ICES CM 2010/G:28
Estimating uncertainty of marine
multi-species models
12∗
Bjarki Thor Elvarsson
1
, Gunnar Stefansson
1
University of Iceland, Reykjavik, Iceland.
2
Marine Research Institute, Reykjavik, Iceland
∗
Presenter
Bootstrap
Introduction
I There are numerous approaches to estimate uncertainty for marine multi-species
models. One popular approach is a normal approximation to the distribution of
parameter estimates where the variance - covariance matrix is derived from the
Hessian matrix of the likelihood function.
I Here we will compare the variance estimates from the Hessian approach to the
results from:
. Monte Carlo simulation where a two stock model is simulated with error on
survey indices.
. Bootstrap simulation for cod in Icelandic waters
I We use the model for Cod in Icelandic waters introduced in [2], and a bootstrap
approach was defined in [3].
I Bootstrap resampling based on spatio-temporal data-units as illustrated by the
figure below. In the figure the waters around Iceland has been divided into small
areas. The data collected in each of the regions is aggregated by age and length
within that region. The aggregated data is then used as a sampling unit in the
bootstrap.
68°
Gadget
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Parameter estimate
25% quantiles
2.5% quantiles
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Results
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Results
Monter Carlo simulations
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Recruitment
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I Independently a simulator in R, R-Gadget, has been developed. It implements a
set of commonly used features of Gadget’s ecosystem simulator.
I One species living in two regions, split into two substocks representing the
maturity stages. Cannibalism of the immature substock of the mature is defined
via suitability functions.
I Two fleets are simulated:
. Commercial fleet that operates throughout the year in both regions.
. Spring survey.
I Survey index and landings in kilograms are calculated. The survey index is
calculated with log-normal error. In all 100 simulated dataset were created.
I The suitability parameters, effort and stock recruitment were estimated in
Gadget for each of the simulated datasets.
I The resulting parameter distribution arising for the simulation were compared to
the Hessian approximation.
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number (millions)
I Gadget (Globally applicable Area Disaggregated General Ecosystem Toolbox) [1]
is a software program that encompasses three main (optional/customizable)
components:
1. Ecosystem simulator. The basic unit of the simulator is the number of
individuals of a certain species, age, length and maturity living in some region
at a certain timestep. At each timestep the following is simulated:
I Migration between region. It is described by migration matrices.
I Consumption by predator/fleet is defined by suitability functions.
I Growth is implemented using length update.
I Maturation, the oldest group of the immature substock is moved to the
youngest of the mature substock.
2. A set of likelihood components to incorporate various datasets.
3. An optimizer used for parameter estimation.
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1984
1985
1990
1995
2000
1986
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1998
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2002
year
Year
The figures of above show an estimate of the recruitment in the years 1984 to
2003. The figure on the right shows the results from the bootstrap
approximation of uncertainty while the figure on the left show the hessian
approximation. The bootstrap method yields a more conservative (and
realistic) approximation of uncertainty.
1.2
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Recruitment
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Year
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True Value
Parameter estimate
25% quantiles
2.5% quantiles
True Value
Mean
Median
25% quantiles
2.5% quantiles
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Recruitment
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Conclusion
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I An unaltered Hessian approach to approximate uncertainty appears to be
inappropriate in the test cases illustrated here.
I The Hessian approach’s super-optimistic approximation of uncertainty for the
cod can probably be explained by correlation in the measurements, making the
effective degrees of freedom considerably less. Therefore considerable care needs
to be made when using the Hessian approach.
I The bootstrap approach presented here seems to perform better than the
Hessian approach.
Acknowledgements
10
Year
The figures above shows the distribution of yearly recruitment as estimated by
the Hessian approach (figure on the left) and the MC simulation (figure on the
right). Inferences based on the Hessian approach would fail to include the
correct value for the recruitment for three years out 10.
The work presented here was supported by the Marine Research Institute
(MRI), Reykjavik, Iceland, uses data from the MRI databases and software
developed at MRI.
References
[1] Begley, J. and Howell,D. 2004. An overview of Gadget, the globally applicable
area-disaggregated general ecosystem toolbox. ICES CM, 1-15
[2] Taylor, L. and Begley, J. and Kupca, V. and Stefansson, G., 2007. A simple implementation
of the statistical modelling framework Gadget for cod in Icelandic waters. African Journal of
Marine Science 29: 223:245.
[3] Taylor, L., Trenkel, V.M., Kupca, V., Stefansson, G., 2008. A bootstrap method for
estimating bias and variance in statistical multispecies. Arxiv preprint arXiv:0807.3677.
Contact:
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