MODELING THE MOVEMENTS OF COWBIRDS: APPLICATION TOWARDS MANAGEMENT AT THE LANDSCAPE SCALE

ABSTRACT. Brood parasitism by brown‐headed cowbirds (Molothrus ater) reduces the reproductive success of two endangered bird species at Fort Hood, Texas. A successful management program has focused on trapping cowbirds at feeding locations, grassland areas almost always associated with the presence of cattle. To enhance the efficacy of this effort, we developed an individual‐based model that predicted visitation rates by cowbirds to all potential feeding locations at Fort Hood and the surrounding landscape. Utilizing GRASS‐GIS and SWARM, the model incorporated the spatial arrangement of habitats, daily movements of cattle, and daily movements of cowbirds from their breeding sites to feeding locations. We simulated four types of movements by cow‐birds as they searched for cattle: 1) random walk, 2) direct return to previous locations (i.e., memory), 3) return to previous locations with en route assessment (i.e., memory with limited perception of the current state of the system), and 4) omniscience. Straight‐line distances between breeding and feeding locations for cowbirds that used the memory‐with‐perception rule were similar to independent telemetry results, and total search distances for this movement type approached those of omniscience. Both movement distance measures were inversely related to perception distance. Maps of cowbird visits to feeding areas differed among movement rules but were not strongly affected by the density of breeding cow‐birds. Maps also identified locations where trapping efforts could reduce parasitism within specific areas known to support endangered species. While it seems plausible that cowbirds are able to remember foraging locations and to perceive their surroundings as they travel, additional studies are needed to document their cognitive abilities. By simulating movements of individual cowbirds across a dynamic landscape, model results may help to strengthen ongoing cowbird control efforts.     

Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016     

MANAGEMENT STRATEGY EVALUATION OF PHEROMONE‐BAITED TRAPPING TECHNIQUES TO IMPROVE MANAGEMENT OF INVASIVE SEA LAMPREY

We applied a management strategy evaluation (MSE) model to examine the potential cost‐effectiveness of using pheromone‐baited trapping along with conventional lampricide treatment to manage invasive sea lamprey. Four pheromone‐baited trapping strategies were modeled: (1) stream activation wherein pheromone was applied to existing traps to achieve 10^?12 mol/L in‐stream concentration, (2) stream activation plus two additional traps downstream with pheromone applied at 2.5 mg/hr (reverse‐intercept approach), (3) trap activation wherein pheromone was applied at 10 mg/hr to existing traps, and (4) trap activation and reverse‐intercept approach. Each new strategy was applied, with remaining funds applied to conventional lampricide control. Simulating deployment of these hybrid strategies on fourteen Lake Michigan streams resulted in increases of 17 and 11% (strategies 1 and 2) and decreases of 4 and 7% (strategies 3 and 4) of the lakewide mean abundance of adult sea lamprey relative to status quo. MSE revealed performance targets for trap efficacy to guide additional research because results indicate that combining lampricides and high efficacy trapping technologies can reduce sea lamprey abundance on average without increasing control costs.     

Adaptive‐impulsive function projective synchronization for a class of time‐delay chaotic systems

This article investigates the function projective synchronization (FPS) for a class of time‐delay chaotic system via nonlinear adaptive‐impulsive control. To achieve the FPS, suitable nonlinear continuous and impulsive controllers are designed based on adaptive control theory and impulsive control theory. Using the generalized Babarlat's lemma, a general condition is given to ensure the FPS. Here, the time‐delay chaotic system is assumed to satisfy the Lipschitz condition while the Lipschitz constants are estimated by augmented adaptation equations. Numerical simulation results are also presented to verify the effectiveness of the proposed synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 333–341, 2015     

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.     

MULTISPECIES AND SINGLE‐SPECIES MODELS OF FISH POPULATION DYNAMICS: COMPARING PARAMETER ESTIMATES

Abstract Population features inferred from single‐species, age‐structured models are compared to those inferred from a multispecies, age‐structured model that includes predator‐prey interactions among three commercially harvested fish species—walleye pollock, Atka mackerel, and Pacific cod—on the Aleutian Shelf, Alaska. The multispecies framework treats the single‐species models and data as a special case of the multispecies model and data. The same data from fisheries and surveys are used to estimate model parameters for both single‐species and multispecies configurations of the model. Additionally, data from stomach samples and predator rations are used to estimate the parameters of the multispecies model. One form of the feeding functional response, predator pre‐emption, was selected using AIC from seven alternative models for how the predation rate changes with the densities of prey and possibly other predators. Differences in estimated population dynamics and productivity between the multispecies and single‐species models were observed. The multispecies model estimated lower mackerel population sizes from 1964–2003 than the single‐species model, while the spawning biomass of pollock was estimated to have declined more than three times faster since 1964 by the multispecies model. The variances around the estimates of spawning biomass were smaller for mackerel and larger for pollock in the multispecies model compared to the single‐species model.     

VIABILITY MODEL OF TROPHIC INTERACTIONS IN MARINE ECOSYSTEMS

ABSTRACT. An attempt to use viability models for studying marine ecosystems is proposed as a possible alternative to classical ecosystem modeling. Viability models do not consider optimal solutions but instead define all possible evolutions of a dynamical system under given constraints. Applied to marine ecosystems, a viability model is formulated based on the trophic coefficients of a mass‐balanced model. This requires relatively few assumptions about the processes involved and can integrate uncertainty associated with the required estimates of input parameters. An iterative algorithm is proposed to calculate the viability kernel, i.e., the envelope of all viable trajectories of the ecosystem. An application to the Benguela ecosystem is presented, considering interactions between detritus, phytoplankton, zooplankton, pelagic fish, demersal fish and fisheries. Results show how a viability kernel could be used to better define the healthy states of a marine ecosystem, by defining what states should be avoided. The paper discusses how viability models of trophic interactions could help to define a new ecosystem‐based indicator for fisheries management. It then discusses how this approach can potentially contribute to a paradigm shift that is emerging in the management of renewable resources.     

A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.     

Function vector synchronization based on fuzzy control for uncertain chaotic systems with dead‐zone nonlinearities

In this article, a fuzzy adaptive control scheme is designed to achieve a function vector synchronization behavior between two identical or different chaotic (or hyperchaotic) systems in the presence of unknown dynamic disturbances and input nonlinearities (dead‐zone and sector nonlinearities). This proposed synchronization scheme can be considered as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization, generalized projective synchronization, and so forth) in the sense that the master and slave outputs are assumed to be some general function vectors. To practically deal with the input nonlinearities, the adaptive fuzzy control system is designed in a variable‐structure framework. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is used to prove the boundedness of all signals of the closed‐loop control system as well as the exponential convergence of the corresponding synchronization errors to an adjustable region. The synchronization between two identical systems (chaotic satellite systems) and two different systems (chaotic Chen and Lü systems) are taken as two illustrative examples to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 234–249, 2016     

Modeling the spread of bird flu and predicting outbreak diversity

Avian influenza, commonly known as bird flu, is an epidemic caused by H5N1 virus that primarily affects birds like chickens, wild water birds, etc. On rare occasions, these can infect other species including pigs and humans. In the span of less than a year, the lethal strain of bird flu is spreading very fast across the globe mainly in South East Asia, parts of Central Asia, Africa and Europe. In order to study the patterns of spread of epidemic, we made an investigation of outbreaks of the epidemic in one week, that is from February 13–18, 2006, when the deadly virus surfaced in India. We have designed a statistical transmission model of bird flu taking into account the factors that affect the epidemic transmission such as source of infection, social and natural factors and various control measures are suggested. For modeling the general intensity coefficient f(r), we have implemented the recent ideas given in the article Fitting the Bill, Nature [R. Howlett, Fitting the bill, Nature 439 (2006) 402], which describes the geographical spread of epidemics due to transportation of poultry products. Our aim is to study the spread of avian influenza, both in time and space, to gain a better understanding of transmission mechanism. Our model yields satisfactory results as evidenced by the simulations and may be used for the prediction of future situations of epidemic for longer periods. We utilize real data at these various scales and our model allows one to generalize our predictions and make better suggestions for the control of this epidemic.     

OPTIMAL GRAZING MANAGEMENT RULES IN SEMI‐ARID RANGELANDS WITH UNCERTAIN RAINFALL

Abstract. We study optimal adaptive grazing management under uncertain rainfall in a discrete‐time model. As in each year actual rainfall can be observed during the short rainy season, and grazing management can be adapted accordingly for the growing season; the closed‐loop solution of the stochastic optimal control problem does not only depend on the state variable, but also on the realization of the random rainfall. This distinguishes optimal grazing management from the optimal use of most other natural resources under uncertainty, where the closed‐loop solution of the stochastic optimal control problem depends only on the state variables. Solving this unusual stochastic optimization problem allows us to critically contribute to a long‐standing controversy over how to optimally manage semi‐arid rangelands by simple rules of thumb.     

THE VALUE OF SHORT‐RUN CLIMATE FORECASTS IN MANAGING THE COASTAL COHO SALMON (ONCORHYNCHUS KISUTCH) FISHERY IN WASHINGTON STATE

ABSTRACT. . In recent years our understanding of the intricate connections between climate variability, marine and freshwater environmental conditions and the responses of fish stocks has improved considerably. With predictable relationships between the environment and stock abundance, fishery managers should be able to forecast variation in stock survival and recruitment. Such forecasts present an opportunity for increasing the economic value of fisheries and for achieving other management objectives, such as stock conservation and maintenance of population diversity. After describing a 4‐step framework for addressing the question ‘What is a forecast worth?’ in a fishery decision‐making context, we introduce the management system for Washington's coastal coho salmon (Oncorhynchus kisutch) fishery. Then we apply the 4‐step framework to estimate the value of improved run size forecasts in the annual harvest management of coho salmon in Washington State. Our principal analytical tool is a stochastic simulation model that incorporates the main characteristics of the fishery. The paper concludes with a discussion of opportunities and constraints to the use of climate‐based forecasts in fishery management on various spatial and temporal scales, and we consider the challenges associated with forecasting variations in fish stock size caused by shifts in climate and related ocean conditions.     

Network theory and behavioral finance in a heterogeneous market environment

This article addresses the stock market as a complex system. The complexity of the stock market arises from the structure of the environment, agent heterogeneity, interactions among agents, and interactions with market regulators. We develop the idea of a meta‐model, which is a model of models represented in an agent‐based model that allows us to investigate this type of market complexity. The novelty of this article is the incorporation of various complexities captured by network theoretical models or induced by investment behavior. The model considers agents heterogeneous in terms of their strategies and investment behavior. Four investment strategies are included in the model: zero‐intelligence, fundamental strategy, momentum (trend followers), and adaptive trading strategy using the artificial neural network algorithm. In terms of behavior, the agents can be risk averse or loss occupied with overconfidence or conservative biases. The agents may interact with each other by sharing market sentiments through a structured scale‐free network. The market regulator controls the market through various control tools such as the risk‐free rate and taxation. Parameters are calibrated to the S&P500. The calibration is implemented using a scatter search heuristic approach. The model is validated using various stylized facts of stock return patterns such as excess kurtosis, auto‐correlation, and ARCH effect phenomena. Analysis at the macro and micro level of the market was performed by measuring the sensitivity of volatility and market capital and investigating the wealth distributions of the agents. We found that volatility is more sensitive to the model parameters than to market capital, and thus, the level of volatility does not affect market capital. In addition, the findings suggest that the efficient market hypothesis holds at the macro level but not at the micro level. © 2016 Wiley Periodicals, Inc. Complexity 21: 530–554, 2016     

PID control for chaotic synchronization using particle swarm optimization

In this paper, we attempt to use the proportional-integral-derivative (PID) controller to achieve the chaos synchronization for delayed discrete chaotic systems. Three PID control gains can be optimally determined by means of using a novel optimization algorithm, called the particle swarm optimization (PSO). The algorithm is motivated from the organism behavior of fish schooling and bird flocking, and involves the social psychology principles in socio-cognition human agents and evolutionary computations. It has a good numerical convergence for solving optimization problem. To show the validity of the PSO-based PID control for chaos synchronization, several cases with different initial populations are considered and some simulation results are shown.     

Spike patterns in a reaction–diffusion ODE model with Turing instability

We explore a mechanism of pattern formation arising in processes described by a system of a single reaction–diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions between cellular processes and diffusing growth factors. We focus on the model of early carcinogenesis proposed by Marciniak‐Czochra and Kimmel, which is an example of a wider class of pattern formation models with an autocatalytic non‐diffusing component. We present a numerical study showing emergence of periodic and irregular spike patterns because of diffusion‐driven instability. To control the accuracy of simulations, we develop a numerical code on the basis of the finite‐element method and adaptive mesh grid. Simulations, supplemented by numerical analysis, indicate a novel pattern formation phenomenon on the basis of the emergence of nonstationary structures tending asymptotically to a sum of Dirac deltas. Copyright © 2013 John Wiley & Sons, Ltd.     

SOLVING DYNAMIC WILDLIFE RESOURCE OPTIMIZATION PROBLEMS USING REINFORCEMENT LEARNING

ABSTRACT. An important technical component of natural resource management, particularly in an adaptive management context, is optimization. This is used to select the most appropriate management strategy, given a model of the system and all relevant available information. For dynamic resource systems, dynamic programming has been the de facto standard for deriving optimal state‐specific management strategies. Though effective for small‐dimension problems, dynamic programming is incapable of providing solutions to larger problems, even with modern microcomputing technology. Reinforcement learning is an alternative, related procedure for deriving optimal management strategies, based on stochastic approximation. It is an iterative process that improves estimates of the value of state‐specific actions based in interactions with a system, or model thereof. Applications of reinforcement learning in the field of artificial intelligence have illustrated its ability to yield near‐optimal strategies for very complex model systems, highlighting the potential utility of this method for ecological and natural resource management problems, which tend to be of high dimension. I describe the concept of reinforcement learning and its approach of estimating optimal strategies by temporal difference learning. I then illustrate the application of this method using a simple, well‐known case study of Anderson [1975], and compare the reinforcement learning results with those of dynamic programming. Though a globally‐optimal strategy is not discovered, it performs very well relative to the dynamic programming strategy, based on simulated cumulative objective return. I suggest that reinforcement learning be applied to relatively complex problems where an approximate solution to a realistic model is preferable to an exact answer to an oversimplified model.     

Randomized allocation processes

Many dynamic resource allocation and on‐line load balancing problems can be modeled by processes that sequentially allocate balls into bins. The balls arrive one by one and are to be placed into bins on‐line without using a centralized controller. If n balls are sequentially placed into n bins by placing each ball in a randomly chosen bin, then it is widely known that the maximum load in bins is ln n /ln ln n?(1+o(1)) with high probability. Azar, Broder, Karlin, and Upfal extended this scheme, so that each ball is placed sequentially into the least full of d randomly chosen bins. They showed that the maximum load of the bins reduces exponentially and is ln ln n/In d+Θ(1) with high probability, provided d<2. In this paper we investigate various extensions of these schemes that arise in applications in dynamic resource allocation and on‐line load balancing. Traditionally, the main aim of allocation processes is to place balls into bins to minimize the maximum load in bins. However, in many applications it is equally important to minimize the number of choices performed (the allocation time). We study adaptive allocation schemes that achieve optimal tradeoffs between the maximum load, the maximum allocation time, and the average allocation time. We also investigate allocation processes that may reallocate the balls. We provide a tight analysis of a natural class of processes that each time a ball is placed in one of d randomly chosen bins may move balls among these d bins arbitrarily. Finally, we provide a tight analysis of the maximum load of the off‐line process in which each ball may be placed into one of d randomly chosen bins. We apply this result to competitive analysis of on‐line load balancing processes. ©2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 297–331, 2001     

Synchronization of memristor‐based delayed BAM neural networks with fractional‐order derivatives

This article deals with the problem of synchronization of fractional‐order memristor‐based BAM neural networks (FMBNNs) with time‐delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional‐order 0 < α < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master‐slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite‐time synchronization of FMBNNs with fractional‐order 1 < α < 2, using Mittag‐Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time‐delay and fractional‐order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity 21: 412–426, 2016     

A MODEL OF CHINOOK SALMON POPULATION DYNAMICS INCORPORATING SIZE‐SELECTIVE EXPLOITATION AND INHERITANCE OF POLYGENIC CORRELATED TRAITS

Abstract Concern regarding the potential for selective fisheries to degrade desirable characteristics of exploited fish populations is growing worldwide. Although the occurrence of fishery‐induced evolution in a wild population has not been irrefutably documented, considerable theoretical and empirical evidence for that possibility exists. Environmental conditions influence survival and growth in many species and may mask comparatively subtle trends induced by selective exploitation, especially given the evolutionarily short time series of data available from many fisheries. Modeling may be the most efficient investigative tool under such conditions. Motivated by public concern that large‐mesh gillnet fisheries may be altering Chinook salmon in western Alaska, we constructed a stochastic model of the population dynamics of Chinook salmon. The model contained several individually based components and incorporated size‐selective exploitation, assortative mating, size‐dependent female fecundity, density‐dependent survival, and the heritability of size and age. Substantial reductions in mean size and age were observed under all scenarios. Concurrently reducing directional selection and increasing spawning abundance was most effective in stimulating population recovery. Use of this model has potential to improve our ability to investigate the consequences of selective exploitation and aid development of improved management strategies to more effectively sustain fish and fisheries into the future.     

Optimal fishery with coastal catch

In many spatial resource models, it is assumed that an agent is able to harvest the resource over the complete spatial domain. However, agents frequently only have access to a resource at particular locations at which a moving biomass, such as fish or game, may be caught or hunted. Here, we analyze an infinite time‐horizon optimal control problem with boundary harvesting and (systems of) parabolic partial differential equations as state dynamics. We formally derive the associated canonical system, consisting of a forward–backward diffusion system with boundary controls, and numerically compute the canonical steady states and the optimal time‐dependent paths, and their dependence on parameters. We start with some one‐species fishing models, and then extend the analysis to a predator–prey model of the Lotka–Volterra type. The models are rather generic, and our methods are quite general, and thus should be applicable to large classes of structurally similar bioeconomic problems with boundary controls. Recommedations for Resource Managers

• Just like ordinary differential equation‐constrained (optimal) control problems and distributed partial differential equation (PDE) constrained control problems, boundary control problems with PDE state dynamics may be formally treated by the Pontryagin's maximum principle or canonical system formalism (state and adjoint PDEs).
• These problems may have multiple (locally) optimal solutions; a first overview of suitable choices can be obtained by identifying canonical steady states.
• The computation of canonical paths toward some optimal steady state yields temporal information about the optimal harvesting, possibly including waiting time behavior for the stock to recover from a low‐stock initial state, and nonmonotonic (in time) harvesting efforts.
• Multispecies fishery models may lead to asymmetric effects; for instance, it may be optimal to capture a predator species to protect the prey, even for high costs and low market values of the predators.