OBSERVABILITY AND OBSERVERS IN A FOOD WEB

The problem of the possibility to recover the time-dependent state of a whole population system out of the observation of certain components has been studied in earlier publications, in terms of the observability concept of mathematical systems theory. In the present note a method is proposed to effectively calculate the state process. For an illustration an observer system for a simple food web is numerically constructed

VERTICUM-TYPE SYSTEMS APPLIED TO ECOLOGICAL MONITORING

In the paper ecological interaction chains of the type resource – producer – primary user – secondary consumer are considered. The dynamic behaviour of these four-level chains is modelled by a system of differential equations, the linearization of which is a verticum-type system introduced for the study of industrial verticums. Applying the technique of such systems, for the monitoring of the considered ecological system, an observer system is constructed, which makes it possible to recover the whole state process from the partial observation of the ecological interaction chain

Observer design for open and closed trophic chains

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. Such systems-theoretical approach has been applied before by the authors to Lotka–Volterra type population systems. In the present paper this methodology is extended to a non-Lotka–Volterra type trophic chain of resource–producer–primary consumer type and numerical examples for different observation situations are also presented

Design of a Cascade Observer for a Model of Bacterial Batch Culture with Nutrient Recycling

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Recent Developments in Monitoring of Complex Population Systems

The paper is an update of two earlier review papers concerning the application of the methodology of mathematical systems theory to population ecology, a research line initiated two decades ago. At the beginning the research was con- centrated on basic qualitative properties of ecological models, such as observability and controllability. Observability is closely related to the monitoring problem of ecosystems, while controllability concerns both sustainable harvesting of population systems and equilibrium control of such systems, which is a major concern of conservation biology. For population system, observability means that, e.g. from partial observation of the system (observing only certain indica- tor species), in principle the whole state process can be recovered. Recently, for different ecosystems, the so-called ob- server systems (or state estimators) have been constructed that enable us to effectively estimate the whole state process from the observation. This technique offers an efficient methodology for monitoring of complex ecosystems (including spatially and stage-structured population systems). In this way, from the observation of a few indicator species the state of the whole complex system can be monitored, in particular certain abiotic effects such as environmental contamina- tion can be identified. In this review, with simple and transparent examples, three topics illustrate the recent develop- ments in monitoring methodology of ecological systems: stock estimation of a fish population with reserve area; and observer construction for two vertically structured population systems (verticum-type systems): a four-level ecological chain and a stage-structured fishery model with reserve area

Nonlinear Sliding Mode Observer Applied to Microalgae Growth

Modeling biological processes, such as algae growth, is an area of ongoing research. The ability to understand the multitude of parameters that influence this system provides a platform for better understanding the dynamics of microalgae growth. Empirical modeling efforts look to understand sources of driving nutrients that influence harmful algal blooms (HABs). These harmful algal blooms are dense aggregates that have an increasingly negative impact on local economics, marine and freshwater systems, and public health. They result from a high influx of nitrogen and nutrients that drive the algae biomass to exponentially grow. This growth blocks out the sun, potentially releases dangerous toxins, and suffocates marine life, damaging ecosystems, especially in Florida. Modeling microalgae behavior and growth is complex due to its nonlinear behavior and coupled variables. Recently, cultivating oleaginous microalgae for biofuel production has been another region of ongoing research, especially application of observer theory to estimate internal parameters that are not easily measured in algal systems. Linear observer theory has generally been applied to algae growth systems to estimate internal parameters that are beyond hardware sensor capabilities, but they are still severely limited. Nonlinear observer theory application to biological systems is still relatively new. This thesis explores the application of a nonlinear observer based off sliding mode to an algae system. Sliding mode is derived from modern control theory and is based off variable structure control. An algae system is modeled using the widely accepted Droop model for algae growth and a linear and nonlinear sliding mode observer is developed for the system to estimate internal nitrogen within the algae biomass

Innovation and Diffusion

The contribution made by innovation and new technologies to economic growth and welfare is largely determined by the rate and manner by which innovations diffuse throughout the relevant population, but this topic has been a somewhat neglected one in the economics of innovation. This chapter, written for a handbook on innovation, provides a historical and comparative perspective on diffusion that looks at the broad determinants of diffusion, economic, social, and institutional, viewed from a microeconomic perspective. A framework for thinking about these determinants is presented along with a brief nontechnical review of modeling strategies used in different social scientific literatures. It concludes with a discussion of gaps in our understanding and potential future research questions.

MONITORING ENVIRONMENTAL CHANGE IN AN ECOSYSTEM

The monitoring and analysis of the processes taking place in an ecosystem is a key issue for a sustainable human activity. A system of populations, as the biotic component of a complex ecosystem is usually affected by the variation of its abiotic environment. Even in nearly natural ecosystems an abiotic effect like climatic implications of global warming may cause important changes in the dynamics of the population system. In ecosystems involving field cultivation or any industrial activity; the abiotic parameter in question may be the concentration of a substance, changing e.g. as a result of pollution, application of a pesticide, or a fertilizer, etc. In many cases the observation of the densities of each population may be technically complicated or expensive, therefore the question arises whether from the observation of the densities of certain (indicator) populations, the whole state process of the population system can be uniquely recovered. The paper is aimed at a methodological development of the state monitoring, under the conditions of a changing environment. It is shown, how the technique of mathematical systems theory can be applied not only for the approximate calculation of the state process on the basis of the observed data, even under the effect of an exogene abiotic change with known dynamics; but in certain cases, also for the estimation of the unknown biological effect of the change of an abiotic parameter. The proposed methodology is applied to simple illustrative examples concerning a three-species predator-prey system

OPEN- AND CLOSED-LOOP EQUILIBRIUM CONTROL OF TROPHIC CHAINS

If a nearly natural population system is deviated from its equilibrium, an important task of conservation ecology may be to control it back into equilibrium. In the paper a trophic chain is considered, and control systems are obtained by changing certain model parameters into control variables. For the equilibrium control two approaches are proposed. First, for a fixed time interval, local controllability into equilibrium is proved, and applying tools of optimal control, it is also shown how an appropriate open-loop control can be determined that actually controls the system into the equilibrium in given time. Another considered problem is to control the system to a new desired equilibrium. The problem is solved by the construction of a closed-loop control which asymptotically steers the trophic chain into this new equilibrium. In this way, actually, a controlled regime shift is realized

Development of a Health Management Information System for the Mountain Gorilla (Gorilla Beringei)

The Mountain Gorillas of Central Africa are one of the most highly endangered species in the world, with only 740 individuals surviving. One of the greatest threats to this species is disease. Health of wildlife is continually garnering more attention in the public arena due to recent outbreaks of diseases such as West Nile and High Pathogenic Avian Influenza. However, no system currently exists to facilitate the management and analysis of wildlife health data. The research conducted herein was the development and testing of a health information monitoring system for the mountain gorillas entitled Internet-supported Management Program to Assist Conservation Technologies or IMPACT?. The system functions around a species database of known or unknown individuals and provides individual-based and population-based epidemiological analysis. The system also uses spatial locations of individuals or samples to link multiple species together based on spatial proximity for inter-species comparisons. A syndromic surveillance system or clinical decision tree was developed to collect standardized data to better understand the ecology of diseases within the gorilla population. The system is hierarchical in nature, using trackers and guides to conduct daily observations while specially trained veterinarians are used to confirm and assess any abnormalities detected. Assessment of the decision tree indicated that trackers and guides did not observe gorilla groups or individuals within groups similarly. Data suggests that, to be consistent, trackers and guides need to conduct observations even on the day that veterinarians collect data. Validity and reliability remain to be tested in the observation instrument. Assessment of pathogen loads and distributions within species surrounding the gorillas indicates that humans have the greatest pathogen loads with 13 species, followed by cattle and chimpanzees (11), baboon (10), gorillas (9), and rodents (3). Spatial aggregation occurred in Cryptosporidium, Giardia, and Trichuris; however, there is reason to question the test results of the former 2 species. These data suggest that researchers need to examine the impact of local human and domestic animal populations on gorillas and other wildlife