# The effect of ageing errors on Von Bertalanffy parameters estimation using a Bayesian sensitivity analysis approach

Lucie Aulus Giacosa, Philippe Gaudin, Jean-Christophe Aymes, Francois Gueraud, Matthias Vignon

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## To cite this version:

Lucie Aulus Giacosa, Philippe Gaudin, Jean-Christophe Aymes, Francois Gueraud, Matthias Vignon. The effect of ageing errors on Von Bertalanffy parameters estimation using a Bayesian sensitivity analysis approach. 6. International Otolith Symposium IOS 2018, Apr 2018, Keelung, Taiwan. 295 p., 2018, Sixth International Otolith Symposium Handbook. hal-02154547

HAL Id: hal-02154547

https://hal.science/hal-02154547

Submitted on 12 Jun 2019

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Distributed under a Creative Commons Attribution 4.0 International License
# THE EFFECT OF AGEING ERRORS ON VON BERTALANFFY
## PARAMETERS ESTIMATION (VBGF)

## Using a Bayesian sensitivity analysis approach

UMR ECOBIOP, ÉCOLOGIE COMPORTEMENTALE ET BIOLOGIE DES POPULATIONS DE POISSONS

Lucie Aulus Giacosa, Philippe Gaudin, Jean-Christophe Aymes, François Guéraud, Matthias Vignon

## Context

The analysis of age and growth information contained in the **scales of fish** has become a standard technique in fish population dynamics model. Commonly modeled using Von Bertalanffy growth function (VBGF), inferring growth for fish is dependent upon an accurate description of the age-length relationship, which may be undermined by ageing errors. Ageing errors frequently arise either from disagreements between scales, readers or inability of scales to reflect true age (i.e. erosion, false growth ring). Here we use a Bayesian approach to infer Salmo trutta (L.) VBGF's parameters from scale samples. Inferred from scale readings of 60 fish, age at capture (for all fish) and age at migration (for the anadromous fish) were extracted based on a hierarchical design with blind double reading using 4 scales per fish. We estimated VBGF's parameters under different parametrization in the number of scales and reader per fish.

Hierarchical design (Nested sampling)

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## Localization

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## Models

$$L_{i,t} = L_{\infty i} + e^{-K_i (t_i - t_0)}$$

$$L_{\infty i} = a + \varepsilon_{1i}, \quad a \sim \text{dunif}(500, 1000)$$

$$K_i = b + \varepsilon_{2i}, \quad b \sim \text{dnorm}(0.6, 0.001)$$

$$t_0 \sim \text{dunif}(-10, 0.5)$$

## Results

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n = number of convergent bootstrap for each model

Models 1 to 12 are made upon information of 60 fish.

Model 13 : readers agreed at least on ageing 54 fish by reading one scale

Model 14 : readers agreed at least on ageing 33 fish by reading two scales

Model 15 : readers agreed at least on ageing 27 fish by reading three scales

Model 16 : readers agreed at least on ageing 16 fish by reading four scales

## Variance analyses

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$$\text{AGE} \sim \text{rpt}(\text{age} \sim (1|\text{Fish}) + (1|\text{Reader}) + (1|\text{Scale}), \text{datatype}=\text{Poisson}, \dots)^*$$

$$\text{MEASURE} \sim \text{rpt}(\text{rt} \sim (1|\text{Fish}) + (1|\text{Reader}) + (1|\text{Scale}), \text{datatype}=\text{Gaussian}, \dots)^*$$

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Random selection of one scale read by one reader
→ More variation in approximating the parameters of VBGF growth function but similar average size-at-age compared with models with two readers and four scales.

Complete dataset (model 12) versus consensual dataset (model 16) on four scales → same average results and variation around the mean curve → individual effect of growth.

Determination of the VBGF's parameters is more **precise** for consensual dataset.

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Age **accuracy** can be proven or estimated with methods such as capture-mark-recapture (CMR). Agreement in the age determination between reader (consensual readings) is a selection of fish for which **precision** is 100% but it does not mean that the determination is accurate and represents the entire population.**

**Sources of variance** in the age determination should be investigated before any results interpretation. By doing so, we can empirically determine the **robustness** of VBGF's parameters at a population scale in our study.*** Going further, variance on age should be integrated at the **individual level**.

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<footnote>* Stoffel, M. A., Nakagawa, S. and Schielzeth, H. (2017), rptR: repeatability estimation and variance decomposition by generalized linear mixed-effects models. Methods Ecol Evol, 8: 1639-1644.</footnote>

<footnote>** Beamish, R. J., et G. A. McFarlane. « The Forgotten Requirement for Age Validation in Fisheries Biology ». Transactions of the American Fisheries Society 112</footnote>

<footnote>*** Cope, Jason M, et André E Punt. « Admitting ageing error when fitting growth curves: an example using the von Bertalanffy growth function with random effects ». Canadian Journal of Fisheries and Aquatic Sciences 64, no 2 (1 février 2007): 205-18.</footnote>