Predicting overfishing and extinction threats in multispecies fisheries

The Eventual Threat Index (T)

The central premise of our approach is that the shared threat of effort in a given multispecies fishery links the fates of species in a way that allows the fates of all species to be predicted if the fate of any one species can be predicted. The fates of some “key” species can be predicted based on their influence on the economic or regulatory factors that determine maximum fishing effort in the fishery. Other species’ fates can be predicted by measuring their vulnerabilities to long-term depletion by the fishery relative to the key species. For the purposes of our approach, we define a “species” at the population level and a “fishery” as a group of fishermen using a particular type of gear to target a particular group of species in a particular region, with roughly uniform relative catch rates of the species (29).

For each fishery, j, we measure the “vulnerability” to long-term depletion of species i at time t [denoted V_ij(t)], using three population-specific pieces of data that are readily available for many fisheries: population size [N(t)] (e.g., ref. 30), average catch-per-unit effort [CPUE(t)] (e.g., ref. 31), and maximum per-capita growth rate (r) (e.g., refs. 30, 32):

Vulnerability measures the fraction of species i’s maximum population growth rate [r_iN_i(t)] lost on average to each unit of fishing effort (e.g., hooks, days fished, etc.) (10, 11). Because fishing effort is shared by all species, the fishery’s relative long-term impacts on different species can be predicted by measuring their relative vulnerabilities as defined in Eq. 1 (Fig. 1A). We derive the mathematical properties of relative vulnerabilities in a general theoretical model in SI Materials and Methods. In general, effort levels greater than 1/V put a species on a path to extinction, as this implies the total catch rate (CPUE*Effort) is larger than the maximum population growth rate (rN).

If a fishery is profitable, effort increases until either profit declines to zero because commercially valued species become depleted (10, 11) or regulations prevent further increase because species protected by management become depleted (Fig. 1 B and C). Profitability or regulations thus impose an upper bound on fishing effort in the fishery that determines which species will likely experience a severe decline or extinction.

Except in rare cases (19, 33), a fishery would be expected to cease operation before all of its commercially valued species are driven extinct, due to a lack of profitability, regulatory intervention, or both (e.g., ref. 34). Thus, there is at least one species in most fisheries whose importance to the fishery’s profits or regulations ensures that the fishery will close before this species is driven extinct. Because high profits and nonbinding limits on the exploitation of managed species in a fishery tend to lead to increases in effort (10, 11), most fisheries also have one or more commercially valued or managed species that are likely to be exploited at least at a minimum rate. Species having both of these properties are key species because their long-term fates are most easily predicted or bounded. We predict the long-term threat of current fishing practices to a given species by calculating its vulnerability relative to a key species in each fishery in which it is caught.

In a managed fishery, the most vulnerable species targeted by management is a likely key species, as fishing effort is likely to increase only until this species reaches the minimum population size or maximum exploitation rate allowed by management (Fig. 1C). In an unmanaged fishery, the species generating the most revenue is a likely key species, as its importance to the fishery’s profits will likely prevent it from being either driven extinct or underexploited (10, 11). In the analysis presented here, we identify key species in this manner. However, our approach to threat prediction is robust to many other approaches to identifying key species (SI Materials and Methods). For instance, if a key species could be profitably driven extinct due to the presence of another valued species that is more robust, the other valued species would become the key long before the first was near extinction.

Fish species are typically caught in multiple fisheries so to be practical the threat measure must capture the vulnerability to harvest of each species across all of the fisheries in which it is caught. For each fishery, we measure its impact on species i relative to that fishery’s key species at time t, using the ratio, V_ij(t)/V_key,j(t). This ratio can also be measured by replacing measures of CPUE in Eq. 1 with total catch in the fishery, if this is easier to measure, as effort will cancel out (Catch = CPUE*Effort). We measure the combined threat of all fisheries to species i at time t by calculating the “eventual threat index”, T_i(t),

T_i(t) sums the V_ij(t)/V_key,j(t) ratios for all fisheries catching species i, including where species i is a key species, and weights the V_ij(t)/V_key,j(t) for each fishery j by the catch of its key species in year t (Catch_key,jj(t)) as a fraction of its key species’ total catch from all fisheries in year t (∑_kCatch_key,jk(t)).

If fishing practices and relative efforts in different fisheries do not change, then T_i(t) becomes a constant through time, denoted T_i*, even as total effort changes (SI Materials and Methods). Fishery managers commonly evaluate threats to populations by comparing their estimated abundances (N) and mortality rates (F, where F = Catch/N) to those producing MSY (N_MSY and F_MSY) (e.g., refs. 3, 4, 24–28, 30). With the common assumption in fisheries that the fishing mortality rate, F at MSY for a species, F_MSY, is half of its maximum growth rate, r (35), T_i* can be shown (SI Materials and Methods) to have the useful property

where F_i* is species i’s long-term fishing mortality rate, and is a weighted average of the long-term fishing mortality rates of the key species of fisheries catching species i. Thus, T_i(t) predicts the long-term mortality rate (F) that current fishing practices at time t would eventually impose on species i relative to the key species of the fisheries in which it is caught, were these fishing practices to continue indefinitely (Fig. 1D).

Managed fisheries often aim to maintain their target species at their MSY populations (2–4). This would mean that if all fisheries were well managed, and consequently the fishing mortality rate of species i (F_i/F_MSY) would approach T_i* in the long term (i.e., F_i*/F_i,MSY = T_i*). Fig. 1E illustrates this property in a simulation model (Materials and Methods). Unmanaged fisheries tend to overfish their target species (10, 11) [i.e., ]. Because key species are unlikely to be driven extinct by their fisheries (10, 11, 34), it can be assumed that an upper bound on fishing effort is set by F_key* ≤ r (i.e., harvest rate ≤ maximum growth rate) for all key species. Because we are assuming F_MSY = r/2, this implies . Thus, it is reasonable to assume that

Under these assumptions, measured T_i(t) values should be interpreted as implying that current fishing practices at time t pose a high threat of species i’s eventual extinction if T_i(t) ≥ 2 (because this implies F_i* ≥ r_i), a high threat of eventual overfishing and a possible threat of extinction with poor management if 1 < T_i(t) < 2, a possible threat of overfishing with poor management if 0.5 < T_i(t) ≤ 1, and a very low threat of overfishing if T_i(t) ≤ 0.5 (Fig. 1D). Fishing gear, targeting behaviors, and management often change in response to evolving technology (e.g., ref. 36), markets (e.g., ref. 37), or political climate. Thus, T_i(t) should be remeasured on a regular basis.

If assuming that r = 2F_MSY or that MSY is a measurable and desired target for management is inappropriate (e.g., ref. 38), our index, T_i(t), can still be used to predict threats, but the threshold values for interpretation (T_i(t) = 2, 1, 0.5) would need to be adjusted (SI Materials and Methods). Our approach can also be adapted to incorporate age structure, by altering the procedure for measuring vulnerabilities (SI Materials and Methods).

Case Study: Western and Central Pacific Tuna and Billfish

To test our approach, we use historical data for eight tuna and billfish populations of the Western and Central Pacific (39) to estimate yearly T values from the 1950s to the present time, using Eqs. 1 and 2. We compare each population’s earliest possible T and V estimates (1953–1967, depending on the population) to their observed abundance and exploitation trends from these early years up until the most recent year for which data are available (1997–2009, depending on the population) (Figs. 2–4) (24–28, 30, 40–44) (SI Materials and Methods). These populations are the northern and southern populations of Pacific albacore tuna (Thunnus alalunga), bigeye tuna (T. obesus), blue marlin (M. nigricans), the northern and southern Pacific striped marlin (T. audax), North Pacific swordfish (Xiphias gladius), and yellowfin tuna (Thunnus albacares). Northern and southern populations of some species are treated separately because they are considered ecologically distinct (25, 26, 40, 42, 43). We use international catch data from longline, purse-seine, and pole-and-line fisheries (31) (Fig. 3), together accounting for 92% of all reported tuna and swordfish catch in this region in 2010 (45). For the purposes of estimating T, we define “fisheries” spatially by dividing the Western and Central Pacific Fisheries Commission (WCPFC) Convention area (39) into 15 regions (Fig. S1) (∼30° × 30°), having roughly uniform relative catch rates within fisheries (45). We also distinguish between shallow- and deep-set longline catch and between purse-seine catch from schools associated and unassociated with floating objects, as these are known to have different catch rates (46, 47). We also tried other ways of distinguishing fisheries for our analysis and found our predictions were robust to these alternatives (SI Materials and Methods and Fig. S2). We estimate historical T values, assuming open access, as there was little international management of these fisheries before the 1980s (48). For all populations, we find our T estimates robust to considerations of older data limitations (SI Materials and Methods). We use 3-y moving geometric averages of T to reduce noise. We compare T values to average annual fishing mortality rates (denoted U) (30) from the fisheries studied (U_Combined = combined catch/average population biomass) (Fig. 2 and SI Materials and Methods) instead of instantaneous fishing mortality (F), as the latter is difficult to estimate without seasonal and size- or age-structured catch and population data, which are not publicly available for these fisheries (31). For the same reason, we also use average annual measures of CPUE and maximum per-capita growth rate in estimating V and T (SI Materials and Methods).

Longline fishing effort began to expand rapidly in the 1950s and 1960s, using predominantly shallow sets targeting bigeye and yellowfin tuna in northern and equatorial regions and albacore tuna in southern regions (31, 49) (Fig. 3 and Table S1). There was little effort in the purse-seine and pole-and-line fisheries (31). At this time, T estimates (Fig. 2) predicted that North Pacific swordfish and all three marlin populations were on paths toward extinction (T > 2), South Pacific albacore and bigeye tuna were on paths toward overfishing (1 < T < 2), and there were low threats to yellowfin and North Pacific albacore tuna (T ≤ 0.5). In the mid-1970s, the tuna-targeting longline fishery largely shifted toward using deeper sets, with many of the remaining shallow sets targeting swordfish (49) (Fig. 3 and Table S1). This shift in fishing technology led to reductions in the threat level predicted by T for most species (Figs. 2 and 3) because the profits from the shallow-set longline fishery were now heavily dependent in many places on swordfish, which has high vulnerability relative to other species (Table S1). This limited the capacity of the shallow-set swordfish fishery to threaten other species. Additionally, the catch rates of swordfish and albacore tuna were lower in the deep-set longline fisheries that were targeting bigeye and yellowfin. As a result of this technological shift, T estimates for North Pacific swordfish, South Pacific albacore tuna, and blue marlin no longer indicated a threat beginning in the late 1970s and continuing to the early 1990s (Figs. 2–4). Also in the 1970s, the purse-seine and pole-and-line fisheries began to expand, targeting primarily skipjack tuna (Katsuwonus pelamis), with yellowfin and bigeye tuna as significant by-catch (31, 47), particularly in purse-seine sets targeting schools associated with floating objects (47). This led to increases in T values for yellowfin and bigeye tuna. An eventual threat to yellowfin is predicted beginning in the early 1990s (T > 1) (Figs. 2 and 4) as an increasing fraction of purse-seine landings came from purse-seine sets targeting associated schools (Fig. 3).

T values from as early as the 1950s have consistently predicted threats of eventual extinction (T ≥ 2) or overfishing (T > 1) from then-current fishing technologies for both northern and southern striped marlin populations (extinction), for blue marlin (extinction, pre-1975, and overfishing until the 1990s), and for bigeye tuna (overfishing) (Figs. 2 and 4). As predicted, all four of these populations eventually did experience mortality rates from these fisheries (U_Combined) exceeding U_MSY, but not until decades after T values predicted this (Fig. 2). Our predictions provided a warning beginning 40 y before this occurred for bigeye tuna and South Pacific striped marlin. These four populations also suffered significant population declines and have abundances currently either at (bigeye tuna) or below (striped marlin) N_MSY (25–27) (Fig. 4). Blue marlin’s N_MSY is unknown (28). These depletions were only recognized three or more decades after they could have been predicted by measuring T (Fig. 4). Blue marlin has also experienced a significant range contraction in this region (23). The first stock assessments identifying these populations as overfished (N < N_MSY) or experiencing overfishing (F > F_MSY or U > U_MSY) came out in the 1980s or later (25–28, 50, 51) (Fig. 4).

T values from the last two decades predict a threat of eventual overfishing to yellowfin tuna (Fig. 2). Although it has not yet become overfished (N > N_MSY, U_Combined < U_MSY) (Figs. 2 and 4) (41), its mortality rate is steadily increasing (Fig. 2), and it has undergone a marked population decline since T predicted a threat (Fig. 4). Early T values (1950–1970) indicated a threat to South Pacific albacore tuna (Fig. 2), and it suffered a significant decline during that period, leading to concern for an overfishing threat in an early stock assessment (52) (Fig. 4). More recent T values (post-1970s) have not indicated a threat (Fig. 2), and it is not currently considered to be overfished or experiencing overfishing (24, 40). Its population has been relatively stable (Fig. 4). Similarly, more recent T values for North Pacific swordfish and albacore tuna do not indicate a threat and neither population appears to be on a trajectory toward overfishing (42, 43) (Figs. 2 and 4).

Our most recent estimates of T, under the assumption of open access, suggest that the northern and southern striped marlin population and yellowfin and bigeye tuna face severe overfishing, and the striped marlin populations may face extinction (Figs. 2 and 4), if these fisheries are poorly managed and current technologies remain the same. The striped marlin populations are particularly threatened by deep-set longline fisheries; and yellowfin and bigeye tuna are particularly threatened by purse-seine fisheries targeting schools associated with floating objects (Fig. 3). Purse-seine fisheries targeting associated schools have received recent conservation attention (47). However, shallow-set longline fisheries have received far more conservation attention than deep-set fisheries, as shallow sets tend to have higher by-catch rates (46). Because of the key species’ (bigeye and yellowfin tuna) relatively lower vulnerabilities in the deep-set fishery, our results suggest that effort in the deep-set fishery has a greater potential to profitably increase in the future. If this occurs, striped marlin would be highly impacted. Although a continued expansion of purse-seine fishing might mitigate some of the threat to the striped marlin by depleting yellowfin and bigeye tuna, the possible threat of deep-set longline fisheries merits further study.

Discussion

For each of the four populations currently believed to be experiencing or to have recently experienced overfishing (F > F_MSY or U > U_MSY) (24–28), our approach was able to predict a threat of eventual overfishing or extinction starting from as early as the 1950s (Figs. 2 and 4), before each began its dramatic population decline (Fig. 4). Moreover, for all populations except North Pacific albacore tuna, which has a very low mortality rate, estimates of T and U_Combined/U_MSY appear to be converging (Fig. 2), consistent with the theory underlying the use of T as an eventual threat predictor (SI Materials and Methods). Because these results suggest that our approach can predict threats well in advance of high mortality rates and declines in abundance (Figs. 2 and 4), its use in these and other fisheries may provide time to adopt preventative management before fishery closures or other highly disruptive interventions are needed. Of the four populations predicted by our approach to be currently threatened, only the striped marlins are already severely overfished (N < N_MSY) (25–27, 41). Thus, it could be possible to avoid severe depletion of yellowfin and bigeye tuna in this region.

Multispecies tuna fisheries are also known to significantly impact sharks, sea turtles, and other by-catch species in the Pacific and elsewhere (7, 53–55). The slow population growth and high recent catch rates of these species suggest they likely have high vulnerabilities, and many could be threatened with extinction (7, 53–55). Our approach, along with recent advances in by-catch monitoring and data-poor abundance estimation methods (53–55), could be used to rapidly assess future extinction threats posed by current fishing practices to by-catch species worldwide.

Internationally cooperative management of large high-seas fisheries can be challenging (2, 3), but will be critical to protecting weak stocks and by-catch species in tuna and billfish fisheries (7, 17, 23, 24, 53–55). Managing each fishery to protect its most vulnerable species is one possible solution (56). However, such “weak-stock management” can cause faster-growing populations to be underexploited, which lowers profits and decreases food supplies (56). Trade-offs between conservation and yield could be mitigated by improving the species selectivity of fishing technologies (7, 36). Measurements of T and V/V_key can be used to set selectivity goals and monitor progress. Marine protected areas or other spatial fishing restrictions, which can provide refuges or reduce impacts on species’ spawning grounds, are also useful management tools that have been implemented in some fisheries, including some Pacific tuna fisheries (57). Another option is to manage the relative sizes of different fisheries with different catch rates, for example the deep-set longline and purse-seine fisheries. This type of management could mitigate both over- and underharvesting without requiring technological advances by equalizing species’ aggregate catch rates. Recent studies suggest that some spatial management strategies, such as maritime zoning (57) or setting regional catch quotas for fishery-wide goals (58), could accomplish this in Pacific tuna (57) and groundfish (58) fisheries.

Our approach, like all other approaches to threat assessment, is subject to uncertainties associated with measurement of populations’ sizes, growth rates, and catch rates (30) and should be interpreted accordingly. Moreover, we strongly encourage the incorporation of size- or age-structure data when using our approach, whenever possible, and describe a possible method for incorporating age structure in SI Materials and Methods.

Our approach is designed to identify direct threats to populations from fisheries in which the populations of interest are not the key species. It is not relevant to a species that is the key species in most or all of the fisheries in which it is caught. It is for this reason that we do not present T values for skipjack tuna. Although many species severely threatened by fishing are weak stocks or by-catch species in multispecies fisheries (6–9), a few target species, such as southern bluefin tuna (17) and caviar-producing sturgeons (19), are threatened by their high and increasing rarity value (19). Our approach is also not designed to predict indirect threats from fishing mediated by species interactions. If T_i > 2, current practices are likely to lead to a harvest rate of species i that exceeds its maximum growth rate, guaranteeing extinction. However, extinction or severe depletion can be caused indirectly by fishing at a much lower level. For example, a recent sea otter decline in Alaska may be linked to a trophic cascade caused by offshore fisheries (59)—a threat our approach would not have detected. Further research is needed to develop preventative approaches for threats from species interactions and rarity value.

Growing human populations and rising food demands are putting increasing pressure on marine ecosystems (2–4). Long-term costs and societal impacts of conservation could be substantially reduced by shifting resources toward preventative measures, instead of rescuing already threatened species (60). Developing cost-effective approaches that can predict future threats to species is a valuable tool for conservation. Our results illustrate that a simple mechanistic theory has the potential to effectively predict species threats well into the future, thus allowing time for preventative management actions.

Materials and Methods

Mathematical derivations of the properties and generalizations of the eventual threat index, T, can be found in SI Materials and Methods. A detailed description of our data sources and methods for the case study can also be found in SI Materials and Methods (Figs. S1–S4). This includes population, catch, effort, and price data; estimates of population growth rates; estimates of populations’ vulnerabilities; methods for determining the key species in each fishery; and an analysis exploring the sensitivity of our case-study results to older data limitations and different means of defining key species and fisheries.

Simulation Model: Fig. 1E.

Fig. 1E shows the results of a simulated model designed to illustrate the properties of T in fisheries managed to exploit their target species at MSY. The model simulates two fisheries each catching three species. Fishery 1 targets species 1 and fishery 2 targets species 2, but both fisheries catch both species 1 and 2, as well as a by-catch species, i. All three species are assumed to have logistic growth and linear catch rates, such that the instantaneous rate of population change of species x (where x = 1, 2, i) at time t is given by

Here, E_j(t) is the level of effort in fishery j at time t, and q_xj is the per-capita per-unit-effort catch rate of species x in fishery j, which we assume is constant in this model. Vulnerability, V_xj(t) = q_xj/r_x is constant. Fishing effort in both fisheries (j, k = 1, 2; k ≠ j) grows according to Eq. 5:

Here, a is a constant determining the adjustment rate of effort to the target species exploitation rate relative to its target rate (F_MSY). We use the following parameter values: {N_x,MSY = 1, N_x(0) = 2 for all x; E₁(0) = E₂(0) = 0.1; r₁ = r₂ = 1; r_i = 0.5; q₁₁ = q₂₂ = q_i1 = q_i2 = 0.1; q₁₂ = q₂₁ = 0.05; a = 0.35}. Species 1 is the key species in fishery 1, and species 2 is the key species in fishery 2 for the calculation of T_i(t).

Supplementary Material