Social decision-making driven by artistic explore-exploit tension

We studied social decision-making in the rule-based improvisational dance $There$ $Might$ $Be$ $Others$, where dancers make in-the-moment compositional choices. Rehearsals provided a natural test-bed with communication restricted to non-verbal cues. We observed a key artistic explore-exploit tension in which the dancers switched between exploitation of existing artistic opportunities and riskier exploration of new ones. We investigated how the rules influenced the dynamics using rehearsals together with a model generalized from evolutionary dynamics. We tuned the rules to heighten the tension and modeled nonlinear fitness and feedback dynamics for mutation rate to capture the observed temporal phasing of the dancers' exploration-versus-exploitation. Using bifurcation analysis, we identified key controls of the tension and showed how they could shape the decision-making dynamics of the model much like turning a "dial" in the instructions to the dancers could shape the dance. The investigation became an integral part of the development of the dance

On the sympatric evolution and evolutionary stability of coexistence by relative nonlinearity of competition

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field [...]Comment: PLOS ONE, in pres

Dynamic and Thermodynamic Models of Adaptation

The concept of biological adaptation was closely connected to some mathematical, engineering and physical ideas from the very beginning. Cannon in his "The wisdom of the body" (1932) used the engineering vision of regulation. In 1938, Selye enriched this approach by the notion of adaptation energy. This term causes much debate when one takes it literally, i.e. as a sort of energy. Selye did not use the language of mathematics, but the formalization of his phenomenological theory in the spirit of thermodynamics was simple and led to verifiable predictions. In 1980s, the dynamics of correlation and variance in systems under adaptation to a load of environmental factors were studied and the universal effect in ensembles of systems under a load of similar factors was discovered: in a crisis, as a rule, even before the onset of obvious symptoms of stress, the correlation increases together with variance (and volatility). During 30 years, this effect has been supported by many observations of groups of humans, mice, trees, grassy plants, and on financial time series. In the last ten years, these results were supplemented by many new experiments, from gene networks in cardiology and oncology to dynamics of depression and clinical psychotherapy. Several systems of models were developed: the thermodynamic-like theory of adaptation of ensembles and several families of models of individual adaptation. Historically, the first group of models was based on Selye's concept of adaptation energy and used fitness estimates. Two other groups of models are based on the idea of hidden attractor bifurcation and on the advection--diffusion model for distribution of population in the space of physiological attributes. We explore this world of models and experiments, starting with classic works, with particular attention to the results of the last ten years and open questions.Comment: Review paper, 48 pages, 29 figures, 183 bibliography, the final version accepted in Phys Life Re

Dynamics of Similar Populations: The Link Between Population Dynamics and Evolution

We provide the link between population dynamics and the dynamics of Darwinian evolution via studying the joint population dynamics of "similar" populations. Similarity implies that the "relative" dynamics of the populations is slow compared to, and decoupled from, their "aggregated" dynamics. The relative dynamics is simple, and captured by a Taylor expansion in the difference between the populations. The emerging evolution is directional, except at the "singular" points of the evolutionary state space, where "evolutionary branching" may happen

Limit cycles analysis and control of evolutionary game dynamics with environmental feedback

Recently, an evolutionary game dynamics model taking into account the environmental feedback has been proposed to describe the co-evolution of strategic actions of a population of individuals and the state of the surrounding environment; correspondingly a range of interesting dynamic behaviors have been reported. In this paper, we provide new theoretical insight into such behaviors and discuss control options. Instead of the standard replicator dynamics, we use a more realistic and comprehensive model of replicator–mutator dynamics, to describe the strategic evolution of the population. After integrating the environment feedback, we study the effect of mutations on the resulting closed-loop system dynamics. We prove the conditions for two types of bifurcations, Hopf bifurcation and Heteroclinic bifurcation, both of which result in stable limit cycles. These limit cycles have not been identified in existing works, and we further prove that such limit cycles are in fact persistent in a large parameter space and are almost globally stable. In the end, an intuitive control policy based on incentives is applied, and the effectiveness of this control policy is examined by analysis and simulations

Escenarios de ramificaciones evolutivas en el marco de las dinámicas adaptativas: Teoría y aplicaciones al cambio tecnológico

gráficosIn this thesis, we have reviewed the theory of Adaptive Dynamics, a theoretical background originated in evolutionary biology linking demographic dynamics to evolutionary changes, allowing it to describe evolutionary dynamics in the long-term when considering innovations as small and rare events in the market time scale. From this perspective, three mathematical models have been formulated to describe evolutionary branching: the coexistence between resident and similar innovative technologies and their further divergence in the evolutionary space. The first model addresses the problem of determining conditions on the energy market diversification from adaptive dynamics and the impact the imposition/allocation of taxes/subsidies may have on controlling market diversification. The second model explores the Coffee Berry Borer (Hypothenemus hampei) and its role in the evolutionary diversification of the coffee market; the influence that consumer's preference and control practices have on diversification is studied in detail, and correspond to the main source of insights. Finally, the third model in the fifth chapter, describes the competition among public transport systems, considering the number of transported passengers as the differentiation attribute is presented, the analysis allows to answer the question of under what condition the market diversifies, and which are the levels of transported passengers that will be reached in the long term depending on the budget allocation rate destined to increase the number of users. Adaptive dynamics describes evolution through an ordinary differential equation known as the canonical equation, which smooths on a continuous path the successive processes of innovation and substitution. This approach considers interactions to be the evolutionary driving force and considers the feedback between evolutionary change and the selection forces that agents undergo. One of the main (general) contributions of this thesis is to illustrate in detail how the theory of adaptive dynamics is very useful in areas of knowledge quite distant from evolutionary biology, in particular for engineering, given that its results predict the systems' long-term dynamics, as well as to control in the demographic/market timescale and to influence the long-term behavior of the evolving attributes in the evolutionary timescale. (Texto tomado de la fuente)En la ejecución de esta tesis, hemos revisado la teoría de la dinámicas adaptativas, un trasfondo teórico que se origina en la biología evolutiva, que vincula la dinámica demográfica con los cambios evolutivos, y permite describir la dinámica evolutiva a largo plazo al considerar las innovaciones como eventos pequeños y raros en la escala de tiempo del mercado. Desde esta perspectiva, se han formulado tres modelos matemáticos que permiten describir la ramificación evolutiva, es decir, la coexistencia entre tecnologías innovadoras residentes y similares y su posterior divergencia en el espacio evolutivo. El primer modelo aborda el problema de determinar las condiciones para la diversificación del mercado energético a partir de las dinámicas adaptativas y el impacto que la imposición/asignación de impuestos/subsidios puede tener en el control de la diversificación del mercado. El segundo modelo explora la broca del café (Hypothenemus hampei) y su papel en la diversificación evolutiva del mercado cafetero; la influencia que las preferencias de los consumidores y las prácticas de control tienen sobre la diversificación se estudia en detalle y corresponde a la principal fuente de información. Además, en el quinto capítulo, se presenta un modelo para la competencia entre los sistemas de transporte público, considerando el número de pasajeros transportados como el atributo de diferenciación; el análisis permite responder a la pregunta bajo qué condiciones se diversifica el mercado y cuáles son los niveles de pasajeros transportados que se alcanzarán a largo plazo dependiendo de la tasa de asignación presupuestaria destinada a aumentar el número de usuarios. La teoría de las dinámicas adaptativas describe la evolución a través de una ecuación diferencial ordinaria conocida como ecuación canónica, que suaviza en una trayectoria continua los procesos sucesivos de innovación y sustitución. Este enfoque considera las interacciones como la fuerza impulsora de la evolución y tiene en cuenta la retroalimentación entre el cambio evolutivo y las fuerzas de selección que sufren los agentes. Una de las principales contribuciones mas generales de esta tesis es ilustrar en detalle cómo la teoría de las dinámicas adaptativas es útil en áreas de conocimiento bastante distantes de la biología evolutiva, en particular para la ingeniería, dado que sus resultados permiten predecir el comportamiento de los sistemas a largo plazo, así como controlar dicho comportamiento en la escala de tiempo demográfica/de mercado e influir en la dinámica a largo plazo de los atributos en evolución en la escala de tiempo evolutiva.DoctoradoDoctor en Ingeniería - Ingeniería AutomáticaMathematical modeling of innovations and technological changeEléctrica, Electrónica, Automatización Y Telecomunicacione

Multi-objective Active Control Policy Design for Commensurate and Incommensurate Fractional Order Chaotic Financial Systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, an active control policy design for a fractional order (FO) financial system is attempted, considering multiple conflicting objectives. An active control template as a nonlinear state feedback mechanism is developed and the controller gains are chosen within a multi-objective optimization (MOO) framework to satisfy the conditions of asymptotic stability, derived analytically. The MOO gives a set of solutions on the Pareto optimal front for the multiple conflicting objectives that are considered. It is shown that there is a trade-off between the multiple design objectives and a better performance in one objective can only be obtained at the cost of performance deterioration in the other objectives. The multi-objective controller design has been compared using three different MOO techniques viz. Non Dominated Sorting Genetic Algorithm-II (NSGA-II), epsilon variable Multi-Objective Genetic Algorithm (ev-MOGA), and Multi Objective Evolutionary Algorithm with Decomposition (MOEA/D). The robustness of the same control policy designed with the nominal system settings have been investigated also for gradual decrease in the commensurate and incommensurate fractional orders of the financial system