Behavioral Ecology Advance Access originally published online on November 8, 2006
Behavioral Ecology 2007 18(1):215-221; doi:10.1093/beheco/arl071
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Interference from a game theoretical perspective: shore crabs suffer most from equal competitors
Royal Netherlands Institute for Sea Research (NIOZ), Department of Marine Ecology and Evolution, PO Box 59, NL—1790 AB, Den Burg, Texel, The Netherlands
Address correspondence to I.M. Smallegange, who is now at Max Planck Institute for Ornithology, Vogelwarte Radolfzell, Schlossallee 2, 78315 Radolfzell, Germany. E-mail: smallegange{at}orn.mpg.de.
Received 20 March 2006; revised 26 July 2006; accepted 23 September 2006.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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In virtually all natural systems, interference competition among individuals is asymmetric. Here, we used game theoretical models on contest behavior to predict how time lost in agonistic interactions could affect strength of interference under asymmetric competition. We hypothesized that interference through time lost in agonistic interactions would result in a greater reduction in available foraging time and overall feeding rate under symmetric competition than under asymmetric competition. We tested this hypothesis for male shore crabs (Carcinus maenas) that foraged on mussels (Mytilus edulis) in an experiment where prey levels were kept constant. We varied absolute size of crabs (juveniles, small adults, large adults), mussel density (4, 16, 32 per 0.25 m2), and competitor size (smaller, equal, larger). Large adults spent more time in aggressive behaviors than juveniles or small adults, possibly because large adults were more persistent in interfering or because large adults were intrinsically more aggressive, as the experiment was conducted in the mating season. When handling prey, crabs mostly avoided competitors, but juveniles and small adults did so more than large adults. When searching for prey, crabs mostly displaced smaller competitors but threatened or avoided size-matched or larger competitors. By avoiding a competitor, the focal crab lost time but the competitor often did not, and this asymmetry in agonistic behavior is not yet incorporated in models on contest behavior. However, overall, negative effects of others were strongest with size-matched competitors, in line with our hypothesis.
Key words: aggressive behavior, dominance, energetic war of attrition, functional response, ideal free distribution, sequential assessment game.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Competition among foragers can be exploitative, in which case foragers reduce the feeding rates of others indirectly by reducing available prey. Foragers can also directly reduce the feeding rates of others when they compete over prey through social interactions, which is referred to as interference competition (Begon et al. 1990
). Interference competition among foragers is either symmetric or asymmetric (Keddy 1989). In the former case, animals have a similar effect upon one another, but in any population individuals are not intrinsically equal and interference competition among foragers is thus mostly asymmetric. Through interference competition, competitively superior individuals may gain relatively more access to shared prey by negatively affecting the foraging behavior of competitively inferior individuals (Vahl et al. 2005) and may even exclude individuals from a mutually preferred feeding site (Donazar et al. 1999; Franke and Janke 1999; Sol et al. 2000; Davey et al. 2005). In this way, asymmetric interference competition can affect the structure of local populations and together with forager density drive the population dynamics of species (Nilsson 2001; Aljetlawi and Leonardsson 2002).
The mechanisms through which interference competition arises vary. In agonistic interactions, foragers may lose prey items to kleptoparasitic competitors (Brockmann and Barnard 1979) or foragers may lose valuable foraging time and energy associated with agonistic interactions. Exactly in what way asymmetries in competitive ability affect the intensity and outcome of agonistic interactions is the central focus of game theoretical models on contest behavior. Examples of such game theoretical models are the sequential assessment model (SAM) (Enquist and Leimar 1983; Leimar and Enquist 1984; Enquist et al. 1990), war of attritions (WOAs) (WOA without assessment [WOA-WA], Mesterton-Gibbons et al. 1996, and the energetic WOA [E-WOA], Payne and Pagel 1996, 1997; Payne 1998), and the cumulative assessment model (CAM) (Payne 1998). These game theoretical models assume different dynamics of an agonistic interaction and a different process of termination of an agonistic interaction. However, all models predict a similar relationship between the difference in competitive ability between 2 contestants and the duration of their agonistic interaction (Taylor and Elwood 2003): as the competitive abilities of the 2 contestants become more evenly matched, the duration of their agonistic encounter increases. Hence, regardless of whether agonistic interactions between animals are played out according to SAM, WOA-WA, E-WOA, or CAM, interference through time lost in agonistic interactions is always predicted to be stronger under symmetric competition than under asymmetric competition. As a result, the reduction in foraging time would be highest for foragers that encounter an individual of equal competitive ability. For foragers that encounter a competitively inferior individual, or even a competitively superior individual, the reduction in foraging time would be minimal.
In this study, we aim to assess the strength of asymmetric interference competition for shore crabs (Carcinus maenas [L.]) that forage on mussels (Mytilus edulis [L.]). We hypothesize that strength of interference in terms of time lost in agonistic interactions is stronger under symmetric competition than under asymmetric competition. Therefore, crabs that encounter a conspecific of equal competitive ability are predicted to suffer a greater reduction in available foraging time and thus overall have lower feeding rates than crabs that encounter a conspecific that is of a different competitive ability. Shore crabs are good subjects for this work because they mainly suffer interference through time lost in agonistic interactions, at least under symmetric competition (Smallegange et al. 2006). Also, their competitive ability in agonistic interactions is highly correlated with the size of their larger claw (Sneddon et al. 1997), which makes this an easy variable to manipulate. Larger crabs are then competitively superior to smaller crabs in agonistic interactions, but smaller crabs may be competitively superior with respect to exploitation competition (under limiting food conditions) (Persson 1985). Therefore, to prevent exploitation competition, we use an experimental tank that is specifically designed to replenish (almost instantaneously) each consumed prey (Smallegange et al. 2006). In an experiment, we then score the time budget and feeding rates of juvenile and adult shore crabs in relation to the size of their competitor and the availability of prey.
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METHODS |
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Predators and prey
Male shore crabs were caught in July 2002 from a fyke located at the south tip of Texel, The Netherlands. Shore crabs were maintained in individual holding tanks (18.0 x 12.5 x 6.5 cm) with a 1-cm layer of sand at the bottom. Tanks were kept submerged in a large basin with continuously running seawater. Water temperature in the basin was between 18 and 21 °C. Photoperiod was kept at a 12:12 h light:dark cycle with the experiment carried out in the light period. Only undamaged right-handed male crabs that were predominantly green were used in order to reduce variability associated with morphology, gender, and molt status. Major chela length (MCL) in shore crabs is highly correlated with their competitive ability in agonistic interactions (Sneddon et al. 1997
). Therefore, crabs were sized according to their MCL using electronic calipers, and we also measured their carapace width (CW: the distance between the tips of the outermost lateral spines on the carapace). Crabs were then assigned to one of 3 sizes that correspond with 3 life stages: juveniles (MCL: 14–17 mm, CW: 28–31 mm, n = 25), small adults (MCL: 19–25 mm, CW: 36–43 mm, n = 30), and large adults (MCL: 29–35 mm, CW: 51–58 mm, n = 25). Crabs were accustomed to circumstances in the laboratory for at least 1 week to equalize physiological states. Crabs had ad libitum access to mussels and were also fed cod and pollack bait every other day. Before the start of an experimental trial, crabs were starved for 2 days. Shore crabs can survive for 3 months without food (Wallace 1973). Hence, this short period of food deprivation sufficed to keep them healthy yet motivated to forage for food. After the experiment, crabs were held in the laboratory for 5 more days to make sure they were not in proecdysis (none were), after which they were released.
Samples of intertidal mussels were scraped from ballast piers at the coast of Den Helder, The Netherlands, in July 2002, and any attached fouling organisms were removed. We used mussels of maximum length 8–12 mm. For juveniles and small adults, this size range overlaps within their preferred and optimal size range (juveniles: 7–10 mm shell length; small adults: 10–15 mm shell length). For large adults, this size range is slightly lower than the preferred range of mussel sizes (14–21 mm shell length). However, crabs mainly reject mussels that are too big rather than too small, and therefore, this size range is suitable to offer the juveniles, small adults, and large adults (calculations are based on Smallegange and van der Meer [2003] where the preferred and optimal range of mussel width relative to MCL was 0.16–0.24). Mussels were kept in a large basin with continuously running seawater under the same light and temperature conditions as the crabs.
Behavioral observations and experimental design
To avoid detrimental effects of prey depletion, the experimental tank was divided into 2 compartments by a slowly rotating partition; while crabs foraged on one side of the partition, the observer replenished any eaten mussels on the other side (Smallegange et al. 2006). The time that crabs need to open mussels of 8–12 mm maximum shell length varies from 4 to 8 min depending on the size of the crab (Smallegange and van der Meer 2003). Therefore, the angular velocity of the partition was set at approximately 10 x 10–3 rad s–1, so that even in the most extreme case (i.e., lowest mussel density and 2 large adults eating at the same time) consumed mussels could be adequately replenished. Mussels were buried randomly just below the sediment surface.
In each experimental trial, 2 crabs, a focal crab and a competitor crab, foraged in the tank and the activities of only the focal crab were scored to obtain independent observations. We varied absolute crab size (juveniles, small adults, large adults), mussel density (4, 16, 32 mussels per tank), and competitor size (smaller, size matched, larger). Competitor sizes were chosen such that crabs of each (focal) size would forage with a smaller, size-matched, or larger competitor. For small adults, this resulted in the combinations small adult–juvenile, small adult–small adult, and small adult–large adult. To provide smaller competitors for juveniles and larger competitors for large adults, 2 additional crab sizes were distinguished, 11–14 mm MCL (n = 5) and >37 mm MCL (n = 5). This design entails that the relative size differences between focal and competitor crabs differed between the absolute crab sizes (juveniles, small adults, large adults). If juveniles, small adults, or large adults would therefore respond differently to the treatments, this would be reflected in a significant interaction "crab size x competitor size." All trials started when crabs had accustomed to the tank for 10 min. All trials were videotaped using a Sony digital video camera recorder DCR-TRV900E and analyzed using the Observer 3.0 (Noldus Information Technology 1997) as an event recorder. We scored the behaviors "search" (i.e., probing and moving of sand), "handle" (or eating), and "interfere" (avoid, displace, threat, fight). We also scored the number of kleptoparasitic events.
The experimental design followed a repeated measures approach with focal crabs as subjects, mussel density and crab size as the among-subjects factors, and competitor size as the within-subjects factor. Because competitor size is the within-subjects factor, this means that each focal crab was presented with each type of competitor (smaller, size matched, larger). The within-subjects factor and error term was decomposed into a linear and quadratic component. Hence, it could be tested whether crabs responded in a linear fashion to increasing competitor size (e.g., food intake rate would decrease or increase with increasing competitor size) or whether responses of crabs fell along a quadratic curve (e.g., food intake rate was highest or lowest with size-matched competitors). Treatment combinations were replicated 5 times. This means that for each combination of the among-subjects factors crab size and prey density, 5 focal crabs were used, which sums up to a total of 3 x 3 x 5 = 45 focal crabs. Each focal crab of each crab size was presented with a smaller, size-matched, and larger competitor crab, which were randomly selected from a stock of 15 competitor crabs (5 smaller, 5 size-matched, and 5 larger crabs). Because we had 15 competitor crabs available for each crab size, this sums up to 15 x 3 = 45 competitor crabs. In total, we conducted 135 observations or trials: 3 crab sizes x 3 prey densities x 3 competitor sizes x 5 replicates = 135. All trials were conducted in random order with the restriction that a focal or competitor crab was allowed a recovery period of at least 60 min after each trial (Rovero et al. 2000). Data analysis was concerned with the time period in which the focal crab searched for and ate one mussel (thus starting when the focal crab had finished eating a mussel and ending when the focal crab had finished consuming a second mussel). We refer to this period as total time, which is equal to the inverse of the standardized food intake rate.
The above design was used to test effects of variation in crab size, mussel density, and competitor size on handling time, search time, interference time (the sum of all time spent avoiding, displacing, threatening, fighting), foraging time (sum of search time and time spent interfering during searching), and total time (sum of search time, handling time, and interference time). Behavior durations were log transformed, assuming multiplicative effects of the various treatment factors. When necessary for log transformation, zero values of the variable of interest were replaced with the lowest observed value within that variable. Log-transformed interference time invalidated the normality assumption; therefore, a permutation approach was used to obtain significance levels (Manly 1997). A total of a 1000 random permutations of all observations were obtained, and each time the analysis was performed as a complete data analysis (in R, Ihaka and Gentleman 1996). The F-value obtained using the observed data was compared with the 95% point of the distribution of (sorted) F-values obtained from the random permutations, which we refer to as the critical F-value. Treatment effects on other response variables were analyzed with the appropriate procedures in SYSTAT 10 (SPSS Inc., Chicago, IL).
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RESULTS |
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In this experimental study, we investigated the agonistic and foraging behavior of juvenile, small adult, and large adult shore crabs in relation to variation in mussel density and the size of the competitor. Handling time differed between the different crab sizes (Table 1) and was highest for juveniles and lowest for large adults (Figure 1). Handling time was not affected by variation in mussel density (Figure 2) or competitor size (Figure 3) or any of the interactions (Table 1). Search time was affected by mussel density, crab size, and competitor size (Table 2). Search time decreased with increasing mussel density (Figure 2) and increased with increasing crab size (Figure 1). Search time also varied with competitor size (Table 2) and was highest for crabs that foraged with a size-matched competitor than with a smaller or larger competitor (Figure 3), which is reflected by the significant quadratic component of competitor size (Table 2). The time that crabs spent interfering also changed with variation in mussel density, crab size, and competitor size (Table 2). Interference time was much higher at the lowest mussel density than at the other mussel densities (Figure 2). In the process of finding a mussel, juveniles spent the least time interfering, whereas interference time was highest for large adults (Figure 1). Interference time also depended on the size of the competitor (Table 2) and increased linearly with increasing competitor size (Figure 3), reflected by the significant linear component of competitor size (Table 2). None of the interactions affected interference time (Table 2).
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), interference time (
), foraging time (
), and total time (
) for each crab size. Vertical lines are standard error of mean, but for some response variables, standard error lines are covered by the symbols. For each response variable, letters denote significant differences between the levels at 
= 0.05. There was no significant effect of crab size on total time.
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Because both interference time and search time decreased with increasing mussel density, foraging time (i.e., the sum of search time and time spent interfering during searching) also decreased with increasing mussel density (Table 2, Figure 2). Likewise, foraging time increased with increasing crab size (Table 2, Figure 1) and was highest for crabs that foraged with a size-matched competitor (significant quadratic component of competitor size Table 2, Figure 3). Total time (sum of search time, handling time, and interference time) did not differ between the different crab sizes (Table 1, Figure 1) because handling time decreased, but search time increased with increasing crab size and interference time was only a small part of handling and search time. Total time was also not affected by competitor size (Table 1, Figure 3). Total time did decrease with increasing mussel density (Table 1, Figure 2) because of a strong decrease in search time with increasing mussel density. One kleptoparasitic event occurred when a large adult was foraging at mussel density 4 and lost its mussel to a larger competitor.
We summarized the foraging behaviors search and handle and the interference behaviors "fight," "avoid," "displace," and "threat" in transition matrices to show the probability (P) with which handling and searching crabs engaged in interference behaviors in relation to the size of the competitor (Table 3). Because juveniles and small adults did not differ in their time spent interfering, we combined their transition matrices. Overall, juveniles and small adults were less aggressive than large adults because juveniles and small adults were most likely to handle prey after searching and vice versa, rather than to engage in aggressive behaviors like large adults. Crabs mostly avoided competitors when they were handling prey, but juveniles and small adults avoided competitors more often than large adults did. Crabs never displaced a larger competitor, and large adults never avoided a smaller competitor. Crabs were more likely to avoid a larger competitor while searching or handling than to displace a smaller competitor while searching or handling.
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DISCUSSION |
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Effect of absolute size and competitor size on interference behaviors
The relative time that juveniles and small adults spent interfering was lower than the relative time that large adults spent interfering, a phenomenon also observed in crayfish (Schroeder and Huber 2001
). In shore crabs, this difference in time spent interfering between the different sizes might relate to their corresponding life stages. Large adults might be intrinsically more aggressive as they fight over access to females in the mating season (van der Meeren 1994), during which the experiment was conducted. Juveniles on the other hand are cryptic in their aggressive behavior and hide or move away when disturbed rather than raising their claws in a threat display as large adult shore crabs do (McVean 1976). In our experiment, juveniles and small adults indeed avoided competitors more often than large adults did. Alternatively, a crab's persistence in interfering might be greater for larger crabs than for smaller crabs (Payne and Pagel 1996, 1997) as a result of which large adults were able to spend more time interfering than juveniles and small adults.
Although time spent interfering varied between the different crab sizes, crabs of all sizes spent less time interfering with a smaller competitor than with a size-matched or larger competitor. We hypothesized from the game theoretical models SAM, WOA-WA, E-WOA, and CAM that strength of interference through time lost in agonistic interactions would be greatest under symmetric competition. Crabs indeed spent most time interfering with a size-matched competitor and less time interfering with a smaller competitor, but crabs did not spend less time interfering with a larger competitor than with a size-matched competitor. What might have contributed to this asymmetry in time spent interfering is the fact that crabs avoided larger competitors, but hardly ever avoided smaller competitors. Furthermore, crabs displaced smaller crabs but did not displace smaller crabs as often as they avoided larger crabs, and crabs never displaced larger competitors. As a result, interference time was lowest when a crab foraged with a smaller competitor but was highest when a crab foraged with a size-matched or larger competitor. Apart from time spent interfering, crabs also lost foraging time through a reduction in their searching efficiency. That is, the time that crabs required to search for a mussel was longer when they foraged with a size-matched competitor than when they foraged with a larger competitor. This response might be due to increased vigilance for size-matched competitors, for instance, because individuals of similar size have greater difficulty to assess their relative competitive ability and hence to assess their chance of winning a possible encounter (Enquist and Leimar 1983; Enquist et al. 1990). Increased vigilance may also serve to assess a suitable opportunity to steel a prey item from a competitor (Smith et al. 2001b), although sometimes a kleptoparasite can detect opportunities to kleptoparasitize without compromising its own feeding rate (Smith et al. 2002). However, crabs probably did not increase their vigilance to assess opportunities to steel prey from a competitor of similar size as only one successful kleptoparasitic event was observed and this occurred when a competitor stole a prey item from the smaller focal individual.
As a result of the time spent interfering and the reduction in searching efficiency, foraging time (the sum of search time and time spent interfering during searching) was significantly higher with size-matched competitors (P = 0.006). The total time (thus also including handling time and time spent interfering during handling) of a crab that foraged with an equally sized crab was 23% and 13% higher than the total time of a crab that foraged with a smaller or larger competitor. These differences in total time were, however, not significant, probably because of a low power of the statistical test. Apparently, including the handling time masks the statistically significant effect on foraging time.
Applying game theoretical predictions to interference behaviors
In studies on foraging behavior where interference competition occurs through kleptoparasitism, game theory is often applied to assess stable strategies on when to kleptoparasitize and when not (Stillman et al. 1997; Broom and Ruxton 1998) or to assess how animals should allocate time to defending prey, attacking a feeding competitor, or avoiding confrontation (Sirot 2000). However, game theoretical models on contest behavior like SAM, WOA-WA, E-WOA, and CAM have not yet been integrated in studies on foraging behavior. These models predict a negative correlation between the difference in competitive ability between 2 competitors and the duration of an agonistic interaction (Enquist and Leimar 1983; Enquist et al. 1990; Payne and Pagel 1996, 1997; Payne 1998). Such models often assume that an important circumstantial cost of these agonistic interactions is loss of foraging time and thus a reduction in foraging success (Payne 1998). Here we showed that crabs lost time in agonistic interactions, which reduced their foraging success and indeed crabs suffered the greatest reduction in foraging success under symmetric competition. This result confirms that at least one important consequence of these agonistic interactions is a reduction in foraging success. For shore crabs, this reduction in foraging success was a result of various agonistic interactions. Crabs engaged in direct physical contact (fight), crabs engaged in interactions without physical contact (threat, displace, being vigilant), but crabs also avoided larger competitors by which the competitor appeared not affected. We did not set out to assess which of the different game theoretical models would apply best to the agonistic behaviors of crabs but merely used their (similar) predictions as a hypothesis for strength of interference. However, the agonistic behavior avoid, where only one individual of a pair loses time, stands out because this asymmetry in agonistic behavior is not taken into account in models of contest behavior. Nevertheless, if predictions from game theoretical models on contest behavior are to be a more integral part of foraging ecology, a challenge arises for game theoreticians as to how and when animals should allocate time to such agonistic behaviors under asymmetric competition.
Another point concerns the fact that predictions of game theoretical models on agonistic behaviors also entail the outcome of agonistic interactions over the resource at stake. In this study, prey availability was constant and prey items were scattered throughout the tank; crabs would thus not have been able to exclude others from the food source. Hence, crabs lost (foraging) time in agonistic interactions but in fact did not gain exclusive access to prey if they had won an encounter. However, if prey could be defended from competitors, then dominant foragers with a relatively high competitive ability would more often gain access to food and have higher feeding rates than subordinate individuals (also summarized in the resource defense theory: Warner 1980; Grant 1993; and see also Vahl et al. 2005). One might argue that a situation where foragers could potentially exclude others from the food source is more at the heart of game theoretical models than a situation where foragers exploit a standing stock of prey that cannot be defended. It would therefore be valuable to the field of contest behavior and foraging behavior to evaluate predictions of models as SAM, WOA-WA, E-WOA, and CAM for a predator–prey system where interference over defendable resources is mainly through time lost in agonistic interactions.
Consequences of time lost in interference behaviors
Interference can have a significant impact on the distribution of animals across different habitats. The interplay between interference competition and the distribution of animals is summarized in the concept of the ideal free distribution (Fretwell and Lucas 1970), which assumes that animals have perfect knowledge on habitat qualities and are free to go to that habitat that maximizes their fitness rewards. In ideal free distribution models for animals of differing competitive abilities that forage on a standing stock of prey, animals are assumed to suffer most from the more dominant, in our case larger competitors (Holmgren 1995; van der Meer 1997; Adler et al. 2001; Hamilton 2002). Because decisions on where to forage depend on what others do, an ideal free distribution model may be classified as a game theoretical model. Animals of unequal competitive ability are predicted to distribute in a truncated or semitruncated manner: animals segregate themselves by competitive ability across patches, or more dominant competitors only occur in the best habitats where food availability is highest and the subordinate animals occur mixed across habitats. This displacement of subordinates from preferred habitats is observed for several species (Gilbert et al. 1999; Szabo 2002; Davey et al. 2005). If, like we observed in this study, animals suffer interference most from competitors of equal competitive ability but less from competitors of unequal competitive ability, predictions on their distribution change dramatically. More specifically, if habitats differ in quality, but not extremely such that all animals only go to the best habitat(s), the ratio of competitive abilities of animals will be the same across habitats. This is only the case if the strength of interference for a dominant individual that encounters a subordinate individual is equal to the strength of interference for that subordinate individual encountering that dominant individual. To our knowledge, no study has investigated the distribution of crabs of different sizes over a range of habitats of different food qualities, hence this hypothesis cannot be falsified.
Although in our study animals suffered interference most from size-matched competitors, neither empirical nor theoretical studies on the distribution of animals, such as those mentioned above, have considered this scenario. This is most likely the case because many empirical studies on asymmetric interference competition have reported the fact that animals suffer most from interference from dominant individuals (Ens and Goss-Custard 1984; Alonso et al. 1997; Smith et al. 2001a; Stillman et al. 2002). The reason for this is that in those studies, kleptoparasitic interactions mostly led to interference among animals and the most successful individuals were the dominant individuals that stole prey from subordinate individuals. Models of interference competition have subsequently been based on interference through kleptoparasitism (Ruxton et al. 1992; Stillman et al. 1997; Sirot 2000), forming the basis for a number of ideal free distribution models (Holmgren 1995; van der Meer 1997; Adler et al. 2001; Hamilton 2002). Also, a whole body of literature exists on the dynamics of habitat selection driven by cannibalistic interactions, where larger foragers are potential (cannibalistic) predators for smaller conspecifics, which are then displaced to other habitats (Jormalainen and Shuster 1997; Moksnes et al. 1998; Sillett and Foster 2000; Claessen 2002; Gard 2005). However, if interference is mainly through time lost in being vigilant or in agonistic interactions, animals might incur the greatest loss in foraging time from individuals of similar competitive ability (Enquist and Leimar 1983; Enquist et al. 1990; Payne and Pagel 1996, 1997; Payne 1998). Such a relationship between time spent in agonistic interactions and relative differences in competitive ability has been observed for many animal species (Glass and Huntingford 1988; Smith et al. 1994; Molina-Borja et al. 1998; Andersen et al. 2000; Pratt et al. 2003), but appropriate models on their distribution and population dynamics still remain to be developed.
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ACKNOWLEDGEMENTS |
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The authors would like to thank Maurice Sabelis and Wouter Vahl for discussion and comments and Sieme Gielis for collection of the crabs.
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