Optimal harvesting policy of an inland fishery resource under incomplete information

A new mathematical model for finding the optimal harvesting policy of an inland fishery resource under incomplete information is proposed in this paper. The model is based on a stochastic control formalism in a regime‐switching environment. The incompleteness of information is due to uncertainties involved in the body growth rate of the fishery resource: a key biological parameter. Finding the most cost‐effective harvesting policy of the fishery resource ultimately reduces to solving a terminal and boundary value problem of a Hamilton‐Jacobi‐Bellman equation: a nonlinear and degenerate parabolic partial differential equation. A simple finite difference scheme for solving the equation is then presented, which turns out to be convergent and generates numerical solutions that comply with certain theoretical upper and lower bounds. The model is finally applied to the management of Plecoglossus altivelis, a major inland fishery resource in Japan. The regime switching in this case is due to the temporal dynamics of benthic algae, the main food of the fish. Model parameter values are identified from field measurement results in 2017. Our computational results clearly show the dependence of the optimal harvesting policy on the river environmental and biological conditions. The proposed model would serve as a mathematical tool for fishery resource management under uncertainties.     

Optimization model to start harvesting in stochastic aquaculture system

Establishment of cost‐effective management strategy of aquaculture is one of the most important issues in fishery science, which can be addressed with bio‐economic mathematical modeling. This paper deals with the aforementioned issue using a stochastic process model for aquacultured non‐renewable fishery resources from the viewpoint of an optimal stopping (timing) problem. The goal of operating the model is to find the optimal criteria to start harvesting the resources under stochastic environment, which turns out to be determined from the Bellman equation (BE). The BE has a separation of variables type structure and can be simplified to a reduced BE with a fewer degrees of freedom. Dependence of solutions to the original and reduced BEs on parameters and independent variables is analyzed from both analytical and numerical standpoints. Implications of the analysis results to management of aquaculture systems are presented as well. Numerical simulation focusing on aquacultured Plecoglossus altivelis in Japan validates the mathematical analysis results. Copyright © 2017 John Wiley & Sons, Ltd.     

Mathematics teaching before and after the Meiji Restoration

This paper outlines mathematical education before the Meiji Restoration, and how it changed as a result. The Meiji Restoration in 1868 completely changed the social structure of Japan. In the Edo period (1600?C1868) Japan was divided into domains (han) governed by local lords (daimyo). Tokugawa Shogunate supervised local lords and governed Japan indirectly. In the Edo period there were no wars for more than two centuries and many people participated in cultural activities. Japanese mathematics developed in its own way under the influence of old Chinese mathematics. Japan also had a good education system so that the literacy rate was quite high. Each domain had its own school for samurai but mainly education was provided privately. Private schools for elementary education were called terakoya, in which mainly reading and writing and often arithmetic by the soroban (Japanese abacus) were taught. In the Edo period the soroban (abacus) was the only tool for computation and Arabic numerals were not used. The Meiji government was eager to establish a modern centralized state in which education played a key role. In 1872 the Ministry of Education declared the Education Order, whereby in elementary schools only western mathematics should be taught and the soroban should not be used. But almost all teachers only knew Japanese traditional mathematics ??wasan?? so they insisted on using the soroban. This was the starting point of a long dispute on the soroban in elementary education in Japan. Two Japanese mathematicians, KIKUCHI Dairoku and FUJISAWA Rikitaro, played a central role in the modernization of mathematical education in Japan. KIKUCHI studied mathematics in England and brought back English synthetic geometry to Japan. FUJISAWA was a student of KIKUCHI at the Imperial University and studied mathematics in Germany. He was the first Japanese mathematician to make a contribution to original research in the modern sense. He published a book on mathematical education in elementary school, which built the foundation of mathematical education in Japan.     

MODELING THE DYNAMICS OF FISHERY STOCK RECOVERY: IMPLICATIONS FOR THE ASSESSMENT OF NATURAL RESOURCE DAMAGES

ABSTRACT. During the restoration planning phase of the natural resource damage assessment (NRDA) process, potential injuries to natural resources and services are evaluated in terms of the nature, degree and extent of injury so that the need for and scale of restoration actions can be ascertained. Injuries are quantified by comparing the condition of the injured natural resource relative to baseline (pre‐injury) conditions. The “Type A” procedures are used to quantify damages from smaller spills and rely on a standardized methodology and computer model to calculate injury and value of damages. In this model, fishery stock changes from injuries and resulting changes in user participation are not treated as dynamic. If true stock growth and re‐growth are indeed dynamic, then the Type A model is likely underestimating fishery losses. The purpose of this paper is to illustrate the potential for such underestimation by comparing simulated stock and harvest losses under dynamic treatment and a static treatment that more closely represents the way stock and service losses are estimated under the current NRDA process.     

Values in Japanese mathematics education: their historical development

Individual mathematics teachers may value different aspects of teaching and learning mathematics, but at the same time their value systems are under the influence of socially shared values. This paper describes such values in Japanese mathematics education from a historical and normative perspective. After the introduction of Western mathematics into the modern school system in the Meiji period (1868?C1912), the people of Japan struggled to adapt and absorb it onto the foundation of Japanese tradition. In the subsequent development of Japanese mathematics education, the integration of both practical and theoretical aspects have been issues, alongside changes in educational focus and in society at large, which are symbolically represented by the enrolment rates at all of elementary, secondary, and tertiary education levels. Mathematics education in Japan has also been subject to international influences, such as the reform movement and the modernization movement, at critical junctures in its development. Key concepts such as mathematical ideas, mathematical thinking, and mathematical activities are traces of such historical efforts by the Japanese mathematics education community, and represent their socially shared values.     

On selective harvesting of an inshore–offshore fishery: a bioeconomic model

A bioeconomic model is developed for the selective harvesting of a single species, inshore–offshore fishery, assuming that the growth of the species is governed by the Gompertz law. The dynamical system governing the fishery is studied in depth; the local and global stability of its non-trivial steady state are examined. Existence of a bionomic equilibrium is established under different parametric considerations. The optimal harvest policy is discussed by invoking Pontryagin's Maximum Principle. Lastly, the results are illustrated with the help of a numerical example.     

A mixed integer programming model of a multicohort single-species fishery

Many marine fisheries are under pressure from overfishing. Fisheriesmanagement is a complex process because of the need to considerthe interaction of the biological components of the fishery,the technical characteristics of the fishing fleet, and theeconomic aspects of the fishing industry. In this paper, a mixedinteger programming (MIP) model for determining the policy tomaximize the long-run economic benefit from a single-speciesmulticohort fishery is developed. The model takes account ofthe biological, technical, and economic characteristics of thefishery, using integer variables to model the fishing activities.An iterative procedure for solving the model using commercialMIP software is described, and the viability of this procedureis illustrated using data for the western mackerel fishery.     

On selective harvesting of an inshore-offshore fishery: a bioeconomic model

In the present paper, a bioeconomic model is developed for the selective harvesting of a single species, inshore-offshore fishery, assuming that the growth of the species is governed by the Gompertz law. The dynamical system governing the fishery is studied in depth; the local and global stability of its non-trivial steady state are examined. Existence of a bionomic equilibrium is established under different parametric considerations. The optimal harvest policy is discussed by invoking Pontryagin's Maximum Principle. Lastly, the results are illustrated with the help of a numerical example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A MODEL OF THE NORTH CAROLINA BAY SCALLOP FISHERY WITH ENDOGENOUS FISHING EFFORT AND ENTRY

The principal purpose of this model is to aid in the evaluation and design of regulations that affect the fishery. It differs from most previous models with a similar purpose in three ways. (1) Daily fishing costs are assumed to vary among fishermen. (2) Daily fishing effort is determined endogenously rather than being treated as a control variable. (3) Entry into the fishery is determined endogenously up to a cap imposed by the regulatory agency. The model explains the adverse reaction to a proposed attempt to increase the value of the fishery by delaying the opening date. The model is used to predict the economic consequences of four feasible sets of regulations.     

DEA-based predictors for estimating fleet size changes when modelling the introduction of rights-based management

The introduction of individual transferable quotas (ITQs) into a fishery is going to change not only the amount of catch a fleet can take, but often also changes the fleet structure, particularly if total allowable catches are decreased. This can have an impact on the economic, social and environmental outcomes of fisheries management. Management Strategy Evaluation (MSE) modelling approaches are recognised as the most appropriate method for assessing impacts of management, but these require information as to how fleets may change under different management systems. In this study, we test the applicability of data envelopment analysis (DEA) based performance measures as predictors of how a fishing fleet might change under the introduction of ITQs and also at different levels of quota. In particular, we test the assumption that technical efficiency and capacity utilisation are suitable predictors of which boats are likely to exit the fishery. We also consider scale efficiency as an alternative predictor. We apply the analysis to the Torres Strait tropical rock lobster fishery that is transitioning to an ITQ-based management system for one sector of the fishery. The results indicate that capacity utilisation, technical efficiency and scale efficiency are reasonable indicators of who may remain in the fishery post ITQs. We find that the use of these measures to estimate the impacts of lower quota levels provides consistent fleet size estimates at the aggregate level, but which individual vessels are predicted to exit is dependent on the measure used.     

Regulation of a prey-predator fishery by taxation

Bioeconomic exploitation of a prey-predator fishery is discussed by using a reasonable catch-rate function instead of the usual 'catch-per-unit-effort hypothesis'. The model is based on the assumption that only the prey species is harvested. A regulatory agency controls exploitation of the fishery by imposing a tax per unit biomass of the landed fish. The fishing effort is taken as a dynamic variable depending on the capital invested in the fishery. The dynamical system consisting of the growth equations of the species and also the fishing effort is formulated. The existence and stability of steady states are discussed. The optimal tax policy is studied with the help of Pontryagin's maximum principle. Finally, some numerical examples are carried out to illustrate the results of the model.     

IN-SEASON FISHERY MANAGEMENT: A BAYESIAN MODEL

A Bayesian model is presented for optimizing harvest rates on an uncertain resource stock during the course of a fishing season. Pre-season stock status information, in the form of a “prior” probability distribution, is updated using new data obtained through the operation of the fishery, and harvest rates are chosen to achieve a balance between conservation concerns and fishing interests. A series of fishery scenarios are considered, determined by the stock size distribution and the timing distribution; the uncertainty in the fish stock is seen to have a rather complex influence on optimal harvest rates. The model is applied to a specific example, the Skeena River sockeye salmon fishery.     

Sustainable Yield Analysis in a Multicohort Single-species Fishery: A Mathematical Programming Approach

The concept of sustainable yield, i.e. the fish catch that can be maintained in the long run from a fishery in a steady state, is widely used in fisheries management. In traditional methods of sustainable yield analysis, based on the Schaefer model of a fish stock, the age structure of the stock is ignored. Approaches based on the Beverton-Holt multicohort fish population model take account of age structure but assume that instantaneous natural and fishing mortality rates are constant throughout the year. Using a fish population model in which this assumption is not required, a mixed integer programming model is developed for the analysis of a multicohort single-species fishery in a steady state. This new method of sustainable yield analysis is demonstrated using data for the western mackerel fishery. Comparisons with results from other studies of this fishery are presented.     

An infinite horizon mathematical programming model of a multicohort single species fishery

Fishery policy evaluation should take account of the initial state of the fishery and the population dynamics of the fish stock. Although multicohort bioeconomic fishery policy evaluation models have been developed, the results from these models depend on the choice of planning period and the desired state of the stock at the end of this period. In this paper it is noted that these limitations can be overcome by evaluating fishery policy over an infinite time horizon, and a mixed integer programming (MIP) model is developed for carrying out this form of analysis in a multicohort single species fishery. This new MIP model allows policies to be evaluated over an infinite horizon by incorporating results from a steady state fishery model into a multiperiod framework. The use of this MIP model in determining policies for reaching and maintaining a steady state is illustrated.     

The dynamics of Japanese and American interpersonal events: Behavioral settings versus personality traits

Psychologists and sociologists have had a long and keen interest in whether situations or personality traist are the predominant determinants of behavior. This affect control study and two earlier ones (Smith et al., 1994, 2001) are consistent with recent psychological research indicating that East Asians are more influenced by situational influences and less by internal dispositions than Americans. This implies that Japanese are less likely than Americans to invoke correspondence biases like the fundamental attribution error. The results argue for a gendered Generalized Other in Japan. Still, the Japanese setting equations share fundamental commonalities with their American cousins such as relatively large stability and behavioral morality effects.     

Resource leasing and optimal periodic capital investments

In this paper we analyse a fishery resource exploitation model in which a single firm or a cartel has leased the rights to manage the resources independently. Two variables, resource level and the capital level, determine the dynamics of the resource system. The leasing contract includes an incentive for the agent to maintain the resource level high. The main result is that sole-agent resource management and efficiency of the resource use do not necessarily imply that the fishery is stabilized at a unique steady state level. Instead, the optimal resource exploitation may lead to periodic capital investments in fishing vessels and gear which in turn causes cycles in the resource economy. We show analytically that nonzero discount rate and low capital depreciation rate both favor the conditions under which periodic optimal solutions may occur. Simulation results related to a Baltic herring fishery are used to illustrate the results.This research was partly supported by the Austrian Science Foundation under contract number P7783. The support of the Academy of Finland and Yrjö Jahnsson Foundation to V. K. is greatly appreciated. We thank Carl Folke, Mikael Hildén and Steffen Jørgensen and three anonymous referees for helpful comments. V. K. thanks the Beijer Institute of the Royal Swedish Academy of Science for its hospitality.     

Risk-sensitive and risk-neutral control for continuous-time hidden Markov models

In this paper the optimal control of a continuous-time hidden Markov model is discussed. The risk-sensitive problem involves a cost function which has an exponential form and a risk parameter, and is solved by defining an appropriate information state and dynamic programming. As the risk parameter tends to zero, the classical risk-neutral optimal control problem is recovered. The limits are proved using viscosity solution methods.The first author wishes to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centers Program. The support of NSERC Grant A7964 is acknowledged by the second author, as is the hospitality of the Department of Systems Engineering and the Cooperative Research Centre for Robust and Adaptive Systems, Australian National University, in July 1993.     

Mathematics as Connection Making in Japanese Elementary Schools

Connection making is one of the major standards proposed by the National Council of Teachers of Mathematics, however, unlike problem solving, it has no long history of being designated as a goal of mathematics teaching. An examination of classroom observations of mathematics lessons taught in Japan reveal that connection making appears to be an implicit if not explicit standard for Japanese mathematics education. As a perspective from which to re-examine and re-assess our own practice, this paper describes several episodes of connection making as they occurred in Japanese elementary school classrooms. By reflecting upon the methods used in these classrooms, other approaches to connection making are suggested and explored.     

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research 3, 385-390]as an effective way to estimate the pasture mean. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling(MERSS) is considered for the best linear unbiased estimators(BLUEs) for the simple linear regression model. The BLUEs for this model under MERSS are derived. The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.     

Studying sample lessons rather than one excellent lesson: A Japanese perspective on the TIMSS videotape classroom study

The findings of the TIMSS Videotape Classroom Study include aspects of mathematics lessons showing a strong resemblance between Germany and the US in difference to Japan. This paper discusses some of the features that appear to make Japanese lessons different from the other two countries. In particular, the paper examines the goals of lessons described by Japanese teachers, how lessons are structured and implemented, and the emphasis on alternative solutions to a problem in the teaching and learning processes. The characteristics of Japanese lessons identified by the TIMSS Videotape Classroom Study can naturally be interpreted as indications of teachers' efforts to foster students' mathematical thinking in the classroom.