Christoffer Moesgaard Albertsen

Abstract:
Our main contribution is to examine the reliability of confidence intervals using the SAM state-space fish stock assessment model used for the assessment of many stocks by the International Council for the Exploration of the Seas. We focus on frequentist statistical inferences and more specifically on inference conditioned on specific values of the state-space model random effects drawn from their process distribution. This is somewhat consistent with simulation self-test procedures that are commonly used to examine the reliability of state-space assessment model results. However, recent research has indicated that some estimation bias may be expected in the conditional setting. Hence, we also investigate recently proposed bias corrected confidence intervals appropriate for the conditional inference setting. The SAM simulation coverage probabilities of 95% confidence intervals for SSB and Fbar were usually slightly larger than 95%, but in a small number of years these coverage probabilities could be much smaller than 95%. The bias corrected confidence intervals were more reliable. When averaged over years, the SAM and bias corrected confidence interval coverage probabilities were similar for the Northeast Artic cod and saithe case studies, but the bias corrected confidence intervals performed much better overall for the haddock case study.

Abstract:
We developed and validated a mixed-stock analysis (MSA) method with 59 single-nucleotide polymorphisms selected from genome-wide data to assign individuals to populations in mixed-stock samples of Atlantic herring from the North and Baltic seas. We analysed 3734 herring from spawning locations and scientific catches of mixed feeding stocks to demonstrate a “one-fits-all” tool with unprecedented accuracy for monitoring spatio-temporal dynamics throughout a large geographical range with complex stock mixing. We re-analysed time-series data (2002–2021) and compared inferences about stock composition with estimates from morphological data. We show that contributions from the western Baltic spring-spawning stock complex, which is under management concern, have likely been overestimated. We also show that a genetically distinctive population of western Baltic autumn spawners, ascribed low fisheries importance, contributes non-negligible and potentially temporally increasing proportions to mixed-stock aggregations, calling for a re-evaluation of stock definitions. MSA data can be implemented in stock assessment and in a variety of applications, including marine ecosystem description, impact assessment of specific fleets, and stock-rebuilding plans.

Abstract:
Stock assessment models are often used to inform fisheries management and need therefore to be thoroughly validated. Different diagnostics exist to validate models including the analysis of standardized residuals. Standardized residuals are commonly calculated by subtracting prediction from the observation and dividing the result with the estimated standard deviation (i.e., Pearson residuals). Many currently applied stock assessment models fit to compositional observations (e.g., age, length or stock compositions) using multivariate distributions. These distributions create correlation between observations, which are propagated in the residuals if estimated as Pearson. This study shows that using Pearson residuals to analyze goodness of the fit, when data are fitted using a multivariate distribution, is incorrect and one-step-ahead (OSA) or forecast quantile residuals should be used instead. For such distributions, OSA residuals are independent and standard normally distributed for correctly specified models. This study describes the calculation of OSA residuals specifically to de-correlate compositional observations for the multivariate distributions most commonly used in assessment models. This allows composition observations to be evaluated with the same statistical rigor as residuals from uncorrelated observations. This also prevents the possible wrong interpretation of Pearson residuals and the rejection of a correct model. We have developed an R-package that estimates OSA residuals externally to the model for models that do not include random processes. For models that use random processes, the distributions are now developed in Template Model Builder and explained in detail here for internal use.

Abstract:
Ocean warming is causing shifts in the distributions of marine species, but the location of suitable habitats in the future is unknown, especially in remote regions such as the Arctic. Using satellite tracking data from a 28-year-long period, covering all three endemic Arctic cetaceans (227 individuals) in the Atlantic sector of the Arctic, together with climate models under two emission scenarios, species distributions were projected to assess responses of these whales to climate change by the end of the century. While contrasting responses were observed across species and seasons, long-term predictions suggest northward shifts (243 km in summer versus 121 km in winter) in distribution to cope with climate change. Current summer habitats will decline (mean loss: −25%), while some expansion into new winter areas (mean gain: +3%) is likely. However, comparing gains versus losses raises serious concerns about the ability of these polar species to deal with the disappearance of traditional colder habitats. Climate change creates additional habitat for Arctic endemic cetaceans in winter but causes severe habitat loss in summer.

Abstract:
Reference points are used in fisheries management to infer stock status and inform future fishing opportunities. They can be estimated externally to the assessment model assuming attributes such as stock size to be known without error, or internally where the uncertainty can be accounted for in the estimation. Little is known about the effect of choosing one approach over another on reference point estimates. We compare maximum sustainable yield (MSY) reference points obtained internally in the assessment model (SAM) with those obtained by external estimation (EqSim) via simulations using 11 stocks with known and unknown stock–recruitment relationships (SRRs). Internal estimation of reference points does better on average than external estimation in terms of bias, variance, and SRR selection. Coverage probability of the reference point confidence intervals is good for the internal approach. Stochasticity considerations via re-sampling in the external approach can lead to bias. Bias in reference points have consequences on future yield, stock development, and status. However, it is difficult to predict them by solely looking at bias because they depend on current stock status, recruitment, and extent of bias, but also bias direction since a harvest control rule might compensate for the bias in the future.

Abstract:
This study investigates stock mixing of genetically distinct Atlantic cod (Gadus morhua) stocks in the Kattegat, an area geographically located between the North Sea and the Baltic Sea, by combining genetic population identification with habitat assignments from hatch to capture from otolith microchemistry. Cod captured in Kattegat were genetically assigned to either the North Sea or the endemic Kattegat population. Otolith chemical fingerprints differed significantly between populations during the larval and pelagic juvenile stage with higher strontium and lower barium and manganese concentrations in the North Sea population than the Kattegat population, indicating that North Sea cod are spawned in the North Sea or Skagerrak and drift into the Kattegat during the early life stages. Individual cod of both populations undertook frequent, but predominantly short term, migrations to other areas than the Kattegat, with < 25 % of individuals remaining resident within the Kattegat throughout their life. Across seasons and age classes, the two populations were both most frequently distributed in the Kattegat (67 %), with approximately 25 % of both population distributed in the western Baltic Sea and less than 10 % in the Skagerrak/North Sea. This study demonstrates the usefulness of this approach to infer population-specific connectivity and migration trajectories for individual fish and its potential applications in basic and applied fields of fish ecology and fisheries sciences.

Abstract:
Understanding migration patterns and habitat use is of great importance for management and conservation of marine living resources. The chemical composition of otoliths is influenced by the surrounding environment; therefore, they are indispensable data archives. To extract migration patterns and historical habitat use of individual fish, we analyse otolith chemical compositions obtained by laser ablation inductively coupled plasma mass spectrometry by a regime-switching state-space model. The state-space model filters the measurement noise from the environmental signal. In turn, the filtered signal is converted to geographical positions through a calibration of strontium to salinity. The method is validated by a simulation study and applied to 404 Atlantic cod otoliths.

Abstract:
Arctic top predators are expected to be impacted by increasing temperatures associated with climate change, but the relationship between increasing sea temperatures and population dynamics of Arctic cetaceans remains largely unexplored. Narwhals (Monodon monoceros) are considered to be among the most sensitive of Arctic endemic marine mammals to climate change due to their limited prey selection, strict migratory patterns and high site fidelity. In the context of climate change, we assume that the population dynamics of narwhals are partly influenced by changes in environmental conditions, with warm areas of increasing sea temperatures having lower abundance of narwhals. Using a unique large dataset of 144 satellite tracked narwhals, sea surface temperature (SST) data spanning 25 years (1993-2018) and narwhal abundance estimates from 17 localities, we (1) assessed the thermal exposure of this species, (2) investigated the SST trends at the summer foraging grounds, and (3) assessed the relationship between SST and abundance of narwhals. We showed a sharp SST increase in Northwest, Mideast and Southeast Greenland, whereas no change could be detected in the Canadian Arctic Archipelago (CAA) and in the Greenland Sea. The rising sea temperatures were correlated with the smallest narwhal abundance observed in the Mideast and Southeast Greenland (<2,000 individuals), where the mean summer sea temperatures were the highest (6.3°C) compared to the cold waters of the CAA (0.7°C) that were associated with the largest narwhal populations (>40,000 individuals). These results support the hypothesis that warming ocean waters will restrict the habitat range of the narwhal, further suggesting that narwhals from Mideast and Southeast Greenland may be under pressure to abandon their traditional Arctic habitats due to ocean warming.

Abstract:
Gillnet fisheries are one of the main anthropogenic causes of harbour porpoise (Phocoena phocoena, L. 1758) mortality in the Baltic Sea. A new kind of acoustic alerting device (Porpoise ALert, PAL) was tested in commercial gillnet fisheries of the Western Baltic. PAL emits 133 kHz synthetic harbour porpoise communication signals, unlike conventional acoustic deterrent devices (‘pingers‘) which emit artificial noise. Trials were conducted by three commercial gillnet vessels conducting 778 trips during standard fishing operations from 2014 to 2016. 1,120 PAL-equipped net strings were tested against 1,529 simultaneously set control strings with no devices. We tested two versions of the PAL (v1 and v2). These were spaced < 210 metres apart from each other on the gillnet floatlines, all devices pointing in the same direction to ensure complete acoustic coverage of the strings. Two vessels fished in Kiel Bight and around Fehmarn Island in German waters, and the third vessel fished in the Öresund, in inner Danish waters. Overall, 18 harbour porpoises were bycaught in control strings (mean 0.01 ± 0. 1 per haul), while five harbour porpoises were bycaught in strings equipped with PALs (0.004 ± 0.07 per haul). Number of net string bycatches were analysed using a generalized linear mixed model (GLMM). The model applied to all observations revealed that the expected bycatch was significantly influenced by PAL deployment (p < 0.05), decreasing the expected bycatch by 64.9% (95% confidence interval (CI): 8.7 - 88.7%). PAL effectiveness was also increased by reducing device spacing to <210 m (16 bycatches in control, 3 in PAL strings; mean bycatch reduction 79.7%). Additional model cases were applied to the data and are discussed. We conclude that with this specific communication signal, PAL can significantly reduce harbour porpoise bycatch in gillnets deployed in the Western Baltic Sea, thus reconciling anthropogenic activities with protection of the marine environment.

Abstract:
Reference points are central in the current management of marine living resources. However, reference points are estimated from data and model estimates. Therefore, they are inherently uncertain. We present two objective methods for estimating reference points and quantifying their uncertainty. The first method uses per-recruit calculations, while the second method relies on a long-term forecast of the managed system. Confidence intervals are calculated through a combination of the implicit function theorem and the delta method. Both methods are illustrated for 12 recruitment models using data from the Northeast Arctic cod assessment. Finally, the methods are validated in a simulation study.

Abstract:
We describe and illustrate a spatio-temporal modelling approach for analyzing age- or size-specific catch-per-unit-of-effort (CPUE) data to develop indices of relative abundance and associated composition data. The approach is based on three concepts: 1) composition data that are used to determine the component of the population represented by the index should be weighted by CPUE (abundance) while the composition data used to represent the fish removed from the stock should be weighted by catch; 2) due to spatial non-randomness in fishing effort and fish distribution, the index, index composition, and catch composition, should be calculated at a fine spatial scale (e.g., 1°x1°) and summed using area weighting; and 3) fine-scale spatial stratification will likely result in under-sampled and unsampled cells and some form of smoothing method needs to be applied to inform these cells. We illustrate the concepts by applying them to yellowfin tuna (Thunnus albacares) in the eastern Pacific Ocean.

Abstract:
Animal telemetry data are often analysed with discrete time movement models. These models are defined with regular time steps. However, telemetry data from marine animals are observed irregularly. To account for irregular data, a time-irregularised first-difference correlated random walk model with drift is introduced. The model generalizes the commonly used first-difference correlated random walk with regular time steps by allowing irregular time steps, including a drift term, and by allowing different autocorrelation in the two coordinates. The model is applied to data from a ringed seal collected through the Argos satellite system, and is compared to related movement models through simulations. Accounting for irregular data in the movement model results in accurate parameter estimates and reconstruction of movement paths. Further, the introduced model can provide more accurate movement paths than the regular time counterpart. Extracting accurate movement paths from uncertain telemetry data is important for evaluating space use patterns for marine animals, which in turn is crucial for management. Further, handling irregular data directly in the movement model allows efficient simultaneous analyses of several animals.

Abstract:
The effects of climate change constitute a major concern in Arctic waters due to the rapid decline of sea ice, which may strongly alter the movements and habitat availability of Arctic marine mammals. We tracked 98 bowhead whales by satellite over an 11-year period (2001-2011) in Baffin Bay - West Greenland to investigate the environmental drivers (specifically sea surface temperature and sea ice) involved in bowhead whale’s movements. Movement patterns differed according to season, with aggregations of whales found at higher latitudes during spring and summer likely in response to sea-ice retreat and increasing sea temperature (SST) facilitated by the warm West Greenland Current. In contrast, the whales moved further south in response to sea temperature decrease during autumn and winter. Statistical models indicated that the whales targeted a narrow range of SSTs from -1.5 to 2°C. Sea surface temperatures are predicted to undergo a marked increase in the Arctic, which could expose bowhead whales to both thermal stress and altered stratification and vertical transport of water masses. With such profound changes, bowhead whales may face extensive habitat loss. Our results highlight the need for closer investigation and monitoring in order to predict the extent of future distribution changes.

Abstract:
Fisheries management is mainly conducted via single-stock assessment models assuming that fish stocks do not interact, except through assumed natural mortalities. Currently, the main alternative is complex ecosystem models which require extensive data, are difficult to calibrate, and have long run times. We propose a simple alternative. In three case studies each with two stocks, we improve the single-stock models, as measured by AIC, by adding correlation in the cohort survival. To limit the number of parameters, the correlations are parameterized through the corresponding partial correlations. We consider six models where the partial correlation matrix between stocks follows a band structure ranging from independent assessments to complex correlation structures. Further, a simulation study illustrates the importance of handling correlated data sufficiently by investigating the coverage of confidence intervals for estimated fishing mortality. The results presented will allow managers to evaluate stock statuses based on a more accurate evaluation of model output uncertainty. The methods are directly implementable for stocks with an analytical assessment and does not require any new data sources.

Abstract:
Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.

Abstract:
Electronic telemetry is frequently used to document animal movement through time. Methods that can identify underlying behaviors driving specific movement patterns can help us understand how and why animals use available space, thereby aiding conservation and management efforts. For aquatic animal tracking data with significant measurement error, a Bayesian state-space model called the first-Difference Correlated Random Walk with Switching (DCRWS) has often been used for this purpose. However, for aquatic animals, highly accurate tracking data are now becoming more common. We developed a new hidden Markov model (HMM) for identifying behavioral states from animal tracks with negligible error, called the hidden Markov movement model (HMMM). We implemented as the basis for the HMMM the process equation of the DCRWS, but we used the method of maximum likelihood and the R package TMB for rapid model fitting. The HMMM was compared to a modified version of the DCRWS for highly accurate tracks, the DCRWS_NOME formula, and to a common HMM for animal tracks fitted with the R package moveHMM. We show that the HMMM is both accurate and suitable for multiple species by fitting it to real tracks from a grey seal, lake trout, and blue shark, as well as to simulated data. The HMMM is a fast and reliable tool for making meaningful inference from animal movement data that is ideally suited for ecologists who want to use the popular DCRWS implementation and have highly accurate tracking data. It additionally provides a groundwork for development of more complex modeling of animal movement with TMB. To facilitate its uptake, we make it available through the R package swim.

Abstract:
Stock assessment models rely on aggregated and uncertain data, which makes it difficult to choose a family of distributions for modelling errors on observations a priori. By implementing several observational likelihoods, modelling both numbers- and proportions-at-age, in an age based state-space stock assessment model, we compare the model fit for each choice of likelihood along with the implications for spawning stock biomass and average fishing mortality. We show that the model fit is improved by modelling the correlation of observations within years. Through a simulation study, we demonstrate that whether likelihoods based on numbers-at-age or proportions-at-age provide the best model fit depends on where the data uncertainty lies. If the measurement uncertainty in the total catch is high compared to the measurement uncertainty in age classification, numbers-at-age is preferred, whereas in the opposite situation proportions-at-age provide the best model fit. However, the best choice of observational likelihood differs for different stocks, and the choice is important for the conclusions drawn from the assessment model.

Abstract:
Tracking of marine animals has increased exponentially in the past decade, and the resulting data could lead to an in-depth understanding of the causes and consequences of movement in the ocean. However, most common marine tracking systems are associated with large measurement errors. Accounting for these errors requires the use of hierarchical models, which are often difficult to fit to data. Using three case studies, we demonstrate that Template Model Builder (TMB), a new R package, is an accurate, efficient, and flexible framework for modelling movement data. First, to demonstrate that TMB is as accurate but 30 times faster than bsam, a popular R package used to apply state-space models to Argos data, we model polar bear (Ursus maritimus) Argos data and compare the locations estimated by the models to GPS locations of these same bears. Second, to demonstrate how TMB's gain in efficiency and frequentist framework facilitate model comparison, we develop models with different error structures and compare them to find the most effective model for light-based geolocations of rhinoceros auklets (Cerorhinca monocerata). Finally, to maximize efficiency through TMB's use of the Laplace approximation of the marginal likelihood, we model behavioural changes with continuous rather than discrete states. This new model directly accounts for the irregular sampling intervals characteristic of Fastloc-GPS data of grey seals (Halichoerus grypus). Using real and simulated data, TMB is shown to be a fast and powerful tool for modelling marine movement data. We discuss how TMB's potential reaches beyond marine movement studies.

Abstract:
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

Abstract:
In the Baltic Sea two genetically distinct cod stocks are found, the “Eastern Baltic cod” and “Western Baltic cod”. In this study we evaluated the applicability of otolith shape analysis for classification of individuals caught in mixed stock fishery, using SNP (Single nucleotide polymorphism) based genetic validation of the otolith based classifications. The otoliths of eastern Baltic cod were generally wider in the dorso-ventral direction in relation to the anterior-posterior length than those of western Baltic cod. These differences were captured by otolith area and 7 – 10 Elliptic Fourier Descriptors of primarily low number harmonics. Traditional standardisation of Descriptors in relation to size could not remove the size effect entirely, highlighting the need for a balanced size-stratified baseline sample. Genetic validation of otolith shape based classification of samples from the mixed-stock area revealed that in both approaches eastern Baltic otoliths had a higher risk of being classified as western Baltic cod than the opposite, but classification success was considerably lower when using a baseline of spawning individuals than when a baseline consisting of genotyped individuals from all areas was used. Furthermore, the latter to a large extent removed a strong size related trend in classification success with low success in small eastern and large western Baltic cod. These results demonstrate the interplay of environmental and genetic influences on otolith shape, which complicates the application of otolith shape for stock discrimination in mixed-stock scenarios. Rigours genetic validation and further studies on the temporal dynamics of shape formation are necessary.

Abstract:
Fishing gears have negative impacts on seafood quality, especially on fish in the mixed trawl fishery targeting Norway lobster (Nephrops norvegicus). In this fishery, which is worth about € 80 millions in Denmark alone, the quality of fish can be significantly improved by simple gear changes. A trawl codend divided into an upper and lower codend was designed to separate fish from Norway lobster during the fishing process by encourage fish to swim into the upper codend by using a frame at the entrance of the lower codend. Separate codends for fish and Norway lobster in the same gear provide the opportunity to selectively reduce small low-value fish, which will reduce catch weight and sorting time onboard the vessel. For this horizontally divided test codend and a standard codend, in which the catch was mixed, quality assessments were performed on the same batches of fish during three steps of the value chain: i) aboard the fishing vessel; ii) at the Fishermen's Collection Central, and iii) in the production plant. Four species of fish and fillets from fish caught in the upper codend of the test codend were of significantly better quality for several of the assessed parameters compared with those caught in the standard codend: i) newly caught fish showed significantly less scale loss and discolourations and had significantly better texture; ii) landed fish had significantly better skin appearance and texture and significantly fewer discolourations; and iii) fillets showed significantly fewer blood spots and had significantly better texture. There were no differences in injuries for newly caught fish or gaping and bruises for fillets between the test and standard codends. The decrease in catch-related damages in the test codend is explained by little contact between fish and animals with hard or spiny surfaces due to successful separation of fish and Norway lobster into the upper and lower codends, respectively, and by lower catch weight in the upper codend of the test codend compared with the standard codend. The decrease in damages may also improve quality indirectly by inflicting less stress to the fish and subsequently give better texture, which offers advantages such as pre-rigor filleting and fresher products for the market. Significant improvements in fish quality can potentially increase the catch value in nationally important fisheries.

Abstract:
State-space models (SSM) are often used for analyzing complex ecological processes that are not observed directly, such as marine animal movement. When outliers are present in the measurements, special care is needed in the analysis to obtain reliable location and process estimates. Here we recommend using the Laplace approximation combined with automatic differentiation (as implemented in the novel R-package: Template Model Builder (TMB)) for the fast fitting of continuous time multivariate non-Gaussian SSMs. Through Argos satellite tracking data, we demonstrate that the use of continuous time t-distributed measurement errors for error-prone data is more robust to outliers and improves the location estimation compared to using discretized time t-distributed errors (implemented with a Gibbs sampler) or using continuous time Gaussian errors (as with the Kalman filter). Using TMB, we are able to estimate additional parameters compared to previous methods, all without requiring a substantial increase in computational time. The model implementation is made available through the R-package argosTrack.

Abstract:
Survival after transplantation of mussel seeds is crucial for the production output of blue mussels (Mytilus edulis L.) in bottom cultures. Hence, an understanding of the interactions between bed formation, habitat structure and performance of mussel seed of different origins can contribute to an optimization of the production. The effect of substrate composition and timing of formation of a mussel bed in relation to aggregation and attachment of mussels were investigated with mussel seeds obtained from two different sources: mussel seed dredged from a natural mussel bed and mussel seed collected from a suspended long line culture. The mussels were applied to experimental units of complex and smooth substrate on the sea bed. Data on aggregation (day 0, day 1 and day 2), attachment strength (day 2 and 30), loss (day 2 and 30) and growth (day 0–30) of mussels were collected during the experiment. The results showed that complex substrate indeed had a stabilizing effect on the mussel structure resulting in less aggregation and increased attachment strength. The 3D matrix forming a mussel bed was achieved faster on complex substrate, and led to reduced mortality of transplanted mussels. Despite significantly lower specific growth rates on the complex substrate, the total biomass of mussels was significantly higher on complex substrate compared to on smooth substrate due to the higher survival of mussels. Furthermore, suspended mussels aggregated more and faster and had a stronger and more rapid attachment as compared to bottom mussels. Consequently, it was concluded that when transplanting mussels, seeding with substrate increases surface complexity on the seabed and increases survival of the mussels.

Abstract:
Hatchery-reared juvenile turbot Psetta maxima were tagged with Passive Integrated Transponder (PIT) tags and released at three different depths in a sandy bay in Denmark. About 2–7% of the released fish were registered daily to monitor their distribution using a tag antenna mounted on a modified beam trawl, thus avoiding actually sampling the fish. The change in distribution of the three groups was adequately represented by a two-dimensional movement model. Movement along the shore was described by a Brownian motion with group specific drift. Movement perpendicular to the shore line was described by a Cox–Ingersoll–Ross process with a group specific attraction point. All three groups exhibited similar depth preferences of 1.7 m. Immediately after the release, fish were concentrated around the release points but after one day, fish had moved to the preferred depth and subsequently maintained their position at this depth. Farmed turbot exhibited strong site fidelity and an innate behaviour for selecting a preferred depth.

Abstract:
This article considers the development in house prices. Whether prices are moving up or down, they generate debate in the media. Further, the price development is attributed great economic importance, wich makes it problematic when the prices are reported as rising one day, while it is reported that they are falling the following day. This article gives a thorough introduction to how the development in house prices is measured; including why measuring residential property prices development is so complicated and subject to great uncertainty. Thus, both the calculation and the data basis have a decisive bearing on the conclusion drawn.