Scottish Marine and Freshwater Science Vol 6 No 15: Spatial dynamics of scallops in relation to the Orkney dive fishery. Report of Fishing Industry Science Alliance (FISA) Project 03/12

Results

Depletion Experiments at Wyre

The outcomes of the five depletion fishing experiments at Wyre are summarised according to three scallop size-groups in Table 1 and Figure 4. Convincing patterns of declining catch per dive are shown in most cases, the notable exception being the smallest size group (<80 mm shell width) in June 2014, for which the catch rate increased from 10 to 31 scallops between the first and second dives. Inspection of fitted values from the full maximum likelihood model ( time * size) indicated no obvious patterns of lack-of-fit by the model, but the Pearson statistic for goodness-of-fit was significant _X ( ²=50.474, df=16, P<0.001), taken to indicate over-dispersion in the count data rather than a structural failure of the model. This statistic was used to estimate a variance inflation factor ĉ=3.155 that was taken forward into quasi-likelihood-based model inference. Sample size for the model was 45, being the number of survey occasions (five) × the number of size-groups (three). After accounting for this over-dispersion, and adjusting for small sample size, the 'best' (most parsimonious) model was selected by minimum value of QAIC _c as representing variation in capture probabilities between size-groups but not between occasions ( size, Table 2). Model selection was unambiguous, with relative likelihoods for alternative models being negligible, thus no need was seen for model averaging to account for model uncertainty. Accordingly, the estimates in Table 1 and the depletion lines in Figure 4 are based on capture probabilities and population estimates from the size model.

As might be expected, estimated capture probability increased with scallop size, being 0.33, 0.68 and 0.79 per dive for scallops in the <80 mm, 80-110 mm and >110 mm shell width size-groups respectively (Table 1). It is likely that differences in fishing efficiency between individual divers contributed to variability of the catch rates about the overall depletion trends shown in Figure 4, but comparisons of model residuals between individual divers show no obvious patterns.

Population estimates were lowest in the >110 mm shell width size-group, varying from 16 (0.023 .m ^‑2) in June 2014 to 87 (0.12 .m ^‑2) in June 2013 (Table 1), the difference being due, at least in part, to fishery removals during the depletion experiments. Smaller size-groups were higher in abundance, the highest estimate being 173 (0.24 .m ^‑2) for scallops in the 80-110 mm size-group in October 2013. Overall numbers estimated to be in the survey area ranged from 168 (0.24 .m ^‑2) in June 2014 to 339 (0.48 .m ^‑2) in October 2013.

Table 1

Summary of scallop catches for depletion fishing experiments at Wyre. Capture probabilities per dive and population estimates are from the selected maximum-likelihood depletion model (see Table 2). 95% confidence intervals are shown in brackets. Lower limits for population size are given as the sum of catches on each occasion, which in all cases exceeded the statistical lower 95% confidence limit. Density estimates are calculated for the plot area of 712 m ².

(a) 25 June 2013

	<80 mm shell width		80-110 mm shell width		>110 mm shell width
Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive
1	0	41	0	56	0	74
2	41	15	56	6	74	6
3	56	13	62	0	80	4
Capture probability per dive:	0.327 (0.193-0.497)		0.678 (0.588-0.756)		0.794 (0.659-0.884)
Population estimate:	99 (69-169)		64 (62-102)		87 (84-129)
Scallop density (.m -2):	0.139 (0.097-0.238)		0.090 (0.087-0.143)		0.122 (0.118-0.181)

(b) 8 August 2013

	<80 mm shell width		80-110 mm shell width		>110 mm shell width
Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive
1	0	47	0	53	0	8
2	47	32	53	15	8	12
3	79	34	68	10	20	0
Capture probability per dive:	0.327 (0.193-0.497)		0.678 (0.588-0.756)		0.794 (0.659-0.884)
Population estimate:	162 (113-257)		81 (78-122)		20 (20-46)
Scallop density (.m -2):	0.228 (0.159-0.361)		0.113 (0.110-0.171)		0.028 (0.028-0.064)

(c) 7 October 2013

	<80 mm shell width		80-110 mm shell width		>110 mm shell width
Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive
1	0	57	0	94	0	11
2	57	21	94	27	11	5
3	78	3	121	4	16	1
Capture probability per dive:	0.327 (0.193-0.497)		0.678 (0.588-0.756)		0.794 (0.659-0.884)
Population estimate:	116 (81-193)		129 (125-179)		17 (17-42)
Scallop density (.m -2):	0.164 (0.114-0.272)		0.182 (0.176-0.252)		0.024 (0.024-0.058)

(d) 18 November 2013

	<80 mm shell width		80-110 mm shell width		>110 mm shell width
Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive
1	0	32	0	112	0	39
2	32	30	112	43	39	1
3	62	25	155	12	40	1
Capture probability per dive:	0.327 (0.193-0.497)		0.678 (0.588-0.756)		0.794 (0.659-0.884)
Population estimate:	125 (87-205)		173 (167-229)		41 (41-73)
Scallop density (.m -2):	0.176 (0.122-0.288)		0.243 (0.235-0.322)		0.058 (0.058-0.103)

(e) 13 June 2014

	<80 mm shell width		80-110 mm shell width		>110 mm shell width
Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive	Cumulative Catch	Catch per Dive
1	0	10	0	43	0	12
2	10	31	43	22	12	2
3	41	9	65	12	14	2
Capture probability per dive:	0.327 (0.193-0.497)		0.678 (0.588-0.756)		0.794 (0.659-0.884)
Population estimate:	72 (50-131)		80 (77-121)		16 (16-40)
Scallop density (.m -2):	0		10		0

Figure 4: Leslie plots for scallop depletion experiments at Wyre; the negative slope of each line represents the probability of capture per dive for each size group; the point at which each line intercepts the horizontal axis (x-axis) represents the estimated population size of scallops within the survey area. Capture probabilities and population estimates were derived from the selected maximum-likelihood model fitted to the data (see Tables 1 and 2) rather than by regression using the Leslie method.

Tagging and Recapture at Wyre

Size-frequency data for scallops tagged and recaptured at Wyre are shown in Figure 5, and recapture data are shown in Table 3 summarised for three size groups using the 'reduced m-array' format (Burnham et al., 1987). Recapture rates were very high, without significant patterns of difference between tag types (Figure 6; _X ²=2.74, df=6, P=0.841). Goodness-of-fit testing indicates that the time- and size-structured CJS model framework ( time * size for both survival/fidelity and capture probabilities) is a suitable basis for inference ( _X ²=0.113, df=3, P=0.990, based on cell expectations for the reduced m-array, with pooling across expected values <2). Effective sample size for the tagging and recapture data is 450, calculated as the total number of releases included in the reduced m-arrays (Table 3). This figure was used in the adjustment for small sample size in model selection. The model with the lowest value of AIC _c represents differences between sampling intervals in survival/fidelity probabilities and variations between size-groups in capture probabilities ( time, size, Table 4). The capture probability model is consistent with the pattern of variation determined in the modelling of depletion data (Table 2). However, several alternative models appear equally defensible for the model (differences in QAIC _c of around 2 or less), such that it is appropriate to consider model uncertainty in deriving final estimates of demographic rates and recapture probabilities. Model average values of capture probabilities on each survey occasion and size-group, and survival/fidelity probabilities for each survey interval and size-group, were calculated using the weights in the right-hand column of Table 4). These are shown in comparison with estimates from the 'best' model ( time-dependent survival/fidelity probabilities, size-dependent capture probabilities) in Figure 7. For ease of interpretation, the daily survival/fidelity probabilities, , have been converted into monthly (30-day) loss rates as 1-ø ³⁰. In general the estimates are similar in scale. A possible explanation of the apparent trends of decline in capture probabilities over the survey series shown in the model average estimates is given below. Loss rates appear to be lowest during the late summer to autumn period, being highest for the November 2013 to June 2014 interval, possibly indicating higher rates of mortality and/or emigration during winter and/or spring.

Figure 7 also shows comparable estimates of capture probability derived from the depletion model, cumulated over the three dives on each occasion by using Eq. 2. These are consistently higher than the estimates from tag-recapture, by about 22% for scallops <80 mm shell width and 26-27% in larger scallops. Aside from statistical lack of precision in the estimates, there are two likely explanations for this discrepancy. The first possibility is that a proportion of scallops may be effectively invisible to divers on any given survey occasion, so that the depletion capture probabilities refer only to the non-cryptic portion of the population. Provided that the visibility of individual scallops varies between occasions, the cryptic portion of the population would be 'visible' over the longer term in the tag recaptures. This perhaps also accounts for the trends of decline in capture probability apparent in the model average values from tag recapture, since the opportunity for cryptic scallops to become visible to divers declines as the end of the survey series becomes evident. A second possible explanation, is that the definition of 'population' differs subtly between the depletion and tag recapture experiments: in the depletion experiments, the population is strictly contained within the survey plot, whereas emigrants from this survey plot are visible to the tagging experiment provided that that emigration is temporary. The two explanations, heterogeneity of capture probabilities and temporary emigration, are both plausible and not mutually exclusive. Both point to a possible incompatibility between the population estimates from the depletion experiments and the population dynamics represented by the tag recapture modelling. This incompatibility is explored in the next section, considering spatial and population dynamics at a small spatial scale.

Figure 5: Size-frequency distributions of tag releases and recaptures at Wyre.
Note that these data include multiple recaptures of individual tags (see Figure 6) and that growth in shell width occurs between tagging and recapture.

Figure 6: Recapture frequencies for tagged scallops at Wyre.

Table 2

Model selection statistics for maximum likelihood depletion models fitted to scallop catch data for the Wyre depletion site. Capture model defines constraints of capture probability between sampling occasions ('time') and shell width groups ('size'); ln L is the log-likelihood of the model; NP is the number of separately identifiable model parameters (before accounting for estimation of a dispersion coefficient); QAIC _c is the quasi-likelihood version of the Akaike Information Criterion, adjusted for small sample size; QAIC _c difference is the difference of model QAIC _c from the minimum value; weight is the relative model probability. The 'best' (smallest value of QAIC _c) model for the data is highlighted.

Table 3

Scallop tag recapture data for the Wyre depletion fishing site, summarised in 'reduced m-array' format. Each row of the table gives numbers from each release cohort first recaptured on each occasion. Release totals for each occasion include re-releases of previously tagged scallops recaptured on that occasion. Re-releases of scallops that had grown between size groups are included in the release totals for the recipient size group.

(a) Shell width <80 mm

		First recaptures
Occasion	Releases	August 2013	October 2013	November 2013	June 2014	Never recaptured
June 2013	17	13	1	1	0	2
August 2013	60		34	8	0	18
October 2013	41			14	3	24
November 2013	11				0	11

(b) Shell width 80-110 mm

		First recaptures
Occasion	Releases	August 2013	October 2013	November 2013	June 2014	Never recaptured
June 2013	38	21	5	1	0	11
August 2013	63		43	12	0	8
October 2013	99			69	2	28
November 2013	82				4	78

(c) Shell width >110 mm

		First recaptures
Occasion	Releases	August 2013	October 2013	November 2013	June 2014	Never recaptured
June 2013	2	2	0	0	0	0
August 2013	4		3	0	0	1
October 2013	13			8	0	5
November 2013	20				1	19

Table 4

Model selection statistics for CJS-type models fitted to scallop tag recapture data for the Wyre depletion fishing site. Survival / fidelity model refers to probabilities of remaining within the survey area; recapture model refers to probability of capture on survey occasions; these probabilities are allowed to vary between occasions ( time), shell width groups ( size: <80 mm, 80-110 mm, >110 mm), both ( time * size), or neither ( constant). ln L is the log-likelihood kernel; NP is the number of separately identifiable model parameters; AIC _c is Akaike Information Criterion, adjusted for sample size; AIC _c difference is the difference of model AIC _c from the minimum value; weight is the relative model likelihood, used as a weight in calculating model average parameter values. The 'best' (smallest value of AIC _c) model for the data is highlighted with yellow shading. Other candidate models ( AIC _c differences of around 2 or less) are shown with grey shading.

Figure 7: Recapture probabilities and loss rates of scallops at the Wyre depletion fishing site. Left-hand column shows total recapture probability on each occasion, estimated by depletion fishing and by tag recaptures. Right-hand column shows emigration/mortality rates between occasions scaled to 1 month (30 days) estimated by tag recaptures. 'Best model' estimates are from the best fitting model for tag recaptures ( time-dependent survival/fidelity probabilities, size-dependent capture probabilities); 'model average' estimates are weighted averages across tag recapture models, accounting for model uncertainty.

Small Scale Spatial and Population Dynamics

As noted above, it is not possible to distinguish between permanent emigration and mortality in the tag recapture models; both processes are simply modelled (through survival/fidelity probabilities) as permanent losses to the tagged population available to be recaptured within the survey area. An instantaneous natural mortality rate of M=0.15 .yr ^-1 is assumed in stock assessments of Scottish scallops (Dobby et al., 2012). Assuming that this rate is constant through the year and that it is representative of scallops at Wyre (both are likely to be untrue to some degree, but there is no reasonable basis for alternative assumptions), we can use Eq. 4 and Eq. 5 to obtain separate estimates of emigration probabilities. As can be seen in Table 5, the loss rates modelled using tag recaptures appear to be dominated by emigration rather than mortality - compare values before and after adjustment for mortality between Table 5a and Table 5c, and between Table 5b and Table 5d. In considering small scale population dynamics no adjustment is made for mortality and it is assumed that losses not accounted by growth or fishing removals are due primarily to movements out of the survey area.

Table 5

Scallop emigration/mortality rates for the Wyre depletion fishing site, estimated from tag recaptures. Emigration is separated from mortality in (c) and (d) under an assumed instantaneous annual natural mortality rate of 0.15.

(a) Total emigration/mortality between depletion fishing occasions

	Shell Width
Interval	<80 mm	80-110 mm	>110 mm
June - August 2013	0.248	0.408	0.239
August - October 2013	0.255	0.182	0.589
October - November 2013	0.447	0.182	0.361
November 2013 - June 2014	0.986	0.994	0.995

(b) Emigration/mortality scaled to monthly (30-day) rates

	Shell Width
Interval	<80 mm	80-110 mm	>110 mm
June - August 2013	0.177	0.300	0.170
August - October 2013	0.137	0.096	0.157
October - November 2013	0.345	0.134	0.274
November 2013 - June 2014	0.462	0.518	0.534

(c) Assumed total emigration between depletion fishing occasions

	Shell Width
Interval	<80 mm	80-110 mm	>110 mm
June - August 2013	0.234	0.397	0.225
August - October 2013	0.237	0.162	0.271
October - November 2013	0.437	0.168	0.350
November 2013 - June 2014	0.985	0.993	0.994

(d) Assumed emigration scaled to monthly (30-day) rates

	Shell Width
Interval	<80 mm	80-110 mm	>110 mm
June - August 2013	0.166	0.292	0.159
August - October 2013	0.126	0.084	0.146
October - November 2013	0.337	0.123	0.265
November 2013 - June 2014	0.455	0.513	0.529

Transitions between size-groups owing to growth are estimated using Eqs. 7 and 8, based on growth between consecutive survey occasions measured in tagged scallops (Figure 8, Table 6). Collecting together these transition probabilities, loss rates between survey occasions estimated from tag recaptures (interpreted as primarily emigration) and population estimates on each survey occasion from the depletion experiments, a complete schedule of movements into and out of the survey area can be constructed based on Eqs. 6, 9, 10 & 11 (Table 7). The main point to note is that, once growth and fishing removals have been accounted for, substantial numbers of scallops are inferred to have been moving into and out of the survey area. A negative estimate of immigration for the largest size-group in October 2013 could be due to unaccounted removals, i.e. unknown fishing activities in the area during the preceding survey interval, but is more likely to be due to a lack of precision in the population dynamic process estimates rather than a process error per se. Table 8 shows a revised population dynamic schedule based on applying tag recapture estimates of capture probability to the catch numbers recorded on each occasion. This addresses the issue of incompatibility of population definition between depletion and tag recapture models. Qualitatively, the conclusions from this revised schedule are the same: substantial turnover of the scallop population at all size-groups relative to the abundance of the population in the survey area. Table 9 aggregates the movement estimates over the size-groups for both versions of the population dynamic schedule, and expresses these in terms of scallop densities.

The main difference between the two schedules is that using the larger estimates of population size from the tag recapture modelling causes estimated numbers of both movers (emigrants and immigrants) and non-movers (residents) to be increased.

Tables 7-9 provide estimates of total population fluxes between survey occasions at the Wyre site. In Tables 10 and 11 the scallop movements are expressed on monthly (30 day) basis, per unit area and per 'head' of population, for schedules based on estimates of population size from depletion modelling and tag recapture modelling respectively. This provides a more readily interpreted basis for comparisons between size groups and survey intervals. Percentages of population present are calculated based on the average of population estimates for the start and end of an interval, having first accounted for fishery removals at the beginning of the interval. Overall, immigration is greater than emigration, compensating for fishery removals. For the smallest size-group, immigration in June 2014 possibly includes a small element of recruitment; this immigration compensates for growth into the next size-group as well as for emigration, which is true also for the 80-110 mm shell width group as well. The final outcome of this analysis is that spatial turnover of scallops at the smallest spatial scale (metres to tens of metres, depending on the directionality of movements in relation to the survey strip) is estimated to have been more than a quarter of the population per month on average, varying over time from about 10-50% of the population. This is based on immigration estimates for overall population numbers estimated by depletion modelling; similar results are obtained based on population numbers estimated by tag recapture modelling, except that the upper limit of turnover is closer to 40%.

Table 6

Transfer rates between scallop size groups due to growth at the Wyre depletion fishing site.

	Shell Width Group Transition
Interval	<80 mm to 80-110 mm	80-110 mm to >110 mm
June - August 2013	0.319	0.081
August - October 2013	0.372	0.115
October - November 2013	0.235	0.088
November 2013 - June 2014	0.724	0.253

Figure 8: Growth of tagged scallops between depletion fishing occasions at Wyre: relationship of shell width at release (x-axis) and shell width at recapture (y-axis) for consecutive depletion fishing occasions. Dashed lines show the estimated sizes (y-axis) above which scallops released in one size class (<80 mm and 80-110 mm shell width) will have growth to the next size class (80-110 mm and >110 mm shell width, respectively) by the next occasion.

Table 7

Population dynamics schedule for scallops at the Wyre depletion fishing site, based on depletion fishing and tagging data. Population numbers are derived from depletion model with size-dependent recapture probabilities; emigration rates between occasions are derived from model-averaged fidelity values from CJS-type models fitted to tagging data. Note that 'emigration' includes an element of natural mortality. Note also that any apparent mismatch of totals is due to rounding of numbers to integer values.

(a) Shell width <80 mm

		Losses			Gains
Occasion	Population	Emigration	Growth	Residents	Immigration
June 2013	99	25	24
August 2013	162	42	45	51	112
October 2013	116	52	15	76	40
November 2013	125	123	1	49	76
June 2014	72			0	71

(b) Shell width 80-110 mm

		Losses				Gains
Occasion	Population	Emigration	Growth	Removals	Residents	Growth	Immigration
June 2013	64	23	3	8
August 2013	81	15	8	0	31	24	26
October 2013	129	23	9	3	58	45	26
November 2013	173	161	0	11	94	15	63
June 2014	80				1	1	78

(c) Shell width >110 mm

		Losses			Gains
Occasion	Population	Emigration	Removals	Residents	Growth	Immigration
June 2013	87	1	82
August 2013	20	6	0	4	3	14
October 2013	17	4	5	14	8	-5
November 2013	41	20	21	8	9	25
June 2014	16			0	0	16

Table 8

Population dynamics schedule for scallops at the Wyre depletion fishing site, based on depletion fishing and tagging data. Population numbers are derived from CJS-type models fitted to tagging data. Note that 'emigration' includes an element of natural mortality. Note also that any apparent mismatch of totals is due to rounding of numbers to integer values.

(a) Shell width <80 mm

		Losses			Gains
Occasion	Population	Emigration	Growth	Residents	Immigration
June 2013	113	28	27
August 2013	168	43	46	58	110
October 2013	128	57	17	78	50
November 2013	149	147	1	54	95
June 2014	91			1	91

(b) Shell width 80-110 mm

		Losses				Gains
Occasion	Population	Emigration	Growth	Removals	Residents	Growth	Immigration
June 2013	87	32	4	8
August 2013	106	19	10	0	43	27	36
October 2013	169	30	12	3	77	46	45
November 2013	224	212	0	11	123	17	84
June 2014	122				1	0	120

(c) Shell width >110 mm

		Losses			Gains
Occasion	Population	Emigration	Removals	Residents	Growth	Immigration
June 2013	110	7	82
August 2013	24	7	0	22	4	-2
October 2013	20	6	5	17	10	-7
November 2013	53	32	21	10	12	31
June 2014	24			0	0	23

Table 9

Population dynamic schedule for scallops at the Wyre depletion site, aggregated across size-groups and shown separately for population estimates from depletion modelling and tag recapture modelling.

(a) Numbers based on population estimates from depletion modelling

Occasion	Population	Emigration	Removals	Residents	Immigration
June 2013	250	49	90
August 2013	263	62	0	85	152
October 2013	263	79	8	149	62
November 2013	339	304	32	151	164
June 2014	168			1	165

(b) Densities .m ^-2 based on population estimates from depletion modelling

Occasion	Population	Emigration	Removals	Residents	Immigration
June 2013	0.351	0.068	0.126
August 2013	0.370	0.087	0.000	0.119	0.213
October 2013	0.369	0.112	0.011	0.209	0.087
November 2013	0.476	0.427	0.045	0.213	0.230
June 2014	0.236			0.002	0.231

(c) Numbers based on population estimates from tag recapture modelling

Occasion	Population	Emigration	Removals	Residents	Immigration
June 2013	311	67	90
August 2013	298	69	0	123	144
October 2013	317	93	8	172	89
November 2013	427	391	32	188	210
June 2014	237			2	234

(d) Densities .m ^-2 based on population estimates from tag recapture modelling

Occasion	Population	Emigration	Removals	Residents	Immigration
June 2013	0.436	0.094	0.126
August 2013	0.418	0.097	0.000	0.172	0.202
October 2013	0.446	0.131	0.011	0.242	0.125
November 2013	0.599	0.549	0.045	0.264	0.295
June 2014	0.436	0.094	0.126

Table 10

Movements of scallops into and out of the Wyre depletion fishing site, based on population estimates from depletion modelling.

(a) Monthly number of scallops emigrating per m ²

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	0.0236	0.0219	0.0011	0.0466
Aug-Oct 2013	0.0292	0.0103	0.0041	0.0436
Oct-Nov 2013	0.0522	0.0231	0.0044	0.0797
Nov-Jun 2014	0.0251	0.0327	0.0041	0.0620
Average	0.0325	0.0220	0.0034	0.0580

(b) Monthly emigration as percentage of average population present

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	12.8	22.8	6.2	15.7
Aug-Oct 2013	14.9	7.0	15.6	11.8
Oct-Nov 2013	30.8	11.0	11.7	19.1
Nov-Jun 2014	18.2	19.3	16.1	18.6
Average	19.2	15.0	12.4	16.3

(c) Monthly numbers of scallops immigrating per m ²

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	0.1073	0.0249	0.0134	0.1456
Aug-Oct 2013	0.0281	0.0183	-0.0035	0.0428
Oct-Nov 2013	0.0762	0.0632	0.0251	0.1645
Nov-Jun 2014	0.0145	0.0159	0.0033	0.0336
Average	0.0565	0.0360	0.0096	0.0966

(d) Monthly immigration as percentage of average population present

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	58.4	25.9	76.6	48.9
Aug-Oct 2013	14.3	12.4	-13.4	11.6
Oct-Nov 2013	44.9	30.1	66.7	39.4
Nov-Jun 2014	10.4	9.4	12.7	10.1
Average	32.0	19.5	35.7	27.5

Table 11

Movements of scallops into and out of the Wyre depletion fishing site, based on population estimates from tag recapture modelling.

(a) Monthly number of scallops emigrating per m ²

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	0.0269	0.0308	0.0065	0.0642
Aug-Oct 2013	0.0301	0.0136	0.0048	0.0485
Oct-Nov 2013	0.0576	0.0303	0.0056	0.0934
Nov-Jun 2014	0.0300	0.0431	0.0065	0.0796
Average	0.0362	0.0295	0.0059	0.0714

(b) Monthly emigration as percentage of average population present

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	13.6	23.7	17.7	17.6
Aug-Oct 2013	14.5	7.0	15.6	11.2
Oct-Nov 2013	29.5	11.1	11.6	18.1
Nov-Jun 2014	17.7	18.3	16.5	17.9
Average	18.8	15.0	15.4	16.2

(c) Monthly numbers of scallops immigrating per m ²

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	0.1051	0.0344	-0.0015	0.1380
Aug-Oct 2013	0.0351	0.0318	-0.0046	0.0623
Oct-Nov 2013	0.0951	0.0844	0.0314	0.2109
Nov-Jun 2014	0.0185	0.0243	0.0048	0.0476
Average	0.0635	0.0437	0.0075	0.1147

(d) Monthly immigration as percentage of average population present

Interval	<80 mm	80-110 mm	>110 mm	Total
Jun-Aug 2013	53.2	26.5	-4.1	37.9
Aug-Oct 2013	16.9	16.5	-14.9	14.4
Oct-Nov 2013	48.8	30.8	65.5	40.8
Nov-Jun 2014	10.9	10.3	12.2	10.7
Average	32.5	21.0	16.7	26.0

Discussion

It is well known that king scallops are mobile at spatial scales ranging from metres to kilometres (e.g. Baird & Gibson, 1956). In a tagging study in Irish waters, Gibson (1953) recorded movements of up to 1.6 km over a period of about 8 months, but noted that most scallops were recaptured close to their release locations. Such mobility must play an important role in determining the relationship between the stock and any fishery. For a dive fishery, such as that in Orkney waters, which targets small, discrete areas for fishing operations, movements at scales down to tens of metres will affect the likelihood of local depletion, and hence the frequency with which individual areas can be targeted.

To our knowledge, this is the first study that has described patterns of spatial turnover in a scallop population at a small spatial scale. The main finding is that turnover on a strip of ground 178 m by 4 m averaged more than 25% per month over the year, and could be up to 50% per month during the summer months. Even over winter and spring, when lower water temperatures would be expected to reduce swimming activity, turnover rates of around 10% per month were estimated. These rates are taken from estimates of the contributions of immigration to population density at any one time, hence are a fair reflection of the capacity for a ground to be re-stocked. These results suggest that, at least at this small spatial scale, it is possible for a fished ground to be restored to pre-fishing scallop population levels in under a year. This conclusion is, of course, contingent on the existence of undepleted stocks in areas adjacent to the fishing grounds, which is perhaps true only for small fishing patches in a stock which is lightly exploited overall.

Further work is needed to determine the real implications of this scale of movements on the Orkney stock. This includes analysis of data from the wider tagging study in Orkney once sufficient tag returns have been recorded, and also processing and analysis of data from the Scapa Bay and Fara depletion studies, neither of which has yet been possible within the resources available for this study. Some further model development and implementation of a fully integrated tagging and depletion model would be beneficial, although it is perhaps likely that this would not qualitatively change the nature of findings from the study reported here. Beyond these analyses, collection of more comprehensive biological sampling data for Orkney waters would allow inferences about current exploitation rates to be drawn, which would form an important context for interpreting the implications of movements for fishery sustainability.