From 070dabe8284da2907836905fff9b908db04c01c7 Mon Sep 17 00:00:00 2001 From: eric-pedersen Date: Mon, 1 May 2023 15:45:56 -0400 Subject: [PATCH 1/9] added a section discussing connections with other spatiotemporal modelling appoaches --- paper/paper.bib | 44 ++++++++++++++++++++++++++++++++++++++++++++ paper/paper.md | 14 ++++++++++++-- 2 files changed, 56 insertions(+), 2 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index 31ffdd7e..ba5c1b5c 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -1,3 +1,47 @@ +@book{rueGaussianMarkovRandom2005, + title = {Gaussian {{Markov}} random fields: theory and applications}, + author = {Rue, Havard and Held, Leonhard}, + year = {2005}, + publisher = {{CRC press}}, + address = {{New York}} +} + + +@misc{anderson2022sdmTMB, + title = {{{sdmTMB}}: an {{R}} package for fast, flexible, and user-friendly generalized linear mixed effects models with spatial and spatiotemporal random fields}, + shorttitle = {{{sdmTMB}}}, + author = {Anderson, Sean C. and Ward, Eric J. and English, Philina A. and Barnett, Lewis A. K.}, + year = {2022}, + month = may, + primaryclass = {New Results}, + pages = {2022.03.24.485545}, + publisher = {{bioRxiv}}, + doi = {10.1101/2022.03.24.485545}, + urldate = {2023-05-01}, + abstract = {Geostatistical data\textemdash spatially referenced observations related to some continuous spatial phenomenon\textemdash{} are ubiquitous in ecology and can reveal ecological processes and inform management decisions. However, appropriate models to analyze these data, such as generalized linear mixed effects models (GLMMs) with Gaussian random fields, are often computationally intensive and challenging to implement, interpret, and evaluate.Here, we introduce the R package sdmTMB, which implements predictive-process SPDE- (stochastic partial differential equation) based spatial and spatiotemporal models. Estimation is conducted via maximum marginal likelihood with Template Model Builder (TMB) but can be extended to penalized likelihood or Bayesian inference. We describe the statistical model, illustrate the package's use through two case studies, and compare the functionality, speed, and interface to related software.We highlight advantages of using sdmTMB for this class of models: (1) sdmTMB provides a flexible interface familiar to users of glm(), lme4, glmmTMB, or mgcv; (2) estimation is often faster than alternatives; (3) sdmTMB provides simple out-of-sample cross validation; (4) non-stationary processes (time-varying and spatially varying coefficients) are easily constructed with a formula interface; and (5) sdmTMB includes features not available as a combination in related packages (e.g., delta/hurdle models, penalized smoothers and break-point effects, anisotropy, abundance index standardization).We hope that sdmTMB's user-friendly interface will open this useful class of models to a wider audience within species distribution modelling and beyond.}, + archiveprefix = {bioRxiv}, + chapter = {New Results}, + copyright = {\textcopyright{} 2022, Posted by Cold Spring Harbor Laboratory. This pre-print is available under a Creative Commons License (Attribution 4.0 International), CC BY 4.0, as described at http://creativecommons.org/licenses/by/4.0/}, + langid = {english} +} + + + +@article{thorson2019Guidance, + title = {Guidance for decisions using the {{Vector Autoregressive Spatio-Temporal}} ({{VAST}}) package in stock, ecosystem, habitat and climate assessments}, + author = {Thorson, James T.}, + year = {2019}, + month = feb, + journal = {Fisheries Research}, + volume = {210}, + pages = {143--161}, + issn = {0165-7836}, + doi = {10.1016/j.fishres.2018.10.013}, + urldate = {2023-05-01}, + abstract = {Fisheries scientists provide stock, ecosystem, habitat, and climate assessments to support interdisplinary fisheries management in the US and worldwide. These assessment activities have evolved different models, using different review standards, and are communicated using different vocabulary. Recent research shows that spatio-temporal models can estimate population density for multiple locations, times, and species, and that this is a ``common currency'' for addressing core goals in stock, ecosystem, habitat, and climate assessments. I therefore review the history and ``design principles'' for one spatio-temporal modelling package, the Vector Autoregressive Spatio-Temporal (VAST) package. I then provide guidance on fifteen major decisions that must be made by users of VAST, including: whether to use a univariate or multivariate model; when to include spatial and/or spatio-temporal variation; how many factors to use within a multivariate model; whether to include density or catchability covariates; and when to include a temporal correlation on model components. I finally demonstrate these decisions using three case studies. The first develops indices of abundance, distribution shift, and range expansion for arrowtooth flounder (Atheresthes stomias) in the Eastern Bering Sea, showing the range expansion for this species. The second involves ``species ordination'' of eight groundfishes in the Gulf of Alaska bottom trawl survey, which highlights the different spatial distribution of flathead sole (Hippoglossoides elassodon) relative to sablefish (Anoplopoma fimbria) and dover sole (Microstomus pacificus). The third involves a short-term forecast of the proportion of coastwide abundance for five groundfishes within three spatial strata in the US West Coast groundfish bottom trawl survey, and predicts large interannual variability (and high uncertainty) in the distribution of lingcod (Ophiodon elongatus). I conclude by recommending further research exploring the benefits and limitations of a ``common currency'' approach to stock, ecosystem, habitat, and climate assessments, and discuss extending this approach to optimal survey design and economic assessments.}, + langid = {english} +} + @article{thorson_using_2017, title = {Using spatio-temporal models of population growth and movement to monitor overlap between human impacts and fish populations}, diff --git a/paper/paper.md b/paper/paper.md index dbd6a006..2bd44fa1 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -60,7 +60,8 @@ While the initial application of this model was modelling Newfoundland and Labra 5. Visualization of results, including confidence and prediction intervals. 6. One-step-ahead prediction of biomass for model validation and scenario-based forecasting. -Although it was developed in a fisheries context, the package is suitable to model spatially-structured population dynamics in general. + Although it was developed in a fisheries context, the package is suitable to model spatially-structured population dynamics in general. + # Package design @@ -79,9 +80,18 @@ The key workflow steps are: ![The sspm workflow.\label{fig:workflow}](../man/figures/flowchart.png){width=90%} + +# Connections to other spatiotemporal stock assessment approaches + +The general approach used by `sspm` of using a statistical model to estimate spatiotemporally varying population varying biomass indices is closely connected to approaches used by other modern model-based spatial abundance estimation software, such as the `VAST` R package [@thorson2019Guidance] and the `sdmTMB` R package [@anderson2022sdmTMB]. Our method shares the same approach as both `VAST` and `sdmTMB` of using spatially explicit models to estimate local biomass density (\autoref{fig:workflow} steps 1,2, and 4), then aggregating up from those models to predict aggregate stock-level metrics such as total biomass and productivity (\autoref{fig:workflow} steps 8). The multiplicative surplus production model used by `sspm` is also similar to the vector-autoregessive model for biomass changes used by these two packages, as both `VAST` and `sdmTMB` can model local temporal changes as autoregressive processes on the link-scale of a generalized linear model [@thorson2019Guidance]. + +One major difference between the `sspm` package and other model-based spatiotemporal modelling packages is its special-purpose nature. The `spm_smooth` function uses a computationally simpler (although somewhat less flexible) Conditional Autoregressive (CAR) model [@rueGaussianMarkovRandom2005] for modelling spatial variation in covariates and biomass, as compared to the more complex spatial random effects possible with `VAST` and `sdmTMB`; this has the advantage of computational speed and less user knowledge of how to set up complex spatial grids, although it is less flexible. This means that `sspm` should be easier to adapt to novel fisheries than more complex packages that require more user modelling knowledge. + +The other benefit of `sspm`, relative to other modelling packages, is the ability to model productivity rates directly (\autoref{fig:workflow} steps 5 and 6), rather than implicitly via an auto-regressive processes as used in `VAST` or `sdmTMB`. This means that it is possible in `sspm` to model nonlinear relationships between environmental covariates and productivity, or to easily include factors such as time-lagged effects of predictors on productivity in a given year. This approach does, however, sacrifice the ability to propagate measurement error into uncertainty about rates of change. One of the future directions for development of this package is to include variance propagation methods into the surplus production modelling step. + # Acknowledgements -This research was supported by the canadian Department of Fisheries of Oceans (DFO) Sustainable fisheries Science Fund, and by a Discovery Grant from the canadian Natural Sciences and Engineering Research Council (NSERC) to E. J.Pedersen. We thank Fonya Irvine and John-Philip Williams for their help in testing the package and providing feedback on model implementation. +This research was supported by the Canadian Department of Fisheries of Oceans (DFO) Sustainable fisheries Science Fund, and by a Discovery Grant from the Canadian Natural Sciences and Engineering Research Council (NSERC) to E. J.Pedersen. We thank Fonya Irvine and John-Philip Williams for their help in testing the package and providing feedback on model implementation. # References From 8b80ff9f2890bd4a0480ca2ee336b7abbc5e9812 Mon Sep 17 00:00:00 2001 From: eric-pedersen Date: Mon, 1 May 2023 19:47:03 +0000 Subject: [PATCH 2/9] [Bot] build pdf --- paper/paper.pdf | Bin 497475 -> 520820 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/paper/paper.pdf b/paper/paper.pdf index 0d71aed48e646455059c6c6150af6e9ac31cd8a6..7214dfb2b01988d7447bef1c8e590c1b65ea0e0c 100644 GIT binary patch delta 82404 zcmZs?LzFID54KshZQC|a*|vSkHlDI=+qPY&Y}>Z2e!stabx(SaGRRt)W#_tcXQ-Co z>4>oY1t!fh01__kQWO#&z|PJ_Bp^Wae?J&!7bi0#TNsaxYdxtr6K<#8)w(%Cq%0W+ zP!#BL=?u`>8h-dUrgRl-6T(XKx!$*1-gfXHpQv1YjEzvGvx!tuN9e=>&0Z*h@u+{l zKbL|JQQcpcc>)z*;(Ey{gH-K*OM+uQ9-cqTb_Jmsd!o}m08aRVrEZ!skq(xC3X_)v zSAgxe!8%YL;PYv+YvHDlC_Mj9_t(p-T%g~l-}_}$@`kh}T(8yFM0X-kB*4}uwG-e}@wbwLSfhiV6@KNO;b>Xg9}8o=~10UAXMm)<$y z)R2=GfI*@=aL%!JvKKqo&dR066bb 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+++++++++++++++++++++++++++++++++ 1 file changed, 33 insertions(+) diff --git a/paper/paper.bib b/paper/paper.bib index ab1cea92..ee274aad 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -1,3 +1,36 @@ + +@article{pedersen_stochastic_2017, + title = {A stochastic surplus production model in continuous time}, + volume = {18}, + issn = {1467-2979}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/faf.12174}, + doi = {10.1111/faf.12174}, + language = {en}, + number = {2}, + urldate = {2023-05-02}, + journal = {Fish and Fisheries}, + author = {Pedersen, Martin W and Berg, Casper W}, + year = {2017}, + pages = {226--243}, +} + +@article{winker_jabba_2018, + title = {{JABBA}: {Just} {Another} {Bayesian} {Biomass} {Assessment}}, + volume = {204}, + issn = {0165-7836}, + shorttitle = {{JABBA}}, + url = {https://www.sciencedirect.com/science/article/pii/S0165783618300845}, + doi = {10.1016/j.fishres.2018.03.010}, + language = {en}, + urldate = {2023-05-02}, + journal = {Fisheries Research}, + author = {Winker, Henning and Carvalho, Felipe and Kapur, Maia}, + month = aug, + year = {2018}, + pages = {275--288}, +} + + @article{thorson_spatio-temporal_2019, title = {Spatio-temporal models of intermediate complexity for ecosystem assessments: {A} new tool for spatial fisheries management}, volume = {20}, From 17d5f1615c477315614b303ddf9c59e5221077f5 Mon Sep 17 00:00:00 2001 From: eric-pedersen Date: Tue, 2 May 2023 18:38:20 +0000 Subject: [PATCH 6/9] [Bot] build pdf --- paper/paper.pdf | Bin 522870 -> 523697 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/paper/paper.pdf b/paper/paper.pdf index b17d47083d0065750362c39a15ef0eedb34a70c0..778d95561587f9a517449a6b2fe55190f53277d2 100644 GIT binary patch delta 25781 zcmZs?Q>-pb(=@!7ZQHhO+qP}N!QW@k^&51W`2zx_Wgd(eTDD-9Ow7mpGS`WB5@djsR-|uAWnmN zeYOeoe$R27v>)!P|N4#@sPt$?u>frH|1rKnXZ`MM{K9j;-Cu4x7zl4<&*ypV4_&VU zY~jyV3EKL0xzfX2N)HUM1n7TueZLM@chOONem1f@}>v0Z~S~y 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deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index a8ffe11e..177ec985 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -125,7 +125,8 @@ @article{karp_accounting_2019 editor = {Maravelias, Christos}, month = apr, year = {2019}, - pages = {fsz048}, + pages = {1305--1315}, + volume = {76}, file = {Karp et al. - 2019 - Accounting for shifting distributions and changing.pdf:/home/vlucet/Zotero/storage/JP6BDALA/Karp et al. - 2019 - Accounting for shifting distributions and changing.pdf:application/pdf}, } @@ -242,10 +243,12 @@ @article{zhang_longer_2021 @article{prager_suite_1994, title = {A suite of extensions to a nonequilibrium surplus-production}, + journal = {Fishery Bulletin - National Oceanic and Atmospheric Administration}, language = {en}, author = {Prager, Michael H}, year = {1994}, - pages = {17}, + volume = {92}, + pages = {374--389}, file = {Prager - A suite of extensions to a nonequilibrium surplus-.pdf:/home/vlucet/Zotero/storage/4HHXRZ4Y/Prager - A suite of extensions to a nonequilibrium surplus-.pdf:application/pdf}, } @@ -297,7 +300,6 @@ @book{gotelli_primer_2008 file = {Snapshot:/home/vlucet/Zotero/storage/L24AL4DI/a-primer-of-ecology-9780878933181.html:text/html}, } - @article{thorson_importance_2015, title = {The importance of spatial models for estimating the strength of density dependence}, volume = {96}, @@ -313,7 +315,6 @@ @article{thorson_importance_2015 pages = {1202--1212}, } - @book{walters_fisheries_2004, address = {Princeton, N.J., U.S.A.}, title = {Fisheries ecology and management}, @@ -340,7 +341,7 @@ @book{wood_generalized_2017 @techreport{dfo_assessment_2019, type = {techreport}, institution = {Canadian Science Advisory Secretariat (CSAS)}, - title = {An assessment of {Northern} {Shrimp} (\textit{{Pandalus} borealis}) in {Shrimp} {Fishing} {Areas} 4–6 and of {Striped} {Shrimp} (\textit{{Pandalus} montagui}) in shrimp fishing area 4 in 2018}, + title = {An Assessment of {Northern} {Shrimp} (Pandalus borealis) in {Shrimp} {Fishing} {Areas} 4–6 and of {Striped} {Shrimp} (Pandalus montagui) in Shrimp Fishing Area 4 in 2018}, number = {2019/027}, author = {{DFO}}, year = {2019}, @@ -348,17 +349,13 @@ @techreport{dfo_assessment_2019 } @techreport{pedersenNewSpatialEcosystembased2021, - type = {Can. {Sci}. {Advis}. {Sec}. {Res}. {Doc}.}, - title = {A new spatial ecosystem-based surplus production model for {SFA} 4-6 {Northern} {Shrimp}}, - number = {2022/062}, + type = {Canadian Science Advisory Secretariat (CSAS) Research Document}, + title = {A New Spatial Ecosystem-Based Surplus Production Model for {SFA} 4-6 {Northern} {Shrimp}}, author = {Pedersen, Eric J. and Skanes, Katherine and Le Corre, Nicolas and Koen-Alonso, Mariano and Baker, Krista}, year = {2022}, - pages = {1-64}, - url = {https://publications.gc.ca/collections/collection_2022/mpo-dfo/fs70-4/Fs70-4-2022-012-eng.pdf}, + url = {https://www.dfo-mpo.gc.ca/csas-sccs/Publications/ResDocs-DocRech/2022/2022_062-eng.html} } - - 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Subject: [PATCH 3/9] addressing issue #125 --- paper/paper.bib | 24 ++++++++++++++++++++++-- paper/paper.md | 12 +++++++----- 2 files changed, 29 insertions(+), 7 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index ba5c1b5c..ab1cea92 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -1,3 +1,22 @@ +@article{thorson_spatio-temporal_2019, + title = {Spatio-temporal models of intermediate complexity for ecosystem assessments: {A} new tool for spatial fisheries management}, + volume = {20}, + copyright = {© 2019 John Wiley \& Sons Ltd}, + issn = {1467-2979}, + shorttitle = {Spatio-temporal models of intermediate complexity for ecosystem assessments}, + url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/faf.12398}, + doi = {https://doi.org/10.1111/faf.12398}, + language = {en}, + number = {6}, + urldate = {2021-03-30}, + journal = {Fish and Fisheries}, + author = {Thorson, James T. and Adams, Grant and Holsman, Kirstin}, + year = {2019}, + note = {\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/faf.12398}, + pages = {1083--1099}, +} + + @book{rueGaussianMarkovRandom2005, title = {Gaussian {{Markov}} random fields: theory and applications}, author = {Rue, Havard and Held, Leonhard}, @@ -298,10 +317,11 @@ @techreport{dfo_assessment_2019 @techreport{pedersenNewSpatialEcosystembased2021, type = {Can. {Sci}. {Advis}. {Sec}. {Res}. {Doc}.}, title = {A new spatial ecosystem-based surplus production model for {SFA} 4-6 {Northern} {Shrimp}}, - number = {2022/nn}, + number = {2022/062}, author = {Pedersen, Eric J. and Skanes, Katherine and Le Corre, Nicolas and Koen-Alonso, Mariano and Baker, Krista}, year = {2022}, - pages = {in press}, + pages = {1-64}, + url = {https://publications.gc.ca/collections/collection_2022/mpo-dfo/fs70-4/Fs70-4-2022-012-eng.pdf}, } diff --git a/paper/paper.md b/paper/paper.md index 2bd44fa1..d8c872c1 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -81,17 +81,19 @@ The key workflow steps are: ![The sspm workflow.\label{fig:workflow}](../man/figures/flowchart.png){width=90%} -# Connections to other spatiotemporal stock assessment approaches +# Connections to other surplus-production based stock assessment approaches -The general approach used by `sspm` of using a statistical model to estimate spatiotemporally varying population varying biomass indices is closely connected to approaches used by other modern model-based spatial abundance estimation software, such as the `VAST` R package [@thorson2019Guidance] and the `sdmTMB` R package [@anderson2022sdmTMB]. Our method shares the same approach as both `VAST` and `sdmTMB` of using spatially explicit models to estimate local biomass density (\autoref{fig:workflow} steps 1,2, and 4), then aggregating up from those models to predict aggregate stock-level metrics such as total biomass and productivity (\autoref{fig:workflow} steps 8). The multiplicative surplus production model used by `sspm` is also similar to the vector-autoregessive model for biomass changes used by these two packages, as both `VAST` and `sdmTMB` can model local temporal changes as autoregressive processes on the link-scale of a generalized linear model [@thorson2019Guidance]. +The `sspm` package uses a model-based, random-effects based approach to estimate the effects of ecosystem drivers on surplus production across space and time. Our approach is conceptually related to the stochastic stock assessment approaches used by the R packages `spict` [@pedersen_stochastic_2017] and `jabba` [@winker_jabba_2018] R packages for surplus production modelling, in that we assume that biomass dynamics can be modelled as effectively a logistic growth model with both process and measurement error. While `sspm` does not currently have the capacity to model biomass dynamics as a continuous-time process, as with `spict`, or incorporate prior parameter information on catchability or biomass dynamics as in `jabba`, `sspm` can model spatially and temporally varying productivity, which is currently not possible in these models. -One major difference between the `sspm` package and other model-based spatiotemporal modelling packages is its special-purpose nature. The `spm_smooth` function uses a computationally simpler (although somewhat less flexible) Conditional Autoregressive (CAR) model [@rueGaussianMarkovRandom2005] for modelling spatial variation in covariates and biomass, as compared to the more complex spatial random effects possible with `VAST` and `sdmTMB`; this has the advantage of computational speed and less user knowledge of how to set up complex spatial grids, although it is less flexible. This means that `sspm` should be easier to adapt to novel fisheries than more complex packages that require more user modelling knowledge. +The `sspm` package can be viewed as a spatiotemporal Model of Intermediate Complexity [a 'MICE-in-space' model; @thorson_spatio-temporal_2019] that can incorporate effects of other species and ecosystem drivers as well as changes in fishing pressure on stock status. Our approach is closely connected to approaches used by other modern model-based spatial abundance estimation software, such as the `VAST` R package [@thorson_spatio-temporal_2019] and the `sdmTMB` R package [@anderson2022sdmTMB]. Our method shares the same approach as both `VAST` and `sdmTMB` of using spatially explicit models to estimate local biomass density (\autoref{fig:workflow} steps 1,2, and 4), then aggregating up from those models to predict aggregate stock-level metrics such as total biomass and productivity (\autoref{fig:workflow} steps 8). The multiplicative surplus production model used by `sspm` is also conceptually similar to the vector-autoregessive model for biomass changes used by these two packages, as both `VAST` and `sdmTMB` can model local temporal changes as autoregressive processes on the link-scale of a generalized linear model. The `sspm` package cannot, however, model the dynamics of multiple species simultaneously; multi-species modelling would require generating a separate surplus production model (\autoref{fig:workflow} steps 5 and 6) for each species of interest. -The other benefit of `sspm`, relative to other modelling packages, is the ability to model productivity rates directly (\autoref{fig:workflow} steps 5 and 6), rather than implicitly via an auto-regressive processes as used in `VAST` or `sdmTMB`. This means that it is possible in `sspm` to model nonlinear relationships between environmental covariates and productivity, or to easily include factors such as time-lagged effects of predictors on productivity in a given year. This approach does, however, sacrifice the ability to propagate measurement error into uncertainty about rates of change. One of the future directions for development of this package is to include variance propagation methods into the surplus production modelling step. +One major difference between the `sspm` package and other model-based spatiotemporal modelling packages is its special-purpose nature. The default `spatial_smooth` function uses a computationally simpler (although somewhat less flexible) Intrinsic Conditional Autoregressive (ICAR) model [@rueGaussianMarkovRandom2005] for modelling spatial variation in covariates and biomass, as compared to the more complex spatial random effects possible with `VAST` and `sdmTMB`. This has the advantage of computational speed and less user knowledge of how to set up complex spatial grids, although it is less flexible. This means that `sspm` should be easier to adapt to novel fisheries than more complex packages that require more user modelling knowledge. Further, it is possible to specify alternative spatial smoothers than the ICAR model in the `spatial_smooth` function via the `bs=` argument, although this functionality has not been well-tested and should be considered experimental. + +The other benefit of `sspm`, relative to other modelling packages, is the ability to model productivity rates directly (\autoref{fig:workflow} steps 5 and 6), rather than implicitly via an auto-regressive processes as used in `VAST` or `sdmTMB`. This means that it is possible in `sspm` to model nonlinear relationships between environmental covariates and productivity, or to easily include factors such as time-lagged effects of predictors on productivity in a given year. This approach does, however, sacrifice the ability to propagate measurement error into uncertainty about rates of change. One of the future directions for development of this package is to include variance propagation methods into the surplus production modelling step. # Acknowledgements -This research was supported by the Canadian Department of Fisheries of Oceans (DFO) Sustainable fisheries Science Fund, and by a Discovery Grant from the Canadian Natural Sciences and Engineering Research Council (NSERC) to E. J.Pedersen. We thank Fonya Irvine and John-Philip Williams for their help in testing the package and providing feedback on model implementation. +This research was supported by the Canadian Department of Fisheries of Oceans (DFO) Sustainable fisheries Science Fund, and by a Discovery Grant from the Canadian Natural Sciences and Engineering Research Council (NSERC) to E.J.Pedersen. We thank Fonya Irvine and John-Philip Williams for their help in testing the package and providing feedback on model implementation. # References From c9dfa2607c87b2de3e6ec8d2385417f65ad38096 Mon Sep 17 00:00:00 2001 From: eric-pedersen Date: Tue, 2 May 2023 18:35:54 +0000 Subject: [PATCH 4/9] [Bot] build pdf --- paper/paper.pdf | Bin 520820 -> 522870 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/paper/paper.pdf b/paper/paper.pdf index 7214dfb2b01988d7447bef1c8e590c1b65ea0e0c..b17d47083d0065750362c39a15ef0eedb34a70c0 100644 GIT binary patch delta 45139 zcmV)WK(4>^RG!Vp_ibwad`gkLA}lDYcW*82Ht21^C;&|MvCs#>OsRM|=BaW5&L4 zUX?XM`?xq4h1ao3C#7U<8N&W7uaxuU#w8IvKK|*iKh$#m1J-_Qb>*W_3b?RR3U5M3nFv!trD>bU*ja4NPmAcLV1^ZN7x`*zgUriRBrG9;1yC_ zNmc1~`F(n$s%ACmWJPp}P<3rW9E8@MD<*#Rf8++H^=JcOmtMAt1XiJe+lsa5*(Myk z)&ZPZa2uw9h84iDWQ^d7I8V_5qx0;~bGu-xABvgg4ij2NaBOxaQ&gT&VjJM|-x2LK z+rIPFUTyisrv+!GK)zaN1FUPp2hQXLA=wG!_wr1n+gp2Wj;Gm1nd!m!KijPAE*vgj ze->TQ?TjIoyCW%dag&Kwcg;TQytd8!G}~r@mu~kS*L8zCYxB1Fd=hq}atL|S4L!o zJ!I99C(aWJxU7zbl)e7tS(FSKC6J`=fW!vjefJ8e2HoOK*4`;^&!O2iBkv}HqV?Rg z=#Gr0KCyjF)w^v&^kjv0b4tW1pZJ<4T4u_&D>e(?Io!c*RWg59_v|NUQ&%-@e}0$E zu-5`4LtEJOwd68(gMiafSQ%zTVFXC9%?RYq=2=XQbO}_aCqZQ)iPpx6KrvJ{ddYs?A|6LBF7S9%Ig9I#lt~@&rnRFuziDLfO7- zxi36d=O;v=lM-;2nMDC`@ivZLf9X*DMgtvdCORhoT7WG?Rj=T;^8m(>v2aK*`cKx4 zaYoqaCaT32Lc@A`CpBgDWC>^NmyAvJJa#4d_@v~mwQ%@}yOJ+vnc{7;Y@_l<`r#x$ z4aZ^bNjn_aEs`)<5|8Aavv1c%1ZR83*K%gVo#|oRbw_DlxlRqnv88vFf9MGb3{gOH zPmJfj>M!l&$qP#t?oGF;Si@Mpa2hni)$FElsrwPkj-xD^B=hiX%lNt*t#^HIwuyk1(-8 z_Jj~Q_VpHGMs#VG{yhgirbDM3IQq2?hZM@AG>RgwD9&dgI4(sHG>%k1YMA$#TMP~Cu7$|^i&i=G>VBB^C!wGfIC7F1Se@p7;**-^ew((R! 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