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Kobayashi Y.,Kochi University of Technology | Ohtsuki H.,Graduate University for Advanced Studies | Wakano J.Y.,Meiji Institute for Advanced Study of Mathematical science
Theoretical Population Biology | Year: 2016

It has long been debated if population size is a crucial determinant of the level of culture. While empirical results are mixed, recent theoretical studies suggest that social connectedness between people may be a more important factor than the size of the entire population. These models, however, do not take into account evolutionary responses of learning strategies determining the mode of transmission and innovation and are hence not suitable for predicting the long-term implications of parameters of interest. In the present paper, to address this issue, we provide a gene-culture coevolution model, in which the microscopic learning process of each individual is explicitly described as a continuous-time stochastic process and time allocation to social and individual learning is allowed to evolve. We have found that social connectedness has a larger impact on the equilibrium level of culture than population size especially when connectedness is weak and population size is large. This result, combined with those of previous culture-only models, points to the importance of studying separate effects of population size and internal social structure to better understand spatiotemporal variation in the level of culture. © 2016 Elsevier Inc.


Kobayashi Y.,Meiji Institute for Advanced Study of Mathematical science | Ohtsuki H.,Graduate University for Advanced Studies
Theoretical Population Biology | Year: 2014

Learning abilities are categorized into social (learning from others) and individual learning (learning on one's own). Despite the typically higher cost of individual learning, there are mechanisms that allow stable coexistence of both learning modes in a single population. In this paper, we investigate by means of mathematical modeling how the effect of spatial structure on evolutionary outcomes of pure social and individual learning strategies depends on the mechanisms for coexistence. We model a spatially structured population based on the infinite-island framework and consider three scenarios that differ in coexistence mechanisms. Using the inclusive-fitness method, we derive the equilibrium frequency of social learners and the genetic load of social learning (defined as average fecundity reduction caused by the presence of social learning) in terms of some summary statistics, such as relatedness, for each of the three scenarios and compare the results. This comparative analysis not only reconciles previous models that made contradictory predictions as to the effect of spatial structure on the equilibrium frequency of social learners but also derives a simple mathematical rule that determines the sign of the genetic load (i.e.whether or not social learning contributes to the mean fecundity of the population). © 2013 Elsevier Inc.


Zu J.,Xi'an Jiaotong University | Zu J.,Meiji University | Wang K.,Military School of Engineering | Mimura M.,Meiji Institute for Advanced Study of Mathematical science
Mathematical Biosciences | Year: 2011

On the ecological timescale, two predator species with linear functional responses can stably coexist on two competing prey species. In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate under what conditions such a coexistence is also evolutionarily stable, and whether the two predator species may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in capture rates and a predator with a high capture rate for one prey has a low capture rate for the other and vice versa. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly convex in the vicinity of the singular strategy and the interspecific prey competition is not strong, then this singular strategy is an evolutionary branching point, near which the resident and mutant predator populations can coexist and diverge in their strategies. Second, we find that after branching has occurred in the predator phenotype, if the trade-off curve is globally convex, the predator population will eventually branch into two extreme specialists, each completely specializing on a particular prey species. However, in the case of smoothed step function-like trade-off, an interior dimorphic singular coalition becomes possible, the predator population will eventually evolve into two generalist species, each feeding on both of the two prey species. The algebraical analysis reveals that an evolutionarily stable dimorphism will always be attractive and that no further branching is possible under this model. © 2011.


Zu J.,Meiji University | Zu J.,Southwest Petroleum University | Mimura M.,Meiji Institute for Advanced Study of Mathematical science | Yuichiro Wakano J.,Meiji Institute for Advanced Study of Mathematical science
Journal of Theoretical Biology | Year: 2010

This paper considers the evolution of phenotypic traits in a community comprising the populations of predators and prey subject to Allee effect. The evolutionary model is constructed from a deterministic approximation of the stochastic process of mutation and selection. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy and evolutionary branching. We find that the strong Allee effect of prey facilitates the formation of continuously stable strategy in the case that prey population undergoes evolutionary branching if the Allee effect of prey is not strong enough. Secondly, we show that evolutionary suicide is impossible for prey population when the intraspecific competition of prey is symmetric about the origin. However, evolutionary suicide can occur deterministically on prey population if prey individuals undergo strong asymmetric competition and are subject to Allee effect. Thirdly, we show that the evolutionary model with symmetric interactions admits a stable limit cycle if the Allee effect of prey is weak. Evolutionary cycle is a likely outcome of the process, which depends on the strength of Allee effect and the mutation rates of predators and prey. Crown Copyright © 2009.


Zu J.,Meiji University | Mimura M.,Meiji Institute for Advanced Study of Mathematical science | Takeuchi Y.,University of Shizuoka
Journal of Theoretical Biology | Year: 2011

In this paper, with the method of adaptive dynamics and geometric technique, we investigate the adaptive evolution of foraging-related phenotypic traits in a predator-prey community with trade-off structure. Specialization on one prey type is assumed to go at the expense of specialization on another. First, we identify the ecological and evolutionary conditions that allow for evolutionary branching in predator phenotype. Generally, if there is a small switching cost near the singular strategy, then this singular strategy is an evolutionary branching point, in which predator population will change from monomorphism to dimorphism. Second, we find that if the trade-off curve is globally convex, predator population eventually branches into two extreme specialists, each completely specializing on a particular prey species. However, if the trade-off curve is concave-convex-concave, after branching in predator phenotype, the two predator species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist. The analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible under this model. © 2010.


Heisler E.,Hiroshima University | Suematsu N.J.,Meiji University | Suematsu N.J.,Meiji Institute for Advanced Study of Mathematical science | Awazu A.,Hiroshima University | Nishimori H.,Hiroshima University
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

When an ensemble of self-propelled camphor boats move in a one-dimensional channel, they exhibit a variety of collective behaviors. Under certain conditions, the boats tend to cluster together and move in a relatively tight formation. This type of behavior, referred to as clustering or swarming here, is one of three types recently observed in experiment. Similar clustering behavior is also reproduced in simulations based on a simple theoretical model. Here we examine this model to determine the clustering mechanism and the conditions under which clustering occurs. We also propose a method of quantifying the behavior that may be used in future experimental work. © 2012 American Physical Society.


Sano Y.,Nihon University | Takayasu H.,Sony | Takayasu H.,Meiji Institute for Advanced Study of Mathematical science | Takayasu M.,Tokyo Institute of Technology
Progress of Theoretical Physics Supplement | Year: 2012

We confirm Zipf's law and Heaps' law using various types of documents such as literary works, blogs, and computer programs. Independent of the document type, the exponents of Zipf' law are estimated to be approximately 1, whereas Heaps' exponents appear to be dependent on the observation size, and the estimated values are scattered around 0.5. By definition, randomly shuffled documents reproduce Zipf's law and Heaps' law. However, artificially generated documents using the empirically observed Zipf's law and number of distinct words do not reproduce Heaps' law. We demonstrate that Heaps' law holds for artificial documents in which a certain number of distinct words are added to empirically observed distinct words. This suggests that the number of potential distinct words considered in the creation of a given document can be predicted.


Wakano J.Y.,Meiji Institute for Advanced Study of Mathematical science | Hauert C.,University of British Columbia
Journal of Theoretical Biology | Year: 2011

Cooperators and defectors can coexist in ecological public goods games. When the game is played in two-dimensional continuous space, a reaction diffusion model produces highly irregular dynamics, in which cooperators and defectors survive in ever-changing configurations (Wakano et al., 2009. Spatial dynamics of ecological public goods. Proc. Natl. Acad. Sci. 106, 7910-7914). The dynamics is related to the formation of Turing patterns, but the origin of the irregular dynamics is not well understood. In this paper, we present a classification of the spatio-temporal dynamics based on the dispersion relation, which reveals that the spontaneous pattern formation can be attributed to the dynamical interplay between two linearly unstable modes: temporal instability arising from a Hopf-bifurcation and spatial instability arising from a Turing-bifurcation. Moreover, we provide a detailed analysis of the highly irregular dynamics through Fourier analysis, the break-down of symmetry, the maximum Lyapunov exponent, and the excitability of the reaction-term dynamics. All results clearly support that the observed irregular dynamics qualifies as spatio-temporal chaos. A particularly interesting type of chaotic dynamics, which we call intermittent bursts, clearly demonstrates the effects of the two unstable modes where (local) periods of stasis alternate with rapid changes that may induce local extinction. © 2010 Elsevier Ltd.


Nakahashi W.,Meiji Institute for Advanced Study of Mathematical science
Theoretical Population Biology | Year: 2010

Humans strongly depend on individual and social learning, both of which are highly effective and accurate. I study the effects of environmental change on the evolution of the effectiveness and accuracy of individual and social learning (individual and social learning levels) and the number of pieces of information learned individually and socially (individual and social learning capacities) by analyzing a mathematical model. I show that individual learning capacity decreases and social learning capacity increases when the environment becomes more stable; both decrease when the environment becomes milder. I also show that individual learning capacity increases when individual learning level increases or social learning level decreases, while social learning capacity increases when individual or social learning level increases. The evolution of high learning levels can be triggered when the environment becomes severe, but a high social learning level can evolve only when a high individual learning level can simultaneously evolve with it. © 2010 Elsevier Inc.


Sano Y.,Nihon University | Yamada K.,Waseda Institute for Advanced Study | Watanabe H.,Tokyo Institute of Technology | Takayasu H.,Sony | And 2 more authors.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013

To uncover an underlying mechanism of collective human dynamics, we survey more than 1.8 billion blog entries and observe the statistical properties of word appearances. We focus on words that show dynamic growth and decay with a tendency to diverge on a certain day. After careful pretreatment and the use of a fitting method, we found power laws generally approximate the functional forms of growth and decay with various exponents values between -0.1 and -2.5. We also observe news words whose frequencies increase suddenly and decay following power laws. In order to explain these dynamics, we propose a simple model of posting blogs involving a keyword, and its validity is checked directly from the data. The model suggests that bloggers are not only responding to the latest number of blogs but also suffering deadline pressure from the divergence day. Our empirical results can be used for predicting the number of blogs in advance and for estimating the period to return to the normal fluctuation level.

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