male having a larger body size than left.Male and female individuals occupy their respective burrows during the non-reproductive season (a); sexually active male (left burrow) invades the burrow of receptive female (centre burrow -note ovary development) after digging a temporary connection from its burrow to nearby female burrow during reproductive season (b); male returning to its own burrow (left burrow) after copulation with the receptive female, the latter carrying eggs (centre burrow -note eggs carried externally) and male (right burrow) digging a temporary connection from its burrow to another nearby burrow in search of receptive females (c).The right male being larger than left.