How Should We Harvest an Animal that Can Live for Centuries?

Simulations

Because (τ + ν) and τ were highly correlated, results using each were similar; for simplicity, only the results from τ are discussed here.

Deviance tables showed that the effects of F_target, τ, and M were better predictors of mean biomass, yield, variation in yield, and time without fishing (t_F=0) than any of the other candidate predictors or interactions tested (Table 2). Biomass tended to decrease with increasing F_target, while yield, variation in yield, and t_{F = 0} tended to increase as F_target increased (2, 3). Increasing M resulted in higher yields, more variation in yield, and less time without fishing. Higher values of τ produced higher biomass, more time without fishing, less yield, and greater variation in yield.

Table 2. Deviance table results for models predicting ocean quahog mean scaled biomass (, where SSB = spawning stock biomass and B₀ = unfished biomass), mean scaled yield (), CV of yield (CV[Y]), and years without fishing due to management (t_{F = 0}) over 100-year simulations (n = 50,000 runs). The candidate predictors were the target fishing mortality (F_target), steepness (h), natural mortality (M), the fraction of B₀ corresponding to the biomass threshold (τ), standard deviation of assessment error (σ_At), amount of autocorrelation in assessment error (φ), standard deviation of implementation error (σ_Ft), and interactions of potential interest. Only predictors that explained at least 5% of the deviance relative to the null model are shown.

Response	Significant predictors (% of deviance explained)
	Ftarget (80.2), τ (10.6), Ftarget · τ (5.1)
	Ftarget (52.7), M (27.5), τ (14.9)
CV(Y)	Ftarget (87.9), M (6.3)
tF=0	Ftarget (59.3), σAt (19.7), τ (41.17), M (5.5)

There were two cases in which variables other than F_target, τ, or M were important in the deviance table analysis. The variable was significant in predicting t_F=0 (Table 2); increases in produced more time without fishing (Figure 2). Finally, the F_target · τ interaction was an important predictor of mean biomass (Table 2). The interaction was, however, probably only meaningful at higher values of F_target (Figure 4). The effect of τ appeared to be relatively constant at low values of F_target; in particular, Figure 4 illustrates that mean biomass did not change much across all values of τ when F_target was less than F_threshold.

Simulated Management over Different Spatial Scales

The effect of spatial scale on management was minor across most of the response variables tested, at least when considering the first 100 years of simulation. Mean biomass was not substantially different between the treatments of spatial scale, but mean yield was greater under the single-stock management scenario (Table 3; Figure 5). However, the higher yields resulted in a tendency to overharvest and a higher probability of fishery closures due to management intervention. Under the separate-stocks management scenario, regional closures resulted in lower yield overall and more variation in yield but fewer years without fishing, as at least one region was usually above the B_threshold—and thus was open to fishing—as long as F_target was low.

Table 3. Deviance table results from simulations testing possible spatial structures of ocean quahog management. Inputs were models predicting mean scaled biomass (, where SSB = spawning stock biomass and B₀ = unfished biomass), mean scaled yield (), CV of yield (CV[Y]), and years without fishing due to management (t_{F = 0}) over 100-year simulations (n = 50,000 runs). The total biomass and yield were based on summed values from four regional stocks that were either managed separately or as a single stock, each assessed every 5 years. The candidate predictors are defined in Table 2.

Response	Significant predictors (% of deviance explained)
Separate stocks
	Ftarget (82.9), τ (9.3)
	τ (73.1), M (20.4)
CV(Y)	Ftarget (94.2)
tF=0	Ftarget (76.3), σAt (9.8), τ (8.7)
Single stock
	Ftarget (79.4), τ (15.1)
	M (36.5), τ (48.6), h (11.0)
CV(Y)	Ftarget (95.6)
tF=0	Ftarget (80.2), σAt (13.6)

Recruitment Model Sensitivities

One potential weakness is that the recruitment model may not accurately represent ocean quahog recruitment. The fishery is simply too young relative to the ocean quahog's generation time for us to detect any compensatory response to fishing. Therefore, any specification of a recruitment model based on observed data is potentially a poor representation of long-term ocean quahog recruitment when the population is subject to fishing.

The extraordinary longevity of ocean quahogs does mitigate this dilemma in one respect at least, as the current age structure of the population provides information about historical recruitment patterns. The analysis of Powell and Mann (2005) identified strong recruitment classes from decades prior to the start of the fishery. Thus, although we cannot predict the strength of any potential compensatory response in recruitment, we can be relatively confident that the simulation is approximating the frequency of strong recruitment events given a virgin population. The recruitment model used here integrated over a reasonable range of h-values and included a stochastic pulse recruitment component; the results did not appear to be sensitive to h over the range tested (Table 2).

The recruitment model was designed to mimic what little is known about ocean quahog recruitment. There is a small but noticeable amount of recruitment that happens each year. There are large year-classes that occur infrequently, sometimes with decades between them, and such year-classes appear to be random in periodicity. The magnitude of these year-classes is unknown, but there is anecdotal evidence that they can be very large. For example, the scallop survey run by the U.S. National Marine Fisheries Service once collected more than thirty-thousand 3-cm (∼6-year-old) ocean quahogs in a single 1.85-km tow using a 2.4-m scallop dredge on Georges Bank.

The specific values used for the recruitment parameters (, , and ; equation 9) did not affect the overall results. Values leading to more-frequent pulse recruitment events of higher magnitude tended to result in a higher B₀, while less-frequent and volatile recruitment had the opposite effect. Because biomass and yield performance statistics were scaled to be a fraction of B₀, the starting biomass was unimportant.

Due to the large sample of simulations, the timing and magnitude of pulse recruitments in individual runs did not influence the overall results. However, they did influence individual results, particularly over the first 100 years of simulation. Early strong recruitment events tended to produce relatively high biomass and stable yield. This effect was balanced by runs in which recruitment was poor early in the time series, thereby producing low biomass and variable yields (due to fishery closures). The high number of simulations averaged these effects out, such that the timing of recruitment did not matter over the set of all simulations. In application to the real ocean quahog population, however, the period of strong recruitment events is likely to be important.

The use of a Beverton–Holt curve as the underlying mean spawning stock–recruit relationship around which annual fluctuations occurred was arbitrary, but there was no reason to expect that overcompensation leading to a Ricker-type curve (Ricker 1954) was warranted. Beverton–Holt dynamics have been used to model other long-lived, slow-growing stocks (Grigg 1984).

Other uncertainties included M, which was most important in predicting mean yield (Table 2). True M for ocean quahogs is unknown, but the range over which the simulations integrated should have encompassed it based on what is known about longevity. The highest value (M = 0.03) implies that only 1% of a cohort would survive to 154 years, whereas the low value (M = 0.01) predicts that 1% of a cohort would survive to 460 years. Those survival schedules appear unlikely based on the aging studies that have taken place (see Kilada et al. 2006; Harding et al. 2008) and because only one individual ocean quahog older than 460 years has been found to date (Butler et al. 2013).

Ocean quahog growth is known to be slow, but it should probably be studied in greater detail, as most of the work done on this topic is geographically limited (Kilada et al. 2006). Variability in growth was not explicitly considered here except as a factor in analyzing the effects of spatial management. From the perspective of managers, overestimation of M and growth would be problematic, as it implies a more-productive fishery and would tend to result in overly aggressive tactical management (e.g., higher F and lower SSB allowed). Industry would be more concerned with the underestimation of M and growth, which would produce overly conservative management quantities and would result in loss of potential yield. The results presented here should be reasonably robust to misspecification of M and variation in growth up to the magnitude shown in Table 1.

Simulation

Possible compensatory responses to fishing pressure were difficult to discern in the “short-term” (100-year) simulation series. The effect of h was masked by the stronger effects of F and the implementation of the control rule. When the population was simulated over 1,000 years with fishing, the effect of h was easier to see. When h was high, the population was able to compensate and stabilize at higher levels of fishing intensity, producing higher mean yields. At low h, the population could not adequately compensate for fishery removals, and the yields were low because the fishery was closed frequently due to implementation of the control rule. In all cases, the mean biomass was relatively stable over 1,000 years, indicating that the control rule appears to work well at all h-values (and B_threshold levels) tested. The combination of an effective control rule and the size selectivity of the fishery, which allows ocean quahogs to have many years of reproduction before they are vulnerable to the fishery, probably dampens the effect of h on the population.

The effects of M on population-level response variables were largely predictable. A higher M, which implies a more-productive population, resulted in a higher yield and biomass. The relationship between M and time without fishing due to depletions and closures was interesting and illustrates some unusual properties. Although there was noise, a higher M was associated with a decrease in t_{F = 0} (Figure 2). The mechanism behind this result is the interaction of growth and the peculiarities of extreme longevity. When M was low, the population age structure tended to accumulate in the old age-classes, for which growth was very slow. At low M, ocean quahogs lived for a very long time beyond the age when they reached maximum length. Thus, even when the population is fished down, it can be quite old and therefore slow to replace biomass with growth. The result when fishing was applied was a depletion in biomass that took a long time to rebuild. When M was high, the population age structure was more concentrated in the young ages, for which growth is relatively rapid, and the population could replace lost biomass with growth in fewer years.

Higher assessment error increased the probability that the fishery would be closed due to management intervention. Misspecification of biomass tended to produce poor management advice and inappropriate use of the control rule. When assessment error was high, the resource was fished when it should have been closed to fishing, or the fishery was closed when it should have remained open. Both of these situations would tend to cause a higher probability of closure over time, as the population was either fished into depletion without necessary intervention, which would increase rebuilding time, or the fishery was closed without cause.

Maintaining very low fishing pressure was important in maintaining an ocean quahog fishery in simulation. In the short term (100 years), F_target values greater than 0.03 did not produce higher average yields than F_target values near 0.03. However, on average, F_target greater than 0.03 did result in a greater number of years without fishing due to management intervention and also reliably produced lower mean biomass values and greater variation in yield (Figures 2, 3). Although there was some risk of fishery closure at all of the F-values tested, F_target values less than 0.03 kept the probability of closure below 25% and kept the length of expected closure to one assessment cycle (i.e., 5 years) on average (Table 4; Figure 2). Minimizing the length and probability of fishery closures is particularly advantageous for a market-limited fishery in which additional supply has little additional value but in which there is constant demand. Such a market currently exists for ocean quahogs, which are an important constituent of mass-produced canned clam chowder (a soup sold in the USA and elsewhere; Serchuk and Murawski 1997) but have been fished at about 70% of quota for the last 10 years (Chute et al. 2013). The findings here support previous research recommending low harvest rates for long-lived shellfish (Zhang and Hand 2006), including the ocean quahog (Thorarinsdottir and Jacobson 2005).

Results from the simulations were noisy, but the evidence suggests that SSB_threshold values on the lower end of the spectrum tested (0.25−0.50) may be suitable for ocean quahogs. Lower SSB_threshold values tended to produce less variation around higher yields as well as fewer fishery closures (Figures 2, 3). Lower SSB_threshold did produce lower mean biomass, but none of the SSB_threshold values tested resulted in high extinction likelihoods over 100 or 1,000 years. This is apparent in Figure 4, where the left margin of the contour plots show little variation over all tested values of τ, particularly when F_target is low (e.g., F_target < F_threshold = 0.022).

The SSB_threshold and SSB_target values were less important than F_target in part because low fishing pressure and the control rule were sufficient to maintain the population over 100 years. It is also important to emphasize that relatively early maturation, slow growth, and fishery selectivity play an important role in maintaining the ocean quahog population. These factors combine to give young ocean quahogs many years of reproductive capacity before they become vulnerable to fishing.

Simulated Management over Different Spatial Scales

Some modest benefits were evident for the separate-stocks management scenario as simulated here, although these depended on the market peculiarities that exist for ocean quahogs. Single-stock management tended to produce higher yields on average. However, the loose control provided by coarse spatial management implies that high biomass in one region can mask very low biomasses in other regions, similar to concerns raised by Molton et al. (2012) for populations with low intermixing levels. Such a situation could lead to depleted biomass conditions, as the high-biomass region regressed to average biomass levels and the low-biomass regions were rapidly fished down without triggering the necessary management intervention. This pattern resulted in higher yields on average over the first 100 years of the fishery, but as noted above, increased yield has little value in the ocean quahog fishery due to market limitations. Increased yield may also be associated with an increased risk of regional economic extinctions, which would take a very long time to rebuild due to the slow growth rate of ocean quahogs, but increased yield could also mitigate biological depletions, particularly if the threshold for economic extinction is high relative to the density of spawners required for successful reproduction.

There is an open question regarding the minimum density of spawning ocean quahogs required for effective reproduction. Because ocean quahogs are sessile broadcast spawners, they must occur at densities that are sufficient to permit the genetic material from males and females to interact. If ocean quahogs are fished below this density, depensation might ensue. For this reason and to reduce the probability of fishery closures, it would be prudent to manage separate regional aggregations independently, particularly if they are reproductively isolated. One possible safeguard in this regard would be the use of regional spatial refuges, which have been recommended for slow-growing, long-lived demersal fish species (King and McFarlane 2003). A spatial refuge might be effective for maintaining a regionally dense spawning aggregation, but it would have to be carefully placed to provide population-level benefits, which depend on the effective dispersal of larval animals. The dispersal of ocean quahogs has not been extensively studied but certainly relies on current forcing and temperature to a large extent (Zhang et al. 2015).

Discussion of refuges often leads to discussion of rotational management, a strategy in which an area is temporarily closed to fishing while a large recruit class grows to optimal size (i.e., ∼L_∞). Area closures have been used successfully for other shellfish resources in the USA (NEFSC 2010). Because of their slow growth, ocean quahogs are very poorly suited to this type of management. An area would have to be closed for several decades to allow a large recruit class to reach a size that could be efficiently caught and processed. By the time the area would be reopened, most of the fishers who paid the opportunity cost of foregoing fishing inside the area would be retired (if not dead).

Simulations run over 1,000 years with fishing indicated that there was relatively little return in yield on F_target values greater than 0.03. Furthermore, fishing at F_target less than 0.03 induced a lower probability of depletion (and closures), whereas fishing at F_target greater than 0.03 incorporated some risk that the fishery would be closed for a substantial portion (often >50%) of the 1,000 years.

The results of this simulation study support the following recommendations. First, ocean quahog fisheries should be prosecuted with very low F, as F_target values exceeding 0.03 tended to result in fishery closures while not having much of an effect on yield. Second, given a low F_target and the current control rule, ocean quahog fisheries are likely to tolerate a relatively low B_threshold value, as mean biomass was similar for threshold values between 0.25·B₀ and 0.50·B₀. Finally, an understanding of spatial structure is important for maintaining a functional fishery. Regions experiencing independent recruitment should be managed as separate entities, as stocks that were managed separately were less likely to experience depletion resulting in fishery closure.

These findings generally support previous advice regarding the management of long-lived species. Deep-sea fisheries, which are typically composed of long-lived, slow-growing fish, are often overexploited and rapidly fished down to economic extinction (Koslow et al. 2000). Low exploitation rates (1–2% of B_virgin) have been recommended as potentially sustainable for these fisheries (Clark and Tracey 1994; Large et al. 2003).

The species most similar to the ocean quahog in terms of life history is probably the geoduck clam Panopea abrupta, which can live for more than 150 years. The geoduck clam presents an interesting case study because it is managed in typical fishery fashion in Canada but is managed more like a tree in the USA (Orensanz et al. 2004). In Canada, the fishery operates under a target exploitation rate of approximately 1% of B_virgin. In the state of Washington, tracts of sea bottom (comprising a targeted percentage of the total biomass) are leased to fishers, who can then exploit them as they see fit. Tracts are only included in the pool of potentially leased area once the geoduck clams have recovered from any previous harvest. Both of these methods are controversial, and neither has been in place long enough (i.e., relative to the life span of a geoduck clam) to demonstrate which method is superior. It has been suggested that a simulation study similar to the one presented here might be a more useful way to determine a harvest strategy for geoduck clams (Orensanz et al. 2004).

Long-lived animals are difficult to manage sustainably. Effective management will depend on the particulars of life history and the characteristics of harvesters. Uncertainty regarding either the biology of the species or the behavior of harvesters will make management even more difficult. Management strategy evaluation through simulation can be an effective tool for choosing between harvest strategies for long-lived organisms, despite uncertainties.