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When first hatched, and before the disappearance of the yolk sac, the larvae (European) feed on larval snails and crustaceans, on diatoms, and on peridinians, but they soon begin taking copepods, and depend exclusively on these for a time after they get to be 12 mm. long, especially on the little Pseudocalanus elongatus. As they grow older they feed more and more on the larger copepods and amphipods, pelagic shrimps, and decapod crustacean larvae.

Zooplankton indices as covariates in WHAM

Herring Research Track Review
11 March 2025

Sarah Gaichas, Jon Deroba, Adelle Molina

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Does food drive recruitment of Atlantic herring?

Atlantic herring, Clupea harengus

Atlantic herring illustration, credit NOAA Fisheries

"The herring is a plankton feeder.... Examination of 1,500 stomachs showed that adult herring near Eastport were living solely on copepods and on pelagic euphausiid shrimps (Meganyctiphanes norwegica), fish less than 4 inches long depending on the former alone, while the larger herring were eating both." (Collette et al., 2002)

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When first hatched, and before the disappearance of the yolk sac, the larvae (European) feed on larval snails and crustaceans, on diatoms, and on peridinians, but they soon begin taking copepods, and depend exclusively on these for a time after they get to be 12 mm. long, especially on the little Pseudocalanus elongatus. As they grow older they feed more and more on the larger copepods and amphipods, pelagic shrimps, and decapod crustacean larvae.

Which indicators are potential covariates for recruitment?

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Which indicators are potential covariates for recruitment?

Boosted regression tree (Molina 2024) investigated relationships between environmental indicators and Atlantic herring recruitment estimated in the assessment.

Larval and juvenile food (zooplankton), egg predation, and temperature always highest influence

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Maps of key areas for Herring assessment indices. The full VAST model grid is shown in brown.Maps of key areas for Herring assessment indices. The full VAST model grid is shown in brown.Maps of key areas for Herring assessment indices. The full VAST model grid is shown in brown.

Maps of key areas for Herring assessment indices. The full VAST model grid is shown in brown.

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NEFSC survey strata definitions are built into the VAST northwest-atlantic extrapolation grid already. We defined additional new strata to address the recreational inshore-offshore 3 mile boundary. The area within and outside 3 miles of shore was defined using the sf R package as a 3 nautical mile (approximated as 5.556 km) buffer from a high resolution coastline from thernaturalearth R package. This buffer was then intersected with the current FishStatsUtils::northwest_atlantic_grid built into VAST and saved using code here. Then, the new State and Federal waters strata were used to split NEFSC survey strata where applicable, and the new full set of strata were used along with a modified function from FishStatsUtils::Prepare_NWA_Extrapolation_Data_Fn to build a custom extrapolation grid for VAST as described in detail here.

Exploratory zooplankton indices in the stock assessment

Use as a basis the new herring stock assessment in Woods Hole Assessment Model (WHAM) (Stock et al., 2021).

We are using the devel version of WHAM: https://github.com/timjmiller/wham/tree/devel

Model mm192 is our starting point.

Zooplankton indices were explored as covariates on herring recruitment.

Recruitment is modeled as deviations from the "recruitment scaling parameter", leaving one option for modeling effects of covariates on recruitment: "controlling".

A "controlling" recruitment covariate results in a time-varying recruitment scaling parameter.

Covariates explored:

  • Jan-Jun (Spring) large copepods in spring herring BTS strata with lag-0 to represent food for pre-recruit juveniles
  • Jul-Dec (Fall) small copepods in fall herring BTS strata with lag-1 to represent food for larvae in general
  • Sep-Feb small copepods in herring larval area with lag-1 to represent food for larvae more specifically

  • Combinations of large and small copepod covariates above

  • Optimal temperature duration (days) during the fall larval season, September-December

  • Sensitivity: Turn off NAA RE and then try fitting with the most robust recruitment covariates.

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Implementing each index

We evaluated

  • Options for covariate input (millions of cells vs. log(cells), VAST estimated SE vs. WHAM estimated SE)
  • Options for covariate observation model ("rw" vs. "ar1")
  • Options for recruitment link ("none" vs. "controlling-linear" with lag-0 for large copepods, lag-1 for small copepods, and lag-1 for larval temperature duration)
  • No attempts were made to fit polynomial effects although this is possible in WHAM

Short story:

  • Models with covariates input on the log scale generally converged
  • Models with WHAM estimated covariate SE ("est_1") generally converged
  • Under the above conditions, most models with and without the recruitment link converged for all covariates
  • Models with the Jan-Jun (Spring) large copepods covariate also converged with input as millions of cells and VAST estimated SE
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Overview of results shown for each model

Summary table comparing across models with and without recruitment covariates turned on

Diagnostics shown:

  • WHAM's fit to the covariate time series
  • One step ahead residuals for WHAM's fit
  • Estimated time varying recruitment scaling parameter with N age 1

Finally, recruitment sigma compared with base, covariate beta with CI

The main diagnostics we used to determine if the model was improved by covariates were:

  • model converged and Hessian matrix invertable
  • dAIC lowest
  • recruitment sigma reduced (how much?)
  • estimated covariate effect CI does not include 0
  • direction of covariate effect is sensible
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Results: Spring large copepods covariate: model summary

Models with no covariates had slightly better AIC than comparable models with recruitment links

Model ecov_process                 ecov_how           ecovdat conv pdHess       NLL  dAIC     AIC  rho_R rho_SSB rho_Fbar
 m10           ar1                     none     logmean-est_1 TRUE   TRUE -1793.611     0 -3325.2 0.8684  0.5901  -0.2314
 m14           ar1 controlling-lag-0-linear     logmean-est_1 TRUE   TRUE -1794.325   0.6 -3324.6 0.8999  0.5844  -0.2296
  m2            rw                     none     logmean-est_1 TRUE   TRUE -1790.837   3.5 -3321.7 0.8683  0.5901  -0.2314
  m6            rw controlling-lag-0-linear     logmean-est_1 TRUE   TRUE -1791.227   4.7 -3320.5 0.8844  0.5846    -0.23
 m11           ar1                     none meanmil-logsigmil TRUE   TRUE -1509.570 566.1 -2759.1 0.8682  0.5901  -0.2314
 m15           ar1 controlling-lag-0-linear meanmil-logsigmil TRUE   TRUE -1510.349 566.5 -2758.7 0.9081   0.592  -0.2379
  m3            rw                     none meanmil-logsigmil TRUE   TRUE -1506.709 569.8 -2755.4 0.8594  0.5907  -0.2362
  m7            rw controlling-lag-0-linear meanmil-logsigmil TRUE   TRUE -1507.424 570.4 -2754.8 0.8104   0.594  -0.2448
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Results: Spring large copepods covariate: logscale ar1 diagnostics

lgCopeSp2 m10 fit

lgCopeSp2 m10 osa

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Results: Spring large copepods covariate: logscale ar1 recruitment

lgCopeSp2 m10 rec

lgCopeSp2 m14 rec

Without covariate, recruitment variance is 0.823, and with is 0.797; lgCopeSpring2 beta_1 is -0.407, CI -1.063, 0.25

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Results: Spring large copepods covariate: logscale rw diagnostics

lgCopeSp2 m2 fit

lgCopeSp2 m2 osa

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Results: Spring large copepods covariate: logscale rw recruitment

lgCopeSp2 m10 rec

lgCopeSp2 m14 rec

Without covariate, recruitment variance is 0.823, and with is 0.804; lgCopeSpring2 beta_1 is -0.45, CI -1.438, 0.538

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Results: Spring large copepods covariate: natural scale ar1 diagnostics

lgCopeSp2 m11 fit

lgCopeSp2 m11 osa

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Results: Spring large copepods covariate: natural scale ar1 recruitment

lgCopeSp2 m11 rec

lgCopeSp2 m15 rec

Without covariate, recruitment variance is 0.823, and with is 0.791; lgCopeSpring2 beta_1 is -4.5\times 10^{-4}, CI -0.00128, 3.8\times 10^{-4}

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Results: Spring large copepods covariate: natural scale rw diagnostics

lgCopeSp3 m11 fit

lgCopeSp3 m11 osa

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Results: Spring large copepods covariate: natural scale rw recruitment

lgCopeSp2 m3 rec

lgCopeSp2 m7 rec

Without covariate, recruitment variance is 0.823, and with is 0.793; lgCopeSpring2 beta_1 is -4.3\times 10^{-4}, CI -0.00126, 4\times 10^{-4}

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Results: Fall small copepods covariate: model summary

Models with no covariates had slightly better AIC than the ar1 model with recruitment links

Model ecov_process                 ecov_how       ecovdat conv pdHess       NLL  dAIC     AIC  rho_R rho_SSB rho_Fbar
  m10          ar1                     none logmean-est_1 TRUE   TRUE -1797.177     0 -3332.4 0.8682  0.5901  -0.2314
   m2           rw                     none logmean-est_1 TRUE   TRUE -1796.175   0.1 -3332.3 0.8682  0.5901  -0.2314
  m14          ar1 controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1797.931   0.5 -3331.9 0.8486  0.6001  -0.2333
   m6           rw controlling-lag-1-linear logmean-est_1 TRUE  FALSE -1794.370   ---     ---    ---     ---      ---
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Results: Fall small copepods covariate: logscale ar1 diagnostics

smCopeFall2 m10 fit

smCopeFall2 m10 osa

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Results: Fall small copepods covariate: logscale ar1 recruitment

smCopeFall2 m10 rec

smCopeFall2 m14 rec

Without covariate, recruitment variance is 0.823, and with is 0.79; smcopeFall2 beta_1 is -1.013, CI -2.715, 0.689

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Results: Sep-Feb small copepods in herring larval area covariate: model summary

Model with ar1 covariate had slightly better AIC than models without recruitment links

Model ecov_process                 ecov_how       ecovdat conv pdHess       NLL  dAIC     AIC  rho_R rho_SSB rho_Fbar
  m14          ar1 controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1791.900     0 -3319.8  0.814  0.5966  -0.2327
   m2           rw                     none logmean-est_1 TRUE   TRUE -1789.657   0.5 -3319.3 0.8683  0.5901  -0.2314
  m10          ar1                     none logmean-est_1 TRUE   TRUE -1790.469   0.9 -3318.9 0.8683  0.5901  -0.2314
   m6           rw controlling-lag-1-linear logmean-est_1 TRUE  FALSE -1785.746   ---     ---    ---     ---      ---
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Results: Sep-Feb small copepods in herring larval area covariate: logscale ar1 diagnostics

smCopeSepFeb2 m10 fit

smCopeSepFeb2 m10 osa

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Results: Sep-Feb small copepods in herring larval area covariate: logscale ar1 recruitment

smCopeSepFeb2 m10 rec

smCopeSepFeb2 m14 rec

Without covariate, recruitment variance is 0.823, and with is 0.77; smcopeSepFeb2 beta_1 is -0.85, CI -1.883, 0.182

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Alternate: Sep-Feb small copepods in fall herring survey strata covariate

Both rw and ar1 models worked with covariates, rw better fit

Model ecov_process                 ecov_how       ecovdat conv pdHess       NLL  dAIC     AIC  rho_R rho_SSB rho_Fbar
   m6           rw controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1791.981   0.0 -3322.0 0.7592  0.6023  -0.2327
  m14          ar1 controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1792.464   1.1 -3320.9 0.7943  0.5971  -0.2329
   m2           rw                     none logmean-est_1 TRUE   TRUE -1790.196   1.6 -3320.4 0.8682  0.5901  -0.2314
  m10          ar1                     none logmean-est_1 TRUE   TRUE -1790.734   2.5 -3319.5 0.8683  0.5901  -0.2314
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Results: Sep-Feb small copepods in herring larval area covariate: logscale rw diagnostics

smCopeSepFeb2_fallstrat m2 fit

smCopeSepFeb2_fallstrat m2 osa

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Results: Sep-Feb small copepods in herring larval area covariate: logscale rw recruitment

smCopeSepFeb2_fallstrat m2 rec

smCopeSepFeb2_fallstrat m6 rec

Without covariate, recruitment variance is 0.823, and with is 0.762; smcopeSepFeb2 beta_1 is -1.01, CI -2.11, 0.089

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Results: Sep-Feb small copepods in herring larval area covariate: logscale ar1 diagnostics

smCopeSepFeb2 m10 fit

smCopeSepFeb2 m10 osa

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Results: Sep-Feb small copepods in herring larval area covariate: logscale ar1 recruitment

smCopeSepFeb2 m10 rec

smCopeSepFeb2 m14 rec

Without covariate, recruitment variance is 0.823, and with is 0.757; smcopeSepFeb2 beta_1 is -0.976, CI -2.044, 0.093

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Results: Both Spring large copepods and Sep-Feb small copepods in herring larval area: model summary

Models with and without ar1 covariates linked to recruitment had the same AIC

Model ecov_process                   ecov_how       ecovdat conv pdHess       NLL dAIC     AIC  rho_R rho_SSB rho_Fbar
   m2          ar1                       none logmean-est_1 TRUE   TRUE -1771.328  0.0 -3272.7 0.8682  0.5901  -0.2314
   m4          ar1 controlling-lag-0/1-linear logmean-est_1 TRUE   TRUE -1773.347  0.0 -3272.7 0.8529  0.5922  -0.2313
   m1           rw                       none logmean-est_1 TRUE   TRUE -1767.742  3.2 -3269.5 0.8683  0.5901  -0.2314
   m3           rw controlling-lag-0/1-linear logmean-est_1 TRUE   TRUE -1769.627  3.4 -3269.3 0.8001  0.5976  -0.2321
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Results: Both Spring large copepods and Sep-Feb small copepods: logscale rw diagnostics

lgCopeSpring m1 fit

lgCopeSpring2 m1 osa

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Results: Both Spring large copepods and Sep-Feb small copepods: logscale rw diagnostics

smCopeSepFeb m1 fit

smCopeSepFeb2 m1 osa

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Results: Both Spring large copepods and Sep-Feb small copepods: logscale rw recruitment

both m1 rec

both m3 rec

Without covariates, recruitment variance is 0.823, and with is 0.755; smcopeSepFeb2 beta_1 is -0.88, CI -1.929, 0.169

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-

Results: Duration of optimal larval temperature, Sept-Dec: model summary

  Model ecov_process                 ecov_how       ecovdat conv pdHess       NLL  dAIC     AIC  rho_R rho_SSB rho_Fbar
    m4           rw controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1827.543     0 -3393.1 0.6543  0.5984 -0.2323
    m3           rw                     none logmean-est_1 TRUE   TRUE -1826.370   0.4 -3392.7 0.8682  0.5901 -0.2314
    m8          ar1 controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1826.627   3.8 -3389.3 0.6714   0.598 -0.2324
    m7          ar1                     none logmean-est_1 TRUE   TRUE -1825.511   4.1   -3389 0.8682  0.5901 -0.2314
    m2           rw controlling-lag-1-linear    mean-est_1 TRUE   TRUE -1650.465 354.2 -3038.9 0.6473  0.5976 -0.2321
    m1           rw                     none    mean-est_1 TRUE   TRUE -1649.265 354.6 -3038.5 0.8594  0.5907 -0.2362
    m6          ar1 controlling-lag-1-linear    mean-est_1 TRUE   TRUE -1649.607 357.9 -3035.2 0.6643  0.5971 -0.2322
    m5          ar1                     none    mean-est_1 TRUE  FALSE -1644.890   ---     ---    ---     ---     ---
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Results: Duration of optimal larval temperature, Sept-Dec: logscale rw diagnostics

LarvalTempDuration/m3 fit

LarvalTempDuration/m3 osa

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Results: Duration of optimal larval temperature, Sept-Dec: logscale rw recruitment

LarvalTempDuration/m3 rec

LarvalTempDuration/m4 rec

Without covariate, recruitment variance is 0.823, and with is 0.79; LarvalTempDuration beta_1 is 2.066, CI -0.657, 4.789

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Results: Duration of optimal larval temperature, Sept-Dec: logscale ar1 diagnostics

LarvalTempDuration/m7 fit

LarvalTempDuration/m7 osa

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Results: Duration of optimal larval temperature, Sept-Dec: logscale ar1 recruitment

LarvalTempDuration/m7 rec

LarvalTempDuration/m8 rec

Without covariate, recruitment variance is 0.823, and with is 0.791; LarvalTempDuration beta_1 is 2.032, CI -0.711, 4.775

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Sensitivity: Remove NAA RE, add September - December duration of larval optimal temperature: model summary

Both rw and ar1 models worked with covariates, rw better fit

Model ecov_process                 ecov_how       ecovdat conv pdHess       NLL  dAIC     AIC  rho_R rho_SSB rho_Fbar
  m4            rw controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1762.281     0 -3266.6 1.6108  0.3339   -0.121
  m8           ar1 controlling-lag-1-linear logmean-est_1 TRUE   TRUE -1761.214   4.2 -3262.4 1.6872  0.3341  -0.1213
  m3            rw                     none logmean-est_1 TRUE   TRUE -1748.086  26.4 -3240.2 3.5003  0.3664  -0.1424
  m7           ar1                     none logmean-est_1 TRUE   TRUE -1747.227  30.1 -3236.5 3.5003  0.3664  -0.1424
  m2            rw controlling-lag-1-linear    mean-est_1 TRUE   TRUE -1585.263 354.1 -2912.5 1.5766  0.3325  -0.1206
  m1            rw                     none    mean-est_1 TRUE   TRUE -1570.980 380.6   -2886 3.5014  0.3662  -0.1421
  m5           ar1                     none    mean-est_1 TRUE   TRUE -1570.163 384.3 -2882.3 3.5003  0.3673  -0.1437
  m6           ar1 controlling-lag-1-linear    mean-est_1 TRUE  FALSE -1584.188   ---     ---    ---     ---      ---
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Duration of optimal larval temperature, Sept-Dec: logscale rw diagnostics

LarvalTempDurationsens/m3 fit

LarvalTempDurationsens/m3 osa

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Duration of optimal larval temperature, Sept-Dec: logscale rw recruitment

LarvalTempDurationsens/m3 rec

LarvalTempDurationsens/m4 rec

Without covariate, recruitment variance is 0.833, and with is 0.503; LarvalTempDuration beta_1 is 5.122, CI 2.709, 7.535

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Discussion

The duration of optimal larval temperature covariate resulted in slightly better model fits and reduced recruitment variability relative to the model without covariates. The effect of optimal larval temperature on recruitment was postive, as hypothesized, with fewer days of optimal temperature resulting in a lower recruitment scaling parameter. However, the confidence interval of the effect included 0.

While some of the zooplankton time series also resulted in slightly better model fits and reduced recruitment variability relative to the model without covariates, the effects of zooplankton were negative on recruitment. This relationship is opposite the hypothesized relationship between herring and food, which was expected to be positive.

The sensitivity run removing NAA RE resulted in a much stronger impact of the optimal larval temperature on recruitment.

Thoughts?

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Thank you! References

Collette, B. B. et al. (2002). Bigelow and Schroeder's Fishes of the Gulf of Maine, Third Edition. 3rd ed. edition. Washington, DC: Smithsonian Books. ISBN: 978-1-56098-951-6.

Stock, B. C. et al. (2021). "The Woods Hole Assessment Model (WHAM): A general state-space assessment framework that incorporates time- and age-varying processes via random effects and links to environmental covariates". En. In: Fisheries Research 240, p. 105967. ISSN: 0165-7836. DOI: 10.1016/j.fishres.2021.105967. URL: https://www.sciencedirect.com/science/article/pii/S0165783621000953 (visited on May. 26, 2021).

Slides available at https://noaa-edab.github.io/presentations
Contact: Sarah.Gaichas@noaa.gov

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Does food drive recruitment of Atlantic herring?

Atlantic herring, Clupea harengus

Atlantic herring illustration, credit NOAA Fisheries

"The herring is a plankton feeder.... Examination of 1,500 stomachs showed that adult herring near Eastport were living solely on copepods and on pelagic euphausiid shrimps (Meganyctiphanes norwegica), fish less than 4 inches long depending on the former alone, while the larger herring were eating both." (Collette et al., 2002)

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When first hatched, and before the disappearance of the yolk sac, the larvae (European) feed on larval snails and crustaceans, on diatoms, and on peridinians, but they soon begin taking copepods, and depend exclusively on these for a time after they get to be 12 mm. long, especially on the little Pseudocalanus elongatus. As they grow older they feed more and more on the larger copepods and amphipods, pelagic shrimps, and decapod crustacean larvae.

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