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Patterns and implications of skip-molting for the Eastern Bering Sea snow and Tanner crab (Chionoecetes opilio and C. bairdi)
Fisheries Research 210 (2019) 63–70
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Patterns and implications of skip-molting for the Eastern Bering Sea snow and Tanner crab (Chionoecetes opilio and C. bairdi)
T
James T. Murphy Cascadia Sciences, 4403 Francis Ave. N. #4, Seattle, WA, 98103, USA
A R T I C LE I N FO
A B S T R A C T
Handled by George A. Rose
Male skip-molting, defined for this study as when adolescent male snow or Tanner crab (Chionoecetes opilio and C. bairdi) do not molt during the winter/spring molting season, reduces the abundances of large mature males by requiring skip-molters survive at least one additional year of natural mortality before molting resumes and by increasing terminal molting at smaller sizes. These dynamics have obvious consequences for fisheries that only target and retain large mature males. Though considered common in Atlantic Canada (AC) snow crab and recently documented in Sea of Japan snow crab, skip-molting remains unexamined for Eastern Bering Sea snow and Tanner crab populations. Using chela height and shell condition data collected from 1989 to 2017, sizespecific proportions of skip-molting were estimated for each species. Estimated size-specific proportions for snow crab resemble those reported for AC snow crab populations; estimated Tanner crab proportions are about twice that for snow crab when accounting for size differences between the species. Population simulations indicate skip-molting can reduce the biomass of large mature males by 12–47% relative to a population with no skipmolting, depending on species and assumptions of skip-molter survival. Regression models developed to identify important covariates of skip-molting explained only modest variation in the data (i.e., low deviance explained). Additional histological and physiological data are needed to validate classification of skip-molters from field measurements. Skip-molting proportions may have been underestimated due to shell condition misclassification of skip-molters. The stock assessments for EBS snow and Tanner crab do not consider skip-molting and assume all adolescent males molt annually. The effects of misspecified growth dynamics on assessment estimates warrant further research.
Keywords: Eastern Bering Sea Snow crab Tanner crab Skip-molting Population dynamics Growth
1. Introduction Adolescent male snow and Tanner crab (Chionoecetes opilio and C. bairdi) produce viable spermatophores but have not terminally molted (molted-to-maturity) and acquired the enlarged chelae (claws) and other secondary sexual characteristics of adult males (Paul and Paul, 1995; Sainte-Marie et al., 2008). These males have three possible growth pathways at the time of the winter/spring molting season: i) undergo a pubertal molt to a larger adolescent size, ii) undergo a terminal molt to a larger and final adult size, or iii) skip-molt, not molt and remain as an adolescent crab at the same size for at least 10–12 months (Benhalima et al., 1998; Dawe et al. 2012; Yamamoto et al., 2018). For snow crab and Tanner crab fisheries which only target and retain large males, such as in the Eastern Bering Sea (EBS) and in Atlantic Canada (AC), each pathway has fishery management implications due to possible decreases in abundance of large males targeted by the fisheries. All three of these growth pathways for males have been extensively
analyzed for snow crab populations in AC (Conan and Comeau, 1986; Sainte-Marie et al., 1995; Benhalima et al., 1998; Comeau et al., 1998; Dutil et al., 2010; Dawe et al., 2012), and, to a lesser degree, for Sea of Japan snow crab populations (Yamasaki and Kuwahara, 1991; Yamamoto et al., 2015, 2018). Male adolescent growth and terminal molting have been studied for populations of EBS snow crab (Somerton, 1981; Otto, 1998; Somerton et al., 2013), EBS Tanner crab (Somerton, 1981; Zheng, 2008) and Gulf of Alaska Tanner crab (Donaldson et al., 1981; Paul and Paul, 1995; Tamone et al., 2007). Male skip-molting, however, has not been described previously for EBS snow and Tanner crab. (Skip-molting for female Chionoecetes is much easier to analyze than for males due to the distinct body morphology of mature females and has been found negligible for EBS snow crab females (Orensanz et al., 2007), EBS Tanner crab females (J. Murphy, unpubl. data), and AC snow crab females (Dawe et al., 2012).) Skip-molting impacts male population dynamics by incurring at least 10–12 months of mortality without an increase in size and by delaying the terminal molt for at least the same amount of time. As
E-mail address: [email protected]. https://doi.org/10.1016/j.fishres.2018.10.006 Received 29 April 2018; Received in revised form 27 August 2018; Accepted 9 October 2018 Available online 23 October 2018 0165-7836/ © 2018 Elsevier B.V. All rights reserved.
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2. Materials and methods
timing of terminal molt is a function of both size and age (Dawe et al., 2012), skip molting will also increase the percentage of males terminally molting at smaller sizes. Skip-molters typically resume molting after approximately 10–12 months (Benhalima et al., 1998; Hebert et al., 2002; Yamamoto et al., 2018) though a small percentage will skip at least two consecutive molting seasons (Dawe et al., 2012; Yamamoto et al., 2018). Skip-molting was recently documented for Sea of Japan snow crab, where 28% of adolescent males collected before the molting season and reared in aquaria were skip-molters; 6% of males skipped at least 2 molting seasons (Yamamoto et al., 2018). Yamamoto et al. (2018) listed possible explanatory mechanisms for skip-molting based on AC studies: lower temperatures (Taylor et al., 1993; Dawe et al., 2012), food limitation (Dutil et al., 2010), and density-dependent effects (Hebert et al., 2002). Dawe et al. (2012) concluded that higher rates of skip-molting for larger adolescent snow crab in their study were likely due to the proportionally greater bioenergetics demands on larger crab. Skip-molting occurrence and effects for AC snow crab populations have been documented for over two decades (Taylor et al., 1993; Benhalima et al., 1998; Comeau et al., 1998; Hebert et al., 2002; Dutil et al., 2010; Dawe et al., 2012). Taylor et al. (1993) described extensive skip-molting due to very cold water temperatures and its negative consequences for the snow crab fishery in southeastern Newfoundland (Canada). Benhalima et al. (1998), using detailed histological analyses to determine molting status, reported that 30% of sampled adolescent males collected in the southern Gulf of St. Lawrence (sGSL) from 1990 to 1992 were skip-molters and noted the potential implications for management and population dynamics. Comeau et al. (1998) estimated 44% of adolescent snow crab males in 1989 in Bonne Bay (Gulf of St. Lawrence) skip-molted and that these skip-molters had high mortality rates. Hébert et al. (2016) reported the proportions of skip-molters in the male snow crab adolescent population in the sGSL could reach 50–60% of all adolescent males ≥ 50 mm carapace width (CW) and that high skip-molting rates of adolescent males in 2015 were likely responsible for lower than forecasted abundances of large males available to the fishery in 2016. Skip-molting of male Tanner crab in the EBS and Gulf of Alaska have been mentioned previously (Donaldson et al., 1981; Somerton, 1982), but these earlier studies occurred before the male terminal molt in the Chionoecetes genus became an accepted life-history trait (Conan and Comeau, 1986). Discussion of skip-molting in these studies could be addressing the lack of molting by an adult male post-terminal molt rather than of an adolescent male not molting during the winter/spring molting season. While not focused on estimating skip-molting rates at the population level or its impacts on growth and population dynamics, Zaleski and Tamone (2014) analyzed several categories of male snow crab, including skip-molters (described as adolescent oldshell). That study appears to be the first to document EBS snow crab skip-molting in the literature. They found skip-molters had significantly lower levels of the crustacean reproductive hormone methyl farnesoate and significantly higher gonadosomatic index values than recently molted adolescents. By using field data to first identify skip-molters (morphometric and shell condition data) and validating these classifications by finding distinct physiological patterns for skip-molters relative to normal molters, Zaleski and Tamone (2014) reported the first conclusive evidence of skip-molting for EBS snow crab and showed that field data could adequately identify skip-molters. The objectives of this study are i) describe the patterns of skipmolting for EBS male snow and Tanner crab; ii) identify important covariates of skip-molting with regression models; and iii) determine the effect of skip-molting on population dynamics and mature male biomass with population simulations.
2.1. Survey data overview All data came from the annual National Oceanic and Atmospheric Administration (NOAA) summer EBS groundfish and crab survey (survey, hereafter) from 1989 to 2017. Daly et al. (2016) describes in detail the operation and history of the survey and details of the biological sampling. The survey conducts 30 min bottom trawls across a fixed grid of approximately 375 survey stations covering 140,350 nmi2 (Daly et al., 2016). Captured snow and Tanner crab from either the entire haul or a subsample are enumerated and measured for sex, carapace width (CW), and shell condition. Shell condition data are recorded as ordinal integer values from 1 to 5 describing shell condition (1 is a just molted crab with a soft shell while 5 is severely degraded shell from a crab presumably at least several years past their last molt). Crabs with shell conditions values of 1 or 2 are described as newshell, and crabs with values of 3, 4, or 5 are described as oldshell. At the time of the summer survey, newshell crabs are presumed to have molted in the spring or winter of the same calendar year; oldshell crabs are presumed to be at least one year past their last molt, which has typically been assumed to be the terminal molt. 2.2. Chela height data At a subset of stations, subsamples of Tanner and snow crab males from the initially sampled catch are further measured for chela height data, which entails paired measurements of carapace width and a single chela height along with shell condition. These chela height data are used to classify the maturity status of individual male crabs to generate population-level estimates of size-specific proportions that are mature. Systematic, annual chela height collection in the survey began in 1989 for snow crab and in 1990 for Tanner crab. From 1990–2007, chela height data were collected for both species during the survey. No chela height data were collected in 2008. From 2009–2017, snow crab data were collected in 2009, 2011, 2013, 2015, and 2017; Tanner crab data were collected in 2010, 2012, 2014, 2016, and 2017. The chela height data collection protocol for the survey was described in Otto (1998): i) the right chela is measured; ii) oldshell crabs are preferentially oversampled due to less common occurrence; iii) a representative size range is chosen; and iv) crabs with a missing cheliped or with different sized right and left chelipeds are not measured (indicating injury or regeneration). Beginning in 2009, chela height data have been recorded to the nearest 0.1 mm (1 mm prior); exploratory analyses showed that results from each time period are similar, and all data since 1989 were used. Exploratory analyses also showed that the chela height data appeared to have many outliers; therefore, chela height to carapace width ratios were calculated for all samples by species and samples in the bottom and top 2.5% percentiles were removed from the data. This study analyzes only non-terminally molted snow crab males > 45 mm CW and Tanner crab > 65 mm CW; these crabs are considered adolescent males that normally molt each spring (Paul and Paul, 1989; Dawe et al., 2012). Survey data indicate very few oldshell males occur below these sizes, and skip-molting rates are therefore negligible. Analyses for this study used 5 mm CW size classes to partition the data. To ensure a minimum annual sample size of 5 for each 5 mm CW size class, the maximum snow crab size considered was 116 mm CW and the maximum Tanner crab size was 136 mm CW. Less than 1% of CW values for adolescent crabs from the chela height data were greater than these upper size limits considered. Adolescent crabs can be separated from mature, terminally molted, adult males based on allometric relationships between chela height data and carapace width, which change at the terminal molt (Somerton, 1981). Dividing lines estimated from a mixture of regressions clustering 64
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corresponding total number of adolescent newshell males sampled for chela height data; and wo, j, y and wn, j, y are weighting factors for oldshell and newshell males to correct for the preferential sampling of oldshell males during chela height data collection. Weighting factor wo, j, y = pos, j, y / poc, j, y , where pos, j, y is the proportion of all oldshell males sampled in the survey data for the given size class and year and poc, j, y is the proportion of all oldshell males sampled in the chela height data for the given size class and year. Weighting factor wn, j, y is calculated similarly but with proportions of newshell males in the survey and chela height data. 2.5. Regression models Binomial generalized linear models were developed to identify important explanatory variables for the estimated skip-molt proportions for both species. (Exploratory analyses showed that generalized additive models had similar values of deviance explained; therefore, the simpler modeling approach was chosen.) The saturated model with the complete set of variables considered was
logit (μj, k, y ) = β0 + Sizej + Depthk + Tempk, y + Year
where μj, k, y is the skip-molt proportion for 5 mm CW size class j at station k in year y . Proportions were calculated with raw data as small sample sizes at the size class/station level for both the general haul catch and for the chela height samples made determination of sampling bias in the chela data uncertain at that level of resolution. β0 is the intercept; Sizej represents the mid-point of size-class j ; Depthk is the bottom depth at station k ; Year represents annual effects; and Tempk, y is bottom temperature at station k in year y at time of summer survey sampling. Size , Depth , and Temp were numeric and continuous variables in the model and Year was a factor (one level for each year). Models with all possible combinations of explanatory variables were run implemented in the R statistical language (version 3.5.1) using the glm function. AIC was used for model selection (lower values indicating a better fitting model for the given number of estimated parameters and maximum likelihood value).
Fig. 1. Classification results of non-terminally molted (below dividing line) and terminally molted (above dividing line) males in the chela height data (1989–2017). Data were collected at both the 1.0 and 0.1 mm resolution. See text for dividing line details.
algorithm (Grün and Leisch, 2008) were provided by National Marine Fisheries Service (pers. comm., L. Rugolo, Alaska Fisheries Science Center, Seattle) to assign maturity status to sampled males of each species (Fig. 1). The dividing line equation was log10(CH ) = β0 + β1 log10(CW ) where CH and CW are chela height (mm) and carapace width (mm) and β0 and β1 are regression coefficients. Tanner crab coefficients are β0 = −1.578645 and β1 = 1.400180 ; snow crab coefficients are β0 = −1.204329 and β1 = 1.265084 . Males with observed chela height greater than the model predicted value were classified as terminally molted. A male crab was classified as a skipmolter from the chela height data if it was both non-terminally molted and in oldshell condition (Dawe et al., 2012).
2.6. Population simulation with skip-molting A size and stage-based simulation model for males of each species was developed to evaluate impacts of skip-molting on population dynamics. The models, based on the modeling framework developed in the 1990s for red king crab (Zheng et al., 1995) and Tanner crab (Zheng et al., 1998) and in use for snow and Tanner crab assessment modeling (Stockhausen, 2016; Szuwalski and Turnock, 2016), follow crabs by 5 mm CW size classes and by immature (non-terminally molted) and mature (terminally molted) stages. Population dynamics are identical for both species. Following stock assessment conventions, the snow crab model tracks abundances by 22 size classes: 25–29 mm, 30–34 mm, …, 130–134 mm; and the Tanner crab model has 32 size classes: 25–29 mm, 30–34 mm, …, 180–184 mm. The model is described with column vectors of length kj , where kj represents number of size classes, and matrices of dimension kj x kj . Immature abundances in year y + 1 are
2.3. Chela height data summary Total annual sample sizes and annual sample sizes by 5 mm CW size bin for both species for newshell adolescent and skip-molted/oldshell adolescent males were tabulated and size summary statistics calculated (which used all data above the minimum size limits for each species). As temperature has been identified as the dominant factor for snow crab skip-molting (Taylor et al., 1993; Dawe et al., 2012), as well as for snow and Tanner crab growth in general (Somerton, 1981; Burmeister and Sainte-Marie, 2010), temperature distributions of sampled immature males by 5 mm CW size classes for each species were summarized.
Ni, y + 1 = Xy + 1 + Wy + 1 + Ry + 1,
Annual population-level skip-molt proportions for each species by 5 mm CW size class j in year y , sj, y, were calculated as
wo, j, y oj, y wo, j, y oj, y + wn, j, y nj, y
(3)
where Ni, y + 1 is a vector of size-specific immature abundances; Xy + 1 is a vector of immature crabs that molted in year y ; Wy + 1 is a vector of sizespecific abundances that skip-molted in year y ; and Ry + 1 is a size-specific vector of recruits. Xy + 1 is
2.4. Size-specific skip-molt proportions from chela height data
sj , y =
(2)
Xy + 1 = (I − Q) GST (I − Z ) Ni, y ,
,
(4)
where Z is a diagonal matrix of size-specific skip-molting probabilities; ST is a diagonal matrix of annual survival for normal molters and mature crabs; G is a size transition matrix; and Q is a diagonal matrix of post-molt maturation probabilities. The model assumes that crabs do
(1)
where oj, y is the total number of adolescent oldshell males sampled for chela height data for the given size class and year; nj, y is the 65
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not skip-molt two years in a row and Wy + 1 is then
Wy + 1 = SW ZXy ,
(5)
where SW is a diagonal matrix of annual survival for skip-molters. Sizespecific mature male abundances are
Nm, y + 1 = QGST (I −Z ) Ni, y + ST Nm, y.
(6)
where subscript m denotes mature males. The duration of a typical period between a molt being skipped and the resumption of molting is 10–12 months (Benhalima et al., 1998; Hebert et al., 2002; Yamamoto et al., 2018); for this model 12 months is assumed to avoid undue model complexity. Total annual recruitment was assumed constant at 106 . Size-transition matrices, probabilities of maturation, and recruitment size distributions were from recent stock assessments for both species (Stockhausen, 2016; Szuwalski and Turnock, 2016). A brute-force parameter search was employed to find the set of sizespecific skip-molting probabilities that resulted in size-specific skipmolt proportions similar to the estimated mean proportions in Fig. 5. No fishery catch was implemented to simplify the analysis. Annual survival is then a function of natural mortality, and is set at 0.68 for all males of both species based on snow crab modeling results from Murphy et al. (2018). Additionally, the consequences of possible lower skip-molt survival on mature biomass levels were examined with sensitivity analyses. This sensitivity analysis was motivated by Comeau et al. (1998), who described the mortality of skip-molters as “massive” in their study. Though Comeau et al. (1998) is the only study to explicitly associate skip-molting with lower survival, Dutil et al. (2010) also speculated that skip-molting may indicate poor physiological condition, further suggesting a plausible correlation with skip-molting and lower survival. The 3 scenarios implemented assume survival during the year subsequent to skip-molting to be 90% (0.61), 80% (0.54), and 70% (0.48) of the baseline annual survival of 0.68. These scenarios also required increases in the skip-molting probabilities from the baseline scenario so that calculated skip-molt proportions were all equal for all model runs. All initial size-specific abundances were seeded with values of 4 × 10 4 , and the model for each species was run for 50 years to ensure reaching steady-state dynamics. From year 50 values, total mature biomass for all males and total biomass of large mature males were calculated using the midpoint of each size class and length-weight relationships from Daly et al. (2016). Total male mature biomass is the primary reference point for management of the EBS snow and Tanner crab fisheries, which only target and retain large mature males. For snow crab, the size range of large mature males was defined as size classes ≥ 100 mm CW (≥ 101 mm CW is minimum size accepted by EBS commercial processors); for Tanner crab, the size range was ≥ 140 mm (≥ 140 mm CW is legal size limit in the EBS). The percent decrease in biomass relative to a non-skip-molting scenario (i.e., all diagonal elements of Z set to zero) was used to assess the effects of skipmolting and skip-molter survival.
Fig. 2. Annual sample sizes of adolescent males in the chela height data (1989–2017) by shell condition. Oldshell condition denotes skip-molters. Vertical grey lines indicate years with no sampling.
16 mm); skip-molter mean size was 102 mm CW (s.d. = 16 mm). Tanner crab temperature distributions were similar across sizes with the interquartile range between 2 and 4 °C for all sizes (Fig. 4). Snow crab temperature distributions increased with increasing size (Fig. 4); the interquartile range of the 45 mm CW size bin was -1.0 to 0.5 while the interquartile range of 115 mm CW size class was about 1.0 to 3.0 °C. The trend in snow crab distributions reflect both ontogenetic movement from the shallower and colder northeast to the deeper and warmer southwest (Otto, 1998; Zheng et al., 2001; Murphy et al., 2011) and lower growth rates in colder waters (Burmeister and Sainte-Marie, 2010). 3.2. Annual size-specific skip-molt proportions The oldshell weighting factor global mean (mean across all size classes and years) for Tanner crab was 0.83 (s.d. = 0.29), indicating a 21% mean oversampling rate for oldshell males for chela height data sampling. The newshell weighting factor global mean for newshell Tanner crab was 1.19 (s.d. = 0.33), indicating a 16% mean undersampling rate. The means of annual Tanner crab skip-molt proportions increased from 0.02 for the 65 mm CW size class to a maximum of 0.41 for the 130 mm CW size class (Fig. 5); 95% confidence intervals also increased with increasing size due to higher variability in the larger sizes due to small sample sizes (Figs. 3 and 5). The annual means of raw skip-molt proportions, unadjusted for sampling bias in the chela height data, were on average 22% higher (s.d. = 13%) than the corresponding adjusted values (Fig. 5). The oldshell weighting factor global mean for snow crab was 0.62 (s.d. = 0.26), indicating a 61% mean oversampling rate. The newshell weighting factor global mean for snow crab was 1.41 (s.d. = 0.53), indicating a 29% mean undersampling rate. The means of annual snow crab skip-molt proportions increased from 0.01 for the 45 mm CW size class to 0.42 for the 115 mm CW size class (Fig. 5); 95% confidence
3. Results 3.1. Chela height data summary 9,895 adolescent male Tanner crab ≥ 65 mm CW sampled from 1990 to 2017 were analyzed. Mean annual sample size was 430 (s.d. = 251; range: 149–1093) (Fig. 2). 17, 958 adolescent snow crabs ≥ 45 mm CW sampled from 1989 to 2017 were analyzed. Mean annual sample size was 748 (s.d. = 530; range: 117–2228) (Fig. 2). For both species newshell sample sizes were highest for smaller sizes while intermediate sizes had the highest skip-molter sample sizes (Fig. 3). Adolescent newshell snow crab mean size was 76 mm CW (s.d. = 15 mm); skip-molter mean size was 84 mm CW (s.d. = 17 mm). Adolescent newshell Tanner crab mean size was 91 mm CW (s.d. = 66
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Fig. 4. Temperature distributions of adolescent males in the chela height data (1989–2017) by 5 mm carapace width size classes. Fig. 3. Sample sizes of adolescent males in the chela height data (1989–2017) by shell condition and by 5 mm carapace width size classes. Oldshell condition denotes skip-molters. Line is mean of annual values.
intervals also increased with larger sizes. The annual means of raw skipmolt proportions were on average 45% higher (s.d. = 18%) than the corresponding unadjusted values (Fig. 5). 3.3. Regression models The final Tanner crab model was the saturated model with size, temperature, depth, and year effects as explanatory variables (deviance explained: 21%, AIC: 7222) (Table 1). Estimated regression coefficients were positive for depth, size, and temperature (Table 1). Models with a subset of the variables of the final models were also run to identify the importance of individual variables. Results from a temperature, year effects model (19%, 7346); temperature and size model (14%, 7756); and size only model (8%, 8279) show that size, temperature, and year effects were the most important explanatory variables for the Tanner crab skip-molt proportions with depth having only modest influence. The final snow crab model was also the saturated model with size, temperature, depth and year effects (deviance explained: 22%, AIC: 13,330). Regression coefficients were positive for depth and size but negative for temperature (Table 1). Results from a size, temperature, and year effects model (21%, 13,506), size and temperature model (20%, 13,553), and temperature only model (10%, 15,006), indicate that temperature and year effects were the most influential explanatory variables and depth and size had modest influence. 3.4. Population simulation
Fig. 5. Mean of annual estimated skip-molt proportions by 5 mm carapace width size classes with 95% confidence interval (1989–2017). Raw proportions (dashed line) are unadjusted for preferential sampling of oldshell crab. Horizontal line at 0.4 for visual reference.
To approximate observed snow crab skip-molt proportions, snow crab size-specific skip-molting probabilities for the baseline skip-molt survival of 0.68 were 25–45% higher than the corresponding skip-molt proportions for the same size class (Fig. 6). For the scenarios with lower 67
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Table 1 Parameter estimates for final regression models, excluding year effects. Species
Variable
Df
Coefficient
Std. error
p value
Snow crab (n = 6,151)
Intercept Size Depth Temperature Intercept Size Depth Temperature
1 1 1 1 1 1 1 1
−5.19 0.007 0.013 0.663 −8.257 0.053 0.012 −0.156
0.287 0.001 0.001 0.019 0.287 0.002 0.001 0.028
< 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10
Tanner crab (n = 10,093)
Table 2 Percent decrease in total mature biomass and large mature biomass by skipmolt annual survival (survival during year following skipped-molt), relative to no assumed skip-molting. (0.68 survival is same value for normal molters). Skip-molt survival
0.68 0.61 0.54 0.48
skip-molter survival, skip-molting probabilities were increased by 16, 22, and 30% as annual survival decreased from 0.68 to 0.61, 0.54, and 0.48 to ensure the same skip-molt proportions as in the baseline survival scenario. The decrease of total biomass of large mature snow crab males relative to a no skip-molting scenario increased from 12% for the baseline survival scenario to 24% when skip-molter survival was at the lowest value of 0.48 (Fig. 6, Table 2). Decreases in biomass of large mature males were about 35% greater than decreases of total mature biomass for each survival scenario (Table 2). To approximate observed Tanner crab skip-molt proportions, snow crab size-specific skip-molting probabilities for the baseline skip-molt survival of 0.68 were 35–50% higher than the corresponding skip-molt
Snow crab
Tanner crab
Total mat. bio.
Large mat. bio.
Total mat. bio.
Large mat. bio.
9 12 14 18
12 16 19 24
14 19 23 29
23 32 37 47
proportions for the same size class (Fig. 6). Skip-molting probabilities were increased by 15, 20, and 28% as skip-molter survival decreased from the baseline scenario to achieve the same skip-molt proportions as in the baseline skip-molter survival scenario. The decrease of total biomass of large mature Tanner crab males relative to a no skip-molting scenario increased from 23% for the baseline survival scenario to 47% when skip-molter survival was 0.48 (Fig. 6, Table 2). Decreases in biomass of large mature males were about 65% greater than decreases of total mature biomass for each survival scenario (Table 2).
Fig. 6. Results of population simulations. 68
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4. Discussion
non-terminally molted males molt each year. The simulation results suggest that exploring the effects of skip-molting on population dynamics warrants attention, however. The EBS snow and Tanner crab models are fit to size-based data for the immature and mature lifehistory stages. Chela height data can be used to further partition immature data into normal molter and skip-molter components. Then, the assessment model can subsequently model these two immature stages and the mature stage. A random effects/state-space modeling framework would likely be useful (Murphy et al., 2018). Additionally, estimates of male immature and mature survey biomass, which are critical inputs into the assessment models, assume that all oldshell males are mature. This assumption means that survey estimates of mature biomass are biased high and immature biomass estimates are biased low. The simulation results indicate that lower skip-molter survival can strongly influence population dynamics. The impetus for exploring effects of skip-molter survival came from Comeau et al. (1998), who reported that skip-molters had “massive” mortality when attempting to molt again and this mortality significantly impacted male abundances and from Dutil et al. (2010), who speculated that poor physiological condition may contribute to skip-molting. However, explicit estimates of lower skip-molter survival have not been reported. Additional live culture studies (e.g., Yamamoto et al., 2018) appear required to further understanding of skip-molt survival and identify responsible biological mechanisms. Another modeling consideration is the potential difference in sizespecific terminal molting probabilities between skip-molters and nonskip molters. Dawe et al. (2012) concluded that size at terminal molt was a function of both age and size and gave the example of a small male that had undergone more skip-molts at lower temperatures could be older than larger males that had undergone fewer skipped-molts at higher temperatures. (This example would also seem true even if thermal experiences were similar.) This suggests that higher size-specific estimates of terminal molting probabilities for skip-molters could be required for biologically realistic implementation of skip-molting dynamics. An extensive tagging study in AC showed that oldshell snow crab mature males more than one year past their terminal molt can be misclassified as newshell males (Fonseca et al., 2008). This misclassification for snow crab is assumed to happen regularly during EBS survey sampling and can be inferred from implausibly high natural mortality estimates for mature males that are based on accounting of newshell and oldshell abundances (Otto, 1998; Zheng, 2003; Murphy et al., 2018). However, whether this also happens for snow and Tanner crab skip-molters is not known but seems plausible. Misclassification of skip-molters as newshell males would result in under-estimated skipmolt proportions. (Misclassifying actual recently molted newshell crabs as oldshell is presumed unlikely due to their new carapaces having a distinctly bright and unblemished appearance, and the results of Otto (1998); Zheng, 2008, and Murphy et al. (2018) suggest that this does not occur at any significant rates in the EBS.) While the estimated skip-molt proportions seem reasonable, additional steps can help improve their estimation and general understanding of EBS snow and Tanner crab skip-molting dynamics. Histological analyses and physiological data can distinguish timing of molting (Benhalima et al., 1998; Tamone et al., 2007) and differentiate between normal molters and skip-molters (Benhalima et al., 1998; Hebert et al., 2002). By objectively quantifying the timing of a crab’s last molt, histological and physiological data could improve estimation of skip-molting rates and quantify field misclassification rates of shell condition. A random sampling framework would eliminate the need to account for potential sampling bias for analyses of the chela height data.
Size-specific skip-molt proportions estimated for snow crab appear similar to those reported for AC snow crab by Dawe et al. (2012). Dawe et al. (2012) reported multiple sets of estimated size-specific skip-molt proportions, stratified by region and bottom temperature at time of sampling. Generally, these estimated proportions were near zero for 40 mm CW crab and then rose to 0.30–0.60 for crab > 100 mm CW. The temperature distribution data of sampled males reported in Dawe et al. (2012) also appear generally similar to the snow crab temperature distributions reported in this study. Estimated snow crab skip-molt proportions from this study are also similar to the results of Yamamoto et al. (2018), who reported a 28% skip-molting rate for snow crab males 83–123 mm CW from the Sea of Japan. The binomial regressions for both species explained modest variation in the data (i.e., low deviance explained). Dawe et al. (2012) performed similar regressions but did not report any metric of model performance such as deviance explained. While the temperature regression coefficient for final Tanner crab model was negative, the temperature coefficient for the final snow crab model was unexpectedly positive. This positive relationship is in apparent contradiction of the results of Dawe et al. (2012), who found temperature and skip-molt proportions to be negatively correlated. However, snow crab males undergo large scale ontogenetic movements from colder waters in the northeast of the EBS shelf to warmer and deeper waters in the southeast. The positive relationship estimated between temperature and snow crab skip-molting rates is likely due to the confounding of size and temperature values from larger males occupying warmer waters than younger males as seen in Fig. 4. Given that snow crab growth patterns are a function of cumulative thermal history and not just immediate thermal experience (Dawe et al., 2012), EBS male snow crab ontogenetic movement patterns will obscure temperature-growth relationships derived from survey data, which provides only a single snapshot of thermal history. This study appears to be the first to assess the impacts of Chionoecetes skip-molting with population modeling. Though skipmolting is well studied in AC, population models are not used to inform management actions, and skip-molting data has not been used to parameterize a population model. The main finding of the simulation model is that skip-molting may at least moderately decrease biomass of large males targeted and retained by their fisheries. With modest assumptions of lower survival for one year for skip-molters, the decreases in biomass can become much greater. Another important simulation model result is that decreases in mature male Tanner crab biomass is about twice that for snow crab when comparing population dynamics with and without skip-molting (Table 2). Though size-specific skip-molting proportions are actually similar between snow crab and Tanner crab, such proportions are not directly comparable as Tanner crab have larger adult sizes; e.g., a 100 mm CW male snow crab is considered a large snow crab but would only be an intermediate sized Tanner crab. If comparing intermediate sized, non-terminally molted males, such as 70–95 mm CW for snow crab and 90–120 mm CW for Tanner crab, then Tanner crab skip-molt proportions are at least twice as large (Fig. 5). The higher skip-molting rates for Tanner crab may be due to EBS Tanner crab population being at the northern extent of its range in the Eastern Pacific and possibly close to its lower thermal tolerance levels. Comparison of skip-molting rates in warmer regions such as the Gulf of Alaska would help further understanding of temperature effects on Tanner crab skip-molting and differences with snow crab skip-molting. A more complete understanding of the population dynamics consequences of skip-molting will require integrating skip-molting into a statistical population or assessment model with actual fits to observed skip-molter abundances and comparing how model estimates differ from models without skip-molting dynamics. The EBS snow and Tanner crab assessment models do not consider skip-molting and assume all
Acknowledgements Bob Foy, Buck Stockhausen, Jack Turnock, and Louis Rugolo (all at 69
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NOAA’s Alaska Fisheries Science Center, USA) provided survey data, stock assessment estimates, and maturation data. M.S.M. Siddeek (ADF &G), Darrell Mullowney (DFO), and one anonymous reviewer provided very helpful reviews and comments.
(Decapoda, Majidae). Melteff, B. (Ed.), The Proceedings of the International Symposium on King and Tanner Crabs. Lowell Wakefield Fisheries Symposium Series. 95–103. Paul, A.J., Paul, J.M., 1995. Molting of functionally mature male Chionoecetes bairdi Rathbun (Decapoda: Majidae) and changes in carapace and chela measurements. J. Crustac. Biol. 15, 686–692. https://doi.org/10.2307/1548818. Sainte-Marie, B., Raymond, S., Brethes, J.C., 1995. Growth and maturation of the benthic stages of male snow crab, Chionoecetes opilio (Brachyura, Majidae). Can. J. Fish. Aquat. Sci. 52, 903–924. https://doi.org/10.1139/f95-091. Sainte-Marie, B., Gosselin, T., Sévigny, J.M., Urbani, N., 2008. The snow crab mating system: opportunity for natural and unnatural selection in a changing environment. Bull. Mar. Sci. 83, 131–161. Somerton, D.A., 1981. 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A snow crab, Chionoecetes opilio (Decapoda, Majidae), fishery collapse in Newfoundland. Fish Bull. 92, 412–419. Yamamoto, T., Yamada, T., Kinoshita, T., Ueda, Y., Fujimoto, H., Yamasaki, A., Hamasaki, K., 2015. Growth and moulting of wild-born immature snow crabs, Chionoecetes opilio (Fabricius, 1788) (Decapoda, Majoidea), in the laboratory. Crustaceana 88, 911–922. https://doi.org/10.1163/15685403-00003454. Yamamoto, T., Yamada, T., Kinoshita, T., Ueda, Y., Yamasaki, A., Hamasaki, K., 2018. Moulting and growth in earlier and later moulters of adolescent male snow crabs (Chionoecetes opilio) (Brachyura: Majoidea) under laboratory conditions. Invertebr. Reprod. Dev. 62, 49–55. https://doi.org/10.1080/07924259.2017.1398189. Yamasaki, A., Kuwahara, A., 1991. The terminal molt of male snow crab in the Japan Sea. Nippon Suisan Gakkaishi 57, 1839–1844. Zaleski, M.A.F., Tamone, S.L., 2014. Relationship of molting, gonadosomatic index, and methyl farnesoate in male snow crab (Chionoecetes opilio) from the eastern Bering Sea. J. Crustac. Biol. 34, 764–772. https://doi.org/10.1163/1937240x-00002271. Zheng, J., 2003. Uncertainties of natural mortality estimates for eastern Bering Sea snow crab, Chionoecetes opilio. Fish. Res. 65, 411–425. https://doi.org/10.1016/j.fishres. 2003.09.029. Zheng, J., 2008. Temporal changes in size at maturity and their implications for fisheries management for eastern Bering Sea Tanner crab. J. Northwest Atlantic Fish. Sci. https://doi.org/10.2960/J.v41.m623. Zheng, J., Murphy, M.C., Kruse, G.H., 1995. A length-based population-model and stockrecruitment relationships for red king crab, Paralithodes camtschaticus, in Bristol Bay, Alaska. Can. J. Fish. Aquat. Sci. 52, 1229–1246. Zheng, J., Kruse, G.H., Murphy, M.C., 1998. A length-based approach to estimate population abundance of Tanner crab, Chionoecetes bairdi, Bristol Bay, Alaska. Jamieson, G.S., Campbell, A. (Eds.), Proceedings of the North Pacific Symposium on Invertebrate Stock Assessment and Management 91–105. Zheng, J., Kruse, G.H., Ackley, D.R., 2001. Spatial distribution and recruitment patterns of snow crabs in the eastern Bering Sea. In: Kruse, G.H., Bez, N., Booth, A., Dorn, M.W., Hills, S., Lipcius, R.N., Pelletier, D., Roy, C., Smith, S.J., Witherell, D. (Eds.), Spatial Processes and Management of Marine Populations. University of Alaska Sea Grant, AK-SG-01-02, pp. 233–256.
References Benhalima, K., Moriyasu, M., Hebert, M., 1998. A technique for identifying the earlypremolt stage in the male snow crab Chionoecetes opilio (Brachyura: Majidae) in Baie des Chaleurs, southern Gulf of St. Lawrence. Can. J. Zool. Can. Zool. 76, 609–617. https://doi.org/10.1139/cjz-76-4-609. Burmeister, A., Sainte-Marie, B., 2010. Pattern and causes of a temperature-dependent gradient of size at terminal moult in snow crab (Chionoecetes opilio) along West Greenland. Polar Biol. 33, 775–788. https://doi.org/10.1007/s00300-009-0755-6. Comeau, M., Conan, G.Y., Maynou, F., Robichaud, G., Therriault, J.C., Starr, M., 1998. Growth, spatial distribution, and abundance of benthic stages of the snow crab (Chionoecetes opilio) in Bonne Bay, Newfoundland, Canada. Can. J. Fish. Aquat. Sci. 55, 262–279. https://doi.org/10.1139/cjfas-55-1-262. Conan, G.Y., Comeau, M., 1986. Functional maturity and terminal molt of male snow crab, Chionoecetes opilio. Can. J. Fish. Aquat. Sci. 43, 1710–1719. Daly, B.J., Armistead, C.E., Foy, R.J., 2016. The 2016 Eastern Bering Sea Continental Shelf Bottom Trawl Survey: Results for Commercial Crab Species. 167 pp. Available at. U.S. Dep. Commer., NOAA Tech. Memo. NMFS-AFSC-327 (Accessed 10 March 2017). https://www.afsc.noaa.gov/Publications/AFSC-TM/NOAA-TM-AFSC-327. pdf. Dawe, E.G., Mullowney, D.R., Moriyasu, M., Wade, E., 2012. Effects of temperature on size-at-terminal molt and molting frequency in snow crab Chionoecetes opilio from two Canadian Atlantic ecosystems. Mar. Ecol. Prog. Ser. 469, 279–296. https://doi.org/ 10.3354/meps09793. Donaldson, W.E., Cooney, R.T., Hilsinger, J.R., 1981. Growth, age and size at maturity of Tanner crab, Chionoecetes bairdi M. J. Rathbun, in the northern Gulf of Alaska (Decapoda, Brachyura). Crustaceana 40, 286–302. https://doi.org/10.1163/ 156854081x00750. Dutil, J.D., Dion, C., Gamache, L., Larocque, R., Ouellet, J.F., 2010. Ration and temperature effects on the condition of male adolescent molter and skip molter snow crab. J. Shellfish Res. 29, 1025–1033. https://doi.org/10.2983/035.029.0404. Fonseca, D.B., Sainte-Marie, B., Hazel, F., 2008. Longevity and change in shell condition of adult male snow crab Chionoecetes opilio inferred from dactyl wear and mark-recapture data. Trans. Am. Fish. Soc. 137, 1029–1043. https://doi.org/10.1577/t07079.1. Grün, B., Leisch, F., 2008. FlexMix version 2: finite mixtures with concomitant variables and varying and constant parameters. J. Stat. Softw. 28, 1–35. https://doi.org/10. 18637/jss.v028.i04. Hebert, M., Benhalima, K., Miron, G., Moriyasu, M., 2002. Moulting and growth of male snow crab, Chionoecetes opilio (O. Fabricius, 1788) (Decapoda, Majidae), in the southern Gulf of St. Lawrence. Crustaceana 75, 671–702. https://doi.org/10.1163/ 156854002760202679. Hébert, M., Wade, E., DeGrâce, P., Moriyasu, M., 2016. The 2015 assessment of the snow crab (Chionoecetes opilio) stock in the southern Gulf of St. Lawrence (Areas 12, 19, 12E and 12F). DFO Can. Sci. Advis. Sec. Res. Doc 2016/087. 43 pp. Murphy, J.T., Hollowed, A.B., Anderson, J.J., 2011. Snow crab spatial distributions: examination of density-dependent and independent processes. In: Kruse, G.H., Eckert, G.L., Foy, R.J., Lipcius, R.N., Sainte-Marie, B., Stram, D.L., Woodby, D. (Eds.), Biology and Management of Exploited Crab Populations Under Climate Change. University of Alaska Sea Grant AK-SG-10-01, pp. 1–47. Murphy, J.T., Rugolo, L., Turnock, B.J., 2018. Estimation of annual, time-varying natural mortality and survival for Eastern Bering Sea snow crab (Chionoecetes opilio) with state-space population models. Fish. Res. 205, 122–132. https://doi.org/10.1016/j. fishres.2018.04.001. Orensanz, J.M., Ernst, B., Armstrong, D.A., 2007. Variation of female size and stage at maturity in snow crab (Chionoecetes opilio) (Brachyura: Majidae) from the eastern Bering Sea. J. Crustac. Biol. 27, 576–591. Otto, R.S., 1998. Assessment of the eastern Bering Sea snow crab, Chionoecetes opilio, stock under the terminal molt hypothesis. Jamieson, G.S., Campbell, A. (Eds.), Proceedings of the North Pacific Symposium on Invertebrate Stock Assessment and Management. Can. Spec 09–124. Paul, A.J., Paul, J.M., 1989. The size at the onset of maturity in male Chionoecetes bairdi
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Patterns and implications of skip-molting for the Eastern Bering Sea snow and Tanner crab (Chionoecetes opilio and C. bairdi)
T
James T. Murphy Cascadia Sciences, 4403 Francis Ave. N. #4, Seattle, WA, 98103, USA
A R T I C LE I N FO
A B S T R A C T
Handled by George A. Rose
Male skip-molting, defined for this study as when adolescent male snow or Tanner crab (Chionoecetes opilio and C. bairdi) do not molt during the winter/spring molting season, reduces the abundances of large mature males by requiring skip-molters survive at least one additional year of natural mortality before molting resumes and by increasing terminal molting at smaller sizes. These dynamics have obvious consequences for fisheries that only target and retain large mature males. Though considered common in Atlantic Canada (AC) snow crab and recently documented in Sea of Japan snow crab, skip-molting remains unexamined for Eastern Bering Sea snow and Tanner crab populations. Using chela height and shell condition data collected from 1989 to 2017, sizespecific proportions of skip-molting were estimated for each species. Estimated size-specific proportions for snow crab resemble those reported for AC snow crab populations; estimated Tanner crab proportions are about twice that for snow crab when accounting for size differences between the species. Population simulations indicate skip-molting can reduce the biomass of large mature males by 12–47% relative to a population with no skipmolting, depending on species and assumptions of skip-molter survival. Regression models developed to identify important covariates of skip-molting explained only modest variation in the data (i.e., low deviance explained). Additional histological and physiological data are needed to validate classification of skip-molters from field measurements. Skip-molting proportions may have been underestimated due to shell condition misclassification of skip-molters. The stock assessments for EBS snow and Tanner crab do not consider skip-molting and assume all adolescent males molt annually. The effects of misspecified growth dynamics on assessment estimates warrant further research.
Keywords: Eastern Bering Sea Snow crab Tanner crab Skip-molting Population dynamics Growth
1. Introduction Adolescent male snow and Tanner crab (Chionoecetes opilio and C. bairdi) produce viable spermatophores but have not terminally molted (molted-to-maturity) and acquired the enlarged chelae (claws) and other secondary sexual characteristics of adult males (Paul and Paul, 1995; Sainte-Marie et al., 2008). These males have three possible growth pathways at the time of the winter/spring molting season: i) undergo a pubertal molt to a larger adolescent size, ii) undergo a terminal molt to a larger and final adult size, or iii) skip-molt, not molt and remain as an adolescent crab at the same size for at least 10–12 months (Benhalima et al., 1998; Dawe et al. 2012; Yamamoto et al., 2018). For snow crab and Tanner crab fisheries which only target and retain large males, such as in the Eastern Bering Sea (EBS) and in Atlantic Canada (AC), each pathway has fishery management implications due to possible decreases in abundance of large males targeted by the fisheries. All three of these growth pathways for males have been extensively
analyzed for snow crab populations in AC (Conan and Comeau, 1986; Sainte-Marie et al., 1995; Benhalima et al., 1998; Comeau et al., 1998; Dutil et al., 2010; Dawe et al., 2012), and, to a lesser degree, for Sea of Japan snow crab populations (Yamasaki and Kuwahara, 1991; Yamamoto et al., 2015, 2018). Male adolescent growth and terminal molting have been studied for populations of EBS snow crab (Somerton, 1981; Otto, 1998; Somerton et al., 2013), EBS Tanner crab (Somerton, 1981; Zheng, 2008) and Gulf of Alaska Tanner crab (Donaldson et al., 1981; Paul and Paul, 1995; Tamone et al., 2007). Male skip-molting, however, has not been described previously for EBS snow and Tanner crab. (Skip-molting for female Chionoecetes is much easier to analyze than for males due to the distinct body morphology of mature females and has been found negligible for EBS snow crab females (Orensanz et al., 2007), EBS Tanner crab females (J. Murphy, unpubl. data), and AC snow crab females (Dawe et al., 2012).) Skip-molting impacts male population dynamics by incurring at least 10–12 months of mortality without an increase in size and by delaying the terminal molt for at least the same amount of time. As
E-mail address: [email protected]. https://doi.org/10.1016/j.fishres.2018.10.006 Received 29 April 2018; Received in revised form 27 August 2018; Accepted 9 October 2018 Available online 23 October 2018 0165-7836/ © 2018 Elsevier B.V. All rights reserved.
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2. Materials and methods
timing of terminal molt is a function of both size and age (Dawe et al., 2012), skip molting will also increase the percentage of males terminally molting at smaller sizes. Skip-molters typically resume molting after approximately 10–12 months (Benhalima et al., 1998; Hebert et al., 2002; Yamamoto et al., 2018) though a small percentage will skip at least two consecutive molting seasons (Dawe et al., 2012; Yamamoto et al., 2018). Skip-molting was recently documented for Sea of Japan snow crab, where 28% of adolescent males collected before the molting season and reared in aquaria were skip-molters; 6% of males skipped at least 2 molting seasons (Yamamoto et al., 2018). Yamamoto et al. (2018) listed possible explanatory mechanisms for skip-molting based on AC studies: lower temperatures (Taylor et al., 1993; Dawe et al., 2012), food limitation (Dutil et al., 2010), and density-dependent effects (Hebert et al., 2002). Dawe et al. (2012) concluded that higher rates of skip-molting for larger adolescent snow crab in their study were likely due to the proportionally greater bioenergetics demands on larger crab. Skip-molting occurrence and effects for AC snow crab populations have been documented for over two decades (Taylor et al., 1993; Benhalima et al., 1998; Comeau et al., 1998; Hebert et al., 2002; Dutil et al., 2010; Dawe et al., 2012). Taylor et al. (1993) described extensive skip-molting due to very cold water temperatures and its negative consequences for the snow crab fishery in southeastern Newfoundland (Canada). Benhalima et al. (1998), using detailed histological analyses to determine molting status, reported that 30% of sampled adolescent males collected in the southern Gulf of St. Lawrence (sGSL) from 1990 to 1992 were skip-molters and noted the potential implications for management and population dynamics. Comeau et al. (1998) estimated 44% of adolescent snow crab males in 1989 in Bonne Bay (Gulf of St. Lawrence) skip-molted and that these skip-molters had high mortality rates. Hébert et al. (2016) reported the proportions of skip-molters in the male snow crab adolescent population in the sGSL could reach 50–60% of all adolescent males ≥ 50 mm carapace width (CW) and that high skip-molting rates of adolescent males in 2015 were likely responsible for lower than forecasted abundances of large males available to the fishery in 2016. Skip-molting of male Tanner crab in the EBS and Gulf of Alaska have been mentioned previously (Donaldson et al., 1981; Somerton, 1982), but these earlier studies occurred before the male terminal molt in the Chionoecetes genus became an accepted life-history trait (Conan and Comeau, 1986). Discussion of skip-molting in these studies could be addressing the lack of molting by an adult male post-terminal molt rather than of an adolescent male not molting during the winter/spring molting season. While not focused on estimating skip-molting rates at the population level or its impacts on growth and population dynamics, Zaleski and Tamone (2014) analyzed several categories of male snow crab, including skip-molters (described as adolescent oldshell). That study appears to be the first to document EBS snow crab skip-molting in the literature. They found skip-molters had significantly lower levels of the crustacean reproductive hormone methyl farnesoate and significantly higher gonadosomatic index values than recently molted adolescents. By using field data to first identify skip-molters (morphometric and shell condition data) and validating these classifications by finding distinct physiological patterns for skip-molters relative to normal molters, Zaleski and Tamone (2014) reported the first conclusive evidence of skip-molting for EBS snow crab and showed that field data could adequately identify skip-molters. The objectives of this study are i) describe the patterns of skipmolting for EBS male snow and Tanner crab; ii) identify important covariates of skip-molting with regression models; and iii) determine the effect of skip-molting on population dynamics and mature male biomass with population simulations.
2.1. Survey data overview All data came from the annual National Oceanic and Atmospheric Administration (NOAA) summer EBS groundfish and crab survey (survey, hereafter) from 1989 to 2017. Daly et al. (2016) describes in detail the operation and history of the survey and details of the biological sampling. The survey conducts 30 min bottom trawls across a fixed grid of approximately 375 survey stations covering 140,350 nmi2 (Daly et al., 2016). Captured snow and Tanner crab from either the entire haul or a subsample are enumerated and measured for sex, carapace width (CW), and shell condition. Shell condition data are recorded as ordinal integer values from 1 to 5 describing shell condition (1 is a just molted crab with a soft shell while 5 is severely degraded shell from a crab presumably at least several years past their last molt). Crabs with shell conditions values of 1 or 2 are described as newshell, and crabs with values of 3, 4, or 5 are described as oldshell. At the time of the summer survey, newshell crabs are presumed to have molted in the spring or winter of the same calendar year; oldshell crabs are presumed to be at least one year past their last molt, which has typically been assumed to be the terminal molt. 2.2. Chela height data At a subset of stations, subsamples of Tanner and snow crab males from the initially sampled catch are further measured for chela height data, which entails paired measurements of carapace width and a single chela height along with shell condition. These chela height data are used to classify the maturity status of individual male crabs to generate population-level estimates of size-specific proportions that are mature. Systematic, annual chela height collection in the survey began in 1989 for snow crab and in 1990 for Tanner crab. From 1990–2007, chela height data were collected for both species during the survey. No chela height data were collected in 2008. From 2009–2017, snow crab data were collected in 2009, 2011, 2013, 2015, and 2017; Tanner crab data were collected in 2010, 2012, 2014, 2016, and 2017. The chela height data collection protocol for the survey was described in Otto (1998): i) the right chela is measured; ii) oldshell crabs are preferentially oversampled due to less common occurrence; iii) a representative size range is chosen; and iv) crabs with a missing cheliped or with different sized right and left chelipeds are not measured (indicating injury or regeneration). Beginning in 2009, chela height data have been recorded to the nearest 0.1 mm (1 mm prior); exploratory analyses showed that results from each time period are similar, and all data since 1989 were used. Exploratory analyses also showed that the chela height data appeared to have many outliers; therefore, chela height to carapace width ratios were calculated for all samples by species and samples in the bottom and top 2.5% percentiles were removed from the data. This study analyzes only non-terminally molted snow crab males > 45 mm CW and Tanner crab > 65 mm CW; these crabs are considered adolescent males that normally molt each spring (Paul and Paul, 1989; Dawe et al., 2012). Survey data indicate very few oldshell males occur below these sizes, and skip-molting rates are therefore negligible. Analyses for this study used 5 mm CW size classes to partition the data. To ensure a minimum annual sample size of 5 for each 5 mm CW size class, the maximum snow crab size considered was 116 mm CW and the maximum Tanner crab size was 136 mm CW. Less than 1% of CW values for adolescent crabs from the chela height data were greater than these upper size limits considered. Adolescent crabs can be separated from mature, terminally molted, adult males based on allometric relationships between chela height data and carapace width, which change at the terminal molt (Somerton, 1981). Dividing lines estimated from a mixture of regressions clustering 64
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corresponding total number of adolescent newshell males sampled for chela height data; and wo, j, y and wn, j, y are weighting factors for oldshell and newshell males to correct for the preferential sampling of oldshell males during chela height data collection. Weighting factor wo, j, y = pos, j, y / poc, j, y , where pos, j, y is the proportion of all oldshell males sampled in the survey data for the given size class and year and poc, j, y is the proportion of all oldshell males sampled in the chela height data for the given size class and year. Weighting factor wn, j, y is calculated similarly but with proportions of newshell males in the survey and chela height data. 2.5. Regression models Binomial generalized linear models were developed to identify important explanatory variables for the estimated skip-molt proportions for both species. (Exploratory analyses showed that generalized additive models had similar values of deviance explained; therefore, the simpler modeling approach was chosen.) The saturated model with the complete set of variables considered was
logit (μj, k, y ) = β0 + Sizej + Depthk + Tempk, y + Year
where μj, k, y is the skip-molt proportion for 5 mm CW size class j at station k in year y . Proportions were calculated with raw data as small sample sizes at the size class/station level for both the general haul catch and for the chela height samples made determination of sampling bias in the chela data uncertain at that level of resolution. β0 is the intercept; Sizej represents the mid-point of size-class j ; Depthk is the bottom depth at station k ; Year represents annual effects; and Tempk, y is bottom temperature at station k in year y at time of summer survey sampling. Size , Depth , and Temp were numeric and continuous variables in the model and Year was a factor (one level for each year). Models with all possible combinations of explanatory variables were run implemented in the R statistical language (version 3.5.1) using the glm function. AIC was used for model selection (lower values indicating a better fitting model for the given number of estimated parameters and maximum likelihood value).
Fig. 1. Classification results of non-terminally molted (below dividing line) and terminally molted (above dividing line) males in the chela height data (1989–2017). Data were collected at both the 1.0 and 0.1 mm resolution. See text for dividing line details.
algorithm (Grün and Leisch, 2008) were provided by National Marine Fisheries Service (pers. comm., L. Rugolo, Alaska Fisheries Science Center, Seattle) to assign maturity status to sampled males of each species (Fig. 1). The dividing line equation was log10(CH ) = β0 + β1 log10(CW ) where CH and CW are chela height (mm) and carapace width (mm) and β0 and β1 are regression coefficients. Tanner crab coefficients are β0 = −1.578645 and β1 = 1.400180 ; snow crab coefficients are β0 = −1.204329 and β1 = 1.265084 . Males with observed chela height greater than the model predicted value were classified as terminally molted. A male crab was classified as a skipmolter from the chela height data if it was both non-terminally molted and in oldshell condition (Dawe et al., 2012).
2.6. Population simulation with skip-molting A size and stage-based simulation model for males of each species was developed to evaluate impacts of skip-molting on population dynamics. The models, based on the modeling framework developed in the 1990s for red king crab (Zheng et al., 1995) and Tanner crab (Zheng et al., 1998) and in use for snow and Tanner crab assessment modeling (Stockhausen, 2016; Szuwalski and Turnock, 2016), follow crabs by 5 mm CW size classes and by immature (non-terminally molted) and mature (terminally molted) stages. Population dynamics are identical for both species. Following stock assessment conventions, the snow crab model tracks abundances by 22 size classes: 25–29 mm, 30–34 mm, …, 130–134 mm; and the Tanner crab model has 32 size classes: 25–29 mm, 30–34 mm, …, 180–184 mm. The model is described with column vectors of length kj , where kj represents number of size classes, and matrices of dimension kj x kj . Immature abundances in year y + 1 are
2.3. Chela height data summary Total annual sample sizes and annual sample sizes by 5 mm CW size bin for both species for newshell adolescent and skip-molted/oldshell adolescent males were tabulated and size summary statistics calculated (which used all data above the minimum size limits for each species). As temperature has been identified as the dominant factor for snow crab skip-molting (Taylor et al., 1993; Dawe et al., 2012), as well as for snow and Tanner crab growth in general (Somerton, 1981; Burmeister and Sainte-Marie, 2010), temperature distributions of sampled immature males by 5 mm CW size classes for each species were summarized.
Ni, y + 1 = Xy + 1 + Wy + 1 + Ry + 1,
Annual population-level skip-molt proportions for each species by 5 mm CW size class j in year y , sj, y, were calculated as
wo, j, y oj, y wo, j, y oj, y + wn, j, y nj, y
(3)
where Ni, y + 1 is a vector of size-specific immature abundances; Xy + 1 is a vector of immature crabs that molted in year y ; Wy + 1 is a vector of sizespecific abundances that skip-molted in year y ; and Ry + 1 is a size-specific vector of recruits. Xy + 1 is
2.4. Size-specific skip-molt proportions from chela height data
sj , y =
(2)
Xy + 1 = (I − Q) GST (I − Z ) Ni, y ,
,
(4)
where Z is a diagonal matrix of size-specific skip-molting probabilities; ST is a diagonal matrix of annual survival for normal molters and mature crabs; G is a size transition matrix; and Q is a diagonal matrix of post-molt maturation probabilities. The model assumes that crabs do
(1)
where oj, y is the total number of adolescent oldshell males sampled for chela height data for the given size class and year; nj, y is the 65
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not skip-molt two years in a row and Wy + 1 is then
Wy + 1 = SW ZXy ,
(5)
where SW is a diagonal matrix of annual survival for skip-molters. Sizespecific mature male abundances are
Nm, y + 1 = QGST (I −Z ) Ni, y + ST Nm, y.
(6)
where subscript m denotes mature males. The duration of a typical period between a molt being skipped and the resumption of molting is 10–12 months (Benhalima et al., 1998; Hebert et al., 2002; Yamamoto et al., 2018); for this model 12 months is assumed to avoid undue model complexity. Total annual recruitment was assumed constant at 106 . Size-transition matrices, probabilities of maturation, and recruitment size distributions were from recent stock assessments for both species (Stockhausen, 2016; Szuwalski and Turnock, 2016). A brute-force parameter search was employed to find the set of sizespecific skip-molting probabilities that resulted in size-specific skipmolt proportions similar to the estimated mean proportions in Fig. 5. No fishery catch was implemented to simplify the analysis. Annual survival is then a function of natural mortality, and is set at 0.68 for all males of both species based on snow crab modeling results from Murphy et al. (2018). Additionally, the consequences of possible lower skip-molt survival on mature biomass levels were examined with sensitivity analyses. This sensitivity analysis was motivated by Comeau et al. (1998), who described the mortality of skip-molters as “massive” in their study. Though Comeau et al. (1998) is the only study to explicitly associate skip-molting with lower survival, Dutil et al. (2010) also speculated that skip-molting may indicate poor physiological condition, further suggesting a plausible correlation with skip-molting and lower survival. The 3 scenarios implemented assume survival during the year subsequent to skip-molting to be 90% (0.61), 80% (0.54), and 70% (0.48) of the baseline annual survival of 0.68. These scenarios also required increases in the skip-molting probabilities from the baseline scenario so that calculated skip-molt proportions were all equal for all model runs. All initial size-specific abundances were seeded with values of 4 × 10 4 , and the model for each species was run for 50 years to ensure reaching steady-state dynamics. From year 50 values, total mature biomass for all males and total biomass of large mature males were calculated using the midpoint of each size class and length-weight relationships from Daly et al. (2016). Total male mature biomass is the primary reference point for management of the EBS snow and Tanner crab fisheries, which only target and retain large mature males. For snow crab, the size range of large mature males was defined as size classes ≥ 100 mm CW (≥ 101 mm CW is minimum size accepted by EBS commercial processors); for Tanner crab, the size range was ≥ 140 mm (≥ 140 mm CW is legal size limit in the EBS). The percent decrease in biomass relative to a non-skip-molting scenario (i.e., all diagonal elements of Z set to zero) was used to assess the effects of skipmolting and skip-molter survival.
Fig. 2. Annual sample sizes of adolescent males in the chela height data (1989–2017) by shell condition. Oldshell condition denotes skip-molters. Vertical grey lines indicate years with no sampling.
16 mm); skip-molter mean size was 102 mm CW (s.d. = 16 mm). Tanner crab temperature distributions were similar across sizes with the interquartile range between 2 and 4 °C for all sizes (Fig. 4). Snow crab temperature distributions increased with increasing size (Fig. 4); the interquartile range of the 45 mm CW size bin was -1.0 to 0.5 while the interquartile range of 115 mm CW size class was about 1.0 to 3.0 °C. The trend in snow crab distributions reflect both ontogenetic movement from the shallower and colder northeast to the deeper and warmer southwest (Otto, 1998; Zheng et al., 2001; Murphy et al., 2011) and lower growth rates in colder waters (Burmeister and Sainte-Marie, 2010). 3.2. Annual size-specific skip-molt proportions The oldshell weighting factor global mean (mean across all size classes and years) for Tanner crab was 0.83 (s.d. = 0.29), indicating a 21% mean oversampling rate for oldshell males for chela height data sampling. The newshell weighting factor global mean for newshell Tanner crab was 1.19 (s.d. = 0.33), indicating a 16% mean undersampling rate. The means of annual Tanner crab skip-molt proportions increased from 0.02 for the 65 mm CW size class to a maximum of 0.41 for the 130 mm CW size class (Fig. 5); 95% confidence intervals also increased with increasing size due to higher variability in the larger sizes due to small sample sizes (Figs. 3 and 5). The annual means of raw skip-molt proportions, unadjusted for sampling bias in the chela height data, were on average 22% higher (s.d. = 13%) than the corresponding adjusted values (Fig. 5). The oldshell weighting factor global mean for snow crab was 0.62 (s.d. = 0.26), indicating a 61% mean oversampling rate. The newshell weighting factor global mean for snow crab was 1.41 (s.d. = 0.53), indicating a 29% mean undersampling rate. The means of annual snow crab skip-molt proportions increased from 0.01 for the 45 mm CW size class to 0.42 for the 115 mm CW size class (Fig. 5); 95% confidence
3. Results 3.1. Chela height data summary 9,895 adolescent male Tanner crab ≥ 65 mm CW sampled from 1990 to 2017 were analyzed. Mean annual sample size was 430 (s.d. = 251; range: 149–1093) (Fig. 2). 17, 958 adolescent snow crabs ≥ 45 mm CW sampled from 1989 to 2017 were analyzed. Mean annual sample size was 748 (s.d. = 530; range: 117–2228) (Fig. 2). For both species newshell sample sizes were highest for smaller sizes while intermediate sizes had the highest skip-molter sample sizes (Fig. 3). Adolescent newshell snow crab mean size was 76 mm CW (s.d. = 15 mm); skip-molter mean size was 84 mm CW (s.d. = 17 mm). Adolescent newshell Tanner crab mean size was 91 mm CW (s.d. = 66
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Fig. 4. Temperature distributions of adolescent males in the chela height data (1989–2017) by 5 mm carapace width size classes. Fig. 3. Sample sizes of adolescent males in the chela height data (1989–2017) by shell condition and by 5 mm carapace width size classes. Oldshell condition denotes skip-molters. Line is mean of annual values.
intervals also increased with larger sizes. The annual means of raw skipmolt proportions were on average 45% higher (s.d. = 18%) than the corresponding unadjusted values (Fig. 5). 3.3. Regression models The final Tanner crab model was the saturated model with size, temperature, depth, and year effects as explanatory variables (deviance explained: 21%, AIC: 7222) (Table 1). Estimated regression coefficients were positive for depth, size, and temperature (Table 1). Models with a subset of the variables of the final models were also run to identify the importance of individual variables. Results from a temperature, year effects model (19%, 7346); temperature and size model (14%, 7756); and size only model (8%, 8279) show that size, temperature, and year effects were the most important explanatory variables for the Tanner crab skip-molt proportions with depth having only modest influence. The final snow crab model was also the saturated model with size, temperature, depth and year effects (deviance explained: 22%, AIC: 13,330). Regression coefficients were positive for depth and size but negative for temperature (Table 1). Results from a size, temperature, and year effects model (21%, 13,506), size and temperature model (20%, 13,553), and temperature only model (10%, 15,006), indicate that temperature and year effects were the most influential explanatory variables and depth and size had modest influence. 3.4. Population simulation
Fig. 5. Mean of annual estimated skip-molt proportions by 5 mm carapace width size classes with 95% confidence interval (1989–2017). Raw proportions (dashed line) are unadjusted for preferential sampling of oldshell crab. Horizontal line at 0.4 for visual reference.
To approximate observed snow crab skip-molt proportions, snow crab size-specific skip-molting probabilities for the baseline skip-molt survival of 0.68 were 25–45% higher than the corresponding skip-molt proportions for the same size class (Fig. 6). For the scenarios with lower 67
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Table 1 Parameter estimates for final regression models, excluding year effects. Species
Variable
Df
Coefficient
Std. error
p value
Snow crab (n = 6,151)
Intercept Size Depth Temperature Intercept Size Depth Temperature
1 1 1 1 1 1 1 1
−5.19 0.007 0.013 0.663 −8.257 0.053 0.012 −0.156
0.287 0.001 0.001 0.019 0.287 0.002 0.001 0.028
< 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10 < 1e-10
Tanner crab (n = 10,093)
Table 2 Percent decrease in total mature biomass and large mature biomass by skipmolt annual survival (survival during year following skipped-molt), relative to no assumed skip-molting. (0.68 survival is same value for normal molters). Skip-molt survival
0.68 0.61 0.54 0.48
skip-molter survival, skip-molting probabilities were increased by 16, 22, and 30% as annual survival decreased from 0.68 to 0.61, 0.54, and 0.48 to ensure the same skip-molt proportions as in the baseline survival scenario. The decrease of total biomass of large mature snow crab males relative to a no skip-molting scenario increased from 12% for the baseline survival scenario to 24% when skip-molter survival was at the lowest value of 0.48 (Fig. 6, Table 2). Decreases in biomass of large mature males were about 35% greater than decreases of total mature biomass for each survival scenario (Table 2). To approximate observed Tanner crab skip-molt proportions, snow crab size-specific skip-molting probabilities for the baseline skip-molt survival of 0.68 were 35–50% higher than the corresponding skip-molt
Snow crab
Tanner crab
Total mat. bio.
Large mat. bio.
Total mat. bio.
Large mat. bio.
9 12 14 18
12 16 19 24
14 19 23 29
23 32 37 47
proportions for the same size class (Fig. 6). Skip-molting probabilities were increased by 15, 20, and 28% as skip-molter survival decreased from the baseline scenario to achieve the same skip-molt proportions as in the baseline skip-molter survival scenario. The decrease of total biomass of large mature Tanner crab males relative to a no skip-molting scenario increased from 23% for the baseline survival scenario to 47% when skip-molter survival was 0.48 (Fig. 6, Table 2). Decreases in biomass of large mature males were about 65% greater than decreases of total mature biomass for each survival scenario (Table 2).
Fig. 6. Results of population simulations. 68
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4. Discussion
non-terminally molted males molt each year. The simulation results suggest that exploring the effects of skip-molting on population dynamics warrants attention, however. The EBS snow and Tanner crab models are fit to size-based data for the immature and mature lifehistory stages. Chela height data can be used to further partition immature data into normal molter and skip-molter components. Then, the assessment model can subsequently model these two immature stages and the mature stage. A random effects/state-space modeling framework would likely be useful (Murphy et al., 2018). Additionally, estimates of male immature and mature survey biomass, which are critical inputs into the assessment models, assume that all oldshell males are mature. This assumption means that survey estimates of mature biomass are biased high and immature biomass estimates are biased low. The simulation results indicate that lower skip-molter survival can strongly influence population dynamics. The impetus for exploring effects of skip-molter survival came from Comeau et al. (1998), who reported that skip-molters had “massive” mortality when attempting to molt again and this mortality significantly impacted male abundances and from Dutil et al. (2010), who speculated that poor physiological condition may contribute to skip-molting. However, explicit estimates of lower skip-molter survival have not been reported. Additional live culture studies (e.g., Yamamoto et al., 2018) appear required to further understanding of skip-molt survival and identify responsible biological mechanisms. Another modeling consideration is the potential difference in sizespecific terminal molting probabilities between skip-molters and nonskip molters. Dawe et al. (2012) concluded that size at terminal molt was a function of both age and size and gave the example of a small male that had undergone more skip-molts at lower temperatures could be older than larger males that had undergone fewer skipped-molts at higher temperatures. (This example would also seem true even if thermal experiences were similar.) This suggests that higher size-specific estimates of terminal molting probabilities for skip-molters could be required for biologically realistic implementation of skip-molting dynamics. An extensive tagging study in AC showed that oldshell snow crab mature males more than one year past their terminal molt can be misclassified as newshell males (Fonseca et al., 2008). This misclassification for snow crab is assumed to happen regularly during EBS survey sampling and can be inferred from implausibly high natural mortality estimates for mature males that are based on accounting of newshell and oldshell abundances (Otto, 1998; Zheng, 2003; Murphy et al., 2018). However, whether this also happens for snow and Tanner crab skip-molters is not known but seems plausible. Misclassification of skip-molters as newshell males would result in under-estimated skipmolt proportions. (Misclassifying actual recently molted newshell crabs as oldshell is presumed unlikely due to their new carapaces having a distinctly bright and unblemished appearance, and the results of Otto (1998); Zheng, 2008, and Murphy et al. (2018) suggest that this does not occur at any significant rates in the EBS.) While the estimated skip-molt proportions seem reasonable, additional steps can help improve their estimation and general understanding of EBS snow and Tanner crab skip-molting dynamics. Histological analyses and physiological data can distinguish timing of molting (Benhalima et al., 1998; Tamone et al., 2007) and differentiate between normal molters and skip-molters (Benhalima et al., 1998; Hebert et al., 2002). By objectively quantifying the timing of a crab’s last molt, histological and physiological data could improve estimation of skip-molting rates and quantify field misclassification rates of shell condition. A random sampling framework would eliminate the need to account for potential sampling bias for analyses of the chela height data.
Size-specific skip-molt proportions estimated for snow crab appear similar to those reported for AC snow crab by Dawe et al. (2012). Dawe et al. (2012) reported multiple sets of estimated size-specific skip-molt proportions, stratified by region and bottom temperature at time of sampling. Generally, these estimated proportions were near zero for 40 mm CW crab and then rose to 0.30–0.60 for crab > 100 mm CW. The temperature distribution data of sampled males reported in Dawe et al. (2012) also appear generally similar to the snow crab temperature distributions reported in this study. Estimated snow crab skip-molt proportions from this study are also similar to the results of Yamamoto et al. (2018), who reported a 28% skip-molting rate for snow crab males 83–123 mm CW from the Sea of Japan. The binomial regressions for both species explained modest variation in the data (i.e., low deviance explained). Dawe et al. (2012) performed similar regressions but did not report any metric of model performance such as deviance explained. While the temperature regression coefficient for final Tanner crab model was negative, the temperature coefficient for the final snow crab model was unexpectedly positive. This positive relationship is in apparent contradiction of the results of Dawe et al. (2012), who found temperature and skip-molt proportions to be negatively correlated. However, snow crab males undergo large scale ontogenetic movements from colder waters in the northeast of the EBS shelf to warmer and deeper waters in the southeast. The positive relationship estimated between temperature and snow crab skip-molting rates is likely due to the confounding of size and temperature values from larger males occupying warmer waters than younger males as seen in Fig. 4. Given that snow crab growth patterns are a function of cumulative thermal history and not just immediate thermal experience (Dawe et al., 2012), EBS male snow crab ontogenetic movement patterns will obscure temperature-growth relationships derived from survey data, which provides only a single snapshot of thermal history. This study appears to be the first to assess the impacts of Chionoecetes skip-molting with population modeling. Though skipmolting is well studied in AC, population models are not used to inform management actions, and skip-molting data has not been used to parameterize a population model. The main finding of the simulation model is that skip-molting may at least moderately decrease biomass of large males targeted and retained by their fisheries. With modest assumptions of lower survival for one year for skip-molters, the decreases in biomass can become much greater. Another important simulation model result is that decreases in mature male Tanner crab biomass is about twice that for snow crab when comparing population dynamics with and without skip-molting (Table 2). Though size-specific skip-molting proportions are actually similar between snow crab and Tanner crab, such proportions are not directly comparable as Tanner crab have larger adult sizes; e.g., a 100 mm CW male snow crab is considered a large snow crab but would only be an intermediate sized Tanner crab. If comparing intermediate sized, non-terminally molted males, such as 70–95 mm CW for snow crab and 90–120 mm CW for Tanner crab, then Tanner crab skip-molt proportions are at least twice as large (Fig. 5). The higher skip-molting rates for Tanner crab may be due to EBS Tanner crab population being at the northern extent of its range in the Eastern Pacific and possibly close to its lower thermal tolerance levels. Comparison of skip-molting rates in warmer regions such as the Gulf of Alaska would help further understanding of temperature effects on Tanner crab skip-molting and differences with snow crab skip-molting. A more complete understanding of the population dynamics consequences of skip-molting will require integrating skip-molting into a statistical population or assessment model with actual fits to observed skip-molter abundances and comparing how model estimates differ from models without skip-molting dynamics. The EBS snow and Tanner crab assessment models do not consider skip-molting and assume all
Acknowledgements Bob Foy, Buck Stockhausen, Jack Turnock, and Louis Rugolo (all at 69
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NOAA’s Alaska Fisheries Science Center, USA) provided survey data, stock assessment estimates, and maturation data. M.S.M. Siddeek (ADF &G), Darrell Mullowney (DFO), and one anonymous reviewer provided very helpful reviews and comments.
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