The NEFSC, in preparing Management Trask Assessment Reports, use a WHAM model to make estimates of spawning stock biomass and biomass at maximum sustainable yield. What is the data that the model uses and could you explain the logic that the model uses?
**WHAM (Woods Hole Assessment Model) is a flexible, state-space age-structured stock assessment framework developed by NEFSC scientists (primarily Tim Miller, Brian Stock, and collaborators).** It is widely used in Northeast U.S. Management Track Assessment Reports to estimate spawning stock biomass (SSB), fishing mortality, and reference points such as biomass at maximum sustainable yield (BMSY or SSB_MSY proxies). It generalizes and extends the earlier ASAP (Age-Structured Assessment Program) model while adding state-space features like random effects and environmental covariates. (LINK) (LINK)
### Data Used by WHAM
WHAM is configured to use the same core data types as ASAP (and can directly import ASAP3 data files), making it straightforward to transition existing Northeast assessments. All observations are treated as having error (observation error), and the model separates this from process error in the population dynamics.
Key data inputs include: (LINK) (LINK)
– **Fishery catch data** (by fleet, e.g., commercial and recreational; often separated by gear or season):
– Aggregate catch (total landings + discards) in weight, by year and fleet.
– Catch-at-age compositions (proportions-at-age in the catch).
– **Survey/index data** (multiple fleets/surveys, e.g., NEFSC bottom trawl surveys in spring/fall, acoustic surveys, or other indices):
– Aggregate indices of abundance (biomass or numbers, by year and index).
– Index age compositions (proportions-at-age from surveys).
– **Biological inputs** (usually provided as empirical time series or fixed/age-specific values):
– Weight-at-age (empirical WAA matrices, used for biomass calculations and sometimes M).
– Maturity-at-age (ogive or time series, for SSB).
– Natural mortality (M; often fixed or age-specific as a starting point, but can be estimated).
– **Optional environmental/climate covariates** (e.g., Cold Pool Index, Gulf Stream Index, temperature time series):
– Observed environmental data (with their own observation error).
– These can link to recruitment, M, catchability, etc.
– **Other** (stock-specific): Selectivity patterns (logistic, double-logistic, or age-specific), catchability (q), and sometimes tagging data (not yet fully implemented in standard WHAM).
Data are provided via an R list object or ASAP3 file. Age compositions use flexible likelihoods (e.g., multinomial, Dirichlet-multinomial, logistic-normal). Aggregate catch and indices use log-normal error. Environmental observations use normal error. (LINK)
In Management Track updates, NEFSC scientists update these data through the most recent year (e.g., commercial/recreational catch, survey indices) and re-fit the model (often with the same configuration as the prior research track benchmark).
### Logic and Model Structure
WHAM is an **age-structured state-space model** implemented in R + TMB (Template Model Builder) for fast maximum likelihood estimation (with random effects). It models the **true (unobserved) population state** (numbers-at-age, NAA) while fitting to noisy observations. This allows explicit separation of **process error** (random variation in biology) from **observation error** (sampling/measurement error in data). (LINK) (LINK)
#### Core Population Dynamics (Process Model)
– **Numbers-at-age (NAA)** follow standard age-structured dynamics:
– Recruitment (age-1 or age-0): Often from a stock-recruit relationship (e.g., Beverton-Holt, Ricker, or mean recruitment) or treated as random effects. Can incorporate environmental effects (linear, polynomial, with lags).
– Older ages: Survival from previous year/age: \( N_{a,y} = N_{a-1,y-1} \exp(-Z_{a-1,y-1}) + \) deviations, where total mortality \( Z = F + M \), fishing mortality \( F_{a,y} = F_y \times s_{a,y} \) (full F times selectivity).
– Plus group for oldest ages.
– **Random effects (process errors)** are the key innovation over classical SCAA models:
– On NAA transitions/survival (recruitment deviations + age/year-specific survival deviations; can be independent, AR(1), or 2D AR(1) correlated over age and time).
– On natural mortality M (log-scale, age/year random effects).
– On selectivity (logit-scale deviations, time- or age-varying).
– On catchability q (for indices).
– These use flexible covariance (iid, AR(1), 2D AR(1)) to capture autocorrelation and reduce retrospective bias. (LINK)
– **Environmental covariates** are also state-space: true (latent) environmental state has process error (random walk or AR(1)); observations have error. Effects link nonlinearly to recruitment, M, etc.
The model is fit by maximizing the joint likelihood (data + random effects penalties). This propagates uncertainty naturally into projections and reference points.
#### How SSB Is Estimated
Spawning stock biomass in year *y* is derived directly from the estimated NAA:
\[
\text{SSB}_y = \sum_a N_{a,y} \times \text{maturity}_a \times W_{a,y}
\]
(where \( W_{a,y} \) is weight-at-age). It is calculated at the start of the year or spawning time (stock-specific). The state-space framework smooths and uncertainty-weights the NAA estimates using all data sources. (LINK)
#### How BMSY (and Related Reference Points) Are Estimated
WHAM internally computes biological reference points (BRPs) with uncertainty propagation (via random effects and parameter uncertainty):
– **Often uses SPR (spawning potential ratio) proxies**, common in Northeast assessments: e.g., F_{35\%} or F_{40\%} SPR (fishing mortality that reduces spawning potential per recruit to 35–40% of unfished levels). These are calculated from yield-per-recruit or equilibrium projections using recent averages for selectivity, WAA, maturity, and M.
– **MSY-based points** (F_MSY, SSB_MSY, MSY) can be derived via stock-recruit relationship + equilibrium calculations or projections at the proxy F.
– Projections incorporate random effects, environmental trajectories (if used), and uncertainty for short-term forecasts and status determination (overfished/overfishing). (LINK)
In practice, for many NEFSC Management Track stocks (e.g., bluefish, winter flounder, yellowtail flounder), the base WHAM configuration is chosen during research track benchmarks and then updated with new data. Random effects often reduce retrospective patterns and better account for productivity changes.
This framework makes WHAM more robust to time-varying processes (recruitment, M, selectivity) than traditional models while still being computationally efficient. Full technical details and examples are in the WHAM R package vignettes (timjmiller.github.io/wham) and the primary paper (Stock & Miller 2021). Specific stock reports provide the exact configuration used for each assessment.