Developments In Ecological Modeling Based On Cellular Automata

The models with focus on spatial clumping generally fail to consider the effects of local interactions and spatial contrasting. These factors are sometimes conclusive to the developments of ecosystems. Cellular Automata are individual potent systems in which many simple components act together locally to bring complex patterns, which may explain “self-organizing” behavior. Since cellular automaton has ability to consider local influences and spatial disparateness, it has been applied to various fields. This paper attempts to highlight important aspects of Cellular Automata and is centered on the development and application of the approach to ecological modeling. The results indicate that spatially distinct models such as cellular automata have a special capacity to connect the local operations and universal figures hence resulting in complex patterns. Keywords: Cellular automata, ecological modeling, spatially contrastin

A Symmetric Intraguild Predation Model for the Invasive Lionfish and Native Grouper

Abstract Lionfish are top-level venomous predators native to the Indo-Pacific Ocean. Over the past decade, the species Pterois volitans and P. miles have become established throughout most of the western Atlantic Ocean, where they drastically impact coral reef communities. Overfishing of native species, such as grouper, who share their niche with lionfish may be the reason for the lionfish's success; research has suggested that at high density, groupers can act as a lionfish biocontrol. To determine if competition or predation is the mechanism behind lionfish suppression, we construct a symmetric intraguild predation model of lionfish, grouper, and prey. Thus, we assume lionfish and grouper compete for prey in addition to consuming juveniles of the other species. Holling type I functional responses are used to represent fecundity and predation. We conduct an equilibrium stability analysis and bifurcation analysis of the general model, and find that the system is able to coexist in an equilibrium or sustainable oscillations. After estimating parameter ranges, simulations and a sensitivity analysis indicate the parameters most influential to lionfish growth rate. The implied control strategies are then tested by varying harvesting and predation rates

Dynamical Models of Biology and Medicine

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicin

Optimization and Control of Agent-Based Models in Biology: A Perspective

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them

Managing infectious diseases over connected populations: a non-convex optimal control

The paper develops an optimal control model to analyse various management options for infectious diseases that occur in metapopulations, under both Nash and cooperative behaviour. As pathogens are renewable resources with negative value, the problem may be non-convex. Since the disease can be transmitted across various connected populations, externalities are involved. Both aspects deserve attention as two issues arise: a) is eradication of the disease in finite time preferable to indefinite treatment? b) are cooperative solutions well-behaved? The problem is solved numerically and the results indicate that while eradication is likely to be an optimal strategy when initial levels of infections are relatively low, the internalisation of between-population externalities (as indicated by the first order necessary conditions of the cooperative optimal control problem) might not always be possible. Also, ignoring these two aspects can lead to inadequate policy design.infectious diseases; metapopulation; non-convexities; optimal control

Collective Information Processing and Criticality, Evolution and Limited Attention.

Im ersten Teil analysiere ich die Selbstorganisation zur Kritikalität (hier ein Phasenübergang von Ordnung zu Unordnung) und untersuche, ob Evolution ein möglicher Organisationsmechanismus ist. Die Kernfrage ist, ob sich ein simulierter kohäsiver Schwarm, der versucht, einem Raubtier auszuweichen, durch Evolution selbst zum kritischen Punkt entwickelt, um das Ausweichen zu optimieren? Es stellt sich heraus, dass (i) die Gruppe den Jäger am besten am kritischen Punkt vermeidet, aber (ii) nicht durch einer verstärkten Reaktion, sondern durch strukturelle Veränderungen, (iii) das Gruppenoptimum ist evolutionär unstabiler aufgrund einer maximalen räumlichen Selbstsortierung der Individuen. Im zweiten Teil modelliere ich experimentell beobachtete Unterschiede im kollektiven Verhalten von Fischgruppen, die über mehrere Generationen verschiedenen Arten von größenabhängiger Selektion ausgesetzt waren. Diese Größenselektion soll Freizeitfischerei (kleine Fische werden freigelassen, große werden konsumiert) und die kommerzielle Fischerei mit großen Netzbreiten (kleine/junge Individuen können entkommen) nachahmen. Die zeigt sich, dass das Fangen großer Fische den Zusammenhalt und die Risikobereitschaft der Individuen reduziert. Beide Befunde lassen sich mechanistisch durch einen Aufmerksamkeits-Kompromiss zwischen Sozial- und Umweltinformationen erklären. Im letzten Teil der Arbeit quantifiziere ich die kollektive Informationsverarbeitung im Feld. Das Studiensystem ist eine an sulfidische Wasserbedingungen angepasste Fischart mit einem kollektiven Fluchtverhalten vor Vögeln (wiederholte kollektive Fluchttauchgängen). Die Fische sind etwa 2 Zentimeter groß, aber die kollektive Welle breitet sich über Meter in dichten Schwärmen an der Oberfläche aus. Es zeigt sich, dass die Wellengeschwindigkeit schwach mit der Polarisation zunimmt, bei einer optimalen Dichte am schnellsten ist und von ihrer Richtung relativ zur Schwarmorientierung abhängt.In the first part, I focus on the self-organization to criticality (here an order-disorder phase transition) and investigate if evolution is a possible self-tuning mechanism. Does a simulated cohesive swarm that tries to avoid a pursuing predator self-tunes itself by evolution to the critical point to optimize avoidance? It turns out that (i) the best group avoidance is at criticality but (ii) not due to an enhanced response but because of structural changes (fundamentally linked to criticality), (iii) the group optimum is not an evolutionary stable state, in fact (iv) it is an evolutionary accelerator due to a maximal spatial self-sorting of individuals causing spatial selection. In the second part, I model experimentally observed differences in collective behavior of fish groups subject to multiple generation of different types of size-dependent selection. The real world analog to this experimental evolution is recreational fishery (small fish are released, large are consumed) and commercial fishing with large net widths (small/young individuals can escape). The results suggest that large harvesting reduces cohesion and risk taking of individuals. I show that both findings can be mechanistically explained based on an attention trade-off between social and environmental information. Furthermore, I numerically analyze how differently size-harvested groups perform in a natural predator and fishing scenario. In the last part of the thesis, I quantify the collective information processing in the field. The study system is a fish species adapted to sulfidic water conditions with a collective escape behavior from aerial predators which manifests in repeated collective escape dives. These fish measure about 2 centimeters, but the collective wave spreads across meters in dense shoals at the surface. I find that wave speed increases weakly with polarization, is fastest at an optimal density and depends on its direction relative to shoal orientation