added a section discussing connections with other spatiotemporal mode…

…lling appoaches

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},

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