The FISHE Process

Depletion-Corrected Average Catch (DCAC) uses historical catch data and an estimated natural mortality rate to determine potential sustainable yield. An extension of potential-yield models, DCAC is based on the theory that average catch is sustainable if stock abundance has not changed substantially. The method differs from simple extrapolation of average catch to estimate sustainable yield by correcting for the initial depletion in fish abundance typical of many fisheries. DCAC divides the target stock into two categories: a sustainable yield component and an unsustainable “windfall” component, which is based upon a one-time drop in stock abundance for a newly established fishery. DCAC calculates a sustainable fishery yield, provided the stock is kept at historical abundance levels.

Software for conducting DCAC can be downloaded free of charge from the NOAA Fisheries Toolbox website at https://nmfs-fish-tools.github.io/. 

Inputs:

• Common Life History Parameters
• Historical catch data (preferably ten years or more), including average catch and any approximate relative changes in stock size during the period the catch was taken
• Estimated initial catch or unfished biomass
• Natural mortality rate (M) (preferably .02 or smaller, making this method more suitable for long-lived fish than for short-lived fish)
• Ratio of the fishing rate at Maximum Sustainable Yield (FMSY) to the natural mortality rate (M) (F_MSY/M)

Outputs:

• Sustainable Yield* (based on average catch).

*Not to be used for setting overfishing limits (OFLs) because it does not account for low stock size.

Input Sensitivities, Assumptions and Caveats:

• Performs poorly with low starting abundance levels and should be used with caution for targets that are in rebuilding programs
• Assumes life history data are accurate
• Assumes change in stock status over time is known
• Assumes average catch has been sustainable if abundance has not changed
• Assumes catch is composed of both Sustainable catch and "Windfall" (unsustainable) catch. Model adjusts average catch to account for the Windfall
• Assumes summing the catch over the time series (years of available data) represents relationships of F_MSY/M and B_MSY/B₀

Reference points:

• stock status-based reference point to estimate sustainable yield, as a reference value to control F.
• F_MSY /M
• B_MSY /B_o

Recommendations:

Fishing mortality is adjusted through harvest control methods (e.g. catch limits, seasons, or spatial closures) based on how far apart these values are from TRP & LRP for OFL.

Depletion-Based Stock Reduction Analysis (DB-SRA) combines DCAC with a probability analysis to more closely link stock production with biomass and evaluate potential changes in abundance over time. Using Monte Carlo simulations, DB-SRA provides probability distributions for stock size over a given time period, under varying recruitment rates. The addition of a probability analysis increases the reliability and decreases uncertainties associated with historical biomass estimates generated from DCAC, however this method requires a complete time series of historical catch data, which rules it out for many data-limited fisheries.

Inputs:

• Common Life History Parameters
• Complete time series of historical catches
• Level of current depletion
• Estimate of age at recruitment to the fishery
• Natural mortality rate (M)

Outputs:

• Probability distributions for biological reference points such as: unfished biomass; MSY; the overfishing limit (OFL), and the distributions of stock size over time
• The most productive fishing rate (F) relative to natural mortality (M) (F_MSY/M)
• The most productive stock size relative to unfished (B_MSY/B₀)

Input Sensitivities, Assumptions and Caveats:

• Performs poorly with low starting abundance levels and should be used with caution for targets that are in rebuilding programs
• Assumes life history data are accurate
• Need to be certain that you have catch data from the start of the fishery
• Assumes approximate relative changes in stock size over time is known
• Assumes average catch has been sustainable if abundance has not changed
• Assumes catch is composed of both Sustainable catch and "Windfall" (unsustainable) catch. (Model adjusts average catch to account for the Windfall)
• Assumes summing the catch over the time series (years of available data) represents relationships of F_MSY/M and B_MSY/B₀

Reference points:

• stock status-based reference point to estimate sustainable yield, as a reference value to control F
• F_MSY /M
• B_MSY /B₀

Recommendations:

Adjust fishing mortality through harvest control methods (e.g. catch limits, seasons, or spatial closures) based on how far apart these values are from TRP & LRP for OFL.

The CMSY method implements a stock-reduction analysis with Schaefer biomass dynamics similar to the original Catch-MSY method. It requires a prior distribution on population growth (r) and carrying capacity (K) as well as priors on the relative proportion of biomass at the beginning and end of the time series compared to unfished biomass (depletion). The method assumes r and K do not change over time. CMSY was modified from the original Catch-MSY method to generate biomass trends, in addition to Maximum Sustainable Yield (MSY), from all viable r-K pairs and produce an estimate of B/BMSY from the median trend. This was done by running the Schaefer model repeatedly using the catch time series and each viable r-K pair, and computing the arithmetic mean biomass ratio in each year along with upper and lower quartiles.

Inputs:

• Catch time series (including discards)
• Estimated ranges of stock size in the first and final years of catch data (B_initial and B_final)
• Life history information (i.e. r and K growth rates)

Outputs:

• Maximum Sustainable Yield (MSY)
• A time series of biomass
• A time series of B/B_MSY

Input Sensitivities, Assumptions and Caveats:

• Population growth and carrying capacity (r and K) are assumed to be constant
• Biomass assumed to be a fraction of the carrying capacity at both the beginning and end of the time series of catch data and the growth rate
• Based on Schaefer surplus production model, the overall effects of recruitment, growth, and mortality are pooled into a single production function
• Stock depletion is extremely difficult to estimate, particularly with limited data. Methods have been developed, such as the use of boosted regression tree models that correlate depletion with a range of predictors calculated from catch data, which can improve depletion estimates.
• Assumes catch is known without error
• Assumes stock is undifferentiated (no age, size, or gender differences)
• Assumes only a narrow range of r-K combinations can maintain the population
• Assumes population does not collapse or exceed the carrying capacity
• Ignores the age structure of the stock and does not consider individual growth, recruitment, or the vulnerability of the fish to the fishing gear
• Produces imprecise and biased estimates of B/B_MSY, especially for lightly exploited stocks
• They are also poor classifiers of stock status, but do a lot better in superensembles (combining models to emphasize their particular strengths and downplay their weaknesses)

Reference points:

• B/B_MSY: derived from the modeling approach as described above
• Stock status-based reference point to estimate sustainable yield, as a reference value to control F: F_MSY =r/2
• MSY calculated as: MSY=r*k/4

Recommendations:

Adjust fishing mortality through harvest control methods (e.g. catch limits, seasons, or spatial closures) based on how far apart these values are from TRP & LRP for OFL.

A surplus production model (SPM) is one of the most basic population dynamics models. SPMs view the population as a single unit of biomass, with all individuals (i.e., all age classes) having the same growth and mortality rates. They rely on relatively basic ideas of growth and death and sustainable exploitation. Variation in the population size results from both increases due to growth and reproduction (i.e., production) and decreases due to natural mortality (M) and fishing mortality (F). This method estimates stock biomass and fishing mortality using catch, effort, and any available indices of relative abundance. Estimated biomass and fishing mortality can be examined relative to reference points to determine stock status.

The SPM model we provide in the downloadable Workbook, and linked here, is for the Schaefer model, which assumes the population is at equilibrium. Other SPM models exist, some which do not depend on this assumption (which may be preferable, especially as climate change impacts increase), but these methods generally require more data.

Note: Surplus production models are sometimes called "biomass dynamic models."

Inputs:

• Total catch (if discards are low, then can be just landings), stock biomass estimate
• Preferably more than 10 years of catch and abundance data
• Catchability
• Effort
• Index of relative abundance, such as CPUE, depletion or biomass estimate (optional)

Outputs:

• Estimate of MSY
• Time series of biomass, which can be used to estimate B/B_MSY
• Time series of fishing mortality, which can be used to estimate F/F_MSY

Input Sensitivities, Assumptions and Caveats:

• Sensitive to life history phenomena not incorporated (e.g., age of recruitment);
• Sensitive to survival and growth rate inaccuracies or fluctuations
• Assumes population is at equilibrium
• Assumes the stock has been at both high and low abundance levels
• Assumes catch is known without error
• Assumes stock is undifferentiated (no age, size, or gender differences)
• Assumes catch and/or index is linearly related to the stock abundance
• Assumes entire population covered by catch and index

Reference points:

• F_MSY
• F10%B
• F40%B
• B_MSY

Recommendations:

• Fishing mortality is adjusted through harvest control methods (e.g. catch limits, seasons, or spatial closures) based on how far apart these values are from TRP & LRP.
• Surplus production models produce relative estimates of MSY and F_MSY, and estimates of q (catchability: the parameter that scales abundance indices into biomass estimates), which can be scaled to steepness of the recruitment curve to increase the certainty.

Note: For the purposes of the below discussion, and throughout the FISHE website, the term “Marine Protected Area (MPA)” refers explicitly to an area that has been fully closed off to fishing and other marine uses. Sometimes these areas are called “No-Take Zones” or have other, more specific names, while “MPA” in some places may refer to a less strict form of area-based management (i.e., a “mixed-use area,” or an area where just some forms of fishing are prohibited). However, the following method, and all FISHE methods that rely on “MPAs,” will only work if the area in question is fully closed to all fishing activities. Furthermore, for this method to work, the MPA must also be designed based on scientific guidance, well-enforced, and old enough to have allowed species within its bounds to recover to “unfished” levels.

The Marine Protected Area-Based Decision Tree uses spatially explicit catch and age-length data gathered from fishery-independent scientific surveys from both inside and outside no-take marine protected areas (MPAs) to set and further refine total allowable catch. The data from inside the MPA are used as a baseline for an unfished population. Model inputs are life-history characteristics such as size and age at maturity and natural mortality, catch-per-unit effort (CPUE) information, and age-length data collected from inside and outside marine reserves. Total allowable catch (TAC) is calculated using the current CPUE and target CPUE levels, and then further adjusted with each successive step of the decision tree. The MPA-Based Decision Tree allows managers to set and refine the TAC by assuming that populations within MPAs are representative of an unfished baseline. This assumption should be carefully checked, as illegal fishing, the placement of the MPA in unusually good habitat, and other factors can affect it.  Also, because marine reserves are usually relatively small compared to fishing grounds, care must be taken when extrapolating results to areas that are significantly larger than the MPAs used as reference areas.

Inputs:

• Life-history characteristics such as size and age at maturity and natural mortality rate (M)
• Fishery-independent monitoring of catch-per-unit-effort (CPUE) by size class, OR age-length data collected from inside and outside a well-enforced marine protected area (MPA)
• Current catches or running average can be used to set initial (hypothetical) Total Allowable Catch (TAC) as an input to the decision tree

Outputs:

• Total Allowable Catch (TAC)

Input Sensitivities, Assumptions and Caveats:

• Assumes life history data are accurate
• Assumes individual fish length measurements are accurate
• Assumes length-at-age relationships are accurate
• Assumes the mean generation time of the target from FishBase is accurate
• Assumes habitat quality and productivity is similar inside and outside of MPA for sampled areas
• Assumes populations within MPA are representative of unfished populations (i.e., MPA is old enough and well-enforced enough for fish populations to have equilibrated to unfished conditions)
• Assumes the MPA is large enough to reasonably extrapolate results to the fishing area

Reference points:

• Ratio of size-specific CPUE inside reserve:CPUE outside reserve (i.e., fished area)
• For each level of this CPUE inside:outside ratio (i.e., each step in the decision tree), proxy reference levels of biomass and spawning potential ratio that will be within acceptable thresholds for management goals are provided

Recommendations:

Fishing mortality is adjusted by varying total allowable catch to increase observed CPUE to Xs and away from Y.

The Length-based Integrated Mixed Effects (LIME) method for estimating Spawning Potential Ratio (SPR) works by simulating population dynamics for different age groups (using length as a proxy for age) under varying levels of fishing mortality and recruitment. This allows for the estimation of SPR without depending on the assumption that the population is currently at equilibrium. Additionally, LIME helps analysts tell whether a shift in length composition of the catch (e.g., higher proportions of small fish being caught) is likely due to a shift in fishing mortality, or to a recruitment pulse (e.g., a bigger batch of juveniles joining the population in a given year), which is difficult to determine using other methods (though local knowledge can help).  Each annual recruitment is treated as a random event, while mean recruitment and standard deviation are treated as fixed effects.

LIME uses length of individuals in the catch as a proxy for age based on standard relationships between length and age, so it requires at least one year of length-frequency data. Maximum Sustainable Yield (MSY) is estimated by finding the fishing mortality rate that maximizes Yield-per-Recruit. One of the strengths of LIME is that it can accommodate catch trend and fish abundance data to improve the accuracy of the SPR estimates.  Moreover, with the addition of catch and abundance data, LIME can be used to estimate spawning stock biomass and catchability. 

Simulation testing indicates that LIME produces unbiased estimates of SPR across a range of fishing mortality and recruitment scenarios for a wide variety of species with different life history types  (e.g., opportunistic: small, rapidly maturing, short-lived fishes; periodic: highly fecund fishes with longer life spans; and equilibrium: fishes with fewer offspring but with high parental care and juvenile survivorship), although the method may overestimate SPR for short-lived species (less than 20 years). Using a monthly time step in the model when assessing short-lived species can reduce this bias, while an annual time step results in good results for longer-lived species. Simulation also suggests that at least 100 fish from the catch should be sampled for best results and that care should be taken to include samples from the full range of length frequencies.

Methods like LIME that do not assume equilibrium may be especially important in fisheries that are strongly affected by climate change, since this increases the risk of non-equilibrium conditions.  For more information on LIME, see Rudd and Thorson (2017) and to run LIME, click on the GitHub link (see below).

Inputs:

• Length-frequency data from the catch (sample size at least 100 fish for species that live less than 20 years, at least 500 for species that live longer than 20 years)
• Life history parameters (fecundity, von Bertalanffy (k), natural mortality (M), age-at-maturity, length at age relationships)
• Weight to length parameters (W_a, W_b)
• Fecundity at age parameters (f_a, f_b)

Outputs:

• Selectivity of the gear (lengths at which 50% and 90% of the fish are caught)
• Maximum Sustainable Yield
• Fishing mortality
• Fishing mortality rate that maximizes yield per recruit
• Spawning Potential Ratio (the ratio of current reproductive capacity to maximum potential reproductive capacity of an unfished population)
• Spawning stock biomass (if catch and biomass data are added)

Input Sensitivities, Assumptions and Caveats:

• Assumes individual fish length measurements are accurate
• Assumes length data are representative of length distribution in stock
• Assumes Natural mortality rate (M) is known and accurate
• Assumes life history data are accurate, particularly sensitive to growth and maturity parameter
• Assumes length samples represent length composition of the catch without bias

Reference points:

• F_MSY
• Target reference point for fast growing species: SPR₂₀; slow growing species: SPR₄₀

Recommendations:

• Adjust fishing mortality with harvest control methods (e.g. catch limits, seasons, or spatial closures) based on harvest control rules triggered by status indicators relative to reference points.
• Run LIME with monthly time step for species that live less than 20 years
• Run LIME with annual time step for species that live longer than 20 years