## About

113

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Introduction

I have two main research interests namely, (i) the use of mathematical models (Ordinary-, Partial-, Delay-, and Stochastic differential equations) to describe physical/biological phenomena and processes (ii) Inverse and ill-posed physical and bio-mathematical problems, with emphasis on regularization, optimization, and uncertainty.
My current research focuses on uncertain predictability and controllability of marine population dynamics. I aim to derive bounded approximation of state variables, when data is sparse and uncertain, and the underlying drivers of the system dynamics are vaguely understood.
Lately, my interest has expanded to include research into how species migration is dictated by the combined effects of variability in the physical environment and species ecology.

## Publications

Publications (113)

The stock-recruit relationship is a foundational concept in fisheries science, bridging the connection between parental populations (stock) and progeny (recruits). Traditional approaches describe this relationship using closedform analytical functions, which represent only a restricted subset of the broader class of possibilities. This paper advoca...

This paper presents a modeling framework for tracking the spawning migration of the capelin, which is a fish species in the Barents Sea. The framework combines an individual-based model (IBM) with artificial neural networks (ANNs). The ANNs determine the direction of the fish's movement based on local environmental information, while a genetic algo...

The schooling behavior of fish can be studied through simulations involving a large number of interacting particles. In such systems, each individual particle is guided by behavior rules, which include aggregation towards a centroid, collision avoidance, and direction alignment. The movement vector of each particle may be expressed as a linear comb...

For marine species, several life stages link parents to their progeny (recruits), through a process referred to as recruitment. Current stock recruitment (SR) functions encapsulate this multi-stage relationship in a closed-form mathematical expression, which explicitly relates the biomass of parents, to the number of recruits. This functional relat...

We consider modeling and prediction of Capelin distribution in the Barents Sea based on zero-inflated count observation data that vary continuously over a specified survey region. The model is a mixture of two components; a one-point distribution at the origin and a Poisson distribution with spatio-temporal intensity, where both intensity and mixin...

Identifying spawning sites of fish often involves extensive egg and larval sampling surveys over potential spawning sites, or by backward-tracking advected larvae to their source. Due to the vastness of the Barents Sea capelin spawning areas, back-tracking methods have limited application. Egg and larval surveys that provide information about spawn...

We consider the challenge in estimating the natural mortality, M, in a standard statistical fish stock assessment model based on time series of catch- and abundance-at-age data. Though anecdotal evidence and empirical experience lend support to the fact that this parameter may be difficult to estimate, the current literature lacks a theoretical jus...

We consider a model for predicting the spatio-temporal distribution of a marine species based on zero-inflated count observation data that vary continuously over a specified survey region. The model is a mixture of two components; a one-point distribution at the origin and a Poisson distribution with spatio-temporal intensity, where both intensity...

Capelin (Mallotus villosus) is a short-lived (1-4 years) fish species, that plays a crucial role by dominating the intermediate trophic level in the Barents Sea. Several episodes of extreme biomass decline (collapse) have been observed during the last three decades. We postulate that these collapses might be regulated by food availability (bottom-u...

This paper uses a two-parameter logistic function to model the dynamics of length-at-maturation for the Barents Sea capelin over the past 47 years. We estimate the function parameters using a combination of length-age data from scientific surveys, and commercial catch statistics.
Using temporal variability in the function parameters, we demonstrate...

The REDUS project (2016-2020) has been a strategic project at the Institute of Marine Research (IMR) aimed at quantifying and reducing the uncertainty in data-rich and age-structured stock assessments (e.g., cod, herring, haddock, capelin). Work was organized in four topical work-packages: Fisheries-dependent (catch) surveys and assessment modeling...

It is assumed that maturation in the Barents Sea capelin is length-dependent, and that fish of at least 14 cm will potentially spawn. Current assessment and management models for the stock are based on this assumption of constant maturity at length (MaL). Using data from scientific surveys, this paper examines the validity of the constant MaL assum...

This paper presents a method for estimating dynamic parameters of a system of non-linear Ordinary Differential Equations (ODEs), which describes the time-dependent dynamics of a marine population. The methodology represents the model parameters with a tessellation of Voronoi cells. It then uses a prescribed rule to generate multiple realizations of...

This paper considers a general state-space stock assessment modeling framework that integrates a population model for a fish stock and a data model. This way observed data are linked to unobserved quantities in the population model. Using this framework, we suggest two modifications to improve accuracy in results obtained from the stock assessment...

This paper investigates stability conditions of an empirical predator-prey system using a model that includes a single delay term, τ , in description of the predator dynamics. We derive theoretical conditions on τ , in terms of other model parameters, and determine how changes in these conditions define different stability regimes of the system. We...

A bstract
This paper uses a Lotka-Volterra (predator-prey) modeling framework to investigate the dynamical link between the biomass of an empirical predator, and that of its prey. We use a system of ordinary (ODE) differential equations to describe the system dynamics, and derive theoretical conditions for stability, in terms of system parameters....

Studies describing and hypothesizing the impact of climate change and environmental processes on vital rates of fish stocks are increasing in frequency, and concomitant with that is interest in incorporating these processes in fish stock assessments and forecasting models. Previous research suggests that including environmental drivers of fish recr...

[This corrects the article DOI: 10.1371/journal.pone.0208078.].

This paper presents a modeling framework that captures the impulsive biomass dynamics (bust-boom) of a fish stock. The framework is based on coupling a Hawkes-process model to a discrete-time, ages-structured population dynamics model. Simulation results are presented to demonstrate the efficacy of the framework in capturing impulsive events in the...

We introduce a statistical methodology that integrates Granger’s pair-wise causal
analysis and its expansion to causality basedon the log-likelihood (Partial pairwise causality), and Akaike’s power contribution approach in the whole frequency domain (Total causality). Although the initial idea was proposed by Ozaki (2012), it has hitherto not been...

This paper provides a statistical methodology for quantifying causality in complex dynamical systems, based on analysis of multidimensional time series data of the state variables. The methodology integrates Granger’s causality analysis based on the log-likelihood function expansion (Partial pair-wise causality), and Akaike’s power contribution app...

Matlab codes for generating simulation data and conducting the analysis.
(ZIP)

Predicting future states of harvested marine populations requires an understanding of how intrinsic time delay processes and volatile phenomena (e.g., impulsive mortality) act in concert to alter the dynamic population trajectory. Separately, the effects (on population dynamics) of time-delays, and impulses, have been studied theoretically by sever...

The stock assessment model SAM (state-space assessment model) is an important tool for analysing fishery data and is used for abundance estimation of several different fish stocks. We demonstrate incongruous formulations in the equations that relate the catch data to fish abundance, and in the fishery and natural mortality rates. We present example...

Using simple illustrative examples, this note highlights some of the caveats with gradient-based algorithms. This class of algorithms underpins the state-of-the-art modelling platform in fisheries science. The goal is to sound a cautionary note about an increasing trend in fisheries science, where blind faith is being invested in results obtained f...

The dynamics of marine populations are usually forced by biotic and abiotic factors occurring at different intensity levels and time scales. Deriving the time frame within which each factor has a causal influence is important for predicting population trajectories. This paper presents a statistical methodology for establishing (i) the strength of c...

This paper uses a stage-structured model that is defined by a system of Delayed Differential Equations (DDEs), to represent the dynamics of a single-species marine population. Numerical simulations are performed, using the model, to investigate how (i) harvest and birth pulses, and (ii) time delays, regulate the population dynamics of the perturbed...

The Beverton–Holt, Ricker and Deriso functions are three distinct descriptions of the link between a parental population size and subsequent offspring that may survive to become part of the fish population.
This paper presents a model consisting of a system of ordinary differential equations, which couples a stage of young fish with several adult s...

Marine systems are complex and difficult to observe so comprehensive monitoring programs for entire systems are necessarily limited. Mathematical and statistical models have therefore become central tools to assess marine populations, and predict their future status. The modeling processes are usually based on one or several time series of observat...

Understanding and predicting patterns arising from the dynamics of marine food webs is central to trophic and community ecology and numerical models of food webs constitute a primary tool to simulate these dynamics. Food web simulation models are often highly complex while at the same time often too constrained to reproduce the level of variability...

In marine science, it is usually assumed that there is a functional relationship between the parental population size and subsequent offsprings. The function is referred to as the Stock Recruitment Function (SRF). Determining the SRF translates to the optimization problem of estimating a set of parameters using past and sparse observation, which ar...

This paper explores the stochastic dynamics of a simple foodweb system using a network model that mimics interacting species in a biosystem. It is shown that the system can be described by a set of ordinary differential equations with real-valued uncertain parameters, which satisfy a set of linear inequality constraints. The constraints restrict th...

A conceptually simple framework is presented for assessing the stock size for Northeast Arctic (NEA) cod using a parsimonious, age-structured statistical model. The framework accounts for data and model parameter uncertainties, and allows us to track how these uncertainties propagate through the modeling process to affect model predictions and deri...

This paper presents a parsimonious framework for exploring the
behavior of a biosystem of interacting species when the system dynamics is
both stochastic and vaguely understood. The framework represents the system
by a network model whose dynamics is governed by set of coupled ordinary
differential equations, and involves a finite set of unknown an...

Since 1998, the assessment model framework Bifrost/Captool has been used for advice on total allowable catch for the Barents Sea capelin (Mallotus villosus) stock. However, since the management is based on a target escapement strategy, and most capelin die after spawning, viewed in retrospect, there is hardly any possibility of checking whether the...

Quantifying populations in changing environments involves fitting highly non-linear and non-convex population dynamic models to distorted observations. Derivatives of the objective function with respect to parameters might be expensive to obtain, unreliable or unavailable.
The aim of this paper is to illustrate the use of derivative-free optimizati...

A novel approach to model food-web dynamics, based on a combination of chance (randomness) and necessity (system constraints), was presented by Mullon et al. in 2009. Based on simulations for the Benguela ecosystem, they concluded that observed patterns of ecosystem variability may simply result from basic structural constraints within which the ec...

This paper presents a brief review of the present state of knowledge in stock–recruitment forecasting, including process and
current methodological challenges to predicting stock–recruitment. The discussion covers the apparent inability of models
to accurately forecast recruitment even when environmental covariates are included as explanatory varia...

Arctic and Antarcticmarine systems have incommon high latitudes, large seasonal changes in light levels, cold air and sea temperatures, and sea ice. In other ways, however, they are strikingly different, including their: age, extent, geological structure, ice stability, and foodweb structure. Both regions contain very rapidly warming areas and clim...

The Northeast Arctic cod (Gadus morhua L.: NEAC) remains the most abundant cod stock in the North Atlantic, while the catches of the partially co-occurring Norwegian coastal cod (NCC) stocks have dramatically decreased in recent years. To ensure effective management of the two stocks, it is necessary to know if the population genetic structure is a...

Fisheries generally target a limited range of stocks from a complex and dynamic ecosystem, and adapting our assessment and management strategies to this reality is a challenge. Stock assessment within ICES and elsewhere has generally been conducted on a single-species basis. This is a pragmatic approach that has allowed for high quality single-spec...

Arctic and Antarctic marine systems have in common high latitudes, large seasonal changes in light levels, cold air/sea temperatures, and sea ice. In other ways they are strikingly different, including: geological structure; ice stability; and food webs. Both regions contain rapidly warming areas; reported climate impacts and future projections are...

The application of data storage tags bears the potential for a quantum leap in the research on fish migrations, because not only first-capture and recapture positions are known, but at least theoretically, the migration path during the period at large can be reconstructed. Position, however, cannot be measured directly but has to be estimated using...

Developing marine ecosystem models is inherently difficult because of the diversity and complexity of ecological processes to account for, the presence of non--linearities, and the broad range of spatial and temporal scales to cover. In general, the fundamental ecosystem processes involve several unknown components and parameters. Here, we adopt a...

The rules for setting quotas for NorthEast Arctic cod (NEAc) are based on how estimates of stock parameters relate to defined biological reference points obtained from the Extended Survivors Analysis (XSA) model, calibrated using bottom trawl survey data from the Barents Sea. In this paper we use simulations to investigate how the precision in esti...

Vølstad, J. H., Korsbrekke, K., Nedreaas, K. H., Nilsen, M., Nilsson, G. N., Pennington, M., Subbey, S., and Wienerroither, R. 2011. Probability-based surveying using self-sampling to estimate catch and effort in Norway's coastal tourist fishery. – ICES Journal of Marine Science, 68: 1785–1791.
Recreational fishing as a tourist activity has become...

Based on vertical movement data derived from electronic storage tags (DST) attached to fish, we construct a stochastic model that aims at capturing the main characteristics of the observations over one year. We use a mixed Ornstein-Uhlenbeck process to model attraction to a limited number of concentration points on the depth axis. A methodology for...

Republikken Mosambik dukket opp i 1994 som et skjørt nytt demokrati som har
prøvd å innføre en fri markedsøkonomi. Mosambik har holdt ut en bitter historie.
Portugisiske koloniherrer forsømte utviklingen innenlands. Dette bidro til år med
økonomisk krise, etter at landet fikk selvstendighet i 1975 og en borgerkrig som
varte fra 1977 til 1992.

SUMMARY The Hamiltonian Monte Carlo (HMC) algorithm is a Markov Chain Monte Carlo (MCMC) technique, which combines the advantages of Hamiltonian dynamics methods and Metropolis Monte Carlo approach, to sample from complex distributions. The HMC algorithm incorporates gradient information in the dynamic trajectories and thus suppresses the random wa...

The Hamiltonian Monte Carlo (HMC) algorithm is a Markov Chain Monte Carlo (MCMC) technique, which combines the advantages of Hamiltonian dynamics methods and Metropolis Monte Carlo approach, to sample from complex distributions. The HMC algorithm incorporates gradient information in the dynamic trajectories and thus suppresses the random walk natur...

The inversion of laboratory centrifuge data to obtain capillary pressure functions in petroleum science leads to a Volterra integral equation of the first kind with a right-hand side defined by a set of discrete data. The problem is ill-posed in the sense of Hadamard [4]. The discrete data lead to a discretized equation of the form $$
A\overrightar...

Electronic Data Storage Tags (DSTs) have the potential of providing long term, high-resolution observation data of individual
fish in the ecosystem. However, traditional time series analysis methods are limited in extracting the required information
from DSTs. The continuous wavelet transform (CWT) is a tool for decomposing a time series into insta...

Quantifying fish stocks through modeling involves estimating time-varying parameters such as growth, stock recruitment, mortality rates and fishing levels. Each of these parameters vary non-uniformly and non-smoothly with time. For a given parameter, e.g., growth, the standard approach has been to estimate a single value of the parameter per time-s...

Unsteady-state (USS) core flood experiments provide data for deriving two-phase relative permeability and capillary pressure functions. The experimental data is uncertain due to measurement errors, and the accuracy of the derived flow functions is limited by both data and modeling errors.
History matching provides a reasonable means of deriving in-...

Reservoir production forecasts are essentially uncertain due to the lack of data. Specifically, it is impossible to estimate detailed heterogeneity in a reservoir. In order to mitigate the ambiguity of a model, production data is incorporated into a history-matching process. However, there is insufficient data to constrain the subsurface properties...