Shepherd's method for the decomposition of seasonal length frequencies into age classes.

```
slca(x, type = 1, fryr=NULL, Linf = NULL, K = NULL, t0 = NULL,
Lrange = NULL, Krange = NULL)
```

x

the dataframe containing the seasonal length frequencies. The first column contains the lower limit of the length bin as a single numeric value, and the second and remaining columns contain the number of fish in each length bin for each seasonal length frequency. The increment of length frequencies should be constant, e.g. every 3 cm. Empty cells must be coded as zeros. Column headers are not required.

type

the analysis to be conducted: 1=*explore*, 2=*evaluate*.

fryr

the fraction of the year corresponding to when each seasonal length frequency was collected. Enter one numeric value for each length frequency separated by commas within the concatentation function, e.g. c(0.2,0.45). Values must be entered for type=1 and type=2.

Linf

the von Bertalanffy L-infinity parameter. If type=2, then value must be entered.

K

the von Bertalanffy growth parameter. If type=2, then value must be entered.

t0

the von Bertalanffy t-sub zero parameter. If type=2, the value must be entered.

Lrange

the L-infinity range (minimum and maximum) and increment to explore. If type=1, then values must by entered. The first position is the minimum value, the second position is the maximum value, and the third position is the increment. Values should be separated by commas within the concatentation function, e.g. c(100,120,10).

Krange

the K range and increment to explore. If type=1, then values must by entered. The first position is the minimum value, the second position is the maximum value, and the third position is the increment. Values should be separated by commas within the concatentation function, e.g. c(0.1,0.3,0.02).

If type=1, tables of goodness of fit measures versus L-infinity and K parameters, and t0 values versus L-infinity and K parameters. If type=2, table of age classes produced from slicing the length frequencies.

There are two analytical steps. In the "explore" analysis, a set of von Bertalanffy parameters that best describes the growth of the seasonal length groups is selected from a table of goodness-of-fit measures mapped over the range of specified K and L-infinity values. Once the best K and L-infinity parameters are selected, the corresponding t0 value is obtained off the second table. In the "evaluate" analysis, the selected parameters are used to 'slice' the seasonal length frequencies into age classes.

Shepherd, J. G. 1987. A weakly parametric method for the analysis of length composition data. In: D. Pauly and G. Morgan, (eds). The Theory and Application of Length-Based Methods of Stock Assessment. ICLARM Conf. Ser. Manilla.

```
# NOT RUN {
#Data are from Shepherd working document - seasonal length frequencies
# for Raja clavata.
data(Shepherd)
#explore
slca(Shepherd,1,fryr=c(0.2,0.45,0.80),Lrange=c(100,150,10),
Krange=c(0.1,0.3,0.02))
#evaluate
slca(Shepherd,2,fryr=c(0.2,0.45,0.80),Linf=120,K=0.2,t0=0.57)
# }
```

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