Biological reference points for sea scallops (Placopecten ...

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PERSPECTIVE / PERSPECTIVE

Biological reference points for sea scallops (Placopecten magellanicus): the benefits and costs of being nearly sessile1 Stephen J. Smith and Paul Rago

Abstract: In this paper, we concentrate on spatial aspects of growth and reproduction for sea scallops (Placopecten magellanicus) to advance the general theory for development of reference points for sessile animals and to illustrate the general points with several specific examples. Nonlinear mixed effects models can be used to define the spatial distribution of growth rates and their implications for the definition of growth overfishing. We develop a basin model to illustrate that the typical “boom and bust” effects, often attributed to environmental factors, are explained equally well by spatial variations in habitat quality, spatial concentration of fisheries, and dispersal of larvae among areas. Results suggest that incentives to concentrate fishing effort in lower productivity areas may be an effective tool for reducing recruitment variation and improving yields. Reductions in fishing mortality might be possible with closed areas as they can be used to reduce the concentration of effort on high scallop densities. Further, rotational area management strategies can offer the promise of balancing demands for increased yield, prevention of recruitment overfishing, maintaining spawning reserves, and reducing habitat damage and bycatch. Résumé : Notre contribution s’intéresse aux dimensions spatiales de la croissance et de la reproduction du pétoncle géant (Placopecten magellanicus) afin d’améliorer la théorie générale qui sert à l’élaboration de points de référence chez les animaux sessiles et en illustrer les aspects principaux avec plusieurs exemples spécifiques. Les modèles non linéaires à effets mixtes peuvent servir à définir la répartition spatiale des taux de croissance et leurs conséquences sur la définition de la surexploitation de la croissance. Nous avons mis au point un modèle de bassin qui illustre que les effets typiques « d’expansion et d’effondrement » qui sont souvent attribués aux facteurs environnementaux peuvent s’expliquer tout aussi bien par des variations spatiales de la qualité de l’habitat, par la concentration spatiale de la pêche et par la dispersion des larves dans les différentes régions. Nos résultats indiquent que des mesures incitatives pour concentrer l’effort de pêche dans des régions de productivité plus faible peuvent être un outil efficace pour réduire la variation du recrutement et pour améliorer les rendements. L’établissement de zones fermées peut abaisser la mortalité due à la pêche, car elles peuvent servir à réduire la concentration de l’effort de pêche dans les sites de forte densité de pétoncles. De plus, des stratégies de gestion comprenant un rotation des sites de récolte peuvent laisser espérer l’établissement d’un équilibre entre la demande d’un rendement accru, la prévention de la surexploitation du recrutement, le maintien des réserves de fraye, la réduction des dommages à l’habitat et la diminution des prises accessoires. [Traduit par la Rédaction]

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Introduction Application of the precautionary approach to fisheries management requires the definition of target and limit biological reference points (BRP) (e.g., FAO 1996; Hilborn et al. 2001). Biological reference points are observable or cal-

culable quantities that characterize a population’s state. When used to set targets or limits, they represent a tradeoff between mankind’s utilization of a living resource and the resource’s life history traits and productivity. Conceptually, BRPs rest on three primary tenets. First, BRPs rely on well-founded concepts of optimal harvest rates that strike a balance be-

Received 15 May 2003. Accepted 1 April 2004. Published on the NRC Research Press Web site at http://cjfas.nrc.ca on 19 October 2004. J17516 S.J. Smith.2 Invertebrate Fisheries Division, Department of Fisheries and Oceans, Bedford Institute of Oceanography, P.O. Box 1006, Dartmouth, NS B2Y 4A2, Canada. P. Rago. National Marine Fisheries Service, Northeast Fisheries Science Center, Woods Hole, MA 02543, USA. 1 2

This paper is derived from the Workshop on Reference Points for Invertebrate Fisheries, Halifax, Nova Scotia, 2–5 December 2002. Corresponding author (e-mail: [email protected]).

Can. J. Fish. Aquat. Sci. 61: 1338–1354 (2004)

doi: 10.1139/F04-134

© 2004 NRC Canada

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tween growth and mortality. These concepts are primarily circumscribed by yield-per-recruit theory. The second tenet for BRPs requires some consideration of the renewal process — the relationship between stock size and recruitment that often involves poorly understood aspects of reproductive biology and difficult-to-quantify processes governing successful fertilization and survival from zygote to harvestable individuals. The looseness of these linkages often leads to the incorrect assertion that there is no relationship between stock size and recruitment. The third tenet that shapes the establishment of biological reference points is the suite of technical, economic, and social factors defining the fishery. Most of the work on developing reference points has been devoted to fish species and there has been little experience with invertebrate species (Caddy 2004). As fish stocks have declined in eastern North America in recent years, a number of invertebrate fisheries have contributed to a larger part of the total landings. One of these is the sea scallop (Placopecten magellanicus) fishery, which occurs only in the Northwest Atlantic ranging from Cape Hatteras to Labrador. Major fishing areas are located in the US Mid-Atlantic, Canadian and US sides of Georges Bank, Bay of Fundy and approaches, German Bank, Browns Bank, around Sable Island, Middle Ground, Banquereau Bank, and on St. Pierre Bank (Fig. 1). The value of landings in 2002 was in excess of CAN$125 million from Canadian fisheries and US$201 million from US fisheries. There are no explicit definitions of biological reference points with respect to overfishing for sea scallop (P. magellanicus) stocks in Canada. However, many of the recent stock status reports (e.g., DFO 1997, 1998a, 2002a) state that current levels of exploitation are not sustainable. Many different indicators for nonsustainability are used. They include model-based assessments, declining catches, declining catch rates, absence of recruitment in general or in particular areas, related observations on “ageing of size structure”, and declining survey indices when available. Management for all P. magellanicus populations in Canada use some form of size restrictions (meat count/minimum shell height) to ensure some spawning before commercial exploitation and to increase yield per recruit (e.g., DFO 1998a, 2002a, 2002b). Permanent refugia for spawning and other seasonal closures have been applied or proposed in Québec, Newfoundland, and the Bay of Fundy. Catch limits are often used for stocks in a preemptive manner and few have sufficient data to develop total biomass estimates. Enterprise allocation quota schemes have been developed for the Georges Bank (DFO 2002b) and Browns Bank (DFO 1998b) fisheries. Individual transferable quotas have been implemented for the Full Bay Scallop fleet in the Bay of Fundy (DFO 2003). In other areas, where quota management is used, total allowable catches are fished on a competitive basis. In the US, explicit limit and target reference points have been been mandated under the Sustainable Fisheries Act (Public Law 104-297). Biological reference points for scallops in US waters are based on estimates of Fmax from a yield-per-recruit analysis and a relative biomass target computed as the product of the spawning stock biomass per recruit (SSB/R) at Fmax and the median level of recruitment. Biological differences in growth parameters and average recruitment levels are recognized for two broadly defined stock areas: Georges Bank and the Mid-Atlantic. Assessments are

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conducted for these regions, but with the exception of regulations governing access to closed areas, no explicit regulations are in place to control fishing effort between regions. Scallop management in the US is based primarily on input controls. Stock-area specific reference points are not linked to spatially distinct effort regulations. Instead, the fishery is managed by a variety of effort regulations including restrictions on days at sea, maximum crew size, ring size, and so forth. At present, entry of new vessels into the fishery is restricted, but a large reserve of unused licenses constitutes a long-term concern for future management (NEFSC 2002). Effort is regulated by the specification of allowable days at sea. These are allocated to individual permit holders in three categories: full time, part time, and occasional. Full-time scallop vessels are allocated 120 days at sea, whereas parttime and occasional vessels are allocated 48 and 10 days, respectively. Each vessel is required to have a vessel tracking device to monitor vessel location and use of days at sea within the fishery area. Closed areas have been implemented on Georges Bank in December 1994 to protect depleted groundfish stocks and in April 1998 in the Mid-Atlantic area specifically to restrict fishing effort on recruiting scallops. Access to closed areas on Georges Bank was allowed in 1999, 2000, and January 2001. Vessels allowed access were limited by an individual trip limit and restricted by an overall quota for scallops and a bycatch quota for yellowtail flounder. An additional condition of access was the mandatory use of 10 days at sea regardless of the duration required to attain the trip limit. Areas closed to fishing in the Mid-Atlantic in April 1998 were reopened to scallopers in June 2001. Access to these areas is controlled by a trip limit and a mandatory use of a fixed number of days at sea. The controlled-access programs to closed areas can be considered as management experiments to support the development of a revised management plan based on rotational harvest areas. Scallops are simultaneously resilient and vulnerable to exploitation. Resiliency stems from their rapid growth, high fecundity, longevity (>12 years), and a long duration pelagic larva (>30 days) produced over a protracted spawning period (late summer to early fall). These qualities ensure rapid colonization of suitable substrates and depths. Scallop vulnerability, however, arises from the recurring colonization of areas (beds), the locations of which become well known to harvesters in mature fisheries. Avoidance responses and limited advective dispersal properties of adult scallops are insignificant relative to the speed and targeting capabilities of a modern fishing fleet. Finally, the dispersive effects of harvesting may reduce the reproductive contributions of otherwise fecund but relatively immobile adult scallops. When animal movements are minimal and targeting capabilities of the harvesters are high, management policies for BRPs must recognize aspects of the resource concentration profile (see Prince and Hilborn 1998) and the spatial–temporal patterns of harvesting. The importance of incorporating the spatial distribution of population densities, growth, recruitment, and exploitation for sea scallops when evaluating management strategies has been long recognized by Caddy (1975, 1989), Orensanz et al. (1991), and others. To date, little or no allowance has been made for spatial variation in population characteristics or fishing effort for the yield-per-recruit © 2004 NRC Canada

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Fig. 1. Location of major fishing areas for sea scallop (Placopecten magellanicus) in the Northwest Atlantic.

based biological reference points that have been used for sea scallops. This may be mainly due to the lack of spatial information for most scallop stocks in the past, but recent technological innovations may soon permit the implementation of the conceptual frameworks postulated by Caddy and others nearly 30 years ago. Quantum improvements in the ability to map the resources (e.g., Stokesbury 2002; Kostylev et al. 2003), to estimate spatially distributed biological parameters (Smith et al. 2001; Lai and Kimura 2002), to link life history models with hydrodynamic models (Tremblay et al. 1994), and to census the movements of fleets through the use of satellite-based vessel monitoring systems (Robert et al. 2000; Rago and McSherry 2001) will free future reviewers of scallop BRPs from the “limbo of soft commentary” (Orensanz et al. 1998, p. 154). In anticipation of the full implementation of these innovations, we explore the implications of including spatial considerations into the definition of the traditional growth overfishing and recruitment overfishing reference points.

Growth overfishing Growth overfishing is simply defined here as occurring when scallops are caught before they have grown large enough to maximize yield per recruit. Yield-per-recruit anal-

ysis assumes that the population is not changing with respect to character (size composition, growth rates, mortality) or size (constant recruitment) over time. Given these assumptions, the total annual yield from the population at any one time is the same as that from the fishable lifespan of any one of it’s constituent year classes (Beverton and Holt 1957). Sea scallop populations have never been noted for exhibiting constant recruitment (Caddy and Gulland 1983). The impact of highly variable recruitment on defining recruitment overfishing will be discussed in the next section. In this section, we discuss how the spatial variability in growth parameters affects the definition of growth overfishing from yield-perrecruit analysis. In general, published estimates of growth parameters for scallops are calculated for the stock as a whole, ignoring any spatial pattern (e.g., table 3 in Orensanz et al. 1991). However, growth models for scallops that incorporate spatial attributes have been presented before (see references in Smith et al. 2001). Spatial attributes are usually quite coarse, assigning individual growth curves to subareas of the population or associated with spatial proxies such as depth ranges. Although it may be recognized that growth parameters vary spatially, it is usually not clear how this information may be used when describing the population dynamics or, of interest here, defining overfishing. Here, we define a growth model © 2004 NRC Canada

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Fig. 2. Contour plot of estimates of the asymptotic weight (W∞ (g)) from a von Bertalanffy growth mixed-effects model of meat weight as a function of age. Data from June 1996 Bay of Fundy scallop (Placopecten magellanicus) survey data with tow location as grouping variable. Boundary between scallop production areas (SPA) 1 and 4 is indicated on figure.

based on von Bertalanffy dynamics with individual growth characteristics associated with each spatial location. We do this by using a mixed-effects model similar to that of Smith et al. (2001) with each location as the grouping variable. (1)

Wij = (W∞ – w∞i) × [1 – exp(–(K – ki)(aij – (T0 – t0i)))] + εij

where Wij is the meat weight (grams) of scallop j in location i and aij is the age (years) of scallop j in location i. The fixed effects or population parameters are population asymptotic meat weight (W∞), population Brody growth parameter (K, year–1), and the population age at which Wij = 0 (T0). The associated random effects for location i are w∞i, ki, and t0i. The random effects associated with location are all assumed to follow a Normal distribution with zero mean and variance–covariance matrix σ2Di. For the von Bertalanffy model the variance–covariance matrix is of dimension 3 × 3 with diagonal elements σ2w∞, σ2k , and σ2t0 . The general procedure of fitting the nonlinear mixed effects model assumes that the variance–covariance matrix is a general positive definite matrix allowing the fitting algorithm to estimate covariances between the random effects.

For the measurements made for scallops at each location, the error associated with meat weight at each age (εij ) is also assumed to have a normal distribution with zero mean and variance–covariance matrix σ2 Λi . The matrix Λi is initially set to the identity matrix when fitting the model, and hence repeated measurements at the same location are assumed to be independent over age once the random effects have been accounted for. Growth data was collected from every tow in the annual survey of scallops off Digby, Nova Scotia (scallop production areas (SPA) 1 and 4) from 1996 to 1999. To date, ages have only been determined for all of the shells in the 1996 data set. The mixed-effects model in eq. 1 was fit to these data using tow location as the grouping variable. A contour map of the random effects estimates for the W∞ parameters (Fig. 2) shows spatial patterns consistent with bathymetric contours. Based on Beverton and Holt’s (1957) suggestion that food availability would only affect the process of anabolism, we would expect that these patterns in W∞ would reflect varying availability of food with depth (see Shumway et al. 1987). The spatial pattern in Fig. 2 can be reexpressed in terms of Fmax using eq. 6.21 of Quinn and Deriso (1999) © 2004 NRC Canada

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Fig. 3. Contour plot of estimates of the fishing mortality that maximizes yield-per-recruit (Fmax) based on a von Bertalanffy growth mixed-effects model of weight as a function of age. Data from June 1996 Bay of Fundy scallop (Placopecten magellanicus) survey data with tow location as grouping variable. Boundary between scallop production areas (SPA) 1 and 4 is indicated on figure.

(2)

Fmax, i =

ki −M (1 − w ci / w∞ i)(1 + ki / M ) − 1

where ki and w∞i are as defined above, M represents instantaneous annual natural mortality, and wci is the weight of a scallop when it recruits to the fishery in location i. Using this relationship and assuming a constant instantaneous annual natural mortality rate of 0.1, a spatial map of growth overfishing reference points can be derived from the mixed effects growth model results (Fig. 3). The general practice for the Bay of Fundy and many other areas is to calculate growth-overfishing reference points such as Fmax combining all data for each area. For the 1996 data, this results in Fmax = 0.29 for the Digby portion of SPA 1 and 0.31 for SPA 4. Both of the nonspatial estimates of Fmax for each area exceed the estimate obtained for the higher growth areas in the spatial map of Fmax (0.25) where fishing is characteristically concentrated (Fig. 3). The mean Fmax over all tow locations was 0.27, which is less than the equivalent estimates for either scallop production area when spatial considerations were disregarded. In 1996, densities in the high growth areas were low and the data from the survey used to calculate the nonspatial esti-

mates for growth were dominated by scallops from the more marginal growth areas. This implies that estimates of Fmax that ignore spatial variation in growth parameters are very vulnerable to differential settlement patterns and changing densities due to spatial exploitation patterns when calculated from survey data. Spatial estimates calculated via eq. 1 should be more robust to these effects if the survey stations are a random sample of the area. Based on the spatial patterns then, growth overfishing would be avoided by fishing the higher growth areas at a lower rate than the lower growth areas. In practice, this would be counter to standard fishing practice and would be difficult to enforce.

Recruitment To a greater or lesser degree, scallop fisheries oscillate between periods of low abundance and then sudden increases due to episodic recruitment (Caddy and Gulland 1983; Caddy 1989). Orensanz et al. (1991) has reviewed the evidence for relationships between stock and recruitment for most commercial species of scallops. Although some authors have identified recruitment overfishing as having occurred for © 2004 NRC Canada

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Fig. 4. Stock–recruitment data from scallop (Placopecten magellanicus) surveys in scallop production area 4 in the Bay of Fundy. Points are labelled by two-digit year class.

particular scallop species (e.g., Dredge 1988), others have found little evidence to identify a parametric function relating spawning stock to subsequent recruitment (e.g., Naidu 1991; Marelli et al. 1999). On the other hand, there does seem to be a positive relationship between broodstock and spat fall for scallop species in culture situations (Ito and Byakuno 1988, fig. 10). For wild stocks of scallop species, most authors report that environmental influences on the survival of larvae may mask any such relationship if it exists at all (e.g., Caddy 1979; Hancock 1973; Joll and Caputi 1995). One exception to these conclusions is the study by McGarvey et al. (1993) who reported significant positive correlations between stock (measured as egg production) and recruitment for sea scallop on Georges Bank. The pattern for stock and recruitment from the annual surveys in the Bay of Fundy is characteristic of that of other bivalves (e.g., cockles in Hancock 1973). In general, recruitment spikes seem to come from the smaller spawning stock sizes (Fig. 4). This interpretation does have to be tempered with the fact that the spawning stock in 1989 was decimated by a mass mortality event before the late summer spawning period (Smith and Lundy 2002). However, the subsequent recruitment from the larger 1988 spawning stock was also quite poor. Assuming environmental effects are dominant in determining year-class strength, the pattern in Fig. 4 could be interpreted to indicate that no matter what the spawning population size, there are always more than enough eggs in the water and that the few large recruitment events observed over the period of 22 years simply reflect the degree and the relatively rare occurrence of favourable environmental effects. Figure 5 of McGarvey et al. (1993) could be interpreted in the same way with the two large recruitment events coincident with the two largest spawning stock sizes simply

indicating favourable environmental conditions rather than evidence for a direct stock–recruitment relationship. In either case, favourable environmental conditions are rare and the series are not long enough to have seen good recruitment over a larger range of spawning stock sizes. As we showed earlier, there is a spatial pattern for growth parameters in the Bay of Fundy. Egg production for sea scallops has been shown to have an exponential relationship with size (Langton et al. 1987; McGarvey et al. 1992) and, therefore, will also have a similar spatial pattern. Sinclair et al. (1985) proposed that because sea scallop beds in the Northwest Atlantic and Georges Bank have been persistent for long periods of time, they must also be self-sustaining. That is, although some larvae are advected away from the spawning areas, there must be considerable local retention for the scallop beds to persist. Studies of larval transport and abundance in the Bay of Fundy found that although there was some evidence for larval transport, densities of larvae were found to be highest in areas where the greatest biomass of spawners occurred (Tremblay and Sinclair 1988). Given that the number of eggs spawned is a function of the size of the scallops and their abundance, then relationships between spawners and recruits may only be locally evident. McGarvey et al. (1993) reported that the strength of the correlations increased when relationships within and between neighbouring subareas of the northern edge and northeast peak of Georges Bank were considered. Although higher densities of spawners should translate into higher numbers of eggs being spawned, studies of other bivalves have suggested that settlement success of the larvae and hence subsequent recruitment to the commercial fishery may exhibit a negative relationship with the local density of animals (e.g., Hancock 1973). In the case of cockles, Hancock (1973) suggested that the survival of settled larvae is © 2004 NRC Canada

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Can. J. Fish. Aquat. Sci. Vol. 61, 2004 Table 1. Settings for basin – delay difference model for a scallop (Placopecten magellanicus) population. See text for descriptions of the basin and delay difference models. (a) Model parameters. Parameter ρ α ln(a) b Survival (natural) Survival (fishing)

Habitat type Poor 0.72 2.85 –5.5 0.001 0.905 0.905

Fair 0.81 4.79 –5.0 0.0005 0.905 0.740

Good 0.86 5.99 –4.5 0.0004 0.905 0.607

(b) Proportion of larval dispersal to each subarea.a Subareas Subareas 1 Poor 2 Fair 1 Poor 0.75 0.12 2 Fair 0.08 0.75 3 Good 0.00 0.05 4 Fair 0.00 0.00 5 Poor 0.00 0.00

3 Good 0.06 0.12 0.90 0.05 0.00

4 Fair 0.05 0.03 0.03 0.80 0.05

5 Poor 0.02 0.02 0.02 0.15 0.80

a For example, 0.75 of the larvae are retained in the first poor subarea, 0.12 disperse to the neighbouring fair subarea, 0.06 disperse to the centre good subarea, etc. In the second poor subarea (subarea 5), 0.15 of the larvae are lost from the system.

less likely in patches of high densities of already settled animals. The mechanisms that have been identified as being responsible for this reduced survival include competition for space among burrowing bivalves, cannibalism of larvae by settled animals, and competition for food between older animals and newly settled animals. In this context, the pattern illustrated in Fig. 4 may reflect the lower survival of larvae as population size increases. In terms of spatial and temporal variation, we have a number of elements that may have important effects on recruitment that in turn may determine how thresholds for recruitment overfishing could be defined. They include persistent spatial patterns of growth and egg production, a degree of larval retention, density-dependent habitat suitability for larval settlement success rate as a function of spawner density (discussed below), and environmental effects on such processes as growth, larval survival, and settlement success. We used the basin model of MacCall (1990) to explore how these elements could affect the dynamics of a population with characteristics similar to scallops in the Bay of Fundy. The population dynamics were modelled using the following form of the delay-difference model (Hilborn and Walters 1992, p. 335), which is currently used to model the scallop populations in the Digby area for the stock assessment (Smith and Lundy 2002). (3)

Bt+1 = SM SF(ρ + α/wt)Bt + Rt+1

where Bt+1 is the biomass of commercial-sized scallops and Rt+1 is the biomass of recruits in year t + 1. Survival from natural and fishing mortality are SM (SM = exp(–M)) and SF (SF = exp(–F)), respectively. The growth parameters ρ and α are defined below. The average weight of commercial-sized scallops in year t is defined as wt. The area inhabited by the model population was set up as a simple scheme of five equal-sized subareas with the mid-

dle subarea characterized as having good habitat for scallop. The two subareas on either side of the middle subarea were classed as fair habitat and the two end subareas were classed as poor habitat. Parameter values for the growth- and density-dependent habitat survival parameters are given in Table 1a. Growth was modelled using the following linear relationship between weight at age a – 1 (wa–1) and weight at age a (Hilborn and Walters 1992): (4)

w a = α + ρw a −1

Density-dependent habitat suitability was modelled as a decreasing rate of larval settlement success as a function of increasing spawning population size assuming a Ricker stock–recruitment curve, (5)

R = a S exp(–bS)

where R is recruitment and S is spawning stock. Spawner success or larval settlement success in the context of our model is given as (6)

ln(R/S) = ln(a) – bS

MacCall (1990) suggested that the term ln(a) include environmental effects on spawner fecundity and densityindependent effects on offspring mortality. Densitydependent sources of mortality and reduced fecundity are included in the bS term. We use the relationship in eq. 6 to model density-dependent habitat selectivity by reducing settlement success (R/S) as a function of spawning stock. The coefficients a and b used in each of the habitat types are given in Table 1a. Annual per-scallop egg production was estimated using the shell height – egg number relationship presented in Langton et al. (1987). Although Langton et al. do not give the parameters for the curves in their Fig. 2, we estimated the function to be number of eggs = shell height3.7 based on © 2004 NRC Canada

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Fig. 5. Basin model results for a scallop (Placopecten magellanicus) population with no stochastic components. Parameter values are given in Table 1.

information given in the text. We converted this function to be in terms of meat weight instead of shell height by using the allometric relation from table 13 of Smith and Lundy (2002) for 1996 data of meat weight = exp(–11.02)shell height2.94. That is, 3.7 / 2.94

(7)

 meat weight   number of eggs =   ( exp − 11.02)  

An arbitrary mean egg to larvae survival of 1 in 50 000 was assumed for investigations here. Finally, larvae spawned in a habitat are mainly retained in that habitat, although some dispersion was allowed for. The proportion of larvae retained in each subarea or dispersing to neighboring subareas are given in Table 1b. The model was run assuming that natural mortality was equal in all areas and that intensity of fishing would vary directly with the habitat suitability (Table 1a). For this application of the model, the total time series was set at 150 years with no fishing until year 81 to allow the population to come to equilibrium. Before the start of the fishery, the population exhibits a high stable biomass with very low recruitment (Fig. 5). Once the fishery starts, the population oscillates to a lower equilibrium with generally higher and more variable recruitment. When the population has been fished down from the unfished equilibrium, the stock–recruitment relationship roughly resembles the Digby example (Fig. 4) with the largest recruiting year classes coming from the smaller spawner biomass levels (Fig. 6). A simple stochastic version of the model was built by setting the mean egg to larvae survival as a beta random variable with shape parameters of 1 and 49 999 to get the same mean value used above of 1 in 50 000. In this case, the biomass does not reach a stable equilibrium in the 80 years before the fishery but does stay above 21 000 t once the pop-

ulation has grown past the initial conditions (after year 12, Fig. 7). Recruitment is variable before the start of the fishery but this variability increases along with the level of recruitment after the fishery begins. The stock–recruitment pattern looks even more like the Digby pattern (Fig. 8) once the initial biomass has been fished down (after year 5). For both forms of the model, the time series of catch exhibits periodicities similar to those reported for the Bay of Fundy fishery (Fig. 9). Periodicities in the Bay of Fundy catch series have been previously reported as indicative of periodic environmental effects on recruitment (Dickie 1955; Caddy 1979).

Recruitment overfishing Recruitment overfishing is generally assumed to occur when the spawning stock biomass has been reduced by fishing to a point at which reproduction is impaired in some sense. In the standard stock–recruitment presentation such as that given in Fig. 4, the implicit assumption is made that the reproductive productivity for individuals at high and low stock sizes is the same. In the Bay of Fundy, the larger stock sizes were due to large recruiting year classes and, hence, mainly consisted of small scallops. As scallops show an almost linear increase in gamete production with meat weight (ref. eq. 7), the productivity of the larger stock sizes such as in 1988 and 1989 (Fig. 4) will be a function not only of stock size, but also of the average meat weight of the scallops in the population. In fact, the average meat weights for these two years were 9.4 g and 11.1 g, respectively. In 1984 and 1985, the average meat weights were 17.5 g and 17.7 g, respectively, and on a per-scallop basis, the scallops from these smaller year classes should have produced between 1.8 and 2.2 times the number eggs produced by individuals from the larger year classes. © 2004 NRC Canada

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Fig. 6. Stock–recruitment scatter plot during fishery period in the nonstochastic version of basin model.

Fig. 7. Basin model results for a scallop (Placopecten magellanicus) population with stochastic component for fertilization and egg to larval survival. Parameter values are given in Table 1.

In the basin model for the unexploited period (years 1 to 80), the larger stock sizes were characterized by the larger meat weights. However, for the exploited phase of years 81 to 150, the average meat weights were smaller for the larger stock sizes. Thus, the model suggests that smaller average sizes reflect unrealized biomass per recruit when fishing mortality is high. Hart (2003) demonstrated a similar phenomenon for Georges Bank scallops protected from fishing mortality in closed areas.

The traditional definitions of an equilibrium recruitment level that replaces spawning stock implicit in replacement reference points (e.g., Fmed, Frep; Quinn and Deriso 1999) is complicated here by the size composition of the larger spawning stock sizes. For scallops, we can start with assuming that at least one egg per spawner has to survive to one female recruit as a basis for replacement. At equilibrium, the discounted sum of eggs released by a female recruit must produce two recruits (assuming 1:1 sex ratio) that survive © 2004 NRC Canada

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Fig. 8. Stock–recruitment scatter plot during fishery period in stochastic version of basin model.

Fig. 9. Comparison of time series of catches from stochastic and nonstochastic versions of basin model.

the larval stages, settlement, and life on the bottom through to ages 1 to 4 years (e.g., Vaughan and Saila 1976). For the moment, we will assume that fertilization success for all eggs released was constant and density-independent. The baseline survival for replacement is simply 2 divided by the number of eggs produced. Because the number of eggs produced increases with the size of the animal, this replacement can occur at progressively lower rates of survival for larger animals (Fig. 10). For fishing years in the basin model, sur-

vival (the number of recruits at age 4 divided by the number of eggs from which the cohort originated) is rarely above the replacement line except for the larger scallops in the good habitat area. Egg production in the poor habitat areas is not enough for the population to persist because of the relatively small size of the scallops and associated gonads in these areas. It is only the addition of larvae from the adjacent areas that keeps the population in the poor areas from going extinct. The population in the poor areas goes extinct before © 2004 NRC Canada

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Fig. 10. Survival rates from egg to 4 years old for nonfishery period of stochastic version of basin model. Number of eggs calculated from meat weight – egg number relationship in eq. 7. Replacement line refers to a survival such that a minimum of two recruits (assuming 1:1 sex ratio) survive the larval stages, settlement, and life on the bottom through ages 1 to 4 years. Good habitat, 䊊; fair habitat, +; poor habitat, 䉭.

Fig. 11. Survival rates from egg to 4 years old for fishery period of stochastic version of basin model. Number of eggs calculated from meat weight – egg number relationship in eq. 7. Replacement line refers to a survival such that a minimum of two recruits (assuming 1:1 sex ratio) survive the larval stages, settlement, and life on the bottom through ages 1 to 4 years. Good habitat, 䊊; fair habitat, +; poor habitat, 䉭.

the fishery starts when the dispersion matrix in Table 1b is replaced with the identity matrix (no dispersion). In the years before the fishery began, survival was rarely above the replacement line in all habitat types, mainly because carry-

ing capacity had been reached quickly and densitydependent habitat selectivity became a factor in reducing settlement survival (Fig. 11). Therefore, the evaluation of whether or not egg production is enough to replace the © 2004 NRC Canada

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Fig. 12. Estimated survival rates from egg to 4 years old for scallops (Placopecten magellanicus) in scallop production area 4 based on delay-difference model in Smith and Lundy (2002). Replacement line refers to a survival such that a minimum of two recruits (assuming 1:1 sex ratio) survive the larval stages, settlement, and life on the bottom through ages 1 to 4 years. Points labelled by two-digit year class.

spawning stock depends very much on whether the stock is highly exploited or not. For the parameters used in the basin model, it appears that it is mainly the egg production in the good habitat area that is driving the population increases during the exploited phase (as seen in Fig. 7). We evaluated the survival for scallop production area 4 in the Bay of Fundy by ignoring spatial effects and estimating survival rates over the whole area for each cohort to 4 years of age from 1981 to 1998. Again, assuming that the egg – meat weight relationship holds here, we see that there have only been 3 out of 18 years in which survival was such that the number of recruits exceeded the number needed for replacement (Fig. 12). Although these increases were probably due to recruitment from the good habitat areas identified by growth characteristics in Fig. 2, we will continue with this example at the aggregate level. Assuming that densities are not high enough to invoke serious density-dependent habitat selectivity effects, this figure suggests a metric that may be useful as a reference point. That is, based on the observed data, determine the probability that survival will exceed the replacement line survival limit if the average meat weight in the population is X g. For example, at an average meat weight of 12 g, 3 of the 18 survival rates exceeded the replacement line value. However, if the meat weight in 1997 had been larger, say 17 g, then the survival rate for that year would have been high enough to exceed the replacement line. If we assume that survival rate is independent of meat weight, then we can use these modelled survival rates as representative of those that we may encounter in the future and calculate for each meat weight what proportion of the observed rates were above or below the replacement line. These calculations indicate that for an average meat weight

of 17 g, there is only a 22% probability of recruitment equaling or exceeding the replacement line for spawning stock — assuming 100% constant density-independent fertilization success. Lower rates of fertilization success will reduce this probability. One of the open questions in this investigation concerns fertilization success and how it is affected by the density of the spawning scallops. In the next section, we turn to this question using a different set of models.

Density-dependent fertilization rate Langton et al. (1987) suggest that year-class success of scallops may be more closely related to degree of spawning synchrony than to total reproductive output. For sessile sexual species with limited dispersal of gametes, it is obvious that a large biomass is irrelevant if interanimal distances are too great for successful fertilization. Some of the earliest research on bay scallops (Argopecten irradians) suggested the possibility of sperm limitation in natural populations (Belding 1910). Stotz and Gonzalez (1997) suggested that exploitation of Argopecten purpuratus populations had resulted in the complete elimination of scallop beds. Orensanz et al. (1991) recognized that prevention of recruitment overfishing required careful consideration of the biology of the species. They noted that if the threshold density for fertilization success exceeded the threshold for economic profitability, then more drastic measures to preserve spawning areas would be necessary. Empirical data on fertilization success in natural populations are rare and generally qualitative (Levitan and Sewell 1998). Stokesbury (1999) examined spatial distributions at a © 2004 NRC Canada

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Fig. 13. Comparison of model-based relative increase in fertilized scallop eggs for Georges Bank and Mid-Atlantic areas surveyed by NMFS R/V Albatross 1980–2000. Results are expressed as a ratio of annual value to the 1980 to 1995 mean. Closed areas on Georges Bank began in December 1994; closed areas in the Mid-Atlantic region were put in place in April 1998.

scale of centimetres and found aggregations or “clumps” that might be important for ensuring high levels of fertilization. He further suggested, but did not verify experimentally, that scallop movements may be directional to support the formation of clumps. If so, disruption by fishing activity could reduce fertilization rates and subsequent spawning success. Fine-scale aggregations may also facilitate the neurosecretory regulation of spawning. Barber and Blake (1991) summarized a number of studies on a variety of species (Chlamys varia, Patinopecten yessoensis, Pecten albicans) in which release of neurosecretory products was necessary before external stimuli can induce spawning. Hence the “clumps” may be important for synchronization of spawning activities. Quinn et al.’s (1993) modelling of sea urchin populations suggested that the protection of highdensity refuges would be a way of protecting against high rates of exploitation. Claereboudt (1999) developed a fine-scale three-dimensional simulation model of the fertilization process and parameterized it for P. magellanicus. His model allowed for variation in initial density, an aggregation coefficient similar to the “concentration factor” of Prince and Hilborn (1998), and variation in exploitation. Egg production scaled linearly with density, but larvae density declined by over 95% when a simulated stochastic population was subjected to harvest rates on the order of 50%. The nonlinear response to exploitation arose due to increased distances between randomly distributed individuals. Although field data that confirm or refute the concept of localized recruitment overfishing are not available for P. magellanicus stocks, we can use the results of Claereboudt’s model to investigate the relative increase in fertilized egg production since closed areas were used as management tools in the USA fishery. As suggested in

Claerboudt’s figure 3, fertilization success increases linearly with density (number·m–2). If we approximate the fertilization coefficient in Clareboudt’s figure 3 as 0.2, then the number of fertilized eggs is proportional to the product of the fertilization rate and stock biomass. We used the following piecewise linear model to develop an index of fertilized egg production: (8)

EFert = min(0.2D,1)B

where D is relative density ((number·tow–1)·(m2·tow–1)–1· dredge efficiency –1) and B is the estimated total weight of scallop meats per tow. In this exploratory computation, we use a gear efficiency rate of 40% and conservatively assume that egg production is proportional to somatic weight. Average egg production per tow is estimated as the simple average of the n tows sampled each year in the Georges Bank and Mid-Atlantic regions. A time series of such estimates (Fig. 13) illustrates the remarkable increase in the modelbased fertilized egg output since the closed areas were instituted. These results suggest that the egg output from the regions has increased by several orders of magnitude since 1994 on Georges Bank and since 1998 in the Mid-Atlantic region. The methodology that we used does not account for the potential reproduction of localized clusters that might be masked by the overall density estimate based on catch rate data from the fishery or surveys. In unfished scallop beds in Baie des Chaleurs, Quebec, Stokesbury and Himmelman (1993) found most scallops within small clusters of