Combining Individual and Population Based Estimation of Migration Pattern

Background and Justification
Background and justification The goal of population based estimation of migration is to get the best possible information about the movement pattern of the entire population, which is needed in the fish stock assessment models that fishery management decisions are based on. Population based estimates are obtained from studies where a huge number of individuals are tagged with conventional tags.

The goal of individual based estimation of migration is to get the best reconstructed track for each individual, but this reconstruction includes an estimation of the underlying movement pattern. Individual based estimates are obtained in studies where a few individuals are tagged with (expensive) archival tags.

This section is intended to outline why it is important to get reliable estimates of the movement pattern, and how a combined model will benefit the goals of both the population and the individual based estimation of movement patterns.

The importance of including the movement pattern and heterogeneity in fishery management is best be illustrated by considering the opposite. Assume that the stock under consideration have some preferred area, but this area supports only a fraction of the total stock. The rest of the stock is scattered in the remaining area. Fishing effort is concentrated in the area where the fish concentration is high (the preferred area), and the fishing effort is about the same every year. As fishing removes fish from the preferred area, the fish from the surrounding areas migrate into the preferred area. If the fishing pressure is too high the surrounding areas will gradually contain fewer fish, but non-spatial fish stock assessment will not show this until the stock in the preferred area starts to decline (year 4 in figure 1). Even when the stock in the preferred area starts to decline, the non-spatial fish stock assessment will detect a much smaller decline than what has really happened, because it is unaware that the surrounding area was drained first.

Combining the individual and population estimation of migration patterns is an appealing idea. After all, all tagged fish should be equal representatives of its movement pattern, no matter what type of tags they have been equipped with.

A very popular approach for reconstructing individual tracks from archival tagged individuals (Sibert et al. 2003) is based on Kalman filter estimation in a state space model. This basically estimates the underlying movement pattern, and reconstructs each point on the track as the optimal weighted average of the prediction from the movement pattern and the suggestion from the current observation. Notice that the movement pattern is estimated from only one fish.

The raw geolocations from each archival tag are often very noisy, and as a consequence the estimated movement pattern becomes very uncertain. Using the movement pattern estimated from a high number of similar fish in the same area would be desirable, as it would be better determined, more stable, and more representative of the population.

Population based estimation of movement pattern is based on large mark and recapture studies. The study area is partitioned into a number of cells, and the number of tagged fish caught in each cell is matched to the predicted from the underlying movement pattern. The underlying movement pattern is often described via a partial differential equation (Sibert and Fournier 1994).

The population based estimate of the movement pattern would benefit by having a larger sample available. The added number of individuals would likely be insignificant, but each of these added individuals are more closely observed (often each day). Besides adding data, these closely observed individuals would offer better means of detecting misspecification of the model structure and too simple model assumptions.

Even though the idea of combining the two data sources is obviously useful, most research into estimation of movement has focused on solving the problems of each separate estimation. Combining has been suggested as a desirable goal (Sibert and Fournier 2001), but not implemented in practice.

Setting up a combined model is more complex than just the sum of the two separate models. The reason for this is that the fishing effort information, which is already a natural part of the population based model, has to be introduced in the individual based model. To realize that this is necessary, consider the following example: 10 archival tagged individuals are equally likely to move east as west, but the fishing pressure is much higher east of the release point. On average this would result in five tracks moving east, and five tracks moving west, but the tracks moving east would be shorter, as they were more likely to get caught. If fishing effort information were not included in this example an average movement west would be estimated, simply because those tracks were longer, and hence represented more data.

One promising way to use all data in one coherent model is described in chapter 5 of the Ph.D. thesis Nielsen (2004), which also implements a pilot study for this model in a very simple case. The study shows that it is indeed possible to combine the two types of models, and that the combined estimates are superior to the separate.

The timing of this project is good, as a large-scale tagging program is currently being planned in the western and central Pacific Ocean. This multi year tagging program will collect both conventional and archival tagging data from the entire region. A combined model is really the only way to tie the different tagging efforts together, and to make also the archival tagging data useful in stock assessment models.

As fishery management decisions are made on the basis of stock assessment models, this project is directly relevant to fishery management.

Objectives of proposed research
The objectives of the proposed research is to develop, implement, test, and document a combined model to estimate movement from both archival and conventional tags.

The developed model will be placed in the public domain, with all details freely available to all researchers who want to use it. This approach has been very fruitful for the previously released models ‘kftrack’ (Sibert and Nielsen 2002) and ‘kfsst’ (Nielsen and Sibert 2005).

Besides developing the model a case study is planned for Coral sea bigeye tuna. The data, which is made available for this study by John Hampton (Secretariat of the Pacific Community (SPC)) and Karen Evans (Commonwealth Scientific and Industrial Research Organisation (CSIRO)), is a relative small tagging study, but perfect for a first real case, as it includes both archival and conventional taggings in the same area and same time period, and the corresponding fishing effort data. The model and case study experiences will be documented in a paper.

Literature cited:

• Nielsen, A. 2004. Estimating Fish Movement (Ph.D. Thesis). ISBN: 87-7611- 065-6. Available at http://www.dina.kvl.dk/~anielsen/phd
• Nielsen A., and Sibert. J. 2005. KFSST: An add-on package for the statistical environment R to estimate most probable track from archival tagged individuals using raw light-based geolocations and sea surface temperatures. Available at https://www.soest.hawaii.edu/tag-data/tracking/kfsst
• Sibert, J., and Fournier, D. A. 1994. Evaluation of advection-diffusion equations for estimation of movement parameters from tag recapture data. In Interactions of Pacific tuna fisheries, Vol. 1 — Summary report and papers on interaction, FAO Fisheries Technical Paper 336/1, pp. 108–121.
• Sibert, J., and Fournier D. A. 2001. Possible models for combining tracking data with conventional tagging data. In J.R. Sibert and J. Nielsen (Eds.), Electronic Tagging and Tracking in Marine Fisheries (pp. 443-456). Kluwer Academic Publishers, The Netherlands.
• Sibert, J., Musyl, M. K. and Brill, R. W. 2003. Horizontal movements of bigeye tuna (Thunnus obesus) near Hawaii determined by Kalman filter analysis of archival tagging data. Fish. Oceanogr. 12(3):141–151.
• Sibert, J., and Nielsen A. 2002. KFTRACK: An add-on package for the statistical environment R to estimate most probable track from archival tagged individuals. Available at https://www.soest.hawaii.edu/tag-data/tracking/kftrack

Dr. John Sibert
Pelagic Fisheries Research Program
University of Hawaii at Manoa
1000 Pope Road, MSB 312
Honolulu, Hawaii 96822 USA
Phone (808) 956-4109
FAX (808) 956-4104
email: sibert@hawaii.edu