# Estimation of Mortality using Times-At-Large Data from Tagging

### Description

Calculates total instantaneous (Z), natural mortality (M) and/or fishing mortality (F) using times-at-large data and methods of Gulland (1955) and McGarvey et al. (2009).

### Usage

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### Arguments

`relyr` |
a vector of release year (or cohort) for individual times-at-large observations. |

`tal` |
a vector of individual times-at-large observations. |

`N` |
a vector of number of releases for each release year (or cohort). Each individual observation from a release year should have the same N value. |

`method` |
1 = McGarvey et al., 2 = Gulland. Default is all (i.e., c(1,2)). |

`np` |
the number of periods over which to combine data to make period estimates of mortality. Set np=0 to estimate mortality for each release year. |

`stper` |
vector of year values representing the beginning year of each period over which to estimate mortality. The first year in c() must always be the first release year. |

`nboot` |
the number of resamples for the Gulland method. |

### Details

The methods of Gulland (1955) and McGarvey et al (2009) are used to estimate Z, F and M (depending on the method) from tagging times-at-large data. For the Gulland method, the standard error of the Z, M, and F estimates are made using a parametric bootstrap method similar to Tanaka (2006). When periods are specified, period-specific mortality estimates and standard errors are derived by averaging release-year-specific mortality estimates. The standard errors are calculated by taking the square-root of the averaged variances of the estimates. To combine data over all years prior to estimation, change all relyr within a period to the same year value.

### Value

dataframe containing the M, F and Z estimates and associated standard errors by period.

### Author(s)

Gary A. Nelson, Massachusetts Division of Marine Fisheries gary.nelson@state.ma.us

### References

Gulland, J. A. 1955. On the estimation of population parameters from marked members. Biometrika 42: 269-270.

McGarvey, R., J. M. Matthews, and J. E. Feenstra. 2009. Estimating mortality from times-at-large: testing accuracy and precision using simulated single tag-recovery data. ICES Journal of Marine Science 66: 573-581.

Tanaka, E. 2006. Simultaneous estimation of instantaneous mortality coefficients and rate of effective survivors to number of released fish using multiple sets of tagging experiments. Fisheries Science 72: 710-718.

### Examples

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