Simulate expected yield using the Beverton-Holt Yield Per Recruit model for a slot limit

Main wrapper function to estimate yield using the Beverton-Holt YPR model. This main function accepts a range of values for cf, cm, recruitment length, lower slot limit length, and upper slot limit length.

Usage

yprBH_SlotLL(
  recruitmentTL = NULL,
  lowerSL,
  upperSL,
  cfunder,
  cfin,
  cfabove,
  cm,
  lhparms,
  loi = NULL,
  matchRicker = FALSE
)

Arguments

recruitmentTL: A numeric representing the minimum length limit for recruiting to the fishery in mm.
lowerSL: A numeric representing the length of the lower slot limit in mm.
upperSL: A numeric representing the length of the upper slot limit in mm.
cfunder: Single value, conditional fishing mortality under the lower slot limit.
cfin: Single value, conditional fishing mortality within the lower and upper slot limit.
cfabove: Single value, conditional fishing mortality over the upper slot limit.
cm: A numeric vector of conditional natural mortality.
lhparms: A named vector or list that contains values for each N0, tmax, Linf, K, t0, LWalpha, and LWbeta. See makeLH for definitions of these life history parameters. Also see details.
loi: A numeric vector for lengths of interest. Used to determine number of fish that reach desired lengths.
matchRicker: A logical that indicates whether the yield function should match that in Ricker (1975). Defaults to TRUE. The only reason to changed to FALSE is to try to match output from FAMS. See the FAMS vs Ricker article.

Value

A data.frame with the following calculated values:

yieldTotal is the calculated total yield
yieldUnder is the calculated yield under the slot limit
yieldIn is the calculated yield within the slot limit
yieldAbove is the calculated yield above the slot limit
nharvTotal is the calculated total number of harvested fish
ndieTotal is the calculated total number of fish that die of natural death
nharvestUnder is the number of harvested fish under the slot limit
nharvestIn is the number of harvested fish within the slot limit
nharvestAbove is the number of harvested fish above the slot limit
n0die is the number of fish that die of natural death before entering the fishery at a minimum length
ndieUnder is the number of fish that die of natural death between entering the fishery and the lower slot limit
ndieIn is the number of fish that die of natural deaths within the slot limit
ndieAbove is the number of fish that die of natural deaths above the slot limit
nrUnder is the number of fish at time trUnder (time they become harvestable size under the slot limit)
nrIn is the number of fish at time trIn (time they reach the lower slot limit size)
nrAbove is the number of fish at time trAbove (time they reach the upper slot limit size)
trUnder is the time for a fish to recruit to a minimum length limit (i.e., time to enter fishery)
trIn is the time for a fish to recruit to a lower length limit of the slot limit
trOver is the time for a fish to recruit to a upper length limit of the slot limit
avglenUnder is the average length of fish harvested under the slot limit
avglenIn is the average length of fish harvested within the slot limit
avglenAbove is the average length of fish harvested above the slot limit
avgwtUnder is the average weight of fish harvested under the slot limit
avgwtIn is the average weight of fish harvested within the slot limit
avgwtAbove is the average weight of fish harvested above the slot limit
nAtxxx is the number that reach the length of interest supplied. There will be one column for each length of interest.
cm A numeric representing conditional natural mortality
expUnder is the exploitation rate under the slot limit
expIn is the exploitation rate within the slot limit
expAbove is the exploitation rate above the slot limit
FUnder is the estimated instantaneous rate of fishing mortality under the slot limit
FIn is the estimated instantaneous rate of fishing mortality within the slot limit
FAbove is the estimated instantaneous rate of fishing mortality above the slot limit
MUnder is the estimated instantaneous rate of natural mortality under the slot limit
MIn is the estimated instantaneous rate of natural mortality within the slot limit
MAbove is the estimated instantaneous rate of natural mortality above the slot limit
ZUnder is the estimated instantaneous rate of total mortality under the slot limit
ZIn is the estimated instantaneous rate of total mortality within the slot limit
ZAbove is the estimated instantaneous rate of total mortality above the slot limit
SUnder is the estimated total survival under the slot limit
SIn is the estimated total survival within the slot limit
SAbove is the estimated total survival above the slot limit
cfUnder A numeric representing conditional fishing mortality
cfIn A numeric representing conditional fishing mortality
cfOver A numeric representing conditional fishing mortality
recruitmentTL A numeric representing the minimum length limit for recruiting to the fishery in mm.
lowerSL A numeric representing the length of the lower slot limit in mm.
upperSL A numeric representing the length of the upper slot limit in mm.
N0 A numeric representing the initial number of new recruits entering the fishery OR a vector or list that contains named values for each N0, Linf, K, t0, LWalpha, LWbeta, and tmax
Linf A numeric representing the point estimate of the asymptotic mean length (L-infinity) from the von Bertalanffy growth model in mm
K A numeric representing the point estimate of the Brody growth coefficient from the von Bertalanffy growth model
t0 A numeric representing the point estimate of the x-intercept (i.e., theoretical age at a mean length of 0) from the von Bertalanffy growth model
LWalpha A numeric representing the point estimate of alpha from the length-weight regression on the log10 scale.
LWbeta A numeric representing the point estimate of beta from the length-weight regression on the log10 scale.
tmax An integer representing maximum age in the population in years

Details

Details will be filled out later

Author

Jason C. Doll, jason.doll@fmarion.edu

Examples

#Load other required packages for organizing output and plotting
library(ggplot2)  #for plotting
library(dplyr)    #for select
library(tidyr)    #for pivot_longer

# Life history parameters to be used below
LH <- makeLH(N0=100,tmax=15,Linf=592,K=0.20,t0=-0.3,LWalpha=-5.528,LWbeta=3.273)
# conditional natural mortality vector
cm <- seq(from = 0.1, to = 0.9, by = 0.1)
# length of interest vector
loi <- c(200,250,300,325,350)

#Estimate yield based on a protected slot limit
 Res_1 <- yprBH_SlotLL(recruitmentTL=200,lowerSL=250,upperSL=325,
                       cfunder=0.25,cfin=0.0,cfabove=0.15,cm=cm,
                       lhparms=LH,loi=c(200,250,300,325,350))

 Res_1
#>    yieldTotal yieldUnder yieldIn   yieldAbove nharvTotal ndieTotal
#> 1 46197.75428 2134.02263       0 44063.731657 46.4972295 33.877878
#> 2 19470.46525 1661.31736       0 17809.147884 26.2230471 40.820004
#> 3  8398.37800 1251.53890       0  7146.839100 15.3741194 37.919849
#> 4  3685.37197  903.25539       0  2782.116585  9.1781028 31.485803
#> 5  1625.61154  614.90035       0  1010.711189  5.4378755 24.061504
#> 6   707.41176  384.73474       0   322.677013  3.0898650 16.823205
#> 7   292.44938  210.78782       0    81.661558  1.5937619 10.403811
#> 8   103.91797   90.75603       0    13.161937  0.6667805  5.207535
#> 9    22.48605   21.80087       0     0.685181  0.1607166  1.572193
#>   nharvestUnder nharvestIn nharvestAbove    n0die ndieUnder     ndieIn
#> 1    14.3001921          0  32.197037424 16.93639  5.237294  7.7673445
#> 2    11.1865599          0  15.036487211 32.49751  8.676970 11.4974691
#> 3     8.4736976          0   6.900421751 46.64404 10.505888 12.2698331
#> 4     6.1545044          0   3.023598400 59.32995 10.928309 11.0537921
#> 5     4.2212588          0   1.216616732 70.50022 10.170789  8.7018157
#> 6     2.6654563          0   0.424408716 80.08692  8.489694  5.9406702
#> 7     1.4775667          0   0.116195279 88.00243  6.183736  3.3592771
#> 8     0.6466386          0   0.020141855 94.12568  3.617621  1.3904478
#> 9     0.1595880          0   0.001128596 98.26709  1.277330  0.2788736
#>     ndieAbove   nrUnder       nrIn     nrAbove  trUnder     trIn  trOver
#> 1 20.87323905 83.063612 63.5261255 55.75878105 1.761224 2.443479 3.68129
#> 2 20.64556520 67.502485 47.6389553 36.14148621 1.761224 2.443479 3.68129
#> 3 15.14412843 53.355962 34.3763764 22.10654334 1.761224 2.443479 3.68129
#> 4  9.50370239 40.670046 23.5872325 12.53344041 1.761224 2.443479 3.68129
#> 5  5.18889991 29.499778 15.1077308  6.40591513 1.761224 2.443479 3.68129
#> 6  2.39283987 19.913084  8.7579328  2.81726260 1.761224 2.443479 3.68129
#> 7  0.86079792 11.997573  4.3362705  0.97699339 1.761224 2.443479 3.68129
#> 8  0.19946640  5.874316  1.6100560  0.21960825 1.761224 2.443479 3.68129
#> 9  0.01599007  1.732910  0.2959923  0.01711867 1.761224 2.443479 3.68129
#>   avglenUnder avglenIn avglenAbove avgwtUnder avgwtIn avgwtAbove    nAt200
#> 1    225.5013        0    443.8067   149.2303       0  1368.5648 83.063612
#> 2    225.1683        0    424.6353   148.5101       0  1184.3955 67.502485
#> 3    224.7908        0    407.5833   147.6969       0  1035.7105 53.355962
#> 4    224.3558        0    393.1118   146.7633       0   920.1343 40.670046
#> 5    223.8426        0    381.0284   145.6675       0   830.7556 29.499778
#> 6    223.2179        0    370.8494   144.3410       0   760.2978 19.913084
#> 7    222.4198        0    362.0448   142.6588       0   702.7958 11.997573
#> 8    221.3140        0    354.0829   140.3505       0   653.4620  5.874316
#> 9    219.4936        0    346.2120   136.6072       0   607.1089  1.732910
#>       nAt250      nAt300      nAt325     nAt350  cm  expUnder expIn   expAbove
#> 1 63.5261255 58.45086262 55.75878105 48.8794721 0.1 0.2378792     0 0.14257140
#> 2 47.6389553 39.93702691 36.14148621 29.9002613 0.2 0.2252683     0 0.13484863
#> 3 34.3763764 25.93244414 22.10654334 17.1270909 0.3 0.2120703     0 0.12677377
#> 4 23.5872325 15.75263905 12.53344041  9.0017108 0.4 0.1981511     0 0.11826676
#> 5 15.1077308  8.73574294  6.40591513  4.2064335 0.5 0.1833156     0 0.10921127
#> 6  8.7579328  4.24537168  2.81726260  1.6577675 0.6 0.1672608     0 0.09942671
#> 7  4.3362705  1.67453146  0.97699339  0.4990840 0.7 0.1494673     0 0.08860398
#> 8  1.6100560  0.45129000  0.21960825  0.0919120 0.8 0.1288953     0 0.07612528
#> 9  0.2959923  0.04797287  0.01711867  0.0050959 0.9 0.1027330     0 0.06032395
#>      FUnder FIn    FAbove    MUnder       MIn    MAbove    ZUnder       ZIn
#> 1 0.2876821   0 0.1625189 0.1053605 0.1053605 0.1053605 0.3930426 0.1053605
#> 2 0.2876821   0 0.1625189 0.2231436 0.2231436 0.2231436 0.5108256 0.2231436
#> 3 0.2876821   0 0.1625189 0.3566749 0.3566749 0.3566749 0.6443570 0.3566749
#> 4 0.2876821   0 0.1625189 0.5108256 0.5108256 0.5108256 0.7985077 0.5108256
#> 5 0.2876821   0 0.1625189 0.6931472 0.6931472 0.6931472 0.9808293 0.6931472
#> 6 0.2876821   0 0.1625189 0.9162907 0.9162907 0.9162907 1.2039728 0.9162907
#> 7 0.2876821   0 0.1625189 1.2039728 1.2039728 1.2039728 1.4916549 1.2039728
#> 8 0.2876821   0 0.1625189 1.6094379 1.6094379 1.6094379 1.8971200 1.6094379
#> 9 0.2876821   0 0.1625189 2.3025851 2.3025851 2.3025851 2.5902672 2.3025851
#>      ZAbove SUnder SIn SAbove cfUnder cfIn cfOver recruitmentTL lowerSL upperSL
#> 1 0.2678794  0.675 0.9  0.765    0.25    0   0.15           200     250     325
#> 2 0.3856625  0.600 0.8  0.680    0.25    0   0.15           200     250     325
#> 3 0.5191939  0.525 0.7  0.595    0.25    0   0.15           200     250     325
#> 4 0.6733446  0.450 0.6  0.510    0.25    0   0.15           200     250     325
#> 5 0.8556661  0.375 0.5  0.425    0.25    0   0.15           200     250     325
#> 6 1.0788097  0.300 0.4  0.340    0.25    0   0.15           200     250     325
#> 7 1.3664917  0.225 0.3  0.255    0.25    0   0.15           200     250     325
#> 8 1.7719568  0.150 0.2  0.170    0.25    0   0.15           200     250     325
#> 9 2.4651040  0.075 0.1  0.085    0.25    0   0.15           200     250     325
#>    N0 Linf   K   t0 LWalpha LWbeta tmax
#> 1 100  592 0.2 -0.3  -5.528  3.273   15
#> 2 100  592 0.2 -0.3  -5.528  3.273   15
#> 3 100  592 0.2 -0.3  -5.528  3.273   15
#> 4 100  592 0.2 -0.3  -5.528  3.273   15
#> 5 100  592 0.2 -0.3  -5.528  3.273   15
#> 6 100  592 0.2 -0.3  -5.528  3.273   15
#> 7 100  592 0.2 -0.3  -5.528  3.273   15
#> 8 100  592 0.2 -0.3  -5.528  3.273   15
#> 9 100  592 0.2 -0.3  -5.528  3.273   15

# Plot results
# Total Yield vs Conditional Natural Mortality (cm)
ggplot(data=Res_1,mapping=aes(x=cm,y=yieldTotal)) +
  geom_point() +
  geom_line() +
  labs(y="Total Yield (g)",x="Conditional Natural Mortality (cm)") +
  theme_bw()



# Yield under, in, and above the slot limit vs Conditional Natural Mortality (cm)
# Select columns for plotting
plot_data <- Res_1 |>
  select(cm, yieldUnder, yieldIn, yieldAbove) |>
  pivot_longer(!cm, names_to="YieldCat",values_to="Yield")

# Generate plot
ggplot(data=plot_data,mapping=aes(x=cm,y=Yield,group=YieldCat,color=YieldCat)) +
  geom_point() +
  scale_color_discrete(name="Yield",labels=c("Above SL","In SL","Under SL"))+
  geom_line() +
  labs(y="Total Yield (g)",x="Conditional Natural Mortality (cm)") +
  theme_bw() +
  theme(legend.position = "top")+
  guides(color=guide_legend(title="Yield"))