North American Journal of Fisheries Management 29:1555–1566, 2009 [Article] American Fisheries Society 2009 DOI: 10.1577/M08-221.1

Accounting Explicitly for Predation Mortality in Surplus Production Models: an Application to Longfin Inshore Squid

HASSAN MOUSTAHFID,MEGAN C. TYRRELL, AND JASON S. LINK* National Oceanic and Atmospheric Administration Fisheries Service, Northeast Fisheries Science Center, 166 Water Street, Woods Hole, Massachusetts 02543, USA

Abstract.—One approach to better account for ecosystem considerations in fisheries science is to incorporate ecological interactions into conventional stock assessment models. The longfin inshore squid Loligo pealeii is one of two squid species of ecological and commercial significance in the northwest Atlantic Ocean. A surplus production model with quarterly time steps was fitted to longfin inshore squid total removal (fishing and predation removal) and tuned with fishery-dependent, fishery-independent, and predation- dependent indices to examine the effect of incorporating predation into a single-species model. Total consumption of squid by all predatory fish exceeded the landings in most years of this analysis. The model output indicated that biological reference points for longfin inshore squid differ considerably when predation removals are included. It appears that by not including predation, the model underestimates stock biomass and overestimates fishery surplus production. Short-term stochastic projections of such estimates demonstrate that increasing predation mortality and fishing mortality will decrease the biomass of longfin inshore squid. Failing to account for predation when performing stock assessments for longfin inshore squid and other similar forage species may misrepresent reference point estimates and result in management advice that could lead to biomass declines. We envision that the approach presented here will provide requisite information and a useful example towards improving the current modeling practices for longfin inshore squid and similar forage species.

The longfin inshore squid Loligo pealeii is one of the points for this species (Cadrin and Hatfield 1999; two commercially significant species in the northwest NEFSC 2002). Surplus production models have also Atlantic squid fishery. This species plays a vital role in provided the basis of management advice for other the northeast U.S. continental shelf ecosystem as a squid species in other ecosystems (e.g., ICES 1988; major node in the food web, acting as both predator Bravo de Laguna 1989). and prey (Link et al. 2006). This species transfers Despite the array of improvements made to surplus nutrients from secondary consumers (zooplankton and production models, most scientists agree that even with small neritic fishes; Vovk 1972; Tibbetts 1977) to accurate single-species stock assessments, many im- tertiary consumers (medium-sized pelagic and bottom portant ecological factors are not always adequately fishes) and apex predators (large fish, marine birds, addressed. Predation mortality is one biological factor pinnipeds, and small toothed whales; Vovk and that can have considerable impact on biological Khvichiya 1980; Waring et al. 1990; Link et al. 2006). reference points (Hollowed et al. 2000; Overholtz et Recent life history studies of longfin inshore squid al. 2008). suggest that there is a great deal of natural variability Predation mortality has been explicitly modeled in and statistical uncertainty in estimates of growth and catch–age stock assessment models by defining natural mortality (M; Brodziak and Macy 1996; Cadrin predation mortality as a type of fishery (Livingston and Hatfield 1999; Macy and Brodziak 2001). Because and Methot 1998; Hollowed et al. 2000). Overholtz et of this uncertainty, estimates of abundance and fishing al. (2008) presented a further example that explicitly mortality (F) and associated biological reference points incorporated predation mortality in a delay difference from age-based or length-based models thus also have model for stock assessment of the Atlantic herring a great deal of uncertainty (Cadrin and Hatfield 1999; Clupea harengus complex in the Gulf of Maine and NEFSC 2002). Lacking precise information on age and Georges Bank. They treated estimates of Atlantic growth, surplus production models with quarterly time herring consumption by various predators as a second steps are alternatives to the age-structured models fleet and added the consumption estimates to the catch commonly used to derive the biological reference data. This modified time series of removals (predation þ fishery) was entered as inputs to an Atlantic herring * Corresponding author: [email protected] stock assessment model. Results from these single- Received October 21, 2008; accepted May 7, 2009 species models that incorporate predation mortality Published online October 12, 2009 showed that (1) the models that did not account for

1555 1556 MOUSTAHFID ET AL.

FIGURE 1.—Area of the northeastern U.S. continental shelf between the northern edge of Georges Bank (off Cape Cod, Massachusetts) and Cape Hatteras, North Carolina, that encompasses the longfin inshore squid stock. predation mortality underestimated stock biomass rather, we sought to demonstrate and discuss some of (Hollowed et al. 2000) and (2) the assumption of the advantages of executing this approach. constant M in traditional single-species models may be Methods unrealistic. Furthermore, maximum sustainable yield Fishery and Survey Data (MSY) related reference points generated without consideration of temporally variable predation may be For this study of the longfin inshore squid stock, the misleading (Overholtz et al. 2008). Overholtz et al. study area was between the northern edge of Georges (2008) warned that when predator biomass changes Bank (off Cape Cod, Massachusetts) and Cape Hatteras, North Carolina (Figure 1). Commercial substantially over time, and particularly if there are fishery landings data consist of quarterly landings for trends (either seasonal or annual) of consistently longfin inshore squid during 1987–2001; these data increasing or decreasing predator biomass, then were obtained directly from a recent longfin inshore predation mortality should be included in an analysis squid stock assessment (NEFSC 2002). Total catch for of forage species dynamics. Including predation for the 1987–2001 time series was increased by 6% to species that are subject to both fishing mortality and account for discards, based on the average discard rate predation seems highly warranted (Link 2002). during 1989–1998 (Cadrin and Hatfield 1999; NEFSC In this paper, we explore the feasibility of incorpo- 2002). The quarterly periods were January–March rating predation into a stock production model with (winter), April–June (spring), July–September (sum- quarterly time steps for longfin inshore squid. Our mer), and October–December (fall). The summer intent was not to provide a formal stock assessment; fishery occurs during the spring (second) and summer PREDATION IN LONGFIN INSHORE SQUID MODELS 1557

TABLE 1.—Abundance data indices used in six models of longfin inshore squid surplus production: two models derived from Northeast Fisheries Science Center (NEFSC) bottom trawl survey data for autumn and spring quarters; two models based on standardized commercial landings per unit effort (LPUE) for winter and summer fisheries; and two models based on spring and autumn predation-dependent indices (I) (expressed as the total amount of squid biomass consumed per unit of predator; e.g., spiny dogfish).

Model (number/tow) Model (LPUE) Model (squid biomass)

NEFSC NEFSC LPUE LPUE I(predation) I(predation) Year spring autumn winter summer spring autumn

1987 8 10 5 4 6 7 1988 16 35 8 5 6 7 1989 18 40 6 4 14 2 1990 13 30 5 4 24 6 1991 16 35 8 4 20 3 1992 10 26 9 3 23 2 1993 8 18 3 18 1 1994 4 60 29 2 1995 8 20 10 2 1996 3 14 16 2 1997 9 32 9 9 1998 6 16 6 9 1999 14 47 27 26 2000 11 54 19 28 2001 8 29 10 47

(third) quarters, and the winter fishery occurs during luccius bilinearis, red hake Urophycis chuss, spotted the fall (fourth) and winter (first) quarters. These hake U. regia, weakfish Cynoscion regalis, bluefish fishery-dependent indices consist of standardized Pomatomus saltatrix, summer flounder Paralichthys commercial landings per unit effort (LPUE) for dentatus, fourspot flounder Paralichthys oblongus, summer and winter fisheries during 1987–1993. They goosefish Lophius americanus, sea raven Hemitripte- were computed as the ratio of landings and standard- rus americanus, and Atlantic mackerel Scomber ized fishing effort for otter trawl trips that caught at scombrus. least 10% (by weight) longfin inshore squid. Effort was Consumption of longfin inshore squid was estimated standardized using a general linear model with years, from all available stomach content data following the seasons (summer or winter), catch areas, and vessel same method developed in previous studies (Overholtz ton-classes as explanatory factors (NEFSC 1996, 2002; et al. 2000; Link et al. 2002; Overholtz and Link 2007). Table 1). Fisheries-independent indices of abundance In the cases where seasonal data were not available for consisted of Northeast Fisheries Science Center winter and summer quarters, spring data were used as a (NEFSC) autumn and spring bottom trawl survey proxy for winter, and autumn data were used as a proxy estimates of longfin inshore squid abundance from for summer. Data were aggregated into 5-year intervals 1987 to 2001 (Table 1; Azarovitz 1981; NEFC 1988). for all predators except spiny dogfish, silver hake, spotted hake, and fourspot flounder, which were Consumption Data aggregated into 2-year intervals because of the nature We used fish food habits data to estimate consump- (i.e., higher number of samples) of the available data tion of longfin inshore squid. A detailed description of for each predator. the methods for field collection and analysis of The method used to estimate the total daily stomach samples can be found in Link and Almeida consumption was based on average stomach content (2000). data and an hourly gastric evacuation rate (Eggers Seasonal diet data collected from fish stomachs in 1977; Elliott and Persson 1978; Pennington 1985): NEFSC bottom trawl surveys during 1987–2001 were C ¼ 24 3 R 3 Sc ; ð1Þ examined to identify the most important demersal it it it fishes preying on longfin inshore squid in the U.S. where Cit is daily consumption (g) for each predator Northeast region waters. We identified 15 species that species i and time period t (season and year), 24 is day prey on longfin inshore squid: the spiny dogfish length (h), Sit is the mean stomach content weight (g), c Squalus acanthias, smooth dogfish Mustelus canis, is a shape function assumed equal to 1 (Gerking 1994), winter skate Leucoraja ocellata, Atlantic cod Gadus and Rit is the evacuation rate. The variable Rit is morhua, pollock Pollachius virens, silver hake Mer- calculated as 1558 MOUSTAHFID ET AL.

bT Rit ¼ ae ; ð2Þ where r is the intrinsic rate of population growth, K is the carrying capacity (both r and K are assumed to be where a and b are fitted constants and T is seasonal constant), and B is the biomass at time t. bottom temperature (8C) obtained from NEFSC bottom t trawl surveys (Holzwarth and Mountain 1992). Spring The total instantaneous mortality rate (Z) is the sum bottom temperature data were used as a proxy for of F and M. The M can be separated in two components M M M , where M is the mortality rate due to winter, and autumn data were used as a proxy for ¼ 1 þ 2 2 consumption by predators and M is the residual summer. The a and b values in equation (2) were set as 1 0.004 and 0.115, respectively, for teleost predators mortality due to other factors, including disease and (Overholtz et al. 2000; Overholtz and Link 2007) and senescence. The M1 in this computation was assumed to 0.002 and 0.111 for elasmobranch predators (e.g., Tsou be low (0.01 per quarter) and constant over time and Collie 2001). Daily consumption estimates were because disease and senescence are probably low in 0 marine stocks that are subject to both fishing and scaled up to quarterly estimates (Cit) by multiplying by the number of days in each quarter: intense consumption. Although there is evidence that M can be high for semelparous squids (e.g., Hen- 0 1 Cit ¼ Cit 3 91:25: ð3Þ drickson and Hart 2006), we set it to be negligible as a These were then multiplied by predator abundance to simplifying assumption for the purposes of this work. Adding Z in quarter t (Z ) to equation (6), we obtain estimate a total amount of longfin inshore squid t removed by each predator species i for each quarter dB r˜ t ¼ðr˜ Z ÞB B2; ð7Þ of each year: dt t t K t 00 0 Cit ¼ Cit 3 Nit; ð4Þ where r˜ is the rate of population growth when M is zero. where N is predator abundance obtained from the it To predict the biomass and the total yield, equation bottom trawl swept area calculation for each predator (7) can be solved following Prager (1994): species i and each quarter of each year. To estimate the total removal of longfin inshore ðr˜Z Þ ðr˜ ZtÞBte t Btþ1 ¼ ; ð8Þ squid by all predators for each quarter of each year, we 1 ðr˜Zt Þ 00 ðr˜ ZtÞþrK˜ Bt½e 1 summed Cit across all i predators: X where B is the biomass at the start of the quarter t þ 1 00 tþ1 Ct ¼ C : ð5Þ it of each year and Bt is the biomass at the start of the i quarter t of each year. This provided a time series of total predation removal The total yield (fishery yield þ predation removal) of longfin inshore squid for each quarter in each year. can be obtained by integrating: Z Model Structure tþ1 YðfisheryþpredationÞt ¼ ZtBt dt; ð9Þ The approach used to incorporate predation in the t model for longfin inshore squid followed a similar the solution to which is approach developed by Overholtz et al. (2008) for () Atlantic herring. We treated the consumption data as a Z rK˜ 1 1 eðr˜Zt Þ Y t log 1 : second fishing fleet and added the consumption data to ðfisheryþpredationÞt ¼ 1 e rK˜ ðr˜ ZtÞ catch data to form a time series of total removals (predation þ fishery) that could be used as an input into ð10Þ a surplus production model. The average biomass (Bt ) can be estimated as To incorporate predation mortality into a production model, we used the logistic or Graham–Schaefer model YðfisheryþpredationÞt Bt ¼ : ð11Þ (Graham 1935; Schaefer 1954), which is the basis of Zt ASPIC software (Prager 1994, 2005). In the absence of With this last expression, and by setting fishery yield fishing and natural mortality (i.e., F ¼ 0 and M ¼ 0), the equal to the actual catches, we can estimate F and M model assumes logistic population growth in which the 2 as follows: change in stock biomass over time is a quadratic function of biomass: Ft ¼ YðfisheryÞt=Bt ; ð12Þ

dBt r 2 ¼ rBt B ; ð6Þ dt K t M2 ¼ Zt Ft: ð13Þ PREDATION IN LONGFIN INSHORE SQUID MODELS 1559

In this analysis, we tuned the model that incorpo- TABLE 2.—Description of production model runs for longfin rated predation with fishery-independent (survey inshore squid stock assessment (CV ¼ coefficient of biomass), fishery-dependent LPUE, and predation- variation). See Table 1 for descriptions of data sources. dependent indices, the latter being the predation Data sources and quarter Years CV removal expressed as the total amount of squid biomass Model: conventional assessment (fishery only) consumed by a predator, which was assumed to be NEFSC autumn 1987–2001 0.17 proportional to mean squid stock size present during NEFSC spring 1987–2001 0.49 the time when predation took place (Hollowed et al. LPUE winter 1987–1993 0.20 LPUE summer 1987–1993 0.20 2000; Table 1). The objective function to be minimized Model: predation and fishery to estimate the model parameters K, B (biomass at the 0 NEFSC autumn 1987–2001 0.17 beginning of the time series), MSY, and the catch- NEFSC spring 1987–2001 0.49 ability coefficient (q) for each series j when all indices LPUE winter 1987–1993 0.20 are considered is LPUE summer 1987–1993 0.20 I(predation) 1987–2001 0.80 XT ˆ 2 ˆ 2 logUt logUt þ a logIðsurveyÞt logIðsurveyÞt t¼1 bounds from the bootstrap results and uses a 2 þ b logI logIˆ nonparametric analog of the coefficient of variation ðpredationÞt ðpredationÞt 2 (CV), known as the relative interquartile range (RIQ). þ / logBˆ 0 logKˆ ; For each of the longfin inshore squid models, with and 14 ð Þ without predation, 500 bootstrap trials were used. where U is the observed LPUE at time t, Uˆ is the t t Model-Fitting predicted LPUE, I(survey)t is the observed survey ˆ All starting values of biomass (B /K), MSY, and K biomass index, I(survey)t is the predicted survey biomass 0 were based on the maximum removals (harvest and index, I(predation)t is the observed predation-dependent ˆ predation) of longfin inshore squid in the northwest index, I(predation)t is the predicted predation-dependent index, a and b are statistical weighting factors, and u is Atlantic Ocean (e.g., starting guess for MSY in the a penalty term added to the objective function when Bˆ absence of other information can be estimated as half is greater than Kˆ , as discussed in Prager (1994). the largest yield, and a reasonable guess for K is 2–20 To fit the production model and to compare the times the largest recorded yield; see Prager 2005). The biological reference points between the conventional model configurations and CVs of each index within the model and the model incorporating predation, we used models are listed in Table 2. The conventional stock ASPIC software (version 5.10; NOAA Fisheries 2005) assessment model was fitted with fisheries catch data written by Prager (1994, 2005). This program has been and was tuned with LPUE and abundance indices from used extensively in stock assessments of longfin NEFSC spring and autumn bottom trawl surveys. The inshore squid (Cadrin and Hatfield 1999) and was model that incorporated predation was fitted with total accepted by the Overfishing Definition Review Panel removals (fishery removal plus predation removal) and in 1998 (NEFMC 1998). tuned with LPUE, survey abundance indices, and the

The ASPIC package incorporates several extensions I(predation) calculated as the total consumption of squid not found in other stock production models. It uses by one of the main predators of squid, the spiny bootstrapping to construct bias-corrected, nonparamet- dogfish. ric confidence intervals, and it can fit data from up to 10 data series and can be conditioned on catch, which Model Outputs in this analysis means that landings and predation data Reference points.—The biological reference points were assumed to be measured without error and that estimated from standard surplus production models that observation errors are in the abundance indices (Prager only consider F are MSY, biomass at MSY (BMSY ¼ K/ 1994). 2), and F at MSY (FMSY ¼ MSY/BMSY). The reference The model was run with the Monte Carlo phase to points estimated from the model that considers both F avoid local minima. This method improves the initial and predation mortality are maximum usable produc- fit by randomly searching for a better one in the tion (MUP) as the total surplus production for both the neighborhood of the initial fit. Bootstrapping was used fishery and predation, biomass at MUP (BMUP ¼ K/2), to estimate bias in parameter estimates and derived and Z at MUP (ZMUP ¼ MUP/BMUP). The MUP is management quantities of interest (e.g., MSY; Efron analogous to MSY, albeit containing predatory remov- 1982). The ASPIC model computes 80% confidence als. The MUP is more directly comparable with MSY 1560 MOUSTAHFID ET AL.

predation, B, Z, and F were standardized by the new

reference points BMUP, ZMUP, and FMUP, respectively. Thus, we present our results for B, Z, and F in relative terms. Projections of the stock with predation included.— The ASPIC suite includes the program ASPIC Projection (ASPICP), which can be used to make projections of the stock’s response to various manage- ment scenarios. This program estimates the population biomass and mortality rate trajectories with bias- corrected confidence intervals (Prager 1994, 2005). To evaluate potential management options, we FIGURE 2.—Annual consumption (by 15 predatory fish performed 3-year (12-quarter) projections with AS- species) and fishery landings (thousands of metric tons [mt]) PICP by using the results from production model runs of longfin inshore squid in the northwest Atlantic Ocean from 1987 to 2001. to project the longfin inshore squid population forward in time. Six scenarios were forecasted for 2003–2004: the 5-year average (seasonal average for 1997–2001) of for overall stock dynamics, but MUP can be partitioned M2, increasing M2 by 20% per quarter, decreasing M2 into fishery yield and predatory demand (see below) to by 20% per quarter, F ,75% of F , and 5% of contrast between the two. Similarly, Z is analogous MSY MSY MUP FMSY. These scenarios were chosen to demonstrate the to FMSY, but the direct comparison of FMUP (parti- benefit of incorporating predation into conventional tioned out from ZMUP; see below) with FMSY allows for single-species models and should not necessarily be a direct comparison of fishery rate reference points. interpreted as actual management options. These new biological reference points derived from the To partition the total surplus production estimated predation model were compared with their analogues from ASPICP and to estimate the available SF, we used from the conventional model to explore the impact of the same average proportion approach described above. including predation on model outputs. We calculated the SP by multiplying MUP (estimated To partition MUP, we followed the partitioning from ASPICP) by the ratio of average M2 to Z, and the approach, described in Overholtz et al. (2008) as SF was estimated by subtracting the SP from the total ‘‘average proportion.’’ This approach is based on the surplus production. average M2 as a fraction of ZMUP. The surplus for predators (SP) is calculated by multiplying the MUP by Results Consumption the ratio of the average M2 to ZMUP: The total annual consumption of longfin inshore M SP ¼ MUP 3 2 : ð15Þ squid by the 15 predatory fish averaged 58,000 metric ZMUP tons and ranged between 31,000 and 139,000 metric The surplus for the fishery (SF) is estimated by tons from 1987 to 2001 (Figure 2). Consumption was subtracting the SP from the MUP: high in the early 1990s, declined in the mid-1990s, and then increased to the highest level of the time series in SF ¼ MUP SP: ð16Þ 2001. Compared with predation removals, landings were generally lower (from 1987 to 2001) by an Following the same approach used to estimate F average factor of about three. Landings declined after (equation 12), we can estimate the new fishery 1999 because of frequent seasonal closures of the mortality reference point (F )as MUP directed fishery. Consumption of longfin inshore squid by the finfish predators was generally lowest during the FMUP ¼ SF=BMUP: ð17Þ third quarter of each year. Relative biomass and relative mortality.—Prager Analysis of consumption during 1987–2001 by each (1994) warned that absolute levels of stock biomass predator showed that elasmobranchs (particularly spiny (and related quantities), which include uncertainty in dogfish) preyed heavily on longfin inshore squid, the estimate of q, are usually estimated with less accounting for 90% of the total consumption (Figure precision by production models. He suggested present- 3). Total annual consumption of longfin inshore squid ing relative mortality and relative biomass trends, by spiny dogfish during this period averaged 48,000 which are year-specific estimates of B standardized by metric tons (range, 25,000–120,000 metric tons).

BMSY and F standardized by FMSY. For the model with Consumption of longfin inshore squid by teleost PREDATION IN LONGFIN INSHORE SQUID MODELS 1561

FIGURE 3.—Seasonal consumption (metric tons [mt]) of longfin inshore squid by 15 predatory fish species in the northwest Atlantic Ocean, 1987–2001. species was dominated by silver hake and spotted hake; four times higher than F throughout the entire time the combined annual average consumption of longfin series. Predation mortality rates were relatively high in inshore squid by these two species was 2,600 metric the mid-1990s, reaching time series peaks of 0.80 in tons (580–8,600 metric tons). the first quarter of 1994 and 0.78 in the second quarter of 1996. Model Outputs In the conventional model, the biological reference

In the predation model, partitioning mortality rates points (e.g., BMSY) were generally higher than in the into F and M2 exhibited clear patterns, with M2 being predation model (Table 3). The conventional model higher than F (Figure 4). Predation mortality rates were indicated that an MSY of 10,560 metric tons/quarter variable during 1987–2001 but were typically three to could be produced by the longfin inshore squid stock

IGURE F 4.—Stacked area graph presenting seasonal predation (M2) and fishing mortality (F) rates for longfin inshore squid in the northwest Atlantic Ocean, 1987–2001. 1562 MOUSTAHFID ET AL.

TABLE 3.—Biological reference points (BRPs) for longfin inshore squid estimated from traditional production model runs with fishery data only based on maximum sustainable yield (MSY); new biological reference points estimated from the model including both predation and fishery data; and the total maximum usable (surplus) production (MUP) partitioned into surplus for the fishery (SF) and surplus for predators (SP; B ¼ biomass in metric tons, F ¼ fishing mortality, Z ¼ total mortality).

New BRPs (predation and fishery) Traditional BRPs (fishery only)

Quantity estimated Point estimate Quantity estimated Point estimate

B ratio (B/BMUP) 0.58 B ratio (B/BMSY) 1.37 F ratio (F/FMUP) 1.16 F ratio (F/FMSY) 0.77 Z ratio (Z/ZMUP) 2.41 BMUP (metric tons) 139,500 BMSY (metric tons) 33,140 MUP (metric tons/quarter) 35,530 MSY (metric tons/quarter) 10,560 SF (metric tons/quarter) 7,448 SP (metric tons/quarter) 28,082

when stock biomass is approximately at a BMSY of Under the 5-year average of Z (Figure 7), the 33,140 metric tons/quarter. The predation model partitioned yield available for the fishery in the indicated that an MUP of 35,530 metric tons/quarter projected 3 years would remain relatively stable at an could be produced when the stock biomass is at a BMUP average level of 5,400 metric tons/quarter. However, of 139,500 metric tons/quarter, over three times the the predation removal is projected to be two to five conventional model’s analogous values. Conversely, times greater than the fishery removal. the available SF was less than that estimated by the conventional model (Table 3). Discussion

The relative biomass (B/BMUP) estimates from the This analysis confirms that explicitly incorporating predation model were consistently below the reference predation into a surplus production model is feasible. level, in contrast to estimates from the conventional The simplest way is to create a time series of total model (Figure 5A). The biomass ratio point estimates removals (predation þ fishery), which can be used as an ranged from 0.78 to 1.46 (RIQ ¼ 0.22) for the input into production models. The model solves for the conventional model and from 0.13 to 0.79 (RIQ ¼ combined mortalities (predation þ fishery) to derive 0.50) for the predation model. Similarly, the relative variables of interest. A method to partition the two trends from the conventional model suggest that F was components (predation þ fishery) was then developed mostly under the reference level from 1988 to 1995; to further delineate key factors influencing stock exceptions occurred in 1989 and 1993, when F dynamics. This approach is similar to the approach exceeded the reference level (Figure 5B). From 1995 developed for Atlantic herring (Overholtz et al. 2008) to 2000, the relative F generally increased; it declined but in this case was applied to longfin inshore squid (a in latter years. Compared with the conventional model, short-lived species) by means of a surplus production the trend in relative mortality rates (Z/ZMUP) and (F/ model. Surplus production models are widely used in FMUP) was mostly above the reference level in the stock assessment when it is not possible to apply age- predation model. structured assessment methods. The present work was not intended to serve as a formal stock assessment but Projections with Predation Included rather to demonstrate that incorporating predation into Short-term projections (i.e., six scenarios forecasted an existing production modeling package is imminently for 2003–2004) suggest that the biomass could have tractable. increased in the preceding 2 years if Z did not exceed In general, consumption of longfin inshore squid the 5-year (1998–2002) average (Figure 6). However, was very low during summer and higher during the increasing M2 (e.g., by 20% each quarter) and fixing F winter. This seasonal variability in consumption can be at the 5-year average level could decrease the biomass explained by the seasonal distribution patterns of of squid to below BMUP (Figure 6a). Conversely, longfin inshore squid on the northeast U.S. continental decreasing M2 results in higher biomass projections. shelf. During late autumn, longfin inshore squid move Similarly, the F at FMSY or at 75% of FMSY will not offshore to overwinter in warmer waters along the result in a biomass increase when M2 is left at the 5- continental shelf (Cadrin and Hatfield 1999; Hatfield year average level (Figure 6b). A substantial reduction and Cadrin 2002; Jacobson 2005). As such, longfin of F to 5% of FMSY was projected to result in inshore squid are probably more vulnerable to these 15 increasing biomass to BMUP. predator species at this time of the year. During the PREDATION IN LONGFIN INSHORE SQUID MODELS 1563

FIGURE 5.—Estimated trajectories for longfin inshore squid relative reference points from a conventional assessment model that included fishery mortality (F) only and a model that included both predation mortality and F: (A) relative biomass

(conventional model: ratio of biomass [B] to biomass at maximum sustainable yield [BMSY]; predation model: ratio of B to biomass at maximum usable production [BMUP]) and (B) relative mortality rate (conventional model: ratio of F to FMSY; predation model: ratio of total mortality [Z]toZMUP and ratio of F to FMUP). The horizontal line represents the reference level of 1.0. early summer, longfin inshore squid move inshore for the relative contribution of fishing versus predation on spawning and presumably have lower spatial overlap prey removals of forage species (e.g., Buckel et al. with the main predators (e.g., spiny dogfish and silver 1999; Overholtz et al. 2000; Overholtz and Link 2007), hake). These seasonal differences in spatial overlap, thus confirming that predation represents an important and hence consumption, will certainly have implica- process in the regulation of the longfin inshore squid tions for management scenarios and ultimately strate- population. Previous stock assessment models applied gies that account for predation. to longfin inshore squid showed that the models were In this analysis, predation removals of longfin sensitive to assumed estimates of M (Cadrin and inshore squid exceeded the landings in most of the Hatfield 1999; NEFSC 2002). Our results indicate that years from 1987 to 2001. These results are similar to predation mortality changes seasonally and interann- other studies in the U.S. Northeast that have examined ually and confirm that predation is a very important 1564 MOUSTAHFID ET AL.

FIGURE 7.—Projected quarterly yield (thousands of metric tons [mt]) of longfin inshore squid in the fishery (broken line) and in predation removals (solid line) for the 5-year average of total mortality (see Figure 6).

current analysis affirms that predation should be accounted for when performing the analysis of stock status of a species such as longfin inshore squid. These results further indicate that short-term projec- tions of parameter estimates that incorporate predation FIGURE 6.—Projected relative biomass of longfin inshore are feasible and that various scenarios representing squid for a model incorporating both fishery mortality (F) and different management actions can be explored. By predation mortality (M ) under (A) three different M 2 2 examining scenarios involving changes to M or F,we scenarios: 5-year average (1997–2001) of the total mortality 2 demonstrated that increasing either type of mortality rate (Z), increasing M2 by 20% per quarter, and decreasing M2 by 20% per quarter; and (B) four F scenarios: 5-year average decreases the projected biomass of longfin inshore

(1997–2001) of Z, F at maximum sustainable yield (FMSY), squid. Longfin inshore squid are essentially an annual % % 75 of FMSY, and 5 of FMSY. The horizontal line represents species in which there is little overlap between the reference level of 1.0. successive generations. In these circumstances, squid biomass is likely to be available to predators and component in the dynamics of the longfin inshore fisheries for only a limited period, and if F and M2 are squid population. It seems wise to continue to include both simultaneously high, recruitment overfishing this key ecological consideration in stock assessments could be expected given the fact that squid both recruit for the longfin inshore squid and for similar forage to the fishery and spawn in the same year. species (Link 2002). Therefore, the next longfin There are several limitations for the interpretation of inshore squid stock assessment in this region (or our model results and some obvious known uncertain- others) might wish to consider explicitly incorporating ties. For example, we assumed that past predator predation mortality. consumption patterns of longfin inshore squid would Incorporating predation into a conventional single- remain stable regardless of changes in squid abun- species production model has clear implications for dance, equivalent to a type I or early stage type II model outputs. Our analysis shows that the new functional response. If, however, this squid’s predators biological reference points (e.g., BMUP) estimated by have a type III functional response (prey switching the model incorporating predation were higher than when prey density reaches a low level), then our those from a conventional assessment model. The projections may be altered. Investigating the functional conventional model showed that biomass increased feeding responses of major demersal fish predators in above the reference level and that relative trends in F the region should be conducted to improve the were below the reference level; however, when accuracy of these types of models. Additionally, the predation was incorporated into the model, biomass consumption estimates given by this study are very remained under the reference level and F was above the conservative because squid are cannibalistic (Whitaker reference level. These results are consistent with other 1978) and are the main prey for large pelagic fish, sea studies that have incorporated predation into single- birds, and marine mammals; predation by these latter species models (e.g., Livingston and Methot 1998; groups is not included in this analysis. Long-finned Hollowed et al. 2000; Overholtz et al. 2008). The pilot whales Globicephala melas in particular feed PREDATION IN LONGFIN INSHORE SQUID MODELS 1565 predominantly on squid and have a higher incidence of and effort of all involved. This work was supported by overlap with longfin inshore squid than with other prey the Lenfest Ocean Program (Grant Number 2004- species (Overholtz and Waring 1991; Gannon et al. 001492-105). Reference to trade names does not imply 1997; Overholtz and Link 2007). Further analyses endorsement by the U.S. Government. should also incorporate removal from cannibalism and consumption by odontocete whales and sea birds to References better quantify the impact of predation on longfin Azarovitz, T. R. 1981. A brief historical review of the Woods inshore squid. Incorporating q for predator abundance Hole Laboratory trawl survey time series. Canadian estimates, and hence consumption estimates, will Special Publication of Fisheries and Aquatic Sciences probably also increase estimates of predation because 58:62–67. Bravo de Laguna, J. 1989. Managing an international these are based upon minimum swept area methods of multispecies fishery: the Saharan trawl fishery for predator abundance. In addition to predator abundance, cephalopods. Pages 591–612 in J. F. Caddy, editor. the degree of spatial–temporal overlap between squid Marine invertebrate fisheries: their assessment and and their predators will influence the amount squid management. Wiley, New York. removal. Although the predation removal estimates are Brodziak, J. K. T., and W. K. Macy. 1996. Growth of long- high compared with fisheries catch, these current finned squid, Loligo pealei, in the northwest Atlantic. estimates of longfin inshore squid predation should U.S. National Marine Fisheries Service Fishery Bulletin 94:212–236. be considered conservative. There are also other known Buckel, J. A., M. J. Fogarty, and D. O. Conover. 1999. areas where the model could be improved, or at least Foraging habits of bluefish, Pomatomus saltatrix, on the the assumptions verified, given the availability of U.S. East Coast continental shelf. U.S. National Marine forthcoming and novel data on seasonality of squid Fisheries Service Fishery Bulletin 97:758–775. predators and on other factors that influence residual Cadrin, S. X., and E. M. C. Hatfield. 1999. Stock assessment of longfin inshore squid, Loligo pealeii. Northeast mortality (i.e., M1). Further work should also examine the impacts of various methods to partition the new Fisheries Science Center Reference Document 99-12, Woods Hole, Massachusetts. reference points into the constituent components: Efron, B. 1982. The jackknife, the bootstrap, and other fishery and predation. resampling plans. Society for Industrial and Applied The expanded production model accounting for the Mathematics, Philadelphia. ecological interactions presented here was suitably Eggers, D. M. 1977. Factors in interpreting data obtained by applied to a longfin inshore squid stock. Despite the diel sampling of fish stomachs. Journal of the Fisheries caveats noted above, we suspect that our results are Research Board of Canada 34:290–294. robust when compared with similar investigations (e.g., Elliott, J. M., and L. Persson. 1978. The estimation of daily rates of food consumption for fish. Journal of Animal Livingston and Methot 1998; Hollowed et al. 2000; Ecology 47:977–991. Overholtz et al. 2008). This model has changed our Gannon, D. R., A. J. Read, J. E. Craddock, K. M. Fristrup, and perception of the relative status of longfin inshore J. R. Nicolas. 1997. Feeding ecology of long-finned pilot squid; reference points are vastly different when whales Globicephala melas in the western North predation is incorporated. Failing to account for Atlantic. Marine Ecology Progress Series 148:1–10. predation when performing stock assessments for Gerking, S. D. 1994. Feeding ecology of fish. Academic longfin inshore squid and other similar forage species Press, San Diego, California. Graham, M. 1935. Modern theory of exploiting a fishery, and may misrepresent reference point estimates and result application to North Sea trawling. Journal du Conseil in management advice that could lead to biomass International pour L’Exploration de la Mer 37:199–204. decline. Given the importance of this prey species in Hatfield, E. M. C., and S. X. Cadrin. 2002. Geographic and the northeast U.S. continental shelf ecosystem, im- temporal patterns in size and maturity of the longfin proved understanding of the total and relative sources inshore squid (Loligo pealeii) off the northeastern United of mortality for this stock seems warranted. States. U.S. National Marine Fisheries Service Fishery Bulletin 100:200–213. Acknowledgments Hendrickson, L. C., and D. R. Hart. 2006. An age-based cohort model for estimating the spawning mortality of We thank past and present members of the Food semelparous cephalopods with an application to per- Web Dynamics Program for collecting and maintaining recruit calculations for the northern shortfin squid, Illex the database that enabled us to execute this work. We illecebrosus. Fisheries Research 78:4–13. also thank W. Overholtz for prior comments and Hollowed, A. B., J. N. Ianelli, and P. A. Livingston. 2000. Including predation mortality in stock assessments: a suggestions in the development of these models. 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