Depletion-Based Stock Reduction Analysis (DB-SRA) is an assessment method for data-limited fisheries in cases where approximate catches are known from the start of exploitation, but there are no indices of abundance or informative composition data. DB-SRA requires an approximate natural mortality rate (M) and age at maturity. A production function is specified based on the relative location of maximum productivity to carrying capacity, and the relationship of FMSY to M. Given a probability distribution for the depletion level (i.e. B/B0) near the end of the time series, the method derives a probability distribution for unfished biomass B0, and distributions for management reference points. The method was published by Dick and MacCall (Fisheries Research 110:331-341). Arnold and Heppell have evaluated DB-SRA using retrospective analysis.
DB-SRA is best suited for situations in which there is a time-series of historical catches, ideally from the start of the fishery. Also, DB-SRA requires priors on multiple parameters. Some of these can be inferred from the literature but the prior on recent depletion (biomass relative to carrying capacity) drives the results to a substantial extent. Senstivity to this prior should be ideally be examined.
This package is run from R and installed from CRAN. R can be installed from https://cran.r-project.org/.
The recommended way to run R is using RStudio. After you have installed R, then install RStudio. It can be found at https://www.rstudio.com/products/rstudio/download/.
There are several implementations of DB-SRA. The supported version of DB-SRA is available from the fishmethods package within R. Another version can be found in the Data-Limited Methods Toolkit. To use DB-SRA, you first need to install the fishmethods package.
A reference manual for fishmethods and therefore dbsra can be found at “https://cran.r-project.org/web/packages/fishmethods/fishmethods.pdf”.
If you are using this code for the first time, then you need to change eval=FALSE to eval=TRUE.
Check_Install.packages <- function(pkg){
new.pkg <- pkg[!(pkg %in% installed.packages()[, "Package"])]
if (length(new.pkg))
install.packages(new.pkg,dependencies = TRUE) else print(paste0("'",pkg,"' has been installed already!"))
sapply(pkg, require, character.only = TRUE)
}
Check_Install.packages("fishmethods")
## [1] "'fishmethods' has been installed already!"
## Loading required package: fishmethods
## fishmethods
## TRUE
NB Once you have installed fishmethods, you don’t need to run the install.packages code chunk again.
library(fishmethods)
Example <- read.csv("Catches.csv")
# Read in the simulated annual catch data set
Example <- Example[-c(1:11),c(1,3)]
# We have removed the first 11 rows of data as these are all prefishery and zero, also removed the fleet column as only one fleet so not needed
names(Example) <- c("year","catch")
# this makes sure the headings are correct for later use
print(head(Example))
## year catch
## 12 1971 98.9982
## 13 1972 199.1610
## 14 1973 991.5380
## 15 1974 988.8430
## 16 1975 1978.3500
## 17 1976 1999.4000
Our data set was created using Stock Synthesis based on an age at 50% maturity of roughly 10-11 years and a rate of natural mortality of 0.2yr-1 for females and 0.25yr-1 for males. The catch data are in metric tons.
DB-SRA is run using the function dbsra. There are many inputs to this function. These can be divided into general (required) inputs, those related to the priors and those related to the other aspects of the assessment.
The model is run by calling dbsra. The results are the posteriors for the parameters (K, BMSY, MSY, FMSY, UMSY, OFL, BMSY, Bt/K, FMSY/M, BMSY/K, biomass in the last year). The OFL is the catch for the first projection year based on applying FMSY to current biomass. Note that the examples here are based on 100 simulations. This is insufficient for an actual assessment.
The biomass estimates from each simulation are not stored in memory but are automatically saved to a .csv file named “Biotraj-dbsra.csv”. Yearly values for each simulation are stored across columns. The first column holds the likelihood values for each simulation (1 = accepted, 0 = rejected). The number of rows equals the number of simulations (nsims). Thus an error “None of the runs had a likelihood equal to 1” means that none of the runs were accepted.
There are 14 graphs. The default is to produce all of them. A combination of graphs can be selected using the c() statement e.g. c(1,13) or c(1:13).
Below we run the model close to the example settings. This is a reasonably uninformed model (as would often be the case) and shows how DBSRA works in accepting and rejecting various parameter permutations.
par(mfrow=c(2,2))
dbsraOut <- dbsra(year = Example$year,
catch = Example$catch,
catchCV = NULL,
catargs = list(dist="none",low=0,up=Inf,unit="MT"),
agemat=4,
k = list(low=100,up=500000,tol=0.01,permax=1000),
b1k = list(dist="none",low=0.01,up=0.99,mean=1,sd=0.1),
btk = list(dist="beta",low=0.01,up=0.99,mean=0.3,sd=0.1,
refyr=max(Example$year)+1),
fmsym = list(dist="lnorm",low=0.1,up=2,mean=-0.223,sd=0.2),
bmsyk = list(dist="beta",low=0.05,up=0.95,mean=0.4,sd=0.05),
M = list(dist="lnorm",low=0.001,up=1,mean=-1.609,sd=0.4),
graph=c(1:14),
nsims = 100,grout=2)
The output from the function includes a summary of the specified priors (object Initial), the selected parameters (object Parameters) and the values for the management reference points (object Estimates).
print(dbsraOut$Initial)
## Distr Lower Upper Mean SD
## Fmsy/M lnorm 0.1 2 -0.223 0.2
## Br/K beta 0.01 0.99 0.3 0.1
## Bmsy/K beta 0.05 0.95 0.4 0.05
## M lnorm 0.001 1 -1.609 0.4
## refyr <NA> 2002 <NA> <NA> <NA>
## B1/K none 0.01 0.99 1 0.1
print(dbsraOut$Parameters)
## Mean (ll=1) Median (ll=1) 2.5% (ll=1) 97.5% (ll=1) min (ll=1) max (ll=1)
## Fmsy/M 0.752 0.7432 0.5458 1.0090 0.53002146 1.0231011
## Bt/K 0.343 0.3434 0.2036 0.5303 0.19863864 0.5644684
## Bmsy/K 0.388 0.3920 0.3037 0.4369 0.25346124 0.4758752
## M 0.168 0.1624 0.0861 0.3477 0.07081843 0.4886967
## B1/K 1.000 1.0000 1.0000 1.0000 1.00000000 1.0000000
print(dbsraOut$Estimates)
## Mean (ll=1) Median (ll=1) 2.5% (ll=1) 97.5% (ll=1) min (ll=1)
## MSY 2782.432 2727.4521 1840.9497 3774.0821 1.749838e+03
## Bmsy 27703.817 27374.7302 17700.6517 36471.7207 1.658075e+04
## Fmsy 0.125 0.1163 0.0590 0.3060 5.447684e-02
## Umsy 0.106 0.1019 0.0554 0.2115 5.040933e-02
## OFL 2567.882 2363.7366 1142.6355 4619.6790 1.097507e+03
## Brefyr 24515.234 22959.4675 14181.2751 40499.8337 1.321638e+04
## K 71635.047 70786.7114 46861.5149 88343.7228 4.633733e+04
## max (ll=1)
## MSY 3.830901e+03
## Bmsy 3.824943e+04
## Fmsy 3.155663e-01
## Umsy 2.310451e-01
## OFL 5.110425e+03
## Brefyr 4.336656e+04
## K 9.785325e+04
The biomass trajectory is saved to a file Biotraj-dbsra.csv in the working directory. The first column indicates whether a simulation (in rows) is accepted (indicated as a “1”) or rejected (“0”), which should be ignored. These results could therefore be plotted in your own way. We use the example plot of the biomass trajectories here as this is quite a useful plot and easily modified.
par(mfrow=c(1,1))
# Read in the biomass output, remove the rejected trajectories, and add headers
Years <- c(Example$year,Example$year[length(Example$year)]+1)
BioT <- read.csv("Biotraj-dbsra.csv",head=F)
BioT <- BioT[BioT[,1]==1,-1]
colnames(BioT) <- Years
Nyear <- length(Years)
BiomassSummary <- matrix(0,ncol=5,nrow=Nyear)
for (Iyear in 1:Nyear)
BiomassSummary[Iyear,] <- quantile(BioT[,Iyear],
prob=c(0.05,0.25,0.5,0.75,0.95))
ymax <- max(BiomassSummary)
plot(Years,BiomassSummary[,3],xlab="Year",
ylab="Biomass",ylim=c(0,ymax*1.1),
yaxs="i",type="l",xaxs="i")
polygon(c(Years,rev(Years)),c(BiomassSummary[,1],
rev(BiomassSummary[,5])),col="gray50")
polygon(c(Years,rev(Years)),c(BiomassSummary[,2],
rev(BiomassSummary[,4])),col="gray90")
lines(Years,BiomassSummary[,3],col='red',lwd=2)
Stock status (biomass relative to carrying capacity) can be evaluated from the Bt/K output using dbsraOut$Parameters. It is possible to conduct projections based on the results of DB-SRA using the dlproj function. The key inputs for this function are:
ProjRes <- dlproj(dlobj=dbsraOut,projyears=5,projtype=2,projcatch=c(1400,1400,1000,1000,100))
print(summary(t(ProjRes$ProjBio)))
## 2002 2003 2004 2005
## Min. :13216 Min. :13670 Min. :14231 Min. :15270
## 1st Qu.:17970 1st Qu.:19488 1st Qu.:20106 1st Qu.:21204
## Median :22959 Median :24354 Median :25869 Median :27562
## Mean :24515 Mean :25659 Mean :26862 Mean :28503
## 3rd Qu.:28043 3rd Qu.:29123 3rd Qu.:30353 3rd Qu.:32048
## Max. :43367 Max. :45414 Max. :47427 Max. :49783
## 2006 2007
## Min. :16335 Min. :18318
## 1st Qu.:22390 1st Qu.:24680
## Median :29650 Median :32708
## Mean :30157 Mean :32714
## 3rd Qu.:34182 3rd Qu.:37345
## Max. :52076 Max. :55192
It is possible to apply control rules other than the Overfishing Limit (OFL) control rule to the results from DB-SRA. For example, the following code computes a posterior for the catch limit based on a control rule that sets the exploitation rate to EMSY when stock size is above 35% of K and reduces it linearly to zero at 20% of K. Note that this code does not assume that refyr is the last year+1.
# Extract the biomass for last year+1 and the parameters that are selected
CurrentBiomass <- BioT[,Nyear]
Parameters <- dbsraOut$Values[dbsraOut$Values[,1]==1,-1]
Nvectors <- length(CurrentBiomass)
# Find the multiplier for the catch limits
Multiplier <- rep(1,Nvectors)
for (Isim in 1:Nvectors)
{
if (CurrentBiomass[Isim] < 0.2*Parameters$K[Isim])
{
Multiplier[Isim] <- 0
}
else
{
if (CurrentBiomass[Isim] < 0.35*Parameters$K[Isim])
Multiplier[Isim] <- (CurrentBiomass[Isim]/Parameters$K[Isim]-0.2)/(0.35-0.2)
}
}
CatchLimits <- CurrentBiomass*Parameters$Umsy*Multiplier
par(mfrow=c(2,2))
hist(CurrentBiomass/Parameters$K[Isim],xlab="Depletion",main="")
hist(Multiplier,xlab="Multiplier",main="")
hist(CatchLimits,xlab="Catch Limit",main="")
Out of interest, how well do we do if we use (close to) the actual values from the simulation? The run below sets the parameters close to the actual values, although with a uniform distribution around the values, not as a beta or lognormal distribution, which would make the model very informative. The exception is the value for K for which we use an uninformative prior.
par(mfrow=c(2,2))
dbsraOutNew <- dbsra(year = Example$year,
catch = Example$catch,
catchCV = NULL,
catargs = list(dist="none",low=0,up=Inf,unit="MT"),
agemat=10,
k = list(dist="unif",low=20000,up=250000,mean=21000, sd=0.05),
b1k = list(dist="unif",low=0.95,up=0.99, mean=0.98, sd=0.05),
btk = list(dist="unif",low=0.20,up=0.30,mean=0.27,sd=0.04,
refyr=max(Example$year)+1),
fmsym = list(dist="unif",low=0.65,up=0.85, mean=0.8, sd=0.05),
bmsyk = list(dist="unif",low=0.2,up=0.3,mean=0.261,sd=0.05),
M = list(dist="unif",low=0.2,up=0.3, mean=0.25,sd=0.05),
graph=c(1:14),
nsims = 100,grout=1)
## Warning in dbsra(year = Example$year, catch = Example$catch, catchCV = NULL, :
## <3 runs were rejected!
Let’s compare the two sets of parameter values:
Compare <- as.data.frame(cbind(rownames(dbsraOut$Estimates),dbsraOut$Estimates[,"Median (ll=1)"],dbsraOutNew$Estimates[,"Median (ll=1)"]))
names(Compare) <- c("Estimate", "Median Uninformed", "Median Informed")
print(Compare)
## Estimate Median Uninformed Median Informed
## 1 MSY 2727.4521 3186.0663
## 2 Bmsy 27374.7302 21052.0597
## 3 Fmsy 0.1163 0.1816
## 4 Umsy 0.1019 0.1481
## 5 OFL 2363.7366 3206.059
## 6 Brefyr 22959.4675 21247.3087
## 7 K 70786.7114 84638.0202
Dick, E.J. and A.D. MacCall. 2011. Depletion-Based Stock Reduction Analysis: A catch-based method for determining sustainable yields for data-poor fish stocks. Fisheries Research 110:331-341. https://doi.org/10.1016/j.fishres.2011.05.007.
Arnold, L.M. and S.S. Heppell, 2015. Testing the robustness of data-poor assessment methods to uncertainty in catch and biology: a retrospective approach. ICES Journal of Marine Science 72:243-250. https://doi.org/10.1093/icesjms/fsu077.
Carruthers, T.R., Punt, A.E., Walters, C.J., MacCall, A., McAllister, M.K., Dick, E.J. and J. Cope. 2015. Evaluating methods for setting catch limits in data-limited fisheries. Fisheries Research 153:48-68. https://doi.org/10.1016/j.fishres.2013.12.014.
Wetzel, C.R. and A.E. Punt. 2011. Evaluating the performance of data-moderate and catch-only assessment methods for U.S. west coast groundfish. Fisheries Research 171:170-187. https://doi.org/10.1016/j.fishres.2015.06.005.
Dick, E.J. and A.D. MacCall. 2010. Estimates of sustainable yield for 50 data-poor stocks in the Pacific Coast groundfish fishery management plan. Technical memorandum. Southwest fisheries Science Centre, Santa Cruz, CA. National Marine Fisheries Service, National Oceanic and Atmospheric Administration of the U.S. Department of Commerce NOAA-TM-NMFS-SWFSC-460.
Cope, J., Dick, E.J., MacCall, A., Monk, M., Soper, B. and C. Wetzel. 2013. Data-moderate stock assessments for brown, China, copper, sharpchin, stripetail and yellowtail rockfishes and English and rex soles in 2013.