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

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

Arguments

data

a dataframe of parameters

  • year years,

  • yield catch in weight of fishery per year,

  • effort fishing effort per year,

  • CPUE catch per unit of effort per year (optional).

method

indicating if Schaefer or Fox model should be applied. First assumes a logistic relationship between growth rate and biomass, whereas second assumes it to foolow the Gompertz distribution (Richards 1959). Default is the dynamic Schaefer model.

B0_init

numeric; if realistic initial estimate for virgin biomass is available. If NA initial estimate for virgin biomass is set to two times average yield of all or part of yield values (see B0_est).

B0_est

intital value of virgin biomass estimating using all yield values (NA) or first years of time series, then provide numerical representing number of years

effort_unit

multiplication factor for the unit of effort. Default is 1.

plot

logical; if TRUE (default) a graph is displayed

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

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

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