Description Usage Arguments Details Value Author(s) References Examples

Fits three growth models to length and weight-at-age data.

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`intype` |
the input format: 1= individual size data; 2 = mean size data. Default intype=1. |

`unit` |
the size unit: 1= length; 2 = weight. Default unit=1. |

`size` |
the vector of size (length or weight) data. |

`age` |
the vector of ages associated with the size vector. |

`calctype` |
if intype=1, 1 = use individual size data; 2 = calculate mean size from individual size data. Default calctype=1. |

`wgtby` |
weighting scheme: 1 = no weighting; 2 = weight means by inverse variance. Weighting of individual data points is not allowed. Default wgtby=1. |

`s2` |
if intype=2 and wgtby=2, specify vector of sample variances associated with mean size-at-age data. |

`error` |
the error structure: 1 = additive; 2 = multiplicative. Default error=1. |

`specwgt` |
if |

`Sinf` |
the starting value for |

`K` |
the starting value for |

`t0` |
the starting value for |

`B` |
the length-weight equation exponent used in the von Bertalanffy growth model for weight. Default B=3. |

`graph` |
logical value specifying if fit and residual plots should be drawn. Default graph = TRUE. |

`control` |
see function |

Three growth models (von Bertalanffy, Gompert and logistic) are fitted to length- or weight-at-age data using nonlinear least-squares (function *nls*).
If individual data are provided, mean size data can be calculated by specifying *calctype*=2. When fitting mean size data,
observations can be weighted by the inverse sample variance(*wgtby*=2), resulting in weighted nonlinear least squares. Additive or multiplicative
error structures are specified via *error*. See page 135 in Quinn and Deriso (1999) for more information on error structures.

If unit is weight,
the exponent for the von Bertalanffy growth in weight model is not estimated and must be specified (*B*).

Plots of model fit and residuals are generated unless *graph*=FALSE.

List containing list elements of the equation/structure and *nls* output for each model.
Information from *nls* output can be extracted using standard functions (e.g., *summary()*).

Gary A. Nelson, Massachusetts Division of Marine Fisheries [email protected]

Quinn, T. J. and R. B. Deriso. 1999. Quantitative fish dynamics. Oxford University Press. 542 pages.

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```
Loading required package: MASS
Loading required package: boot
Loading required package: bootstrap
Loading required package: lme4
Loading required package: Matrix
Loading required package: numDeriv
$vonbert
[1] "Model: Sinf*(1-exp(-K*(t-t0)))+e" "Response: Individual Length"
[3] "Least Squares: Unweighted"
$vout
Nonlinear regression model
model: size ~ Sinf * (1 - exp(-(K * (age - t0))))
data: x
Sinf K t0
211.7875 0.3781 -0.9156
residual sum-of-squares: 356005
Number of iterations to convergence: 4
Achieved convergence tolerance: 9.288e-06
$gompertz
[1] "Model: Sinf*exp(-exp(-K*(age-t0)))+e"
[2] "Response: Individual Length"
[3] "Least Squares: Unweighted"
$gout
Nonlinear regression model
model: size ~ Sinf * exp(-exp(-K * (age - t0)))
data: x
Sinf K t0
201.9056 0.5496 0.1215
residual sum-of-squares: 357835
Number of iterations to convergence: 6
Achieved convergence tolerance: 3.569e-06
$logistic
[1] "Model: Sinf/(1+exp(-K*(age-t0))+e" "Response: Individual Length"
[3] "Least Squares: Unweighted"
$lout
Nonlinear regression model
model: size ~ Sinf/(1 + exp(-K * (age - t0)))
data: x
Sinf K t0
195.9021 0.7281 0.6935
residual sum-of-squares: 359655
Number of iterations to convergence: 6
Achieved convergence tolerance: 9.261e-06
```

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