Individual and Population Based Estimation of Migration Pattern
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)
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.
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
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
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.
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. 108121.
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):141151.
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