README.md

In quantifish/TagGrowth: Mixed effects model of capture-mark-recapture-age data

Welcome to TagGrowth

The software TagGrowth includes an estimation model for analysing growth using tag-recapture data where the individual fish have been aged upon recapture and a model for simulating growth of individual fish to test the performance of the estimation model.

Table of contents

• Introduction
• Installation
• Case study
• Simulation study
• Further reading

Introduction

Variation among individuals can be easily included by treating each individual's demographic parameters as a random effect that arises from a population-level distribution. We start with the specialized von Bertalanffy growth function:

where dL/dt is change in length as a function of time, a scales with energy acquisition, and k represents metabolic upkeep costs. However, individuals that are more highly active may obtain more food (increased a) and simultaneously have greater upkeep costs (increased b). Following Shelton et al. (2013), we include this correlation via the following equation:

where γ and Ψ approximate the allometric scaling of energy costs and acquisition. Integration then yields:

where

where Δt is the number of time-periods elapsed between length intervals, and where the Brody growth coefficient k = b (as in the conventional von Bertalanffy growth function). Readers are referred to Shelton et al. (2013) for an expanded model that incorporates variability in γ over time, although we retain the assumption that b varies among individuals (and hence has subscript i), where it follows a normal distribution (truncated at zero) with estimated mean and variance parameters.

Following previous notation, parameters are estimated by integrating across all random effects b, while noting that Eq. 15 also requires estimation of Li(t0), i.e., the length upon first observation for each individual.

Installation

Install the package from R using

# Install package
install.packages("devtools")
devtools::install_github("quantifish/TagGrowth")

# Load package
library(TagGrowth)

Please see the examples folder for an example of how to run the model.

Case study

A case stduy is done using Antarctic toothfish in examples/case_study/. The tag-recapture (TR.RData) and aging (AGE.RData) data are linked using the script Link_AGE_TR.R. The linked data set is provided in data/ATR_mod.RData. The original data sets TR.RData and AGE.RData are not provided.

We implement this model using the Template Model Builder (TMB) software called from R using the TMB package (https://github.com/kaskr/adcomp). The model is written in C++ inst/executables/ATR.cpp, and an R script Fit_Models.R loads the data and fits the model. The script plot.R is also provided to plot the outputs of the case study.

Simulation study

A simulation study based on Antarctic toothfish is done in examples/simulation_study/. Simulation is done in Simulate_Growth.R. Estimation is then done using Estimate_Simulations.R. The script plot.R is also provided to plot the outputs of the case study.

Further reading

A Zotero (https://www.zotero.org/) bibliography is provided in examples/TagGrowth.rdf.

We used codecogs (http://www.codecogs.com/latex/eqneditor.php) to render equations in this README.

quantifish/TagGrowth documentation built on May 26, 2019, 12:36 p.m.