New England Cod Collapse and the Climate

To improve fishery management, there is an increasing need to understand the long-term consequences of natural and anthropogenic climate variability for ecological systems. New England’s iconic cod populations have been in decline for several decades and have recently reached unprecedented lows. We find that 17% of the overall decline in Gulf of Maine cod biomass since 1980 can be attributed to positive phases of the North Atlantic Oscillation (NAO). This is a consequence of three results: i) a 1-unit increase in the NAO winter index is associated with a 17% decrease in the spring biomass of age-1 cod the following year; ii) this NAO-driven decrease persists as the affected cohort matures; iii) fishing practices appear to exacerbate NAO’s direct biological effect such that, since 1913, a 1-unit increase in the NAO index lowers subsequent cod catch for up to 19 years. The Georges Bank cod stock displays similar patterns. Because we statistically detect a delay between the NAO and subsequent declines in adult biomass, our findings imply that observed current NAO conditions can be used in stock forecasts, providing lead time for adaptive policy. More broadly, our approach can inform forecasting efforts for other fish populations strongly affected by natural and anthropogenic climatic variation.

Iceland. 1 This index was obtained annually from

S.1.2 Cod surveyed biomass and catch
Surveyed age-specific biomass during the spring for the Gulf of Maine and Georges Bank Atlantic cod fisheries come from the latest stock assessments, primarily the 55th Northeast Regional Stock Assessment Workshop (SAW) produced by the Northeast Fisheries Science Center (NEFSC). 3,4 We use data directly reported from stock surveys which may be subject to various biases related to survey design. iii For the Gulf of Maine, annual spring biomass surveys were conducted for each age cohort from 1970-2012 (from Table   A58 in NEFSC (2013)) and extended to 2013 (using Tables 1.22 and 1.26 in NEFSC (2014)). Unfortunately, age-specific total biomass is not available from spring surveys of the Georges Bank. Instead, we obtain the number of fish collected by cohort (also known as abundance) from the annual spring surveys (Table B15 in NEFSC (2013)) and multiply each value by the yearly-average weight by age from the annual spring surveys (Table B17a in NEFSC (2013)) to impute age-specific biomass from . Fall survey data for both stocks was pulled from the same sources: Table A59 for Gulf of Maine and Table A60 for Georges Bank.
We restrict attention to only cod ages 1 to 6 and avoid modeling NAO effects on older cod because they are sampled less frequently in stock assessment surveys. Over our respective sample periods, 8.1% of all cod surveyed are age 7 or older in the Gulf of Maine. For Georges Bank, that percentage is 5.2%. For cod age cohort 1 to 6, biomass values (in kg) for each fishery and year are almost all strictly positive. iv Total commercial catch (also known as landings) from U.S. and foreign boats was also obtained from a combination of NEFSC stock assessment reports. Because the 55th SAW only reported commercial catch i Available here: https://climatedataguide.ucar.edu/sites/default/files/climate_index_files/nao_station_djfm_0. txt ii Available here: https://climatedataguide.ucar.edu/climate-data/hurrell-north-atlantic-oscillation-nao-index-pc-based iii Available here: http://nefsc.noaa.gov/publications/crd/crd1311/ iv The only exception are Gulf of Maine age-1 biomass in 2011 and age-6 biomass in 1987 which are recorded as zero values. Given the positive values in years prior and after these zero values, we believe this is due to recording error. To avoid missing values when we apply a log-transformation to biomass, we replace these two zero values with an imputed value based on a linear interpolation of age specific biomass from the previous and following data years. This minor data imputation is not essential to our results. starting in 1932 for the Gulf of Maine (Tables A8-A9 in NEFSC (2013)), we augment our data to include an earlier 5 and the latest stock assessment 4 yielding a continuous catch time series for . Similarly, commercial landings for the Georges Bank fishery (Table B1 in NEFSC (2013)) was extended back to 1893 using an earlier stock assessment 6 to obtain a continuous catch time series for 1893-2011.

S.2 Statistical models
This section describes the statistical models used to establish the following empirical relationships for the Gulf of Maine and Georges Bank cod fisheries: 1) the effect of winter NAO on winter SST, 2) the effect of past and current winter NAO on age-specific surveyed biomass, 3) the effect of past and current winter NAO on surveyed adult biomass (summed over ages [2][3][4][5][6], and 4) the effect of past and current winter NAO on commercial catch. Each model is also presented with related diagnostic checks. For all our results, we use a distributed lag time-series linear regression model.

S.2.1 Modeling NAO effects on SST
To establish the relationship between winter NAO and winter SST, we first obtain an average annual winter SST value, SST t , for each fishery by averaging grid-cell-level SST values from the NOAA OI SST Dataset within the spatial bounds of each fishery as defined by the NEFSC (see fig. 1 in main text). We run the following regression model: where ω is a constant, φ captures the linear effect of current winter NAO and µ p captures the effect of a in Tables A and B correspond to the spatially explicit correlation map shown in Figure 1 in the main text and provides justification for the joint detrending of NAO and SST values using a quadratic time trend.

S.2.2 Modeling NAO effects on age-specific surveyed biomass
In order for current NAO events to forecast subsequent adult cod biomass, we must establish 1) that NAO lowers the survival rate of cod larvae and 2) that this birth-year NAO effect persists as the cod cohort matures. Testing for the persistent of birth-year NAO impacts as a cohort matures helps to rule out possible mean-reverting patterns due to higher growth rates at lower stock levels. For each of the two cod fisheries, we estimate the effects of current and past NAO events on cod stock (in kg) of age a in year t, biomass at by running the following Ricker time-series regression: where SSB a,t−a is spawning stock during birth year. α a is a constant, β aτ captures the age-specific linear effect of NAO τ periods ago, λ1 and λ2 capture density dependence of the recruitment effect during birth year, and γ ap captures the effect of a pth-order polynomial time trend. There are three classes of NAO effects. When τ = a, β aτ captures the effect of an earlier NAO event that occurred during a cohort's birth year. We call this the birth-year NAO effect and is our primary effect of interest. When τ < a, β aτ captures the effect of NAO on cod that is age-1 and older. We call this the post-birth-year or adult NAO effect.
Finally, when τ > a, β aτ captures the effect of NAO on the biomass of subsequent generations due to a drop in the spawning stock biomass. We call this the pre-birth-year or intergenerational NAO effect. As we will show, we find the most consistent evidence for a birth-year NAO effect across both cod fisheries. Standard errors use the Newey-West adjustment which allows for serial correlation and heteroscedasticity of arbitrary form in the error terms over an optimally chosen window of time. 7,8 In our preferred models, we include current and lagged NAO terms up to and including birth-year NAO such that L must be no smaller than the age of the cohort, a.  Figure 2 in the main text. Each model includes a 3rd-order polynomial time trend and the same number of lagged NAO terms as the cohort's age. In the next subsection, we justify these and other modeling decisions.
For the Gulf of Maine fishery, a 1-unit increase in the NAO index during a cohort's birth year is associated with a -13% change in surveyed biomass for that cohort at age 1. This effect persists as the cohort matures to age 6, with statistically significant effects ranging from -8 to -19% (Table C). Because biomass is imputed and not directly observed for the Georges Bank fishery, birth-year NAO effects are noisier for age-1 cod.
However, we find that a 1-unit increase in birth-year NAO similarly lowers the surveyed biomass of cod ages 2 to 5 by -9 to -16% (Table G). This persistent effect appears to dissipate by age 6, though an effect of -17% is detected for NAO occurring five years ago which may capture the birth-year NAO effect. This may be due to errors in age assignment during cod surveys as the age of older fish may be harder to determine. For both fisheries we pick up some post-birth-year NAO effects but they do not persist systematically like birth-year NAO effects.
We preform the same analysis on fall survey cod biomass data. There is a genetically different population that spawns in the fall than in the spring. For GOM, significant effects are seen for age-2 cod and above, but not for age-1 cod (Table R). This is consistent with the fact that NAO is a mode of winter climate variability, so it should theoretically only impact spring recruitment. Results for Georges Bank stock do not show significant NAO-birth-year effects for any age cohort (Table S) We also estimate Eq. S.2 using an alternative principal component-based (PC) DJFM NAO index which allows for spatial shifts in the pressure centers of the NAO. This is for comparison with the benchmark station-based Hurrell index, which uses sea-level pressure (SLP) differences defined over fixed spatial areas.

Model selection tests
Order of polynomial time trends: We must determine N in Equation S.2, the order of the polynomial time trend for each age cohort. If both cod stocks and NAO exhibited trending behavior during this period, our model might detect a statistical relationship between these two variables that is driven by a common trend. Results in Tables C and G address this issue by jointly removing a 3rd-order polynomial time trend.

5
In Tables D and H, we examine whether higher or lower order polynomial trends affect the stability of the birth-year NAO effect for each age cohort and fishery separately. Specifically, we vary the order of included time-trend terms from 1 to 5 across Columns (1)- (5) respectively. Each horizontal panel shows a different age cohort; thus each "cell" presents the birth-year NAO effect and related statistics from separate regressions. to that shown in Panels (A) and (B) of Figure 2 in the main text. Furthermore, the Akaike Information Criteria 9 is similar in magnitude across the columns. For the Georges Bank fishery, age 2 to age 5 birth-year NAO effects are also relatively stable across trend specifications (Table H). However, there appears to be a unit root for age 2, age 3, and age 6 cohorts models.
We posit that a unit root may have been artificially generated due to the imputed nature of Georges Bank surveyed biomass discussed in Section S. The presentation structure is similar to that of Table D  In Table F, we display the additional pre-birth-year effects to explore if NAO has any intergenerational v The optimal lag length chosen for each DF-GLS tests is based on a AIC statistic.
6 effects for the Gulf of Maine. If an NAO event reduces a birth-year cohort's biomass and this reduction persists to when the cohort is reproductively mature, then the biomass of that cohort's offspring may also be negatively affected. This implies that birth-year NAO effects may transmit past a single generation. Atlantic cod typically reach reproductive maturity beginning at age 2. 6 If intergenerational effects exist, we may detect the adverse impacts of NAO two years prior to the birth of a particular cohort. It is worth noting, however, that intergenerational effects may not necessarily follow a clear 2-year interval as reproduction occurs continuously once a fish reaches reproductive maturity. Thus, our tests for intergenerational effects are likely to be imprecise.
In Table F, we extend the number of lags for all age cohorts to age 4, displaying all NAO coefficients.
We do not estimate further lags given our limited sample size and so are unable to detect intergenerational effects for cohorts older than age 4. Table F provides some, though weak, evidence that birth-year NAO effects persist beyond a single generation for the Gulf of Maine. In Column (1) we find that age-1 biomass decreases in response to NAO events four and six years prior, roughly corresponding to NAO events felt by one and two earlier generations. We also find a one-generation effect for age-2 and age-4 cod, but fail to find an intergenerational effect for age-3 cod. For the Georges Bank fishery, we also find that the birth-year NAO effect is stable to the exclusion of post-birth-year NAO terms and the inclusion of pre-birth-year NAO effects (Table I). We also find even weaker evidence of intergenerational effects with a one-generation effect detected for age-3 and age-4 cod only (Table J).
Nonlinearity: Equation S.2 implicitly assumes that birth-year NAO has a linear effect on age-specific surveyed biomass. We test for whether linearity is an overly restrictive assumption in Figure B for both fisheries. Following Equation S.2, we first regress log(biomass at ) on a constant, all post-birth-year NAO terms, birth-year spawning stock in levels and log, and a 3rd-order polynomial time trend and obtain the residuals. We perform the same partialling-out procedure for N AO t−τ . We then fit the two residuals using a bivariate local polynomial regression allowing for data-driven flexible functional forms. 12 Panel (A) of Figure   B shows the bivariate relationship between surveyed biomass for ages [1][2][3][4][5][6] cod and birth-year NAO for the Gulf of Maine. For the Gulf of Maine, the partialed-out age-specific biomass has an approximately linear relationship with partialed-out birth-year NAO for all age cohorts. For Georges Bank, Panel (B) of Figure   B shows similar linearity for the relationship between age-specific biomass and birth-year NAO effects with the exception of age 1 and age 3 biomass.

Time-varying effects Equation S.2 implicitly assumes that the birth-year NAO effect is constant over
the course of the sample period. Previous papers have noted that environmental-recruitment relationships may be changing over time. 13 We statistically test for time-varying effects by conducting a rolling-window analysis of our birth-year NAO recruitment effect (i.e. on age-1 cod). Figure C plots coefficients from 20-year wide estimation windows for the Gulf of Maine cod, the stock with the longer time-series data. There is no linear trend, positive or negative, in the relationship over time during the past four decades. There does appear to be non-trending, low-frequency cyclicality in the relationship whose mean is captured by my full sample estimates. Figure C shows my full sample confidence intervals as red lines.
To demonstrate that the birth-year NAO effect on cod recruitment is not being confounded by adult cod biomass, we augment our model of age-1 surveyed biomass to include the previous year's surveyed adult biomass (summed over ages [2][3][4][5][6] in Column (3) of Tables C and G. vi Again, our birth-year NAO effect is largely unaffected.

S.2.3 Modeling winter SST effects on age-specific spring-surveyed biomass
To examine the effects of local winter SST on age-specific cod biomass, we estimate a variant of Eq. S.2 replacing all NAO terms with SST terms. Birth-year winter SST effects were not detected for year-1 cod and do not show persistence after year-4 (Table P). We do not detect a birth-year SST effect for any age in Georges Bank (Table Q).
vi We prefer to use surveyed adult biomass as a proxy for "spawning stock biomass" (SSB) because constructing SSB requires cohort-specific weights that are typically based on modeling assumptions.

S.2.4 Decomposing NAO's effect on adult cod biomass decline since 1980
NAO has generally been in a positive phase over the last few decades (Figure 2, Panel (E)). We are interested in examining the contribution of these recent positive NAO events on the observed overall decline in adult cod biomass since 1980 as shown in Panels (C) and (D) of Figure 2. We first estimate an aggregate version of Eq. S.2 across cod ages 2-6, where α A is a constant, β A τ captures the linear effect of NAO τ periods ago and γ Ap captures the effect of a pth-order polynomial time trend. Following our earlier age-specific biomass regressions, we include up to 6 lagged NAO terms such that L = 6. Odd numbered columns in Table K show estimates of β τ for the Gulf of Maine fishery. Results are equivalent to a biomass weighted sum of estimates from Table C.
Using a 3rd-order polynomial time trend displayed in Column (5), a 1% increase in NAO 4, 5, and 6 years ago lowers current adult cod biomass by 8%, 6% and 11% respectively. These effects are relatively stable across 2nd-4th order polynomial time trend specifications but do change when only a linear time trend is included. Similar results are shown for the Georges Bank fishery in Table L. With a 3rd-order polynomial time trend as shown in Column (5), a 1% increase in NAO 3, 4, 5, and 6 years ago lowers current adult cod biomass by 8%, 10%, 9% and 7% respectively. Results are largely robust to the order of the polynomial time trend. Even numbered columns of Tables K and L also include an additional control for previous year catch. As discussed above, this specification contains a "proxy control" problem and is not preferred. For both fisheries, our results are unaffected by the inclusion of previous year catch.
To construct the decomposition shown in Panels (C) and (D) of Figure 2, we perform the following procedure: 15 1. Estimate Eq. S.3 with L = 6 and N = 3 using the full sample.
2. Predict adult biomass without NAO using only secular time trends: 3. Predict adult biomass with NAO starting in 1980 and secular time trends: 1980,2013]. The green line examines adult cod dynamics with NAO "turned-on" starting in 1980. The difference between the green and orange lines represent the added contribution of the NAO on adult biomass. To get the percentage contribution in the overall adult biomass decline due to the NAO from period t = s1 to t = s2, we calculate the following: In practice, due to noisy biomass values, we take the average values over the

S.2.5 Modeling NAO effects on cod catch
Cod catch is a function of cod biomass and fishing effort. By examining catch, we can indirectly explore how fishing effort may have historically dampened or enhanced the direct biophysical impact of birth-year NAO on biomass. We model commercial cod catch, catch t with the following regression model: where In the Gulf of Maine fishery, we find that a 1-unit increase in NAO is associated with a -3 to -6% change in catch that lasts up to 19 years after the initial event. We find persistent effects of similar magnitude for up to 15 years after a 1-unit increase in NAO for the Georges Bank fishery.

Model selection tests
In Tables N and O we conduct       Serial correlation and heteroscedasticity robust Newey-West standard errors with optimal bandwidth. 90% confidence intervals shown. Horizontal red lines show 90% confidence interval for the full sample effect.  16 Notes: Each column shows the coefficient from a time-series regression of winter SST (DJFM), in degrees Celsius, averaged over grid-cells in the George's Bank fishery on NAO. Order of polynomial time trend varies across columns. Serial correlation and heteroscedasticity robust Newey-West standard errors with optimal bandwidth. *** p<0.01, ** p<0.05, * p<0.1  1971-2013 1971-2013 1972-2013 1972-2013 1973-2013 1973-2013 1974-2013 1974-2013 1975-2013 1975-2013 1976-2013 1976-2013 Number of trends Notes: Each column shows coefficients from a time-series regression model of log cohort-specific spring cod biomass on current and past NAO, adult biomass (ages 2 and up) from the spawning year of that cohort, and trend terms. Some models additionally include control for previous year catch. Coefficients shaded in gray capture birth-year NAO effects. Coefficients in bold correspond to coefficients shown in Figure 2 of the main text. Serial correlation and heteroscedasticity robust Newey-West standard errors with optimal bandwidth. *** p<0.01, ** p<0.05, * p<0.1  Figure 2 of the main text. Model AIC statistic and p-value from Dickey-Fuller tests model residual against the presence of a unit root also shown. *** p<0.01, ** p<0.05, * p<0.1, − p>0.1  Figure 2 of the main text. Model AIC statistic and p-value from Dickey-Fuller tests model residual against the presence of a unit root also shown. *** p<0.01, ** p<0.05, * p<0.1, − p>0.1  1971-2013 1972-2013 1973-2013 1974-2013 Number of trends  3  3  3  3  Newey-West bandwidth  17  6  13 17 Notes: Each column shows coefficients from a time-series regression of log age-specific spring cod biomass on current and past NAO. Coefficients shaded in gray capture birth-year NAO effects. All models include a 3rdorder polynomial time trend. Serial correlation and heteroscedasticity robust Newey-West standard errors with optimal bandwidth. *** p<0.01, ** p<0.05, * p<0.1  Notes: Each column shows coefficients from a time-series regression model of log cohort-specific spring cod biomass on current and past NAO, adult biomass (ages 2 and up) from the spawning year of that cohort, and trend terms. Some models additionally include control for previous year catch. Coefficients shaded in gray capture birth-year NAO effects. Coefficients in bold correspond to coefficients shown in Figure 2 of the main text. Serial correlation and heteroscedasticity robust Newey-West standard errors with optimal bandwidth. *** p<0.01, ** p<0.05, * p<0.1  Figure 2 of the main text. Model AIC statistic and p-value from Dickey-Fuller tests model residual against the presence of a unit root also shown. *** p<0.01, ** p<0.05, * p<0.1, − p>0.1  Figure 2 of the main text. Model AIC statistic and p-value from Dickey-Fuller tests model residual against the presence of a unit root also shown. *** p<0.01, ** p<0.05, * p<0.1, − p>0.1  1979-2011 1980-2011 1981-2011 1982-2011 Number of trends  3  3  3  3  Newey-West bandwidth  16  16  16 16 Notes: Each column shows coefficients from a time-series regression of log age-specific spring cod biomass on current and past NAO. Coefficients shaded in gray capture birth-year NAO effects. All models include a 3rdorder polynomial time trend. Serial correlation and heteroscedasticity robust Newey-West standard errors with optimal bandwidth. *** p<0.01, ** p<0.05, * p<0.1  1970-2013 1970-2013 1970-2013 1970-2013 1970-2013 1970-2013 1970-2013 1970-2013 Number of trends  Sample period 1978-2011 1978-2011 1978-2011 1978-2011 1978-2011 1978-2011 1978-2011 1978-2011 Number of trends     1983-2013 1983-2013 1984-2013 1984-2013 1985-2013 1985-2013 1986-2013 1986-2013 1987-2013 1987-2013 1988-2013 1988-2013 Number of trends Notes: Each column shows coefficients from a time-series regression model of log cohort-specific spring cod biomass on current and past SST, adult biomass (ages 2 and up) from the spawning year of that cohort, and trend terms. Some models additionally include control for previous year catch. Coefficients shaded in gray capture birth-year SST effects. Serial correlation and heteroscedasticity robust Newey-West standard errors with optimal bandwidth. *** p<0.01, ** p<0.05, * p<0.1