Type:	Package
Title:	Tropical Fisheries Analysis
Version:	1.6.6
Date:	2025-04-06
Depends:	R (≥ 3.0.0)
Imports:	Matrix, msm, reshape2, MASS, GenSA, GA, stats, utils, parallel, doParallel
LazyData:	true
Description:	A compilation of fish stock assessment methods for the analysis of length-frequency data in the context of data-poor fisheries. Includes methods and examples included in the FAO Manual by P. Sparre and S.C. Venema (1998), "Introduction to tropical fish stock assessment" (https://openknowledge.fao.org/server/api/core/bitstreams/bc7c37b6-30df-49c0-b5b4-8367a872c97e/content), as well as other more recent methods.
License:	GPL-3
NeedsCompilation:	no
BugReports:	https://github.com/tokami/TropFishR/issues
URL:	https://github.com/tokami/TropFishR
Encoding:	UTF-8
RoxygenNote:	7.3.2
Suggests:	graphics, grDevices, knitr, rmarkdown, plyr
VignetteBuilder:	knitr
Packaged:	2025-05-01 14:41:52 UTC; tobm
Author:	Tobias K. Mildenberger [aut, cre], Marc H. Taylor [aut], Matthias Wolff [aut]
Maintainer:	Tobias K. Mildenberger <t.k.mildenberger@gmail.com>
Repository:	CRAN
Date/Publication:	2025-05-01 15:40:02 UTC

Bhattacharya's method

Description

Find relative frequencies and frequency distribution of distinct cohorts in the observed length frequency distribution by resolving it into Gaussian components.

Usage

Bhattacharya(param, n_rnorm = 1000, savePlots = FALSE)

Arguments

Details

This method includes the identify function, which allows to choose points on a graphical device manually. To stop this process please press right mouse click on the graph, and in case you are working on a windows maschine click on "Stop". An error will be caused if the graphical device is closed manually. After you have selected the points for regression analysis you will be asked if you want to redo the selection or if you want to continue. Please enter in the Console "y" for continuation if you are satisfied with your selection and the corresponding Gaussian distribution or enter "redo" if you want to repeat the selection procedure. This function allows a maximum of 12 cohorts or seperate distributions in one sample. Please find more details in the Vignette of this package or in the FAO manual by Sparre and Venema (1998) (Section 3.4.1, p. 80).

Value

A list with the input parameters and

• regressionLines dataframe with intercept, slope, start and end points of the regression lines,

• Lmean_SD_list dataframe with the mean length (Lmean), standard deviation (SD), and seperation index (SI) for each cohort,

• bhat_results dataframe with the results of the Bhattacharya method,

• distributions list with the x and y values of selected distributions,

• cohort_plots list with analysis plots (when savePlots = TRUE).

References

Bhattacharya, C.G., 1967. A simple method of resolution of a distribution into Gaussian components, Biometrics, 23:115-135

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# The following example requires to choose certain values for the regression analyses:
# first cohort:   point  2 to  8
# second cohort:  point 12 to 17
# third cohort:   point 19 to 23
# fourth cohort:  point 26 to 30


 data(synLFQ1)
 Bhattacharya(param = synLFQ1)

ELEFAN

Description

Electronic LEngth Frequency ANalysis for estimating growth parameter.

Usage

ELEFAN(
  lfq,
  Linf_fix = NA,
  Linf_range = NA,
  K_range = exp(seq(log(0.1), log(10), length.out = 100)),
  C = 0,
  ts = 0,
  MA = 5,
  addl.sqrt = FALSE,
  agemax = NULL,
  flagging.out = TRUE,
  method = "optimise",
  cross.date = NULL,
  cross.midLength = NULL,
  cross.max = FALSE,
  hide.progressbar = FALSE,
  plot = FALSE,
  contour = FALSE,
  add.values = TRUE,
  rsa.colors = terrain.colors(20),
  plot_title = TRUE
)

Arguments

Details

This functions allows to perform the K-Scan and Response surface analysis to estimate growth parameters. It combines the step of restructuring length-frequency data (lfqRestructure) followed by the fitting of VBGF curves through the restructured data (lfqFitCurves). K-Scan is a method used to search for the K parameter with the best fit while keeping the Linf fixed. In contrast, with response surface analysis both parameters are estimated and the fits are displayed in a heatmap. Both methods use optimise to find the best t_anchor value for each combination of K and Linf. To find out more about t_anchor, please refer to the Details description of lfqFitCurves. The score value Rn_max is comparable with the score values of the other ELEFAN functions (ELEFAN_SA or ELEFAN_GA) when other settings are consistent (e.g. 'MA', 'addl.sqrt', 'agemax', 'flagging.out').

Value

A list with the input parameters and following list objects:

• rcounts: restructured frequencies,

• peaks_mat: matrix with positive peaks with distinct values,

• ASP: available sum of peaks, sum of posititve peaks which could be potential be hit by growth curves,

• score_mat: matrix with scores for each Linf (only Linf_fix) and K combination,

• t_anchor_mat: maximum age of species,

• ncohort: number of cohorts used for estimation,

• agemax: maximum age of species,

• par: a list with the parameters of the von Bertalanffy growth function:

  • Linf: length infinity in cm,

  • K: curving coefficient;

  • t_anchor: time point anchoring growth curves in year-length coordinate system, corrsponds to peak spawning month,

  • C: amplitude of growth oscillation (if seasonalised = TRUE),

  • ts: summer point of oscillation (ts = WP - 0.5) (if seasonalised = TRUE),

  • phiL: growth performance index defined as phiL = log10(K) + 2 * log10(Linf);

• Rn_max: highest score value

References

Brey, T., Soriano, M., and Pauly, D. 1988. Electronic length frequency analysis: a revised and expanded user's guide to ELEFAN 0, 1 and 2.

Pauly, D. 1981. The relationship between gill surface area and growth performance in fish: a generalization of von Bertalanffy's theory of growth. Meeresforsch. 28:205-211

Pauly, D. and N. David, 1981. ELEFAN I, a BASIC program for the objective extraction of growth parameters from length-frequency data. Meeresforschung, 28(4):205-211

Pauly, D., 1985. On improving operation and use of ELEFAN programs. Part I: Avoiding "drift" of K towards low values. ICLARM Conf. Proc., 13-14

Pauly, D., 1987. A review of the ELEFAN system for analysis of length-frequency data in fish and aquatic invertebrates. ICLARM Conf. Proc., (13):7-34

Pauly, D. and G. R. Morgan (Eds.), 1987. Length-based methods in fisheries research. (No. 13). WorldFish

Pauly, D. and G. Gaschuetz. 1979. A simple method for fitting oscillating length growth data, with a program for pocket calculators. I.C.E.S. CM 1979/6:24. Demersal Fish Cttee, 26 p.

Pauly, D. 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators (Vol. 8). WorldFish.

Quenouille, M. H., 1956. Notes on bias in estimation. Biometrika, 43:353-360

Somers, I. F., 1988. On a seasonally oscillating growth function. ICLARM Fishbyte 6(1): 8-11.

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2): 407 p.

Tukey, J., 1958. Bias and confidence in not quite large samples. Annals of Mathematical Statistics, 29: 614

Tukey, J., 1986. The future of processes of data analysis. In L. V. Jones (Eds.), The Collected Works of John W. Tukey-philosophy and principles of data analysis: 1965-1986 (Vol. 4, pp. 517-549). Monterey, CA, USA: Wadsworth & Brooks/Cole

Examples

data(alba)

### Response Surface Analysis (varies Linf and K) ###

# 'cross' method (used in FiSAT)
fit1 <- ELEFAN(
   lfq = alba, method = "cross",
   Linf_range = seq(from = 10, to = 20, length.out = 10),
   K_range = exp(seq(from = log(0.1), to = log(2), length.out = 20)),
   cross.date = alba$dates[3], cross.midLength = alba$midLengths[4],
   contour = TRUE
)
fit1$Rn_max; unlist(fit1$par)
plot(fit1); points(alba$dates[3], alba$midLengths[4], col=2, cex=2, lwd=2)

# 'cross' method (bin with maximum score crossed)
fit2 <- ELEFAN(
   lfq = alba, method = "cross",
   Linf_range = seq(from = 10, to = 20, length.out = 20),
   K_range = exp(seq(from = log(0.1), to = log(2), length.out = 20)),
   cross.max = TRUE,
   contour = TRUE
)
fit2$Rn_max; unlist(fit2$par)
plot(fit2); points(alba$dates[7], alba$midLengths[9], col=2, cex=2, lwd=2)


# 'optimise' method (default)
fit3 <- ELEFAN(
   lfq = alba, method = "optimise",
   Linf_range = seq(from = 10, to = 20, length.out = 10),
   K_range = exp(seq(from = log(0.1), to = log(2), length.out = 20)),
   contour = TRUE
)
fit3$Rn_max; unlist(fit3$par)
plot(fit3)


### K-Scan (varies K, Linf is fixed) ###

# 'cross' method
fit4 <- ELEFAN(
   lfq = alba, method = "cross",
   Linf_fix = 10,
   K_range = round(exp(seq(from = log(0.1), to = log(2), length.out = 50)),2),
   cross.date = alba$dates[3], cross.midLength = alba$midLengths[4],
   plot = FALSE
)
fit4$Rn_max; unlist(fit4$par)
plot(fit4); points(alba$dates[3], alba$midLengths[4], col=2, cex=2, lwd=2)

ELEFAN_GA

Description

Electronic LEngth Frequency ANalysis with genetic algorithm used for estimating growth parameters.

Usage

ELEFAN_GA(
  lfq,
  seasonalised = FALSE,
  low_par = NULL,
  up_par = NULL,
  popSize = 50,
  maxiter = 100,
  run = maxiter,
  parallel = FALSE,
  pmutation = 0.1,
  pcrossover = 0.8,
  elitism = base::max(1, round(popSize * 0.05)),
  MA = 5,
  addl.sqrt = FALSE,
  agemax = NULL,
  flagging.out = TRUE,
  seed = NULL,
  monitor = FALSE,
  plot = FALSE,
  plot.score = TRUE,
  ...
)

Arguments

Details

A more detailed description of the generic algorithm (GA) can be found in Scrucca (2013). The score value fitnessValue is not comparable with the score value of the other ELEFAN functions (ELEFAN or ELEFAN_SA).

Value

A list with the input parameters and following list objects:

• samplingPeriod: length of sampling period in years,

• samplingDays: time of sampling times in relation to first sampling time,

• delta_t: array with time differences between relative sampling time set to zero and other sampling times,

• rcounts: restructured frequencies,

• peaks_mat: matrix with positive peaks with distinct values,

• ASP: available sum of peaks, sum of posititve peaks which could be potential be hit by growth curves,

• ncohort: maximum age of species,

• agemax: maximum age of species,

• par: a list with the parameters of the von Bertalanffy growth function:

  • Linf: length infinity in cm,

  • K: curving coefficient;

  • t_anchor: time point anchoring growth curves in year-length coordinate system, corrsponds to peak spawning month,

  • C: amplitude of growth oscillation (if seasonalised = TRUE),

  • ts: summer point of oscillation (ts = WP - 0.5) (if seasonalised = TRUE),

  • phiL: growth performance index defined as phiL = log10(K) + 2 * log10(Linf);

• Rn_max: highest value of fitness function, (comparable with ELEFAN and ELEFAN_SA).

References

Brey, T., Soriano, M., and Pauly, D. 1988. Electronic length frequency analysis: a revised and expanded user's guide to ELEFAN 0, 1 and 2.

Pauly, D. and N. David, 1981. ELEFAN I, a BASIC program for the objective extraction of growth parameters from length-frequency data. Meeresforschung, 28(4):205-211

Scrucca, L. (2013). GA: a package for genetic algorithms in R. Journal of Statistical Software, 53(4), 1-37.

Examples

# load data and view catch length frequencies
data(synLFQ4)
plot(synLFQ4, Fname="catch")

# Genetic algorithm
# (if using a multicore processor,
#   consider adding the argument 'parallel=TRUE'
#   to reduce computation time)
output <- ELEFAN_GA(synLFQ4, seasonalised = TRUE,
   low_par = list(Linf = 70, K = 0.25, t_anchor = 0, C = 0, ts= 0),
   up_par = list(Linf = 90, K = 0.7, t_anchor = 1, C = 1, ts = 1),
   popSize = 40, maxiter = 50, run = 20,
   MA = 11, plot = TRUE, seed = 1111)
output$par
output$ASP
output$Rn_max

# compare fitness score (fESP) to
# that calculated with "true" growth parameter values
plot(output, draw = FALSE)
lfqFitCurves(output, par=list(Linf=80, K=0.5, t_anchor=0.25, C=0.75, ts=0.5),
       draw = TRUE, col=1, flagging.out = FALSE)$fESP
lfqFitCurves(output, par=output$par, draw = TRUE, col=2, flagging.out = FALSE)$fESP
legend("top", legend=c("orig.", "GA"), lty=2, col=1:2, ncol=2)

ELEFAN_SA

Description

Electronic LEngth Frequency ANalysis with simulated annealing for estimating growth parameters.

Usage

ELEFAN_SA(
  lfq,
  seasonalised = FALSE,
  init_par = list(Linf = 50, K = 0.5, t_anchor = 0.5, C = 0, ts = 0),
  low_par = NULL,
  up_par = NULL,
  SA_time = 60 * 1,
  maxit = NULL,
  nb.stop.improvement = NULL,
  SA_temp = 1e+05,
  verbose = TRUE,
  MA = 5,
  addl.sqrt = FALSE,
  agemax = NULL,
  flagging.out = TRUE,
  plot = FALSE,
  plot.score = TRUE
)

Arguments

Details

A more detailed description of the simulated annealing (SA) can be found in Xiang et al. (2013). The score value cost_value is not comparable with the score value of the other ELEFAN functions (ELEFAN or ELEFAN_GA).

Value

A list with the input parameters and following list objects:

• rcounts: restructured frequencies,

• peaks_mat: matrix with positive peaks with distinct values,

• ASP: available sum of peaks, sum of posititve peaks which could be potential be hit by growth curves,

• ncohort: maximum age of species,

• agemax: maximum age of species,

• par: a list with the parameters of the von Bertalanffy growth function:

  • Linf: length infinity in cm,

  • K: curving coefficient;

  • t_anchor: time point anchoring growth curves in year-length coordinate system, corrsponds to peak spawning month,

  • C: amplitude of growth oscillation (if seasonalised = TRUE),

  • ts: summer point of oscillation (ts = WP - 0.5) (if seasonalised = TRUE),

  • phiL: growth performance index defined as phiL = log10(K) + 2 * log10(Linf);

• Rn_max: highest score value (absolute value of cost function, comparable with ELEFAN and ELEFAN_GA).

References

Brey, T., Soriano, M., and Pauly, D. 1988. Electronic length frequency analysis: a revised and expanded user's guide to ELEFAN 0, 1 and 2.

Pauly, D. and N. David, 1981. ELEFAN I, a BASIC program for the objective extraction of growth parameters from length-frequency data. Meeresforschung, 28(4):205-211

Xiang, Y., Gubian, S., Suomela, B., & Hoeng, J. (2013). Generalized simulated annealing for global optimization: the GenSA Package. R Journal, 5(1), 13-28.

Examples

## synthetic lfq data example
data(synLFQ4)
plot(synLFQ4, Fname="catch")

# ELEFAN_SA (takes approximately 30 seconds)
output <- ELEFAN_SA(synLFQ4, SA_time = 60*0.5, seasonalised = TRUE, MA = 11,
  init_par = list(Linf = 75, K = 0.5, t_anchor = 0.5, C = 0.5, ts = 0.5),
  low_par = list(Linf = 70, K = 0.3, t_anchor = 0, C = 0, ts = 0),
  up_par = list(Linf = 90, K = 0.7, t_anchor = 1, C = 1, ts = 1))
output$par
output$Rn_max

# view fit
plot(output)

# or
plot(output, draw = FALSE)
lfqFitCurves(output, col=1, par=output$par, draw=TRUE)$ESP

# compare to original parameters
tmp <- lfqFitCurves(output, col=4, lty=1,
   par=list(Linf=80, K=0.5, t_anchor=0.25, C=0.75, ts=0.5), draw=TRUE)
tmp$fESP
output$Rn_max

Empirical formulas for the estimation of natural mortality

Description

Functions to calculate the instantaneous natural mortality rate (M) according to 12 different empirical formulas.

Usage

M_empirical(
  Linf = NULL,
  Winf = NULL,
  K_l = NULL,
  K_w = NULL,
  temp = NULL,
  tmax = NULL,
  tm50 = NULL,
  GSI = NULL,
  Wdry = NULL,
  Wwet = NULL,
  Bl = NULL,
  schooling = FALSE,
  method
)

Arguments

Details

Function adapted from the mortality function of the fishmethods package by Gary A. Nelson (https://cran.r-project.org/web/packages/fishmethods/index.html).

Depending on the method different input parameters are required:

• "AlversonCarney" requires K_l and tmax,

• "Gislason" requires Linf, K_l and Bl,

• "GundersonDygert" requires GSI,

• "Hoenig" requires tmax,

• "Lorenzen" requires Wwet,

• "Pauly_Linf" requires Linf, K_l and temp,

• "Pauly_Winf" requires Winf, K_w and temp,

• "PetersonWroblewski" requires Wdry,

• "RikhterEfanov" requires tm50,

• "Roff" requires K_l and tm50,

• "Then_tmax" requires tmax,

• "Then_growth" requires Linf and K_l.

If accounting for schooling behaviour M is multiplied by 0.8 according to Pauly (1983).

Value

A matrix of M estimates.

Source

https://cran.r-project.org/web/packages/fishmethods/index.html

References

Alverson, D. L. and M. J. Carney. 1975. A graphic review of the growth and decay of population cohorts. J. Cons. Int. Explor. Mer 36: 133-143.

Gislason, H., N. Daan, J. C. Rice, and J. G. Pope. 2010. Size, growth, temperature and the natural mortality of marine fish. Fish and Fisheries 11: 149-158.

Gunderson, D. R. and P. H. Dygert. 1988. Reproductive effort as a predictor of natural mortality rate. J. Cons. Int. Explor. Mer 44: 200-209.

Hoenig, J. M. 1983. Empirical use of longevity data to estimate mortality rates. Fish. Bull. 82: 898-903.

Lorenzen, K. 1996. The relationship between body weight and natural mortality in juvenile and adult fish: a comparison of natural ecosystems and aquaculture. J. Fish. Biol. 49: 627-647.

Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. Int. Explor. Mer: 175-192.

Pauly, D., 1983. Some simple methods for the assessment of tropical fish stocks. FAO Fish.Tech.Pap., (234): 52p. Issued also in French and Spanish

Peterson, I. and J. S. Wroblewski. 1984. Mortality rate of fishes in the pelagic ecosystem. Can. J. Fish. Aquat. Sci. 41: 1117-1120.

Rikhter, V.A., and V.N. Efanov, 1976. On one of the approaches to estimation of natural mortality of fish populations. ICNAF Res.Doc., 76/VI/8: 12p.

Roff, D. A. 1984. The evolution of life history parameters in teleosts. Can. J. Fish. Aquat. Sci. 41: 989-1000.

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Then, A. Y., J. M. Hoenig, N. G. Hall, D. A. Hewitt. 2015. Evaluating the predictive performance of empirical estimators of natural mortality rate using information on over 200 fish species. ICES J. Mar. Sci. 72: 82-92.

Examples

M_empirical(Linf = 80, K_l = 0.5, temp = 25, tmax = 30,
     method = c("Pauly_Linf","Hoenig"))

Von Bertalanffy Growth function (VBGF)

Description

This function applies the von Bertalanffy growth function (VBGF). It allows to calculate ages from lengths or lengths from ages based on the special, generalised or seasonalised VBGF.

Usage

VBGF(param, t = NA, L = NA, na.rm = FALSE)

Arguments

Details

Based upon which input parameters are given one of the following VBGF types is applied: "special", "generalised", or "seasonalised" VBGF.

Value

A vector with estimated lengths corresponding to provided ages.

References

Somers, I. F. (1988). On a seasonally oscillating growth function. Fishbyte, 6(1), 8-11

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# calculation of lengths
# with t0
t <- seq(0,6,0.1)
Lt <- VBGF(list(Linf=80, K=0.6, t0=-0.1),t=t)
plot(t, Lt, t="l")

# with L0
t <- seq(0,6,0.1)
Lt <- VBGF(list(Linf=80, K=0.6, L0=2),t=t)
plot(t, Lt, t="l")

# with Winf
t <- seq(0,6,0.1)
Wt <- VBGF(list(Winf=4000, K=0.8), t=t)
plot(t, Wt, t="l")

# seasonalised VBGF
t <- seq(0,6,0.1)
Lt <- VBGF(list(Linf=80, K=0.6, t0=-0.1, ts=0.5, C=0.75),t=t)
plot(t, Lt, t="l")


# calculation of ages
L <- seq(2,200,0.1)
t <- VBGF(L = L, list(Linf=210, K=0.8, C= 0.75))
plot(t, L, t="l")

Virtual Population Analysis (VPA)

Description

This function applies the Virtual Population Analysis (VPA) or Cohort analysis (CA). Methods used to estimate stock biomass and fishing mortality per age/length group.

Usage

VPA(
  param,
  catch_columns = NA,
  catch_unit = NA,
  catch_corFac = NA,
  terminalF = NA,
  terminalE = NA,
  analysis_type = "VPA",
  algorithm = "new",
  plus_group = TRUE,
  plot = FALSE
)

Arguments

Details

The main difference between virtual population analysis (VPA) and cohort analysis (CA) is the step of calculating the fishing mortality per age class or length group. While CA works with an approximation by assuming that all fish are caught during a single day, which makes the calcualtion easier, VPA assumes that the fish are caught continuously, which has to be solved by the trial and error method (Sparre and Venema, 1998). For the age-based VPA/CA the catch has to be provided in numbers (or '000 numbers), while for the length-based VPA/CA the catch can also be provided in weight (tons or kg) by using the argument catch_unit. The catch has to be representative for fished species, that means there should not be other fisheries fishing the same stock. If this is the case catch_corFac can be used as a raising factor to account for the proportion of fish caught by other fisheries. When the model should follow a real cohort instead of a pseudo cohort, catch has to be provided as matrix. The model then starts to follow the first age class in the first column. If catch matrix is shorter than the number of age classes, the age or length classes without catch information are omitted. It is recommended to only follow a real cohort if there is enough information for all age classes (test with: dim(catch)[1] <= dim(catch)[2]). If plus_group is TRUE a different calculation for the survivors of the last length group is used (for more details please refer to Sparre & Venema (1998)).

Value

A list with the input parameters and following list objects:

• classes.num: numeric age classes or length groups (without plus sign),

• catch.cohort: a vector with the catch values which were used for the analysis (exists only if catch was a matrix),

• FM_calc: a vector with the ifshing mortality (M),

• Z: a vector with the total mortality (Z),

• survivors: a vector with the number of fish surviving to the next age class or length group (same unit than input catch vector),

• annualMeanNr: ta vector with the mean number of fish per year (same unit than input catch vector),

• meanBodyWeight: a vector with the mean body weight in kg,

• meanBiomassTon: a vector with the mean biomass in tons,

• YieldTon: a vector with the yield in tons,

• natLoss: a vector with the number of fish died due to natural mortality,

• plot_mat: matrix with rearranged survivors, nat losses and catches for plotting;

References

Jones, R., 1984. Assessing the effects of changes in exploitation pattern using length composition data (with notes on VPA and cohort analysis). FAO Fish.Tech.Pap., (256): 118p.

Jones, R., 1990. Length-cohort analysis: the importance of choosing the correct growth parameters. Journal du Conseil: ICES Journal of Marine Science, 46(2), 133-139

Pope, J.G., 1972. An investigation of the accuracy of virtual population analysis using cohort analysis. Res.Bull.ICNAF, (9):65-74

Pope, J.G., 1979. A modified cohort analysis in which constant natural mortality is replaced by estimates of predation levels. ICES C.M. 1979/H:16:7p. (mimeo)

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

References for weight-length relationship parameters (a & b): Dorel, D., 1986. Poissons del'Atlantique nord-est relations taille-poids. Institut Francais de Recherche pour l'Exploitation de la Mer. Nantes, France. 165 p.

Examples

#_______________________________________________
# Virtual Popuation Analysis with age-composition data
data(whiting)
output <- VPA(param = whiting, catch_columns = 1, terminalE = 0.5, analysis_type = "VPA")
plot(output)
#_______________________________________________
# Pope's Cohort Analysis with age-composition data
data(whiting)
VPA(whiting, terminalE = 0.5, catch_columns = 3, analysis_type = "CA",
   plot= TRUE, plus_group = TRUE)

#_______________________________________________
# Virtual population analysis with length-composition data
data(hake)
VPA(hake, terminalE = 0.5, analysis_type = "VPA", plot = TRUE,
    catch_unit = "'000", plus_group = TRUE)
#_______________________________________________
# Jones's Cohort Analysis with length-composition data
data(hake)
VPA(hake, terminalE = 0.5, analysis_type = "CA", plot = TRUE,
   catch_unit = "'000", plus_group = TRUE)

Beverton & Holt's Z-Equations

Description

A method to estimate the instantaneous total mortality rate (Z) based on a method derived by Beverton and Holt (1956).

Usage

Z_BevertonHolt(param, catch_columns = NA, Lprime_tprime)

Arguments

Details

The first length group or age class within the list object midLengths or age will be used as the Lprim or tprime (length of recruitment to fishery).

Value

A list with the input parameters and following objects:

• tmean or Lmean: mean age or length of fish,

• tprime or Lprime: some age or length for which all fish of that length and longer are under full exploitation,

• Z: total mortality.

References

Beverton R.J.H and S.J. Holt, 1956. A review of methods of estimating mortality rates in exploited fish populations, with special reference to sources of bias in catch sampling. Rapp.P.-v.Reun.CIEM, 140:67-83

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# based on length-frequency data
data(synLFQ2)
Z_BevertonHolt(synLFQ2, catch_columns = 2, Lprime_tprime = 47.5)

# based on age composition data
data(synCAA1)
Z_BevertonHolt(synCAA1, catch_columns = 3, Lprime_tprime = 2.5)

Estimate Z from CPUE data

Description

Method to estimate the instantaneous total mortality rate (Z) from catch per unit of effort (CPUE) data according to standard, Heincke's, or Robson & Chapman's method.

Usage

Z_CPUE(param, method = "standard", omit_age1 = FALSE)

Arguments

Details

In Heincke's and RobsonChapman's method age groups older than 4 are lumped, because age groups older than 3 or 4 are said to be hard to seperate (Ricker, 1975). Sparre and Venema (1998) recommend to omit the first age group in case it is not fully exploited by the fishery.

Value

A list with input parameters and a Z value or matrix depending on the method.

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Sparre, P., Venema, S.C., 1999. Introduction to tropical fish stock assessment. Part 2. Excercises. FAO Fisheries Technical Paper, (306.2, Rev. 2). 94 p.

Ricker, W.E., 1975. Computation and interpretation of biological statistics of fish populations. Bull.Fish.Res.Board Can., (191):382 p.

Examples

# load data
data(synCPUE)

# run model with standard method
Z_CPUE(synCPUE, method = "standard")

# run model with Heincke's method
Z_CPUE(synCPUE, method = "Heincke")

# run model with Robson and Chapman's method
Z_CPUE(synCPUE, method = "RobsonChapman", omit_age1 = TRUE)

Length-frequency data of the clam Abra alba

Description

Length-frequency data of the clam Abra alba as presented by Brey et al. (1988). Includes 7 approximately bi-monthly samplings of A. alba binned into 14 length classes. The data is of class "lfq", which can be used used e.g. in functions estimating growth parameters: ELEFAN, ELEFAN_SA or ELEFAN_GA.

Usage

data(alba)

Format

A list of class lfq consisting of:

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column).

Source

Brey, T., Soriano, M., and Pauly, D. 1988. Electronic length frequency analysis: a revised and expanded user's guide to ELEFAN 0, 1 and 2. ICLARM Contrib. 261.

Examples

data(alba)

# plot raw catch frequencies
plot(alba, Fname = "catch")

# plot restructured frequencies
alba <- lfqRestructure(alba, MA=5)
plot(alba, Fname = "rcounts")


# ELEFAN_SA fitting
set.seed(1)
fitSA <- ELEFAN_SA(
  alba, seasonalised = TRUE,
  init_par = list(Linf=14.5, K=1.1, t_anchor=0.4, ts=0, C=0.2),
  low_par = list(Linf=13, K=0.7, t_anchor=0, ts=0, C=0),
  up_par = list(Linf=15.5, K=1.5, t_anchor=1, ts=1, C=1),
  SA_time = 60
)
unlist(fitSA$par)
fitSA$Rn_max

# plot ELEFAN_SA results
plot(alba, Fname = "catch", draw = FALSE)
lfqFitCurves(fitSA, col=2, par=fitSA$par, draw=TRUE)$Rn_max

bream data

Description

Data of a covered codend experimental catch of the species Threadfin bream (Nemipterus japonicus) in South China Sea. This data can be analysed with the function select.

Usage

data(bream)

Format

A list consiting of:

• midLengths the midlengths of size classes,

• numCodend the number of fish retained in codend,

• numCover the number of fish retained in cover,

• msCodend the meshsize of codend.

Source

Jones, R., 1976. Mesh regulation in the demersal fisheries of the South China Sea area. Manila, South China Sea Fisheries Development and Coordinating Programme, SCS/76/WP/34: 75 p.

Examples

data(bream)
str(bream)
summary(bream)

Catch curve

Description

This function applies the (length-converted) linearised catch curve to age composition and length-frequency data, respectively. It allows to estimate the instantaneous total mortality rate (Z). Optionally, the gear selectivity can be estimated and the cumulative catch curve cna be applied.

Usage

catchCurve(
  param,
  catch_columns = NA,
  cumulative = FALSE,
  calc_ogive = FALSE,
  reg_int = NULL,
  reg_num = 1,
  auto = FALSE,
  plot = TRUE
)

Arguments

Details

This function includes the identify function, which asks you to choose two points from a graph manually. The two points which you choose by clicking on the plot in the graphical device represent the start and end of the data points, which should be used for the analysis. Based on these points the regression line is calculated. When the selection ogive is calculated by means of the catch curve the assumption is made, that Z is constant for all year classes or length groups, respectively. Accoring to Sparre and Venema (1998) this assumption might be true, because F is smaller for young fish (Selectivity) while M is higher for young fish (high natural mortality). The selectivity for not fully exploited old fish (e.g. due to gillnet fishery) can not be calculated yet by use of the catch curve. Based on the format of the list argument catch and whether the argument catch_columns is defined, the function automatically distinguishes between the catch curve with variable parameter system (if catch is a vector) and the one with constant parameter system (if catch is a matrix or a data.frame and catch_columns = NA). In the case of the variable parameter system the catches of one year are assumed to represent the catches during the entire life span of a so called pseudo-cohort. The cumulative catch curve does not allow for the estimation of the selectivity ogive.

Value

A list with the input parameters and following list objects:

• classes.num, tplusdt_2, t_midL, or ln_Linf_L: age, relative age or subsitute depending on input and method,

• lnC or lnC_dt: logarithm of (rearranged) catches,

• reg_int: the interval used for the regression analysis,

• linear_mod: linear model used for the regression analysis,

• Z: instantaneous total mortality rate, confidenceInt

• se: standard error of the total mortality;

• confidenceInt: confidence interval of the total mortality;

in case calc_ogive == TRUE, additionally:

• intercept: intercept of regression analysis,

• linear_mod_sel: linear model used for the selectivity analysis,

• Sobs: observed selection ogive,

• ln_1_S_1: dependent variable of regression analysis for selectivity parameters,

• Sest: estimated selection ogive,

• t50: age at first capture (age at which fish have a 50 probability to be caught),

• t75: age at which fish have a 75

• L50: length at first capture (length at which fish have a 50 probability to be caught),

• L75: length at which fish have a 75

References

Baranov, F.I., 1926. On the question of the dynamics of the fishing industry. Nauchn. Byull. Rybn. Khoz, 8 (1925), 7-11

Beverton, R.J.H. and S.J. Holt, 1956. A review of methods for estimating mortality rates in exploited fish populations, with special reference to sources of bias in catch sampling. Rapports et Proces verbaux des Reunions, Conseil Table3

Chapman, D., and D.S Robson, 1960. The analysis of a catch curve. Biometrics, 354-368

Edser, T., 1908. Note on the number of plaice at each length, in certain samples from the southern part of the North Sea, 1906. Journal of the Royal Statistical Society, 686-690

Heincke, F., 1913. Investigations on the plaice. General report. 1. The plaice fishery and protective regulations. Part I. Rapp.P.-v.Reun.CIEM, 17A:1-153 + Annexes

ICES, 1981. Report of the Ad hoc working group on the use of effort data in assessment, Copenhagen, 2-6 March 1981. ICES C.M. 1981/G:5 (mimeo)

Jones, R., and N.P. Van Zalinge, 1981. Estimates of mortality rate and population size for shrimp in Kuwait waters. Kuwait Bull. Mar. Sci, 2, 273-288

Pauly, D., 1983. Length-converted catch curves: a powerful tool for fisheries research in the tropics (part I). ICLARM Fishbyte, 1(2), 9-13

Pauly, D., 1984. Length-converted catch curves: a powerful tool for fisheries research in the tropics (part II). ICLARM Fishbyte, 2(1), 17-19

Pauly, D., 1984. Length-converted catch curves: a powerful tool for fisheries research in the tropics (III: Conclusion). ICLARM Fishbyte, 2(3), 9-10

Ricker, W.E., 1987. Computation and interpretation of biological statistics of fish populations. Bull.Fish.Res.Board Can., (191):382 p.

Robson, D.S., and D.G. Chapman, 1961. Catch curves and mortality rates. Trans.Am.Fish.Soc., 90(2):181-189

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Van Sickle, J. 1977. Mortality rates from size distributions: the application of a conservation law. Oecologia, Berl., 27(4):311-318

Examples

#_______________________________________________
# Variable paramter system (with catch vector)
# based on length frequency data
data(goatfish)
output <- catchCurve(goatfish)
summary(output$linear_mod)

# based on age composition data
data(whiting)
catchCurve(whiting, catch_columns = 1)

#_______________________________________________
# Constant parameter system based on age composition data (with catch matrix)
catchCurve(whiting)

#_______________________________________________
# Cumulative Catch Curve
# based on length frequency data
data(goatfish)
catchCurve(goatfish, cumulative = TRUE)

# based on age composition data
data(synCAA2)
catchCurve(synCAA2, cumulative = TRUE)

#_______________________________________________
# Catch Curve with estimation of selection ogive
data(synLFQ3)
output <- catchCurve(synLFQ3, calc_ogive = TRUE)
summary(output$linear_mod_sel)
 

# the same with predefined selection for regression line:
data(synLFQ3)
output <- catchCurve(synLFQ3, calc_ogive = TRUE, reg_int = c(9,21))
plot(output, plot_selec = TRUE)

Date - Year conversion

Description

Convert dates to numeric years with decimal as fraction of a year

Usage

date2yeardec(date)

Arguments

Value

a scalar (class 'numeric')

Examples

date2yeardec(Sys.Date())

Emperor data

Description

This dataset contains information about sky emperor (Lethrinus mahsena) and its fisheries of offshore Mauritius banks (Nazareth banks). It can be used for production models (prod_mod and prod_mod_ts).

Usage

data(emperor)

Format

A dataframe containing: 1. year years, 2. Y yield, 3. CPUE CPUE or abundance index

Source

Dharmendra, D., Solmundsson, J., 2005. Stock assessment of the offshore Mauritian banks using dynamic biomass models and analysis of length frequency of the Sky Emperor (Lethrinus mahsena). Fisheries Training Program The United Nations University, 61

Examples

data(emperor)
str(emperor)
summary(emperor)

Gillnet data

Description

Data of an experiment with several gillnets with different mesh sizes. Data can be analysed with function select_Millar.

Usage

data(gillnet)

Format

A list consiting of:

• midLengths the midlengths of size classes,

• meshSizes the meshsizes,

• catchPerNet_mat a matrix with the numbers in catch of the corresponding mesh sizes (same order),

Source

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3), 471-477.

Holt, S. J. 1963. A method for determining gear selectivity and its application. ICNAF Special Publication, 5: 106-115.

Examples

data(gillnet)
str(gillnet)
summary(gillnet)

Millar's original gillnet selectivity fitting function

Description

Function to estimate selectivity parameters from experimental data. This function is applied within select_Millar to derive starting parameters. select_Millar is the recommended function for selectivity estimation.

Usage

gillnetfit(
  data,
  meshsizes,
  rtype = "norm.loc",
  rel.power = NULL,
  plotlens = NULL,
  details = FALSE
)

Arguments

Value

list of fitted parameters

Source

https://www.stat.auckland.ac.nz/~millar/selectware/

References

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3):471-477

Examples

data(gillnet)

dat <- matrix(c(gillnet$midLengths, gillnet$CatchPerNet_mat),
         byrow = FALSE, ncol=(dim(gillnet$CatchPerNet_mat)[2]+1))

gillnetfit(data = dat, meshsizes = gillnet$meshSizes)

Yellowstriped goatfish data

Description

Data of Yellowstriped goatfish (Upeneus vittatus) from Manila Bay, Philippines. Can be used for the estimation of the instantaneous mortality rate (Z) by means of catchCurve.

Usage

data(goatfish)

Format

A list consisting of:

• midLengths: mid points of length classes,

• catch: a vector with catches in numbers,

• Linf: infinite length in cm [cm],

• K: growth coefficent per year [1/year].

Source

Ziegler, B., 1979. Growth and mortality rates of some fishes of Manila Bay, Philippines, as estimated from analysis of length-frequencies. Thesis. Kiel University, 115 p.

Examples

data(goatfish)
str(goatfish)
summary(goatfish)

Estimation of growth parameter using length-at-age data

Description

This function estimates growth parameters from length-at-age data. It allows to perform different methods: Gulland and Holt, Ford Walford plot, Chapman's method, Bertalanffy plot, or non linear least squares method (LSM).

Usage

growth_length_age(
  param,
  method,
  Linf_est = NA,
  Linf_init = 10,
  K_init = 0.1,
  t0_init = 0,
  CI = FALSE,
  ci.level = 0.95,
  age_plot = NULL,
  do.sim = FALSE
)

Arguments

Details

Gulland and Holt plot assumes infinitestimal delta t (only reasonable approximation of growth parameters if delta t is small). Ford Walford plot and Chapman assume constant time intervals between ages (delta t). The Bertalanffy plot is a robust method, however it requires an estimate of Linf. As long as this estimate is reasonable the resulting estimate of K is reasonable. For a first estimate of Linf the Powell Wetherall method powell_wetherall can be used. Otherwise, the largest fish or the average of the ten largest fish can be used for a small or large sample, respectively. All lengths have to be smaller than Linf as otherwise the logarithm is not defined. Oldest fish (if larger than Linf) have to be omitted. Non-linear least squares fitting is the preferred method to estimate growth parameters according to Sparre and Venema (1998). If CI = TRUE the confidence interval of parameters is calculated and plotted.

Value

A list with the input parameters and following parameters:

• x: independent variable used for regression analysis,

• y: dependent variable used for regression analysis,

• mod: (non) linear model,

• Linf: infinite length for investigated species in cm [cm],

• K: growth coefficent for investigated species per year [1/year],

• t0: theoretical time zero, at which individuals of this species hatch (only for Bertalanffy plot and LSM method).

• estimates: dataframe with growth parameters and confidence intervals (only if LSM method was applied).

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# synthetical length at age data
dat <- list(age = rep(1:7,each = 5),
   length = c(rnorm(5,25.7,0.9),rnorm(5,36,1.2),rnorm(5,42.9,1.5),rnorm(5,47.5,2),
   rnorm(5,50.7,0.4),rnorm(5,52.8,0.5),rnorm(5,54.2,0.7)))
growth_length_age(dat, method = "GullandHolt")

# Bertalaffy plot
growth_length_age(dat, method = "BertalanffyPlot", Linf_est = 50)

# non linear least squares method

output <- growth_length_age(param = dat, method = "LSM",
     Linf_init = 30, CI = TRUE, age_plot=NULL)
summary(output$mod)

Growth from tagging data

Description

This function estimates growth parameters from tagging data. Munro plot is applied

Usage

growth_tagging(param, method, Linf_range = c(5, 600), time_unit = "year")

Arguments

Details

If Munro plot is applied the optimal Linf value is found by minimizing the coefficient of variation (CV = sd(K)/mean(K)). For this iterative method the optimise function is applied. The histogram of the individual K values allows to distinguish potential differences in growth performance between individuals. t0 can not be estimated by Munro plot, neither by the Gulland Holt method.

Value

A list with the input parameters and following parameters:

• x: independent variable used for regression analysis,

• y: dependent variable used for regression analysis,

• reg_coeffs: regression coefficients,

• r2: r squared of regression analysis,

• Linf: infinite length for investigated species in cm [cm],

• K: growth coefficent for investigated species per year [1/year],

• conf_int_K: confidence intervals of K (only if Gulland Holt method was applied).

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Sparre, P., Venema, S.C., 1999. Introduction to tropical fish stock assessment. Part 2. Excercises. FAO Fisheries Technical Paper, (306.2, Rev. 2). 94 p.

Wolff, M., 1984. Early setback for scallop culture in Peru.

Examples

# from Wolff (1984)
dat <- list(L1 = c(40,46,29,30,18,31,48,49,59,58,61,65,57,55),
   L2 = c(85,53,55,56,25,43,70,59,62,80,72,83,65,56),
   delta_t = c(289,26,84,77,14,38,89,38,28,149,89,74,38,21))
growth_tagging(param = dat, "Munro", time_unit = "day", Linf_range=c(80,120))
growth_tagging(param = dat, "GullandHolt", time_unit = "day")


# from Sparre and Venema (1999)
dat <- list(L1 = c(9.7,10.5,10.9,11.1,12.4,12.8,14.0,16.1,16.3,17.0,17.7),
   L2 = c(10.2,10.9,11.8,12.0,15.5,13.6,14.3,16.4,16.5,17.2,18.0),
   delta_t = c(53,33,108,102,272,48,53,73,63,106,111))
growth_tagging(param = dat, "Munro", time_unit = "day", Linf_range = c(10,40))
growth_tagging(param = dat, "GullandHolt", time_unit = "day")

Haddock data

Description

Data of a covered codend experimental catch of the haddock (Melanogrammus aeglefinus). Can be used for function select_Millar.

Usage

data(haddock)

Format

A list consisting of:

• midLengths the midlengths of size classes,

• numCodend the number of fish retained in codend,

• numCover the number of fish retained in cover,

Source

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3), 471-477.

Examples

data(haddock)
str(haddock)
summary(haddock)

Hake data

Description

This dataset contains length-frequency data and biological characteristics about hake (Merluccius merluccius) and its fisheries off Senegal. It can be used for VPA or predict_mod.

Usage

data(hake)

Format

A list consisting of: 1. a vector with midlengths of size classes, 2. a vector with catch in numbers, 3. K value, 4. Linf value, 5. M value, 6. a value, 7. b value, 8. a vector with fishing mortalities, and 9. a vector with average value of fish per kg

Source

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(hake)
str(hake)
summary(hake)

Create lfq data from length measurements

Description

Convert raw length measurements to length frequency data (lfq class).

Usage

lfqCreate(
  data,
  Lname,
  Dname,
  Fname = NA,
  bin_size = 1,
  species = NA,
  stock = NA,
  comment = "",
  Lmin = 0,
  length_unit = "cm",
  plus_group = FALSE,
  aggregate_dates = FALSE,
  plot = FALSE
)

Arguments

Value

A list of "lfq" class with

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column).

Examples

# create random data
set.seed(1)
data <- data.frame(length.mm. = sample(c(rpois(300, lambda = 60),
           rpois(200, lambda = 100), rpois(100, lambda = 150)),
           size = 1000, replace = TRUE),
           dates = seq.Date(as.Date("2015-10-02"),as.Date("2016-08-28"),
           length.out = 1000))
# create lfq data
lfq_dat <- lfqCreate(data,Lname = "length.mm.", Dname = "dates", aggregate_dates = TRUE,
   length_unit = "mm", bin_size = 0.5, plot=TRUE, plus_group=c(TRUE,15.75))

Fitting VBGF growth curves through lfq data

Description

Thsi function estimates von Bertalanffy growth function (VBGF) curves for a set of growth parameters.

Usage

lfqFitCurves(
  lfq,
  par = list(Linf = 100, K = 0.1, t_anchor = 0.25, C = 0, ts = 0),
  agemax = NULL,
  flagging.out = TRUE,
  lty = 2,
  lwd = 1,
  col = 1,
  draw = FALSE,
  tincr = 0.05
)

Arguments

Details

t_anchor subsitutes the starting point from known from Fisat 2. This parameter is necessary for anchoring the growth curves on the time axis. It does not subsitute t0. However, it corresponds to the peak spawning of the species (x intercept of growth curve) and has values between 0 and 1, where 0 corresponds to spawning at the 1st of January and 0.999 corresponds to the 31st of December. The default value of 0.25 or 3/12 corresponds the third month of the year, March.

Value

A list with the input parameters and following list objects:

• Lt: dataframe with ages and lengths of the cohorts,

• agemax: maximum age of species.

• ncohort: number of cohorts,

• ASP: available sum of peaks, sum of posititve peaks which could be potential be hit by growth curves. This is calculated as the sum of maximum values from each run of posive restructured scores.

• ESP: available sum of peaks,

• fASP: available sum of peaks,

• fESP: available sum of peaks,

References

Brey, T., Soriano, M., and Pauly, D. 1988. Electronic length frequency analysis: a revised and expanded user's guide to ELEFAN 0, 1 and 2.

Pauly, D. 1981. The relationship between gill surface area and growth performance in fish: a generalization of von Bertalanffy's theory of growth. Meeresforsch. 28:205-211

Pauly, D. and N. David, 1981. ELEFAN I, a BASIC program for the objective extraction of growth parameters from length-frequency data. Meeresforschung, 28(4):205-211

Pauly, D., 1985. On improving operation and use of ELEFAN programs. Part I: Avoiding "drift" of K towards low values. ICLARM Conf. Proc., 13-14

Pauly, D., 1987. A review of the ELEFAN system for analysis of length-frequency data in fish and aquatic invertebrates. ICLARM Conf. Proc., (13):7-34

Pauly, D. and G. R. Morgan (Eds.), 1987. Length-based methods in fisheries research. (No. 13). WorldFish

Pauly, D. and G. Gaschuetz. 1979. A simple method for fitting oscillating length growth data, with a program for pocket calculators. I.C.E.S. CM 1979/6:24. Demersal Fish Cttee, 26 p.

Pauly, D. 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators (Vol. 8). WorldFish.

Quenouille, M. H., 1956. Notes on bias in estimation. Biometrika, 43:353-360

Somers, I. F., 1988. On a seasonally oscillating growth function. ICLARM Fishbyte 6(1): 8-11.

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2): 407 p.

Tukey, J., 1958. Bias and confidence in not quite large samples. Annals of Mathematical Statistics, 29: 614

Tukey, J., 1986. The future of processes of data analysis. In L. V. Jones (Eds.), The Collected Works of John W. Tukey-philosophy and principles of data analysis: 1965-1986 (Vol. 4, pp. 517-549). Monterey, CA, USA: Wadsworth & Brooks/Cole

Examples

data(synLFQ5)
res <- lfqRestructure(synLFQ5, MA=11)
plot(res)
tmp <- lfqFitCurves(res, par=list(Linf=80,K=0.5,t_anchor=0.25), draw=TRUE)

Modify lfq data for further analysis

Description

Modify length-freqeuncy (LFQ) data. Allows to summarise catch matrix of LFQ data to one column per year. This is required for e.g. catchCurve. Allows to change bin size of LFQ data. Allows to ad plus group to catch matrix.

Usage

lfqModify(
  lfq,
  par = NULL,
  bin_size = NA,
  aggregate = NA,
  vectorise_catch = FALSE,
  plus_group = FALSE,
  minDate = NA,
  maxDate = NA,
  years = NA,
  Lmin = NA,
  Lmax = NA,
  lfq2 = NA
)

Arguments

Value

lfq object with rearranged catch matrix (yearly sums) and growth parameters if provided.

Examples

data(synLFQ4)

## summarise catch matrix per year
lfq_sum <- lfqModify(synLFQ4, vectorise_catch = TRUE)

## change bin size
lfq_bin <- lfqModify(synLFQ4, bin_size = 4)

## add plus_group
lfq_plus <- lfqModify(synLFQ4, plus_group = 85.5)

Restructuring of length frequency data

Description

First step of the Electronic LEngth Frequency ANalysis (ELEFAN), which is restructuring length-frequency data (lfq). This is done according to a certain protocol, described by many authors (see Details or References for more information).

Usage

lfqRestructure(param, MA = 5, addl.sqrt = FALSE)

Arguments

Details

This function is used prior to fitting of growth curves (e.g. in ELEFAN, ELEFAN_SA functions). It restructures a length frequency data set according to a list of steps to emphasise cohorts in the data. The steps can be found in various publications, see e.g. Brey et al. (1988) or Pauly and David (1981). Here, the most recent steps documented in Gayanilo (1997) are followed.

Value

A list with the input parameters and following list objects:

• rcounts: restructured frequencies,

• peaks_mat: matrix with uniquely numbered positive peaks,

• ASP: available sum of peaks, sum of posititve peaks which could be potential be hit by growth curves. This is calculated as the sum of maximum values from each run of posive restructured scores,

• MA: moving average used for restructuring.

References

Brey, T., Soriano, M., and Pauly, D. 1988. Electronic length frequency analysis: a revised and expanded user's guide to ELEFAN 0, 1 and 2.

Gayanilo, Felimon C. FAO-ICLARM stock assessment tools: reference manual. No. 8. Food & Agriculture Org., 1997.

Pauly, D. 1981. The relationship between gill surface area and growth performance in fish: a generalization of von Bertalanffy's theory of growth. Meeresforsch. 28:205-211

Pauly, D. and N. David, 1981. ELEFAN I, a BASIC program for the objective extraction of growth parameters from length-frequency data. Meeresforschung, 28(4):205-211

Pauly, D., 1985. On improving operation and use of ELEFAN programs. Part I: Avoiding "drift" of K towards low values. ICLARM Conf. Proc., 13-14

Pauly, D., 1987. A review of the ELEFAN system for analysis of length-frequency data in fish and aquatic invertebrates. ICLARM Conf. Proc., (13):7-34

Pauly, D. and G. R. Morgan (Eds.), 1987. Length-based methods in fisheries research. (No. 13). WorldFish

Pauly, D. and G. Gaschuetz. 1979. A simple method for fitting oscillating length growth data, with a program for pocket calculators. I.C.E.S. CM 1979/6:24. Demersal Fish Cttee, 26 p.

Pauly, D. 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators (Vol. 8). WorldFish.

Quenouille, M. H., 1956. Notes on bias in estimation. Biometrika, 43:353-360

Somers, I. F., 1988. On a seasonally oscillating growth function. ICLARM Fishbyte 6(1): 8-11.

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2): 407 p.

Tukey, J., 1958. Bias and confidence in not quite large samples. Annals of Mathematical Statistics, 29: 614

Tukey, J., 1986. The future of processes of data analysis. In L. V. Jones (Eds.), The Collected Works of John W. Tukey-philosophy and principles of data analysis: 1965-1986 (Vol. 4, pp. 517-549). Monterey, CA, USA: Wadsworth & Brooks/Cole

Examples

# data and plot of catch frequencies
data(synLFQ4)
plot(synLFQ4, Fname="catch")

# restructuring and calculation of ASP
synLFQ4 <- lfqRestructure(synLFQ4, MA=11)
synLFQ4$ASP

# plot of restructured scores and fit of soVBGF growth curves
plot(synLFQ4)
lfqFitCurves(synLFQ4,
 par=list(Linf=80, K=0.5, t_anchor=0.25, C=0.75, ts=0),
 draw=TRUE
)$fASP

Bhattacharya plot

Description

This function plots the seperated frequency distributions and selected regression lines of Bhattacharya method.

Usage

## S3 method for class 'Bhattacharya'
plot(x, analysisPlot = TRUE, ...)

Arguments

Details

This function plots the results of the Bhattacharya method.

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

## Not run: 
 data(synLFQ1)
 output <- Bhattacharya(param = synLFQ1)
 plot(output)

## End(Not run)

VPA plot

Description

This function plots the survivors, catches, natural losses, and fishing mortality resulting from the VPA model.

Usage

## S3 method for class 'VPA'
plot(
  x,
  yaxis = "numbers",
  display_last_class = TRUE,
  xlabel = NA,
  ylabel1 = "Population",
  ylabel2 = "Fishing mortality",
  ylim = NA,
  ylim_FM = NA,
  plot.bars = TRUE,
  plot.FM = TRUE,
  plot.legend = TRUE,
  ...
)

Arguments

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(whiting)
output <- VPA(whiting, terminalF = 0.5)
plot(output, display_last_class = FALSE)

data(hake)
output <- VPA(hake, terminalE = 0.5, catch_unit = "'000")
plot_mat <- output$plot_mat[,-c(1,2)]  # remove first two length classes
class(plot_mat) <- "VPA"
plot(plot_mat, xlabel = "Midlengths [cm]")

Plotting catch curve

Description

This function plots the results from the catchCurve model.

Usage

## S3 method for class 'catchCurve'
plot(
  x,
  xaxis = "age",
  plot_selec = FALSE,
  col = c("blue", "darkgreen", "orange", "darkred"),
  cex = 1.5,
  xlim = NULL,
  ylim = NULL,
  xlab = "default",
  ylab = "default",
  ...
)

Arguments

Details

A function to plot the results of the catchCurve model.

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(synLFQ3)
output <- catchCurve(synLFQ3, calc_ogive = TRUE, reg_int = c(9,21))
plot(output, plot_selec = TRUE)

Plotting of length frequency data (with VBGF curves)

Description

This function plots length frequency (lfq) samples sequentially arranged in time. An object of "lfq" class is obatined by applying the lfqRestructure function. In case growth parameters are known, von Bertalanffy growth curves can be plotted through the lfq samples.

Usage

## S3 method for class 'lfq'
plot(
  x,
  Fname = "rcounts",
  par = NULL,
  agemax = NULL,
  rel = FALSE,
  y = NA,
  curve.col = 1,
  hist.sc = 0.5,
  hist.col = c("white", "black", "orange", "darkgreen"),
  image.col = NULL,
  region.col = NULL,
  zlim = NULL,
  zlimtype = "balanced",
  date.axis = "traditional",
  date.at = seq(as.Date("1500-01-01"), as.Date("2500-01-01"), by = "months"),
  date.format = "'%y-%b",
  xlab = "",
  ylab = "Length classes",
  draw = TRUE,
  ...
)

Arguments

Details

This function uses lfqFitCurves when growth parameters are provided to plot growth curves, this can be turned off with draw = FALSE.

References

Brey, T., Soriano, M., and Pauly, D. 1988. Electronic length frequency analysis: a revised and expanded user's guide to ELEFAN 0, 1 and 2.

Pauly, D. 1981. The relationship between gill surface area and growth performance in fish: a generalization of von Bertalanffy's theory of growth. Meeresforschung. 28:205-211

Pauly, D. and N. David, 1981. ELEFAN I, a BASIC program for the objective extraction of growth parameters from length-frequency data. Meeresforschung, 28(4):205-211

Pauly, D., 1985. On improving operation and use of ELEFAN programs. Part I: Avoiding "drift" of K towards low values. ICLARM Conf. Proc., 13-14

Pauly, D., 1987. A review of the ELEFAN system for analysis of length-frequency data in fish and aquatic invertebrates. ICLARM Conf. Proc., (13):7-34

Pauly, D. and G. R. Morgan (Eds.), 1987. Length-based methods in fisheries research. (No. 13). WorldFish

Pauly, D. and G. Gaschuetz. 1979. A simple method for fitting oscillating length growth data, with a program for pocket calculators. I.C.E.S. CM 1979/6:24. Demersal Fish Comittee, 26 p.

Pauly, D. 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators (Vol. 8). WorldFish.

Quenouille, M. H., 1956. Notes on bias in estimation. Biometrika, 43:353-360

Somers, I. F., 1988. On a seasonally oscillating growth function. ICLARM Fishbyte 6(1): 8-11.

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2): 407 p.

Tukey, J., 1958. Bias and confidence in not quite large samples. Annals of Mathematical Statistics, 29: 614

Tukey, J., 1986. The future of processes of data analysis. In L. V. Jones (Eds.), The Collected Works of John W. Tukey philosophy and principles of data analysis: 1965-1986 (Vol. 4, pp. 517-549). Monterey, CA, USA: Wadsworth & Brooks/Cole

Examples

data(alba)
res <- lfqRestructure(alba)

# simple plot or reconstructed frequencies
plot(x = res, Fname = "rcounts")

# add VBGF curves
plot(res, Fname = "rcounts", par = list(Linf = 14, K = 1.1, t_anchor = 0.3))

# add soVBGF curves, adjust hist.sc and xlim
plot(res, Fname = "catch", curve.col=4,
  par = list(Linf = 14, K = 1.1, t_anchor = 0.3, C = 0.2, ts = 0.75),
  hist.sc = 0.9,
  xlim=range(res$dates)+c(-30, 0)
)

# adjust image colors
plot(res, Fname = "rcounts", image.col = NA )
plot(res, Fname = "rcounts", image.col = rev(cm.colors(21)) )
plot(res, Fname = "rcounts", image.col = colorRampPalette(c("red","grey90","green"))(21))

# solid plot region color
plot(res, xlim=range(res$dates)+c(-60, 60),
  hist.sc=0.75, image.col="grey90") # leaves gaps
plot(res, xlim=range(res$dates)+c(-60, 60),
  hist.sc=0.75, region.col="grey90") # full coverage

# low-level plot additions
plot(res)
abline(h=4, lty=2)
mtext("Restructured frequencies (MA=5)", line=0.25, side=3)

Plotting prediction models yield per recruit and Thompson & Bell

Description

This function plots objects of the class "predict_mod", which are results of the function predict_mod.

Usage

## S3 method for class 'predict_mod'
plot(
  x,
  type = "ypr",
  xaxis1 = "FM",
  yaxis1 = "Y_R.rel",
  yaxis2 = "B_R.rel",
  yaxis_iso = "Lc",
  identify = FALSE,
  mark = FALSE,
  contour = TRUE,
  xlab = NA,
  ylab1 = NA,
  ylab2 = NA,
  ylab3 = NA,
  plot_refs = c("F01", "Fmax", "F05", "F04"),
  cols_refs = c("goldenrod2", "darkred", "darkgreen", "darkorange"),
  ...
)

Arguments

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

## Not run: 
# Nemipterus marginatus - age structured data
threadfin <- list(Winf = 286,K = 0.37, t0 = -0.2, M = 1.1, tr = 0.4)

output <- predict_mod(threadfin, FM_change = seq(0,6,0.1),
   tc_change = seq(0.2,1,0.2), type = 'ypr')
plot(output)

# hake - length structured data
data(hake)
hake$Lr <- 35
select.list <- list(selecType = 'trawl_ogive', L50 = 20, L75 = 24)
output <- predict_mod(param = hake, FM_change = seq(0,0.4,0.05),
                      curr.E = 0.4, curr.Lc = 40,
                      Lc_change = seq(5,80,1), s_list = select.list,
                      type = 'ypr', plot = FALSE)
plot(output, type = "Isopleth", xaxis1 = "FM", yaxis1 = "Y_R.rel",
   identify = FALSE)


## End(Not run)

Plotting production models

Description

This function plots CPUE and yield values against fishing effort resulting from the production models (prod_mod).

Usage

## S3 method for class 'prod_mod'
plot(x, display_MSY = TRUE, ...)

Arguments

References

Fox, W. W. Jr., 1970. An exponential surplus-yield model for optimizing exploited fish populations. Trans.Am.Fish.Soc., 99:80-88

Graham, M., 1935. Modern theory of exploiting a fishery and application to North Sea trawling. J.Cons.CIEM, 10(3):264-274

Schaefer, M., 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bull.I-ATTC/Bol. CIAT, 1(2):27-56

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(trawl_fishery_Java)
output <-  prod_mod(data = trawl_fishery_Java)
plot(output, display_years = TRUE)

Plotting time series production models

Description

This function plots objects of the class "prod_mod_ts".

Usage

## S3 method for class 'prod_mod_ts'
plot(x, correlation_plots = FALSE, ...)

Arguments

References

Dharmendra, D., Solmundsson, J., 2005. Stock assessment of the offshore Mauritian banks using dynamic biomass models and analysis of length frequency of the Sky Emperor (Lethrinus mahsena). Fisheries Training Program The United Nations University, 61

Examples

data(emperor)
output <-  prod_mod_ts(emperor, method  = "Fox")
plot(output, correlation_plots = TRUE)

Plot of recruitment patterns

Description

This function plots the recruitment patterns from the recruitment model.

Usage

## S3 method for class 'recruitment'
plot(
  x,
  percent = TRUE,
  col = "darkgreen",
  xtitle = "default",
  ytitle = "default",
  ...
)

Arguments

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

dat <- list(midLengths = seq(2,98,4),
               catch = c(0.6,17.6,93,83.2,12.6,0.3,0,0,0,1,17.1,51.4,
               26.1,2.2,0.2,4.5,21.6,17.6,3.7,8.7,10.6,6.3,5.6,2.9,0.8),
               Linf = 100,
               K = 0.5)
output <- recruitment(param = dat, tsample = 0.25)
plot(output, percent = FALSE)

Selectivity plot

Description

This function plots the selectivity estimates of the function select.

Usage

## S3 method for class 'select'
plot(x, regression_fit = TRUE, cols = c("darkgreen", "orange"), ...)

Arguments

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(tilapia)
output <- select(tilapia, plot = FALSE)
plot(output, regression_fit = TRUE)

data(bream)
output <- select(bream, plot = FALSE)
plot(output, regression_fit = TRUE)

Millar's selectivity plot

Description

This function plots the selectivity estimates of Millar's selectivity model (select_Millar).

Usage

## S3 method for class 'select_Millar'
plot(
  x,
  plotlens = NULL,
  standardise = TRUE,
  deviance_plot = TRUE,
  selectivity_plot = TRUE,
  xlab_dev = "Length [cm]",
  xlab_sel = "Length [cm]",
  ylab_dev = "Mesh size [cm]",
  ylab_sel = "Relative retention",
  title_dev = "Deviance residuals",
  title_sel = NULL,
  ...
)

Arguments

Details

This function draws a selectivity plot for the object class "select_Millar", which is created by applying Millar's selectivity model select_Millar.

References

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3), 471-477.

Examples

data(gillnet)

output <- select_Millar(gillnet, x0 = c(60,4), rel.power = rep(1,8),
   rtype = "norm.loc", plot = FALSE)

plot(output, plotlens = seq(40,90,0.1), deviance_plot = FALSE)

Powell-Wetherall method

Description

A method to estimate the instantaneous total mortality rate (Z) and the infinite length of the von Bertalanffy growth equation (Powell, 1979; Wetherall et al., 1987).

Usage

powell_wetherall(
  param,
  catch_columns = NA,
  savePlots = FALSE,
  reg_int = NULL,
  main = "Powell-Wetherall plot"
)

Arguments

Details

The first length group or age class within the list object midLengths or age will be used as the Lprim or tprime (length of recruitment to fishery). This function includes the identify function, which asks you to choose two points from a graph manually. The two points which you choose by clicking on the plot in the graphical device represent the start and end of the data points, which should be used for the analysis. Based on these points the regression line is calculated. The Powell and Wetherall method only works with length-frequency data.

Value

A list with the input parameters and follwing objects:

• tmean or Lmean: mean age or length of fish,

• Z: total mortality;

and/or following objects when applying the Powell and Wetherall method:

• Lmean_Lprime: dependent variable for regression analysis,

• Lprime: some length for which all fish of that length and longer are under full exploitation,

• Linf_est: infinite length in [cm] (Linf),

• se_Linf: standard error of Linf,

• confidenceInt_Linf: confidence interval for Linf,

• ZK: total mortality divided by K (Z/K),

• se_ZK: standard error of Z/K,

• confidenceInt_ZK: confidence interval of Z/K;

References

Powell, D.G., 1979. Estimation of mortality and growth parameters from the length- frequency of a catch. Rapp.P.-v.Reun.CIEM, 175:167-169

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Wetherall, J.A., J.J. Polovina and S. Ralston, 1987. Estimating growth and mortality in steady-state fish stocks from length-frequency data. ICLARM Conf.Proc., (13):53-74

Examples

data(synLFQ3)
powell_wetherall(synLFQ3)

data(synLFQ5)
powell_wetherall(synLFQ5, catch_columns = 1:12)

Prediction models

Description

This function applies Beverton & Holt's yield per recruit model as well as the Thompson & Bell model. These models predict catch, yield, biomass and economic values for different fishing mortality scenarions (in combination with gear changes).

Usage

predict_mod(
  param,
  type,
  FM_change = NA,
  E_change = NA,
  FM_relative = FALSE,
  Lc_change = NULL,
  tc_change = NULL,
  s_list = NA,
  stock_size_1 = NA,
  age_unit = "year",
  curr.E = NA,
  curr.Lc = NA,
  plus_group = NA,
  Lmin = NA,
  Lincr = NA,
  plot = FALSE,
  mark = TRUE,
  hide.progressbar = FALSE
)

Arguments

Details

The Thompson and Bell model incorporates an iteration step simulating the stock by means of the stock_sim function. In case changes in gear characteristics - here measured in terms of Lc or tc, the length or age at first capture, respectively - should be explored, a list with selectivity information about the gear has to be provided and the prediction models make use of the selectivity select_ogive function. Sparre and Venema (1998) recommend to treat the last length class always as plus group. This model is very sensitive to zero observations in the ultimate length classes. If unrealistic results are returned, it is recommended to cut length classes with zero observations, group them in a plus group or to change the interval between length classes. Equations which are used in this function assume isometric growth, an assumption often not met. Further, the assumption that there is no relationship between the parental stock size and progeny over a wide range of fishing mortalities or exploitation values, respectively, is also said to be untrue. By default, the functions assume knife-edge recruitment and selection of gears (Sparre and Venema, 1998). If E_change instead of FM_change is used the range is cut at E=0.9, because higher values of E correspond to unrealistic high values of fishing mortality. If no selectivity information is given (by use of s_list), knife edge selectivity with L50 equal to the first argument of Lc_change is assumed.

Value

A list with the input parameters and dependent on the model type following list objects:

• type = 'ypr'

  • FM: fishing mortalities,

  • Lc or tc: lengths or ages at first capture,

  • list_Lc_runs: a list with dataframes for each Lc value:

    • FM_change: fishing mortalities

    • E: expoitation rates

    • Ty: mean age in annual yield

    • LY: mean length in annual yield

    • Wy: mean weight in annual yield

    • Y_R.rel: relative yield per recruit (change in catch in weigth per recruit relative to initial Y/R value)

    • B_R.rel: relative biomass per recruit

    • Y_R: yield per recurit (catch in weight per recruit)

    • B_R: biomass per recruit

    • B_R.percent: percentage biomass per recurit in relation to virgin biomass per recruit

  • df_Es: a dataframe with references points (columns) for different Lc values (rows)

  • df_current: a dataframe with the exploitation status, yield and biomass values of current exploitation or selectivity (if E_curr or Lc_tc_curr provided).

• type = 'ThompBell'

  • dt: delta t,

  • N: population number,

  • dead: deaths due to natural reasons,

  • C: catch,

  • Y: yield,

  • B: biomass,

  • V: value,

  • totals: summed up values (total catch, total yield, total value, average biomass),

  • totC: total catches for different x factors,

  • totY: total yield values for different x factors,

  • totV: total values for different x factors,

  • meanB: average biomasses for different x factors,

  • F_change: fishing mortality changes;

• type = 'ThompBell' and Lc_change provided

  • FM_change: fishing mortality changes,

  • Lc_change: changes in length at first capture,

  • Lt: lengths at age,

  • sel: probability of capture,

  • mat_FM_Lc_com.C: catch matrix for all fishing mortality and Lc/tc combinations,

  • mat_FM_Lc_com.Y: yield matrix for all fishing mortality and Lc/tc combinations,

  • mat_FM_Lc_com.V: value matrix for all fishing mortality and Lc/tc combinations,

  • mat_FM_Lc_com.B: biomass matrix for all fishing mortality and Lc/tc combinations;

References

Berkeley, S.A., and Houde, E.D., 1980. Swordfish, Xiphias gladius, dynamics in the Straits of Florida. ICES C.M., 11.

Beverton, R.J.H., and Holt, S.J., 1964. Table of yield functions for fishery management. FAO Fish. Tech. Pap. 38, 49 p.

Beverton, R.J.H., and Holt, S.J., 1966. Manual of methods for fish stock assessment. Pt. 2: Tables of yield functions. FAO Fisheries Technical Paper, (38)Rev.1:67 p.

Boerema, L.K., and J.A. Gulland, 1973. Stock assessment of the Peruvian anchovy (Engraulis ringens) and management of the fishery. Journal of the Fisheries Board of Canada, 30(12):2226-2235

Garcia, S. and N.P. van Zalinge, 1982. Shrimp fishing in Kuwait: methodology for a joint analysis of the artisanal and industrial fisheries. pp. 119-142 In: Report on the Workshop on assessment of the shrimp stocks of the west coast of the Gulf between Iran and the Arabian Peninsula. Fisheries development in the Gulf. Rome, FAO, FI:DP/RAB/80/015/1, 163 p.

Gulland, J.A., 1983. Fish stock assessment: a manual of basic methods. FAO/Wiley, New York.

Gulland, J.A. and Boerema, L., 1973. Scientific advice on catch levels. Fish. Bull. (US) 71:325-335.

Jones, R.E. 1957. A much simplified version of the fish yield equation. Doc. No. P. 21. Paper presented at the Lisbon joint meeting of International Commission Northwest Atlantic-Fisheries, International Council for the Exploration of the Sea, and Food and Agriculture Organization of the United Nations. 8 p. [Mimeo].

Millar, R.B., and Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3):471-477

Pauly, D., 1980. A selection of simple methods for the assessment of tropical fish stocks. FAO Fisheries Circulars (FAO). no. 729.

Pauly, D., 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators. ICLARM Stud. Rev. 8, 325 p.

Pauly, D. and M. Soriano. 1986. Some practical extensions to Beverton and Holt's relative yield-per-recruit model, p. 491-495. In J.L. Maclean, L.B. Dizon and L.V. Hosillos (eds.) The First Asian Fisheries Forum. Asian Fisheries Society, Manila.

Schaefer, M.B., 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Inter-Am. Trop. Tuna Comm., Bull. 1(2):27-56.

Schaefer, M.B., 1957. A study of the dynamics of the fishery for yellowfin tuna in the eastern tropical Pacific Ocean. Inter-Am. Trop. Tuna Comm., Bull. 2:247-268.

Sparre, P., and Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

#______________________________________
# Yiel Per Recruit (YPR) / Beverton and Holt's model
#______________________________________
# age structured data
# Nemipterus marginatus
threadfin <- list(Winf = 286, K = 0.37, t0 = -0.2, M = 1.1, tr = 0.4)

predict_mod(threadfin, FM_change = seq(0,6,0.1),
   tc_change = seq(0.2,1,0.2), type = 'ypr')

# Leiognathus spendens (Pauly, 1980)
ponyfish <- list(Winf = 64, K = 1, t0 = -0.2, M = 1.8, tr = 0.2)

predict_mod(ponyfish, tc_change = c(0.2,0.3,1.0), type = 'ypr', plot=TRUE)

#______________________________________
# length structured data
# Xiphias gladius (Berkeley and Houde, 1980)
swordfish <- list(Linf = 309, K = 0.0949, M = 0.18,
                  a = 0.0003, b = 3, Lr = 90)

select.list <- list(selecType = 'trawl_ogive', L50 = 120, L75 = 132)
#swordfish$midLengths <- seq(60,300,5)

output <- predict_mod(param = swordfish, Lc_change = c(100,118,150,180),
            s_list = select.list, type = 'ypr', Lmin = 90, Lincr = 8)
plot(output)

data(hake)
hake$Lr <- 35
select.list <- list(selecType = 'trawl_ogive', L50 = 50, L75 = 54)
output <- predict_mod(param = hake, FM_change = seq(0,3,0.05),
                      Lc_change = seq(30,70,1), s_list = select.list,
                      type = 'ypr', plot = FALSE, curr.Lc = 50, curr.E = 0.73)
plot(output, type = "Isopleth", xaxis1 = "FM", yaxis1 = "Y_R.rel", mark = TRUE)

output <- predict_mod(param = hake, E_change = seq(0,1,0.1),
                      Lc_change = seq(2,120,2), #s_list = select.list,
                      type = 'ypr', plot = FALSE)
plot(output, type = "Isopleth", xaxis1 = "E", yaxis1 = "B_R")

#______________________________________
#      Thompson and Bell model
#______________________________________
# with age structured data
data(shrimps)

output <- predict_mod(param = shrimps, FM_change = seq(0.1,20,0.1),
     type = "ThompBell", age_unit = "month", plot = TRUE)

#______________________________________
# with length structured data
data(hake)
par(mar = c(5, 4, 4, 7))
predict_mod(param = hake,FM_change = seq(0.1,3,0.05),
     type = 'ThompBell', plot = TRUE)

# create list with selectivity information
select.list <- list(selecType = 'trawl_ogive', L50 = 50, L75 = 55)

output <- predict_mod(param = hake, FM_change = seq(0,2,0.1),
     Lc_change = seq(20,70,1),
     curr.E = 0.4, curr.Lc = 50,
     type = 'ThompBell', s_list = select.list)
plot(output, xaxis1 = "FM", yaxis_iso = "Lc", yaxis1 = "B_R", mark = TRUE)

Production models

Description

Production models are holistic models, which can be used to estimate maximum sustainable yield (MSY) and virgin biomass. This function uses the equilibrium approach to estimate parameters (Schaefer model and Fox model).

Usage

prod_mod(data, plot = FALSE)

Arguments

Details

Production models are also called surplus production models or biomass dynamic models. They can be applied if sufficient data are available: effort and yield parameters have to be expended over a certain number of years. Furthermore, the fishing effort must have undergone substantial changes over the period covered (Sparre and Venema, 1998). Either the catch per unit of effort (CPUE) is inserted into the model directly (objectname: CPUE) or the CPUE is calculated from the catch and effort, then these two vectors should have required units. There are three ways of estimating paramaters of production models, (i) assuming equlibrium conditions, (ii) transforming equation to linear form, or (iii) time-series fitting (Hilborn and Walters, 1992). The first approach corresponds to the Schaefer and Fox model and thus the methodology of this function. The authors recommend to use dynamic fitting methods when possible rather than the equilibrium approach. For dynamic production models please refer to prod_mod_ts.

Value

A list with the input parameters and following list objects:

• Schaefer_lm: intercept and slope of linear model following the Schaefer model,

• Fox_lm: intercept and slope of linear model following the Fox model,

• Schaefer_MSY: MSY according to Schaefer model,

• Schaefer_fMSY: fishing effort yielding in MSY according to Schaefer model,

• Schaefer_Bv: virgin biomass according to Schaefer model,

• ln_CPUE: natural logarithm of CPUE values,

• Fox_MSY: MSY according to Fox model,

• Fox_fMSY: fishing effort yielding in MSY according to Fox model,

• Fox_Bv: virgin biomass according to Fox model.

References

Fox, W. W. Jr., 1970. An exponential surplus-yield model for optimizing exploited fish populations. Trans.Am.Fish.Soc., 99:80-88

Graham, M., 1935. Modern theory of exploiting a fishery and application to North Sea trawling. J.Cons.CIEM, 10(3):264-274

Hilborn, R., Walters, C. J. (1992). Quantitative fisheries stock assessment: choice, dynamics and uncertainty. Reviews in Fish Biology and Fisheries, 2(2), 177-178.

Schaefer, M., 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Bull.I-ATTC/Bol. CIAT, 1(2):27-56

Schaefer, M., 1957. A study of the dynamics of the fishery for yellowfin tuna of the eastern tropical Pacific Ocean [in English and Spanish]. Ibid., 2(6): 245-285

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(trawl_fishery_Java)
prod_mod(data = trawl_fishery_Java, plot = TRUE)

Production models with time series fitting

Description

This function applies the production models under non-equilibrium conditions by applying time series fitting using non-linear least squares minimisation.

Usage

prod_mod_ts(
  data,
  method = "Schaefer",
  B0_init = NA,
  B0_est = NA,
  effort_unit = 1,
  plot = TRUE
)

Arguments

Details

Either catch per unit of effort (CPUE) is inserted into the model directly (by a column CPUE) or CPUE is calculated from the catch and effort, then these two vectors should have required units. Whenever a good estimate for the virigin biomass is available, this estimate should be inserted for B_init. The default approach for the initial estimate of the virgin biomass is to multiply the average yield by 2 (Dharmendra and Solmundsson, 2005). Alternatively, just a part of the time series of yield values can be choosen to represent the virgin biomass. The minimisation procedure is based on least error sum of squares (SSE). For the logistic (Schaefer) method the standard calculation of SSE is applied (sum((CPUE - predicted CPUE)^2)), for the method with Gompertz distribution (Fox) SSE is calculated according to the Thiel's U statistic sqrt(sum(CPUE - predicted CPUE)/sum(CPUE(t) - CPUE(t-1))) (Wittink, 1988).

Value

A list with the input parameters and following list objects:

• Bvec: biomass vector,

• CPUE_hat: predicted CPUE,

• K: carrying capacity,

• r: population growth rate,

• q: catchability coefficient,

• MSY: maximum sustainabale yield (MSY),

• Bmsy: biomass at MSY,

• Emsy: fishing effort at MSY

• Fmsy: fishing mortality at MSY,

References

Dharmendra, D., Solmundsson, J., 2005. Stock assessment of the offshore Mauritian banks using dynamic biomass models and analysis of length frequency of the Sky Emperor (Lethrinus mahsena). Fisheries Training Program The United Nations University, 61

Hilborn, R. and Walters, C., 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman and Hall, New York

Prager, M. H., 1994. A suite of extensions to a non-equilibrium surplus production model. Fishery Bulletin 92: 374-389

Richards, F. J., 1959. A flexible growth function for empirical use. Journal of experimental Botany, 10(2), 290-301.

Wittink, D. R., 1988. The application of regression analysis. Allyn and Bacon. Inc. Boston. MA. 324p.

Examples

data(emperor)
prod_mod_ts(emperor, method = "Schaefer")
prod_mod_ts(emperor, method = "Fox")

Predict gillnet selectivity (old Millar method)

Description

Predict gillnet selectivity (old Millar method)

Usage

rcurves_Millar(type, meshsizes, rel, pars, plotlens)

Arguments

Value

selectivities

Source

https://www.stat.auckland.ac.nz/~millar/selectware/

References

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3):471-477

Recruitment patterns

Description

This function estimates recrutiment patterns from length-frequency data.

Usage

recruitment(param, tsample, catch_column = NA, plot = FALSE)

Arguments

Details

This function calculates recruitment patterns of a stock by backward projection onto the length axis of a set of length frequency data using the (special, generalised or seasonalised) von Bertallanfy growth curve (vBGF, Pauly 1982). The method assumes that (i) all fish in a data set grow as described by a single set of growth parameters and (ii) one month out of twelve always has zero recruitment. The second assumption is probably not met, since temperate species may contain more than one month with zero recruitment, while tropical species may have more constant recruitment without months of no recruitment. If t0 is not provided, a relative recruitment pattern will be estimated without specific month values returned in the results. However, an estimate of t0 can be obtained by the time lag between peak spawning and recruitment. Several length-frequency data sets can be used to estimate the recrutiment pattern by providing catch as a matrix and setting catch_column to NA (default). Then the fraction per time is calculated for each size class in each sample and then pooled together. For the generalised vBGF, D is required, for the seasonalised vBGF C, ts and D.

Value

A list with the input parameters and following list objects:

• ti: actual age,

• tS_frac: age at which the length was zero expressed as fraction of the year,

• cor_months: corresponding months,

• months: numeric months (relative if no t0 is not given),

• months_abb: months (only presented if t0 is given),

• all_recruits: number of recruits per month as matrix if several length-frequency data sets are provided,

• mean_recruits: (mean) number of recruits per month,

• per_recruits: precentage number of recruits per month.

References

Brey, T., Soriano, M., Pauly, D., 1988. Electronic length frequency analysis. A revised and expanded user's guide to ELEFAN 0, 1 and 2. (Second edition). Berichte aus dem Institut f??r Meereskunde Kiel, No 177, 31p.

Moreau, J., & Cuende, F. X., 1991. On improving the resolution of the recruitment patterns of fishes. Fishbyte, 9(1), 45-46.

Pauly, D., 1982. Studying single-species dynamics in a tropical multispecies context. In Theory and management of tropical fisheries. ICLARM Conference Proceedings (Vol. 9, No. 360, pp. 33-70).

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# one sample
dat <- list(midLengths = seq(2,98,4),
               catch = c(0.6,17.6,93,83.2,12.6,0.3,0,0,0,1,17.1,51.4,
               26.1,2.2,0.2,4.5,21.6,17.6,3.7,8.7,10.6,6.3,5.6,2.9,0.8),
               Linf = 100,
               K = 0.5,
               t0 = 0)
recruitment(param = dat, tsample = 0.25)


# several samples
data(synLFQ4)

# add growth parameters
synLFQ4$Linf <- 80
synLFQ4$K <- 0.5
synLFQ4$t0 <- 0.25

# retrieve sampling times from catch matrix
s_dates <- as.POSIXlt(synLFQ4$dates, format="%d.%m.%Y")

recruitment(param = synLFQ4, tsample = s_dates$yday/365, plot = TRUE)


plot(synLFQ4, Fname = "catch",
   par = list(Linf = 80, K = 0.5, t_anchor = 0.25, C = 0.75, ts = 0),
   ylim = c(0,80))

Millar's selectivity types

Description

This function returns a function corresponding to the type of curve which was selected to represent the selectivity of nets or hooks.

Usage

rtypes_Millar(rtype)

Arguments

Details

Function adapted from the selectivity functions provided by Prof. Dr. Russell Millar (https://www.stat.auckland.ac.nz/~millar/). Until now following curves are incorporated: "norm.loc" for a normal curve with common spread, "norm.sca" for a normal curve with variable spread, "lognorm" for a lognormal curve, "binorm.sca" for a bi-normal curve, "bilognorm" for a bi-lognormal curve, "tt.logistic" for a control and logistic curve.

Source

https://www.stat.auckland.ac.nz/~millar/selectware/

References

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3), 471-477.

Selectivity model

Description

This function estimates the selecitvity of gillnets and trawl nets from experimental catches.

Usage

select(param, plot = FALSE)

Arguments

Details

This function estimates the fractions retained by each net, the optimum lengths for each net, the selection factor (SF), and the standard deviation of the factor (stand.dev). Calculations are based on a normal distribution with common spread. Assumptions of this method are, that (i) the optimum length Lm is proportional to the mesh size (Lm = SF * m), (ii) the selection curves are normally distributed with a common standard deviation, (iii) the nets have the same fishing power (same dimensions and material). Requirements for the experimental set-up are: selection curves corresponding to the two mesh sizes have to overlap, and the nets have to be set in the same area, during the same time. To calculate selection factor (SF), L25, L50 and L75 for trawl nets /fisheries.

Value

A list with the input parameters and following list objects for type = "gillnet": #'

• classes.num: numeric vector with length classes without a plus group,

• SNet1: selection ogive net 1,

• SNet2: selection ogive net 2,

• lnNet2_Net1: logarithm ratio between nets,

• linear_mod: linear model,

• LmNet1: optimum length net 1,

• LmNet2: optimum length net 2,

• SF: selection factor,

• stand.dev: standard deviation of selection factor.

and following objects for type = "trawl_net":

• classes.num: numeric vector with length classes,

• SLobs: observed selection ogive,

• SLest: estimated selection ogive,

• lnSL: logarithm of observed selection,

• linear_mod: linear model,

• S1: constant of selection curve,

• S2: another constant of selection curve,

• L25: length at which 25

• L50: length at which 50

• L75: length at which 75

• SF: selection factor.

References

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# Gillnet selectivity
data(tilapia)
out <- select(param = tilapia)
plot(out)

# Trawl selectivity
data(bream)
select(bream)

Millar's selectivity model

Description

This model estimates the selecitvity of different gears from experimental catches.

Usage

select_Millar(
  param,
  x0 = NULL,
  rtype = "norm.loc",
  rel.power = NULL,
  plot = TRUE
)

Arguments

Details

Model adapted from the selectivity functions provided by Prof. Dr. Russell Millar (https://www.stat.auckland.ac.nz/~millar/). In the deviance plot open circles correspond to negative, closed to positive residuals. The size of the circles is proportional to the square of the residuals. To assess the model fit by the deviance plot it requires some experience, in general the pattern should be random and the sizes not too big. Please refer to Millar's publications and other publications for comparison. The model can produce errors if the starting values (x0) for the optim function are not realistic. Please be aware that if the method is changed the outcoming parameters can greatly vary. Simliarly the starting values have to be adapted when changing the method (rtype).

Source

https://www.stat.auckland.ac.nz/~millar/selectware/

References

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3):471-477

Holt, S. J. 1963. A method for determining gear selectivity and its application. ICNAF Special Publication, 5: 106-115.

Examples

data(haddock)

output <- select_Millar(haddock, x0 = c(-10,0.3,0),
   rtype = "tt.logistic")

plot(output, plotlens=seq(25,35,0.1), deviance_plot = FALSE)
legend("topleft",c("Control","Experimental"), lty=1:2, col=1:2)


# Gillnet
data(gillnet)

# Using inital estimates from old method
select_Millar(gillnet, x0 = NULL, rtype = "norm.loc")$value
select_Millar(gillnet, x0 = NULL, rtype = "norm.sca")$value
select_Millar(gillnet, x0 = NULL, rtype = "lognorm")$value

# Two rtypes which require starting values
select_Millar(gillnet, x0 = c(55,4,65,4,3), rtype="binorm.sca")
select_Millar(gillnet, x0 = c(4,0.2,4.2,0.1,2), rtype="bilognorm")

# Calculation with finer length resolution
output <- select_Millar(gillnet, x0 = NULL, rtype = "lognorm")
plot(output, plotlens=seq(40,90,0.1))

# Use alternate plot settings
output <- select_Millar(gillnet, x0 = NULL, rtype = "lognorm")
ncolor <- length(output$meshSizes)
plot(output, plotlens=seq(40,90,0.1), deviance_plot = FALSE,
 lty=1, col=rainbow(ncolor))
legend("topleft", col=rainbow(ncolor), legend=output$meshSizes,
 lty=1, title="Mesh size [cm]")

 # deviance plot only
 plot(output, plotlens=seq(40,90,0.1), selectivity_plot = FALSE)


# Stacked trammel net
# The data come from two experiments using different mesh sizes
# This analysis assumes common retention curve in both experiments.
# Note that summary function does not produce residual plot
# since lengths are not unique
data(trammelnet)

output <- select_Millar(trammelnet, x0 = c(25,4),
   rtype="norm.loc", rel.power = rep(1,6))

plot(output,plotlens=seq(10,40,0.1))

Selectivity patterns

Description

Based on a few parameters, this function estimates the fraction per length group retained in the net. Different selection curves can be used for the estimation.

Usage

select_ogive(s_list, Lt, Lc = NA)

Arguments

Details

This function is embedded within predict_mod. selecType "knife_edge" only requires a Lc value. "trawl_ogive" requires a Lc (L50) and a L75 value. "lognormal" requires two mesh sizes, an estimate of mu and of sigma. "normal_fixed" requires two mesh sizes with an estimate of the selection factor (SF) and an estimate of sigma.

References

Millar, R. B., Holst, R. (1997). Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3), 471-477.

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# create list with selectivity information
select.list <- list(selecType = 'knife_edge',
   Lc = 34, L75 = 37, tc = 5, meshSizes = c(60,80),
   select_p1 = 2.7977, select_p2 = 0.1175)


# create vector with mid lengths
Lt <- seq(5, 50, 0.01)

# knife edge selectivity
sel_ke <- select_ogive(select.list, Lt)

# trawl ogive selectivity
select.list$selecType = "trawl_ogive"
sel_to <- select_ogive(select.list, Lt)

plot(Lt, sel_ke, type = 'l')
lines(Lt, sel_to, col = 'blue')


# Gillnet selectivity ("lognormal" and "normal_fixed")
select.list$selecType <- "lognormal"
sel_log <- select_ogive(select.list, Lt)

select.list$selecType <- "normal_fixed"
select.list$select_p1 <- 0.2
select.list$select_p2 <- 1.5
sel_nf <- select_ogive(select.list, Lt)

plot(Lt, sel_log, type = 'l')
lines(Lt, sel_nf, col = 'blue')

Shrimp data

Description

Data from the Kuwait shrimp (Penaeus semisulcatus) fishery. They can be used to simulate different management scenarios by applying prediction models (predict_mod). Fishing mortalities were estimated from catch data and biomass estimates were obtained from the swept area method. Recuritment to fishery at the age of one month (Tr = 1).

Usage

data(shrimps)

Format

A list consisting of: 1. age groups [months], 2. meanWeight, 3. meanValue, 4.FM, and 5.M

Source

Garcia, S. and N.P. van Zalinge, 1982. Shrimp fishing in Kuwait: methodology for a joint analysis of the artisanal and industrial fisheries. pp. 119-142 In: Report on the Workshop on assessment of the shrimp stocks of the west coast of the Gulf between Iran and the Arabian Peninsula. Fisheries development in the Gulf. Rome, FAO, FI:DP/RAB/80/015/1, 163 p.

Examples

data(shrimps)
str(shrimps)
summary(shrimps)

Convert FiSAT's starting point to t_anchor value

Description

Starting points returned or chosen within FiSAT are not supported in TropFishR. Instead t_anchor takes on the job of anchoring VBGF growth curves on a temporal axis. This function allows to convert FiSAT's starting points to t_anchor values

Usage

startingPoint2tanchor(param, par, startingLength, startingSample)

Arguments

Value

list with input elements and estimated t_anchor value

Examples

data(synLFQ5)
lfqNEW <- startingPoint2tanchor(synLFQ5, par = list(Linf = 92, K = 0.37),
   startingLength = 31, startingSample = 4)
lfqRest <- lfqRestructure(lfqNEW, MA = 11)
plot(lfqRest,par=list(Linf=lfqRest$Linf,K=lfqRest$K,t_anchor=lfqRest$t_anchor))

Stock simulation

Description

This function estimates stock size, biomass and yield of a stock from fishing mortality per age class or length group. This function is embedded in the Thompson and Bell model (prediction model: predict_mod).

Usage

stock_sim(param, age_unit = "year", stock_size_1 = NA, plus_group = NA)

Arguments

Details

better to treat last group always as a plus group... if stock size 1 not provided assumes 1000 as intital population size make sure that FM is also in same unit as the classes, e.g. when classes in months than also FM has to be provided in 1/months

Value

A list with the input parameters and following list objects:

• dt: delta t,

• N: population numbers,

• dead: number of deaths due to natural mortality,

• C: catch,

• Y: yield,

• B: biomass,

• V: value,

• totals: summarised output:

  • totC total catch,

  • totY total yield,

  • totV total value,

  • meanB mean biomass.

  ,

References

Garcia, S. and N.P. van Zalinge, 1982. Shrimp fishing in Kuwait: methodology for a joint analysis of the artisanal and industrial fisheries. pp. 119-142 In: Report on the Workshop on assessment of the shrimp stocks of the west coast of the Gulf between Iran and the Arabian Peninsula. Fisheries development in the Gulf. Rome, FAO, FI:DP/RAB/80/015/1, 163 p.

Millar, R. B., & Holst, R. (1997). Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3):471-477

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

# age-based stock simulation
data(shrimps)

# option 1: without plus group
stock_sim(shrimps, age_unit = "month")

# option 2: with plus group
stock_sim(param = shrimps, age_unit = "month", plus_group = 11)

# length-based stock simulation
data(hake)

stock_sim(param = hake, stock_size_1 = 98919.3)

Synthetic Catch-at-age data I

Description

Synthetic Catch-at-age data from Sparre & Venema (1998). Can be used for the estimation of the instantaneous total mortality rate (Z) by means of Z_BevertonHolt.

Usage

data(synCAA1)

Format

A list consisting of:

• midAge: a vector of the mid ages of the age groups,

• catch: a matrix with the catches for different years.

Source

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(synCAA1)
str(synCAA1)
summary(synCAA1)

Synthetic Catch-at-age data II

Description

Synthetic Catch-at-age data from Sparre & Venema (1998). Can be used for the estimation of the instantaneous mortality rate (Z) by means of the cumulative catch curve (catchCurve).

Usage

data(synCAA2)

Format

A list consisting of:

• midAge a vector of the mid ages of the age groups,

• catch a matrix with the catches for different years.

Source

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(synCAA2)
str(synCAA2)
summary(synCAA2)

Synthetical catch per unit of effort (CPUE) dataset

Description

Synthetical CPUE dataset from Exercise 4.3 in Sparre & Venema (1999). Can be used to estimate the instantaneous total mortality rate (Z) by means of the function Z_CPUE.

Usage

data(synCPUE)

Format

A dataframe consisting of following columns:

• cohort: name of cohort, e.g. 1982 S, meaning summer cohort of 1982,

• age: age of cohorts,

• CPUE: catch per unit of effort of cohorts.

Source

Sparre, P., Venema, S.C., 1999. Introduction to tropical fish stock assessment. Part 2. Excercises. FAO Fisheries Technical Paper, (306.2, Rev. 2). 94 p.

Examples

data(synCPUE)
head(synCPUE)
str(synCPUE)

Synthetic length-frequency data I

Description

Synthetic length-frequency data as provided in Sparre & Venema (1998). Can be used to apply the function Bhattacharya or ELEFAN.

Usage

data(synLFQ1)

Format

A list consisting of:

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column).

Source

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(synLFQ1)
str(synLFQ1)
summary(synLFQ1)

Synthetic length frequency data II

Description

Synthetic length frequency data from Sparre & Venema (1998). Can be used for the estimation of the instantaneous total mortality rate (Z) by means of Z_BevertonHolt.

Usage

data(synLFQ2)

Format

A list consisting of:

• dates dates of sampling times (class Date),

• midLengths: midpoints of the length classes,

• Linf: infinite length for investigated species in cm [cm],

• K: growth coefficent for investigated species per year [1/year],

• catch: matrix with catches/counts per length class (row) and sampling date (column).

Source

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(synLFQ2)
str(synLFQ2)
summary(synLFQ2)

Synthetic length frequency data III

Description

Synthetic length frequency data from Sparre & Venema (1998). Can be used for the estimation of the instantaneous total mortality rate (Z) by means of Z_BevertonHolt.

Usage

data(synLFQ3)

Format

A list consisting of:

• midLengths: midpoints of the length classes,

• Linf: infinite length for investigated species in cm [cm],

• K: growth coefficent for investigated species per year [1/year],

• t0: theoretical time zero, at which individuals of this species hatch,

• catch: a vector with catches.

Source

Sparre, P., Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Examples

data(synLFQ3)
str(synLFQ3)
summary(synLFQ3)

Synthetic length-frequency data IV (with seasonal oscillation)

Description

Synthetic length-frequency data as generated by the function lfqGen from the fishdynr package (Taylor 2016). Can be used by ELEFAN or ELEFAN_SA. The data is generated with the following von Bertalanffy growth parameters:

• K = 0.5

• Linf = 80

• C = 0.75

• ts = 0.5

• t_anchor = 0.25 (Time when yearly recruitment pulse occurs; e.g. 0 = Jan 1, 0.25 = Apr 1, 0.5 = Jul 1st, 0.75 = Oct 1)

Further settings include:

• Linf.cv = 0.05

• K.cv = 0.05

• L50 = 20 (length at 50% prob. of capture via trawl net)

• wqs = 0 (width between 25% and 75% prob. of capture quantiles; i.e. wqs = 0 is knife-edge selection)

• M = 0.5 (Natural mortality rate)

• harvest_rate = 0.5 (Fishing mortality rate)

Usage

data(synLFQ4)

Format

A list of class lfq consisting of:

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column).

Source

Taylor, M (2016). fishdynr: Fisheries science related population dynamics models. R package version 0.2. https://github.com/marchtaylor/fishdynr

Examples

data(synLFQ4)

# plot of length frequencies
plot(synLFQ4, Fname = "catch")

# plot of restructured length frequencies
synLFQ4 <- lfqRestructure(synLFQ4, MA = 15)
plot(synLFQ4, Fname = "rcounts")

Synthetic length-frequency data V (without seasonal oscillation)

Description

Synthetic length-frequency data as generated by the function lfqGen from the fishdynr package (Taylor 2016). Can be used by ELEFAN or ELEFAN_SA. The data is generated with the following von Bertalanffy growth parameters:

• K = 0.5

• Linf = 80

• C = 0

• ts = 0

• t_anchor = 0.25 (Time when yearly recruitment pulse occurs; e.g. 0 = Jan 1, 0.25 = Apr 1, 0.5 = Jul 1st, 0.75 = Oct 1)

Further settings include:

• Linf.cv = 0.05

• K.cv = 0.05

• L50 = 20 (length at 50% prob. of capture via trawl net)

• wqs = 0 (width between 25% and 75% prob. of capture quantiles; i.e. wqs = 0 is knife-edge selection)

• M = 0.5 (Natural mortality rate)

• harvest_rate = 0.5 (Fishing mortality rate)

Usage

data(synLFQ5)

Format

A list of class lfq consisting of:

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column).

Source

Taylor, M (2016). fishdynr: Fisheries science related population dynamics models. R package version 0.2. https://github.com/marchtaylor/fishdynr

Examples

data(synLFQ5)

# plot of length frequencies
plot(synLFQ5, Fname = "catch")

# plot of restructured length frequencies
synLFQ5 <- lfqRestructure(synLFQ5, MA = 15)
plot(synLFQ5, Fname = "rcounts")

Synthetic length-frequency data VI (without seasonal oscillation)

Description

Synthetic length-frequency data as generated by the function lfqGen from the fishdynr package (Taylor 2016). Can be used by ELEFAN or ELEFAN_SA. The data is generated with the following von Bertalanffy growth parameters:

• K = 0.47 +/- 0.2 (CV)

• Linf = 33.7 +/- 0.05 (CV)

• C = 0

• ts = 0

• t_anchor = 0.25 (Time when yearly recruitment pulse occurs; e.g. 0 = Jan 1, 0.25 = Apr 1, 0.5 = Jul 1st, 0.75 = Oct 1)

Further settings include:

• L50 = 10 (length at 50% prob. of capture via trawl net)

• wqs = 3 (width between 25% and 75% prob. of capture quantiles; i.e. wqs = 0 is knife-edge selection)

• M = 0.8 (Natural mortality rate)

• harvest_rate = 1.3 (Fishing mortality rate)

Usage

data(synLFQ6)

Format

A list of class lfq consisting of:

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column).

Source

Taylor, M (2016). fishdynr: Fisheries science related population dynamics models. R package version 0.2. https://github.com/marchtaylor/fishdynr

Examples

data(synLFQ6)

# plot of length frequencies
plot(synLFQ6, Fname = "catch")

# plot of restructured length frequencies
synLFQ6 <- lfqRestructure(synLFQ6, MA = 7)
plot(synLFQ6, Fname = "rcounts")

Synthetic length-frequency data VII with seasonal oscillation

Description

Synthetic length-frequency data as generated by the function lfqGen from the fishdynr package (Taylor 2016). Can be used by ELEFAN, ELEFAN_SA, or ELEFAN_GA. The data is generated with the following von Bertalanffy growth parameters:

• K = 0.2 +/- 0.1 (CV)

• Linf = 123 +/- 0.05 (CV)

• C = 0.3

• ts = 0

• t_anchor between 0.16 and 0.34 (Time when yearly recruitment pulse occurs; e.g. 0 = Jan 1, 0.25 = Apr 1, 0.5 = Jul 1, 0.75 = Oct 1; repro_wt = c(0, 0, 0.2, 1, 0.6, 0, 0, 0, 0, 0, 0, 0))

Further settings include:

• Lmat = 30.8 (length at maturity)

• L50 = 35 (length at 50% prob. of capture via trawl net)

• wqs = 5 (width between 25% and 75% prob. of capture quantiles; i.e. wqs = 0 is knife-edge selection)

• M = 0.2 (Natural mortality rate)

• harvest_rate = 0.3 (Fishing mortality rate)

Usage

data(synLFQ7)

Format

A list of class lfq consisting of:

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column).

Source

Taylor, M (2016). fishdynr: Fisheries science related population dynamics models. R package version 0.2. https://github.com/marchtaylor/fishdynr

Examples

data(synLFQ7)

# plot of length frequencies
plot(synLFQ7, Fname = "catch")

# plot of restructured length frequencies
synLFQ7 <- lfqRestructure(synLFQ7, MA = 11)
plot(synLFQ7, Fname = "rcounts")

Synthetic length-frequency data VIII with variable harvest rate

Description

Synthetic length-frequency data as generated by the function virtualPop2 from the fishdynr package (Taylor and Mildenberger, 2018). Can be used by ELEFAN, ELEFAN_SA, or ELEFAN_GA. The data is generated with the following von Bertalanffy growth parameters:

• K = 0.5 +/- 0.05 (CV)

• Linf = 80 +/- 0.05 (CV)

• C = 0.0

• ts = 0.0

• t_anchor 0.25 (Time when yearly recruitment pulse occurs; e.g. 0 = Jan 1, 0.25 = Apr 1, 0.5 = Jul 1, 0.75 = Oct 1; repro_wt = c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0))

Further settings include:

• Lmat.f = 40 (length at maturity)

• Lmat.m = 36 (length at maturity)

• L50 = 20 (length at 50% prob. of capture with trawl net (Lc))

• wqs = 4 (width between 25% and 75% prob. of capture quantiles; i.e. wqs = 0 is knife-edge selection)

• M = 0.7 (Natural mortality rate)

• harvest_rate = 1, 0.8, 0.4, 0.1 for years 2014, 2015, 2016, 2017, repsectively (fishing mortality rate)

The average biomass relative to the unfished biomass and the yield per recurit for the years, 2014, 2015, 2016, 2017 is 0.16, 0.21, 0.41, 0.75, and 0.4, 0.43, 0.24, 0.07, respectively. Biomass over Bmsy as estimated with a surplus production model is 0.51, 0.67, 1.27, 2.18. Lopt is 53.33 cm.

Usage

data(synLFQ8)

Format

A list of class lfq consisting of:

• stock Stock ID or name,

• dates dates of sampling times (class Date),

• midLengths midpoints of the length classes,

• catch matrix with catches/counts per length class (row) and sampling date (column),

• comment additional comments to this data set.

Source

Taylor, M & T. K. Mildenberger (2018). fishdynr: Fisheries science related population dynamics models. R package version 0.5. https://github.com/tokami/fishdynr

Examples

data(synLFQ8)

# plot of length frequencies
plot(synLFQ8, Fname = "catch")

# plot of restructured length frequencies
synLFQ8 <- lfqRestructure(synLFQ8, MA = 11)
plot(synLFQ8, Fname = "rcounts")

Tilapia data

Description

A list with characteristics of experimental catches of tilapia Tilapia esculenta with gillnets of two mesh sizes. The Results of the experiment are the midlengths of size classes, the number of fish caught with net 1 & 2, and the meshsizes of both nets. The data can be analysed with the function select.

Usage

data(tilapia)

Format

A list consiting of:

• midLengths the midlengths of size classes,

• numNet1 the number of fish caught with net 1,

• numNet2 the number of fish caught with net 2,

• msNet1 the meshsize of net 1,

• msNet2 and the meshsize of net 2.

Source

Garrod, D.J., 1961. The selection characteristics of nylon gill nets for Tilapia esculenta Graham. J.Cons.CIEM, 26(2):191-203

Examples

data(tilapia)
str(tilapia)
summary(tilapia)

Trammel net data

Description

Data of an experiment with several trammel nets with different mesh sizes. Can be used for function select_Millar.

Usage

data(trammelnet)

Format

A list consiting of:

• $midLengths the midlengths of size classes,

• $meshSizes the meshsizes,

• $catchPerNet_mat a matrix with the numbers in catch of the corresponding mesh sizes (same order),

Source

Millar, R. B., Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3), 471-477.

Examples

data(trammelnet)
str(trammelnet)
summary(trammelnet)

Data from the trawl fishery off the North coast of Java

Description

Times series of catch and effort data from the trawl fishery off the North coast of Java. This dataset can be used for the estimation of maximum sustainable yield by means of the production models (prod_mod and prod_mod_ts).

Usage

data(trawl_fishery_Java)

Format

A dataframe consisting of: 1. year a vector with years, 2. Y yield [1000 tons], and 3. f fishing effort [number of standard vessels].

Source

Dwiponggo, A., 1979. Review of the demersal resources and fisheries in the Java Sea. IPFC:RRD/II/79/Inf.12. Paper presented at the SCORRAD Meeting, 1979, Hong Kong.

Examples

data(trawl_fishery_Java)
str(trawl_fishery_Java)
summary(trawl_fishery_Java)

Whiting data

Description

A dataset of North Sea whiting Merlangius merlangus caught during the period 1974-1980. Can be used for catchCurve and VPA.

Usage

data(whiting)

Format

A list consisting of:

• age: a vector with age groups,

• M: natural mortality rate,

• a: length-weight relationship coefficent (W = a * L^b),

• b: length-weight relationship coefficent (W = a * L^b),

• catch:a matrix with catches from 1974 to 1980.

Source

ICES, 1981. Report of the Ad hoc working group on the use of effort data in assessment, Copenhagen, 2-6 March 1981. ICES C.M. 1981/G:5 (mimeo)

Examples

data(whiting)
str(whiting)
summary(whiting)

Year - Date conversion

Description

Convert numeric years to dates

Usage

yeardec2date(yeardec)

Arguments

Value

date in format "%Y-%m-%d" (class 'Date').

Examples

 yeardec2date(2014.14)

Yield per recruit

Description

Estimates the absolute and relative yield and biomass per recruit and the first order derivative.

Usage

ypr(param, FM_change, t = NA)

Arguments

Details

The Thompson and Bell model incorporates an iteration step simulating the stock by means of the stock_sim function. In case changes in gear characteristics - here measured in terms of Lc or tc, the length or age at first capture, respectively - should be explored, a list with selectivity information about the gear has to be provided and the prediction models make use of the selectivity select_ogive function. Sparre and Venema (1998) recommend to treat the last length class always as plus group. This model is very sensitive to zero observations in the ultimate length classes. If unrealistic results are returned, it is recommended to cut length classes with zero observations, group them in a plus group or to change the interval between length classes. Equations which are used in this function assume isometric growth, an assumption often not met. Further, the assumption that there is no relationship between the parental stock size and progeny over a wide range of fishing mortalities or exploitation values, respectively, is also said to be untrue. By default, the functions assume knife-edge recruitment and selection of gears (Sparre and Venema, 1998).

Value

A list with the input parameters and dependent on the model type following list objects:

• type = 'ypr'

References

Berkeley, S.A., and Houde, E.D., 1980. Swordfish, Xiphias gladius, dynamics in the Straits of Florida. ICES C.M., 11.

Beverton, R.J.H., and Holt, S.J., 1964. Table of yield functions for fishery management. FAO Fish. Tech. Pap. 38, 49 p.

Beverton, R.J.H., and Holt, S.J., 1966. Manual of methods for fish stock assessment. Pt. 2: Tables of yield functions. FAO Fisheries Technical Paper, (38)Rev.1:67 p.

Boerema, L.K., and J.A. Gulland, 1973. Stock assessment of the Peruvian anchovy (Engraulis ringens) and management of the fishery. Journal of the Fisheries Board of Canada, 30(12):2226-2235

Garcia, S. and N.P. van Zalinge, 1982. Shrimp fishing in Kuwait: methodology for a joint analysis of the artisanal and industrial fisheries. pp. 119-142 In: Report on the Workshop on assessment of the shrimp stocks of the west coast of the Gulf between Iran and the Arabian Peninsula. Fisheries development in the Gulf. Rome, FAO, FI:DP/RAB/80/015/1, 163 p.

Gulland, J.A., 1983. Fish stock assessment: a manual of basic methods. FAO/Wiley, New York.

Gulland, J.A. and Boerema, L., 1973. Scientific advice on catch levels. Fish. Bull. (US) 71:325-335.

Jones, R.E. 1957. A much simplified version of the fish yield equation. Doc. No. P. 21. Paper presented at the Lisbon joint meeting of International Commission Northwest Atlantic-Fisheries, International Council for the Exploration of the Sea, and Food and Agriculture Organization of the United Nations. 8 p. [Mimeo].

Millar, R.B., and Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3):471-477

Pauly, D., 1980. A selection of simple methods for the assessment of tropical fish stocks. FAO Fisheries Circulars (FAO). no. 729.

Pauly, D., 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators. ICLARM Stud. Rev. 8, 325 p.

Pauly, D. and M. Soriano. 1986. Some practical extensions to Beverton and Holt's relative yield-per-recruit model, p. 491-495. In J.L. Maclean, L.B. Dizon and L.V. Hosillos (eds.) The First Asian Fisheries Forum. Asian Fisheries Society, Manila.

Schaefer, M.B., 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Inter-Am. Trop. Tuna Comm., Bull. 1(2):27-56.

Schaefer, M.B., 1957. A study of the dynamics of the fishery for yellowfin tuna in the eastern tropical Pacific Ocean. Inter-Am. Trop. Tuna Comm., Bull. 2:247-268.

Sparre, P., and Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.

Yield per recruit with selection ogive

Description

Estimates relative yield and biomass, and the first order derivative.

Usage

ypr_sel(param, FM_change, Lt, P)

Arguments

Details

The Thompson and Bell model incorporates an iteration step simulating the stock by means of the stock_sim function. In case changes in gear characteristics - here measured in terms of Lc or tc, the length or age at first capture, respectively - should be explored, a list with selectivity information about the gear has to be provided and the prediction models make use of the selectivity select_ogive function. Sparre and Venema (1998) recommend to treat the last length class always as plus group. This model is very sensitive to zero observations in the ultimate length classes. If unrealistic results are returned, it is recommended to cut length classes with zero observations, group them in a plus group or to change the interval between length classes. Equations which are used in this function assume isometric growth, an assumption often not met. Further, the assumption that there is no relationship between the parental stock size and progeny over a wide range of fishing mortalities or exploitation values, respectively, is also said to be untrue. By default, the functions assume knife-edge recruitment and selection of gears (Sparre and Venema, 1998).

Value

A list with the input parameters and dependent on the model type.

References

Berkeley, S.A., and Houde, E.D., 1980. Swordfish, Xiphias gladius, dynamics in the Straits of Florida. ICES C.M., 11.

Beverton, R.J.H., and Holt, S.J., 1964. Table of yield functions for fishery management. FAO Fish. Tech. Pap. 38, 49 p.

Beverton, R.J.H., and Holt, S.J., 1966. Manual of methods for fish stock assessment. Pt. 2: Tables of yield functions. FAO Fisheries Technical Paper, (38)Rev.1:67 p.

Boerema, L.K., and J.A. Gulland, 1973. Stock assessment of the Peruvian anchovy (Engraulis ringens) and management of the fishery. Journal of the Fisheries Board of Canada, 30(12):2226-2235

Garcia, S. and N.P. van Zalinge, 1982. Shrimp fishing in Kuwait: methodology for a joint analysis of the artisanal and industrial fisheries. pp. 119-142 In: Report on the Workshop on assessment of the shrimp stocks of the west coast of the Gulf between Iran and the Arabian Peninsula. Fisheries development in the Gulf. Rome, FAO, FI:DP/RAB/80/015/1, 163 p.

Gulland, J.A., 1983. Fish stock assessment: a manual of basic methods. FAO/Wiley, New York.

Gulland, J.A. and Boerema, L., 1973. Scientific advice on catch levels. Fish. Bull. (US) 71:325-335.

Jones, R.E. 1957. A much simplified version of the fish yield equation. Doc. No. P. 21. Paper presented at the Lisbon joint meeting of International Commission Northwest Atlantic-Fisheries, International Council for the Exploration of the Sea, and Food and Agriculture Organization of the United Nations. 8 p. [Mimeo].

Millar, R.B., and Holst, R., 1997. Estimation of gillnet and hook selectivity using log-linear models. ICES Journal of Marine Science: Journal du Conseil, 54(3):471-477

Pauly, D., 1980. A selection of simple methods for the assessment of tropical fish stocks. FAO Fisheries Circulars (FAO). no. 729.

Pauly, D., 1984. Fish population dynamics in tropical waters: a manual for use with programmable calculators. ICLARM Stud. Rev. 8, 325 p.

Pauly, D. and M. Soriano. 1986. Some practical extensions to Beverton and Holt's relative yield-per-recruit model, p. 491-495. In J.L. Maclean, L.B. Dizon and L.V. Hosillos (eds.) The First Asian Fisheries Forum. Asian Fisheries Society, Manila.

Schaefer, M.B., 1954. Some aspects of the dynamics of populations important to the management of the commercial marine fisheries. Inter-Am. Trop. Tuna Comm., Bull. 1(2):27-56.

Schaefer, M.B., 1957. A study of the dynamics of the fishery for yellowfin tuna in the eastern tropical Pacific Ocean. Inter-Am. Trop. Tuna Comm., Bull. 2:247-268.

Sparre, P., and Venema, S.C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. FAO Fisheries Technical Paper, (306.1, Rev. 2). 407 p.