A New Method to Estimate Duration of Molt Stages in Crustaceans

Home , Cancer pagurus

Crabs in Cold Water Regions: Biology, Management, and Economics 351 Alaska Sea Grant College Program • AK-SG-02-01, 2002

David Hankin Humboldt State University, Department of Fisheries, Arcata, California

Abstract The methods of Drach and Tchernigovtzeff (1967) have been used to describe molt stages of many crustacean species, but there have been few attempts to estimate the duration of individual molt stages. Molt staging often requires destructive removal and examination of a suitably trans- parent paired structure (e.g., branchial epipod), thereby ruling out periodic molt staging of single individuals throughout the molting cycle. In a laboratory setting, however, it is possible to either (1) determine the initial molt stage of a crustacean and then hold it until molting takes place, or (2) hold a freshly molted crustacean and determine its molt stage at a prespecified date following molting. Data generated through such experiments, based on many individuals, consist of either (1) initial molt stages and corresponding days to molt, or (2) days post molting and associated molt stages. I show that the existing published method (Buchholz 1991) for estimating duration of molt stages of crustaceans from type 2 laboratory data lacks a rigorous derivation and may generate seriously biased estimates when molt stages have unequal expected durations. I propose alternative estimators of molt stage durations that have improved performance characteristics.

Introduction The crustacean molting cycle consists of a regular sequence of events that can be divided into four major periods: premolt (preparation for an up- coming molting event), ecdysis (the process of molting itself), postmolt (shell-hardening and other changes that take place shortly following ecdysis), and intermolt (a “resting phase” following the postmolt period and preceding preparation for the next molting event). To describe this molting cycle, Drach (1939) and later Drach and Tchernigovtzeff (1967) proposed a standardized set of setal molt stage designations that have been applied 352 Hankin — Duration of Molt Stages with apparent success to many commercially important species, including at least the European edible crab, Cancer pagurus (Drach 1939), Dunge- ness crab, Cancer magister (Miller 1999), blue crab, Callinectes sapidus (Engel 1987), American lobster, Homarus americanus (Aiken 1973) and snow crab, Chionoecetes opilio (Moriyasu and Mallet 1986, O’Halloran and O’Dor 1988). For many crustaceans, and especially for adults of heavily calcified species such as the Dungeness crab, C. magister, no sufficiently transpar- ent structures exist that allow repeated staging of the same individual throughout the molting cycle. Instead, for these species one is generally restricted to one or perhaps two, typically paired, structures that are suitable for accurate molt staging. In the Dungeness crab, for example, only the (paired) first maxilliped (branchial) epipod seems consistently suitable for molt staging (Miller 1999). In the sections that follow, I assume one of two possible experiment types that can produce data suitable for estimation of the duration of individual molt stages. In the first type of experiment, freshly molted crustaceans are sacrificed and molt staged at prespecified, known dates following molting. Generated data consist of the number of “days to stage i” given that an individual has just molted. In the second type of experiment, individuals are collected at a random point in their molt cycle, staged at collection, and then held until they molt. Generated data consist of “days to molt” given initial stage i. Buchholz (1991) presented a method for estimating duration of molt stages of Antarctic krill, Euphausia superba, based on the first type of experiment. In the following section, I suggest that the estimation scheme proposed by Buchholz is flawed, and I propose an alternative scheme that has improved performance characteristics.

Estimator Development Define a sequence of k (pre)molt stages, labeled from earliest (stage 1) to latest (stage k, immediately preceding ecdysis). For a particular individual, the duration of stage i is the realized value, si , of the random variable Si, with expected duration ES() , i = 1,2,…,k. Define the expected total ii= m duration of stages i through j (j > i) as

j ET()ij,,==tm ijÂ l. li=

I assume that the durations of successive stages are statistically independent of one another, and I assume that all individuals in the experiment are of similar age or instar so that the expected durations of molt stages do not vary among individuals. (For an individual crustacean, the assumption of statistical independence implies that if, for example, the duration of molt stage i were uncommonly short (or long), this would not necessarily result in an unusually short (or long) duration of molt stage i + 1. Instead, Crabs in Cold Water Regions: Biology, Management, and Economics 353 the durations of successive molt stages would be independent of one another. This does not imply that individual crustaceans, e.g., those of different size or age, cannot have generally shorter (or longer) duration of molt stages than other crustaceans.) For the “days to stage” experiments, stages 1 through k would typically include the full sequence of postmolt, intermolt, and premolt stages, whereas for the “days to molt” experiments, one might wish to restrict consideration to crustaceans collected in one of µ τ the premolt stages. Targets of estimation are the i and the ij. Buchholz (1991) Method Buchholz’s (1991) methods for estimation of the duration of molt stages were based on data generated from a “days to stage” experiment conducted with Antarctic krill that had just molted. Summarize these generated data by calculating the observed mean number of days from molting to stage i,

D . Buchholz then calculated “lower stage limits,” S , using S = 0 and i i,l 1,l ˆ SDD()/ii1 2, for i > 1. Finally, expected stage durations for stages 1 il, =+- through k–1 were estimated using

DDii11 ˆ ˆˆ +-- miilil=-=SS1,, . + 2

Buchholz did not present an explicit estimator for mk, but a possible estimator, consistent with the preceding logic, might be

ˆ 2(DSˆ ) m kkkl=-, ˆ However, algebraic substitutions for S imply that ˆ DDkk1 , a result kl, m k =-- that does not seem generally appropriate. Buchholz presented no formal derivation for his estimators of molt stage durations, but instead relied on a visual motivation similar to Fig. 1. In the following section, I present numerical evidence, based on simulations, that the Buchholz method for estimation of stage durations does not produce unbiased or accurate estimates of the true target quantities. Here I present a visual argument that implies such numerical simulation results. In Fig. 1, drawn after Buchholz’s (1991) original Table 5, all expected durations of molt stages are equal and his methods appear to generate good estimates of true expected durations. In Fig. 2, however, it is readily apparent that Buchholz’s (1991) methods will not produce unbiased estimates when expected durations of molt stages are unequal. In Fig. 2, if Buchholz’s (1991) methods were used, the estimated mean duration of stage 1 would, on average, be “too small”; the estimated mean durations of stages 2 and 3 would be “too large”; and the estimated mean duration of stage 4 would be “too small.” 354 Hankin — Duration of Molt Stages

Figure 1. Illustration of the methods used by Buchholz (1991) to estimate duration of molt stages. The total number of molt stages, k, has been limited to 5 to simplify presentation. Asterisks denote the expected locations of observed mean days to stage i data, and estimated stage limits are those that would be calculated given the plotted locations of observed mean days to stage i data; realized locations of D i would vary over repetitions of this kind of experiment. In this figure, the expected durations of all molt stages are equal and Buchholz’s (1991) methods would provide the correct estimates of expected durations of molt stages. The (?) at figure bottom reflects ambiguities in the estimator of molt stage duration for the last stage (see Buchholz 1991). Crabs in Cold Water Regions: Biology, Management, and Economics 355

Figure 2. As for Figure 1 except that durations of molt stages are not all equal. Note that in this setting application of Buchholz’s (1991) methods would not provide the correct estimates of expected durations of molt stages. 356 Hankin — Duration of Molt Stages

Proposed New Methods As an alternative to the Buchholz (1991) methods, I propose method of mo- ments (see, e.g., Blum and Rosenblatt 1972) type estimators of the durations of molt stages. These estimators are most easily motivated in the context of the “days to molt” experiments, but the logic applies with only minor variation to the “days to stage” experiments conducted by Buchholz (1991). In the days to molt experiment, the number of days that a crustacean has spent in the molt stage at which it is originally collected is unknown. If crustaceans were collected at random over the full duration of a molting season, however, then one would expect to collect individuals, on average, halfway through whatever molt stage (stage i) were identified at collection. These individuals thereafter have to pass through all subsequent molt stages (stages i + 1 through k) until ecdysis takes place. For k = 5, the above logic leads to the following setup with respect to the expected mean number of days to molt [( EDi )] for a given initial stage, i :

ED()1 05 . 10 . 10 . 10 . 10 . (1) =++++mmmmm1 2345

ED()2 05 . 10 . 10 . 10 . (2) =+++mmmm2345

ED()3 05 . 10 . 10 . (3) =++mmm345

ED()4 05 . 10 . (4) =+mm45

ED()5 05 . (5) = m5

Moment type estimators of durations of molt stages are obtained by setting the observed mean numbers of days to molt () Di equal to their µ corresponding expected values and then solving for the unknown i . Solv- ˆ 2D5 ing equation 5 for the unknown expected duration of stage 5 gives m 5 = . µ If this result is substituted for 5 in equation 4, the resulting estimator for the expected duration of stage 4 is ˆ 24DD45, and so on. In general, for m 4 =- k ≥ 2 stages, the moment type estimators for the duration of stage i are:

ˆ 24DDii12 4 D i...... 4 D k 1 4 D k for ( ki ) odd, (6a) m i =-++ + + + - - - or

ˆ 24DDii12 4 D i...... 4 D k 1 4 D k for ( ki ) even, (6b) m i =-++ + + -+ - - Crabs in Cold Water Regions: Biology, Management, and Economics 357

An equivalent solution to the above equations (for k = 5, but with obvious extension to arbitrary k) can be obtained via a matrix representa- tion of equations 1-5. Define the following matrixes:

ÈD1 ˘ ˆ È.5 1 1 1 1˘ Èm1 ˘ Èm1 ˘ Í ˙ Í ˙ ÍD2 ˙ Í0 .5 1 1 1˙ Í ˙ ˆ Í ˙ Ím2 ˙ Ím2 ˙ ˜ Í ˙ ˆ ˆ D = D3 ; C = Í0 0 .5 1 1˙; m˜˜= Ím3 ˙ ; and m = Ím3 ˙ Í ˙ Í ˙ Í ˙ Í0 0 0 .5 1˙ Í ˙ ˆ D4 m4 Ím4˙ Í ˙ Í ˙ Í ˙ Í0 0 0 0 .5˙ Í ˙ Íˆ ˙ ÍD5 ˙ Î ˚ Îm5 ˚ m5 Î ˚ Î ˚

˜ ˆ -1 ˜ –1 Then, ED ( ) = Cm˜, and m˜ = CD, where C is the matrix inverse of C. Because the underlying structure of the days to molt experiment gen- erates mean days to molt values that are statistically independent among the various stages, an unbiased estimator of variance for the estimated expected duration of stage i (equations 6a or 6b) would be:

k ˆ ˆ ˆ ˆ VVDVD(mi ) =+416()ilÂ () (7) li=+1

Note that the structure of equation 7 implies that errors of estimation will be much larger for estimation of the duration of the earlier molt stages than for the later molt stages. Estimators of the total expected duration of stages i through j are:

j ˆˆ tmij, = Â l =-22DDii++12 + 2 D i +...... +- 2 D j - 1 2 D j for ( ji - ) odd, (8a) li= or

j ˆˆ tmij, = Â l =-22DDii++12 + 2 D i +...... - 2 D j - 1 + 2 D j for ( ji - ) even, (8b) li=

Again, because the estimators of total duration are a linear combination of independent random variables (the D i ), unbiased variance estimators are of the form:

j ˆ ˆ ˆ VVD(tij, ) = 4Â ()l (9) li=

Finally, let ni = the number of crustaceans initially collected in stage i, and let Dij denote the days to molt for the jth crab with initial stage i. Then, an unbiased estimator of variance of the mean days to molt for stage i (re- quired for equations 7 and 9) is: 358 Hankin — Duration of Molt Stages

ni 2 Â ()DDij - i ˆ 1 j=1 VD()i , (10) = n ()n 1 i i -

assuming that ni ≥ 2.

Simulation Methods All simulations were carried out using S-PLUS 2000 Professional, release 2. Simulations of “days to stage” and “days to molt” experiments shared several common features: (1) The total number of molt stages was fixed arbitrarily at k = 5. (2) Durations of successive molt stages were assumed normally distributed, with parameters µ and 2, and statistically inde- i s i pendent. (3) When µ was small and 2 was large, occasional simulated i s i durations that were less than zero had to be truncated to zero. Remaining features of simulations were generally distinct for the “days to stage” as compared to “days to molt” experiments.

Days to Stage Experiments Key steps in simulation of these experiments were as follows: 1. Begin with a known number, N, of just-molted individuals.

2. For each individual, simulate the duration of stages 1 through 5 and

create a “time line” of total length s1 + s2 + s3 + s4 + s5.

3. Specify a fixed sampling interval, D; select a random value, r, with uniform probability on the interval (0, D); and then generate a system- atic set of “sampling occasions”:

rr ,,++DDD r23,, r +...... , r +- ( q 1 ) D , such that

5 5 ()rq+>D 2Â mi but [(rq+-12 )]D <Â mi = Z. i=1 i=1

(In the following Results section, D = 1.) 4. On the jth sampling occasion (1£ j£ q), randomly select an integer sample size, n ª ND/Z, of individuals from the remaining N – (j – 1)n individuals that have not yet been sacrificed to determine molt stage. (If individuals molt prior to the time that they would otherwise be selected for determination of molt stage, they are eliminated from the pool of individuals remaining in the experiment.)

5. For each individual sacrificed on a given sampling occasion, determine the molt stage and record the (non-integer) date of the associated Crabs in Cold Water Regions: Biology, Management, and Economics 359

sampling occasion. Molt stages are determined by reference to the “time line” constructed for each individual in step 2. For example, for a particular individual, if the sampling occasion falls within the interval

[(s1 + s2), (s1 + s2 + s3)], then the individual would be classified as stage 3. 6. Calculate the mean days to stage i for all individuals classified as being in stage i.

7. Use the Buchholz methods and the new proposed methods to estimate the expected durations of molt stages.

8. Repeat steps 1-7 a large number of times (typically, 1,000) and then calculate the approximate expected values, variances, and mean square errors of the estimators of molt stages.

Days to Molt Experiments 1. Begin with N individuals and simulate the durations of stages 1 through k.

2. Construct a “time line” for each individual, as in step 2 above.

3. For each individual, select a random (non-integer) date of collection, ri with uniform probability on the interval

k (,0 Â si ). i=1

The correspondence between the random date of collection and the “time line” for the individual allows identification of the initial stage at collection, as in step 5 above.

4. Record the simulated number of days to molt for each individual as

k Dsrii= ()Â - i . i=1

5. Calculate the mean number of days to molt for each initial molt stage.

6. Estimate the expected durations of individual stages, the expected total duration of all stages, and the associated estimates of variance for these estimates, using equations 6a-9.

7. Repeat steps 1-5 a large number of times (typically, 1,000) and then calculate the approximate expected values, variances, and mean square errors of the estimators of molt stage durations and the associated estimators of their variances. 360 Hankin — Duration of Molt Stages

Table 1. Comparison of performance characteristics of the Buchholz (1991) and new proposed methods for estimation of the expected duration of setal molt stages based on data collected in simulated “days to stage” experiments.

Buchholz estimators Proposed estimators

Mean Mean Molt True Expected square Expected square stage duration value Variance error value Variance error

µ µ µ µ µ σ 2 Case 1. 1 = 2 = 3 = 4 = 5 = 20; = 4 12020.097 0.197 0.207 20.183 0.658 0.692 22020.011 0.159 0.159 19.842 1.916 1.941 32020.013 0.236 0.237 20.176 2.967 2.997 42020.012 0.280 0.280 19.857 4.421 4.442 52020.008 0.751 0.751 20.159 6.610 6.635

µ µ µ µ µ σ 2 Case 2. 1 = 5, 2 = 15, 3 = 25, 4 = 15, 5 = 5; = 1 15 7.559 0.051 6.600 5.187 0.247 0.517 21514.962 0.041 0.043 14.675 0.819 0.924 32519.989 0.056 25.170 25.312 0.950 1.048 41515.038 0.087 0.088 14.655 1.134 1.254 5510.092 0.244 26.171 5.529 1.903 2.183

µ µ µ µ µ σ 2 Case 3. 1 = 5, 2 = 30, 3 = 10, 4 = 20, 5 = 5; = 1 1511.298 0.051 39.718 5.163 0.238 0.265 23018.743 0.044 126.767 29.704 0.738 0.826 31017.512 0.056 56.480 10.401 0.948 1.108 42013.760 0.095 39.027 19.541 1.164 1.375 5512.550 0.279 57.284 5.556 1.840 2.154

Results Days to Stage Experiments Simulations of the “days to stage” experiments showed that the Buchholz method produces essentially unbiased estimators of the true durations of molt stages only when all molt stages are of equal duration. (Table 1, Case 1). The Buchholz estimators have poor performance characteristics when there is a “smooth” increase and/or decrease in the sequence of expected µ µ µ µ µ durations of molt stages (e.g., 1 = 5, 2 = 15, 3 = 25, 4 = 15, 5 = 5, Table µ µ µ 1, Case 2). For an erratic pattern of expected durations ( 1 = 5, 2 = 30, 3 µ µ = 10, 4 = 20, 5 = 5, Table 1, Case 3), performance would be judged completely unacceptable by any reasonable criteria. For the “smooth change” and erratic pattern of expected durations of molt stages, almost all of the mean square error of the Buchholz estimators was due to (squared) statistical bias (see Table 1 and Fig. 2). Crabs in Cold Water Regions: Biology, Management, and Economics 361

For the “days to stage” experiments, the expected values of the alternative moment type estimators were close to the true durations irrespec- tive of the pattern in expected true durations across molt stages. However, variances of these estimators were considerably greater than those of the Buchholz estimators, and variance also increased substantially from the first through the fifth (last) molt stage. However, mean square errors of the moment estimators were considerably less than those of the Buchholz estimators, except for the case of all expected durations equal. Thus, the proposed moment estimators seem generally much more accurate than the Buchholz estimators.

Days to Molt Experiments The following presentation of results concerning performance of the moment type estimators is in reference to a fixed set of expected molt durations equivalent to Case 3 examined for the days to stage i experiments, µ µ µ µ µ namely: 1 = 5, 2 = 30, 3 = 10, 4 = 20, 5 = 5. Generally, the performance of the proposed moment type estimators was acceptable so long as variability in the duration of individual molt stages was relatively modest. Simulated expected values of estimated mean stage durations were close to the true values so long as duration variance did not exceed 1 (Table 2, Cases 1 and 2). Estimators of the expected total duration of all five molt stages were less sensitive to duration variance and had negligible bias or modest positive bias for all levels of duration variance. Expected values of estimators of variance of the estimators of (a) mean duration of individual stages and (b) total expected duration of all premolt stages were extremely close to the true simulated true values for all levels of variation in duration of individual stages. These estimators appear to be essentially unbiased (Table 2). At higher levels of variance in the duration of individual stages (Cases 3 and 4 on Table 2), however, there was evidence of increasing absolute bias in estimated mean stage durations with increasing variance (variances assumed the same for all stages). Estimators of mean stage duration might be classified as “marginally acceptable” for variance = 4 and as unacceptable for variance = 16. In contrast, the estimator of expected total duration of all stages also appeared to develop a small positive bias as the variance in stage durations increased, but this effect was much smaller than for individual stages.

Discussion Results presented in this paper suggest that the Buchholz (1991) estimators for molt stage duration have substantial and generally unpredictable bias for the general case of variable expected durations of molt stages. Substan- tial variability in duration of molt stages was obvious in Buchholz’s (1991) research on Antarctic krill, and in Miller’s (1999) research on Dungeness 362 Hankin — Duration of Molt Stages

Table 2. Simulated performance of the moment type estimators of (a) the expected durations of individual premolt stages, and of (b) the expected sum of all premolt stage durations based on data collected in simulated “days to molt” experiments.

True

Molt expected Stage duration EE(ˆ )( or ˆ) VV(ˆ )( or ˆ) EV[ˆ(ˆ )] or EV [ˆ(ˆ)] mti mti mti µ µ µ µ µ σ 2 Case 1. 1 = 5, 2 = 30, 3 = 10, 4 = 20, 5 = 5; = 0.25 1 5 5.041 16.924 16.077 230 29.942 10.597 10.295 310 10.060 6.788 6.633 420 19.958 2.550 2.455 5 5 5.017 0.341 0.318 1–5 70 70.018 4.618 4.370

µ µ µ µ µ σ2 Case 2. 1 = 5, 2 = 30, 3 = 10, 4 = 20, 5 = 5; = 1 1 5 5.567 17.891 17.750 230 29.534 11.253 11.270 310 10.398 7.026 7.134 420 19.660 2.687 2.696 5 5 5.153 0.375 0.368 1–5 70 70.312 5.155 5.154

µ µ µ µ µ σ2 Case 3. 1 = 5, 2 = 30, 3 = 10, 4 = 20, 5 = 5; = 4 1 5 7.381 23.958 24.100 230 28.220 15.003 14.992 310 11.382 9.245 9.048 420 18.621 3.693 3.608 5 5 5.744 0.572 0.556 1–5 70 71.349 8.308 8.197

µ µ µ µ σ2 Case 4. m1 = 5, 2 = 30, 3 = 10, 4 = 20, 5 = 5; = 16 1 5 13.318 46.746 47.191 230 23.657 27.056 28.199 310 14.891 14.591 15.548 420 15.440 6.613 6.653 5 5 7.586 1.227 1.191 1–5 70 74.892 19.516 19.341 Crabs in Cold Water Regions: Biology, Management, and Economics 363 crabs, and is probably the rule rather than the exception in crustaceans. Only for the special and presumably unlikely case where all molt stage durations are (approximately) equal will the Buchholz approach generate accurate estimates of expected durations of molt stages. The moment type estimators of expected molt stage duration that have been proposed in this paper represent a significant improvement over the Buchholz approach. If there is relatively small variation in the duration of individual stages, then these moment type estimators will generate approximately unbiased estimators of true expected molt stage durations. For “days to stage” experiments, variance of estimated duration increases with order of molt stage so that errors of estimation for the last stage are much more than for the first stage. For the “days to molt” experiments, variances of estimated duration are inversely related to order of molt stage; errors of estimation for the last stage are much less than for the first stage. Errors of estimation of the total duration of all molt stages or of a subset of molt stages (e.g., all premolt stages) are of intermediate magnitude when compared to the ranges of errors of estimation for the first and last stages over which the total duration is estimated. Equations 7 and 9 appear to provide essentially unbiased estimators of variance of the estimated mean durations of individual molt stages and of the sum of a subset of successive stages, respectively, regardless of the magnitude of variation in duration at individual stages. The simulation results presented in this paper assumed that durations of individual stages were normally distributed and that variances of durations were constant and independent of stage means. I also carried out simulations (not reported here) assuming that durations of molt stages were lognormally distributed with constant lognormal variance parameter. This had the effect of creating constant coefficient of variation of molt stage durations. Results from these lognormal simulations were similar to those for the normal simulations. As variation in the duration of molt stages increased, performance of the proposed moment type estimators deteriorated substantially. Increas- ing errors of estimation at increased levels of variation in molt stage duration were anticipated, but simulated patterns in estimator bias were unexpected. These trends suggest that further work on estimator development is needed before these new estimators can be recommended for general application. In particular, it would seem worthwhile to explore the performance of estimators assuming that distributions of duration of individual molt stages followed some other continuous probability density function (perhaps Gamma or Weibull distributions) which do not allow the occasional impossible negative values suggested by the normal distribution with small mean and large variance. Accurate estimates of the duration of molt stages may have important potential uses for estimating size-specific molting probabilities of crustacean species that have a discrete annual or seasonal molting season. If it were possible to accurately identity (predict) the future molting status of 364 Hankin — Duration of Molt Stages animals prior to the beginning of a discrete molting season, then one might classify a preseason sample of individuals into those that would molt and those that would not, thereby generating estimates of size-specific molting probabilities. As noted by Mohr and Hankin (1989), however, a preseason indicator of future molting destiny would need to have a “notification time” that exceeds the duration of the molting season. For example, the majority of female Dungeness crabs molt within an annual molting season lasting about 120 days (Hankin et al. 1997). For this species, a reliable preseason indicator of future molting would therefore need to have a notification time exceeding 120 days. Based on reported studies, it appears that Drach and Tchernigovtzeff’s (1967) premolt stage designated as D-1¢ is the earliest premolt stage which, if identified in the field, could provide a reliable preseason indicator of molting destiny. Aiken (1973), staging pleopods, found that premolt preparation could become indefinitely arrested among individuals initially staged as setal stages C-4 and D-0 (stages that immediately precede stage D-1¢), whereas all individuals initially staged at D-1¢ (or later stages) advanced to molt. O’Halloran and O’Dor (1988), staging maxilliped exopodites, found that stage D-1¢ was the earliest stage at which molting appeared inevitable in the snow crab. Thus, the effective notification time of molt staging, if used as a premolt indicator, would be the sum of the expected durations of all premolt stages from stage D-1¢ up to ecdysis. If molt staging were considered as a possible premolt indicator for use in estimating size-specific molting probabilities, principal attention would focus on estimation of sum of the durations of premolt stages D-l¢ through to ecdysis. Fortunately, the patterns in proportional bias of the estimator of total duration of all stages were much less serious than were patterns in bias of individual molt stage durations. Unless variation in molt stage durations were quite large, it seems that one could place a reasonable level of confidence in estimates of the total duration of all premolt stages based on “days to stage” or “days to molt” data. It is my hope that the estimators and simulation results presented in this paper will stimulate further statistical research on estimation of the duration of molt stages in crustaceans. Among other things, simulation results suggest that it may be important to incorporate variation in molt stage durations directly into estimation schemes. Also, for the “days to stage” or “days to molt” experiments described in this paper, it would seem worthwhile to explore the consequences and possible benefits of variable sample sizes for individuals sacrificed at different intervals post molting (“days to stage” experiments) or collected at different initial stages and then held for molting (“days to molt” experiments). Finally, even for species for which only a single paired structure can be reliably used for staging, it may be possible to remove the second of the pair at some time following initial collection but preceding molting. The additional information provided by staging single individuals on at least two occasions could probably be incorporated into more sophisticated estimation schemes and Crabs in Cold Water Regions: Biology, Management, and Economics 365 might also allow evaluation of the assumption that durations of molt stages are independent of one another.

References Aiken, D.E. 1973. Proecdysis, setal development, and molt prediction in the Amer- ican lobster (Homarus americanus). J. Fish. Res. Board Can. 30:1337-1344. Blum, J.R., and J.I. Rosenblatt. 1972. Probability and statistics. W.B. Saunders. 549 pp. Buchholz, F. 1991. Moult cycle and growth of Antarctic krill Euphausia superba in the laboratory. Mar. Ecol. Prog. Ser. 69:217-229. Drach, P. 1939. Mue et cycle d’intermue les Crustacea Decapodes. Ann. Inst. Ocean Oceanogr. 19:103-392. Drach, P., and C. Tchernigovtzeff. 1967. Sur la methode de determination des stades d’intermue et son application generale aux crustaces. Vie et Milieu. Series A: Biol. Mar. 18(3A):596-610. English translation by Fish. Res. Board Can., Translation Series 1296. Engel, D.W. 1987. Metal regulation and molting in the blue crab, Callinectes sapidus: Copper, zinc, and metallothionein. Biol. Bull. 172(1):69-82. Hankin, D.G., T.H. Butler, P.W. Wild, and Q.L. Xue. 1997. Does intense fishing on males impair mating success of female Dungeness crabs? Can. J. Fish. Aquat. Sci. 54:655-669. Miller, T.W. 1999. Description of setal stages and estimation of their duration in female Dungeness crabs, Cancer magister. M.S. thesis, Humboldt State Univer- sity, Arcata, California. 120 pp. Mohr, M.S., and D.G. Hankin. 1989. Estimation of size-specific molting probabilities in adult decapod crustaceans based on postmolt indicator data. Can. J. Fish. Aquat. Sci. 46:1819-1830. Moriyasu, M., and P. Mallet. 1986. Molt stages of the snow crab Chionoecetes opilio by observation of morphogenesis of setae on the maxilla. J. Crust. Biol. 6:708- 718. O’Halloran, M.J., and R.K. O’Dor. 1988. Molt cycle of male snow crabs, Chionoecetes opilio, from observations of external features, setal changes, and feeding be- havior. J. Crust. Biol. 8:164-176.

Crabs in Cold Water Regions: Biology, Management, and Economics 367 Alaska Sea Grant College Program • AK-SG-02-01, 2002

Assessment and Management of Crab Stocks under Uncertainty of Massive Die-offs and Rapid Changes in Survey Catchability

Jie Zheng and Gordon H. Kruse Alaska Department of Fish and Game, Division of Commercial Fisheries, Juneau, Alaska

Abstract Survey abundance of a stock can drop sharply from one year to the next. Typically, for fish stocks, stock assessment scientists assume that the sharp decrease in abundance is caused by changes in survey catchability, not natural mortality. However, for crab stocks, occasional sharp drops in abundance can be caused by an increase in natural mortality from massive die- offs, which are substantiated by subsequent annual surveys. Lacking auxiliary data on changes in catchability and mortality, stock assessment modelers are challenged to provide fishery management advice for the year in which the shift in survey abundance occurs. In this study, we used the 1999 stock assessment of St. Matthew Island blue king crabs (Paralithodes platypus) as an example to demonstrate our approach. First, we searched for evidence of an increase in natural mortality and decrease in survey catchability. The available evidence was not conclusive enough to rule out either cause. Second, we developed a four-stage catch-survey model to assess the stock under different assumptions of natural mortality in 1999. Finally, we used the model to evaluate the consequences of different natural mortality assumptions on the stock by projecting the stock abundance into the near future. We suggest that a conservative management approach should be taken when the stock-recruitment relationship may be depensatory or when the handling mortality rate of crab bycatch may be high.

Current address for G.H. Kruse: University of Alaska Fairbanks, School of Fisheries and Ocean Sciences, Juneau Center, 11120 Glacier Highway, Juneau, AK 99801-8677. 368 Zheng and Kruse — Assessment and Management of Crab Stocks

Introduction For some crab stocks in Alaska, such as red king crabs (Paralithodes camtschaticus) in Bristol Bay and blue king crabs (P. platypus) in the eastern Bering Sea, annual assessments begin with an annual trawl survey. Survey data are converted to initial survey abundance estimates through area-swept methods that typically do not consider survey measurement errors. A model is later employed to utilize multiple years of data and multiple data sources to filter out the measurement errors for more accurate abundance estimates. Occasionally, survey abundance of a crab stock drops sharply from one year to the next. For example, based on National Marine Fisheries Service (NMFS) trawl surveys in the eastern Bering Sea, abundance of mature (>119 mm carapace length [CL]) male red king crabs in Bristol Bay dropped 66% from 1980 to 1981, and survey abundance of mature (>104 mm CL) male blue king crabs off St. Matthew Island dropped 83% from 1998 to 1999 (Fig. 1). For fish stocks, stock assessment scientists typically assume that a sharp decrease in estimated abundance is caused by changes in survey catchability or measurement errors, not natural mortality. However, for crab stocks, occasionally sharp drops in abundance can be caused by an increase in natural mortality from massive die-offs. Lacking auxiliary data on changes in catchability and mortality, stock assessment modelers are challenged to provide timely fishery management advice under such situations. In this study, we used the 1999 stock assessment of the St. Matthew Island blue king crab stock, the largest blue king crab stock in Alaska, as an example to demonstrate our approach for such situations. We first searched for corroborating evidence of an increase in natural mortality and decrease in survey catchability. We then developed a four-stage catch- survey model to assess the stock under different assumptions of natural mortality in 1999. Finally, we used the model to evaluate the consequences of different natural mortality assumptions on the stock by projecting stock abundance for the near future.

Evidence of Change in Natural Mortality from 1998 to 1999 Inclusion of auxiliary information on stock status other than standard survey data is an important part of contemporary stock assessments. Aux- iliary information is most important when accuracy of the survey data is in doubt. Auxiliary information for St. Matthew Island blue king crabs collected by the Alaska Department of Fish and Game (ADFG) includes past fishery performance, length compositions of landings, observer data, and experimental, nearshore pot-survey data in 1999. Past fishery performance and carapace length compositions of landings do not provide information about natural mortality from 1998 to 1999, but they may help us assess crab population status for 1998. Catch Crabs in Cold Water Regions: Biology, Management, and Economics 369

Figure 1. Length frequency distributions of Bristol Bay male red king crabs from NMFS trawl surveys during 1979-1983 (top) and St. Mat- thew Island male blue king crabs during 1996-2000 (bottom). Abundance estimates are based on area-swept methods. 370 Zheng and Kruse — Assessment and Management of Crab Stocks per pot lift generally declines over time within a season (Fig. 2). During the 1995-1998 seasons, the highest catch rates occurred in 1995 when the fishing season was shortest. Catch rates in 1996 and 1998 were similar. Even with a relatively long season, landings in 1998 fell short of the preseason catch quota, which was 20% of the estimated abundance of mature male crabs. Low catch rates in 1996 and 1998 could be caused by low true crab abundance as well as low catchability associated with broader spatial distributions. Blue king crabs were much more broadly distributed in 1998 than in 1995 based on spatial analysis of pot survey data (Vining et al. 2001). Length compositions and mean sizes of catch during 1995, 1996, and 1998 are similar and are smaller than those in 1997 (Fig. 2). Observer data provide additional information on female and sublegal male (<120-mm CL) crabs. Unfortunately, observer coverage was very limited for this fishery, and only 1-3 out of 90-131 vessels were covered from 1995 to 1998 (Moore et al. 2000). Because the data were obtained from fewer than four vessels, they are confidential by state regulation. Thus, we only summarize the results here and do not provide specific data. Based on limited data, the catch per pot lift for sublegal male and female blue king crabs was highest in 1995 and subsequently lower in 1996, 1997, and 1998 (Moore et al. 2000). The same order applied to legal male (≥120- mm CL) crabs, but their catch rates were better represented by inseason reporting from a large group of vessels. Length compositions of sublegal males from 1995 to 1998 were similar with the highest proportion of old- shell crabs in 1996 (Moore et al. 2000). Mean lengths of caught females were slightly larger in 1995 (93-mm CL) and 1996 (91-mm CL) than those in 1997 and 1998 (both 89-mm CL). Most caught females were old-shell in 1995 and 1996 and new-shell in 1997 and 1998 (Moore et al. 2000). Besides the NMFS annual summer trawl and ADFG triennial pot surveys, the nearshore pot survey conducted by ADFG provided independent information about the blue king crab stock status in 1999. The nearshore pot survey was conducted in August 1999, shortly after the summer trawl survey. Unlike the triennial pot survey in 1998, the 1999 survey was experimental, covered a limited area, and was aimed at gathering information about female reproductive condition and juvenile crab abundance and distribution (Forrest Blau, ADFG, Kodiak, pers. comm.). Six pot-survey stations were comparable for the 2 years, with 40 pot lifts in 1998 and 70 pot lifts in 1999 (Forrest Blau, ADFG, Kodiak, pers. comm.). Among the six stations, mean catches of male, female, and total crabs per pot lift were 0.3, 27.6, and 27.9 crabs in 1998 and 2.6, 13.8, and 16.4 crabs in 1999, respectively. Thus, catches of male crabs per pot lift were higher in 1999 than in 1998, but catch rates were relatively low for both years. Catch per pot lift of female crabs in 1998 was about double that in 1999, and thus catch rates for all crabs were higher in 1998 than in 1999. Taken together, auxiliary fishery-dependent and fishery-independent data do not offer conclusive evidence to support or refute a massive die- off from 1998 to 1999, although the data indicate possible low abundance Crabs in Cold Water Regions: Biology, Management, and Economics 371

Figure 2. Number of legal males per pot lift (top) and length frequency distributions of retained catch (bottom) from the St. Matthew Island blue king crab fishery during 1995-1998. Catch rate data are from inseason fleet reporting, and size distribution data come from ADFG dockside and observer sampling pro- grams. 372 Zheng and Kruse — Assessment and Management of Crab Stocks in 1999. We cannot conclude that the trawl survey greatly overestimated the crab abundance in 1998 and underestimated it in 1999. Our next step is to analyze historical survey data within the content of a population estimation model under assumptions of different levels of natural mortality from 1998 to 1999.

Model Assessment Four-Stage Model A four-stage catch survey analysis (CSA) is principally similar to a full length-based analysis (Zheng et al. 1995) with the major difference being coarser length groups for the CSA. Because of large size categories, the CSA is particularly useful for a small stock with low survey catches each year. Currently, a four-stage CSA is used to assess abundance and pre- scribe fishery quotas for the St. Matthew Island blue king crab fishery. Only male crab abundance is modeled by CSA because the analysis requires commercial catch data and only males may be retained by the fishery. Male crab abundance was divided into four groups: prerecruit-2s (P2), prerecruit-1s (P1), recruits (R), and postrecruits (P). To be of legal size, St. Matthew Island male king crabs must be ≥140 mm carapace width (regulatory measurement), corresponding to males ≥120 mm CL. The average growth increment per molt is about 14 mm CL for adult male blue king crabs (Otto and Cummiskey 1990). We categorized St. Matthew Island male blue king crabs into P2 (90-104 mm CL), P1 (105-119 mm CL), R (new- shell 120-133 mm CL), and P (old-shell ≥120 mm CL and new-shell ≥134 mm CL). For each stage of crabs, the molting portions of crabs “grow” into different stages based on a growth matrix, and the nonmolting portions of crabs remain the same stage. Under the assumption that the survey catchability of legal crabs is equal to 1, the model links the crab abundances in four stages in year t+1 to the abundances and catch in the previous year through natural mortality, molting probability, and growth matrix:

PP22[(1 mmGeN 2 ) 2 ] -Mt , tt+12,21=-+ ttPP +t + PPmmGPmGe1{1[(1 1) 1 ] 2 2 } -Mt, tt+121=-++ ttPPttPP11,, RPmGPmGe(1 1 2 2 ) -Mt, (1) tttPRttPR+11=+,,2 PPPRPmGPmGeCe(2211)--Mttt()yM1 , tttttPPttPP+11=++2,, + -t

where Nt is new crabs entering the model in year t, m1t and m2t are molting probabilities for prerecruit-1s and prerecruit-2s in year t, Gi,j is a growth matrix containing the proportions of molting crabs growing from group i to group j, Mt is natural mortality in year t, Ct is commercial catch in year Crabs in Cold Water Regions: Biology, Management, and Economics 373

t, and yt is the time lag from the survey to the mid-point of the fishery in year t. By definition, all recruits become postrecruits in the following year.

Data The model was fit to NMFS trawl survey and commercial catch data from 1978 to 1999. Survey stations were stratified based on the approach developed by Zheng et al. (1997b). Basically, the number of tows per station was used as a criterion to stratify the stations: (1) frequent two-tow stations were grouped together as one stratum, (2) frequent one-tow stations formed another stratum, and (3) any single station with four or more tows was regarded as a separate stratum. The stratification was constant over time and similar to that used by NMFS during recent years. The area-swept approach was used to estimate average crab density (abundance per nmi2) for each stratum. Crab abundance by length, sex, and shell condition was estimated for each stratum by taking the product of average crab density and total stratum area. Total abundance of the stock was estimated by summing the abundances from all strata. The St. Matthew Island Section of the Northern District of the Bering Sea management area is defined as north of 58º39¢N and south of 61º49¢N. The model was also fit to the ADFG pot survey data in 1995 and 1998. Average catch per pot lift from 95 survey stations was used as an abundance index (Blau and Watson 1999).

Parameter Estimation Survey catchabilities were used to scale absolute abundances to relative (survey) abundances for parameter estimation. For trawl surveys, we assumed that the survey catchability of legal crabs is 1 to reduce the number of parameters and estimated survey catchabilities for prerecruit-1s and prerecruit-2s. For pot surveys, selectivities relative to legal crabs were estimated for prerecruits, and a scaling parameter was estimated for scaling legal crabs per pot lift to absolute crab abundance.

We modeled molting probability for prerecruit-1s, m1t, as a random walk process:

mme11ht, (2) tt+1 = where ht are independent, normally distributed random variables with a mean of zero. To reduce the number of parameters estimated, we used the ratio (1.44) of m1 to m2 from tagging data to estimate m2 from m1. The growth matrix was estimated from tagging data (Otto and Cummiskey 1990). Measurement errors of survey estimates of relative abundances were assumed to follow a lognormal distribution. A nonlinear least squares approach that minimizes the residual sum of squares (RSS) was used to estimate parameters: 374 Zheng and Kruse — Assessment and Management of Crab Stocks

22 RSS= Â {[ln ( P221tttt q+- ) ln ( p 2 + 1 )] + [ ln ( P 111 q +- ) ln ( p 1 + 1 )] t 22 ++-+++-+[(lnRrtt11 ) ln ( )][( ln Pp t 1 ) ln ( t 1 )] 2 2 ++-++[(lnPs22ttt / q 1 ) ln ( ip 2 1 )][( ln Ps 11//lnqip+-111)(t + )] [(lnRq /11 ) ln ( ir )]222[( lnPq / 1 ) ln ( ip 110 )] } ++-+++-++ttttth , (3)

where p2t, p1t, rt, and pt are relative trawl survey (area-swept) abundances (thousands of crabs) of prerecruit-2s, prerecruit-1s, recruits, and postrecruits in year t; ip2t, ip1t, irt, and ipt are catches per 1,000 pot lifts of prerecruit-2s, prerecruit-1s, recruits, and postrecruits from pot surveys in year t; q2 and q1 are trawl survey catchabilities for prerecruit-2s and prerecruit-1s; s2 and s1 are selectivities for prerecruit-2s and prerecruit- 1s; and q is a scaling parameter (per millions of pot lifts) to convert crabs

per pot lift to absolute crab abundance. Pt /q is the expected postrecruits per 1,000 pot lifts in year t. Estimated parameters include natural mortality, molting probabilities, catchabilities, selectivities, crabs entering the model for the first time each year except the first, and total abundance in the first year. Similar to the length-based model (Zheng et al. 1995), we assumed that the relative frequencies of length groups from the first-year trawl survey data approximate the true relative frequencies. Thus, we did not need to estimate length-specific abundance for the first year. We made three assumptions about natural mortality for the time period between the surveys in 1998 and 1999 (M99) compared to mean natural mortality (M) from 1978 to 1998:

(1) M99 was the same as M; (2), M99 was 3 times as high as M; or (3), M99 was 5 times as high as M. Using AD Model Builder (Otter Research Ltd. 1994), we estimated parameters using the quasi-Newton method to minimize RSS.

Model Fit The estimation algorithm converged quickly, and the results were robust in terms of sensitivity to the initial parameter values. Parameter estimates are summarized in Table 1 for three scenarios. Model estimates of abundance fit well with NMFS survey area-swept estimates of abundance (Fig. 3). Abundance of mature male legal crabs declined from the early 1980s to the mid-1980s and then increased and peaked in 1997. Compared to 1998, both mature and legal crab abundances showed substantial decline in 1999. Model estimates of mature male abundance are lower than area- swept estimates in 1996-1998 and higher in 1999.

Different assumptions about M99 resulted in quite different estimates of abundance in 1999 (Fig. 3). Assumption 3 fit the survey data best because it assumed high natural mortality, resulting in small estimated measurement error, whereas assumption 1 had the poorest fit because it assumed constant natural mortality, producing high estimated measurement Crabs in Cold Water Regions: Biology, Management, and Economics 375

Table 1. Parameter estimates for a catch-survey analysis of St. Matthew Island blue king crabs with data from 1978 to 1999.

Natural mortality in 1999

Parameter M 3M 5M

Natural mortality (M) from 1978 to 1998 0.27 0.36 0.32 Trawl catchability: prerecruit-2s (q2) 0.53 0.38 0.41 Trawl catchability: prerecruit-1s (q1) 0.95 0.79 0.83 Trawl catchability: legals 1.00 1.00 1.00 Pot selectivity: prerecruit-2s (s2) 0.29 0.23 0.20 Pot selectivity: prerecruit-1s (s1) 0.71 0.61 0.58 Pot selectivity: legals 1.00 1.00 1.00 Pot scaling parameter (q) 0.30 0.33 0.35 Mean molting probability: prerecruit-2s (m2) 1.00 1.00 1.00 Mean molting probability: prerecruit-1s (m1) 0.91 0.92 0.90 Standard deviation of ht (equation 2) 0.02 0.02 0.03

Growth matrix (G): from Prerecruit-2s Prerecruit-1s

Prerecruit-2s 0.11 0.00 Prerecruit-1s 0.83 0.11 Recruits 0.06 0.83 Postrecruits 0.00 0.06

Three natural mortality options were assumed for the time period between the surveys in 1998 and 1999.

error in 1999. Mortality assumption 2 resulted in an intermediate estimate of abundance in 1999, and the estimated measurement error in 1999 was equal to about the largest measurement error estimated in the past (Fig. 4). We believe the trawl survey underestimated the 1999 abundance, but we are not confident in the results of assumption 1 because of the large estimated measurement errors. Instead we believe that increased mortality and reduced catchability combined to produce the survey results in 1999, and we regard the results based on assumption 2 as the most likely scenario. Some model parameter values vary depending on these three different assumptions about M99 (Table 1). Differences among scenarios are partially due to unavoidable confounding among parameters. For example, estimated natural mortality is negatively confounded with estimated catchability for prerecruit-2s (Table 1). Currently, we lack sufficient additional data to solve such confounding problems. Additional years of survey data will be helpful. The persistent low abundance indicated by the survey in 2000 (Fig. 3) supports our interpretation of high natural mortality in 1999 (Zheng and Kruse 2000b). 376 Zheng and Kruse — Assessment and Management of Crab Stocks

Figure 3. Comparison of abundance estimates (millions of crabs) of St. Matthew Island mature (top) and legal (bottom) male blue king crabs from area-swept estimates and catch-survey analysis. Three assumptions were made for natural mortality in 1999

(M99). M is the estimated natural mortality from 1978 to 1998. Crabs in Cold Water Regions: Biology, Management, and Economics 377

Figure 4. Relative errors [(area-swept estimate – model estimate)/model

estimate] of model fits with M99 = M, M99 = 3M, and M99 = 5M for St. Matthew Island blue king crabs. M is the estimated natural mortality from 1978 to 1998. 378 Zheng and Kruse — Assessment and Management of Crab Stocks

Abundance Projections in 2000 The four-stage model was used to project mature and legal male abundances in 2000 using the assessment results in 1999 and assuming natural mortality from 1999 to 2000 (M00) equal to either M or M99. Natural mortality rates used in the projections are 4% lower than those in Table 1. Natural mortality estimated from the assessment model includes bycatch mortality from the directed pot fishery. In the projections we applied natural mortality and handling mortality separately, and M was reduced accord- ingly. Handling mortality rate of captured but discarded sublegal males was assumed to be 20% for the directed crab fishery. Because few St. Mat- thew Island blue king crabs were caught as bycatch by the groundfish fisheries, bycatch mortality from the groundfish fisheries was not included in the projections. The harvest strategy in 1999 was used to project abundance in 2000. The strategy consists of a fixed mature harvest rate of 20% with a fishery threshold of 0.6 million mature male crabs (about 2 million pounds) and no minimum guideline harvest level. Three levels of catch resulted from assessments of 1999 abundance based on assumptions of M99 = M, 3M, and 5M; zero catch in 1999 was also considered in the projections. There- fore, for each assumption of M99 we projected mature and legal male abundances in 2000 with four levels of catch in 1999. Projected abundances in 2000 varied greatly on different assumptions of natural mortality from 1998 to 1999 and from 1999 to 2000 and on different catch levels (Table 2). As expected, higher natural mortality and catch resulted in lower projections of crab abundance. The projected mature and legal male abundances ranged from 2.32 and 1.90 million when

M99 = M and M00 = M with zero catch in 1999, to 0.13 and 0.07 million when

M99 = 5M and M00 = M99 with a high catch in 1999. There are two kinds of risks here: loss of fishing opportunity (underharvest) and overfishing. If the low survey abundance in 1999 was caused by measurement errors from change in catchability and we assessed the stock using a M99 higher than the real value, fishing opportunity would be lost. In this case, the maximum potential loss of catch in 1999 was 0.509 million crabs (Table 2). However, this loss would be reduced by higher abundance in 2000 and future years and growth in body weight. For example, if M99 = M, the legal crab abundance in 2000 would be 0.43 million crabs more without catch than with 0.509 million catch in 1999 (Table 2). The higher future biomass with lower catch in 1999 would increase future yield and perhaps future recruitment. On the other hand, if M99 was higher than M and we assessed the stock using M99 = M, we might overharvest the stock in 1999. For example, if M99 = 5M and M00 = M, the legal crab abundance in 2000 would be reduced from 0.739 million crabs without catch to 0.317 million crabs with a catch of 0.509 million in 1999 (Table 2). Crabs in Cold Water Regions: Biology, Management, and Economics 379

Table 2. Projections of mature and legal male abundances (millions of crabs) in 2000, and target and estimated mature male harvest rates and over- or underharvest of catch (millions of crabs) in

1999 under different natural mortalities from 1998 to 1999 (M99) and catches for St. Matthew Island blue king crabs.

Abundance Catch Harvest rate

If M00 = M If M00 = M99 Over or Assumption Total under (–) Target Estimated Mature Legal Mature Legal

If M99 = M

M99 = M 0.509 0.000 0.2 0.20 1.846 1.465 1.846 1.465

M99 = 3M 0.295 –0.214 0.2 0.12 2.039 1.646 2.039 1.646

M99 = 5M 0.199 –0.311 0.2 0.08 2.137 1.734 2.137 1.734 No fishing 0.000 –0.509 0.2 0.00 2.319 1.895 2.319 1.895

If M99 = 3M

M99 = M 0.509 0.214 0.2 0.34 0.910 0.655 0.441 0.308

M99 = 3M 0.295 0.000 0.2 0.20 1.082 0.823 0.535 0.400

M99 = 5M 0.199 –0.097 0.2 0.13 1.170 0.903 0.579 0.443 No fishing 0.000 –0.295 0.2 0.00 1.335 1.054 0.641 0.506

If M99 = 5M

M99 = M 0.509 0.311 0.2 0.51 0.513 0.317 0.134 0.071

M99 = 3M 0.295 0.097 0.2 0.30 0.692 0.491 0.195 0.131

M99 = 5M 0.199 0.000 0.2 0.20 0.784 0.574 0.224 0.159 No fishing 0.000 –0.199 0.2 0.00 0.965 0.739 0.262 0.200

M is the estimated natural mortality from 1978 to 1998, and M00 is the natural mortality from 1999 to 2000. As a comparison, area-swept estimates of mature and legal male abundance in 2000 are 1.121 and 0.811 millions of crabs.

Discussion How does a stock assessment modeler deal with a situation when the survey estimate of a stock abundance fell sharply in a given year? We suggested in this study that we should consider the possibility that natural mortality had changed when a decline in survey abundance far ex- ceeded the level explained by estimated survey measurement errors in the past. We proposed the following approach to deal with this situation for a crab stock. First, auxiliary information should be collected to gauge whether a massive die-off has occurred. Collecting auxiliary information should be a routine part of stock assessment and is especially important when the unexpected results from a standard survey occur. The auxiliary information may include past fishery performance, experimental fishing, additional surveys, disease monitoring, and so on. Although the auxiliary data were inconclusive about a change in natural mortality of St. Matthew Island 380 Zheng and Kruse — Assessment and Management of Crab Stocks blue king crabs from 1998 to 1999, the poor fishery performance in 1998 and low catch rates of an experimental nearshore pot survey in 1999 led us to accept the notion that natural mortality in 1999 increased above historical levels. This information helped us make assumptions about natural mortality in 1999 in the modeling step. Second, a model should be used to evaluate different assumptions about natural mortality in the terminal year. Fu and Quinn (2000) showed that annual mortality or trends of natural mortality could be estimated in a length-based model using survey data. However, because of confounding between annual change in natural mortality and survey measurement errors, assumptions have to be made about one to estimate the other. We can assume natural mortality in the terminal year to range from no change from the past to the change that makes the model estimate of stock biomass or abundance equal to the survey estimate in the terminal year. In our study, we examined M99 ranging from M in the past to 5 times M. For each assumed natural mortality level, we examined the associated estimated measurement errors. The level of acceptable measurement error in the terminal year depends on the reliability of the survey data. In our assessment of St. Matthew Island blue king crabs in 1999, we accepted the estimated measurement error in 1999 to be about equal to the largest measurement error estimated in the past. We subjectively attributed the low survey abundance in 1999 to the combination of high natural mortality and high measurement error. Finally, future population projections should be made. Projections serve two purposes: providing population status information for future years and evaluating effects of assessment errors and harvest on the population in the near future. These projections provide important information for decision-making. If the projected population abundance next year is near or below the overfished level, harvest rates may need to be reduced or no harvest will be allowed (Restrepo et al. 1998). Reduced harvest rates result in immediate loss of harvest opportunity and yield, but such loss may be compensated by future increases in harvest opportunity and yield through growth in weight and future reproduction of surviving individuals. The trade-off between immediate loss and future gain can be evaluated using yield-per-recruit or economic yield-per-recruit methods and computer simulations. Projections beyond one year require assumptions about recruitment dynamics and may not be reliable due to uncertainty in the stock assessment in the terminal year. In our study, we made projections only one year ahead because we believe that new survey data in the coming two to three years will help answer the question we ad- dressed in this paper. The long-term effect of assessment errors on the population can be evaluated through computer simulations. The challenge for conducting computer simulations for a crab population is constructing a stock-recruitment (S-R) relationship. Unfortunately, because of a complex reproductive biology and a lack of reliable female abundance data, we cannot Crabs in Cold Water Regions: Biology, Management, and Economics 381 establish an S-R relationship for most crab stocks in Alaska at present, including the St. Matthew Island blue king crab stock. Without the S-R relationship, we assumed random recruitment and autocorrelated recruitment in computer simulations to evaluate harvest strategies for St. Mat- thew Island blue king crabs (Zheng and Kruse 2000a). The S-R relationship has important implications for assessing the effect of assessment errors on a population and optimal harvest strategies. The effect of assessment errors on an expected objective value is usually small unless a threshold exists in the S-R relationship such that overhar- vests could lead to an irreversible stock collapse (Frederick and Peterman 1995). With a more density-dependent S-R curve, a crab stock could be much more vulnerable to overfishing under high handling mortality rates (Zheng et al. 1997a). A conservative approach should be taken to deal with uncertainty when the S-R relationship is depensatory (Frederick and Peter- man 1995). We do not know whether a depensatory threshold exists for a crab stock. However, most king crab stocks in the Gulf of Alaska have been depressed for more than two decades and have not shown signs of recovery. We cannot rule out depensatory S-R relationships for these king crab stocks as well as for other crab stocks, even though we do not have information for such relationships. Because of potential irreversible stock collapse at an extremely low stock abundance, the cost of overharvesting due to assessment errors may greatly outweigh the cost of underharvesting. Therefore, the risk of overharvesting should be minimized when the abundance is very low. Another important factor influencing effects of assessment errors on a population and harvest strategies is handling mortality rate. In Alaska, harvest policies allow harvest of legal-sized male crabs only, and sublegal male and female crabs caught during fishing have to be returned to the sea. Handling mortality reduces future recruitment to fisheries by reduc- ing both prerecruit abundance and spawning biomass. Besides mortality, handling may also produce sublethal effects on crabs, such as reduced growth (Kruse 1993). Handling mortality rate for crab bycatch in the directed fishery is not well known. Based on limited observer data, bycatch of sublegal male and female crabs from the directed blue king crab fishery off St. Matthew Island is relatively high, and total bycatch was often twice as high or higher than the total catch of legal crabs (Moore et al. 2000). Mortality rates for crab bycatch may depend on handling injury, air temperature, wind speed, shell condition, and numerous other factors (Carls and O’Clair 1990; Kruse 1993; Zhou and Shirley 1995, 1996). Exposure of red king and Tanner (Chionoecetes bairdi) crabs to cold air reduces vigor, lowers growth, and leads to increased mortality during ecdysis in severe situations (Carls and O’Clair 1990). In contrast, simulated deck and water impacts caused no increase in mortality of red king crabs, although inju- ries to spines and the rostrum increased with handling (Zhou and Shirley 1995, 1996). Because not all potential contributing factors have been ad- equately studied, the level of handling mortality experienced in Alaskan 382 Zheng and Kruse — Assessment and Management of Crab Stocks crab fisheries remains uncertain. A handling mortality rate of 20% was used in computer simulation studies for king and Tanner crabs (Zheng et al. 1997a; Zheng and Kruse 1999b, 2000a). The possibility of high handling mortality rates may justify a more conservative approach in stock assessments. In our assessment of St. Matthew Island blue king crabs in 1999, we concluded that both measurement error (low survey catchability) and high natural mortality might be causes of the low survey abundance (Zheng and Kruse 1999a). We provided assessment results to managers based on the assumption of M99 = 3M. A better approach may be to provide a probability distribution for M99, with a suggested M; however, it would be a challenge to get a reasonable estimate of this distribution. Due to time constraints and the lack of S-R relationships, we did not conduct computer simulations to evaluate the long-term effects of assessment errors on the population. Given the lack of knowledge on the S-R relationship and uncertainty on handling mortality rate, managers took a conservative approach with the St. Matthew Island blue king crab stock in 1999. The fishery was closed in 1999 due to the perceived depressed stock condition (Zheng and Kruse 1999a). Uncertainty of the assessment for 1999 can only be solved by future survey data. The new harvest strategy adopted in 2000 reduces harvest rates when the estimated stock abundance is below the long-term average level (Zheng and Kruse 2000a), and this conservative approach adds protection to the stock in the context of the assessment uncertainty discussed.

Acknowledgments We thank Rance Morrison of ADFG for providing inseason fishery performance data and Bob Otto and Brad Stevens for providing NMFS survey data. The study was funded, in part, by cooperative agreement NA97FN0129 from the National Oceanic and Atmospheric Administration (NOAA). The views expressed are those of the authors and do not necessarily reflect the views of NOAA or any of its subagencies. This is contribution PP-214 of ADFG, Commercial Fisheries Division, Juneau.

References Blau, S.F., and L.J. Watson. 1999. St. Matthew Island blue king crab survey, 1998. Alaska Department of Fish and Game, Commercial Fisheries Division, Region- al Information Report 4K99-66, Kodiak. 39 pp. Carls, M.G., and C.E. O’Clair. 1990. Influence of cold air exposures on ovigerous red king crabs (Paralithodes camtschatica) and Tanner crabs (Chionoecetes bairdi) and their offspring. In: Proceedings of the International Symposium on King and Tanner Crabs. University of Alaska Sea Grant, AK-SG-90-04, Fairbanks, pp. 329-343. Crabs in Cold Water Regions: Biology, Management, and Economics 383

Frederick, S.W., and R.M. Peterman. 1995. Choosing fisheries harvest policies: When does uncertainty matter? Can. J. Fish. Aquat. Sci. 52:291-306. Fu, C., and T.J. Quinn II. 2000. Estimability of natural mortality and other population parameters in a length-based model: Pandalus borealis Krøyer in Kache- mak Bay, Alaska. Can. J. Fish. Aquat. Sci. 57:2420-2432. Kruse, G.H. 1993. Biological perspectives on crab management in Alaska. In: G.H. Kruse, D.M. Eggers, R.J. Marasco, C. Pautzke, and T.J. Quinn II (eds.), Proceed- ings of the International Symposium on Management Strategies for Exploited Fish Populations. University of Alaska Sea Grant, AK-SG-93-02, Fairbanks, pp. 355-384. Moore, H., L.C. Byrne, and D. Connolly. 2000. Alaska Department of Fish and Game summary of the 1998 mandatory shellfish observer program database. Alaska Department of Fish and Game, Commercial Fisheries Division, Regional Infor- mation Report 4J00-21, Kodiak. 146 pp. Otter Research Ltd. 1994. An introduction to AD Model Builder: For use in nonlinear modeling and statistics. Otter Research Ltd., Nanaimo, British Columbia. Otto, R.S., and P.A. Cummiskey. 1990. Growth of adult male blue crab (Paralithodes platypus). In: Proceedings of the International Symposium on King and Tanner Crabs. University of Alaska Sea Grant, AK-SG-90-4, Fairbanks, pp. 245-258. Restrepo, V.R., G.G. Thompson, P.M. Mace, W.L. Gabriel, L.L. Low, A.D. MacCall, R.D. Methot, J.E. Powers, B.L. Taylor, P.R. Wade, and J.F. Witzig. 1998. Technical guidance on the use of precautionary approaches to implementing national standard 1 of the Magnuson-Stevens Fishery Conservation and Management Act. NOAA Tech. Memo. NMFS-F/SPO-31. 54 pp. Vining, I., F. Blau, and D. Pengilly. 2001. Evaluating changes in the spatial distribution of blue king crab near St. Matthew Island. In: G.H. Kruse, N. Bez, A. Booth, M.W. Dorn, S. Hills, R.N, Lipcius, D. Pelletier, C. Roy, S.J. Smith, and D. Witherell (eds.), Spatial processes and management of marine populations. University of Alaska Sea Grant, AK-SG-01-02, Fairbanks, pp. 327-348. Zheng, J., and G.H. Kruse. 1999a. Stock status of king crab stocks in the eastern Bering Sea in 1999. Alaska Department of Fish and Game, Commercial Fisher- ies Division, Regional Information Report 5J99-09, Juneau. 19 pp. Zheng, J., and G.H. Kruse. 1999b. Evaluation of harvest strategies for Tanner crab stocks that exhibit periodic recruitment. J. Shellfish Res. 18:667-679. Zheng, J., and G.H. Kruse. 2000a. Overview of stock assessment and recommended harvest strategy for St. Matthew Island blue king crabs. Alaska Department of Fish and Game, Commercial Fisheries Division, Regional Information Report 5J00-06, Juneau. 20 pp. Zheng, J., and G.H. Kruse. 2000b. Stock status of king crabs in the eastern Bering Sea in 2000. Alaska Department of Fish and Game, Commercial Fisheries Divi- sion, Regional Information Report 5J00-09, Juneau. 20 pp. 384 Zheng and Kruse — Assessment and Management of Crab Stocks

Zheng, J., M.C. Murphy, and G.H. Kruse. 1995. A length-based population model and stock-recruitment relationships for red king crab, Paralithodes camtschaticus, in Bristol Bay, Alaska. Can. J. Fish. Aquat. Sci. 52:1229-1246. Zheng, J., M.C. Murphy, and G.H. Kruse. 1997a. Analysis of the harvest strategies for red king crab, Paralithodes camtschaticus, in Bristol Bay, Alaska. Can. J. Fish. Aquat. Sci. 54:1121-1134. Zheng, J., M.C. Murphy, and G.H. Kruse. 1997b. Application of catch-survey analysis to blue king crab stocks near Pribilof and St. Matthew islands. Alaska De- partment of Fish and Game, Division of Commercial Fisheries, Alaska Fish. Res. Bull. 4:62-74. Zhou, S., and T.C. Shirley. 1995. Effects of handling on feeding, activity and surviv- al of red king crabs, Paralithodes camtschaticus (Tilesius, 1815). J. Shellfish Res. 14:173-177. Zhou, S., and T.C. Shirley. 1996. Is handling responsible for the decline of the red king crab fishery? In: High latitude crabs: Biology, management, and economics. University of Alaska Sea Grant, AK-SG-96-02, Fairbanks, pp. 591-611. Crabs in Cold Water Regions: Biology, Management, and Economics 385 Alaska Sea Grant College Program • AK-SG-02-01, 2002

Trends in Prevalence of Bitter Crab Disease Caused by Hematodinium sp. in Snow Crab (Chionoecetes opilio) throughout the Newfoundland and Labrador Continental Shelf

Earl G. Dawe Department of Fisheries and Oceans, Science Oceans and Environment Branch, St. John’s, Newfoundland, Canada

Abstract This paper describes the spatial distribution and prevalence of bitter crab disease (BCD) in snow crabs (Chionoecetes opilio) throughout the New- foundland and southern Labrador continental shelf during 1996-2000. This disease or syndrome, caused by a hemo-parasitic dinoflagellate of the genus Hematodinium, occurs predominantly in recently molted (new- shelled) crabs of both sexes and is fatal to the snow crab host. Prevalence determination was based on macroscopic identification of chronic cases in crabs collected during annual fall bottom trawl surveys. Bitter crab disease was most prevalent within the center of the broad snow crab distribution and was rare in the southernmost area. Spatial and annual variations in both distribution and prevalence of BCD were considerable. Prevalence was highest in mature females and intermediate-sized males, but there was annual and spatial variation in size ranges most affected. Relation- ships between catch rates and prevalence of BCD showed no clear evidence of either density dependence or an effect on natural mortality. It is unknown how well disease prevalence in trawl-caught samples represents true prevalence in the population.

Introduction Parasitic dinoflagellates of the genus Hematodinium have been found in the hemolymph of a variety of commercially important crustaceans 386 Dawe — Prevalence of Bitter Crab Disease

(Newman and Johnson 1975, MacLean and Ruddell 1978, Meyers et al. 1987, Field et al. 1992, Shields 1992, Bower et al. 1993, Hudson and Shields 1994, Messick 1994, Wilhelm and Mialhe 1996, Appleton and Vickerman 1998, Messick et al. 1999). Infection of spider crabs of the genus Chionoecetes in Alaska by this parasite has been termed bitter crab syndrome or bitter crab disease (BCD) because meats from heavily parasitized crabs are bitter-tasting and unmarketable, although harmless to humans. Bitter crab disease is 100% fatal to its host (Meyers et al. 1987). Infection is recognizable externally in heavily parasitized crabs by abnor- mal pink or orange coloration of the dorsal carapace and joints of the walking legs, as well as an opaque white “cooked” appearance of the ventral carapace. Often, there are white opaque streaks along the translucent midventral merus leg section. Internally, opaque hemolymph is evident (Meyers et al. 1990). Bitter crab disease was first reported in southeast Alaskan Tanner crabs (C. bairdi) as early as 1974, but was not attributed to infection by Hematodinium sp. until 1986 (Meyers et al. 1987). It has subsequently been found in snow crabs (C. opilio) from the Bering Sea (Meyers et al. 1990), where its prevalence tends to increase with latitude (Morado et al. 2000). Alaskan studies addressing spatial distribution and seasonality of BCD have been primarily based on C. bairdi (Meyers et al. 1987, 1990; Eaton et al. 1991; Love et al. 1993). The duration of the parasite’s life cycle as well as the mode of transmission are unclear. Meyers et al. (1990) noted that the dinoflagellate’s life cycle may be annual with transmission occurring in association with the Tanner crab molting season, either by direct penetration of motile spores through cracks in the new soft cuticle or by cannibalism, especially on newly molted crabs. However, they also noted that the parasite’s life cycle could be longer than 1 year because the development of infectious spores is not in synchrony with the Tanner crab molt cycle, so that crabs that are heavily parasitized in the fall would have been infected in the spring of the previous year, involving a pathogenesis of about 15-18 months. It is also possible, although less likely, that there is some other mode of transmission that is not directly related to molting, such as sexual transmission (Meyers et al. 1996). Taylor and Khan (1995) documented the first known occurrence of BCD in Newfoundland snow crabs (C. opilio) in 1992 and they identified the causative agent as Hematodinium sp. They found, based on sampling in three localized fishing areas during various months, that incidence was very low, at about 0.1% during 1992-1993. Spatial, annual, and seasonal trends in prevalence of this disease in snow crab are unknown in the Newfoundland and Labrador area. Also, possible relationships with crab density, host sex or body size, and water depth are virtually unknown. This is unfortunate because an understand- ing of such trends and relationships may indicate mechanisms for transmission of the disease and factors that regulate its prevalence. Crabs in Cold Water Regions: Biology, Management, and Economics 387

In this paper I describe the spatial distribution and minimum prevalence of BCD in snow crabs throughout the range of snow crab distribution along the eastern Newfoundland and southern Labrador continental shelf. Annual changes in spatial distribution of BCD are described based on 1996- 2000 fall bottom trawl surveys. Further details on effects of year, density, and host sex and body size are provided. The possible effects of this disease on natural mortality levels and recruitment are also considered.

Methods Sampling Snow crab samples were acquired and examined during 1996-2000 fall multispecies stratified random bottom trawl surveys, which extended from the Grand Bank northward throughout the northeast Newfoundland and southern Labrador continental shelf. Spatial stratification of this area, for purposes of survey set allocation is, in part, based on NAFO (Northwest Atlantic Fisheries Organization) divisions. While these divisions hold no biological significance with respect to snow crabs (Fig. 1), they do represent a convenient basis for facilitating spatial comparisons. The surveys utilized the Campelen 1800 survey trawl, a shrimp trawl with mesh size of 44-80 mm and a nylon codend liner of 12.7 mm mesh. The trawl has a wingspread of about 16 m and a footrope equipped with rock-hopper gear. It was fished in standard tows of 15 min duration, at a speed of 3.0 knots, over a distance of 0.75 nautical miles. These multispecies surveys with the Campelen trawl began in 1995, but BCD was not routinely monitored in that year. Snow crab catches were sorted by sex and either fully sampled or, in the case of very large catches, subsampled. A total of 77,670 crabs were sampled across all years (Table 1), representing 74% of all crabs caught. All crabs sampled were measured in carapace width (CW, mm), and maturity was assigned to females (immature versus mature). All crabs were also assigned one of three shell condition categories based on the relative extent of carapace fouling, which approximately reflects time elapsed since molting: (1) new-shelled—these crabs had last molted in spring of the current year; carapaces are clean, white ventrally, and iridescent. (2) intermediate-shelled—these crabs had last molted in spring of the previous year; carapaces are yellowed ventrally, not iridescent, and chelae bear ventral scratches. (3) old-shelled—these crabs last molted at least 2 years ago; carapaces are heavily fouled dorsally and brown ventrally; very old- shelled crabs have soft carapaces due to decalcification and decay in some leg joints. Occurrence of advanced stages of BCD was noted based on macroscopic examination. In cases of unclear external characteristics, crabs were dissected and classified based on observation of the hemolymph. Obser- vation of cloudy or milky hemolymph was taken as support for classifica- tion of such specimens as infected. Specimens displaying clear external 388 Dawe — Prevalence of Bitter Crab Disease

Figure 1. Map of the Newfoundland-southern Labrador continental shelf showing total snow crab catches, as number of individuals per tow, in 2000 in relation to Northwest Atlantic Fisheries Organization (NAFO) divisions. Crabs in Cold Water Regions: Biology, Management, and Economics 389

Table 1. Numbers of crabs caught, examined for BCD, and percentage infected, by year and sex.

Year Sample/ Years Sex Category 1996 1997 1998 1999 2000 pooled

Males Caught 23,087 16,630 15,869 7,392 13,869 76,846 Examined 15,525 13,596 12,821 7,031 9,830 58,803 BCD 120 284 135 41 102 682 % BCD 0.8 2.1 1.1 0.6 1.0

Females Caught 9,547 5,642 2,851 2,165 7,372 27,577 Examined 5,999 4,166 2,293 2,078 4,331 18,867 BCD 91 185 35 25 84 420 % BCD 1.5 4.4 1.5 1.2 1.9

Sexes pooled Caught 32,633 22,271 18,719 9,557 21,241 104,422 Examined 21,524 17,762 15,114 9,109 14,161 77,670 BCD 211 469 170 66 186 1,102 % BCD 1.0 2.6 1.1 0.7 1.3 1.4

characteristics of BCD were randomly selected and dissected to examine the hemolymph and so validate the macroscopic observations. All those specimens displayed milky hemolymph, supporting their categorization as infected.

Treatment and Analysis of Data Most trends in prevalence of BCD are described based on males only, because only males are of economic value and males have a broader size range than females. However, the most general trends are compared between the sexes to determine applicability to the entire population. To examine the relationship between BCD prevalence and size composition in detail within one area, male carapace widths were grouped into 3 mm intervals. To examine the effect of size on prevalence of BCD across all years and the entire survey area, males were grouped into con- secutive size classes, some of which approximate molt classes based on growth per molt data (Moriyasu et al. 1987, Taylor and Hoenig 1990, Hoenig et al. 1994). Five size groups were established. (1) Legal-sized males (≥95 mm CW). (2) Sublegal 1, those which would achieve legal size after one molt (76-94 mm CW) if not terminally molted. (3) Sublegal 2, those which would achieve legal size after two molts (60-75 mm CW) if not terminally molted. All other males were partitioned between a category of (4) sublegal 390 Dawe — Prevalence of Bitter Crab Disease

3 males (41-59 mm CW) and (5) smallest males (<41 mm CW). These latter two groups represent groupings of convenience and do not approximate molt classes. Statistical significance of results was determined by contingency table analysis, for those comparisons that included categorical data. The likeli- hood ratio Chi-square statistic (G2) was used to test the null hypothesis that there was no association between BCD prevalence in males and each of the variables shell condition, year, area, and male size group. The significance of correlations between BCD prevalence and male carapace width was assessed using Spearman’s correlation coefficient (rs). This statistic was also used to test the significance of correlations between BCD prevalence and annual survey catch rate (number per tow) by male size group. In all tests, statistical significance was assessed based on the conventional 0.05 probability level. All analyses were carried out using SAS Basics soft- ware (SAS Institute Inc. 1985).

Results Prevalence and Distribution of Bitter Crab Disease The incidence of BCD was low across the entire fall survey area and all five years (Table 1). Only 1.4% (1,102 specimens) of all crabs examined were found to be infected. Bitter crab disease was consistently about twice as prevalent in females as in males. Annual prevalence was similar among 4 of the 5 years, with a range of 0.7-1.3% for sexes pooled in all years except 1997. Overall prevalence in 1997 was 2.6% (Table 1), with 2.1% of males and 4.4% of females recognized as chronically infected. Bitter crab disease was broadly distributed throughout most of the range of snow crab distribution along the continental shelf from southern Labrador to the northern Grand Bank (NAFO Div. 2J3KL, Fig. 2), but was rarely encountered in the southern portion of the Grand Bank, south of about 47ºN (NAFO Div. 3NO, Fig. 2). It was most prevalent in the center of snow crab distribution, on the northeast Newfoundland Shelf (NAFO Div. 3K) during 1996-1998, whereas it became most prevalent in northern- most Div. 2J in 1999 and virtually absent from all more southern areas. It shifted south again in 2000, to a spatial distribution similar to that of 1998. More detailed consideration of yearly variations in BCD distribution and prevalence is somewhat compromised by annual variation in survey coverage. For example, it appears that BCD was more prevalent in inshore areas in 1998 and 2000 than it was during 1996-1997, but these inshore strata were not included in the 1999 fall survey. Bitter crab disease occurred predominantly in new-shelled crabs that had molted the preceding spring (Fig. 3). Whereas only 69-71% of males examined during 1997-2000 were new-shelled, consistently much higher percentages of those with BCD were found to be new-shelled (91-96%). Relatively high prevalence in intermediate-shelled males during 1996 (25%), the first year of monitoring BCD, was likely related to inexperience of Crabs in Cold Water Regions: Biology, Management, and Economics 391

Figure 2. Distribution by year of survey sets where BCD was encountered (closed circles) versus all other sets (open circles). 392 Dawe — Prevalence of Bitter Crab Disease

Figure 3. Percentage composition of males caught (above) and of those with BCD (below) by shell condition, for each year, across the entire fall survey area.

some observers and subjectivity of shell categories. Only four old-shelled males across all five survey years were categorized as infected, likely re- flecting misclassification of carapace condition. The association of BCD prevalence with male shell condition was highly significant (G2, P < 0.01) for all years, but particularly for each of the years 1997-1999 (P < 0.0001). Prevalence was also very highly significantly (P < 0.0001) associated with year for both new-shelled males (G2 = 161.03) and intermediate-shelled males (G2 = 35.23). Bitter crab disease was recognized, within the new-shelled and intermediate-shelled crabs, in all male size groups and both female maturity categories (Fig. 4). Prevalence in males (excluding old-shelled males) was very highly significantly associated with year (G2, P < 0.0001) and, for all three northern areas between southern Labrador and the northern Grand Crabs in Cold Water Regions: Biology, Management, and Economics 393

Figure 4. Percentage of new-shelled plus intermediate-shelled crabs with BCD by year, division, sex, size group (for males), and maturity (for females). 394 Dawe — Prevalence of Bitter Crab Disease

Bank (NAFO Divisions 2J3KL), with area. Prevalence was also very highly significantly (P < 0.0001) associated with male size group, for the area and years where it was most prevalent (i.e., the northeast Newfoundland Shelf, NAFO Div. 3K, in 1996-1998 and 2000). Bitter crab disease was most prevalent in the intermediate size groups, usually the 41-59 mm CW group (Fig. 4). Highest prevalence for this size group was 16% in Div. 2J in 1999. Prevalence in 41-59 mm CW males within Div. 3K was generally stable over the 3 years 1996-1998, with a range of only 6.9-8.4%, before disap- pearing in 1999. It increased in all size groups in 2000 in both Div. 3K and 3L but remained below 1998 levels. Meanwhile, it decreased in Div. 2J in 2000 to approximate 1998 levels within the two smallest size groups. Bitter crab disease was most uncommon in largest, legal-sized males (≥95 mm CW), with a maximum prevalence of about 0.8% on the northeast New- foundland Shelf (Div. 3K) in 1997 and 1998. Trends in prevalence in new- shelled females generally reflected the trends in males (Fig. 4). Prevalence was usually highest in mature females, as was true for the approximately comparably sized males of 41-59 mm and 60-75 mm CW. The highest prevalence in mature females was about 10% in Div. 3K in 1997 and in Div. 2J in 1999. No consistent annual trends were apparent among areas. Prevalence increased in small males (<41 mm CW) and immature females in all three northern areas (Div. 2J3KL) from 1996 to 1997, but decreased again in 1998 (Fig. 4). Prevalence on the northeast Newfoundland Shelf and northern Grand Bank (Div. 3KL), across all male sizes and both female maturity classes, generally peaked in 1997, virtually disappeared by 1999, and increased again in 2000. In contrast, it generally declined regularly in the most northern area (Div. 2J) over the 3 years 1996-1998 before increasing greatly in 1999 and subsequently declining again in 2000.

Relationships with Density and Abundance To investigate possible relationships between BCD prevalence and crab density I focused on the northeast Newfoundland Shelf (Div. 3K), where prevalence was highest. Prevalence of BCD was compared with catch rate (number per tow) across 3-mm CW groups of males (excluding old-shelled), by year (Fig. 5). Size-specific catch rate was inversely associated with prevalence in most years. Correlations were negative and significant (Spearman’s rs, P < 0.05) for all years except 1999 (P > 0.05), and were highly significant for 1997 and 2000 (P < 0.001). Lowest catch rates and highest BCD prevalence were consistently at intermediate sizes. Peak prevalence by 3-mm group approached 18% in 1996, 16% in 1997 and 1998, and 9% in 2000. Characteristic of this association was a virtual absence of BCD at smallest sizes (smaller than about 24-30 mm CW) and at largest sizes (>114 mm CW) in most years. Survey catch rates were compared with prevalence of BCD across years for each of three areas and five size groups of males, to further explore the relationship between BCD prevalence and density. Only 1 of the 15 Crabs in Cold Water Regions: Biology, Management, and Economics 395

Figure 5. Male carapace width distribution and percentage with BCD by year for NAFO Div. 3K. 396 Dawe — Prevalence of Bitter Crab Disease correlations was barely significant; that for 41-59 mm CW males in Div. 2J

(rs = –0.90, P = 0.04). It is recognized, however, that the probability of incurring at least one such significant correlation due to chance alone is rather high when multiple correlations are generated.

Discussion General Distribution of BCD This study showed that chronic cases of BCD were observed predominantly in recently molted (new-shelled) crabs, supporting the hypothesis that infection is somehow associated with molting. Eaton et al. (1991) found that about 81% of new-shelled and 24% of older-shelled Tanner crabs (C. bairdi) were infected from June 1988 to February 1989 in southeast Alaska. An annual dinoflagellate life cycle in the snow crab host is implied by its apparent predominance in newly molted crabs off Newfoundland and Labrador. Cannibalism, known to be common in at least one Canadian Atlantic region (Lovrich and Sainte-Marie 1997), has been hypothesized as one likely mode of transmission. However, this mode would not be consistent with the predominance of BCD in new-shelled crabs. Results of this study are more supportive of a more direct mode of transmission, such as by motile stages from sediments through the soft new cuticle. It is also possible, however, that this parasitism may actually occur more commonly in older-shelled crabs than the results of our gross observations suggest. It is recognized that infection in general, and in crabs that had not recently molted in particular, may be underestimated in this study, based on external observation only. Recognition of external characteristics of BCD may be reduced in older-shelled crabs with relatively thick, opaque, and heavily fouled carapaces. This possibility is consistent with the relatively higher incidence reported in older-shelled Alaskan Tanner crabs, based on microscopic examination of hemolymph smears (Eaton et al. 1991), than in this study. The factors that may regulate the spatial distribution of BCD are unclear. It is possible that spatial distribution is regulated by ocean circulation features. This is consistent with the concentration of BCD within the center of the broad crab distribution in most years, and the consistent virtual absence of BCD in the southernmost slope region of Div. 3NO. Areas of highest prevalence in southeast Alaskan Tanner crabs have been associated with embayments, arms, and sills, which may serve to retain the infected population, and the causative parasite, within a very localized area (Meyers et al. 1990). Annual changes in spatial distribution of BCD in Newfoundland and southern Labrador C. opilio, particularly the pronounced shift to the north in 1999 and back south in 2000, may be related to changes in circulation patterns, but also may be due to shifts in crab density. Bitter crab disease has clearly been most prevalent in intermediate- sized crabs, but there has been considerable spatial and annual variability Crabs in Cold Water Regions: Biology, Management, and Economics 397 in this size range. This may reflect the overall distribution of intermediate-sized crabs at intermediate depths (Dawe and Colbourne 2002). An- nual shifts in the size range most affected may reflect annual shifts in the distribution of size groups, or it may reflect annual changes in distribution of the dinoflagellate. Relationships of the distribution of the dinoflagellate with such abiotic factors as depth, sediment type, temperature, or salinity are unknown. Eaton et al. (1991) found, from June 1988 to Febru- ary 1989, that prevalence in southeast Alaskan Tanner crabs was not related to sex or carapace width.

Possible Effects on Mortality and Recruitment The inverse relationship between BCD prevalence in males and size-specific catch rate implies a possible effect on mortality, especially of intermediate-sized crabs. However, it is also possible that the low catch rates of intermediate-sized males could reflect a size-related catchability effect. The correlations between annual catch rates and BCD prevalence by male size group failed to detect any convincing negative relationship between BCD prevalence and catch rate that would support an effect of BCD on mortality. Conceivably, positive relationships between BCD prevalence and crab catch rate are possible, if high host density promotes prolifera- tion of the dinoflagellate. Whether any such relationships actually exist will probably remain unknown until a more extensive time series of data accumulates. Although BCD prevalence may be high at very specific carapace widths, the overall low levels do not seem consistent with a substantial effect on mortality. However, true prevalence may be under-represented by these observations. Prevalence may be higher than indicated within the trawl catches because trawls may not efficiently catch diseased crabs that are lethargic and selectively passed over by the trawl footgear. Furthermore, molting is frequent at small sizes (Sainte-Marie et al. 1995) and so the cumulative effect of this mortality across successive instars of a year class may be substantial. It is also possible that the annual October-December trawl surveys may be late relative to the seasonal peak in prevalence, such that considerable mortality may have already occurred each year before the survey. Eaton et al. (1991) reported that BCD in southeast Alaskan Tanner crab was highest in summer (June and August) and decreased in October, in 1988. Meyers et al. (1987) also found, in the same area, a similar seasonal increase in prevalence and intensity of infection. This is similar to seasonality of this parasitic infection in blue crab (Callinectes sapidus) (Newman and Johnson 1975, Messick 1994). Love et al. (1993) found highest prevalence in southeast Alaskan Tanner crab in August of both 1989 (96%) and 1990; prevalence and intensity were both very low throughout October- April, before increasing in May; prevalence was particularly low during October-December, decreasing from about 11-12% in October to 0% in De- cember of 1989. 398 Dawe — Prevalence of Bitter Crab Disease

The crude method of diagnosis in this study likely also contributes to underestimation of true prevalence. Macroscopic examination detects only chronic infections. Eaton et al. (1991) and all others (Meyers et al. 1987, 1990; Love et al. 1993) used hemolymph smears for diagnosis of prevalence in southeast Alaskan Tanner crabs. The prevalence of BCD across the Newfoundland and Labrador Shelf prior to 1996 is unknown. It is known that the parasitism existed in 1995 because it was detected from an inshore 1995 trap survey in Div. 3K, at low levels and in smallest crabs only (Dawe et al. 2000). It was not detected at all during the first year of that survey, in 1994. Other observations support the existence of BCD in northern areas in 1995 including the broad spatial distribution of BCD on the southern Labrador Shelf and northeast Newfoundland Shelf (Div 2J3KL) in 1996, the relatively high prevalence in 1996, and regular decline during 1996-1998 in Div. 2J. Although there are no data on incidence of BCD over the broad survey area prior to 1996, it is suspected that its prevalence was much lower in the early than late 1990s. If this is so, then it suggests that increased prevalence since 1995 may be related to density or the environment. Den- sity of intermediate-sized crabs was particularly high during the mid-1990s, leading to strong recruitment in the late 1990s (Dawe et al. 2001). Also, the period 1995-2000 was an unusually warm period (Colbourne 2001) which may have promoted establishment of BCD within the host population. However, the relationship of BCD prevalence in snow crabs with bottom temperature is presently unknown.

Acknowledgments I thank Joe Drew and Richard Warren for assistance provided with summary, analysis, and presentation of data. I also thank John Brattey, Ber- nard Sainte-Marie, and two anonymous reviewers for critically reviewing earlier drafts of this manuscript.

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