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Integrated Tagging and Catch-at-age analysis (ITCAAN): model development and simulation testing
... The dynamics of tagged fish were similar to that of the entire population. However, each tag cohort, l, defined as a group of fish tagged and released in a given region and year (essentially a recruitment event of tagged fish; Maunder, 2001) was modelled independently through time. Tagging does not necessarily begin in the first year of the model, so a separate time subscript, t, was used to represent the tagging year. ...
... Because datasets were assumed independent, the negative logarithm of the likelihood components was taken and summed to form a single likelihood function to be minimized, and constants were ignored as they did not alter parameter estimates (Hilborn and Mangel, 1997; Polacheck et al., 2006; Maunder and Punt, 2012): The TP term in Equation (9) was removed for both the closed population model and the spatial model without tagging data. Catch and index proportions-at-age along with TPs assumed a multinomial error distribution (Maunder, 2001Maunder, , 2011 Polacheck et al., 2006), whereas fishery yield and survey biomass were assumed to follow a lognormal error distribution. Similarly, a lognormally distributed penalty was added to limit the variation of recruitment estimates from the average recruitment (L Recruitment ). ...
... It should be noted, though, that without tagging data for the entire model time-series, it is difficult to determine if movement dynamics have changed over time or to independently verify the emigration of the large 1987 SN year class to the other stock areas. Additionally, the correlation among movement rates and recruitment estimates in spatially explicit models is a major concern, and has become one of the most difficult to interpret (Maunder, 1998Maunder, , 2001 Maunder and Punt, 2012). Movement and recruitment parameters become confounded because spatially explicit models can equivalently explain a given abundance state by moving fish among regions or " creating " them through recruitment. ...
Ignoring population structure and connectivity in stock assessment models can introduce bias into important management metrics. Tag-integrated assessment models can account for spatially explicit population dynamics by modelling multiple population components, each with unique demographics, and estimating movement among them. A tagging submodel is included to calculate predicted tag recaptures, and observed tagging data are incorporated in the objective function to inform estimates of movement and mortality. We describe the tag-integrated assessment framework and demonstrate its use through an application to three stocks of yellowtail flounder (Limanda ferruginea) off New England. Movement among the three yellowtail flounder stocks has been proposed as a potential source of uncertainty in the closed population assessments of each. A tagging study was conducted during 2003–2006 with over 45 000 tagged fish released in the region, and the tagging data were included in the tag-integrated model. Results indicated that movement among stocks was low, estimates of stock size and fishing mortality were similar to those from conventional stock assessments, and incorporating stock connectivity did not resolve residual patterns. Despite low movement estimates, new interpretations of regional stock dynamics may have important implications for regional fisheries management given the source-sink nature of movement estimates.
... Finally, the length of the tagging time-series is important, because a short time-series will inaccurately capture time-varying movement processes. However, maintaining a tagging program for an extended time period can be extremely costly (Maunder, 2001; Hulson et al., 2011). Tag-shedding, tag-induced mortality, tag mixing, and aging of tagged fish must also be considered when using tag data (Maunder, 2001; Goethel et al., 2011). ...
... However, maintaining a tagging program for an extended time period can be extremely costly (Maunder, 2001; Hulson et al., 2011). Tag-shedding, tag-induced mortality, tag mixing, and aging of tagged fish must also be considered when using tag data (Maunder, 2001; Goethel et al., 2011). ...
Centuries of fisheries research demonstrate that marine species exhibit complex spatial structure. Yet, spatially-explicit population dynamics models have only begun to gain popularity in the last two decades. Ignoring the spatial complexities of sub-population structure can be detrimental to sustainable fisheries management and lead to loss of biocomplexity. Recently, spatially-explicit assessment models have been developed in an attempt to match the spatial scales of natural populations. These models can incorporate a variety of spatial population structures, but are limited by data constraints. We describe a generic spatially-explicit tag-integrated stock assessment framework and the advanced data requirements for successful implementation of these types of models. Application of tag-integrated assessments requires knowledge of the population structure, fine-scale data, and information on connectivity between population components often in the form of tagging data. Spatially-explicit, tag-integrated models also use more conventional assessment information, such as catch-at-age and indices of abundance. The increase in resolution and realistic biological characteristics of spatially-explicit models comes at the cost of data sample size and associated increases in uncertainty. However, the development of fine-scale population models is imperative to effectively assess and manage spatially-structured marine populations.
... Beverton and Holt, 1957), but this information is rarely integrated into stock assessment or management (Caddy, 1999; Quinn and Deriso, 1999; Goethel et al., 2011). Exceptions include Porch et al. (1998) , who used a two-stock virtual population analysis that incorporated mixing for bluefin tuna (Thunnus thynnus); Maunder (2001), who discusses a tag-integrated catch-at-age analysis; Punt et al. (2000), who used tagging data in assessing school sharks (Galeorhinus galeus); and Hampton and Fournier (2001), who extended the MULTIFAN-CL model of Fournier et al. (1998) to include tagging data in their assessment of yellowfin tuna (Thunnus albacares). Before shifting to a sophisticated spatially explicit assessment model, it would first be useful to determine the extent of the mixing problem for a given stock. ...
Atlantic cod (Gadus morhua) in the Northwest Atlantic off New England and southern Atlantic Canada exhibit a complex population structure. This region
has three independently assessed stocks [Georges Bank, Gulf of Maine (GOM), and the 4X stock], all of which are known to mix
with each other. Assessments of these stocks, however, assume no interpopulation mixing. Using simulations, we evaluated impacts
of ignoring mixing resulting from seasonal migrations on the GOM assessment. The dynamics of the three stocks were simulated
according to different scenarios of interstock mixing, and a statistical catch-at-age stock assessment model was fitted to
the simulated GOM data with and without mixing. The results suggest that, while mixing causes measurable bias in the assessment,
under the conditions tested, this model still performed well. Of the bias that does exist, spawning-stock biomass estimates
are relatively sensitive to mixing compared with estimates of recruitment and exploitation rate. The relative timing of seasonal
migration of the three stocks plays a critical role in determining the magnitude of bias. The scale and trends among years
in the bias were driven by how representative the catch and survey data were for the GOM stock; this representation changed
with the mixing rates.
... One such process error would be a change in catchability or selectivity over time and how that error relates to both index and age-composition data (Maunder, 2011). Recent developments in ASA modelling have focused on constructing more complicated types of the ASA model, including spatially explicit (Maunder, 2001) and ecosystem-level models (Quinn and Collie, 2005). For spatially explicit models, for example, dividing age and length compositions into spatially explicit regions creates complications. ...
Hulson, P-J. F., Hanselman, D. H., and Quinn II, T. J. 2012. Determining effective sample size in integrated age-structured
assessment models. – ICES Journal of Marine Science, 69:281–292.
Effective sample size (ESS) is a quantity that allows for overdispersion of variance and is used commonly in integrated age-structured
fishery assessment models to fit age-and-length-composition datasets. Owing to the sources of measurement, observation, process,
and model-specification errors, the ESS is smaller than the actual sample size. In this study, methods to set a priori or to estimate the ESS when confronted with datasets that include these sources of error were investigated. In general, a
number of methods previously proposed to incorporate the ESS resulted in accurate estimation of population quantities and
parameters when different sources of error were included in the data on age and length compositions. Three objective methods
to incorporate the ESS resulted in unbiased population quantities: (i) using sampling theory to derive the ESS from actual
age and length compositions, (ii) iteratively estimating the ESS with the age-structured assessment model, and (iii) estimating
the ESS as a parameter with the Dirichlet distribution.
The Brownie model is an effective statistical method that can be used to estimate age-related fishing and natural mortality from multi-year tag recapture programs. The extension of the Brownie model by Polacheck et al. (2006) to include a Peterson estimator on catch-at-age data enables the estimation of abundance at the same time and improves the prediction of mortality rates. Since its development, the Brownie-Peterson (BP) model has had many applications in large-scale regional tuna tagging programs. The cohort-structured BP model assumes the age of tagged fish is known and, in most applications, requires the age of the fish to be presumed or directly derived from the fish length, constituting a potential source of bias. In this paper, the BP model is extended based on the length of fish at the time of release by integrating the recapture probability of tagged fish over the distribution of age at the length by combining catch-at-length data, length distribution-at-release observations, and growth information. The length-based model extension differs to other full-length structured models in that it is still based on age-structured dynamics, allowing it to provide age-dependent mortality rates while integrating the uncertainty in the age-length relationship. The analytic framework of the length-based model extension is described, and validated using observations simulated from a simple population and tag dynamic model. When parameterized with the correct parameters, the length-based BP model that integrated the catch-at-length data produced relatively accurate estimates of mortality and abundance, and compared to models where the age is assumed to be known, the confidence bounds of estimated parameters are wider. The Brownie model with conditional age at length estimated externally also performed well. The length-based BP model can provide a very useful extension to the existing BP model for analysing large-scale tuna tagging programs where the age data is scarce, but length composition data of sufficient quality can usually be obtained.
Recapture-conditioned models are infrequently used to analyze tag-recovery data, but have been proposed as an alternative to release-conditioned models for estimating movement from tagging studies when tag-loss processes (e.g., tag reporting, tag shedding) can be assumed constant and estimates of these processes are not available. Through simulations, we investigated the performance (bias and precision) of a recapture-conditioned integrated tagging catch-at-age analysis (ITCAAN) that assumes yearly natal homing under varying model complexities and intermixing rates and compared the results to those from a release-conditioned ITCAAN. We also investigated how misspecification of natural mortality, parity in population productivities, tag shedding, and spatially-varying reporting rates affected estimation of model parameters. At low intermixing rates, estimation of total abundance and spawning population abundances was accurate and precise, with precision decreasing when natural mortality was estimated for the recapture-conditioned ITCAAN. Accuracy and precision of individual population abundances declined with higher intermixing rates, with the largest bias and lowest precision occurring when estimating relative reporting rates. Assuming reporting rates were spatially constant in the ITCAAN when they varied regionally in the operating model led to biased estimation of movement rates and population abundances for both ITCAANs; attempting to estimate relative reporting when reporting varied spatially greatly improved parameter estimation compared to assuming spatially constant reporting. When tag shedding was simulated to occur, the recapture-conditioned ITCAAN yielded relatively unbiased estimation of total abundance without additional data on the tag-shedding rate, whereas the release-conditioned ITCAAN requires external data to inform this tag shedding process. Incorrect specification of tag-shedding rates by 20% resulted in only a 5% bias in estimation of total abundance from the release-conditioned ITCAAN. To avoid biased estimation from the release-conditioned model, externally derived data for all tag loss rates (e.g. tag shedding and tag-induced mortality) must be provided to the ITCAAN. Movement rates in the recapture-conditioned ITCAAN framework are theoretically unbiased by spatially uniform loss rates, but yielded biased estimates at high movement rates in this simulation study as a consequence of the model's poor ability to estimate population-specific abundances. For most scenarios investigated, estimation by the release-conditioned ITCAAN was less biased and more precise compared to the estimation by the recapture-conditioned ITCAAN presumably as a consequence of the former providing additional information on region-specific survival. However, both models performed poorly in estimating population specific abundances for scenarios with high intermixing rates and when reporting rates varied regionally but were assumed to be regionally constant in the ITCAANs.
The need for spatial stock assessment models that match the spatiotemporal management and biological structure of marine species is growing. Spatially explicit, tag-integrated models can emulate complex population structure, because they are able to estimate connectivity among population units by incorporating tag-recovery data directly into the combined objective function of the assessment. However, the limited scope of many small-scale tagging studies along with difficulty addressing major assumptions of tagging data has prevented more widespread utilization of tag-recovery data sets within tag-integrated models. A spatially explicit simulation-estimation framework that simulates metapopulation dynamics with two populations and time-varying con-nectivity was implemented for three life history (i.e., longevity) scenarios to explore the relative utility of tagging data for use in spatial assessment models across a range of tag release designs (e.g., annual, historical, periodic, and opportunistic tagging). Model scenarios also investigated the impacts of not accounting for incomplete tag mixing or assuming all fish were fully selected (i.e., that the age composition of tagged fish was unknown). Results demonstrated that periodic tagging (e.g., releasing tags every five years) may provide the best balance between tag program cost and parameter bias. For cost-effective tagging programs, tag releases should be spread over a longer time period instead of focusing on release events in consecutive years, while releasing tags in tandem with existing surveys could further improve the practicality of implementing tag-recovery experiments. However, care should be taken to fully address critical modeling assumptions (e.g., by estimating tag mixing parameters) before incorporating tagging data into an assessment model.
Interpretation of data used in fisheries assessment and management requires knowledge of population (e.g. growth, natural
mortality, and recruitment), fisheries (e.g. selectivity), and sampling processes. Without this knowledge, assumptions need
to be made, either implicitly or explicitly based on the methods used. Incorrect assumptions can have a substantial impact
on stock assessment results and management advice. Unfortunately, there is a lack of understanding of these processes for
most, if not all, stocks and even for processes that have traditionally been assumed to be well understood (e.g. growth and
selectivity). We use information content of typical fisheries data that is informative about absolute abundance to illustrate
some of the main issues in fisheries stock assessment. We concentrate on information about absolute abundance from indices
of relative abundance combined with catch, and age and length-composition data and how the information depends on knowledge
of population, fishing, and sampling processes. We also illustrate two recently developed diagnostic methods that can be used
to evaluate the absolute abundance information content of the data. Finally, we discuss some of the reasons for the slowness
of progress in fisheries stock assessment.
Simulation models are useful and flexible tools that can be used to synthesize information gained from multiple stock identification methods. The assimilation of information from many sources into a population dynamics model can provide a holistic view of stock structure. Application of spatially explicit models within the simulation framework allows the testing of varying hypotheses regarding stock structure and connectivity. Additionally, using this approach we can examine the ecological, assessment, and management implications of complex spatial structure for the fish resource. This chapter summarizes the simulation modeling framework and how it can be applied to investigate population structure. We highlight how stock identification data can be incorporated into simulations and review recent advances in spatial modeling techniques. We conclude with a discussion of seminal case studies, which illustrate how simulation models have impacted our understanding of stock structure in fish populations. Ultimately, simulation models have many limitations because they are simplified abstractions of large and complex natural systems. However, when carefully vetted and used with strict adherence to the scientific method, simulations can be powerful and invaluable tools for examining spatial population structure.
The ISC Shark Working Group has identified tagging data as potentially useful data to examine stock structure hypotheses and provide information on movements for stock-assessments in support of population management. Shark tagging programs in the Pacific have been in operation since the 1960's but there is still limited information on the stock structure of highly migratory pelagic sharks, and movement data from these programs generally have not been included in stock assessments. The tagging data presented here do not support a hypothesis of panmixia of blue shark or shortfin mako stocks in the Pacific Ocean. Rather this evidence suggests at least northern and southern sub-populations of both species, demarked by the equator.
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