Tuna are highly mobile species, and their spatial distribution is potentially affected by multiple factors including environmental conditions, ontogenetic movement, migration, local depletion, currents, etc. Therefore, modelling the spatial distribution of tuna stocks, spatial variability in population processes, spatial distribution of fleets, and fish movement should be considered in tuna stock assessments.
Current tuna assessment models typically address spatial structure using the areas-as-fleets approach (e.g., IATTC assessments in the EPO) or block transfer among a few large regions (e.g., SPC assessments in the WCPO). The areas-as-fleets approach relies on length composition data to estimate a selectivity curve that describes the proportion of the stock by age or length that occupies that region. The block transfer approach estimates movement among regions and typically requires age or length specific movement, often as a functional form, for which information comes from length composition data, tagging data, or assumptions about common catchability among regions for an index of abundance. Often the composition data is overly influential on the estimates of movement rates and can be influenced by biological assumptions such as growth and its spatial variability. Assuming catchability is common across regions requires accurate modelling of the spatial distribution of the (CPUE) index of abundance.
Fine scale modelling of the CPUE data and tagging data is done external to the assessment. This modeling is important to ensure spatial distribution of the stock and fleet are accounted for in the analyses. This is also particularly important to address non-mixing in analyzing the tagging data. Tagging tuna, particularly tropical tuna, is difficult and often restricted in space and time. Fine scale spatial-temporal modelling (Mildenberger et al., 2024) avoids bias from non-mixing while maximizing the content of the data (i.e., not eliminating information (e.g., estimating fishing mortality on tagged fish in the first few time periods independent from that on the total population) from recaptures before the tags are fully mixed with the total population). Therefore, integrating the raw tagging data into the stock assessment model would require a fine spatial-temporal scale stock assessment mode.
There have been some stock-assessment like (estimate parameters) models that use a fine spatial-temporal scale, but these have yet to be used directly to set management action. For example, the SEPODYM model has been used to model tuna in the Pacific Ocean and how the dynamics relates to environmental conditions (e.g., Senina et al., 2021).
The decision on what spatial temporal scale should be used in the model will partly depend on whether integrating the tagging data into the assessment is necessary or if external analysis of the tagging data is adequate (see section on tagging data). A model with flexible spatial and temporal scale could be developed, but some concepts need to be considered.
The block transfer approach can easily be scaled, but it would require an approach to define movement among the cells that reduces the number of parameters. For example, spatial movement rates in terms of advection, diffusion, and taxis parameters could be represented as a MGRF. However, if the temporal scale also needs to be on a finer scale, the fishing and natural mortality on the finer temporal scale needs to be considered. Computational efficiency and parameter estimability might become a concern at finer spatial-temporal scales. Particularly if this interacts with the inclusion of random effects or other desirable aspects of the assessment model (e.g., length-based dynamics).
Change in spatial distribution of the stock could be modelled using spatio-temporal correlation rather than explicit movement. However, this might require a different approach to modelling the population dynamics.
Spatial variation in population and fishing processes may cause complication issues. For example, if growth varies spatially, this causes modelling issues when fish move and change their growth rates such that different fish will have different length-at-age. Explicitly modeling both age and length can facilitate modeling of these processes (see the length-based dynamics section), but consideration needs to be taken about whether growth is genetic, environmental, or both.
Modelling the stock-recruitment relationship (i.e., is the stock-recruitment relationship global or area specific) and how the recruitment is distributed among areas also becomes complicated in spatially structured stock.
Some questions we need to answer:
What is spatial structure needed for?
When do we need to model spatial structure?
When can we model spatial structure without tagging data?
What type of spatial structure do we need for tagging data?
What type of spatial structure is needed in what circumstances?
Do we need to consider length dynamics in spatial models to deal with spatial variations in length based processes (e.g., growth)?
How should movement be defined 1) block transfer parameters (unstructured Markov), 2) advection-diffusion-taxis (mechanistic), 3) or implicitly modeled through GMRFs?
How can movement and/or abundance/fishing mortality information can be taken from fine scale spatio-temporal models (e.g., SEAPODYM) and put into a large area block transfer stock assessment models?
Can a general model include both block transfer models and fine scale spatial-temporal dynamics in the same framework simply by changing the spatial-temporal definitions?
How would catch be assigned to fine temporal scale, could some dynamics (like tagging) be done on a fine scale (to deal with tag mixing) while the population dynamics be done on a course scale?
How should we be incorporating spatial demographic variation in spatial and/or non-spatial assessments? Will approximations work well (e.g., area-weighting of demographics) or does the variation need to be modeled explicitly?
What types of data sources and observation submodels are needed to inform spatial structure? What data sources are expected to be available for use in the future (e.g., stock composition)
Do most tuna stocks have the data necessary for fine-scale spatial models or do existing data better fit within the context of a large box model?
Do we need to be able to readily transition between the scale at which data are collected? (e.g., spatially-aggregated to spatially-explicit catch/compositions)?
Could current fine scale spatio-temporal models (e.g., SEAPODYM. MOMO) be developed into a full stock assessment model?
How robust are spatially-implicit and large box models for providing management advice? Does implementation of fine-scale population dynamics models substantially improve advice? Do their data needs and/or data reporting resolution requirements differ?
At what point should certain management decisions be separated from the stock assessment, using coarse-scale models for defining overall catch advice, while relying on fine-scale models for defining localized management decisions?
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