The role of mathematical modelling in understanding prokaryotic predation

With increasing levels of antimicrobial resistance impacting both human and animal health, novel means of treating resistant infections are urgently needed. Bacteriophages and predatory bacteria such as Bdellovibrio bacteriovorus have been proposed as suitable candidates for this role. Microbes also play a key environmental role as producers or recyclers of nutrients such as carbon and nitrogen, and predators have the capacity to be keystone species within microbial communities. To date, many studies have looked at the mechanisms of action of prokaryotic predators, their safety in in vivo models and their role and effectiveness under specific conditions. Mathematical models however allow researchers to investigate a wider range of scenarios, including aspects of predation that would be difficult, expensive, or time-consuming to investigate experimentally. We review here a history of modelling in prokaryote predation, from simple Lotka-Volterra models, through increasing levels of complexity, including multiple prey and predator species, and environmental and spatial factors. We consider how models have helped address questions around the mechanisms of action of predators and have allowed researchers to make predictions of the dynamics of predator–prey systems. We examine what models can tell us about qualitative and quantitative commonalities or differences between bacterial predators and bacteriophage or protists. We also highlight how models can address real-world situations such as the likely effectiveness of predators in removing prey species and their potential effects in shaping ecosystems. Finally, we look at research questions that are still to be addressed where models could be of benefit

Why Money Trickles Up - Wealth & Income Distributions

This paper combines ideas from classical economics and modern finance with the general Lotka-Volterra models of Levy & Solomon to provide straightforward explanations of wealth and income distributions. Using a simple and realistic economic formulation, the distributions of both wealth and income are fully explained. Both the power tail and the log-normal like body are fully captured. It is of note that the full distribution, including the power law tail, is created via the use of absolutely identical agents. It is further demonstrated that a simple scheme of compulsory saving could eliminate poverty at little cost to the taxpayer.Comment: 45 pages of text, 36 figure

Optimal economic planning and control for the management of ecosystems

In recent years the interest on sustainable systems has increased significantly. Among the many interested problems, creating and restoring sustainable ecosystems is a challenging and complex problem. One of the fundamental problems within this area is the imbalance between species that have a predator-prey relationship. Solutions involving management have become an integral player in many environments. Management systems typically use ad hoc methods to develop harvesting policies to control the populations of species to desired numbers. In order to amalgamate intelligence and structure, ecological systems require a diverse research effort from three primary fields: ecology, economics, and control theory. In this thesis, all three primary fields aforementioned are researched to develop a theoretical framework that includes an optimal trajectory planning system that exploits an ecosystem to maximize profits for the supporting community, and a robust control system design to track the optimal trajectories subjected to exogenous disturbances. Population ecology is used to select a model that identifies the key characteristics a management system needs to understand the behavior of the natural environment. A bioeconomic model is developed to relate the species populations to revenue. The nonlinear ecosystem is transformed into a linear parameter-varying (LPV) system that is then controlled using hinf synthesis and the gain scheduling methodology. The consequences of the results in this thesis are that optimal trajectories of an ecosystem can be obtained by constructing and solving a nonlinear programming problem (NLP), and the LPV based gain scheduling approach produces a robust controller that rejects disturbances and advises quality control policies to the manager an ecosystem. The LPV controller achieves comparable profits with satisfactory tracking performance while minding the induced costs of its high frequency output. Implications of constraining the control effort when designing for robustness are observed. Overall, the theoretical framework provides a solid foundation for future research on the understanding and improvement of ecosystem management

NL4Py: Agent-Based Modeling in Python with Parallelizable NetLogo Workspaces

NL4Py is a NetLogo controller software for Python, for the rapid, parallel execution of NetLogo models. NL4Py provides both headless (no graphical user interface) and GUI NetLogo workspace control through Python. Spurred on by the increasing availability of open-source computation and machine learning libraries on the Python package index, there is an increasing demand for such rapid, parallel execution of agent-based models through Python. NetLogo, being the language of choice for a majority of agent-based modeling driven research projects, requires an integration to Python for researchers looking to perform statistical analyses of agent-based model output using these libraries. Unfortunately, until the recent introduction of PyNetLogo, and now NL4Py, such a controller was unavailable. This article provides a detailed introduction into the usage of NL4Py and explains its client-server software architecture, highlighting architectural differences to PyNetLogo. A step-by-step demonstration of global sensitivity analysis and parameter calibration of the Wolf Sheep Predation model is then performed through NL4Py. Finally, NL4Py's performance is benchmarked against PyNetLogo and its combination with IPyParallel, and shown to provide significant savings in execution time over both configurations

The role of mathematical modelling in understanding prokaryotic predation

With increasing levels of antimicrobial resistance impacting both human and animal health, novel means of treating resistant infections are urgently needed. Bacteriophages and predatory bacteria such as Bdellovibrio bacteriovorus have been proposed as suitable candidates for this role. Microbes also play a key environmental role as producers or recyclers of nutrients such as carbon and nitrogen, and predators have the capacity to be keystone species within microbial communities. To date, many studies have looked at the mechanisms of action of prokaryotic predators, their safety in in vivo models and their role and effectiveness under specific conditions. Mathematical models however allow researchers to investigate a wider range of scenarios, including aspects of predation that would be difficult, expensive, or time-consuming to investigate experimentally. We review here a history of modelling in prokaryote predation, from simple Lotka-Volterra models, through increasing levels of complexity, including multiple prey and predator species, and environmental and spatial factors. We consider how models have helped address questions around the mechanisms of action of predators and have allowed researchers to make predictions of the dynamics of predator–prey systems. We examine what models can tell us about qualitative and quantitative commonalities or differences between bacterial predators and bacteriophage or protists. We also highlight how models can address real-world situations such as the likely effectiveness of predators in removing prey species and their potential effects in shaping ecosystems. Finally, we look at research questions that are still to be addressed where models could be of benefit

Roman Legal Tradition and the Mismanagement of Hunting Resources

Hunting and game-preservation are interrelated: hunting must respect the intentions of game-preservation, and game-preservation must rely on hunting as one method to achieve its intentions. HASENKAMP (1995) applied the Economic Theory of Common Resources to the problem to provide conclusions about the management and conservation of hunting resources. These conclusions are reflected in the existing relevant legal hunting setting in Germany. German Law contains legal principles that confronts the hunter with the objectives of hunting preservation and held him the responsibility for pursuing these goals. In our paper, we derive a model of hunting management, adapting the GORDON/SCHAEFER fisheries model. The conclusions of the model, similar with those of Hasenkamp, are confronted with Portuguese hunting regulation. We conclude that Portugal has a Roman legal tradition with respect to hunting propertyrights. To the Roman conception, the wild animals constitute res nullius (things without owner) that all men can appropriate by ocupatio. The classification of free land implicates the idea that the hunter has the freedom of access to hunt in other’s land, although respecting imposed norms. This tradition of open access is the root-cause of hunting depletion. But, at the same time, the legislator sees it as a form of giving the hunters without land, the possibility of enjoying this activity. This is compatible with the Portuguese tradition, which almost attributes a personality right to the right of hunting.

Risk-driven behaviour in the African leopard:how is leopard behaviour mediated by lion presence?

Agricultural expansion is restricting many carnivore species to smaller tracts of land, potentially forcing increased levels of overlap between competitors by constraining spatial partitioning. Understanding encounters between competitors is important because competition can influence species densities, distributions, and reproductive success. Despite this, little is known of the mechanisms that mediate coexistence between the African leopard (Panthera pardus) and its competitors. This project used GPS radiocollar data and playback experiments to understand risk-driven changes in the leopard’s behaviour and movement during actual and perceived encounters with lions (Panthera leo). Targeted playbacks of lion roars were used to elucidate immediate and short-lived behavioural responses in leopards when lions were perceived to be within the immediate area. To investigate the post-encounter spatial dynamics of leopard movements, the project used datasets from high-resolution GPS radiocollars deployed on leopards and lions with overlapping territories in the Okavango Delta, Botswana. Leopards were found to adapt behaviours and movements when lions were perceived to be nearby. Specifically, roar playbacks elicited longer periods of vigilance than controls, and movement directions were influenced by speaker locations. Further, leopard movements were quicker and more directional after encountering lions. However, adjustments in behaviour and movement were short-lived. The results provide insights into mechanisms used by the leopard to coexist with its competitors and are a useful case study of the methods that could be used to investigate encounter dynamics within other systems