Differences in prevalence of multiple paternity in the spiny spider crab Maja brachydactyla in two localities that differ in female fecundity, ﬁshing intensity, and management measures

and A. Differences in prevalence of multiple paternity in the spiny spider crab Maja brachydactyla in two localities that differ in female fecundity, ﬁshing intensity, and management measures. – Many marine species are under high ﬁshing pressure, which can cause alterations in their mating systems and the structure of their populations. The spiny spider crab Maja brachydactyla is a commercial decapod on the east Atlantic coast. In Galicia, the most exploited region in Spain, the landing of ovigerous females is prohibited, favouring exploitation focused on males. The removal of males, especially the largest ones, may lead to sperm limitation and a reduction in the average size over generations. In these cases, polyandry can work as a mechanism to protect females against sperm limitation and to increase genetic diversity and effective population size. This study analyses the multiple paternity in M. brachydactyla in two localities that differ in female fecundity, ﬁshing intensity, and management measures. Our results showed multiple paternity in this species for the ﬁrst time, with a moderate bias between sires. However, the frequency of multiple paternity was almost seven times higher in the intensely exploited Golfo A´rtabro (NW Spain; 69%) than in Carna (W Ireland; 10%), where exploitation levels and female fecundity are lower.


Introduction
For an adequate management of commercial species, a detailed understanding of their mating systems and biological traits, such as size and age distributions and the intensity of sexual selection, is essential (Emlen and Oring, 1977). In marine species, the selective mortality caused by fishing produces disturbances in these mating systems (Hankin et al., 1997;Gosselin et al., 2005;Sato et al., 2010;Robertson and Butler, 2013;Rains et al., 2016;Pardo et al., 2017). When management measures are aimed at protecting particular sizes or a specific sex, these disturbances are accentuated and an alteration of the structure of the population and a reduction of reproductive potential may occur. This is the case of several crustacean fisheries regulated by minimum landing sizes and prohibitions on the landing of ovigerous females. In these fisheries, the largest males, with a high commercial value, are the main target (Orensanz et al., 1998), resulting in changes in the sex ratio and in the relative male/female size (Kennelly, 1992;Pillans et al., 2005;MacDiarmid and Sainte-Marie, 2006;Fenberg and Roy, 2008;Pardo et al., 2015;Alborés et al., 2019). In femalebiased populations, males have more mating opportunities. In such situations, sperm reserves may not recover between copulations or mating seasons (Kendall and Wolcott, 1999;Sato et al., 2005;Sainte-Marie, 2007;Pardo et al., 2015) or males may invest small amounts of sperm across many mates (Rondeau and Sainte-Marie, 2001;Pardo et al., 2015). In addition, the removal of the largest males will force many females to copulate with V C International Council for the Exploration of the Sea 2021. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. smaller males that may be unable to fill their seminal receptacles and whose sperm plugs may be too small to be effective in preventing further inseminations. All of these situations may cause sperm limitation, promote promiscuity of females, and the consequent multiple paternity of their clutches (Kendall et al., 2002;Gosselin et al., 2003Gosselin et al., , 2005Hines et al., 2003;Hill et al., 2017). It has been suggested that overexploited sex-and size-selectively fished populations use multiple paternity as a compensation mechanism to maintain genetic diversity (Morán and García-Vázquez, 1998;Jennions and Petrie, 2000) and effective population size (Sugg and Chesser, 1994;Martínez et al., 2000;Pearse and Anderson, 2009), as well as to reduce inbreeding (Stockley et al., 1993;Yasui, 1998). Moreover, it has been reported that in populations where there is selective extraction of males, the remaining ones invest less time in mate guarding and they may be smaller than the female they protect (Wilber, 1989;Rondeau and Sainte-Marie, 2001;Pardo et al., 2016), increasing the probability of polyandry and the risk of injury or death of females (Sainte-Marie and Hazel, 1992;Sainte-Marie et al., 2008).
Maja brachydactyla Balss, 1922, is a brachyuran crab of the family Majidae (De Grave et al., 2009;Ng and Richer de Forges, 2015) that occurs in the northeastern Atlantic, from the south of the North Sea to Senegal, including Madeira, the Azores, the Canary Islands, and Cape Verde (Monod, 1966;Kergariou, 1984;Neumann, 1998;Udekem d'Acoz, 1999;Sotelo et al., 2008). Females of eubrachyuran crabs have a pair of seminal receptacles that allow them to store sperm from different copulations and use it for fertilization of successive broods without the need for new matings (Hartnoll, 1968;Diesel, 1991;González-Gurriarán et al., 1998;McLay and Ló pez Greco, 2011). The number of broods per annual cycle and the breeding season of M. brachydactyla varies with latitude due to differences in water temperature (Kergariou, 1984). Females lay up to three broods annually in Galicia (NW Spain) , up to two in France (Kergariou, 1984) and one in Ireland (Rodhouse, 1984;Fahy, 2001).
Maja brachydactyla is a species of great commercial value fished in several countries, such as Spain, United Kingdom, Ireland, France, Portugal, and Morocco (Kergariou, 1984;Le Foll, 1993;González-Gurriarán et al., 1998). Fishing of this species is conducted using multiple gears, although tangle and gill nets are most common in the south of the distribution area and traps in the north (Kelly et al., 2003). The present study is focused on two populations of spiny spider crabs: one in the Golfo Á rtabro (43 21 0 49 00 N 8 21 0 54 00 W, Galicia, Spain) and the other in Carna (53 19 0 13 00 N 9 50 0 36 00 W, Co. Galway, Ireland). The M. brachydactyla fisheries in these two regions differ in their characteristics, such as landings (Table 1) and management measures. Galicia is the principal fishing region of this species in Spain, with around 330 t landed annually (Xunta de Galicia, 2010-2019. In the Ría de Arousa (Galicia), it has been suggested that more than 90% of newly mature specimens are caught each year . In Galicia, there is a fishing closure from June to November, coinciding with the period of terminal moult to adulthood and reproductive migration (González-Gurriarán et al., 1993Bernárdez et al. 2005;Corgos et al., 2006), and the landing of ovigerous females is not permitted during the whole annual cycle. In addition to this, there is a minimum legal landing size of 120 mm of carapace length (CL) for both sexes (DOG N 133, 2019). In contrast, in Ireland, the only regions with an established spider crab fishery to date are Brandon Bay, Tralee Bay, and some regions of the southeast coast (Tully et al., 2006;Fahy and Carroll, 2009;Tully, 2017). Some targeted fishing for large spider crabs occurs periodically in other regions, but populations are not heavily exploited and the species has expanded its range in Ireland in recent decades. In Carna, the spiny spider crab are only caught in small amounts as by-catch in fisheries targeting Homarus gammarus and Cancer pagurus. On the Irish coast, the only restriction on spider crab fishing is a minimum landing size of 130 mm of CL for males and 125 mm for females (Kelly et al., 2003;Fahy andCarroll, 2009). 2003 The aim of this work is to analyse the paternity of the broods of the spider crab M. brachydactyla in two populations with different female fecundity, fishing intensity, and management strategies.

Study specimens
For paternity analysis, 23 ovigerous females ranging in CL from 122 to 180 mm were captured. Thirteen of these were caught by divers in the Golfo Á rtabro, Spain, with a permit emitted by the Consellería do Medio Rural e do Mar of the Xunta de Galicia (regional government, resolution of 18 February 2014) and 10 were caught by local fishermen in Carna, Ireland. The 13 Spanish ovigerous females were captured in January to February, when they were carrying the first brood of the annual cycle. The ten Irish ovigerous females were captured in June, when they were carrying their only brood of the year.

Sample collection
The females from Arousa and Rosslare were dissected and gonads were sampled. All these specimens were cold-anaesthetized at À20 C for 10 min before being sacrificed. From the remaining adult individuals, including the ovigerous females, autotomy of a pereiopod was induced by performing a puncture in one of its joints in order to collect a muscle sample. Ovigerous females were kept in captivity until their first brood reached the developmental stage B described by González-Gurriarán et al. (1993), because eggs from that brood stage are the most suitable for DNA extraction (Rodríguez-Pena et al., 2017). For brood sampling, the eight egg masses adhered to the pleopods were numbered from one to eight, and eggs were collected in a zigzag pattern from pleopods 1, 4, 5, and 8 ( Figure 1). This sampling method allowed us to assess if there was an orderly distribution of the eggs fertilized by different males in the abdominal cavity of the female. If a pattern existed, sampling eggs from different areas of the brood would be more appropriate for detection of multiple paternity than completely random sampling. The egg samples of the females from Golfo Á rtabro were preserved in absolute ethanol until DNA extraction. On the other hand, the samples collected in Carna (Ireland) were frozen and lyophilized to facilitate their transport.

DNA extraction
DNA was extracted from the muscle or gonad of the 141 adult individuals, including the 23 ovigerous females. In addition to this, pooled and individual eggs were processed. For six of the females from the Golfo Á rtabro, DNA was extracted from a pool of five eggs from each pleopod sample, resulting in a total of four pools per female (20 eggs per female). Moreover, the DNA from 8 to 12 individual eggs (2-3 eggs from each pleopod) was extracted for all the ovigerous females.
DNA extraction was conducted using the NZY Tissue gDNA Isolation kit (NZYTech, Portugal), following the protocol indicated by the manufacturer for DNA extraction from animal tissues. After adding the lysis buffer and proteinase K, the samples were homogenized and incubated at 55 C overnight. Sotelo et al. (2007) described specific microsatellites for M. brachydactyla. These microsatellite markers were tested but there were problems in amplifying them correctly. In order to develop new specific markers, a microsatellite-enriched genomic library from a gonad sample was constructed at AllGenetics & Biology SL (A Coruña, Spain). The library was prepared using Nextera XT DNA Library Preparation kit (Illumina), following the manufacturer's instructions, and was enriched with the microsatellite motifs AC, AG, ACG, and ATCT. Once enriched, the library was sequenced in the Illumina MiSeq PE300 platform (Macrogen Inc., Seoul, Korea). A total of 4 035 302 reads were obtained and processed using Geneious 11.1.2 (Kearse et al., 2012) and inhouse developed scripts. For primer design, sequences containing microsatellite loci were selected. Primer pairs were designed using Primer3 (Untergasser et al., 2012) for PCR amplification of 500 microsatellite loci, with primers hybridizing at the flanking regions of tandem repeats.

Microsatellite development and analysis
After preliminary studies, nine microsatellite loci (GenBank accession numbers: MT211631 to MT211639) were selected for having amplified in 73 individuals from the Galician sampling location and 68 from the Irish location. PCRs were performed in a final reaction volume of 12.5 ml, containing 1 ml of DNA (10 ng/ ml), 6.25 ml of the Type-it Microsatellite PCR Kit (Qiagen), 4 ml of PCR-grade water and 1.25 ml of the primer mix. The optimal PCR protocol consisted in an initial denaturation step at 95 C for 5 min, followed by 30 cycles of 95 C for 30 s, 57 C for 90 s, 72 C for 30 s; 8 cycles of 95 C for 30 s, 53 C for 90 s, 72 C for 30 s; and a final extension step at 68 C for 30 min. All PCR batches included a negative control to check for potential cross-contamination. Oligonucleotide tails were attached to the 5 0 ends of the primers to allow for fluorescent labelling. The oligonucleotide tails used were the universal sequences M13 (5'-GGAAACA GCTATGACCAT-3 0 ') and CAG (5'-CAGTCGGGCGTCATC-3 0 '). The two oligonucleotides were labelled with the HEX dye and the FAM dye, respectively. The software Geneious 11.1.2 was used for the analysis of fluorescent profiles and to identify the allele peaks. For each locus (except AG_Mbr_215) and study area, number of alleles (N a ), observed (H o ), and expected (H e ) heterozygosity, deviations from Hardy-Weinberg equilibrium (HWE) and inbreeding coefficient (FIS) were estimated using GenAlEx 6.5 (Peakall and Smouse, 2006). Null allele frequency was estimated using FreeNA (Chapuis and Estoup, 2007).

Considerations for the paternity analysis
First, the PrDM software (Neff and Pitcher, 2002) was used to determine the probability of detecting multiple paternity in a brood. This programme is based on a Monte Carlo simulation, so the probability of detecting multiple paternity may vary slightly in each run. To minimize this effect, ten iterations were performed for each case and the average was computed. Simulations were performed varying the number of loci, the prevalence of multiple paternity, the percentage of contribution of the different sires, and the number of eggs analysed. In addition to this, the software GERUD 2.0 (Jones, 2005) was used to calculate the exclusion probabilities for different loci combinations. The method described by Veliz et al. (2017) for species with high fecundity was used to evaluate the statistical power at population level. In this case, the following parameters were varied: the number of females analysed, the number of eggs analysed per female, the prevalence of multiple paternity, and the contribution of male 1 (the one that fertilizes most of the brood) and male 2 (other males that participate in the fertilization of the brood). This method takes into account the fecundity of the study species. Verísimo et al. Figure 1. Abdomen of a spider crab female with numbered pleopods for sample collection in zigzag. The egg samples for paternity analysis were collected from pleopods 1, 4, 5, and 8.

Differences in prevalence of multiple paternity
(2011) determined that the fecundity of female spider crabs ranged from 125 081 to 530 309 eggs, with an average of 300 192 6 92 912 eggs. For simulations used here, the approximate value of 300 000 eggs was used.

Paternity analysis
Three loci (AG_Mbr_050, AG_Mbr_317, AG_Mbr_438) were selected for the paternity analysis. In a first phase, the egg pools of the six females were analysed to determine if multiple paternity existed in M. brachydactyla. In a second phase, the individual eggs of the 23 broods were genotyped. The 23 corresponding mothers were also genotyped from muscle samples. The PCR protocol was the same as that described for the amplification of the nine microsatellite loci in the subsection "Microsatellite development and analysis".
Genotypes were established using Geneious 11.1.2. The number of broods with multiple paternity, the number of sires of each brood, and the most likely paternal genotypes were determined using the allele frequencies of each study area and the software GERUD 2.0. Taking into consideration the most probable parents, the egg genotypes were checked to determine how the alleles of the different sires were distributed throughout the brood.

Statistical analysis
Possible differences in the prevalence of multiple paternity between the two study localities and the effect of maternal size were examined using a multiple logistic regression analysis conducted with the statistical program R 3.6.3 (R Core Team, 2020).

Microsatellite characterization
Preliminary microsatellite analysis showed that the number of alleles varied between 2 and 15 across the nine loci, being quite similar in both regions (Table 2). Moreover, the loci deviating significantly from the HWE were the same in both areas, except for AG_Mbr_317, which was only significant in NW Spain. The FIS values suggest that there is no inbreeding in either population.

Paternity analysis
For the nine loci, the exclusion probability was calculated by indicating that the genotype of one progenitor was known (Table 3). Three loci with a high individual exclusion probability were selected and their combined exclusion probability was compared with the combined exclusion probability of the nine loci. The exclusion probability for the three selected loci (AG_Mbr_317, AG_Mbr_050, and AG_Mbr_438) was >0.9 for the NW Spain and the SW Ireland sites (0.9427 and 0.9166, respectively). Although by including the nine loci the exclusion probability increases slightly, this does not compensate for the large increase in costs that would result from tripling the number of loci analysed. For this reason, only three loci were amplified for the paternity analysis.
In the initial phase of egg pool analysis, the existence of multiple paternity in M. brachydactyla was confirmed. More than three non-maternal alleles were detected in four of the six broods examined. For the individual eggs, the results obtained with GERUD 2.0 indicated that at least 10 of the 23 broods analysed had been fertilized by more than one male (Table 4). In the broods with multiple paternity, the minimum number of sires was always two, except in one brood where alleles of three males were detected. The contribution of each male to the fertilization of the broods was calculated over the total number of eggs that could be unequivocally assigned to one father. In the case of broods fertilized by two males, the contribution of the main male ranged from 50 to 87.5% (Figure 2). For the brood with three sires, GERUD 2.0 offered four solutions with the same likelihood, three with equal contribution of the males (33.33% each one) and one with a contribution of 40% for males 1 and 2 and a contribution of 20% for male 3. However, these percentages are an approximation since only a small proportion of the whole brood was analysed. Once the eggs from different pleopods were assigned to each father, it was found that, in at least six of the ten broods, the eggs fertilized by different males were partially or totally mixed in the female abdomen. In the remaining four broods, the possible existence of a pleopod pattern in the distribution of the paternal alleles could not been rejected.
The calculation of the probability of detecting multiple paternity in a brood made with the PrDM software indicated that this probability was considerably higher when analysing three loci (AG_Mbr_438, AG_Mbr_317, AG_Mbr_050) than when analysing two (AG_Mbr_317, AG_Mbr_050), but the increment was moderate using five loci (AG_Mbr_325, AG_Mbr_438, AG_Mbr_317, AG_Mbr_050, AG_Mbr_215) instead of three. Table 5 shows only cases in which two males were considered, since in similar conditions, as the number of sires increase, the probability of detecting multiple paternity also increases. For equal contributions from two males, three loci are sufficient to obtain a PrDM around 0.9 analysing 8 eggs and higher than 0.95 analysing 12 eggs. Nevertheless, for a skewed contribution, the probability of detecting multiple paternity decreases considerably.
To estimate the statistical power at the population level, the method described by Veliz et al. (2017) was used, which takes into account the fecundity of the species and the number of females analysed. For the simulations, it was assumed that 50% of the broods in the population were fertilized by more than one male and that the male contribution was biased (95:5), taking into account data reported in other crustacean species (Veliz et al., 2017). For 10 females, the statistical power was 0.8416 analysing 8 eggs and 0.9266 analysing 12. By increasing the number of females to 20, the statistical power also increased, being 0.9749 for 8 eggs and 0.9946 for 12.

Influence of maternal size and population on the prevalence of multiple paternity
Nine of the ten broods fertilized by more than one male came from the Golfo Á rtabro (NW Spain) while only one came from Carna (W Ireland). To determine if this apparent difference between populations was significant and to check if multiple paternity depends on maternal size, a multiple logistic regression model was used. In this model, the paternity of the broods of M. brachydactyla was studied as the independent variable with two levels (0: simple paternity, 1: multiple paternity). In addition, the independent variables "population" (with two levels; 0: Carna, 1: Golfo Á rtabro) and "maternal size" (continuous) were considered. The model proposed was the following: log (p/(1 -p)) ¼ A þ BX þ CZ þ Error, where p is the probability of multiple paternity in the Golfo Á rtabro, X is the maternal size variable, Z is the variable indicating population (Z ¼ 1 for the Golfo Á rtabro and Z ¼ 0 for Carna) and the coefficients of the linear model are A, B, and C. Once the model was adjusted with the available data, the estimates for the parameters were obtained: À9.75 for A, 0.054 for B, and 2.71 for C. The contrasts of significance for each parameter showed that C was significant (p-value ¼ 0.031), that is, the population of the female influences the probability of multiple paternity, but A and B were not significant (p-value ¼ 0.070 Differences in prevalence of multiple paternity No. eggs Pl.

Egg pattern
Golfo Á rtabro and 0.146, respectively), which indicates that the maternal size does not influence the probability of multiple paternity of the broods. For this reason, a simpler model excluding maternal size variable was formulated, using a Fisher's exact test to assess if prevalence of multiple paternity was independent of site. In this model, the dependent variable continued to be the paternity of the broods, while the only independent variable was the population of origin of the female. This test confirmed that the probability of multiple paternity is significantly higher in the Golfo Á rtabro than in Carna (Table 6), multiple paternity being almost seven times more frequent in the Spanish population (0.69) than in the Irish one (0.1).
Moreover, a simple logistic regression model was used to check if the size of the females was correlated with their population of origin. The results showed that the correlation between these variables was not significant (p-value ¼ 0.127).

Discussion
In decapods, broods fertilized by more than one male are the norm (Dennenmoser and Thiel, 2015;McLay and Dennenmoser, 2020). Table 7 summarizes the results of several paternity studies conducted in recent years. In general, the prevalence of multiple paternity is higher in species without specialized sperm storage structures, such as carideans and anomurans (in seven of the nine species, the prevalence was higher than 73%). These two taxa, with relatively few exceptions (e.g. Rasch and Bauer, 2016), do not have sperm storage structures, although they may have receptor areas for temporary holding of the spermatophores, which would allow multiple paternity. Within astacids, the species with annulus ventralis also showed high levels of prevalence (87% on average), while in species with thelycum, the percentage of broods fertilized by more than one male was considerably lower (28% on average). Regarding the analysed brachyurans, which had ventral type seminal receptacles, multiple paternity was not reported in 22% of the species and, in those in which it was detected, its prevalence was 37% on average. Nevertheless, the increase in the complexity of the sperm storage organs is usually associated with an increase in fecundity, since sperm storage allows for a greater number of eggs to be fertilized. This implies that, in species with more developed sperm storage organs, the proportion of offspring analysed in paternity studies is usually lower, which reduces the probability of detecting multiple paternity.
Paternity studies in species with dorsal seminal receptacles are scarce. Hill et al. (2017), analysed the paternity of one Callinectes sapidus clutch, a crab with dorsal seminal receptacles. They    Table 4).
Differences in prevalence of multiple paternity  The brood fertilized by three males was removed from the calculation. ND, no data.
detected multiple paternity in this clutch, but genotyping of the ejaculates stored by many more females suggested a low incidence of polyandry (5.3% of 75 females). This implies that the incidence of multiple paternity may be very low in nature. Due to the lack of more accurate data, C. sapidus was excluded from Table 7.
In the cases of species with multiple paternity, male bias in brood fertilization is very evident in taxa with internal organs of sperm storage, while it is not so obvious in groups without these types of organs.
It should be highlighted that in M. brachydactyla broods, the contribution of the dominant sire was relatively low (66% even excluding the brood with three sires) compared to that observed in other brachyurans (>79%), which could be explained by the arrangement of the sperm masses and the potential sperm mixing in the seminal receptacles. González-Gurriarán et al. (1998) discovered that in M. brachydactyla, when there are multiple sperm masses, they are arranged parallel to the major axis of the receptacles, and when these are very full, the masses are not organized in an orderly manner. Moreover, our observations made during dissections of females mated in captivity with various males suggested that, when copulations occur over short periods of time (from hours to weeks between copulations), it is not possible to distinguish defined sperm masses in the seminal receptacles of the female. Furthermore, in M. brachydactyla, copulation occurs between hard-shelled individuals, there is no post-copulatory guarding, and the existence of sperm plugs has not been reported . It is a species with a terminal moult in both sexes (Kergariou, 1984;Le Foll, 1993;Sampedro et al., 1999), so sperm stored in the seminal receptacles is not susceptible to be lost during moulting. In addition to this, Corgos et al. (2006) suggested that, in M. brachydactyla, small males migrate to mating areas earlier than large ones, probably to maximize their mating opportunities by avoiding agonistic interactions with larger males (Sainte-Marie et al., 1997Rondeau and Sainte-Marie, 2001;Correa et al., 2003). These small males provide females with small amounts of sperm that may be insufficient to fertilize all their eggs. This set of reproductive traits of M. brachydactyla favours polyandry and multiple paternity of broods.
In some of the female spider crabs where both pooled and individual eggs were analysed, the two methods yielded different results. In one of these females, two sires were detected in the pools but only one in the individual eggs. This may be due to the larger sample size (20 vs. 12 eggs) or due to randomness if the contribution of both males to the fertilization of the brood is skewed. In two other females, multiple paternity was not detected using the pool method but was found analysing individual eggs. This could be because one male with a low contribution to brood fertilization shows a low peak in the electropherogram, which may go unnoticed during genotyping of the eggs of the pools.
The zigzag sampling method did not serve to increase the probability of detecting multiple paternity. Although in four of the ten multiply sired broods a segregated pleopod pattern of the parental alleles could not be excluded, in six of them there was an evident mixing. This lack of organization of the paternal alleles had already been reported in some decapod species with less complex sperm storage organs, such as in Orconectes placidus (Walker et al., 2002) or Homarus americanus (Gosselin et al., 2005). This could be due to the mixing of different sperms in the seminal receptacles, the mixing of the eggs fertilized by different males in the abdomen of the female prior to their adhesion to the pleopods or, more likely, to a combination of both.
Our observations of specimens in captivity confirmed that, during oviposition, the eggs are free in the female abdomen where they mix with each other before adhering to the pleopods. On the other hand, in species where the oviduct is connected dorsally to the sperm storage organs, as in C. sapidus (Johnson, 1980), oocytes must pass through the receptacles to reach the vagina. In this case, it would be expected that the sperm of the first male, which copulated have priority in fertilizing the oocytes, although the entry of the oocytes into the receptacle could also favour multiple paternity (McLay and Becker, 2015). In contrast, in brachyurans such as Chionoecetes opilio (Sainte-Marie et al., 2000) and Inachus phalangium (Diesel, 1990), which have ventral type seminal receptacles, the oviduct is connected to the sperm storage organs at a point near the vagina, and the masses are stored dorsoventrally when the receptacles are not very full. These characteristics favour the sperm from the last male to copulate before oviposition, which is localized closest to the oviduct and vagina, being used first to fertilize the brood. Furthermore, larger males might deposit more seminal fluid than smaller ones. Since seminal fluid is probably implicated in the formation of the sperm plug and in the stratification of precedent sperm packages in several brachyuran species, larger males may be more successful in fertilization in a sperm competition context (Pardo et al., 2018).
Although M. brachydactyla also has ventral type seminal receptacles, the spatial arrangement of the sperm masses described in this species by González-Gurriarán et al. (1998) suggests that there is a mixing of the sperm of several males, which would explain the absence of spatial pattern of the paternal alleles within the brood. Koga et al. (1993) proposed that, if there is sperm mixing in the seminal receptacles, the male contribution should be equal (50:50), but this would only be true if two males supplied the female with equal quantities of ejaculate with similar spermatozoa concentration and viability. However, large males tend to provide a greater amount of sperm to females (Sato and Goshima, 2007;Butler et al., 2011;Pardo et al., 2018), which could result in broods dominated by eggs fertilized by the larger male.
In the case of Galician spider crabs, first broods of the annual cycle were analysed. This ensured that females carried high amounts of sperm in their receptacles, maximizing the probability of taking samples from a fully fertilized brood. During the breeding season, female spider crabs incubate their broods in shallow waters, while males remain in the mating areas at a depth of 30-100 m (Le Foll, 1993;Hines et al., 1995;Freire and González-Gurriarán, 1998;González-Gurriarán et al., 2002). Although direct observations by fishermen in the Golfo Á rtabro indicate that sometimes mating occurs in shallow areas after the return migration, the mating of the spider crab on the Galician coast occurs mainly in deep waters in winter (Corgos, 2004).
In general, both within a brood and at the population level, the simulations performed indicated that the probability of detecting multiple paternity was very high for the number of loci, eggs and females analysed in this study. However, the number of analysed females may be insufficient to establish a relationship between the existence of multipaternity and the maternal size. It would be expected that larger females would be able to store the sperm from more copulations in their receptacles. In addition, as they present a higher fecundity (Verísimo et al. 2011), larger females would need to use a greater quantity of the stored sperm, Differences in prevalence of multiple paternity thereby increasing the probability of finding multiple paternity in broods of multiple-mated females. For this reason, we believe that the absence of a relationship between multiple paternity and maternal size may be an artefact due to insufficient sample size. However, another possibility may be that males adjust the amount of ejaculate delivered to the female according to her size, as has been reported in other crustaceans (MacDiarmid and Butler, 1999;Sato et al., 2006). This would imply that large females may not necessarily store multiple sperm masses more frequently than small ones. Therefore, the analysis of a larger number of females, covering the entire size range of both populations, is necessary to clarify this aspect.
The differences in the prevalence of multiple paternity shown in Table 7 for the same species could be due to the analysis of an insufficient number of broods. Urbani et al. (1998) analysed seven broods of C. opilio and found single paternity in all of them. In contrast, Roy (2003) and Sainte-Marie et al. (2008) analysed the offspring of 79 and 20 females of this species, detecting the existence of multiple paternity in 3.8 and 12.5% of them, respectively. Nevertheless, in these cases the differences in the prevalence of multiple paternity may be also due to the different types of females examined [primiparous in Urbani et al. (1998) and Roy (2003); multiparous in Sainte-Marie et al. (2008)] and interannual variability in primiparous females [Roy (2003) considered females in 2 years with very different population sex ratios].
In the case of Metacarcinus edwarsii, the two paternity studies performed (Rojas-Hernández et al., 2014;Pardo et al., 2016) agreed that all the broods analysed (5 and 31) were fertilized by a single male. However, in this case, Pardo et al. (2016) determined that, with the loci and number of eggs analysed in each of the study locations, the PrDM was >0.99. Therefore, they concluded that in the M. edwarsii populations analysed there was really no multiple paternity, its prevalence was negligible or the contribution of the additional sires was too low to be detected.
Although overall prevalence of multiple paternity similar to that in other brachyurans has been recorded in M. brachydactyla (43.5%), the difference found between the population of the Golfo Á rtabro and that of Carna is remarkable. This fact indicates that the paternity of the broods is also influenced by external factors, and not only by the reproductive biology of the species. Below, we discuss a series of hypotheses that aim to explain the differences in the prevalence of multiple paternity between these two populations: (a) Differences in population density. Carna is a locality at the northern limit of the distribution of the spiny spider crab. This trait and the absence of a permanent fishery of this resource in the area (Tully, 2017) suggest that the population may be less dense than in the Golfo Á rtabro. The low density of specimens would limit the availability of sexual partners and, therefore, the level of polygamy. However, some studies have provided data that question the validity of this hypothesis. Kelly et al. (2003) conducted a study in Blackshod, Derrinver, and Cleggan (northernmost regions than Carna) to determine if the area was suitable for the establishment of a fishery targeting at M. brachydactyla. The results, including a CPUE value of $0.76 kg/pot, indicated that the area was appropriate to initiate the exploitation of the spider crab.
The same study suggests that the low recapture rate obtained could be due to the existence of a large stock. In addition, Rodhouse (1984) obtained CPUE data of $0.4 kg/pot in Kilkieran Bay, near Carna. Bates (1981) had already described the spider crab as a common species on the south and west coast of Ireland, where it was considered by fishermen as a pest due to tangling in large numbers in nets set for crayfish (Palinurus elephans). These studies suggest that the population of spider crab in Carna must be dense enough so that there is no shortage of sexual partners.
(b) Differences in female fecundity. As already mentioned, in Galicia females can lay up to three broods in a breeding season while in Ireland they only lay one. Furthermore, fecundity per brood also decreases as latitude increases (Kergariou, 1971(Kergariou, , 1984Verísimo et al., 2011). Since the annual fecundity of Galician females is higher than that of Irish ones, their demand for sperm should also be higher. For this reason, it would be expected that Spanish females will require a greater number of copulations to fill their seminal receptacles and to complete the fertilization of their three broods, while for Irish females one copulation per year may be enough (although another factor to take into consideration would be the quantity of ejaculate passed at each mating). Even though females could carry sperm from previous years in their seminal receptacles, it appears that sperm stored by M. brachydactyla females for more than 10 months shows high levels of genetic damage and has low viability (Rodríguez-Pena et al., unpublished data), so multiple paternity would be improbable with only one annual copulation.
(c) To the best of our knowledge, there is no previous works suggesting that females with high fecundity actively search for more copulations. Nevertheless, Paul (1984) and Lovrich and Sainte-Marie (1994) suggested that females of different species of Chionoecetes were probably capable of assessing their sperm reserve, because they delayed egg extrusion when insufficiently inseminated, presumably in the 'hope' of encountering another mate.
(d) Different levels of sex-and size-selective exploitation. Differences in the level of polyandry between areas with different fishing intensity have been reported in other decapod species (Gosselin et al., 2005;Pardo et al., 2016).
Galicia is the region of Spain where exploitation of M. brachydactyla is most intense, while in Carna there is no stable fishery focused on spider crab. Moreover, in Galicia, M. brachydactyla is managed under a 3-S strategy (Season, Sex, and Size Control), while in Ireland the only measure in effect is size control. Management measures prohibiting the landing of ovigerous females result in male-selective fishing, especially of those of larger size with high commercial value (Fahy and Carroll, 2009). In addition, the individuals of extreme sizes are the scarcest in the population, so they are the most susceptible to disappear due to overexploitation. Several studies have provided data on the alteration of the sex ratio and population size structure caused by size-and sex-selective fishing of spider crab. Within lightly exploited populations, males far outnumber and outsize females (Brosnan, 1981;Rodhouse, 1984;Fox, 1985;Kelly et al., 2003). However, in areas with intense male-selective fishing, the proportion of males and females tends to be similar or slightly female-biased, and both sexes tend to be similar in overall size (Fahy, 2001;Corgos et al., 2006;Fahy and Carroll, 2009). This alteration of the population structure can lead to sperm limitation (Hines et al., 2003;Sato and Goshima, 2007;Sato et al., 2010;Pardo et al., 2015), which may promote multiple mating to ensure the fertilization of the broods. On the other hand, when females mate with multiple small males, even assuming that they obtain a sufficient amount of sperm, the trend over generations may be downwards in the average size of the individuals of the population, as the general ecological and evolutionary literature suggests (Fenberg and Roy, 2008). This will lead to a reduction of the reproductive potential at population level (Sato and Goshima, 2007;Butler et al., 2011;Verísimo et al., 2011). Moreover, our observations under laboratory conditions confirm that small males have difficulties in copulating with females that far outsize them. Therefore, the removal of large males from the population could cause the number of partners compatible with large females to fall.
Taking into account the considerations summarized in point (c), genetic polyandry in the Golfo Á rtabro may be functioning as a compensatory mechanism to avoid sperm limitation caused by a shortage of males, especially those of large size.
In the present study, multiple paternity was reported for the first time in M. brachydactyla, with an overall prevalence of 43.5% and a moderate bias between sires, unlike in other brachyurans. However, the frequency of multiple paternity was almost seven times higher in the intensely exploited Golfo Á rtabro than in Carna, where exploitation levels are low. This difference in the prevalence of multiple paternity could be due to the differences in fertility of M. brachydactyla females in these two latitudes or to the different levels of male-selective fishing for this species in these two localities.
To test these hypotheses it would be informative to analyse the paternity in broods from the Magharees region (Ireland). This population is characterized by intense exploitation focused on large males (Rodhouse, 1984;Fahy and Carroll, 2009) and by an annual cycle of one brood. A low prevalence of multiple paternity, similar to that found in Carna, would suggest that the annual fecundity of females is a factor that can influence the level of polygamy in the population. However, a high frequency of multiple paternity would suggest situations of sperm limitation caused by sex-and size-selective fishing. In addition, genetic analysis of ejaculates from the seminal receptacles of M. brachydactyla females from Carna would be useful to clarify whether the absence of multiple paternity in this locality is due to the absence of multiple mating or to other factors.

Data availability
The microsatellite data of this article are available in the GenBank Nucleotide Database at https://www.ncbi.nlm.nih.gov/genbank/, and can be accessed with accession numbers MT211631 to MT211639.