Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.Comment: Review, 48 pages, 26 figure

Time Scales in Evolutionary Dynamics

Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction and selection leads to dramatic changes in the outcome of evolution. Examples include the selection of the inefficient strategy in the Harmony and Stag-Hunt games, and the disappearance of the coexistence state in the Snowdrift game. Our results hold for any population size and in the presence of a background of fitness.Comment: Final version with minor changes, accepted for publication in Physical Review Letter

The importance of selection rate in the evolution of cooperation

8 pages, 4 figures.-- ArXiv pre-print available at: http://arxiv.org/abs/q-bio/0512045Final publisher version available Open Access at: http://gisc.uc3m.es/~cuesta/papers-year.htmlHow cooperation emerges in human societies is still a puzzle. Evolutionary game theory has been the standard framework to address this issue. In most models, every individual plays with all others, and then reproduces and dies according to what she earns. This amounts to assuming that selection takes place at a slow pace with respect to the interaction time scale. We show that, quite generally, if selection speeds up, the evolution outcome changes dramatically. Thus, in games such as Harmony, where cooperation is the only equilibrium and the only rational outcome, rapid selection leads to dominance of defectors. Similar non trivial phenomena arise in other binary games and even in more complicated settings such as the Ultimatum game. We conclude that the rate of selection is a key element to understand and model the emergence of cooperation, and one that has so far been overlooked.This work is supported by MEC (Spain) under grants BFM2003-0180, BFM2003-07749-C05-01, FIS2004-1001 and NAN2004-9087-C03-03 and by Comunidad de Madrid (Spain) under grants UC3M-FI-05-007, SIMUMAT-CM and MOSSNOHO-CM.Publicad

Effect of spatial structure on the evolution of cooperation

16 pages, 14 figures.-- PACS nrs.: 89.65.−s, 87.23.Ge, 87.23.Kg, 02.50.Le.-- ArXiv pre-print available at: http://arxiv.org/abs/0806.1649Spatial structure is known to have an impact on the evolution of cooperation, and so it has been intensively studied during recent years. Previous work has shown the relevance of some features, such as the synchronicity of the updating, the clustering of the network, or the influence of the update rule. This has been done, however, for concrete settings with particular games, networks, and update rules, with the consequence that some contradictions have arisen and a general understanding of these topics is missing in the broader context of the space of 2×2 games. To address this issue, we have performed a systematic and exhaustive simulation in the different degrees of freedom of the problem. In some cases, we generalize previous knowledge to the broader context of our study and explain the apparent contradictions. In other cases, however, our conclusions refute what seems to be established opinions in the field, as for example the robustness of the effect of spatial structure against changes in the update rule, or offer new insights into the subject, e.g., the relation between the intensity of selection and the asymmetry between the effects on games with mixed equilibria.This work is partially supported by Ministerio de Educación y Ciencia (Spain) under Grants Ingenio-MATHEMATICA and MOSAICO, and by Comunidad de Madrid (Spain) under Grants SIMUMAT-CM and MOSSNOHO-CM.Publicad

Topological Traps Control Flow on Real Networks: The Case of Coordination Failures

We study evolutionary games in real social networks, with a focus on coordination games. We find that populations fail to coordinate in the same behavior for a wide range of parameters, a novel phenomenon not observed in most artificial model networks. We show that this result arises from the relevance of correlations beyond the first neighborhood, in particular from topological traps formed by links between nodes of different degrees in regions with few or no redundant paths. This specificity of real networks has not been modeled so far with synthetic networks. We thus conclude that model networks must be improved to include these mesoscopic structures, in order to successfully address issues such as the emergence of cooperation in real societies. We finally show that topological traps are a very generic phenomenon that may arise in very many different networks and fields, such as opinion models, spread of diseases or ecological networks

Ecoturismo sustentable en la Provincia de Los Rí­os

Una de las formas preferidas en la actualidad para conocer, promocionar e incentivar a realizar turismo en Ecuador, son los llamados “turismo sustentable”. Estos nos permiten presentar en una forma natural, clara, sencilla, dinámica, divertida y sugestiva, los puntos de interés en tanto en cuanto a recursos turí­sticos se refiere que existen en la región, la provincia y también a saber de lo que se trata el turismo, motivando de esa manera al lector, y estos a su vez encuentren razones suficientes para conocer, y por qué no consumar un viaje

Bio-monitoring of metal(loid)s pollution in dry riverbeds affected by mining activity

The aim of this study was to evaluate the most abundant native plants that could be used as a bio-monitor of metal(loid) concentration in dry riverbeds affected by mining activities. Three plants species and their respective rhizospheric soils were sampled from the El Beal (Piptatherum miliaceum, 15 samples), La Carrasquilla (Foeniculum vulgare, 10 samples), and Ponce (Dittrichia viscosa, 12 samples) dry riverbeds from the mining district of Cartegena-La Unión (SE Spain). There is scanty bibliography of the capacity of these species to be used as bio-monitors in the dry riverbeds. Plants categorized as a bio-monitor were established according to the bioaccumulation factor (BF), mobility ratio (MR), and linear correlations between metal(loid) concentrations in plants tissues (root or stem)-rhizospheric soils. The rhizospheric soils were highly contaminated for As, Cd, Pb, and Zn (Cf ≥ 6), and moderately contaminated for Mn (1 ≤ Cf < 3). Piptatherum miliaceum presented on Cd similar mean concentrations on rhizospheric soil and root, BF = 1.07, with a strong correlation soil–root (r = 0.61, p = 0.02). Therefore, of the three species with the capacity to grow in the area, Piptatherum miliaceum showed characteristics to be considered as a bio-monitor for Cd, with a BF > 1, and a positive–significant correlation between the rhizospheric soil and roots.This research (Proyecto PID2019-110311RB-C22) received funding from MCIN/AEI/10.13039/ 501100011033

Spatial distribution and pollution evaluation in dry riverbeds afected by mine tailings

The objective of this study was to evaluate the level of pollution, sources and potential risk of heavy metals (Zn, Cu, Mn, Cd, Cr, Ni, Fe and Pb) and arsenic (As) in four dry riverbeds afected by mine tailing, which drain into one of the biggest coastal lagoon of Europe (Mar Menor). El Beal, La Carrasquilla, Las Matildes and Ponce dry riverbeds sediments were sampled along its course (20, 18, 13, 19 samples were collected, respectively), and total/ soluble metal(loid)s, water soluble ions, nitrogen, and organic/inorganic carbon contents were analyzed. Spatial distribution, principal component analysis (PCA), hierarchical cluster analysis (HCA), contamination factor (Cf), pollution load index (PLI) and potential ecological risk index (RI) were used to identify the possible sources of metal(loid)s and to assess the sediment pollution status. The results showed that the mean total concentrations of As, Cu, Cd, Mn, Zn and Pb exceeded the natural background levels of the study area, with the highest values located close to the mining areas. Correlation and cluster analysis identifed that Cd and Zn were associated mainly with anthropogenic activities for all riverbeds, while Cr and Ni come from parent. PLI graded the four riverbeds as contaminated by heavy metals, while RI manifested that 100% of samples located in El Beal, La Carrasquilla and Las Matildes had a signifcantly high ecological risk. Therefore, this study suggests that mine wastes are the main source of metal(loids) contamination in the dry riverbeds, which results can be used to design actions and measures to reduce the environmental impact of metal(loid)s in the Mar Menor coastal lagoon

Enantioselective Synthesis of 2-Amino-1,1-diarylalkanes Bearing a Carbocyclic Ring Substituted Indole through Asymmetric Catalytic Reaction of Hydroxyindoles with Nitroalkenes

[EN] An asymmetric catalytic reaction of hydroxyindoles with nitroalkenes leading to the Friedel-Crafts alkylation in the carbocyclic ring of indole is presented. The method is based on the activating/directing effects of the hydroxy group situated in the carbocyclic ring of the indole providing nitroalkylated indoles functionalizated at the C-4, C-5, and C-7 positions with high yield, regio-, and enantioselectivity. The optically enriched nitroalkanes were transformed efficiently in optically enriched 2-amino-1,1-diarylalkanes bearing a carbocyclic ring substituted indole.Financial support from the MINECO (Gobierno de Espana; CTQ2017-84900-P) is gratefully acknowledged. C.V. thanks MINECO for a JdC contract. J.R.-B. thanks the Ministry of Education for a Collaboration grant. Access to NMR, MS, and X-ray facilities from the Servei Central de Suport a la Investigacio Experimental (SCSIE)-UV is also acknowledgedVila, C.; Rostoll-Berenguer, J.; Sánchez-García, R.; Blay, G.; Fernandez, I.; Muñoz Roca, MDC.; Pedro, JR. (2018). Enantioselective Synthesis of 2-Amino-1,1-diarylalkanes Bearing a Carbocyclic Ring Substituted Indole through Asymmetric Catalytic Reaction of Hydroxyindoles with Nitroalkenes. The Journal of Organic Chemistry. 83(12):6397-6407. https://doi.org/10.1021/acs.joc.8b0061263976407831

La tutoría educativa y el liderazgo en los alumnos del quinto grado de secundaria de la Institución Educativa Parroquial “San Vicente Ferrer”- Los Olivos, 2013

La investigación tiene como propósito determinar si existe relación entre la Tutoría Educativa y el Liderazgo en los estudiantes adolescentes de una institución educativa estatal parroquial. Pertenece al tipo de investigación básica, nivel descriptivo con diseño correlacional. La muestra representativa a un 95% de intervalo de confianza fue de 120 estudiantes de educación secundaria en el área de Tutoría, a quienes se les suministró dos cuestionarios para determinar la influencia de la Tutoría en el liderazgo. Los instrumentos han sido validados mediante juicio de expertos y han sido sometidos a prueba piloto para determinar el índice de confiabilidad con el alfa de Cronbach; en ambos casos, las puntuaciones y el índice alfa denotan confiabilidad alta. La metodología se basó en el tipo de investigación descriptivo correlacional, perteneciente al método cualitativo con diseño no experimental de corte transversal. Mediante una encuesta hemos hecho la recolección de datos. Los resultados obtenidos mediante la contrastación de hipótesis arrojan que en cuanto a la hipótesis general la variable Tutoría Educativa no influyen significativamente en el liderazgo. En cuanto las hipótesis especificas todas las dimensiones de la Tutoría Educativa, Personal Social, Vocacional, Ayuda Social y Convivencia, no influyen de forma significativa en liderazgo. Es decir, estos resultados demuestran que la tutoría no contribuye al desarrollo del liderazgo de los estudiantes del Quinto grado de Educación Secundaria de la Institución Educativa Parroquial “San Vicente Ferrer” de Los Olivos