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Simulate expected yield using below slot limit regulations using the Beverton-Holt Yield-per-Recruit model

Source: R/yprBH_SlotLL.R
yprBH_SlotLL.Rd

Simulate yield below slot length regulations using the Beverton-Holt Yield-per-Recruit (YPR) model with (possibly) multiple values for conditional natural mortality (cm) and chosen values for the lower and upper lengths of the slot (i.e,. lowerSL and upperSL); conditional fishing mortality below (cfBelow), in (cfIn), and above (cfAbove) the slot; and length when fish recruit to the fishery (recruitmentTL).

Usage

yprBH_SlotLL(
  lowerSL,
  upperSL,
  cfBelow,
  cfIn,
  cfAbove,
  cm,
  lhparms,
  recruitmentTL = NULL,
  loi = NULL,
  matchRicker = FALSE,
  label = NULL
)

Arguments

lowerSL

A single numeric representing the length of the lower slot limit in mm. See details. Must be less than upperSL.

upperSL

A single numeric representing the length of the upper slot limit in mm. See details. Must be less than Linf in lhparms.

cfBelow

A single numeric representing conditional fishing mortality below the lower slot limit length. Must be between 0 and 1 (inclusive).

cfIn

A single numeric representing conditional fishing mortality between the lower and upper slot limit lengths (i.e., "in the slot"). Must be between 0 and 1 (inclusive).

cfAbove

A single numeric representing conditional fishing mortality above the upper slot limit length. Must be between 0 and 1 (inclusive).

cm

A numeric vector of conditional natural mortality values. All values must be between 0 and 1 (inclusive).

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.

recruitmentTL

A single numeric that represents the minimum length (in mm) for recruiting to the fishery. Cannot be greater than lowerSL.

loi

A numeric vector of lengths (in mm) of interest. Used to determine number of fish that reach these lengths. All must be less than Linf in lhparms.

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.

label

An optional string to label the type of slot limit being simulated.

Value

A data.frame with the following calculated values:

  • yieldTotal is the calculated total yield

  • yieldBelow is the calculated yield below 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

  • nharvestBelow is the number of harvested fish below 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

  • ndieBelow 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

  • nrBelow is the number of fish at time trBelow (time they become harvestable size below 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)

  • trBelow 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

  • avglenBelow is the average length of fish harvested below 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

  • avgwtBelow is the average weight of fish harvested below 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

  • expBelow is the exploitation rate below the slot limit

  • expIn is the exploitation rate within the slot limit

  • expAbove is the exploitation rate above the slot limit

  • FBelow is the estimated instantaneous rate of fishing mortality below 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

  • MBelow is the estimated instantaneous rate of natural mortality below 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

  • ZBelow is the estimated instantaneous rate of total mortality below 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

  • SBelow is the estimated total survival below the slot limit

  • SIn is the estimated total survival within the slot limit

  • SAbove is the estimated total survival above the slot limit

For convenience the data.frame also contains the model input values (lowerSL, upperSL, cfBelow, cfIn, cfOver, cm from input vectors; N0; Linf; K; t0; LWalpha; LWbeta; and tmax from lhparms) and, optionally, the string provided in label.

Details

Details will be filled out later.

Note that the main calculations are in the internal yprBH_slot_func (use rFAMS:::yprBH_slot_func to see that source code).

See also

yprBH_MinLL for estimating yield with the yield-per-recruit model using a minimum length limits, or dpmBH_MinLL for estimating yield with a dynamic pool model using a minimum length limit.

See this demonstration page for more examples of this function.

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)

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

Res_1
#>    yieldTotal yieldBelow 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
#>   nharvestBelow nharvestIn nharvestAbove    n0die ndieBelow     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   nrBelow       nrIn     nrAbove  trBelow     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
#>   avglenBelow avglenIn avglenAbove avgwtBelow 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  expBelow 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
#>      FBelow FIn    FAbove    MBelow       MIn    MAbove    ZBelow       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 SBelow SIn SAbove cfBelow 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   label
#> 1 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 2 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 3 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 4 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 5 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 6 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 7 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 8 100  592 0.2 -0.3  -5.528  3.273   15 250-325
#> 9 100  592 0.2 -0.3  -5.528  3.273   15 250-325

# 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 below, in, and above the slot limit vs Conditional Natural Mortality (cm)
# Select columns for plotting
plot_data <- Res_1 |>
  select(cm, yieldBelow, 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","Below 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"))