Abstract
Environmental systems, whether they be weather patterns or predator-prey relationships, are dependent on a number of different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult to accurately predict meaningful behavioral trends far into the future. However, such dynamics do not warrant complete ignorance of different efforts to understand and model close approximations of these systems. Towards this end, we have applied a logical modeling approach to model and analyze the behavioral trends and systematic trajectories that these systems exhibit without delving into their quantification. This approach, formalized by Rene Thomas for discrete logical modeling of Biological Regulatory Networks (BRNs) and further extended in our previous studies as parametric biological linear hybrid automata (Bio-LHA), has been previously employed for the analyses of different molecular regulatory interactions occurring across various cells and microbial species. As relationships between different interacting components of a system can be simplified as positive or negative influences, we can employ the Bio-LHA framework to represent different components of the environmental system as positive or negative feedbacks. In the present study, we highlight the benefits of hybrid (discrete/continuous) modeling which lead to refinements among the fore-casted behaviors in order to find out which ones are actually possible. We have taken two case studies: an interaction of three microbial species in a freshwater pond, and a more complex atmospheric system, to show the applications of the Bio-LHA methodology for the timed hybrid modeling of environmental systems. Results show that the approach using the Bio-LHA is a viable method for behavioral modeling of complex environmental systems by finding timing constraints while keeping the complexity of the model at a minimum.
Highlights
The application of Parametric Biological Linear Hybrid Automata is not new (Ahmad et al, 2009, 2012; Aslam et al, 2014; Paracha et al, 2014 to name a few), in this paper we present its application to a new set of problems, namely the modeling of environmental systems
We successfully model two case studies representing different systems from a broad spectrum of mechanisms encompassed by environmental systems, which shows the versatility of the modeling framework toward its applicability
In the first case study, our framework modeled the arbitrary population levels between different microbes in a freshwater pond, showing how hybrid modeling can be used to study different behavioral tendencies of the populations represented by population balance and overpopulation, while removing the complexity of dealing with actual population numbers
Summary
In contrast to more traditional systems, as studied in other physical sciences, environmental systems are tightly integrated with each other, forming different sub-domains within each system (Hanrahan, 2010). As such, they are difficult to study in isolation since their behavior changes with respect to other environmental factors working in conjunction with each other (Hanrahan, 2010). Certain aspects of the system elude these approaches, such as the larger view of the behaviors of the system–statistical methods do not represent the dynamics of the system, probabilistic approaches lack deterministic predictability, and differential and AI models suffer from high levels of complexity when modeling realistic parameters
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