1 Introduction

Fishers face a multidimensional decision problem that requires choosing where to fish, when to fish, what to target, and how much gear to deploy. Predictive analysis of the fishery generally aims to understand how fishing behavior responds to incentives across these multiple margins (Smith 2012) for the purpose of evaluating policy options or anticipating outcomes from changing conditions. Despite sharp theoretical predictions for open access (Smith 1969) and regulated open access (Homans and Wilen 1997) as well as a growing body of empirical work, our understanding of fishing behavior in realistic settings is largely incomplete. Most studies analyze single-species fisheries, open access, or long-term (inter-seasonal) dynamics. Yet, most real-world fisheries are multispecies, have some form of restricted access, and have interesting short-term (intra-seasonal) dynamics. In this paper, we address this gap in the literature by developing a numerical model to predict qualitative patterns of within-season harvest timing in multispecies fisheries managed with individual fishing quotas (IFQs). We empirically test these predictions using the Norwegian cod, haddock, and saithe trawl fishery.

Timing of catch within the fishing year can have important implications for revenues generated by the fishery, product forms, and response of the fishery to policy changes (Grafton et al. 2000; Homans and Wilen 2005; Smith et al. 2008; Huang and Smith 2014). Some theoretical and empirical bioeconomic models have demonstrated the importance of within-season incentives—including biological conditions, stock effects, discounting, seafood markets, and congestion externalities—in determining these catch patterns (Clark 1980; Boyce 1992; Fell 2009; Valcu and Weninger 2013). Empirical bioeconomic studies have further shown that timing within-season harvest to account for these phenomena could generate substantial rent gains (Larkin and Sylvia 1999; Huang and Smith 2014). However, little is known about the generality of these results in multispecies settings. Our numerical model reveals that tradeoffs across cost and revenue margins can generate complex and non-intuitive behavioral patterns in multispecies settings.

Empirical production models and discrete choice models of fishing behavior provide relevant insights, but neither literature traces out a complete positive theory for intra-seasonal behavior in multispecies fisheries.Footnote 1 Production models treat multispecies outcomes as manifestations of multi-output production technology (Asche et al. 2007; Weninger and Waters 2003; Squires and Kirkley 1991; Squires 1987). However, they abstract away from the temporal distribution of fish within the season and do not address the sequential nature of targeting decisions with associated forward-looking dynamic incentives.Footnote 2 Discrete choice models typically use data on finer time scales such as daily or weekly to analyze incentives driving participation, gear, and location choices (Abbott and Wilen 2011; Eggert and Tveteras 2004; Holland and Sutinen 2000; Smith and Wilen 2005). Yet, with few exceptions, these models focus on single-species fisheries and abstract away from forward-looking dynamics. That is, fishers are assumed to make a sequence of myopic decisions about targeting just one species.Footnote 3 Hence, models that explicitly account for forward-looking dynamics do not consider multispecies targeting (Hicks and Schnier 2008; Huang and Smith 2014), whereas models of species targeting still invoke sequentially myopic decision-making (Stafford 2018; Zhang and Smith 2011).Footnote 4

Recent empirical work on the effects of rights-based fisheries management further highlights these shortcomings and reinforces the need for a richer understanding than currently exists. Using a matched control fishery for each U.S. fishery treated with IFQs (or “catch shares”), Birkenbach et al. (2017) show that on average seasons lengthen for treated fisheries. This finding is broadly consistent with the hypothesis that rights-based management creates incentives to exploit revenue margins (higher prices from spreading catch over the season and avoiding market gluts) in addition to the cost savings expected under these policies (Homans and Wilen 2005). However, individual fisheries within multispecies complexes provide a number of counter-examples in which seasons contract, indicating that behavior is more complicated than existing single-species theory suggests (Birkenbach et al. 2017). Distilling how fishers respond to complex economic, biological, and regulatory considerations is crucial for explaining results such as these and improving managers’ ability to predict behavior under changing policy conditions.

Our central claim is that timing the harvest of fish can involve tradeoffs between cost- and revenue-side considerations, and these tradeoffs can generate non-intuitive patterns of behavior in multispecies settings. Costs may be minimized by concentrating harvest to follow seasonal biological aggregations [e.g., the Lofoten cod fishery (Hannesson et al. 2010; Kvamsdal 2016)] or at the beginning of the season due to stock effects. Revenues, by contrast, may be increased by spreading harvest throughout the season to take advantage of a downward-sloping demand schedule. Discounting creates incentives to generate revenues earlier in the season, counteracting the spreading effect. However, timing decisions are even further complicated by the possibility of participating in other fisheries; a vessel can be in only one place at any point in time. Fishers must therefore consider cost- and revenue-side tradeoffs not only within but also across species.

We develop a numerical bioeconomic model based on the Norwegian cod, haddock, and saithe trawl fisheries to investigate the time-profile of vessel landings throughout the year in a multispecies context. We model fisheries with annual IFQs such that fishers can choose when to harvest during the season but without the threat of a season closure typically associated with industry-wide quotas under regulated open access. We use peer-reviewed and gray literature on the relevant fisheries to parameterize the model.Footnote 5 Through numerical simulations, we generate three testable predictions about intra-seasonal patterns of behavior, and we test these predictions using fishing micro-data on Norwegian trawlers targeting cod, haddock, and saithe. Finally, we extend the numerical model to explore the transition to IFQs and offer an explanation to Birkenbach et al. (2017) for their mixed findings on season length for lower-value species. Our results highlight the importance of understanding the market context in bioeconomic models, the biological context in studies of seafood markets and fishing behavior, and the complex interplay among species targets and fisheries regulations.

2 Numerical Model

We model an owner of IFQs for multiple target species where the regulator sets the total allowable catch (TAC) in each year for each species. Implicitly, we assume that other IFQ holders face the same harvest-sequencing optimization problem and choose the same behavior.

The mechanisms in our model are consistent with our qualitative understanding of the Norwegian trawl fishery. A number of fisheries around the world are conducted similarly, with different species being targeted by the same fleet over the course of a single fishing year. Because there is a global market for whitefish (Gordon and Hannesson 1996; Asche et al. 2002), demand is effectively flat for haddock and saithe. However, cod is sufficiently segmented from the general whitefish market such that Norwegian trawlers face a downward-sloping demand schedule (Asche et al. 2002; Arnason et al. 2004). In our model, we account for harvest smoothing, harvest spikes, within-season harvest trends, concentration on a single-species, and mixed-species harvesting by introducing market conditions, biological aggregations, stock effects, and capacity constraints. Using parameter estimates derived from real Norwegian trawl data, we consider a range of scenarios and the different harvest patterns they generate.Footnote 6

In a given year, a representative IFQ owner seeks to maximize total profits across species (i) and time periods (t). The objective function can therefore be written as:

$$NPV\pi^{Total} = \mathop \sum \limits_{i} \mathop \sum \limits_{t} \rho^{t} \pi_{it}$$
(1)

We can think of t as indexing months within the year such that \(\rho^{t}\) is a monthly discount factor. Discounting changes results in predictable ways that are not qualitatively important for our analysis, but we include it in the analysis for completeness. The IFQ owner chooses species-specific effort (E) to harvest (H) each species i in each period t based on price (P), cost (c), and harvest technology. Fishing effort is thus the control variable in the model. The instantaneous profits can be written as:

$$\pi_{it} = P_{it} H_{it} - cE_{it}$$
(2)

We allow for the possibility of a downward-sloping demand curve for each species with choke price (ai) and slope (bi):

$$P_{it} = a_{i} - b_{i} nH_{it}$$
(3)

where n is the total number of vessels in the fleet that are assumed to behave symmetrically and effectively scales individual harvest to the market level.Footnote 7 By setting bi= 0, we nest the case of the perfectly elastic demand that may plausibly describe some seafood products for which there is a global market with ample substitutes. Different levels of ai can distinguish premium products within the same market. Cod and haddock, for instance, typically fetch higher prices than saithe, though all are competing in the whitefish market.Footnote 8

We model species- and time-specific harvests using Cobb–Douglas technology with two inputs, effort (E) and stock (X):

$$H_{it} = q_{it} E_{it}^{{\alpha_{i} }} X_{it}^{{\beta_{i} }}$$
(4)

We allow for the possibility of a catchability parameter (q) that is time- and species-dependent, which means we can capture changes in catchability due to biological aggregations for spawning or other seasonal changes in fish distributions. We assume that the effort and stock elasticities (\(\alpha_{i}\) and \(\beta_{i}\), respectively) are species-specific but independent of time. For the main results, we assume perfect selectivity. When we generalize the model to allow for non-selective harvest, the results are qualitatively similar. When \(\alpha_{i} = \beta_{i} = 1\) and \(q_{it} = q_{i}\), the production technology for species i reduces to the familiar Schaefer production model in fisheries. When \(\beta_{i} = 0\), production is independent of the stock (no stock effects). As a consequence, per-unit harvest costs are independent of the stock level. When \(\alpha_{i} < 1\) or \(\beta_{i} < 1\), there are diminishing returns to the inputs.Footnote 9

IFQ owners can at most take their share of the TAC for each species so that harvest summed across t does not exceed the quota share for that species:

$$\mathop \sum \limits_{t = 1}^{12} H_{it} \le H_{i}^{quota}$$
(5)

Because we are focused on within-season behavior, we do not model stock recruitment, growth, or natural mortality. These features are more important for the cross-season performance of the fishery (with the exception of annual fisheries, like shrimp). Implicitly, our model is equivalent to assuming that all growth, mortality, and recruitment occur between fishing seasons as in Reed (1979). Thus, the stock (state variable) at t is initial stock less cumulative harvest:

$$X_{it} = X_{i0} - n\mathop \sum \limits_{s = 1}^{t} H_{is}$$
(6)

We add non-negativity constraints on effort:

$$E_{it} \ge 0$$
(7)

We assume that the regulator never sets the TAC above Xi0, so we do not need non-negativity constraints on the stocks. We assume that harvests are also greater than or equal to zero, which closes the model.

In some simulations, we explore effort capacity constraints. In each period, effort summed across species targets is restricted:

$$\mathop \sum \limits_{i}^{{}} E_{it} \le E^{max}$$
(8)

This capacity constraint could imply a time constraint, maximum hull capacity, amount of fishing gear on a vessel, or some combination of these. It is a reflection of a fixed, allocatable input from the individual vessel’s perspective in a similar fashion as agricultural land (Shumway et al. 1984).Footnote 10

With non-selective harvesting, the Schaefer harvest functions are modified as follows:

$$H_{1t} = q_{1} E_{1t} X_{1t} + \bar{q}_{1} E_{2t} X_{1t}$$
(9)

and

$$H_{2t} = q_{2} E_{2t} X_{2t} + \bar{q}_{2} E_{1t} X_{2t}$$
(10)

where \(\bar{q}_{1}\) and \(\bar{q}_{2}\) signify the catchability of species 1 as bycatch when fishing for species 2 and the catchability of species 2 as bycatch when fishing for species 1, respectively (Skonhoft et al. 2012). Thus, the total harvest of a given species equals the amount of that species caught through deliberate targeting, as in the original harvest function, plus the amount of that species caught as bycatch when targeting another species. These bycatch volumes are the product of the bycatch catchability coefficients, the effort expended (on catching the non-bycatch species), and the stock level of the bycatch species. In our simulations with non-selectivity (Appendix C), we consider cases in which 80% of the total catch is the target species (and the remaining 20 percent is bycatch) (80–20) and 60% of the catch is the target species (60–40).

We implement the model using Matlab’s nonlinear solver (FMINCON). Base parameter values are presented in Table 1.

Table 1 Base parameter values used in numerical simulations
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3 Model Results

The numerical model developed in Sect. 2 is used to explain temporal harvest patterns visible in the Norwegian trawl fishery data (Sect. 4). Our main conceptual results are as follows. First, downward-sloping demand creates incentives to spread out harvest that can counteract incentives to concentrate harvest early in the season due to discounting and stock effects. Second, in a multispecies setting, extending the season for a high-value species can shorten the season for a low-value species when per-period effort is constrained. As a consequence, it is possible that low-value species are caught earlier in the fishing season than the high-value species. Third, although biological aggregation increases incentives to concentrate harvest (by lowering costs), in a multispecies setting harvest levels for some species may see little change or even decrease during the period of aggregation. For a high-value species, the revenue-side gains of spreading harvest can dominate cost-side savings from aggregation, whereas the concentration of a low-value species harvest might induce less harvest of another species in that period due to a constraint on available capacity. Our results are robust to including non-selective harvesting as well as heterogeneity in catching power across vessels.

To provide intuition for our main results, we first present scenarios that vary one assumption at a time using a single species. These results establish a baseline understanding for building more complex modeling assumptions. We then analyze optimal behavior when there are two target species while varying multiple assumptions, defined as combinations of parameter values. Outcomes with three target species and varying multiple assumptions are qualitatively similar to the two-species case and are presented in Appendix B.

3.1 Results with a Single Species (Fig. 1)

We optimize the single-species model for four different scenarios: Scenario 1—stock effects and endogenous price (inelastic demand, \(b_{i} > 0\)); Scenario 2—stock effects and exogenous price (perfectly elastic demand, \(b_{i} = 0\)); Scenario 3—biological aggregation and endogenous price; and Scenario 4—biological aggregation and exogenous price. Without loss of generality, we assume aggregation occurs in month 7. In Scenario 1, the optimal strategy is to smooth harvest over the entire year to maintain higher prices. The smoothed harvest path trends downward to reflect discounting and the stock effect, and effort trends upward such that higher harvest costs are delayed. But the smoothing effect driven by product demand dominates the downward trends.Footnote 11 By contrast, the optimal strategy is to exhaust all of the quota in the first period when price is exogenous (Scenario 2). There are no incentives to spread out harvest, and both discounting and the stock effect push harvest into the first period.Footnote 12 This result is important in showing that IFQs alone are not sufficient for spreading out harvest; rather, IFQs must be coupled with market opportunities or production technologies that make this behavior profitable.Footnote 13

Fig. 1
figure 1

Seasonal harvest (top) and effort (bottom) pattern in a single-species fishery. Scenarios include stock effects and endogenous price (1), stock effects and exogenous price (2), biological aggregation and endogenous price (3), and biological aggregation (month 7) and exogenous price (4)

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The results in Scenarios 3 and 4 with biological aggregation parallel those of 1 and 2: endogenous price creates incentives to spread out harvest, and exogenous price concentrates harvest at the beginning of the season. Biological aggregation affects these tendencies by introducing cost savings from harvesting during certain months of the year.Footnote 14 If the cost reduction due to the biological aggregation is sufficiently strong, there is a moderate increase in the harvest during this period even with inelastic demand. This effect is also stronger if demand becomes more elastic, but otherwise the qualitative results in this model are not sensitive to parameter values. With exogenous price, effort spikes in the aggregation period (Scenario 4), and all of the quota is taken in this period.Footnote 15 Overall, the results in Fig. 1 are not surprising, but they provide the intuitive foundation for explaining the more complex multispecies environment below.

3.2 Results with Two Species (Figs. 2 and 3)

For all the multispecies fisheries scenarios, we assume that per-period capacity is constrained in the short run (within-season) due to composition of vessels in the existing fleet. As such, it is the capacity constraint (vessels as fixed inputs) that introduces a tradeoff with respect to how to allocate effort. For two-species models, we assume that the price for species 1 is endogenous (\(b_{1} > 0\)), whereas the price for species 2 is exogenous (\(b_{2} = 0\)). Thus, the single-species intuition implies harvest smoothing for species 1 but not necessarily for species 2, ceteris paribus. In addition, we assume that species 2 is less valuable than species 1, and we operationalize this assumption by making \(a_{1} > a_{2}\).

Fig. 2
figure 2

Two-species harvest (top) and effort (bottom) paths without biological aggregation. Scenarios 1 through 4 reflect the tightest through loosest per-period effort/capacity constraints. Species 1 faces downward-sloping demand, whereas species 2 has perfectly elastic demand. The scenarios for both sets of results include capacity constraints: (1) Tightest (Emax= 1); (2) Moderately tight (Emax= 1.5); (3) Moderate (Emax= 3); and (4) Loose (Emax= 4)

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Fig. 3
figure 3

Two-species harvest (top) and effort (bottom) paths with biological aggregation in months 6 and 7 for both species. The scenarios include capacity constraints: (1) Tightest effort constraint (Emax = 1); (2) Moderately tight effort constraint (Emax = 1.5); (3) Moderate effort constraint (Emax = 3); and (4) Loose effort constraint (Emax = 4)

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We run the model without (Fig. 2) and with (Fig. 3) biological aggregation, where we assume biological aggregation occurs for both species in months 6 and 7. In both cases we vary the capacity constraint from a very tight one to a very loose one.Footnote 16 We investigate four scenarios—ranging from Scenario 1 with the tightest effort constraint to Scenario 4, in which the effort constraint is loosest—as follows:

  1. 1.

    Tightest effort constraint (Emax = 1)

  2. 2.

    Moderately tight effort constraint (Emax = 1.5)

  3. 3.

    Moderate effort constraint (Emax = 3)

  4. 4.

    Loose effort constraint (Emax = 4)

When effort is tightest, it is optimal to allocate all effort to the more valuable species because the endogenously determined price of species 1 is still above the exogenous price of species 2 even when all effort is allocated to species 1. Species 1 harvest trends downward as a result of the stock effect. Effort and harvest are zero for species 2 throughout the year. The short-run effort constraint is sufficiently tight that not all of the season’s quota is taken for species 1, and none of the quota is taken for species 2.

For moderately tight effort, it is optimal to allocate most effort to the higher-value species during the early periods. This plan ensures that the fishery takes all quota of species 1. Then the residual effort is allocated to species 2. Due to stock effects, discounting, and market incentives to smooth species 1 harvest, harvest trends downward slightly for species 1. Eventually, the opportunity cost of harvesting species 2 (in part due to the stock effect on species 1) grows large enough that it is optimal to stop harvesting species 2 and allocate all effort to species 1 in order to harvest all of the season’s quota. As a result, some of the species 2 quota is left unharvested, and empirically we would expect to see periods with landings of both species and other periods with landings of just the high-value species.

For moderate effort, harvest for the endogenously priced species 1 again trends downward, harvest for the exogenously priced species 2 trends downward, all quota of species 1 is taken, and some of species 2 quota is left unfished. Fishing for species 2 does not stop altogether at any point but continues throughout the year. Species 1 effort actually trends upward due to the stock effect; smoothing harvest requires more effort as the season progresses.

When the effort constraint is loose, species 1 harvest still trends downward for the same reasons as above, and all quota is taken. Species 2 harvest similarly trends downward, all quota is taken, and fishing stops when the quota is gone. Because of discounting and the stock effect, it is more valuable to catch species 2 early in the season, and there is no countervailing market incentive to smooth harvest. The qualitative pattern is similar to that of Scenario 2 in which harvest of species 2 ceases in the middle of the year, but the reason differs. In Scenario 2, there is not enough effort to continue harvesting species 2 and still catch all of the high-value species 1 quota. Under a loose effort constraint, there is sufficient slack effort to catch all of the species 2 quota early on and still smooth species 1 harvest optimally (and catch all of the species 1 quota). Hence, the same qualitative pattern—the lower value species harvest is completed first—can emerge for two very different reasons, and distinguishing them empirically is tied to whether seasonal quotas bind for both species. The main results from Fig. 2 all generalize to the case of non-selective harvesting.Footnote 17

Simultaneous biological aggregation of two species and the same four effort scenarios introduces a new set of tradeoffs (Fig. 3). These aggregations produce an incentive to concentrate effort to reduce costs just as in the single-species case, and for the inelastic-demand species there is a tradeoff with the incentive to spread harvest for revenue-side benefits. However, the existence of two target species in the decision forces an interaction between cost savings for the elastic-demand species and revenue creation for the inelastic-demand species.Footnote 18

When per-period effort is tightly constrained, it is optimal to allocate all effort to the more valuable species 1 in non-aggregating periods, but during biological aggregation a small amount of effort is allocated to species 2. Species 1 harvest increases during biological aggregation despite reduced effort and the incentive to smooth harvest from endogenous prices. Even with this relatively tight capacity constraint, all quota of species 1 is taken, but only a part of the quota is taken for species 2.Footnote 19

With moderately tight effort, it is optimal to allocate most but not all effort to the higher-value species 1 in non-aggregation periods. This allocation leads the vessel to take all of its quota for species 1. The residual effort available is allocated to species 2. Species 1 effort and harvest dip during the period of biological aggregation, while species 2 effort increases during biological aggregation period. This pattern reflects market conditions in which the vessel wants to dampen its increase in species 1 harvest during the aggregation period to avoid downward pressure on prices. For species 2, that frees up more effort, and there is no price response as a countervailing force to spread effort over time.

For moderate effort, results are similar as with the moderately tight capacity constraint: downward (upward) trend for species 2 (1) effort, and a spike (dip) in effort for species 2 (1). The only qualitative difference is that there is enough effort to take all quota for both species 1 and species 2. This result parallels the result from the two-species case without biological aggregation.

When effort is loosely constrained, results are similar to Scenario 3 for species 1: a slight downward trend in harvest except for a decrease in harvest (and dip in effort) during the aggregation period. Results are very different from previous scenarios for species 2. Very little of species 2 is taken during most of the year. Both effort and harvest spike dramatically during the aggregation periods. These spikes cause species 1 effort to dip more and harvest to increase less compared to scenarios with tighter effort constraints. In essence, there is sufficient effort to concentrate harvest of species 2 almost exclusively during the aggregation periods.

In summary, the response of harvest for the valuable species during periods when it is aggregating is non-monotonic in the tightness of the capacity constraint. It depends on how the constraint induces behaviors in other parts of the year as well. In fisheries with coastal fleets that coexist with large-scale trawlers, we might expect to see more seasonality in low-value species harvest for the coastal fleet with moderate effort constraints. Coastal vessels would concentrate effort during periods of biological aggregation but cease to fish afterward to target the more valuable species. But if capacity constraints are sufficiently slack for large-scale trawlers, we might expect more seasonality from these larger vessels.

The results provide important insights for fisheries management. With limited capacity, the less valuable species will not be targeted at all. However, with greater capacity available—whether due to overcapitalization left over from an open-access era, poor management that encourages entry/capital stuffing, or technical change that increases productivity—it is profitable to target species 2. A reduction of the quota for species 1 will produce the same result. Hence, the model reveals conditions under which less valuable species are targeted: increased fishing capacity and improved management for key species. The latter is consistent with recent empirical evidence of spillovers in regional fisheries management (Cunningham et al. 2016).Footnote 20

4 Empirical Testing: Norwegian Multispecies Groundfish Trawlers

We analyze seasonal landings patterns in the Norwegian groundfish complex with data from the Norwegian trawl fishery. Groundfish species comprise the most valuable fisheries in Norway (Cojocaru et al. 2019). Although the fleet targeting groundfish harvests a large number of species, cod, haddock, and saithe are the most important in volume and total revenue; thus, we focus our analysis on these three species. All three are part of the global whitefish market that also includes species from other regions such as Alaskan pollock (Gordon and Hannesson 1996; Asche et al. 2002). Other groundfish species are primarily demersal, but shrimp, crab, and limited quantities of pelagic species are also caught by the groundfish fleet. Although fishers can target specific species by choosing where and when to fish, catches usually include some bycatch (Asche 2009). As argued above, the cod market supports modeling downward-sloping demand due to fresh market opportunities, whereas haddock and saithe prices are driven exogenously by the global whitefish market (Asche et al. 2002; Arnason et al. 2004).

Groundfish are managed on a species-by-species basis (Årland and Bjørndal 2002). A total allowable catch (TAC) is set for the most important species based on advice from the International Council for the Exploration of the Sea (ICES), often in collaboration with other countries. The Norwegian share of the quota for the species with a TAC is then divided among different vessel groups and gear types using a rule known as the “trawl ladder” (Guttormsen and Roll 2011).Footnote 21 Regulations vary within the vessel groups and gear types for the regulated species, while the unregulated species remain open access.

While several vessel groups target groundfish, the cod trawler group is the largest in terms of average landings and vessel dimensions, and it is also the most efficient (Guttormsen and Roll 2011).Footnote 22 These factory trawlers range in length from 27 to 76 m and receive between 25 and 30% of the Norwegian TAC for cod, haddock, and saithe, depending on the size of the TAC, with a smaller share in years with smaller TACs. They can operate in rough weather, have the onboard capacity to produce and freeze fillets, and typically fish approximately 300 days each year.Footnote 23 For the three main species, the IFQ system permits a limited degree of transferability (Asche et al. 2009). Other species like Greenland halibut and shrimp require a species-specific license and gear, whereas most of the lower-volume species are unregulated.

Using logbook data provided by the Norwegian Directorate of Fisheries for the years 2004–2006, we characterize the harvest patterns for the trawlers by aggregating the landings into monthly data. We first aggregate across vessels, take monthly averages over these 3 years, and compute the coefficient of variation (CV) over the resulting 12 monthly data points.Footnote 24 By quantity, saithe was the most important species, with over 41.5% of the landings, followed by cod, which accounts for 29%. However, because of substantially higher prices, cod is always the most valuable species. Average prices are 13.68 NOK/kg for cod, 9.21 NOK/kg for haddock, and 5.62 NOK/kg for saithe, so cod revenues are 67% higher than saithe revenues. The three IFQ species together make up 83% of the harvest landed by this fleet. Shrimp is the fourth most important species with an 8% share, and redfish makes up almost 5% of the landings. The remaining species contribute modest quantities and are mostly bycatch. The CVs for cod and haddock suggest that the fleet overall spreads out landings of cod and haddock quite evenly. By contrast, the saithe CV is much higher, suggesting landings that are highly concentrated in time.Footnote 25 Overall, for cod—the high-value IFQ species with potential for market segmentation—harvest follows a relatively uniform pattern across the season, though not perfectly. Haddock—the intermediate-valued IFQ species—follows a harvest pattern similar to cod but peaking at different times and slightly less uniform overall. Saithe—the low-value IFQ species with little potential for market segmentation—follows a strong seasonal harvest pattern.

We now exploit the panel structure of our data to test our theoretical predictions formally. Although our conceptual model generates many hypotheses about within-season behavior, we focus on three that are essential features of multispecies fisheries and that can be tested in our empirical setting.

Proposition 1

Landings of the highest-value species will be the most evenly spread out over the season. This proposition follows directly from the numerical results in Figs. 1 and 2. The rationale for spreading harvest is that the cod market is segmented and price will respond to landing volumes (Asche et al. 2002; Arnason et al.2004), whereas this segmentation does not appear to exist for haddock and saithe.Footnote 26

We follow Birkenbach et al. (2017) and model the concentration of the landings with a Gini coefficient. Indexing species by s, vessel by i, year by t, and denoting the Gini coefficient as G, the empirical specification is:

$$G_{s,i,t} = \delta_{i,t} + \beta_{0} + \beta_{1} HADDOCK + \beta_{2} SAITHE$$
(11)

where the δs are vessel-year fixed effects and the constant, \(\beta_{0} ,\) is the excluded category, cod. If the landings of cod are spread out relative to haddock (and/or saithe), then β1> 0 (and/or β2> 0).

Across specifications using different sets of fixed effects, we find strong evidence in support of this proposition (Table 2). Because cod is the base category, the positive and significant coefficients on haddock and saithe in all three models indicate that these seasons are less spread out. The results are most precisely estimated in the most general model (Model 3) that includes vessel and year interactions, i.e., separate vessel fixed effects for each year. Also, haddock and saithe are not statistically different from each other in any of the models, suggesting that the spreading-out effect is specific to cod.

Table 2 Spread of landings for each species at the vessel level
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Proposition 2

In a multispecies IFQ fishery, species can be landed in reverse order of value. Basic dynamic intuition implies that with fixed prices (and no mediating effects of aggregation), any positive discount rate would lead to sequencing harvests in order of value: fishers would take the high-value species first, followed by the medium-value, and then the low-value. However, when the market creates incentives to spread the catch of the high-value (endogenously-determined price) species, it is possible that the order would reverse. This proposition follows directly from the numerical results in Figs. 1 and 2.

We examine this proposition using two metrics: months to reach 80% of the vessel’s annual landings for the species (M80) and months to reach 90% of the vessel’s annual landings for the species (M90). We use the same empirical model with both metrics:

$$M_{s,i,t}^{80} = \delta_{i,t} + \beta_{0} + \beta_{1} HADDOCK + \beta_{2} SAITHE$$
(12)

If haddock (and/or saithe) is landed faster than cod, then β1< 0 (and/or β2< 0). We run these models both in linear form and using a proportional Cox duration model. The results strongly support the hypothesis: saithe is landed first, followed by haddock, and then cod (Table 3). Although the model is similar to the Gini model above testing for spread of the catch, the results are different in that there is a statistically significant difference between saithe and haddock.Footnote 27 Specifically, the negative and significant coefficients for saithe and haddock in the OLS models indicate that 80% and 90% of annual total landings for these species occur before the 80% and 90% thresholds of cod landings are reached. This means that the lower-value species are landed before the higher-valued species. Moreover, the larger-magnitude coefficients on saithe are statistically different from those on haddock, implying that saithe is landed before haddock. Taken together, these results imply that the species are landed in reverse order of value. The Proportional Cox models reach the same conclusions. Because Cox models are hazard models, the coefficient interpretations are relative to one such that coefficients greater than one imply landing the species earlier in the season.

Table 3 Time for each vessel to reach X% of the landings of a species in each year
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Proposition 3

Biological aggregation increases landings for the low-value species, has little effect on high-value species landings, and decreases landings of the intermediate-value species. This proposition follows directly from numerical results in Fig. 3. Biological cycles such as spawning can trigger stock aggregation, as in the Lofoten cod fishery (Hannesson et al. 2010; Kvamsdal 2016). In the single-species setting, aggregation reduces costs and increases incentives to concentrate landings in this period. However, with multiple species aggregating at the same time—as is the case with cod, haddock, and saithe (Bergstad et al. 1987)—concentrating more effort on one species during aggregation means concentrating less effort on others (Figs. 3 and 4). Because there is a strong incentive to spread out cod harvest, cod harvest will be relatively unaffected; however, increasing saithe harvest during the aggregation period will translate into a reduction in haddock harvest, especially if haddock has more price responsiveness than saithe. Denoting landings as Y and indexing month as m, our empirical Ordinary Least Squares (OLS) regression specification is:

$$Y_{s,i,m,t} = \delta_{i,t} + \gamma_{s,t} + \beta_{0} + \beta_{1} SPAWN + \beta_{2} HADDOCK*SPAWN + \beta_{3} SAITHE*SPAWN$$
(13)

where \(\gamma_{s,t}\) captures species-year fixed effects and SPAWN is an indicator set to one for each month of the spawning season (February through April for all species). If β2 > 0, then landings of haddock increase in response to the spawning season, and similarly for β3 and saithe. The results (Table 4) strongly support Proposition 3: landings of saithe (low-value species) increase significantly in the spawning period (\(\beta_{3} = 65,246.28\)), whereas landings of haddock (medium-value species) decrease significantly (\(\beta_{2} = - 35,974.13\)). When we run the model on the three species individually with vessel-year fixed effects, we see a non-significant coefficient on SPAWN for cod, a negative and significant coefficient for haddock, and a strongly positive coefficient for saithe (Table 4).

Fig. 4
figure 4

Three-species harvest (top) and effort (bottom) paths with biological aggregation for species 1 (months 5 and 6), species 2 (months 6 and 7), and species 3 (months 7 and 8). The capacity constraint scenarios are: (1) Tightest (Emax = 1); (2) Moderately tight (Emax= 1.5); (3) Moderate (Emax= 3); (4) Somewhat loose (Emax= 3.5); and (5) Loosest—no effort constraint. The figure depicts just scenarios 2 and 3

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Table 4 Landings response to biological aggregation
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Overall, our empirical results directly support the key findings of our numerical model. Moreover, these results would be difficult (or impossible) to explain using a single-species dynamic bioeconomic model, market analysis, or production economics alone. Only by modeling multispecies production tradeoffs in a dynamic setting that accounts for market responsiveness do we intuitively account for patterns that would otherwise be surprising.

5 Extending the Multispecies Theory: Transitions to Individual Fishing Quotas

Our model and empirical work suggest possible explanations for a puzzle that emerged in Birkenbach et al. (2017), namely that the season does not expand for all species after implementing rights-based management. The seasons for some species actually contract significantly following the introduction of IFQs; for example, after IFQs took effect, the season for the New England cod fishery extended, but the corresponding season for New England haddock contracted (Birkenbach et al. 2017). Single-species theory of IFQs and associated market incentives predicts the average effect but cannot account for these mixed results (Homans and Wilen 2005). By modeling the period prior to allocating IFQs as one in which harvesters make sequentially myopic decisions, the mechanisms in the same model developed above can account for the possibility that some fisheries experience season compression while others experience decompression. Under sequentially myopic behavior, harvesters allocate effort to the highest-value species. This can involve allocating effort to multiple species based on the concavity of the production function and market incentives, but by construction agents are not forward-looking. Once the industry-wide quota for a species is exhausted, that species drops out of the choice set.

We consider a two-species fishery that transitions to IFQs from regulated restricted access (RRA).Footnote 28 In Fig. 5, species 1 is a fishery facing downward-sloping demand and whose price in a given time period is therefore endogenous to the quantity harvested in that period, whereas species 2 is modeled as a fishery facing perfectly elastic demand. Under RRA, participants optimize period by period—mimicking racing incentives or the threat of season closures when an industry-wide cap is reached—leading them to concentrate more fishing activity in the early part of the season because of discounting and stock effects (top panel). Harvesters first focus on the higher-value species 1, balancing the racing incentives with the higher price achieved by spreading the season. Slack effort is filled in with harvest of species 2 until month 10, when the TAC of species 1 is exhausted and vessels switch to intensively harvesting species 2. Both species’ TACs are reached by month 11, and the seasons end prematurely (the classic “race to fish” result). Under IFQs, by contrast, the quota may be fished at any point throughout the season without risk of closures. As expected when optimizing over all periods at once, vessels maximize profits by spreading out catch of species 1, leading to lower quantities on the market in each period and therefore higher prices due to the downward-sloping demand schedule. Species 2, on the other hand, fetches the same price regardless of quantity, so fishers have no incentive to spread out catch and exhaust the entire quota for species 2 early in the season (a reflection of discounting). Following the transition to IFQs, the Gini coefficient for species 1 falls (indicating a more spread-out season), while the Gini coefficient for species 2 actually increases. This occurs because, as the season for species 1 becomes less rushed, fishing capacity is freed up early in the season such that more effort can be devoted to fishing more intensively for species 2. This result is consistent with the findings in Birkenbach et al. (2017)—that higher-value species with viable fresh markets achieve increases in season length post-catch shares—and also helps to account for the puzzling counterexamples in which seasons for lower-value species in multispecies contexts significantly contracted.

Fig. 5
figure 5

Two-species effort paths before (top) and after (bottom) IFQs. Species 1 faces downward-sloping demand, and species 2 faces perfectly elastic demand (constant price)

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6 Discussion

The single-species results from our model are simple and intuitive. Discounting and stock effects create incentives to harvest more of the TAC early in the season; endogenous price encourages spreading the harvest more uniformly over the season; biological aggregations create incentives to concentrate harvest due to lower harvest cost; and effort constraints generally spread out the harvest. These results are consistent with existing literature on within-season harvest in catch share fisheries (Boyce 1992; Valcu and Weninger 2013). Still, it is worthwhile to emphasize how much harvest patterns can vary depending on market conditions, stock characteristics, and harvesting capacity even in this simple setting.

The basic intuition about fishing behavior rooted in single-species bioeconomic models breaks down when there are multiple target species. In essence, shadow values on fishing constraints in the single-species case can be viewed as representing a partial equilibrium, but the true shadow values are revealed in the general equilibrium that considers all of the feedbacks across species. Effort devoted to one species changes the opportunity cost of effort devoted to another, and these relationships are fully dynamic and bioeconomic. Moreover, feedbacks exist even in the absence of ecological interdependence, a feature that would add further complications to the modeling. Our detailed predictions from multispecies models are reconcilable with economic intuition based on the single-species case, but predicted multispecies harvest and effort patterns within the season are not immediately intuitive without the supporting bioeconomic model. For example, it is not obvious why a fleet would take all of the quota for a low-value species before landing all of the quota for a high-value species. The model shows that this can occur due to market conditions, biological aggregations, and capacity constraints, and we find empirical support in the Norwegian groundfish data for the first two causes, with potential implications for the third.

The Norwegian groundfish IFQ fisheries provide evidence for our main conceptual findings. Harvests of the high-value IFQ species (cod) with fresh markets and corresponding inelastic demand are more spread out than the lower-value saithe and haddock. This finding is consistent with leveraging market timing to avoid gluts. We also find evidence that the species are landed in reverse order of value as our numerical model predicts. The specific conditions for this to occur that are necessary in the two-species model are: enough effort to harvest all quota of both species, exogenous price for the low-value species, and endogenous price for the high-value species. Cod and saithe fit this explanation well. Our empirical results show that haddock (the intermediate-value species) is landed second in the order of three. We also find in our numerical model that biological aggregation provides complicated incentives in multispecies fisheries when one species faces downward-sloping demand and the other does not. The cost-saving incentive to aggregate is unmediated by revenue-side considerations for the low-value species with perfectly elastic demand. But adapting behavior to this incentive can reduce effort devoted to the high-value species during the same period. We find this effect empirically. Relative to cod, more fishing takes place for saithe during aggregation, but this ultimately affects haddock, and haddock harvest actually decreases during aggregation. In essence, the fleet had to reduce harvest of something to focus on saithe during aggregation, and it was most profitable to maintain cod harvest and reduce haddock. The possibility of a high-value cod roe market during spawning, which we do not model, could also contribute to this result.

An important policy implication of our findings is that management of one species can affect the harvest patterns of other target species. If there is slack effort overall, the ability to time the harvest to the market or biological conditions may increase exploitation for other targets (e.g., taking all of the quota rather than just some of it). This result is consistent with findings of spillovers from tightly regulated species to unregulated or less tightly regulated species (Asche et al. 2007; Hutniczak 2014; Cunningham et al. 2016), although our model shows this can happen even when all species have IFQs.

The combination of constrained harvest capacity, species targeting, and effort timing raises interesting management questions. Low-valued species are generally harvested only when available effort is sufficiently high, although stock aggregations can reduce harvest costs and make low-value fish attractive to target such that they are taken before high-value fish. We know that poor management policies can contribute to overcapacity in fisheries despite successful biological control with TACs (Homans and Wilen 1997). Our results suggest that even when vessel quotas are introduced into such a system, as long as excess capacity is not immediately removed, the fleet may continue to target species that may not otherwise have been optimal to exploit. Fixed costs of entry incurred under an open access regime become sunk costs, yet available evidence indicates that capacity reduction after individual vessel quotas are introduced takes time (Grafton et al. 2000; Asche et al. 2014). Moreover, Kroetz et al. (2015) show that restrictions on individual quota trading lead to a fleet composition that squanders some rents. Our results suggest that, depending on cost structure, a key attribute of fleet composition, namely aggregate capacity, can influence how many species are targeted and how much fish ultimately is caught. This implication raises questions of whether legacies of previous management systems cause multispecies fisheries to harvest more species than is optimal and the extent to which particular mixes of fisheries and levels of specialization are artifacts of this history.

The non-intuitive patterns that our model and empirical results reveal are also consistent with sequencing resource stocks in non-renewable resource economics. The conventional wisdom is that, given multiple deposits of the same resource, those with the lowest extraction costs will be depleted first (Herfindahl 1967; Solow and Wan 1976; Lewis 1982). This intuition dates back to Ricardo’s theory of the mine. However, in a two-resource, two-demand case comparable to a multispecies fishery, simultaneous extraction can be optimal over some interval of time (Chakravorty and Krulce 1994). For instance, although oil and coal both generate electricity, oil is more readily used to power vehicles and thus faces additional demand from the transportation sector. Hence, the optimal sequencing of exploitation across these two assets is driven by revenue- as well as cost-side differences between them. The order of extraction of multiple resource deposits may even be reversed from the intuitive Ricardian pattern such that lower-value resources are used first (Amigues et al. 1998).

We close with some suggestions for future research. Our conceptual analysis presumes that the species relevant to the decision problem are all managed with IFQs that are non-tradable within the season.Footnote 29 While this setup describes the Norwegian system accurately, extending the model to allow for trading and vessel heterogeneity could generate more insights. Moreover, when some fisheries are regulated without IFQs, commons issues can further complicate the fisher’s decision environment. The IFQ program in Norway captures much of the groundfish complex but not all of it. Some species are regulated with industry-wide quotas such that they are regulated open access. Others have no restrictions at all and are effectively pure open access. Thus, the general equilibrium for shadow values of effort also includes species not managed with IFQs, and harvest patterns for IFQ species could be influenced by incentives for species outside of the management regime. Further extending our model to allow for IFQ fisheries that contemporaneously exist with fisheries that have racing incentives is an important topic for future research.