中桐 斉之

<title>Abstract</title>The infectious disease (COVID-19) causes serious damages and outbreaks. A large number of infected people have been reported in the world. However, such a number only represents those who have been tested; e.g. PCR test. We focus on the infected individuals who are not checked by inspections. The susceptible-infected-recovered (SIR) model is modified: infected people are divided into quarantined (Q) and non-quarantined (N) agents. Since N-agents behave like uninfected people, they can move around in a stochastic simulation. Both theory of well-mixed population and simulation of random-walk reveal that the total population size of Q-agents decrease in spite of increasing the number of tests. Such a paradox appears, when the ratio of Q exceeds a critical value. Random-walk simulations indicate that the infection hardly spreads, if the movement of all people is prohibited ("lockdown"). In this case the infected people are clustered and locally distributed within narrow spots. The similar result can be obtained, even when only non-infected people move around. However, when both N-agents and uninfected people move around, the infection spreads everywhere. Hence, it may be important to promote the inspections even for asymptomatic people, because most of N-agents are mild or asymptomatic.

<p> Introduction</p><p> This paper investigates whether the "paradox of choice" is applicable to town walking. We conducted an experiment by developing three types of experimental smartphone applications (apps) with different forms of intervention for town walking. We compared the results obtained to identify the types of walking behaviors that would increase the participants' levels of satisfaction, expand consumption in an area, and make people interested in revisiting a town.</p><p> </p><p> Material and Methods</p><p> The apps developed for this study involved three types of intervention, as follows: 1) Type A intervention, in which the app shows multiple designated destinations and does not finish running until all of these have been visited; 2) Type B intervention, in which the app designates a single destination and finishes running after this has been visited, after which the participant is free to walk wherever they wish for a set period of time; and 3) Type C intervention, in which the app finishes running after the person walks wherever they wish for a set period of time. In the experimental design, we ensured that none of the participants knew which form of intervention they were using. In all cases, the apps were set so that the experiment would last at least 30 minutes.</p><p> </p><p> Results</p><p> Comparison among the apps with the three types of intervention the following significant effects. First, the Type B intervention generated more new discoveries during town walking the than Type C intervention (p = . 007). That is, the app that allowed people to walk freely after visiting a single designated point was more likely to result in discoveries than the app that allowed people to walk entirely freely. Second, the results suggested that the Type A intervention was more likely to make people want to visit the town again than Type B (p = . 043). That is, that app that allowed people to walk freely after visiting a single point was more likely to make them want to revisit the town than the app in which they visited multiple designated points.</p><p> </p><p> Discussion</p><p> The results suggest that a "paradox of choice" may exist that is unique to town walking. Specifically, the likelihood of generating the desire to return to a town was lower with the Type A intervention (where multiple destinations are specified) and, furthermore, the likelihood of people making discoveries may be reduced as a result of unconstrained walking, as was the case for the Type C intervention. Based on these results, it is proposed that the most effective method of app assistance for visitors to towns is the Type B intervention in which a minimum number of destinations are visited, after which people are encouraged to walk freely for a set period of time.</p>

Ayu fish form algae-feeding territories in a river during a non-breeding (growing) season. We build a cost-benefit theory to describe the breakdown and formation of territory. In the early stage of a growing season, all fish hold territories at low densities. Once all territory sites are occupied, excess fish become floaters. When fish density further increases, a phase transition occurs: all the territories suddenly break down and fish form a school. In contrast, when the fish density is decreased, territories are suddenly formed from the school. Both theory and experiments demonstrate that ayu should exhibit a historical effect: the breakdown and formation processes of territory are largely different. In particular, the theory in formation process predicts a specific fish behavior: an "attempted territory holder" that tries to have a small territory emerges just before the formation of territory. (C) 2010 Elsevier Ltd. All rights reserved.

Habitat destruction is one of the primary causes of recent mass extinction of biospecies. Even if the destruction is limited to a local and small area, the cumulative destruction increases the risk of extinction. In this paper, we explore the effect of habitat destruction in lattice ecosystems composed of multiple species. Simulations reveal a parity law: the response of the system shows different behaviors by whether the species richness of system is even or odd. The mean-field theory partially predicts such a parity law. (C) 2010 Elsevier B.V. All rights reserved.

An ESS model to better understand the evolutionary dynamics of a primitive non-mating type gamete size was developed with reference to the PBS (Parker, Baker and Smith&apos;s) theory, which was based on total numbers of zygotes formed and the zygote survival rates. We did not include mating types since it has been suggested that primitive mating systems did not have mating types. As input parameters, we used experimental data on gamete motility of marine green algae. Based on hard sphere collision mechanics, we detailed the fertilization kinetics of gametes that swim in water prior to fusing with their partners through a set of coupled, non-linear differential equations. These equations were integrated numerically using typical values of the constant parameters. To estimate the relative zygote survival rate, we used a function that is sigmoid in shape and examined some evolutionarily stable strategies in mating systems that depend on optimizing values of the invasion success ratio.

The conservation of biodiversity is one of the most important problems in this century. Under human management, ecosystems suffer perturbations or disturbances. The investigation of perturbation experiments is essential to conserve species and habitat. We carry out Monte-Carlo simulations on finite-size lattices composed of species (n. &lt;= 4). The value of mortality rate in of top predator is altered to a higher or lower level and a fluctuation enhancement (FE) is explored. Here FE means an uncertainty in population dynamics. It is found for that FE is observed when m is decreased. Namely, when we protect the top predator, its population dynamics becomes very difficult to predict.

Real simulations are performed on a finite size of lattice. It is therefore very difficult to predict a phase diagram on an infinitely large lattice. Here, we present a Finite Size Stability Analysis (FSSA) to know whether the phase is sustainable or not. Although this analysis is a hypothesis, it enables us to determine the boundary of phase diagram. We apply FSSA to multi-state system. For example we study ten-species system in ecology. From computer simulations on various sizes of lattices, we obtain the waiting time tau to extinction. The system is found to have two phases: the coexistence of all species is either unstable or marginally (neutrally) stable. In the latter case, tau diverges on a power law with the increase of lattice size.

Question: Is a rare or low-density species important for the balance of an ecosystem? Features of the model: Perturbation experiments on a model lattice with two common species and one low-density species. Key variables: The low-density species is preyed upon by one of the common species, but it eats the other common species. Meanwhile, the latter common species is eaten by the first common species. Thus the relationship between the three species is cyclic, corresponding to the &apos;rock-paper-scissors&apos; game. Control experiments include only two common species. Perturbation is introduced by decreasing the rate of reproduction of one of the common species. Simulation results: The outcome of perturbations depends strongly on both the low-density species and the perturbation strengths. The responses to perturbation are often paradoxical and different from those expected from the mean-field or global version of the lattice model. Conclusions: The presence of a low-density species can alter the balance of an ecosystem. The conservation biology and management practice of natural ecosystems may be hindered if less. common, unattractive species are ignored.

Ecosystem dynamics can be studied using model populations. Perturbation experiments have often been applied to simulated populations in order to study the uncertainty in ecosystem dynamics. Most of these studies have predicted a stationary state. We report on the uncertainty in the dynamics near extinction. In particular, we explore fluctuation enhancements, i.e., enhanced variability in dynamics of paths to extinction. We examine two dynamic models on a two-dimensional lattice of finite size: (1) the contact process (CP) in which interactions are restricted to occur between adjacent lattice points, and (2) mean-field simulation (MFS), where interactions occur globally, between any pair of lattice points. Computer simulation reveals that, for both CP and MFS, the random drift of density about a stationary state increases with the decrease of steady-state density. Drift is much more pronounced in the vicinity of the critical mortality rate, at the transition to extinction. Simulation demonstrates that MFS shows greater variability when relative mortality rate is low whereas CP shows much more pronounced variability when mortality is near the critical threshold. The CP process shows wider fluctuations while the MFS process shows minimal increases following perturbations that lead to extinction. Because interactions are local for CP, there are a variety of different paths to extinction. (C) 2004 Elsevier B.V. All rights reserved.

Habitat destruction is one of the primary causes of species extinction in recent history. Even if the destruction is restricted to a local area, its accumulation increases the risk of extinction. To investigate the effect of local habitat destruction, we studied two- and three-species model systems. The former contains prey (X) and predator (Y), while the latter is composed of X, Y and a top predator (Z). If the species Z goes extinct, then the latter becomes the former. Species dynamics are modeled within the lattice applying local and global interactions. Local interaction occurs between neighboring lattice points. In contrast, global interaction is allowed between any pair of lattice points, and its dynamics can be represented by the mean-field theory that is equivalent to Lotka-Volterra equation. Barriers, representing habitat loss, are randomly located between adjacent lattice points with the probability p. The barrier interrupts the reproduction of the prey X, but the predators Y and Z suffer no direct damage from the barriers. It is found that the effects of barriers on both species X and Y in the two-species model are usually opposite to those in the three-species model. Namely, if extinction occurs, the influence of habitat destruction on surviving species changes dramatically. We also find that when the density p of barriers increases the two models exhibit different extinction patterns: sometimes species X goes extinct, but sometimes the predator or top predator become extinct depending on the level of barrier density. The mean-field theory adequately predicts such species extinction, but it cannot explain some of the results. We interpret the results as an indirect relation between habitat destruction and species extinction. (C) 2004 Elsevier B.V. All rights reserved.

The so-called Lotka-Volterra model, which is thought to be appropriate for the dynamics of mutualistic relationship, tells us that mutualism does not play positive roles for the stability of ecosystem. When the mutualistic interactions between species are stronger than a certain threshold, population sizes of species unlimitedly increases. In the present paper, in order to prevent the divergence, we apply a lattice model, and introduce extended Lotka-Votterra equations. The latter is the mean-field theory of the former. These models contain the property of competition due to space limitation. In both models population is usually stable, when the intensity of mutualism are strong. In the lattice model, spatial distribution of species naturally evolves into a specific pattern of either mutualism or competition, depending on environmental conditions.

In marine green algae, isogamous and slightly anisogamous species produce positively phototactic gametes: phototactic devices including an eye-spot in both sexes. We numerically simulated gamete behavior in three-dimensions, and found that, all else being equal, phototactic gametes have considerable reproductive advantage over non-phototactic ones because they can search for potential mates on the water surface -- a two-dimensional plane -- rather than in three dimensions. This suggests that slight anisogamy in marine green algae has been maintained by the search efficiencies of phototactic devices in both sexes. However, in some markedly anisogamous species (e.g. the genus Bryopsis), the smaller male gametes have no eye-spot, swim randomly, and do not respond to light stimulus. In contrast, the larger female gametes have an eye-spot and exhibit positive phototaxis. During our study of encounter mechanisms for male and female gametes in this system, we discovered the first pheromonal attraction system in marine green algae. Adding the pheromonal system to our numerical simulations, we discovered that markedly anisogamous species can, through pheremones, achieve 2D search efficiencies on the water surface. Therefore, sexual pheromones as well as phototaxis may be a key to understand the mechanisms of the evolution of isogamy, slight anisogamy and marked anisogamy in marine green algae. Comparing mating efficiency among different mating systems, our results support the idea that the theory based on the two conflicting selection forces of search efficiency and zygote fitness was necessary to explain the evolution of anisogamy in marine green algae. The mating systems appear to be tightly tuned to the environmental conditions of their habitats.

The chemostat theory on two species competition has shown that the dilution rate where transition of dominance occurs is independent of limiting-nutrient concentration. However, we obtained the experimental data indicating that the transition-dilution rate changed with variations in limiting-ammonium concentrations, using the chemostat mixed-culture of the cyanobacterium Microcystis novacekii and the green alga Scenedesmus quadricauda. The transition-dilution rate was dependent on the concentration of limiting ammonium in the influx culture medium. We tried to simulate the experimental results. We introduced the effective dilution rate that depended on nutrient concentration (ammonium concentration in this study). A Monod-type hyperbolic function was used to represent the effective dilution rate for each species. The maximum dilution rate of the function was set to be the mechanical dilution rate (nominal dilution rate) of the chemostat culture. The calculation showed that the nominal transition-dilution rate where transition of dominance occurs decreased with increased concentration. This simulation was well consistent with our experimental data.

The investigation of perturbation experiments is important not only to forecast the effect of human management but also to understand community interactions. In the present paper, the dynamic processes in a prey-predator system are studied on a two-dimensional lattice. It is known that this system exhibits nonequilibrium phase transition of extinction. By computer we carry out perturbation experiments of extinction, and find that in the extinction process of the prey, the fluctuation enhancement (FM) is clearly observed, where FM means a high variation in extinction process. However, in the case of extinction of the predator, this enhancement is not observed. When prey goes extinct, the dynamic process has a lot of variation compared to the extinction of predator. Moreover, it is found that FM is clearly observed by spatially explicit model..

The balance of ecosystems may be altered with/without a less common species. We explore the role of a low-density species in a model ecosystem by perturbation experiments. We build a lattice ecosystem of two common species with/without one low-density species. Consider a two-dimensional lattice consisting of prey, predator and vacant site. We introduce the third low-density species that is preyed by the common prey, while eats the common predator. The relationship among three species is cyclic, corresponding to the Rock-Paper-Scissors game. We perform perturbation experiments by decreasing the reproduction rate of one common species. We then compare the resulting community structures and evaluate the effects of the low-density species and the perturbation strength on the model ecosystems. The simulation results are dependent on both the low-density species and perturbation strengths. The results are often paradoxical and different from those expected from the mean field version of the lattice model. Our results imply that the conservation biology and management practice of natural ecosystems may be hindered if less common unattractive species are ignored. Furthermore, an introduction of a new species may alter the ecosystem balance without changing the apparent structures of the community.

Ecosystem stability is an important issue in conservation of biodiversity. The stability of preypredator systems or competitive systems has been studied extensively. However, natural communities are far more complex than those simple ecosystems. Intraguild predation presents a sound example of a complex ecosystem with both competition and predation. The 3-species ecosystem with intraguild predation is the simplest such complex ecosystem. We studied the spatial pattern dynamics in the 3-species ecosystems with intraguild predation using the lattice version of the Lotka-Volterra model. A food web consists of plant, pure consumer (prey) and predatory consumer, where the latter two consumers show intraguild predation. The simulation of the lattice model shows complex patterns of phase transition with various parameter-dependence. The outcomes depend on the combination of these two reproductive parameters. This suggests that the stability of this ecosystem depends on the environmental parameters of the component species. Our results suggest that the discussion of stability based on the ecosystem structure could be meaningless unless all ecological and life history parameters of the component species are included. Our results indicate that a small human activity may have a relatively large impact on ecosystems by changing the ecological conditions of their component species.

Spatial pattern dynamics in a lattice ecosystem composed of two species is studied. Depending on values of a parameter, the exchange of relationship between competition and symbiosis takes place. While interaction parameters between species are fixed, spatial distribution of species naturally evolves into a specific pattern of either competition or mutualism. (C) 2001 Elsevier Science B.V. All rights reserved.