8. DATA ANALYSIS AND MODELLING

 

8.1 INTRODUCTION

 

Quantitative analysis of fish tagging results has a 100 years history, going back to the first calculations done by C G J Petersen during the 1890s. Petersen (1896) founded the basic theory behind most developments in the use of fish tagging for estimating exploitation rates and population abundance. Since then, many new and improved tagging techniques have been developed, and the analysis and modelling of tagging data has evolved along with new demands and possibilities.

 

In order to meet the objectives of mass tagging studies (systematic tagging in large enough numbers to secure quantitative treatment), adequate tools are needed to handle the large amount of data generated from the recaptures. Similarly, new developments in electronic tags, particularly the fast evolving utilisation of data storage tags (DST), mean that large amounts of data can be obtained on each tagged fish and its environment. In both cases, appropriate models and statistical techniques are crucial in order to make the best use of the available information.

 

Traditionally, many tagging programmes have been carried out without definite goals and hence without a well-considered experimental design. Some have simply sought to provide qualitative information on distribution patterns and migration routes. Such programmes have sometimes been continued for many years to maintain a time series, without reconsidering whether the scientific objectives of the programme are being met. The costs of catching fish for tagging is often high, due mainly to the cost of employing vessels, and tag recovery programmes may also be expensive. The effectiveness of tagging programmes is dependent on the quality of both of these phases and great care must be taken in planning to make best use of available resources. The tagging programme must be carefully planned in order to ensure that the tagged fish are representative of the population. Similarly the recovery programme must obtain representative samples of the fishing mortality of the population. Modelling and analysis tools can be used at all stages of a tagging programme (planning, design, quality control, analysis of results) to improve efficiency and reduce costs.

Two basic goals are to:

 

In the following sections, methodologies applied in the analysis of tagging data will be highlighted (without giving a complete review) under the following headings:

 

The last point includes a brief inspection of modelling and analytical tools utilised for other groups of animal (reptiles, birds and mammals), bearing in mind that these approaches may be of direct relevance to fish tagging studies.

 


8.2 CURRENT METHODOLOGY

8.2.1 Experimental design

 

Substantial errors can be introduced at several stages of tagging experiments. The limited use of tagging in evaluation of commercial fish stocks in the EU at present is closely linked to the uncertainty associated with such data. It is therefore of major interest to highlight these questions and look at potential solutions for the future. The errors associated with the design of tagging experiments that permit quantitative data treatment fall into three categories:

 

 

In addition, an area of growing importance is the design of experiments employing electronic tags and the analysis of the results. This area includes the treatment and analysis of data telemetered through a difficult physical environment from an acoustic transponding tag. Also, time series of data from DSTs need careful handling related to data quality and data refinement. In addition to these new problem areas, experiments with electronic tags are susceptible to the same errors as traditional tagging.

 

Consequently, the success of any kind of quantitative treatment of data from tagging - conventional as well as electronic - depends on the quality of the preparatory work done prior to, in particular in formulating clear, specific goals and setting up a corresponding experimental design. A proper experimental design is the only way to avoid the numerous pitfalls and to minimise the effect of the described errors.

 

Although different problems affect different types of tag or tagging method, the data from all studies need careful scrutiny before the final analysis is undertaken. The overall goal of modelling work connected to this process is to control data quality, improve consistency and fill gaps and holes in broken time series.

 

(a) Release errors

In order to meet the objectives of any tagging study, it is important to ensure that the release programme is well planned. Where large numbers of fish are tagged for assessment purposes, it is important to distribute the releases in the population so that the distribution of recaptures does not diverge from the general assumptions in the analytical models that are used. For example, efficient design of the release programme to comply with initial goals and assumptions might be achieved by combining information about the distribution pattern of the population with data from the commercial fishery and previous tag recovery records. Commonly, the rate of exploitation (u) (the fraction of the fish in a population that is caught at a given time) is assumed to be equal to the relationship between number of recaptures (R) and marked fish (M):

 

which again is equal to the relation between the population catch or sample (C) and (N) (see Ricker 1975, Burnham et al. 1997 for details). However, it is essential that the distribution of the tagged individuals in the population does not reduce or increase the probability of catching marked fish relative to unmarked ones. This can be achieved either by intrinsic mixing of individuals in the population or by distributing tagged individuals in the population in space and also over time. Special attention has to be paid to sampling when designing a tagging programme for studying the effects of sea ranching or cultivation in rivers or lakes (see e.g. Svåsand 1990, Vreeland 1990).

 

In many cases, practical considerations in the tagging phase preclude choosing the optimal experimental design. Further, incomplete knowledge about the structure of fish stocks may prevent an optimal release design being created. Commercially important fish populations, marine as well as anadromous and fresh water species, are often structured both geographically and intrinsically (by size, year class, etc.). This has to be taken into account in the design of tagging experiments by distributing the tagged fish proportionally to geographic and demographic properties of the stock. Numerically this means e.g.

 

where Mij is the number of released fish of age i in area j and Nij is the sub population size at age i in area j. M and N are the total and tagged population sizes. The tagging programmes on Norwegian spring spawning herring (Hamre 1989) and Northern cod (Taggart et al. 1995) are examples of marine stocks where the population structure is taken into account when designing tagging releases. Some of the problems caused by improper or unbalanced release design can be compensated for in a thorough sampling of recaptures and will be dealt with later.

 

Intuitively, the precision of assessments from tag recoveries will be dependent on the number of releases. It should, however, be kept in mind that most models rely rather on the number of recaptures to determine the precision of the estimates. Consequently, based on actual or assumed recapture rates, simulation studies can be run to estimate the number of releases needed to obtain a certain precision (Xiao 1996a).

 

A special concern is related to the number of releases of electronic tags. High price limits the number of releases. Also, the size of tags often makes it necessary only to select larger fish for tagging. In addition, survival may be size dependent (see Chapter. 7). Hence, particular attention should be paid to the design of such experiments when data are to be analysed with the aim of supplying information on population or sub-population properties.

 

(b) Tagging mortality, tag losses

Tagging mortality and tag losses represent a special challenge during numerical treatment of tagging and recapture data. In most cases capture and tagging are very stressful for the fish and can affect survival in the tagged population (tagging mortality, Ricker, 1975). More seriously for modelling and calculations, there is a high risk of varying tagging mortality among releases caused by variation in the capture situation. Fish can be caught at different depths, under different weather conditions and at different times of year and these factors may affect their survival. Reduced survival compared to assumptions leads to underestimates of recaptures and hence rates of exploitation (eq. 7.1) in experiments conducted for stock assessment purposes.

 

Tag loss, by a variety of methods, can seriously affect assessment results from tag-recapture experiments. Fish can shed tags, and external tags can be lost after becoming entangled in fishing gears during capture. Further, an external tag may alter the appearance and/or behaviour to potential predators with subsequent effects on recapture and survival probabilities (Svåsand & Kristiansen 1990). If the releases do not satisfy assumptions on representativity related to the whole population, the recaptures may give misleading results (Turner 1986).

 

In systematic tagging programmes, where mass tagging occurs, for example, routinely every year, the effects of tagging mortality can be estimated through comparison of rates of survival during the first and subsequent years. For example, if the rows in the table below represent the release year and columns the recapture year, an analysis comparing returns (R) for different tagging groups between different years may give valuable information about losses due to tagging.

 

Year 1 2 3 4
1 R11 R12 R13 R14
2   R22 R23 R24
3     R33 R34
4       R44

 

To exploit such possibilities, systematic and long term tagging programs are needed. Varying fishing mortality and tagging mortality make such approaches difficult in practice. A special model (Hamre, 1980) was used to quantify variation in tagging mortality from year to year by means of such information. If the tags are lost due to shedding, predation or other mortality caused by tagging, the effects can also be studied in so-called "dead recovery experiments" where information from tags recovered from dead individuals is used in separated or combined analysis with data from living individuals (Seber 1970, Lebreton et al. 1995, Program MARK-http://www.cnr.colostate.edu/~gwhite/mark/mark.htm).

 

Mortality and tag losses during tagging might also be a serious problem for experiments designed to study and model fish distribution and migration. Loss of tags has been studied for a lot of tag types and species through experiments employing tags with secondary marks. In such tests the fish are doubly identified by a second tag, or by a combination of marking (e.g. finclipping) and tagging (Ricker 1975, Xiao 1996b). Reports over time give information on rates of tag loss in the experiment. The tagging mortality might be size and/or sex specific, and thus lead to inaccurate behaviour models. Particular emphasis should be paid to this problem when data from large electronic tags are used in modelling. These tags potentially expose the fish to a higher risk of dying due to tagging (e.g. of health causes), by entangling in fishnets, or by predation. These effects are discussed in details in chapter 5.

 

In some cases, the effects of tagging on the behaviour and survival of fish and the impacts of tag losses on assessments can also be addressed by developing methods that ignore data or results that are affected. Thus, in the case of tracking studies using electronic tags, data collected in the first few hours or days might be ignored in any analysis because the behaviour of the fish may have been affected by the handling or tagging procedures. Similarly fish can be released sometime prior to the period of interest. For example, in studies of salmonid smolts passing through estuaries, Moore et al. (1995) caught and tagged the fish in freshwater days or weeks before they were expected to emigrate through the estuary. The run-reconstruction model (see Lassen et al. 1988; Potter and Dunkley 1993; Rago et al. 1993) adopts a different approach. By back-calculating the stock size from the surviving spawning stock, tagging mortality and tag loss, which are believed mainly to occur soon after release, can be ignored.

 

(c) Recapture errors

There are two types of errors that can lead to biased or imprecise estimates in population studies based on tag-recapture data:

 Recovery reporting errors - Recaptures are normally reported by commercial fishermen or obtained in automatic screening systems in association with production lines, or special sampling arrangements. Errors may arise from mechanical inefficiency of automatic registration systems, or from human mistakes in recording position, measuring fish length etc., or simply by irregular reporting by the fishermen. To minimise the effect of such errors in the recovery database, simple automatic control routines can be applied when entering information on, for example:

 It is, however, essential that any exclusion or correction of data does not introduce any kind of bias in the database. For example due to the normally quite imprecise reporting of stock parameters, a slight negative growth report shortly after release may occur with the same probability as a similar positive growth.

 Assumption errors - Recoveries recorded from catches not representing the population may seriously bias stock assessment studies based on these data. Similarly, low quality of catch statistics may introduce serious errors in population estimates, if it is assumed that the population/catch ratio equals the tag/recapture one. As an example for the general assumptions needed for modelling, the following are required for to use the Brownie models (Brownie et al. 1985):

    1. the tagged sample is representative of the tagged population
    2. there is no tag loss, or it can be accounted for by double tagging
    3. survival rates are not influenced by tagging
    4. the year of tag recovery is correctly tabulated
    5. the fate of each tagged fish is independent of the fate of other tagged fish
    6. all tagged fish within a tagged cohort have the same annual survival and recovery probabilities in a given year
    7. the survival and recovery probabilities do not depend on the age of the animal
    8. the forces of instantaneous natural and fishing mortality are additive and independent
    9. natural mortality is constant within a year (no seasonal variation) and between years
    10. fishing mortality for a user group is constant for the period of the year that the fishery is operating
    11. tagging takes place over a short period

 

(d) Electronic tags

In addition to the errors and problems described above, analyses of electronic tag data require special attention to quality control and data manipulation. Relatively few tags are normally released compared to conventional tagging experiments, while thousands of data points can be collected from each tag instead of just one. When results are scaled up to the population level it may be difficult to balance the detailed information on the individual level with the variability shown between tags. In other words, particular attention should be paid to the number of recaptures when making inferences about population behaviour from data from individual fish.

 The database from electronic tags is particularly vulnerable to technical failures, or errors, if it is not properly calibrated and controlled. Due to the high value of each individual fish, realistic calibration of each tag and sensor is needed. Normally this is done by the producer, but in many instances it can also be easily tested as part of the tagging protocol. For example, tags with temperature and depth sensors can be attached to a CTD profiler after recording has started and exposed to realistic fish depths and temperatures before the fish is tagged and released. After recovery the CTD measurements and the DST recordings can then be compared or contrasted with original calibration (K. Michalsen, Institute of Marine Research, Bergen, pers. com.). Similar procedures can also be applied to returned tags to test for drift in accuracy of recordings over the whole period for which the tag was at liberty.

 DST data can be corrupted as a result of malfunction of sensors occurring periodically, or at a certain moment during operation. General screening of data is therefore important and such examinations should consider abrupt, as well as gradual, changes towards unrealistic values from the sensors.

 DSTs are often larger than conventional tags and special attention therefore should be paid to effects this might have on recapture results. Stress from a higher drag and entanglement in fishing nets may change behaviour, as well as reduce the number of recorded recaptures. In such cases double tagging combining conventional and electronic tagging may be useful (see e.g. Thorsteinsson 1995).

 

8.2.2 Assessment of abundance and mortality

 Although many tagging studies have been conducted in the past, relatively few such studies are currently being used in the assessment of European fish stocks, and tagging data are utilised in only a small number of ICES stock assessments. To a large extent this reflects the high cost of tagging studies and the difficulty of addressing the problems outlined above. However, the situation contrasts with that in the Pacific, where tagging is applied much more widely and is an integral part of assessments of tuna and salmonid stocks. The difficulties of developing and improving approaches have been exacerbated by the fact that many assessment studies have only been reported in the grey literature. Nevertheless, examples exist which demonstrate the applicability of tagging for operational management. For example, the Norwegian spring spawning herring assessment utilises tag recovery data as an input to tuning the VPA assessment (Anon. 1998). Also, the estimation of exploitation rates for certain North Atlantic and Baltic salmon stocks in marine fisheries is based largely on coded wire tag (CWT) or Carlin tag recovery data (Anon. 1991; Anon. 1995a; Anon. 1995b). Some examples of tagging programmes that have been used to monitor features of importance to management (e.g. exploitation, population distribution and mixing) are given in Table 8.1.

(a) Models

Assessment models utilising tagging data are usually developed to estimate stock abundance and this leads on to methods for estimating mortality (i.e. changes in abundance). Much literature appears on these subjects, and a range of approaches has been proposed for improving basic mark-recovery estimates. Ricker (1975) presented an extensive review of methods to estimate abundance and mortality parameters. A series of approaches are described, beginning with studies which employ one release of tagged fish followed by recaptures in a single period (e.g. Petersen method) to models based upon multiple releases and recapture periods.

Various approaches are proposed for dealing with the biases discussed in preceding sections (e.g. differential tagging mortality, non-random distribution of tags, etc). Multiple tagging studies may be based upon two (e.g. Ricker 1975), three (Bailey method, e.g. Fairfield and Mizroch 1990) or four and more (Jolly-Seber method, e.g. Kunzlik et al. 1986) release and recapture periods. There is an extensive literature on the latter group of models, which has been summarised by Brownie et al. (1985). The method has been used in a wide range of fishery assessments, including reservoir fish populations (Hightower & Gilbert, 1984) and Pacific salmon (Law 1994).

There have been other developments to estimate area or fishery based harvesting. Brooks et al. (1998) have extended models to estimate fishing mortality separately for a commercial and a recreational fishery harvesting the same salmon stock.

An alternative approach has been developed for estimating levels of exploitation of Atlantic salmon stocks in sequential fisheries, which operate through their lives in the sea. These models, referred to as run-reconstruction models, back-calculate the number of fish from a stock (e.g. a river) that were alive at earlier stages in the life cycle using an estimate of the returning spawning stock (Lassen et al. 1988; Potter and Dunkley 1993; Rago et al. 1993). CWT or Carlin tag studies are used to estimate the numbers of fish removed by fisheries and hence the levels of exploitation of the extant stock (i.e. all fish of a single cohort that are alive wherever they are). The run-reconstruction approach has been further developed, in part using the results from the tagging studies, to estimate the stock abundance for large stock groupings (e.g. North American and North East Atlantic). It has also been used to propose preliminary stock conservation limits (Potter et al. 1998), in order to provide advice to the North Atlantic Salmon Conservation Organisation (NASCO).

In studies of diadromous fish, stocks can often be sampled at more than one point on their migration route (e.g. when migrating downstream). Similarly, downstream migrants can be trapped, marked, and then released upstream of the trapping site; they can then be resampled as they pass the trap site for a second time. This technique may provide an opportunity for making mark-recapture estimates using the Petersen method, but the estimate may be biased if both the sampling sites are selective. This problem may be reduced by employing Schaefer’s (1951) stratification method, which has been used to enumerate salmon smolt runs from tagging data from the River North Esk in Scotland (Shearer 1992).

Many tagging studies have been carried out to assess the distribution of various fish stocks or to estimate the stock composition by origin in different areas. In the case of Atlantic salmon, the fact that fish from both North America and Europe migrated to West Greenland was demonstrated by tagging studies (e.g. Anon 1991), although the composition of the stock in that area is now determined by scale analysis or genetic methods (Reddin et al 1988). Tagging studies have been conducted on mackerel in the north-east Atlantic to describe geographical distribution and migration (Iversen & Skagen 1989). The results of these tagging experiments have been used in the consultations between Norway and the European Union to determine the proportion of the stock which should be apportioned to different areas of jurisdiction, and to distribute quotas by country (S. Iversen, Institute of Marine Research, Bergen Norway, pers. comm.).

 

(b) Limitations and problems

Currently, tagging experiments are not extensively used to assess stock abundance or mortality largely due to the cost and the practical difficulties related to tagging a representative sample of the stock and obtaining unbiased recovery data. In addition to the general problems highlighted in Section 8.1, there are specific problems associated with assessment studies. The major commercially exploited fish stocks are usually very large and distributed over a wide area. This means that tagging studies require marking very large numbers of fish on the one hand and on the other that good co-operation is achieved with fisherman to find and report marked fish (Hilborn & Walters 1992). In the past, tagging experiments have often failed because too few fish have been tagged, or because fishermen and other members of the industry have been reluctant to report recoveries.

This problem further emphasises the need to ensure that the objectives of tagging experiments are clearly spelt out and that preliminary modelling is used to determine that tagging and recovery programmes are likely to generate statistically meaningful results. Furthermore, it is important to ensure that at least as much effort is put into the tag recovery programme as the original tagging. This may include extensive advertising of rewards and explaining to fishermen the benefits of reporting recaptures.

Tagging programmes may also depend upon reliable catch records, for example by scaling tag recoveries to the level of the recorded catch. In such circumstances it is important that the catches are reliably reported both in quantity and by location. Otherwise any conclusions drawn from tagging studies may be similarly biased.

In the case of salmon run-reconstruction models, an important element is the estimation of the returning spawning stocks. The difficulty of counting upstream migrants in large rivers tends to limit the use of this approach to smaller systems. These tend to support stocks which return mainly as one-sea-winter fish and thus make it difficult to obtain information on multi-sea-winter stock components. Cost effective methods for river monitoring are therefore required. The approach also depends upon estimates of tag reporting rates, which can often only be approximated.

Table -1. Examples of tagging experiments being used to assess abundance, mortality or stock identity of commercial fish stocks.



Tagging method


Analysing method


Stock


Reference


Application
Internal /metal Ricker, Jolly –Seber

Mortality
Norwegian Spring Spawning Herring Hamre (1989) Results input in tuning of VPA
Internal /metal   Western Mackerel Hamre (1980)
Migration models
Coded Wire Tag (CWT) Run-reconstruction Atlantic salmon Potter and Dunkley

(1993); Rago et al. (1993)
Estimation of exploitation
Carlin Run-reconstruction Baltic salmon Anon, 1995a (ICES) Estimation of exploitation by area
CWT Brownie method Pacific salmon Brooks et al. 1998 Estimation of exploitation by fishery
Carlin Schaeffer Atlantic salmon (Shearer 1992) Estimation of smolt runs
External New exploitation models Northern cod Myers et al. 1994, 1996 Exploitation,

 

8.2.3 Modelling of fish behaviour, movements and migration

 Fish populations have over time developed favourable migration patterns, which in the long term secure advantageous circumstances for survival, recruitment and growth. Although migration and dispersal is not totally under the control of the individual fish, it is fundamentally driven by behaviour that puts (or maintains them) in advantageous circumstances with respect to population survival. However, the movement of individuals in the same environment will not necessarily be identical and this is an important factor to consider when developing fishery models based on tagging results. Whilst random movements undoubtedly occur, fish orientate to a variety of directional stimuli and dispersion cannot generally be considered as simple diffusion. Movements within a specific area may be influenced by many factors, which include the physical environment, food availability, predator avoidance, pollution and so forth.

Modelling of fish behaviour, movements and migration has to a great extent been a theoretical exercise, which tries to synthesise available knowledge and information into a dynamic framework. Because of the very manifold nature of biological processes in nature and the complex interaction between fish and their physical and biological environment, such models become complex and dependent on difficult parameterisation and/or strong assumptions. Such models often suffer from lack of realism because of a lack of adequate data. As a result they are often only used for simulation purposes rather than as operational tools for fish stock assessment and management. This type of modelling suffers further from a lack of understanding of the basic biological processes and motivation behind fish movement and the dynamics in these processes. Recent technological developments including new electronic tags, new software and faster data processing capabilities have opened new possibilities for filling these gaps. There is, however, a demand for new analytical approaches which are constantly being developed and modified according to new achievements in technology and knowledge. These may in future improve the interaction between theoretical developments and practical application. For example the use of multiple tag types or combined methodologies may be necessary to fully develop models for future fisheries applications.


8.2.3.1 Large scale models 

Large-scale models refer here to approaches that cover broad scale movements of populations without emphasis on individual behavioural patterns. Significant contributions to our understanding of large-scale fish migrations have come from conventional tag and recapture experiments. With improvements in electronic devices, and particularly the fast evolving utilisation of data storage tags (DST), a much larger quantity of data on individually tagged fish has now become available which can be related to the position of the fish. These tags are now commonly used for fish migration studies. However, the quality of the data generated from all electronic tags should be assessed and the suitability of analytical procedures critically examined.

 Apart from general analyses of tag recoveries and related data, there are two major categories of mathematical models that are applicable to the study of large scale animal movements - here called differential diffusion models and random walk models (Okubo, 1980). The main difference between the two methodologies is that the first add parameters to the equations, making them larger and more complex. These models consider entire populations. Probability models, on the other hand, modify the existing probabilities as a function of multiple interactions.

 

(a) Differential diffusion models

This category includes models that use differential calculus to solve diffusion equations. Joseph and Sender (1958), Ozmidov (1958), Bowles et al. (1958) have developed the theory of diffusion based on differential calculus. Only Ozmidov’s solution is suitable for describing oceanic diffusion (Fischer, 1973; Okubo, 1971b).

 Salvado developed an approach to the understanding of animal motions and migrations

(1993) from the empirical Green Function. This was based on the development of a point source solution of the differential field equations resulting in a one parameter model, which would be applicable to fisheries simulations based on tagging results.


(b) Random walk models

This group of models is based on probability functions. Despite their implicit insensitivity to environmental conditions, they are used in fisheries assessment (Jones, 1959, 1976; Mullen, 1989) to describe fish dispersion and local population dynamics (Okubo, 1980).

 To add realism and a more directional spatial displacement to diffusion models based on probability functions, there has been an effort to incorporate into their design ecological controlling functions in the form of spatially-explicit and temporally articulate probability distributions (DeAngelis and Yeh, 1984; Marsh and Jones, 1988). Introduction of these "biased" rules to modify movements of fish implies complex decision-making on the part of the organism. In fact, some of these more sophisticated probability models can produce accurate simulations of an organism’s response to heterogeneous environmental conditions (Saila and Shappy, 1963; Kareiva and Shigesada, 1983; Pulliam et al. 1992). Schaefer et al. (1961) and Bayliff (1979) have described approaches based on quantitative analyses. These analyses which use measures of directional and random movements developed by Jones (1959, 1976) are suitable only for random or simple directional movement.

 Darroch (1961) and Arnason (1972, 1973), in their statistical works on analysis of movement data, examined spatially stratified capture recapture models, but under the condition of multiple recaptures. A limitation in these studies is the assumption of equal probability of the capture in all areas, which is unlikely considering the nature of commercial fisheries where tag recoveries are made.

 Burnham et al. (1987) considered traditional models and approaches of mark-recapture studies on spatially structured problems with unequal fishing effort in the spatial strata. Adopting a Markovian movement model, Ishii (1979) simulated the movement of tagged fish and used non-linear minimisation techniques to determine the movement probabilities that optimise the difference between observed and expected number of recoveries in each spatial area. Ishii’s model included parameters such as natural mortality, and tag shedding. Later Sibert (1984) included natural mortality, fishing mortality, and movements between two countries in his analyses, which used tagging data to determine mortality rates and exchange rates between the two countries. Ishii and Sibert used the method of the least squares to estimate the parameters involved in their models.

Schwartz (1988), and Schwartz & Arnason (1990) described the extension of this approach to the statistical analysis of mark-recapture data, using explicit multinomial probability functions. Movements of fish were calculated from differences in stock structures between censuses by Schnabel (in Ryan, 1990) using multiple-mark-recapture studies. Hilborn (1990) developed a model that adopted the maximum likelihood method based on the Poisson distribution and presented a general method for the analysis of movement data from tag returns. This method was based on an extension of the generalised linear model approach adopted from Cormack (1981).

 Mullen (1989) suggested combining differential and probability models by using an approach based on the variable coefficient of diffusion model, in which the local environment affects local population dynamics by creating unique diffusion coefficients for each spatial co-ordinate. Mullen’s coefficient of diffusion was based on a simple bio-economic model taken from Clark (1985). With the inclusion of this coefficient of diffusion, many variables such as the foraging mechanism can be included in the model.


8.2.3.2 Small scale behaviour models

Behavioural models can be considered on a smaller scale than migration models as they tend to describe more localised movement. Computer simulations can provide a good approach for stochastic investigation of animal movements. These simulations require an abstraction of actual animal motion into certain elements, for instance, speed, direction, activity, and rest periods, and an evaluation of the statistical distribution of each of these processes. For this purpose, the assumed relations may be based on actual data, or on theoretical considerations. The required distributions and algorithms can then be programmed into a computer to simulate animal motion. The result is then compared with data to test the applicability of the model; if necessary the model can be modified.

Various forms of animal movements have been described (Fraenkel & Gunn 1961which can be simulated. These are:

 Other processes influencing population ecology (growth, death, predation, competition, etc) can be added to develop a more complete model of fish behaviour. A number of models have been developed but they have normally no direct reference to tagging and will thus not be dealt with in any detail here (an overview with references is given at the CATAG web site http://www.hafro.is/catag). These models facilitate simulation based on modelling of various kineses and taxes and demonstrate potential individual movement in a variable environment based on motivation and behavioural features (see e.g. Rohlf and Davenport 1969, Neill 1979, Okubo 1980,).

 The development of sophisticated electronic tags and telemetric procedures allows for tracking of individually marked animals. Coupled with simultaneous measurements of environmental factors and physiological data there is an inestimable potential for discovering important processes affecting fish populations. The fact that many individuals may be tracked simultaneously may improve the quality of the results and lead to better reproducibility. Thus, new electronic tags can become important in validating and developing the theoretical modelling summarised above toward the development of important scientific and management tools.

Keleher, et al. (1985), carried out radio tagging to study the behaviour and movements of Pacific salmon species in relation to environmental influences and used the t-test to compare movements between species. Separate regression analyses were also developed to relate daily distance travelled to the cumulative precipitation (an indicator of stream flow) of a lake system.

Binkley (1976) presented several mathematical techniques for examining circadian rhythms data that allow the significance of a periodogram peak to be tested. These include:

 In order to establish circadian characteristics, Schulz and Berg (1992) applied the x 2 periodogram test (Sokolove & Bushell, 1978), based on Enright’s method (Enright, 1965) to analyse the daily activity data derived from ultrasonically tagged brown trout in Lake Constance, Switzerland. The coherence of barometric pressure and migration activity was tested with general linear models. Additionally, mean swimming activity, swimming depth and temperature were calculated for day (light intensity > 1 lux) and night (light intensity < 1 lux), and tested with t-tests. Swimming activity during the day (foraging behaviour) was significantly higher than at night in most experiments. Cyclic features in fish behaviour data such as diurnal and tidal patterns have also been studies with circular statistics by e.g. Batschelet (1981) and Moore and Potter (1994).

 Greer Walker et al. (1978a & b), Arnold et al. (1994), Arnold and Holford (1995), Arnold and Metcalfe (1995), have studied migratory behaviour of fish in the North Sea by means of data from electronic tagging. A variety of behaviours shown during the tracking suggests some kind of cues or clues to which the fish might respond under different conditions (Arnold & Metcalfe, 1989; Arnold et al., 1994). Direct observation of behavioural pattern of plaice in relation to tidal current by means of acoustic tagging experiments, initiated development of a migration model using tidal stream vectors calculated from the British Admiralty tidal data. The basis for the approach was obtained by observing the heading of the fish and its speed through the water compared to measurements of tidal stream vectors made with current meters (Arnold et al. 1994). By using vertical migration data from data storage tags Arnold & Holford (1995) were able to predict the rates and scale of horizontal movements and demonstrate that the model is able to estimate the recapture position of the tagged fish with remarkable precision in some circumstances. This work might serve as an example of the potential success by combining information from new electronic tags with physical models in testing behaviour and migration hypothesis.

Migratory behaviour of fish results in temporal changes in the spatial distribution of biomass and is influenced by prey availability, vulnerability to predation, accessibility to fishing gear, and exposure to environmental conditions. The migration route may vary from year to year in response to changing climatic conditions, or environmental factors. The influence of the environment on the fish behaviour has been discussed by Harden Jones (1968), Laevastu & Hela (1970), and Neill (1984). Random walk models have been used in order to model simple movement of fish. DeAngelis and Yeh, (1984) used a biased random walk adopting a hypothetical oceanic coastal region, with environmental heterogeneity built into the model to simulate a realistic situation.


 8.2.3.3 Limitations and problems of tagging studies
 

(i) The general lack of an experimental design is a serious deficiency in many tagging surveys; it can undermine the relevance of the data collected and the analytical procedures.

(ii) The number of fish to be tagged is often based on economic considerations rather than on the basis of ensuring good representation. This has a direct bearing on the type of analyses that can be performed and the confidence limits that ca be achieved.

(iii) Release times and conditions are difficult to standardise in tagging studies.

(iv) Many studies incorporate the results of all recaptures regardless of how much time has elapsed since the release of the tagged animals. There can be problems in interpretation of recovery data from fish that have been at liberty for different periods of time.

(v) The influence of environmental factors on tag recoveries and return rates is poorly understood.

(vi) The availability of data for analyses can be affected by the rate of reporting of recaptured fish by commercial or recreational fishermen

(vii) Results can be seriously confounded by even slight uncertainty in recapture data, lapses in time series, misclassification or mis-reporting of information.

(viii) Data interpretation from DST tags can be compromised by local events (e.g. localised temperature effect) or anomalies, which make comparison with data from other sensor sources with different resolution less accurate.

(ix) Specific problems arise with the application of electronic tags that may be affected by radio or acoustic interference.

(x) Data quality problems caused by environmentally induced background noise or disturbances.


8.2.4 Review of analytical methodologies used for other animal groups

 Tagging studies of migration and behaviour are not exclusive to fish and many applications developed for other species have been and can be adapted for fisheries related work. Models have been developed describing the behaviour of seals, birds, turtle, sharks, insects and mammals and there are many novel analytical approaches, which may be applicable to fisheries studies. A significant number of computer simulations are available particularly for studies relating to animal behaviour which could be adapted for fish behaviour.

 There are several examples of experiments on other species that have been adapted for fisheries work. Dodson & Dohse (1984), for example, adapted a model of directional bias based on olfactory mediated conditioning to study the homing behaviour of American shad (Alosa sapidissima) in the Connecticut River.

Random search has been proposed as a possible mechanism for homing. Whilst a completely random search would appear to be unlikely as a factor in homing, the possibility has been examined by a number of workers. Wilkinson (1952) first demonstrated that random search explained some observed phenomena associated with bird homing. Since then Jones (1959) and Saila & Shappy (1963) have proposed the idea that random search combined with a small amount of directional orientation (possibly of olfactory nature) can theoretically provide reasonable homing results in fish. Wilson & Findley (1972) showed that experimental data on bat homing could be interpreted in terms of the random search hypothesis. All of these studies suggest that random search cannot be excluded as a possible homing mechanism.


Movements of animals within the home range can be considered to be a stochastic process in space, as for example a random walk. However, the walk is not purely random but it must be regarded as a biased walk (Holgate, 1971). That is, the probability of taking a step toward the centre of activity of the home range is greater than moving away from the centre. This kind of random walk, is called centrally biased (Okubo, 1980).

In a random walk, movement is assumed to be discrete. In the limit of increasingly smaller steps, however, the differential equation for probability becomes a generalised diffusion equation describing continuous movement. Then, in the limit, the discrete equation converges to the following equation:

  S ¤ t = w 2¤ k ( x S ) ¤ x + A2T ¤ m2k2 2S¤ x 2; (8.2.4.a.3)

 called Fokker-Plank’s equation for the Ornstein-Uhlenbeck process (Uhlenbeck and Ornstein, 1930; Wang and Uhlenbeck, 1945). Both equations consider the same concept, but the differential one is much more convenient to handle analytically.

Dunn & Gipsen (1977) and Dunn (1978) have proposed a multivariate centrally biased diffusion process as a useful model for the study of home range. The model is characterised in terms of some typical descriptive properties of home range, such as activity centre, activity radius and distributions of turning angle and displacement. An extension of this approach was carried out to test for territorial interaction between two or more individuals in the case of deer, coyote and birds using telemetry data (Okubo, 1980).

 

Siniff and Jessen (1969) simulated the movement of an animal in its home range on the basis of telemetry data for red foxes (Vulpes fulva), snowshoe hare (Lepus americana), and raccoons (Procyon lotor). The telemetry data were obtained from the University of Minnesota’s Cedar Creek automatic tracking system, which continuously monitors the movements of animals carrying miniature radio transmitters (Cochran et al., 1965).

 

Korschgen et al. (1996) used radio-tracking data to investigate the magnitude, timing, and causes of mortality of the canvasback duckling (Aythya valisineria) from hatch to fledging at the Agassiz National Wildlife Refuge (NWR) in north-western Minnesota. The survival rate was estimated with the Kaplan-Meier non-parametric estimator (Kaplan and Meier, 1958) and the Weibull survival parametric model. The resultant plots of log{-log[S(t)]} against log (time) from the Kaplan-Meier procedure were generally linear, indicating that a Weibull survival model would adequately fit the data. The LIFETEST module of SAS (SAS Inst. Inc., 1989) was used to fit the Kaplan-Meier curves and the LIFEREG module of SAS (SAS Inst. Inc., 1989) was used to compute estimated parameters of the Weibull survival model. In general, parametric models provide more precise estimates of survival (Miller, 1983; Klein and Moeschberger, 1989).

 Otis (1994), in his studies on wood duck (Aix sponsa) populations, developed a statistical methodology for computing optimum allocation of banding effort to examine which two banding periods per year were more appropriate.

French and Reed (1989), French et al. (1989) developed a simulation model of seasonal migration based on daily movements of fur seal (Callorhinus ursinus). This migration model is useful both in understanding the movements of fur seals and in identifying where they are vulnerable to impacts following interaction with the results of man’s activities. The model has been used to estimate impacts resulting from hypothetical oil spills in the Bering Sea. The model could also be used to estimate impacts of other localised pollutants or entanglement in marine debris. VHF, ultrasonic tags and satellite-link transmitters have been used to study distribution and movements of grey seals (Hammond et al. 1993). System Argos provides access to information on the location of the transmitted signals and their quality, and any other data that have been transmitted. Information on locations and tracks is cross-referenced to other data to indicate periods of foraging and other behaviours (Thompson et al. 1991).


8.2.5 Population parameters and species interaction

Populations are susceptible to changes in their physical and biological environment that may affect their productivity. Climatic changes my lead to variation in stock parameters and the appearance and disappearance of prey and predator species - caused by man or nature - may profoundly affect harvest levels. Representative pictures of these variations are difficult to monitor, and tag-recapture programmes might in future improve studies, particularly if new technology is fully utilised.

(a) Population parameters

During the past 30 to 35 years, much literature has appeared on the estimation of population parameters based on capture-recapture sampling. Burnham et al. (1987) has considered the general theory for the analysis of multiple interrelated release-recapture data sets. Starting from statistical concepts, they have considered the following relevant points:

 protocols for studies with a control and one treatment,

 Burnham et al. adopted Maximum Likelihood Theory to estimate survival rates, components of variance, and non-linear regression to estimate values for the Von Bertalanffy model of growth parameters (Green et al., 1990).

The dispersal of animals can be classified as random dispersal or density dependent dispersal, which is particulalry important in relation to population dynamics (Ito, 1975). The relationship between animal dispersal and population density has been studied extensively with insects (Okubo, 1980). Morisita (1950) ascertained a relation between animal dispersal and population density in natural populations of water striders. Similar relations were also recognised in experiments with aphids (Ito, 1952) and rice weevils (Kono, 1952), from which it was concluded that for each species there is an associated population pressure that enhances population dispersal. Later Morisita (1954) attempted to quantify this population pressure by experimentally releasing ant lion larvae (Glenuroides japonicus) from a point and observing their dispersal. The movement pattern of individuals was classified as one of two types:

 

 

Morisita’s empirical formulae appear to be of general applicability in describing the time variation of the variance for insect dispersal from a point source and may possibly be applicable to fish under some circumstances.

The relationship between population density and dispersal behaviour is significant when viewed from the standpoint of social processes in communities (Ito, 1961) and Andrewartha and Birch (1954) also assign great importance to dispersal as a reaction to crowding. Overpopulation does not necessarily lead to dispersal, however. A unique characteristic of the Regional Organism Exchange (ROE) model ((Reyes et al. 1994) is the combination of the migration equation with more classical population parameters (Hardin, 1960).


(b) Interaction between species

It is well known that in a real ecosystem the importance of interactions between all the species cannot be overlooked, in particular in the case of predator-prey relationships. One method to estimate the various contributions of stock compositions to multiple and mixed stock fisheries is to measure differences in natural biological characteristics such as age composition, egg diameter, and parasites. Mark-recapture studies can also provide information on the stock composition of the catch. Monte Carlo methods are adopted to evaluate changes in variability and bias caused by changes in tagging rate, catch sampling rate, catch level, stock abundance in the fisheries, and distribution of stocks across fisheries. The overall variability in the Monte Carlo estimates can be surprisingly high and depend principally on variation in tag recovery and distribution of probability of harvest across the species and catch strata.

Random walk models do not normally take into account interactions between individuals and species (Schwarz and Poland, 1975), although exceptions exist (see e.g. Shigesada & Teramoto 1978). This mathematical model of advection and diffusion can explain the spatial distribution of animal populations that are principally controlled by interference between individuals and other environmental conditions. The formulation is based on the assumption that animals move under the influence of the following fundamental forces:

 The DYNUMES model of Pola (1985) is a numerical simulation model of fish migration in the eastern Bering Sea. This multi-species, numerical ecosystem simulation model has a spatial resolution of 63.5 km. Migrations are simulated by redistributing the biomass over the grid and primed by biological and environmental factors such as temperature. In this model the redistribution of biomass for both types of migration is computed using a finite difference advection equation (Laevastu, 1976).

8.3 REQUIREMENTS AND RECOMMENDATION

8.3.1 Experimental design

 


(a) Release errors

Representative distribution of tags in the population is essential for stock assessment studies. This can be obtained either by mixing of tags through migration and movements or through a systematic design for the release program. The extent of the problem may be species or stock specific and thorough population studies are needed for designing proper tagging experiments


 

(b) Tagging mortality, tag losses

Variations in tagging mortality rates and tag losses can seriously bias population studies and should be taken into account in data analysis. Tagging methods that have less effect on the health and behaviour of the fish are desirable.


 

(c) Recapture errors

Full and precise information on the recaptures is required to achieve the desired results. Most assessment models rely on detailed catch statistics to upgrade recapture results to population estimates.

8.3.2 Requirements related to assessment of abundance and mortality

 (a) Mass tagging

The precision of the assessment results obtained from tagging studies is dependent mainly upon the number of tags recovered. One way to improve precision is therefore to increase the number of tagged fish released, but this may increase the costs of the programme unacceptably. Clearly, the development of alternative methods for mass-marking large numbers of fish, preferably with less effect on individuals, would be advantageous. Mass marking (adipose finclipping and/or coded wire tagging) of salmonid smolts has been shown to be practical with the recent development of an automatic smolt tagging machine (http://www.nmt-inc.com).

(b) Recovery

In the past many studies have underestimated the importance of maximising the recovery of tagged fish.


 

(c) Guidelines for modelling

Whilst there is an extensive literature on modelling and assessment methods, there is no up-to-date and user-friendly guide to recent developments in the field.


 

(d) Catch statistics

Catch statistics provide a major input to many models and particular efforts are therefore required to ensure that these reflect, as accurately as possible, the true size and distribution of fishing mortality and landings.


 

(e) Freshwater survey methods

Assessment modelling for fish stocks in freshwater may be restricted by the difficulties of surveying large river systems. In the case of salmon this makes it difficult to model stocks which have a high proportion of multi-sea-winter returns. Studies of species that only occur in large systems (e.g. sturgeon) or that have different types of populations in rivers of different sizes (e.g. salmon) are desirable.


 

(f) Population structures

In the past, many assessment methods have ignored the effects of population and sub-population structures. However, there is an increasing awareness that such structures may be important in the biology of certain species.


 

8.3.3 Modelling of fish behaviour, movement and migration

 (a) Cost efficient development

More extensive international co-operation is needed both to avoid repetition of experiments that have already been already done and to promote wider programmes of research to obtain global results. The establishment of a Web Page within this field could be a useful development.


 

(b) Model validation and experimental design

(c) Migration and behaviour

Data storage tags provide large amounts of information on the behaviour of individual fish and their immediate environment. Such data can fuel the development of a new generation of migration and behaviour models, which have great potential for improving stock assessment and management.


 

  1. Pollution – migration and behaviour

    Knowledge about effects of pollution on fish behaviour, migration and mortality is scarce. In future such information will be important for evaluating the impact of pollution on fish stocks.

     

    Recommendation: Dedicated models describing the behaviour of populations in relation to pollution need to be developed as a tool for monitoring effects of pollution on marine life and as a way of predicting potential impacts of large-scale marine developments prior to their establishment.

     

  2. Data Fusion

Electronic tags can provide environmental, geographical, and physiological information regarding the fish and its environment. Electronic tags, in particular DSTs, can offer data on the dynamics of physical processes that are fundamental to studies of migration and behaviour. Environmental monitoring and modelling approaches to treat such data are well established. Methods which co-ordinate and integrate data from tagging and environmental data in a systematic and coherent way (data fusion) are essential to exploit existing models, develop new approaches and maximise the benefits of expensive tags. Such work will also be important for geographical positioning of tagged fish in a monitored environment.


 

 

 

8.4 REFERENCES

 


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