Optimal exploitation of a fishery employing a non-linear harvesting function

A harvesting function is developed to described the rate of removal of fish from a fish population. The function incorporates the effects of both the handling or processing time of the catch and the competition, between boats in the fleet, for the fish.We will assume that the growth rate of the fish population can be modelled with a concave, dome shaped growth curve. With this assumption, it has been shown that if the rate of harvesting the fish is linearly related to both effort (which can be thought of as some measure of the number of boats in the fleet) and the population size, then the population will tend towards a single equilibrium level which is globally stable. This paper shows that the saturation effects due to the handling time may generate two equilibrium levels (one stable, one unstable) rather than a single globally stable equilibrium. The results of competition between boats are economically undesirable because of the decrease in efficiency. However, this competition may be beneficial to the exploited fish population.Using the harvesting model derived earlier, the steady state or long term optimal harvesting policies as well as the transition paths to these states are developed. The only constraint is on the maximum allowable effort which is effectively an upper limitation on the fleet size or number of man-hours of fishing.     

Model of a chemostat utilising phenol as inhibitory substrate

A pure culture of Acinetobacter lwoffi was grown in a batch and continuous culture using phenol as the limiting substrate. Five kinetic models were applied to the data to determine the kinetic parameters governing growth of the organisms. A non-linear leastsquares technique was used to fit the data to the different functions. No significant differences were found on statistical basis between the models and so a choice was made on the grounds of mathematical simplicity. The so-called ‘Haldane function’ was chosen as the best and utilised in the model describing the steady-state behaviour of the chemostat. This model takes into account the inhibitory character of phenol and also the maintenance energy of the bacteria. Analysis of local stability shows that one can expect to obtain three steady states of which one is the trivial washout state, another is unstable and the third is a high conversion stable steady state.This model was tested with a pure culture of Acinetobacter lwoffi and phenol inlet concentrations of 200, 500 and 1000 mgl^?1. Good agreement was found between the model and the results of the continuous experiments.     

A model system of four species with a unique equilibrium point

A four component model of two competing organisms, each with a specific parasite, has been exercised so as to investigate its equilibria. In addition to the equilibrium to which the model is known to return after moderate disturbance, severe perturbation led to a new steady state which had the appearance of an equilibrium but which was not maintained in the long term. Some discussion of what constitutes equilibrium and of stability of equilibria is presented.     

The economic dynamics of antibiotic efficacy under open access

We analyze the exploitation of an antibiotic in a market subject to open access on the part of antibiotic producers to the common pool of antibiotic efficacy. While the market equilibrium depends only on current levels of antibiotic efficacy and infection of the epidemiological system, the social optimum accounts for the dynamic externalities which relate those levels to the intertemporal use being made of the antibiotic. We show that depending on the parameters of the model, in particular the cost of production and the improvement in the recovery rate that results from antibiotic treatment, the positive steady-state level of antibiotic efficacy to which the system tends under open access can be lower or higher than the level which should prevail in the socially optimal steady state. In fact there are parameter configurations for which the steady states can be exactly the same. However, the paths leading to the steady state always differ.     

A resource-based approach to modelling the dynamics of interacting populations

The procedure for modelling the growth of single-species populations [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecol. Model. 205, 159–168] is improved to be applicable to the study of the dynamics of interacting populations. The improved procedure is based on three assumptions: resource availability changes with population size as a variable, resource supply to populations and population demand for resources are defined as functions of resource availability and population size, and the variables of resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into three equations. The equations can generate the dynamics models of plant, herbivore, and detritivore populations, and their own resources. The models can be used to describe prey–predator dynamics. They naturally contain nonlinear terms for the predator’s numerical and functional responses. Depending on the terms, the fluctuations in resource availability and population size stabilize. The three equations can also generate the dynamics models of different populations consuming the same resources. The analysis of zero isoclines of the models shows that a superior population can be simply defined as one with a higher intrinsic rate of natural increase, that a stable coexistence may be realized with the intraspecific interference or the interspecific facilitation of superiors, and that the interspecific interference or the intraspecific facilitation of inferiors may make the coexistence unstable and the inferiors winners depending on their initial population size.     

Sustained dynamic transience in a Lotka-Volterra competition model system for grassland species

Theoretical approaches, such as the Lotka-Volterra framework, enable predictions about long term species coexistence based on stability criteria, but generally assume temporal constancy of system equations and parameters. In real world systems, temporal variability may interfere with the attainment of stable states. Managed grassland ecosystems in Northwestern Europe experience structural periodic fluctuations in environmental conditions: the seasons. In addition, periodic disturbances such as cutting are very common. Here we show, using a Lotka-Volterra system applied to grassland species with empirically derived parameters, that seasonal variability can result in a time dependent equilibrium and redirection of displacement processes.Parameter estimates differed between species and - in most cases - between the seasons. As a result, five of the fifteen tested species combinations had different outcomes of species interactions between seasons. This indicates that systems remain in dynamic transience over the year as the equilibrium changes and the species composition of the system follows the equilibrium without ever attaining it. The non-attainment of the steady state enables coexistence of species even if there is competitive exclusion in one of the seasons. For three of the fifteen species combinations, cutting frequency affected the long-term coexistence patterns. Cutting resets the biomass of competing species and favours during regrowth those species that have a high growth rate, which can alter species coexistence in comparison to a Lotka-Volterra model without cutting. The Lotka-Volterra framework with seasonally changing empirical parameters predicts coexistence as a possible outcome of systems that in component seasons are characterised by exclusion, and vice versa.     

Nonequilibrium coexistence in a competition model with nutrient storage

Resource competition theory predicts that, in equilibrium, the number of coexisting species cannot exceed the number of limiting resources. In some competition models, however, competitive interactions may result in nonequilibrium dynamics, allowing the coexistence of many species on few resources. The relevance of these findings is still unclear, since some assumptions of the underlying models are unrealistic. Most importantly, these models assume that individual growth directly reflects the availability of external resources, whereas real organisms can store resources, thereby decoupling their growth from external fluctuations. Here we study the effects of resource storage by extending the well-known Droop model to the context of multiple species and multiple resources. We demonstrate that the extended Droop model shows virtually the same complex dynamics as models without storage. Depending on the model parameters, one may obtain competitive exclusion, stable equilibrium coexistence, periodic and non-periodic oscillations, and chaos. Again, nonequilibrium dynamics allows for the coexistence of many species on few resources. We discuss our findings in the light of earlier work on resource competition, highlighting the role of luxury consumption, trade-offs in competitive abilities, and ecological stoichiometry.     

A hierarchical analysis of terrestrial ecosystem model Biome-BGC: Equilibrium analysis and model calibration

The increasing complexity of ecosystem models represents a major difficulty in tuning model parameters and analyzing simulated results. To address this problem, this study develops a hierarchical scheme that simplifies the Biome-BGC model into three functionally cascaded tiers and analyzes them sequentially. The first-tier model focuses on leaf-level ecophysiological processes; it simulates evapotranspiration and photosynthesis with prescribed leaf area index (LAI). The restriction on LAI is then lifted in the following two model tiers, which analyze how carbon and nitrogen is cycled at the whole-plant level (the second tier) and in all litter/soil pools (the third tier) to dynamically support the prescribed canopy. In particular, this study analyzes the steady state of these two model tiers by a set of equilibrium equations that are derived from Biome-BGC algorithms and are based on the principle of mass balance. Instead of spinning-up the model for thousands of climate years, these equations are able to estimate carbon/nitrogen stocks and fluxes of the target (steady-state) ecosystem directly from the results obtained by the first-tier model. The model hierarchy is examined with model experiments at four AmeriFlux sites. The results indicate that the proposed scheme can effectively calibrate Biome-BGC to simulate observed fluxes of evapotranspiration and photosynthesis; and the carbon/nitrogen stocks estimated by the equilibrium analysis approach are highly consistent with the results of model simulations. Therefore, the scheme developed in this study may serve as a practical guide to calibrate/analyze Biome-BGC; it also provides an efficient way to solve the problem of model spin-up, especially for applications over large regions. The same methodology may help analyze other similar ecosystem models as well.     

Endogenous Growth and the Possibility of Eliminating Pollution

This paper studies the effect on optimal growth of the possibility that at some moment in the future a technology is discovered that eliminates pollution. We formalize this possibility as a probability p per unit of time of discovering such a technology. We focus on steady-state behavior and show that the optimal rate of growth increases with the hope of eliminating pollution. For an economy where there is no growth in the steady state of the optimal trajectory when p = 0, a positive p may imply positive growth. The higher the value of the probability, the larger the endogenous rate of growth.     

Renewable resources in an endogenously growing economy: balanced growth and transitional dynamics

We introduce a renewable resource sector into an endogenous growth model of a small economy, deriving the transitional dynamic equilibrium. The model generates a long-run equilibrium in which a resource sector of limited size can coexist with constant ongoing growth elsewhere. The key feature of the model is the allocation of labor between harvesting the resource and its use in the final output sector. This naturally generates the empirically observed negative relationship between resource abundance and growth. We examine both the dynamic and long-run responses of the economy to various shocks pertaining to technological production conditions and resource sector parameters.     

Environmental periodicity and ecosystem stability

Simple ecosystem models involving a primary producer, nutrients, and a herbivore are developed with metabolic dependence on periodic functions representing solar radiation and temperature. Simulation results suggests that the models yield generally stable output provided that equilibrium values for the state variables are positive in the nonperiodic analog. Linear dependence of plant growth on nutrient supply leads to a larger stability domain than that produced by hyperbolic dependence.     

Coalition formation in fisheries with potential regime shift

A system can undergo rapid regime shift in which the growth of natural resources suddenly and permanently declines. We examine how the threat of such a shift alters the strategic management of a common pool renewable resource. We consider exogenous and endogenous threats and examine their effects on both incentives to join a coalition and harvest decisions. We find that an exogenous threat of reduced resource growth may cause the coalition to grow in size, and, perhaps of most interest, we identify conditions under which members of the stable coalition reduce harvest while non-members increase harvest in response to the threat. In contrast, an exogenous threat of total stock collapse may destabilize coalitions, resulting in higher harvest from former members, but reduced harvest by non-members. When the threat of either type of shift is endogenous, the threat of regime shift can induce stable coalitions with more than two members. In particular, we identify cases in which the first best (full cooperation) is sustained as an equilibrium outcome. Finally, we find that the relation between the magnitude of the shift and the size of stable coalitions may be negative.     

Grass feedbacks on fire stabilize savannas

Savannas commonly consist of a discontinuous cover of overstory trees and a groundcover of grasses. Savanna models have previously demonstrated that vegetation feedbacks on fire frequency can limit the density of overstory trees, thereby maintaining savannas. Positive feedbacks of either savanna trees alone or trees and grasses together on fire frequency have been shown to result in a stable savanna equilibrium. Grass feedbacks on fire frequency, in contrast, have resulted in stable equilibria in either a grassland or forest state, but not in a savanna. These results, however, were derived from a system of differential equations that assumes that fire occurrence is strictly deterministic and that vegetation losses due to fire are continuous in time. We develop an alternative formulation of the grass-fire feedback model that assumes that fires are discrete and occur stochastically in time to examine the influence of these assumptions on the predicted state of the system. We show that incorporating fire as a discrete event can produce a recurring temporal refuge in which both grass and trees co-occur in a stable, bounded savanna. In our model, tree abundance is limited without invoking demographic bottlenecks in the transition from fire-sensitive to fire-resistant life history stages. An increasing strength of grass feedback on fire results in regular, predictable fires, which suggests that the system can also be modeled using a set of difference equations. We implement this discrete system using modified Leslie/Gower difference equations and demonstrate the existence of a bounded savanna state in this model framework. Our results confirm the potential for grass feedbacks to result in stable savannas, and indicate the importance of modeling fire as a discrete event rather than as a loss rate that is continuous in time.     

Dynamic compartment approach for modelling regimes of carbon cycle functioning in bog ecosystems

Svirezhev's method of dynamic model design by a given “storage-flow” diagram [Svirezhev Y.M., 1997. On some general properties of trophic networks. Ecol. Model. 99, 7–17] is developed and used for investigating dynamic regimes of carbon cycle functioning in a typical boreal transitional bog ecosystem. Ecosystems are often represented by static “storage-flow” diagrams reflecting their structure and matter or energy transfer between components at fixed time moments. Using the data of such diagrams aggregated in ecological field studies one can construct a dynamic model of the ecosystem to predict its future behaviour and to estimate a response to external perturbations—natural and human. Stability of both current equilibrium and possible alternative steady states and more complicated attractors are studied under two types of parameter perturbation: CO₂ atmospheric concentration increase initiated by greenhouse effect, and change in the rate of carbon output from dead organic matter and litter which depends on the water table level and possible peat excavation. Calculation of bifurcation curves gives areas in the parameter space where stable functioning of carbon cycle is provided. Steady states can be interpreted as raised bog, meadow, forest and fen. CO₂ concentration increase leads the current state of transitional bog to loose stability with appearance of oscillatory dynamics and further evolution to the chaotic attractor. The model is rich by chaotic solutions serving as transition regimes between regular steady and periodic attractors. Another chaotic regime is formed from forest equilibrium and exists in the same area of phase space where current equilibrium is stable.     

Renewable Resources and Economic Sustainability: A Dynamic Analysis with Heterogeneous Time Preferences

In recent years there has been increasing interest in the study of economic sustainability and its relationship with natural resources. This paper attempts to shed some light on the issue by taking into account the individual variations in time preferences for consumption and resource amenity. We characterize the long-run steady state, analyze its asymptotic stability, and explore the transational dynamics from any initial state. The welfare implications of the optimal path are also discussed.     

Exhaustible Resource Allocation in an Overlapping Generations Economy

This paper analyzes competitive allocations of an exhaustible resource in an overlapping generations economy. Conditions are given for the existence of equilibrium extraction rules such that both extraction and investment in future stocks are increasing and continuous in the current stock. The paper then considers the time paths of equilibrium allocations and shows that there are economies where equilibrium resource extractions and prices exhibit nonclassical behavior. This is illustrated through a finite horizon example in which extractions increase and prices decrease over the entire time horizon and an infinite horizon example where there are persistent cycles in extractions and prices and multiple equilibria. The paper concludes by examining welfare issues.     

Learning to predict channel stability using biogeomorphic features

Current human land use activities are altering many components of the river landscape, resulting in unstable channels. Instability may have serious negative consequences for water quality, aquatic and riparian habitat, and for river-related human infrastructure such as bridges and roads. Resource management agencies have developed rapid bioassessment surveys to help assess stability in a fast and cost-effective way. While this assessment can be done for a single site fairly rapidly, it is still time-consuming to apply over large watersheds and assessment activities must be prioritized. We constructed a system that employs commonly available map data as inputs to cost-sensitive variants of decision tree algorithms to predict the relative channel stability of different sites. In particular, we use bagged lazy option trees (LOTs) and bagged probability estimation trees (PETs) to identify all unstable channels while making the smallest number of errors of classifying stable channels as unstable, thereby minimizing cost and maximizing safety. We measured the performance of the classifiers using ROC curves and found that the PETs performed better than the LOTs in situations where the number of instances of the stable and unstable classes were relatively balanced, but the LOTs did better where unstable examples were relatively rare compared to stable, perhaps due to the LOTs’ ability to focus on individual examples.     

Entry Deterrence and Signaling in a Nonrenewable Resource Model

We analyze a nonrenewable resource model in which an incumbent firm faces potential entry from a rival firm. The incumbent has private information about its stock size but the rival can observe extraction. With observable extraction and unobservable stock, the rival can use extraction as a signal about stock, from which it can infer whether entry is likely to be profitable. We characterize the necessary conditions for pooling and separating perfect Bayesian equilibria in a signaling game of resource extraction and provide examples of each. We show that the incumbent will often prefer pooling to separating even though welfare is higher in separating equilibrium.     

Large scale parameter study of an individual-based model of clonal plant with volunteer computing

Understanding clonal strategies (i.e. the ability of plants to reproduce vegetatively) is particularly important to explain species persistence. A clonal individual may be considered as a network of interconnected ramets that colonizes space. Resources in this network can be shared and/or stored. We developed an individual-based model (IBM) to simulate the growth of an individual clonal plant. Typically a realistic IBM requires a large set of parameters to adequately represent the complexity of the clonal plant growth. Simulations in the literature are often limited to small subsets of the parameter space and are guided by the a priori knowledge and with heuristic aims of the researcher. The aim of this paper was to demonstrate the benefit of volunteer computing in computational ecology to systematically browse the parameter space and analyze the simulation results in order to draw rigorous conclusions. To be specific, we simulated clonal plant growth using nine growth rules related to the metabolic process, plant architecture, resource sharing and storage and nineteen input parameters. We chose 2-4 values per input parameter which corresponded to 20 millions of combinations tested through volunteer computing. We used three criteria to evaluate plant performance: plant total resource, ramet production and maximum length of one branch. The 1% top-performing plants were sorted according to these criteria. Plant total resource and ramet production were correlated while considering the top-performing plants. The maximum length of one branch was independent from the other two performance traits. We detected two processes promoting at least one of the plant performance traits: (i) a relatively high metabolic gain (high photosynthetic activity and low production cost for new growth units), a low resource storage and long integration distance for resource sharing; (ii) short spacer lengths and the predominance of elongation of existing branches over branching. Interactive effects between parameter values were demonstrated for more than half of the input parameters. Best performance was reached for plants with slightly different combinations of values for these parameters (i.e. different strategies) rather than a single one (i.e. unique strategy). This modeling approach with volunteer computing enabled us to proceed to large-scale virtual experiments which provided a new quality of insight into ecological processes linked with clonal plant growth.     

Growth,deforestation and the efficiency of the REDD mechanism

This paper assesses the long term impacts of an international transfer called the Reduced Emissions from Deforestation and Degradation (REDD) mechanism, which aims at preserving tropical forests of the recipient economy. This two-sector economy faces a dilemma between economic growth and deforestation. The rural sector can substitute reproducible capital for agricultural land whereas the manufacturing sector only requires capital. The model shows that the REDD mechanism has a non-monotonic effect on steady state welfares. For low transfer schemes, the agricultural output increases with the transfer even though less land is under cultivation. For high transfer schemes, the increase in the transfer may not offset the decrease in the agricultural output. The open-loop symmetric Nash equilibrium in a dynamic deforestation game predicts that redistributing the transfer among a finite number of producers is less efficient in reducing deforestation than in the social optimum.