Cybernetic formulation of control in ecosystems

Hierarchical control formulations are given for a simple predator-prey model: self-optimization of one subsystem, natural multi-goal optimization, man's multiparameter control of an ecosystem and man's control of a self-optimizing ecosystem. Natural multigoal optimization suggests how several levels of an ecosystem can be optimized simultaneously. The idea of management of a self-optimizing ecosystem takes into account the reactions of the ecosystem to man's activity.     

Theory and estimation of the household production function for wildlife recreation

The household production function is an intuitively appealing way to model man's interaction with nature. This paper models the interaction between the household's behavior and publicly provided inputs into wildlife recreation. The paper shows how to compute benefits, assuming that the household production function is known. The household production function approach collapses to the simple travel cost approach when households are unable to substitute their own inputs for publicly provided inputs. In addition, the paper demonstrates the conditions under which the parameters of cost and preference functions can be identified. The conditions for identification are quite restrictive when several choices are endogenous.     

The economic theory of species extinction: Comment on smith

A widely recognized article by Smith suggests that harvesting leading to species extinction may be socially optimal, provided that the species growth-potential is sufficiently low. It is shown that this conclusion hinges on special assumptions about harvest technology which, despite a superficial compatibility with neoclassical production theory, contradict a basic postulate of a pioneering article by Gordon. As soon as Gordon's postulate is taken into account, while all other aspects of Smith's model are maintained, it turns out that even a species with a very low growth potential should not become extinct.     

Simulating fish production using exponential smoothing

The variation over time of the total annual production of pe and the United Kingdom has been described quantitatively using the exponential smoothing technique. The exercise was repeated on annual mackerel landings for the same two countries. It is suggested that in some cases, the production figure for the current year can be used to simulate the following year's value. The greater variations in South Africa's annual production probably gave rise to the poorer results for these data.     

Free energy flow in the process of collecting material for body build up of aquatic organisms

A general formula defining the free energy expenditures in the processes of algal nutrition and zooplankton feeding has been derived. It appears to be symmetrical in respect of space and time scales. In conditions of optimal control the theoretical relationship between effective free energy expenditures and losses appears to be the ‘golden proportion’. The general trends of the system due to the first and second laws of thermodynamics and Prigogine's theorem form a theoretical basis for phenomenological rules of ecosystem's development.     

Intertemporal and intergenerational pareto efficiency revisited

This paper demonstrates that Bishop's formulation deviates in a fundamental way from our model and, in so doing, Bishop has assumed the problem away. Bishop utilizes a utility function that is too general to discriminate the time pattern of consumption from that of production. Hence, the intertemporal nature of the goods that we analyzed cannot be captured by Bishop's representation. Furthermore, we show that current benefit cost methods that discount the benefit stream of a public asset are Pareto intertemporally inefficient.     

The backward incidence of pollution control—some comparative statics in general equilibrium

The backward incidence of stronger pollution controls onto the factors of production is examined in a two sector (one polluting, one not), general equilibrium model. The real returns to labor and capital are found to move in opposite directions that depend on the factor intensity of the nonpolluting sector. The magnitudes of these effects are shown dependent upon the degree of factor intensity in that sector, the ease with which pollution can be removed from the effluent, the ease with which capital and labor can be substituted in either sector, and the price elasticities of demand for the sectors' products.     

The economics of enforcing air pollution controls

The goal of this paper is to determine the likely effect on a firm's control actions of alternative implementation and enforcement policies available to the control agency. Three alternatives are studied, legal enforcement through the new source performance standards set forth by EPA, and two effluent fee enforcement alternatives. First, a generalized model of the effects of implementation and enforcement policies on the firm's control action is developed. This model assumes that the firm is an expected cost minimizer. The model is then applied to the case of particulate matter discharges from coal-fired power plants in order to estimate empirically the effect of policy alternatives on the firm's control efforts. Finally, the results of the model and its empirical application are used to develop policy functions which relate control to the values of various policy parameters. These results lead us to several policy recommendations.     

A note on the willingness to pay approach to the valuation of longevity

A modification of Freeman's model of willingness to pay for reduction of environmental risk to life is presented. Rather than treating work-related, consumption-related, and exogenous hazards as additive components of an overall level of safety, the revised model acknowledges the interdependence of these components. The results derived from this approach imply that (a) willingness to pay for a marginal reduction in risk depends upon the individual's initial level of utility; and (b) willingness to pay for a reduction in a given component of safety is related to the level of each component risk. The results of the revised model become more dramatic at higher levels of risk.     

Turbulence and phytoplankton diversity: A general model of the “paradox of plankton”

The principle of “competitive exclusion” predicts that no two species can occupy the same ecological niche at the same time and place (Hardin, 1960). Hutchinson (1953, 1961) suggested that the vast diversity of phytoplankton observed in many aquatic environments presents an apparent contradiction to this principle. Since all phytoplankton compete for the same basic resources, and since the euphotic zones of most natural waters are relatively homogeneous, such coexisting plankters appear to be simultaneously occupying the same niche. In this paper we present simulation results from a mathematical model wherein we examine the hypothesis that physical turbulence in an aquatic system can mollify interactive pressures between plankton populations and allow coexistence of species competing for the same resources. Using Bella's (1972) highly simplified model as a point of departure, we develop a new model, explicitly incorporating gross physiological mechanisms, to investigate the effects of both advective and turbulent components of water movement on the growth of three competing phytoplankton species. We observed that, in the absence of water motion, no two species were able to coexist, while under the hypothetical conditions of advection without turbulence (laminar flow), just two species were able to occur contemporaneously. Coexistence of all three species was achieved only with the addition of a random turbulent component to the model's hydrodynamic function. Moreover, this general coexistence was observed only when the major turbulent frequency approached the turnover rate of phytoplankton populations. We suggest that there is a limited region of periodicities and magnitudes for hydrodynamic energy in which phytoplankton can coexist, and that most natural aquatic environments fall within this region. We further speculate that, in general, the coupling of physical and biological processes in nature may be influenced by the relative frequency characteristics of those processes.     

Modeling the annual thermal regime of lake Ohrid,Yugoslavia, using daily weather data

The time-dependent characteristics of the five weather variables which control the annual thermal response of Lake Ohrid are analyzed in detail. These are daily values for solar radiation, air temperature, humidity, wind speed and cloud cover. A simple numerical model of the lake's thermal response, forced by thermally driven density mixing, is developed and tested using observed thermal profiles for verification. The numerical model successfully reproduces the major features of the lake's thermal regime over a 6 y period from 1972 to 1977, the average root mean square value for the simulated profiles being 1.2°C with extremes of 2.2 and 0.3°C and a standard deviation of 0.4°C.     

Adequacy of ecosystem models

A formal approach is developed to assess the adequacy of mathematical models to represent a given ecosystem. The procedure is based on the hypothesis that two or several models of an environment can be compared by using a vectorial approach: several model properties are analyzed and related to the model's capability to simulate the observed behaviour and to describe the ecosystem processes. The models are thus ordered from the standpoint of their adequacy. One preliminary model, a more recent one, and four lumped versions of the latter have been tested for adequacy. These models were developed by Wiegert and they describe the behaviour of an algal-fly community energetics in a thermal spring. Results obtained by our procedure agree with Wiegert's but some new points have been emphasized.     

Modelling the biochemical oxidation processes in artificial conditions of waste treatment plants

For natural water bodies there are many models of biochemical oxidation of organic pollutants, from simple to complicated ones. For the artificial conditions of waste water treatment plants there are numerous models of oxidation processes too. The authors believe that a better understanding of these processes in nature would be gained if the oxidation processes in more simple artificial conditions were understood.An attempt has been made to explain the variety of types of models of waste treatment in an activated sludge system or a biofilm reactor by the diffusion mechanism of oxidation of single substrates on the one hand, and by superposition of the kinetics of oxidation of single substrates in measurements of the dynamics of oxidation of a complex pollutant on the other hand.The conditions in which zero- and first-order models are valid in the oxidation of single substrates are derived. Respective formulae for rate constants are given. Monod's model is valid in a broader range of substrate concentration variations. An approximate formula for the half-saturation constant is proposed. Satisfactory agreement with experimental data for glucose and ammonia substrates is shown.The formal character of models being used at present is claimed for multicomponent substrates. The accuracy of the calculation is largely governed by the number of model coefficients. Similar results obtained by Monod's and Grau's models, often used in practice, are emphasized.     

A political economy model of implementing pollution laws

A model of the implementation process as applied in pollution control is developed. It differs from previous bureaucracy models in that it subjects the control agency to pressures from both firms and procontrol citizen groups. Each of these three actors maximizes utility over environmental quality and some other variable. Environmental quality may be in the actor's preference function or it may represent derived demand. Working through the agency budget and other policy variables, each actor constrains another actor's attempts to move policy in preferred directions. This results in movement toward a concensus environmental quality, not necessarily the efficient quality. Several institutional changes are analyzed to demonstrate the workings of the model.     

A test of two models of different levels of complexity for predicting changes of phosphorus concentration in a lake's outflow

The objective of this investigation is to compare the ability of a one-box model and a two-box model to predict the temporal variations of total phosphorus in the outflow of several lakes. The one-box model considers only total phosphorus and treats the lake as well-mixed, all year round. The two-box model considers two phosphorus fractions and the epilimnion and hypolimnion. For five shallow Canadian Shield lakes, some of the temporal variability in lake phosphorus concentrations can be explained on the basis of changes in hydraulic inflows and phosphorus loadings. Both models give roughly similar predictions for shallow lakes with high hydraulic loadings (1–200 m/year) and small variations in total phosphorus concentrations. In comparing the settling and hydraulic outflow mechanisms, a sensitivity analysis shows that both models are more sensitive to the settling rate if the lake's hydraulic loadings are less than 1 m/year, and more sensitive to the outflow rate if the lake's hydraulic loadings are greater than 100 m/year. This analysis suggests a priority for concentrating economic and other resources in conducting field measurement programs for testing phosphorus models.     

Fuel switching,gasoline price controls,and the leaded-unleaded gasoline price differential

The Environmental Protection Agency and others have opposed gasoline price decontrol, alleging a wider posted price differential between leaded and unleaded grades would result, inducing more motorists to switch illegally to leaded gasoline fouling catalytic converters and hence increasing air pollution. EPA's model must assume that only the unleaded price ceiling is binding. It is shown that the resulting excess demand is shifted to a close substitute: leaded gasoline. Hence, controls cause more consumption of leaded fuel in new cars (switching) and more pollution. Thus, decontrol would have a palliative effect, contrary to EPA's claim.     

Testing model feasibility and sufficiency through laboratory simulation: A case study

Complex computer simulations of ecological models often fail to have much impact on later stages of applied research and management. We believe that this reflects a methodological gap. We present a case study where we try to bridge this gap. A recently published general model for insect outbreak has not yet been tested adequately in the field because of the complexity, size, and time involved in real-world insect pest outbreaks. However, a modified version of the model can be used to predict complex dynamics for a laboratory managed population of vinegar flies (Drosophila melanogaster).A comparison of the dynamics of the laboratory system with the simulation predictions allowed us to conclude that the model is “feasible”, i.e. under certain circumstances the model can predict the dynamics of some real system. These results were obtained despite considerable environmental and biological variability, indicating the robustness of the model. The factors chosen for the model appear to be “sufficient” to describe the real system's essential dynamics. Testing for feasibility and sufficiency should, in our opinion, always precede the much more expensive stages of field testing.     

Calculation and use of selectivity coefficients of feeding: Zooplankton grazing

A straightforward method for calculating selectivity coefficients (W_ij) of predation from raw data, mortality rates of prey, filtering rates, feeding rates and electivity indices is derived. Results from a comparison of selectivity coefficients for the copepod Diaptomus oregonensis grazing under a number of experimental conditions suggest that W_ij's for size-selective feeding are invariant, a conclusion also supported by the leaky-sieve model. Recommendations are made on how to use W_ij's in linear and nonlinear feeding constructs for zooplankton and other animals.