Harvest control rule vs optimal harvesting of an age-structured population: The case of the Ibero-Atlantic Sardine Fishery

Research Masters

Tuberculosis in Cape Town: An age-structured transmission model.

BACKGROUND Tuberculosis (TB) is the leading cause of death in South Africa. The burden of disease varies by age, with peaks in TB notification rates in the HIV-negative population at ages 0-5, 20-24, and 45-49 years. There is little variation between age groups in the rates in the HIV-positive population. The drivers of this age pattern remain unknown. METHODS We developed an age-structured simulation model of Mycobacterium tuberculosis (Mtb) transmission in Cape Town, South Africa. We considered five states of TB progression: susceptible, infected (latent TB), active TB, treated TB, and treatment default. Latently infected individuals could be re-infected; a previous Mtb infection slowed progression to active disease. We further considered three states of HIV progression: HIV negative, HIV positive, on antiretroviral therapy. To parameterize the model, we analysed treatment outcomes from the Cape Town electronic TB register, social mixing patterns from a Cape Town community and used literature estimates for other parameters. To investigate the main drivers behind the age patterns, we conducted sensitivity analyses on all parameters related to the age structure. RESULTS The model replicated the age patterns in HIV-negative TB notification rates of Cape Town in 2009. Simulated TB notification rate in HIV-negative patients was 1000/100,000 person-years (pyrs) in children aged <5 years and decreased to 51/100,000 in children 5-15 years. The peak in early adulthood occurred at 25-29 years (463/100,000 pyrs). After a subsequent decline, simulated TB notification rates gradually increased from the age of 30 years. Sensitivity analyses showed that the dip after the early adult peak was due to the protective effect of latent TB and that retreatment TB was mainly responsible for the rise in TB notification rates from the age of 30 years. CONCLUSION The protective effect of a first latent infection on subsequent infections and the faster progression in previously treated patients are the key determinants of the age-structure of TB notification rates in Cape Town.

Application of an Acceleration Scheme for an Age-Structured Diffusion Model

In this paper we propose an optimized algorithm, which is faster compared to previously described finite difference acceleration scheme, namely the Modified Super-Time-Stepping (Modified STS) scheme for age- structured population models with diffusion.

Increasing the Calculation Speed of an Acceleration Scheme for an Age-Structured Diffusion Model

Дойчин Бояджиев, Галена Пеловска - В статията се предлага оптимизиран алгоритъм, който е по-бърз в сравнение с по- рано описаната ускорена (модифицирана STS) диференчна схема за възрастово структуриран популационен модел с дифузия. Запазвайки апроксимацията на модифицирания STS алгоритъм, изчислителното времето се намаля почти два пъти. Това прави оптимизирания метод по-предпочитан за задачи с нелинейност или с по-висока размерност.

Reference Points and Optimal Management in Stochastic Age-Structured Fisheries Models

The purpose of this article is to characterize dynamic optimal harvesting trajectories that maximize discounted utility assuming an age-structured population model, in the same line as Tahvonen (2009). The main novelty of our study is that uses as an age-structured population model the standard stochastic cohort framework applied in Virtual Population Analysis for fish stock assessment. This allows us to compare optimal harvesting in a discounted economic context with standard reference points used by fisheries agencies for long term management plans (e.g. Fmsy). Our main findings are the following. First, optimal steady state is characterized and sufficient conditions that guarantees its existence and uniqueness for the general case of n cohorts are shown. It is also proved that the optimal steady state coincides with the traditional target Fmsy when the utility function to be maximized is the yield and the discount rate is zero. Second, an algorithm to calculate the optimal path that easily drives the resource to the steady state is developed. And third, the algorithm is applied to the Northern Stock of hake. Results show that management plans based exclusively on traditional reference targets as Fmsy may drive fishery economic results far from the optimal.

A-SCALA: an age-structured statistical catch-at-length analysis for assessing tuna stocks in the eastern tropical Pacific Ocean

English: We describe an age-structured statistical catch-at-length analysis (A-SCALA) based on the MULTIFAN-CL model of Fournier et al. (1998). The analysis is applied independently to both the yellowfin and the bigeye tuna populations of the eastern Pacific Ocean (EPO). We model the populations from 1975 to 1999, based on quarterly time steps. Only a single stock for each species is assumed for each analysis, but multiple fisheries that are spatially separate are modeled to allow for spatial differences in catchability and selectivity. The analysis allows for error in the effort-fishing mortality relationship, temporal trends in catchability, temporal variation in recruitment, relationships between the environment and recruitment and between the environment and catchability, and differences in selectivity and catchability among fisheries. The model is fit to total catch data and proportional catch-at-length data conditioned on effort. The A-SCALA method is a statistical approach, and therefore recognizes that the data collected from the fishery do not perfectly represent the population. Also, there is uncertainty in our knowledge about the dynamics of the system and uncertainty about how the observed data relate to the real population. The use of likelihood functions allow us to model the uncertainty in the data collected from the population, and the inclusion of estimable process error allows us to model the uncertainties in the dynamics of the system. The statistical approach allows for the calculation of confidence intervals and the testing of hypotheses. We use a Bayesian version of the maximum likelihood framework that includes distributional constraints on temporal variation in recruitment, the effort-fishing mortality relationship, and catchability. Curvature penalties for selectivity parameters and penalties on extreme fishing mortality rates are also included in the objective function. The mode of the joint posterior distribution is used as an estimate of the model parameters. Confidence intervals are calculated using the normal approximation method. It should be noted that the estimation method includes constraints and priors and therefore the confidence intervals are different from traditionally calculated confidence intervals. Management reference points are calculated, and forward projections are carried out to provide advice for making management decisions for the yellowfin and bigeye populations. Spanish: Describimos un análisis estadístico de captura a talla estructurado por edad, A-SCALA (del inglés age-structured statistical catch-at-length analysis), basado en el modelo MULTIFAN- CL de Fournier et al. (1998). Se aplica el análisis independientemente a las poblaciones de atunes aleta amarilla y patudo del Océano Pacífico oriental (OPO). Modelamos las poblaciones de 1975 a 1999, en pasos trimestrales. Se supone solamente una sola población para cada especie para cada análisis, pero se modelan pesquerías múltiples espacialmente separadas para tomar en cuenta diferencias espaciales en la capturabilidad y selectividad. El análisis toma en cuenta error en la relación esfuerzo-mortalidad por pesca, tendencias temporales en la capturabilidad, variación temporal en el reclutamiento, relaciones entre el medio ambiente y el reclutamiento y entre el medio ambiente y la capturabilidad, y diferencias en selectividad y capturabilidad entre pesquerías. Se ajusta el modelo a datos de captura total y a datos de captura a talla proporcional condicionados sobre esfuerzo. El método A-SCALA es un enfoque estadístico, y reconoce por lo tanto que los datos obtenidos de la pesca no representan la población perfectamente. Además, hay incertidumbre en nuestros conocimientos de la dinámica del sistema e incertidumbre sobre la relación entre los datos observados y la población real. El uso de funciones de verosimilitud nos permite modelar la incertidumbre en los datos obtenidos de la población, y la inclusión de un error de proceso estimable nos permite modelar las incertidumbres en la dinámica del sistema. El enfoque estadístico permite calcular intervalos de confianza y comprobar hipótesis. Usamos una versión bayesiana del marco de verosimilitud máxima que incluye constreñimientos distribucionales sobre la variación temporal en el reclutamiento, la relación esfuerzo-mortalidad por pesca, y la capturabilidad. Se incluyen también en la función objetivo penalidades por curvatura para los parámetros de selectividad y penalidades por tasas extremas de mortalidad por pesca. Se usa la moda de la distribución posterior conjunta como estimación de los parámetros del modelo. Se calculan los intervalos de confianza usando el método de aproximación normal. Cabe destacar que el método de estimación incluye constreñimientos y distribuciones previas y por lo tanto los intervalos de confianza son diferentes de los intervalos de confianza calculados de forma tradicional. Se calculan puntos de referencia para el ordenamiento, y se realizan proyecciones a futuro para asesorar la toma de decisiones para el ordenamiento de las poblaciones de aleta amarilla y patudo.

Structured model-following neuro-adaptive design for attitude maneuver of rigid bodies

A new structured model-following adaptive approach is presented in this paper to achieve large attitude maneuvers of rigid bodies. First, a nominal controller is designed using the dynamic inversion philosophy. Next, a neuro- adaptive design is proposed to augment the nominal design in order to assure robust performance in the presence of parameter inaccuracies as well as unknown constant external disturbances. The structured approach proposed in this paper (where kinematic and dynamic equations are handled separately), reduces the complexity of the controller structure. From simulation studies, this adaptive controller is found to be very effective in assuring robust performance.

Reconciling yield stability with international fisheries agencies precautionary preferences: the role of non constant discount factors in age structured models

International fisheries agencies recommend exploitation paths that satisfy two features. First, for precautionary reasons exploitation paths should avoid high fishing mortality in those fisheries where the biomass is depleted to a degree that jeopardise the stock's capacity to produce the Maximum Sustainable Yield (MSY). Second, for economic and social reasons, captures should be as stable (smooth) as possible over time. In this article we show that a conflict between these two interests may occur when seeking for optimal exploitation paths using age structured bioeconomic approach. Our results show that this conflict be overtaken by using non constant discount factors that value future stocks considering their relative intertemporal scarcity.

A Structured Model of Video Reproduces Primary Visual Cortical Organisation

The visual system must learn to infer the presence of objects and features in the world from the images it encounters, and as such it must, either implicitly or explicitly, model the way these elements interact to create the image. Do the response properties of cells in the mammalian visual system reflect this constraint? To address this question, we constructed a probabilistic model in which the identity and attributes of simple visual elements were represented explicitly and learnt the parameters of this model from unparsed, natural video sequences. After learning, the behaviour and grouping of variables in the probabilistic model corresponded closely to functional and anatomical properties of simple and complex cells in the primary visual cortex (V1). In particular, feature identity variables were activated in a way that resembled the activity of complex cells, while feature attribute variables responded much like simple cells. Furthermore, the grouping of the attributes within the model closely parallelled the reported anatomical grouping of simple cells in cat V1. Thus, this generative model makes explicit an interpretation of complex and simple cells as elements in the segmentation of a visual scene into basic independent features, along with a parametrisation of their moment-by-moment appearances. We speculate that such a segmentation may form the initial stage of a hierarchical system that progressively separates the identity and appearance of more articulated visual elements, culminating in view-invariant object recognition.