Description Usage Arguments Details Value Author(s) Examples

A function that returns the log-likelihood of the model of recruitment, survival and catchability, given capture-recapture data. Model parameters are provided in the function's single argument, which is a vector. Capture-recapture data must be stored in specific-named global variables (see Details).

1 | ```
llRecruit(params)
``` |

`params` |
A vector containing six parameter values (see Details). |

The input `params`

contains the following values:

[tbar] The day when recruitment peaks.

[sigma] The spread in recruitment (days). Approximately 95% of recruitments occur during days [tbar - 2*sigma, tbar + 2*sigma].

[alpha0] Baseline catch rate (per unit effort).

[alpha1] Age-dependence in catch rate.

[beta0] Base-line mortality rate (per day).

[beta1] Age-dependence in mortality rate.

Recruitment is described by a Guassian peak centred on day `tbar`

with spread characterised by `sigma`

. Per-capita catch rate is given by: `alpha0*exp(alpha1*age)`

, where `age`

is the days since recruitment. Per-capita mortality rate is given by: `beta0*exp(beta1*age)`

.

Suppose the survey involves the capture of `I`

animals over `J`

sampling events. The data must be stored and summarised by the following R-variables:

- y
An integer matrix containing the capture data (

`I`

rows and`J`

columns). Rows indicate the animal and columns indicate the sampling event.- f
An integer vector of size

`I`

identifying the sampling event when the animal was first caught. Values lie in the range [1,`J`

].- l
An integer vector of size

`I`

identifying the sampling event when the animal was last caught. Values lie in the range [1,`J`

]. All element satisfy`l`

>=`f`

.- E
A double vector of size

`J`

quantifying the effort applied during each sampling event.- T
An integer vector of size

`J`

providing the day of each sampling event.- T.F
An integer indicating the first possible day of recruitment.

- T.L
An integer (>

`T.F`

) indicating the last possible day of recruitment.

Note that the vectors `f`

and `l`

are determined by the matrix `y`

but must be calculated by the user.

This function is usually used in conjunction with the `optim`

function (see Examples).

A double.

Shane A. Richards ([email protected])

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
guess <- c(3.0, 3.0, 0.2, 0.0, 0.03, 0.1) # dummy model parameters
ll <- llRecruit(guess) # calculate log-likelihood of the model
# find the maximum-likelihood parameter estimates
# box constraint method allows control over parameter estimates
# age-dependent capture is turned off by restricting alpha1 (parameter 4)
# tracer flags are turned on to check for convergence
fit <- optim(par = guess, fn = llRecruit,
lower = c(0, 1.0, 0.10, -0.001, 0.0025, 0.001),
upper = c(6, 5.0, 0.35, 0.001, 0.1000, 0.190),
method = "L-BFGS-B",
control = list(fnscale = -1, trace = 1, maxit = 100, REPORT = 20))
fit$par # display maximum-likelihood parameter estimates
``` |

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