We just developed a F0.1 option for fishing mortality reference points. In adding it to the manual, I took the opportunity to expand the general description of the benchmark (referrence point) module. We will be moving this into the user manual soon, but I thought it useful to give your a preview below:
Rick
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Benchmark (reference point) calculations. This feature of SS is designed to calculate an equilibrium fishing rate intended to serve as a proxy for the fishing rate that would provide maximum sustainable yield (MSY). Then in the forecast module these fishing rates can be used in the projections.
Four reference points can be calculated by SS:
FMSY – Search for the F that produces maximum equilibrium yield (e.g. dead catch), or set FMSY equal to one of the other 3 options
FSPR – Search for the F that produces spawning biomass per recruit that is a specified fraction, termed SPRtarget, of spawning biomass per recruit under unfished conditions. Note that this is in relative terms so does not take into account the spawner-recruit relationship.
FBTGT – Search for the F that produces an absolute spawning biomass that is a specified fraction, termed relative biomass target, of the unfished spawning biomass. Note that this is in absolute terms so takes into account the spawner-recruit relationship.
F0.1 – Search for the F that produces a slope in yield per recruit, dY/dF, that is 10% of the slope at the origin. Note that this option is mutually exclusive with FBTGT. Only one will be calculated and the one that is calculated can serve as the proxy for Fmsy and forecasting.
Estimation: Each of the potential reference points is calculated by searching across a range of F multiplier levels, calculating equilibrium biomass and catch at that F, using Newton-Raphson method to calculate a better F multiplier value, and iterating a fixed number of times to achieve convergence on the desired level.
Calculation: The calculation of equilibrium biomass and catch uses the same code that is used to calculate the virgin conditions and the initial equilibrium conditions. This equilibrium calculation code takes into account all morph, timing, biology, selectivity, and movement conditions as they apply while doing the time series calculations. You can verify this by running SS to calculate Fmsy then hardwire initial F to equal this value, use the F_method approach 2 so each annual F is equal to Fmsy and then set forecast F to be the same Fmsy. Then run SS without estimation and no recruitment deviations. You should see that the population has an initial equilibrium abundance equal to Bmsy and stays at this level during the time series and forecast.
Catch Units: For each fleet, SS always calculates catch in terms of biomass (mt) and numbers (1000s) for encountered (selected) catch, dead catch, and retained catch. These three categories differ only when some fleets have discarding or are designated as a bycatch fleet. SS uses total dead catch biomass as the quantity that is principally reported and the quantity that is optimized when searching for FMSY. The quantity “dead catch” may occasionally be referred to as “yield”.
Biomass Units: The principle measure of fish abundance, for the purpose of reference point calculation, is female reproductive output. This is referred to as SSB (spawning stock biomass) and sometimes just “B” because the typical user settings have one unit of reproductive output (fecundity) per kg of mature female biomass. So when the output label says Bmsy, this is actually the female reproductive output at the proxy for Fmsy.
Fleet allocation: An important concept for the reference point calculation is the allocation of fishing rate among fleets. Internally, this is Bmark_relF(f,s) and it is the fraction of the F multiplier assigned to each fleet, f and season, s. The value, F_multiplier * Bmark_relF(f,s), is the F level for a particular fleet in a particular season and for the age that has a selectivity of 1.0. Other ages will have different F values according to their selectivity.
- The Bmark_relF values can be calculated by SS from a range of years specified in the input for Benchmark Years or it can be set to be the same as the Forecast_RelF, which in turn can be based on a range of years or can be input as a set of fixed values.
- Note that for Bycatch Fleets, the F’s calculated by application of Bmark_relF for a bycatch fleet can be overridden by a F value calculated from a range of years or a fixed F value that is input by the user. If such an override is selected for a bycatch fleet, that F value is not adjusted by changes to the F multiplier. This allows the user to treat a bycatch fleet as a constant background F while the optimal F for other fleets is sought. Also for bycatch fleets, there is user control for whether or not the dead catch from the bycatch fleet is included in the total dead catch that is optimized when searching for Fmsy.
Virgin vs. Unfished: The concept of unfished spawning biomass, SSB_unf, is important to the reference points calculations. Unfished spawning biomass can be potentially different than virgin spawning biomass, SSB_virgin.
- Virgin spawning biomass is calculated from the parameter values associated with the start year of the model configuration and it serves as the basis from which the population model starts and the basis for calculation of stock depletion.
- Unfished spawning biomass can be calculated for any year or range of years, so can change over time as R0, steepness, or biological parameters change.
- In the reference points calculation, the Benchmark Years input specifies the range of time over which various quantities are averaged to calculate the reference points. For biology, selectivity, F’s, and movement the values being averaged are the year-specific derived quantities. But for the SRparms (R0 and steepness), the parameter values themselves are averaged over time.
- During the time series or forecast, the current year’s SSB_unf is used as the basis for the spawner-recruitment curve against which deviations from the spawner-recruitment curve are applied. So if R0 is made time-varying, then the spawner-recruit curve itself is changed. However, if the regime shift parameter is time-varying, then this is an offset from the spawner-recruitment curve and not a change in the curve itself. So changes in R0 will change year-specific reference points and change the expected value for annual recruitments, but changes in regime shift parameter only change the expected value for annual recruitments.
