ANALYSIS OF SENSITIVITY AND UNCERTAINTY IN AN INDIVIDUAL‐BASED MODEL OF A THREATENED WILDLIFE SPECIES

Sensitivity analysis—determination of how prediction variables affect response variables—of individual‐based models (IBMs) are few but important to the interpretation of model output. We present sensitivity analysis of a spatially explicit IBM (HexSim) of a threatened species, the Northern Spotted Owl (NSO; Strix occidentalis caurina) in Washington, USA. We explored sensitivity to HexSim variables representing habitat quality, movement, dispersal, and model architecture; previous NSO studies have well established sensitivity of model output to vital rate variation. We developed “normative” (expected) model settings from field studies, and then varied the values of ≥ 1 input parameter at a time by ±10% and ±50% of their normative values to determine influence on response variables of population size and trend. We determined time to population equilibration and dynamics of populations above and below carrying capacity. Recovery time from small population size to carrying capacity greatly exceeded decay time from an overpopulated condition, suggesting lag time required to repopulate newly available habitat. Response variables were most sensitive to input parameters of habitat quality which are well‐studied for this species and controllable by management. HexSim thus seems useful for evaluating potential NSO population responses to landscape patterns for which good empirical information is available.     

Mathematical Programming Modelling Using MGG

MGG is a software package for the application of mathematicalprogramming (MP). It complements the Sciconic MP code by providinga facility for developing MP models quickly and efficiently,and it enables changes to be made easily to established models.It is available on a wide range of minis and mainframes anda version of it is available as part of the Micro LP systemon IBM PCs and compatibles. MGG is based on an approach to modellingMP problems which stresses the primacy of the mathematical formulation.The process of MP modelling is divided into two stages: modelpreparation and running of the model. The user writes a mathematicalformulation, which MGG converts to matrix generator and reportwriter programs. This is done once to produce the programs whichcan then be run many times on different data. This paper describesMGG and draws comparisons with other matrix generator and mathematicalprogramming languages. It starts by considering how an MP problemcan be described, and then sets out a methodology for formulation.The MGG language is based upon this approach. A simple exampleis presented which is shown both as an algebraic formulationand in the MGG language. The process of building and runningmodels with MGG is then described. Finally, some comments areoffered on experience of using the software.     

MODELING AND MEASURING PRODUCTION PROCESSES FOR A MULTI‐SPECIES FISHERY: ALTERNATIVE TECHNICAL EFFICIENCY ESTIMATES FOR THE NORTHERN SPAIN HAKE FISHERY

ABSTRACT. The economic performance of fisheries is difficult to measure, due to the importance of (multi‐species) biological dynamics, property rights and regulatory issues affecting fishermen's behavior and efficiency. However, an understanding of performance patterns is essential for enhancing the economic and biological viability of fisheries. In this paper we estimate and evaluate alternative primal stochastic approaches to modeling and measuring technical efficiency for the Northern Spain hake fishery. We then compare the resulting efficiency measures to identify variations in their potential interpretation, and application to policy guidance. We find that multi‐output models are more theoretically and empirically justifiable than aggregate output production function models, and provide additional policy‐relevant insights, but that relative production and efficiency estimates are not sub‐stantively affected by model specification.     

INDIVIDUAL‐BASED MODELS AND THE MANAGEMENT OF SHOREBIRD POPULATIONS

Abstract Individual‐based models (IBMs) predict how animal populations will be affected by changes in their environment by modeling the responses of fitness‐maximizing individuals to environmental change and by calculating how their aggregate responses change the average fitness of individuals and thus the demographic rates, and therefore size of the population. This paper describes how the need to develop a new approach to make such predictions was identified in the mid‐1970s following work done to predict the effect of building a freshwater reservoir on part of the intertidal feeding areas of the shorebirds Charadrii that overwinter on the Wash, a large embayment on the east coast of England. The paper describes how the approach was developed and tested over 20 years (1976–1995) on a population of European oystercatchers Haematopus ostralegus eating mussels Mytilus edulis on the Exe estuary in Devon, England. The paper goes on to describe how individual‐based modeling has been applied over the last 10 years to a wide range of environmental issues and to many species of shorebirds and wildfowl in a number of European countries. Although it took 20 years to develop the approach for 1 bird species on 1 estuary, ways have been found by which it can now be applied quite rapidly to a wide range of species, at spatial scales ranging from 1 estuary to the whole continent of Europe. This can now be done within the time period typically allotted to environmental impact assessments involving coastal bird populations in Europe. The models are being used routinely to predict the impact on the fitness of coastal shorebirds and wildfowl of habitat loss from (i) development, such as building a port over intertidal flats; (ii) disturbance from people, raptors, and aircraft; (iii) harvesting shellfish; and (iv) climate change and any associated rise in sea level. The model has also been used to evaluate the probable effectiveness of mitigation measures aimed at ameliorating the impact of such environmental changes on the birds. The first steps are now being taken to extend the approach to diving sea ducks and farmland birds during the nonbreeding season. The models have been successful in predicting the observed behavior and mortality rates in winter of shorebirds on a number of European estuaries, and some of the most important of these tests are described. These successful tests of model predictions raise confidence that the model can be used to advise policy makers concerned with the management of the coast and its important bird populations.     

Bankruptcy prediction by generalized additive models

We compare several accounting‐based models for bankruptcy prediction. The models are developed and tested on large data sets containing annual financial statements for Norwegian limited liability firms. Out‐of‐sample and out‐of‐time validation shows that generalized additive models significantly outperform popular models like linear discriminant analysis, generalized linear models and neural networks at all levels of risk. Further, important issues like default horizon and performance depreciation are examined. We clearly see a performance depreciation as the default horizon is increased and as time goes by. Finally a multi‐year model, developed on all available data from three consecutive years, is compared with a one‐year model, developed on data from the most recent year only. The multi‐year model exhibits a desirable robustness to yearly fluctuations that is not present in the one‐year model. Copyright © 2006 John Wiley & Sons, Ltd.     

Fuzzy systems based on component software

This paper describes hierarchical modeling of fuzzy logic concepts that has been used within the recently developed model of intelligent systems, called OBOA. The model is based on a multilevel, hierarchical, general object-oriented approach. Current methods and software design and development tools for intelligent systems are usually difficult to extend, and it is not easy to reuse their components in developing intelligent systems. The OBOA model tries to reduce these deficiencies. The model starts with a well-founded software engineering principle, making clear distinction between generic, low-level intelligent software components, and domain-dependent, high-level components of an intelligent system. This paper concentrates on modeling and implementation of fuzzy logic concepts within the hierarchical levels of the OBOA model. The fuzzy components described are extensible and adjustable. As an illustration of how these components are used in practice, a practical design example from the domain of medical diagnosis is shown. The paper also suggests some steps towards future design of fuzzy components and tools for intelligent systems.     

Self‐Dual Codes and the Nonexistence of a Quasi‐Symmetric 2‐(37,9,8) Design with Intersection Numbers 1 and 3

We prove that a certain binary linear code associated with the incidence matrix of a quasi‐symmetric 2‐(37, 9, 8) design with intersection numbers 1 and 3 must be contained in an extremal doubly even self‐dual code of length 40. Using the classification of extremal doubly even self‐dual codes of length 40, we show that a quasi‐symmetric 2‐(37, 9, 8) design with intersection numbers 1 and 3 does not exist.     

Basic aspects of geopotential field approximation from satellite‐to‐satellite tracking data

The satellite‐to‐satellite tracking (SST) problems are characterized from mathematical point of view. Uniqueness results are formulated. Moreover, the basic relations are developed between (scalar) approximation of the earth's gravitational potential by ‘scalar basis systems’ and (vectorial) approximation of the gravitational field by ‘vectorial basis systems’. Finally, the mathematical justification is given for approximating the external geopotential field by finite linear combinations of certain gradient fields (for example, gradient fields of multi‐poles) consistent to a given set of SST data. Copyright © 2001 John Wiley & Sons, Ltd.     

Analysis of channel and disk subsystems in computer systems

The information processing industry has shifted from the conventional mathematical computation to information management. Interactive use of a system with large data bases is now widespread, and the data base has become one of the key factors central to an overall system design. This, in turn, has prompted the development of new peripheral devices.The paper focuses on developing and analyzing stochastic models for disk storage systems. A general model is developed to describe the sequence of operations required for accessing a record on a disk. The model is then used to analyze how technological and architectural changes affect system performance. As concrete examples, performance comparison of IBM 3330 disk system with IBM 3380 disk system will be conducted. All analytical results are validated via simulation.Supported by the National Science Foundation under Grant No. ECS-8404071.     

Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming

In this paper, we present a mathematical model for cyclic and non-cyclic scheduling of 12 h shift nurses. The model exploits the fact that a nurse's schedule is made up of an alternating sequence of work-stretch and ‘off-stretch’ patterns. We introduce a concept called a stint, which is a pattern characterized by a start date, a length, a `cost' and the shifts worked. Using the stints as nodes in a network, we construct an acyclic graph on which the nurse's schedules can be defined. The resulting model is essentially a shortest-path problem with side constraints. The model is quite flexible and can accommodate a variety of constraints. With a minor modification, the network is used to define both the cyclic and non-cyclic scheduling problems. The models are illustrated on sample data from a local hospital and solved using CPLEX optimization software on an IBM RISC6000/340 workstation.     

Delivering the shape and space programme of study in the UK national mathematics curriculum using Zeno

The UK national curriculum in mathematics, through the shape and space programme of study, requires that all pupils engage in activities which lead to an understanding of transformation of the plane. This paper introduces Zeno, a package which offers vector operations and transformation primitives in addition to Logo turtle graphics‐like features. It runs on any IBM‐compatible (with CGA or better graphics) or Apple Macintosh personal computer. The paper demonstrates how the Zeno environment can enable pupils to ‘discover’ the central mathematical principles which underpin transformation of the plane.     

Interactive markovian models of ‘progressive’ trends

Non‐linear Markovian models are investigated for a developing society stratified in terms of literacy or some other sociocultural attribute and characterized by two opposing features: a) progressive trends which forbid upper to lower state intergeneration transitions, and b) fertility differential in favour of lower states. The progressive trends in the models arise due to ‘attraction’ of the higher states. Two different limits are considered: one in which all upward transitions are permitted (Maximal Attractor Model) and the other in which only one‐step transitions are allowed (Adjacent Attractor Model). The nature of the critical points of the two models is examined analytically and/or numerically as appropriate to the case in question. In the first model, the society converges to the highest state in due course despite the fertility differential. The three‐state and four‐state cases of the models are considered in some detail. The main interesting result concerns the Adjacent Attractor Model. For the three‐state case, numerical computation reveals this model society locked in an endless cyclic pattern of evolution despite the existence of a progressive trend.     

M/C2/c/K queuing model and optimization for a geriatric care center

Queuing systems with finite buffers are reasonable models for many manufacturing, telecommunication, and healthcare systems. Although some approximations exist, the exact analysis of multi‐server and finite‐buffer queues with general service time distribution is unknown. However, the phase‐type assumption for service time is a frequently used approach. Because the Cox distribution, a kind of phase‐type distribution, provides a good representation of data with great variability, it has a vast area of application in modeling service times. The research focus is twofold. First, a theoretical structure of a multi‐server and finite‐buffer queuing system in which the service time is modeled by the two‐phase Cox distribution is studied. It is focused on finding an efficient solution to the stationary probabilities using the matrix‐geometric method. It is shown that the stationary probability vector can be obtained with the matrix‐geometric method by using level‐dependent rate matrices, and the mean queue length is computed. Second, an empirical analysis of the model is presented. The proposed methodology is applied in a case study concerning the geriatric patients. Some numerical calculations and optimizations are performed by using geriatric data. Copyright © 2015 John Wiley & Sons, Ltd.     

Multiscale agent‐based consumer market modeling

Consumer markets have been studied in great depth, and many techniques have been used to represent them. These have included regression‐based models, logit models, and theoretical market‐level models, such as the NBD‐Dirichlet approach. Although many important contributions and insights have resulted from studies that relied on these models, there is still a need for a model that could more holistically represent the interdependencies of the decisions made by consumers, retailers, and manufacturers. When the need is for a model that could be used repeatedly over time to support decisions in an industrial setting, it is particularly critical. Although some existing methods can, in principle, represent such complex interdependencies, their capabilities might be outstripped if they had to be used for industrial applications, because of the details this type of modeling requires. However, a complementary method—agent‐based modeling—shows promise for addressing these issues. Agent‐based models use business‐driven rules for individuals (e.g., individual consumer rules for buying items, individual retailer rules for stocking items, or individual firm rules for advertizing items) to determine holistic, system‐level outcomes (e.g., to determine if brand X's market share is increasing). We applied agent‐based modeling to develop a multi‐scale consumer market model. We then conducted calibration, verification, and validation tests of this model. The model was successfully applied by Procter & Gamble to several challenging business problems. In these situations, it directly influenced managerial decision making and produced substantial cost savings. © 2010 Wiley Periodicals, Inc. Complexity, 2010     

Efficiency measure,modelling and estimation in combined array designs

In off‐line quality control, the settings that minimize the variance of a quality characteristic are unknown and must be determined based on an estimated dual response model of mean and variance. The present paper proposes a direct measure of the efficiency of any given design‐estimation procedure for variance minimization. This not only facilitates the comparison of different design‐estimation procedures, but may also provide a guideline for choosing a better solution when the estimated dual response model suggests multiple solutions. Motivated by the analysis of an industrial experiment on spray painting, the present paper also applies a class of link functions to model process variances in off‐line quality control. For model fitting, a parametric distribution is employed in updating the variance estimates used in an iteratively weighted least squares procedure for mean estimation. In analysing combined array experiments, Engel and Huele (Technometrics, 1996; 39:365) used log‐link to model process variances and considered an iteratively weighted least squares leading to the pseudo‐likelihood estimates of variances as discussed in Carroll and Ruppert (Transformation and Weighting in Regression, Chapman & Hall: New York). Their method is a special case of the approach considered in this paper. It is seen for the spray paint data that the log‐link may not be satisfactory and the class of link functions considered here improves substantially the fit to process variances. This conclusion is reached with a suggested method of comparing ‘empirical variances’ with the ‘theoretical variances’ based on the assumed model. Copyright © 2003 John Wiley & Sons, Ltd.     

GOLDEN AGES OR MAGIC MOMENTS?

ABSTRACT. The paper is an attempt to refute Quinn's ‘the Golden Age of fisheries population models has ended “hypothesis. The approach is to show it is possible to provide simple matrix based theory for use with delay difference equations applied to products of the 0th to 4th powers of length and numbers at length (Alias” proto‐moments“). It compares these to models just based upon numbers and biomass. It also shows examples (of comparatively little moment) indicating how using multiple proto‐moments could improve the ability of delay difference equations to handle the size dependent processes of maturity, selection, natural mortality rates and predation rates and thus improving the biological reality of these models.     

A cellular automata model can quickly approximate UDP and TCP network traffic

Brooks and Orr [R.R. Brooks and N. Orr, A model for mobile code using interacting automata. IEEE Trans Mobile Computing 2002, 1(4)] present a model for analysis and simulation of mobile code systems based on cellular automata (CA) abstractions. One flaw with that article was a lack of experimental support showing that CA can model IP networks. This article presents CA models, consistent with those in the work of Brooks and Orr, that model the transport layer of IP networks. We show how these models may be generalized for more complicated network topologies. We provide quantitative results comparing the quality of our CA implementation versus the standard network modeling tool ns‐2. The results from the CA model are qualitatively similar to ns‐2, but the CA simulation runs significantly faster and scales better. © 2004 Wiley Periodicals, Inc. Complexity 9:32–40, 2004