Modelling the depletion of forestry resources by population and population pressure augmented industrialization

In this paper, a nonlinear mathematical model is proposed and analysed to study the depletion of forestry resources caused by population and population pressure augmented industrialization. It is shown that the equilibrium density of resource biomass decreases as the equilibrium densities of population and industrialization increase. It is found that even if the growth of population (whether intrinsic or by migration) is only partially dependent on resource, still the resource biomass is doomed to extinction due to large population pressure augmented industrialization. It is noted that for sustained industrialization, control measures on its growth are required to maintain the ecological stability.     

Modelling effects of industrialization,population and pollution on a renewable resource

In this paper, a mathematical model is proposed and analysed to study the simultaneous effect of industrialization, population and pollution on the depletion of a renewable resource. Criteria for local stability, global stability and instability are obtained. It is shown that if the densities of industrialization, population and pollution increase, then the density of the resource biomass decreases and it settles down at its equilibrium level whose magnitude is lower than its original carrying capacity. It is further noted that if these factors increase unabatedly, the resource biomass may be driven to extinction. Computer simulations are also performed to illustrate the results.     

Exclusionary population dynamics in size-structured,discrete competitive systems

A discrete multi-species size-structured competition model is considered. By using decreasing growth functions, we achieve the self-regulation of species. We develop various biologically significant conditions for global convergence to the extinction state of the dominated species in the competitive system. With an example we illustrate coexistence in a chaotic supr transient. The chaotic attractor has an unusual pulsating nature.     

Parasite population dynamics within a dynamic host population

Summary We propose a stochastic process model for a parasite population living within a host population. The host population is described by an immigration-death process. The parasite population in one host is an immigration-birth-death-emigration process. The death of all parasites at the moment of death of their host is regarded as emigration. We derive explicit expressions for the distributions of the size of the host population, of the parasite load of one host individual and of the parasite population in the total host population and obtain conditions for the existence of limiting distributions if time is tending to infinity. For particular lifetime distributions of hosts including parasite induced mortality and heterogeneous infection risk we finally derive properties of the limiting distributions.Dedicated to Klaus Krickeberg on the occasion of his 60th birthday     

The natural environment and optimal population growth

This paper investigates the optimal growth of a population when resources conserved for recreation (or the natural environment) enter the social welfare function. If the CES welfare function and the Cobb-Douglass production function are assumed, the growth rate of a population should be determined as a weighted average of the growth rates of per capita income and of conserved resources per capita. In the long run, there should be a limit to the growth of a population. Examples of numerical solutions for optimal time paths of a population are also presented.     

Biotic complexity of population dynamics

Changes in population size of animal species (lynx, muskrat, beaver, salmon, and fox), show diversification, episodic patterns in recurrence plots, novelty, nonrandom complexity, and asymmetric statistical distribution. These features of creativity characterize bios, a nonstationary pattern generated by bipolar feedback and multi‐agent predator–prey simulations, absent in chaotic attractors. Population series show partial‐autocorrelation, and the time series of the differences between consecutive terms also showed nonrandom patterns, differentiating bios from noise. As biotic patterns are found in quantum, cosmological, meteorological, biological, and economic processes, we propose that bipolar feedback is a generic process that contributes to the evolutionary generation of complexity at multiple levels of organization. © 2007 Wiley Periodicals, Inc. Complexity, 2008.     

Stochastic functional Kolmogorov-type population dynamics

In this paper we stochastically perturb the functional Kolmogorov-type system

into the stochastic functional differential equation

This paper studies existence and uniqueness of the global positive solution, and its asymptotic bound properties and moment average in time. These properties are natural requirements from the biological point of view. As the special cases, we discuss the various stochastic Lotka–Volterra systems.     

An empirical re-examination of natural resource scarcity and economic growth

This paper is concerned with the effect of natural resource scarcity on economic growth in the United States. After defining the notion of scarcity and introducing two measures of scarcity—unit costs and relative resource price—changes in resource scarcity trends for lead, zinc, nickel, aluminium, silver, iron and copper over the most recent three decades are investigated. Only for silver and iron is there any indication that such a change has occurred. For silver, the change is transitory. To the extent that change takes place, it has implications for future economic growth, i.e. natural resource scarcity and economic growth are interrelated. To see whether this is a relevant concern, subsequent to the examination of changing resource scarcity trends an objective effort is made to identify a long-run equilibrium relationship between natural resource scarcity and economic growth. Relying on cointegration techniques, only for the unit cost measure for lead and copper for one of the measures of cointegration is there a suggestion that natural resource scarcity has affected economic growth in the United States over the period 1889–1992.     

Fast game dynamics coupled to slow population dynamics: A single population with hawk-dove strategies

We study a model of a population subdivided into two subpopulations corresponding to hawk and dove tactics. It is assumed that the hawk and dove individuals compete for a resource every Day, I.e., at a fast time scale. This fast part of the model is coupled to a slow part which describes the growth of the subpopulations and the long term effects of the encounters between the individuals which must fight to have an access to the resource. We aggregate the model into a single equation for the total population. It is shown that in the case of a constant game matrix, the total population grows according to a logistic curve whose τ and K parameters are related to the coefficients of the hawk-dove game matrix. Our result shows that high equilibrium density populations are mainly doves, whereas low equilibrium density populations are mainly hawks. We also study the case of a density dependent game matrix for which the gain is linearly decreasing with the total density.     

Innovation as a policy strategy for natural resource protection

Growing global food demands place major strains on water resources, including quality impairments and increased water scarcity. Drawing on the largely separate bodies of literature on externalities and technological innovation, this article develops a dynamic framework to explore the long‐term impacts of alternative policy approaches to the agricultural impacts on water resources. Environmental policies, which focus on correcting environmental externalities, lead to an overall gain because costs to farmers are more than offset by reduced environmental damages. Technology policies, which direct public investments into agricultural eco‐innovations, lead to benefits for farmers as well as the environment. Joint implementation of both types of policies leads to the largest overall gain. In principle, a technology policy alone could have greater environmental benefits than an environmental policy alone. This outcome is most likely in cases where the productivity effect of new technology is large and the cost of research is low. Recommendations for research managers

• As an alternative to traditional environmental policy, investments in research can provide win–win solutions that benefit the environment and agricultural producers.
• Conceivably, eco‐innovations could lead to environmental conditions that are better than those achieved by environmental policy alone.
• Adding research investments to existing environmental policy would lead to further improvements in environmental quality while also benefitting farmers.
• Unlike environmental policies that are perceived to impose costs on agriculture, technology policies impart benefits to farmers and are less likely to face political opposition from industry.
• Technology policies are likely to be the most effective when eco‐innovation leads to technologies that meaningfully reduce environmental impacts and also raise farm productivity.

     

Synergetic Approach and modeling of fish population dynamics

In the last few years it has become increasingly obvious that one of the obstacles in the way of constructing good simulation models of the global ocean ecosystem is a poor understanding of the general principles of marine ecosystems processes. A great number of factors and relationships acting in the marine environment, in combination with the random character of change in many of them, call for the development of new approaches in modeling. In this paper a synergetic approach is proposed. A new paradigm for this approach is discussed. As an example a population with logistic natural growth under different conditions of exploitation is considered. It is shown that the simplest mechanism, that principally changes the behavior of a population in a fluctuating environment, includes fishing and migration. This mechanism explains catastrophic changes in population abundance in cases when no one factor may be seen as exclusive. It is shown that the characteristic level of population number does not correspond to the average balance between input (migration), output (fishing) and the growth of the population. The environment variability leads to stabilization far from equilibrium. This totally conforms to one of the fundamental results in Synergetics which assert that nonequilibrium in the presence of fluctuations may serve as a source of new order.     

Distributed modelling of deterministic and stochastic population dynamics

In many problems of practical purpose, one is interested not only in the study of the total population of the overall system, but also in the distribution of the population depending upon some characteristic parameters. This necessity is patent in biological systems defined on a wide range of distributed features, but it is also in order when one tries to analyze social systems by means of population models. As a matter of fact, with this objective in mind, we deal with infinite species population models.This study discusses this question, proposes a distributed version for the logistic equation, and examines the existence of stationary solutions. The problem of the influence of environmental noise on the dynamics of the distributed population is considered, and a model is proposed. A detailed analysis is carried out around the stationary solution via a linearization technique, and the covariance equation is derived.     

Stochastic population dynamics under regime switching

In this paper we will develop a new stochastic population model under regime switching. Our model takes both white and color environmental noises into account. We will show that the white noise suppresses explosions in population dynamics. Moreover, from the point of population dynamics, our new model has more desired properties than some existing stochastic population models. In particular, we show that our model is stochastically ultimately bounded.     

Competitive Lotka-Volterra population dynamics with jumps

This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show that a stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) we discuss the uniform boundedness of the pth moment with p>0 and reveal the sample Lyapunov exponents; (c) using a variation-of-constants formula for a class of SDEs with jumps, we provide an explicit solution for one-dimensional competitive Lotka-Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our n-dimensional model.     

Baseline models of spatial population dynamics

To understand human population dynamics fully, before considering complex human agency it may be useful to construct baseline models to see where such agency may and may not be necessary. In fact, the dynamics of human populations may be amenable to mathematical modeling with relatively parsimonious mechanisms. We review some of the more prominent of such models, namely, the spatial Galton-Watson (GW) model, modifications of the GW model that add migration and immigration, and the Bolker-Pacala model, in which mortality (or birth rate) is affected by competition. We show that change in the distribution of population density over the last century for 12 American rural states may be captured by the simplest of the models, the spatial GW model.     

An inverse problem in population dynamics

The evolution of population densities of two interacting species in presence of diffusion phenomena is governed by a system of semilinear Volterra integrodifferential parabolic equations. In this system there are time convolution integrals, accounting for past history effects, which are essentially characterized by kernels depending on time only. These delay kernels can be viewed as entries of a 2x2 matrix K. The inverse problem of determining K via suitable population measurements is analyzed.     

On a size-structured population dynamics model

We consider a linear size-structured population dynamics model. For this model with a nonlinear global boundary condition that has a biological meaning, we obtain a solution in constructive form.     

Chaotic population dynamics and biology of the top-predator

We study how the dynamics of a food chain depends on the biology of the top-predator. We consider two model food chains with specialist and generalist top-predators. Both types of food chains display same type of chaotic behavior, short-term recurrent chaos; but the generating mechanisms are drastically different. Food chains with specialist top-predators are dictated by exogenous stochastic factors. On the contrary, the dynamics of those with the generalist top-predator is governed by deterministic changes in system parameters. The study also suggests that robust chaos would be a rarity.