Browsing by Subject "agent-based model"

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  • Ovaskainen, Otso; Somervuo, Panu; Finkelshtein, Dmitri (2020)
    Agent-based models are used to study complex phenomena in many fields of science. While simulating agent-based models is often straightforward, predicting their behaviour mathematically has remained a key challenge. Recently developed mathematical methods allow the prediction of the emerging spatial patterns for a general class of agent-based models, whereas the prediction of spatio-temporal pattern has been thus far achieved only for special cases. We present a general and mathematically rigorous methodology that allows deriving the spatio-temporal correlation structure for a general class of individual-based models. To do so, we define an auxiliary model, in which each agent type of the primary model expands to three types, called the original, the past and the new agents. In this way, the auxiliary model keeps track of both the initial and current state of the primary model, and hence the spatio-temporal correlations of the primary model can be derived from the spatial correlations of the auxiliary model. We illustrate the agreement between analytical predictions and agent-based simulations using two example models from theoretical ecology. In particular, we show that the methodology is able to correctly predict the dynamical behaviour of a host-parasite model that shows spatially localized oscillations.
  • Page, Mathew (Helsingin yliopisto, 2021)
    Tiivistelmä – Referat – Abstract With rising income inequalities and increasing immigration in many European cities, residential segregation remains a key focus for city planners and policy makers. As changes in the socio-spatial configuration of cities result from the residential mobility of its residents, the basis on which this mobility occurs is an important factor in segregation dynamics. There are many macro conditions which can constrain residential choice and facilitate segregation, such as the structure and supply of housing, competition in real estate markets and legal and institutional forms of housing discrimination. However, segregation has also been shown to occur from the bottom-up, through the self-organisation of individual households who make decisions about where to live. Using simple theoretical models, Thomas Schelling demonstrated how individual residential choices can lead to unanticipated and unexpected segregation in a city, even when this is not explicitly desired by any households. Schelling’s models are based upon theories of social homophily, or social distance dynamics, whereby individuals are thought to cluster in social and physical space on the basis of shared social traits. Understanding this process poses challenges for traditional research methods as segregation dynamics exhibit many complex behaviours including interdependency, emergence and nonlinearity. In recent years, simulation has been turned to as one possible method of analysis. Despite this increased interest in simulation as a tool for segregation research, there have been few attempts to operationalise a geospatial model, using empirical data for a real urban area. This thesis contributes to research on the simulation of social phenomena by developing a geospatial agent-based model (ABM) of residential segregation from empirical population data for the Helsinki Metropolitan Area (HMA). The urban structure, population composition, density and socio-spatial distribution of the HMA is represented within the modelling environment. Whilst the operational parameters of the model remain highly simplified in order to make processes more transparent, it permits exploration of possible system behaviour by placing it in a manipulative form. Specifically, this study uses simulation to test whether individual preferences, based on social homophily, are capable of producing segregation in a theoretical system which is absent of discrimination and other factors which may constrain residential choice. Three different scenarios were conducted, corresponding to different preference structures and demands for co-group neighbours. Each scenario was simulated for three different potential sorting variables derived from the literature; socio-economic status (income), cultural capital (education level) and language groups (mother tongue). Segregation increases in all of the simulations, however there are considerable behavioural differences between the different scenarios and grouping variables. The results broadly support the idea that individual residential choices by households are capable of producing and maintaining segregation under the right theoretical conditions. As a relatively novel approach to segregation research, the components, processes, and parameters of the developed model are described in detail for transparency. Limitations of such an approach are addressed at length, and attention is given to methods of measuring and reporting on the evolution and results of the simulations. The potential and limitations of using simulation in segregation research is highlighted through this work.
  • Ovaskainen, Otso; Somervuo, Panu; Finkelshtein, Dmitri (2021)
    In ecology, one of the most fundamental questions relates to the persistence of populations, or conversely to the probability of their extinction. Deriving extinction thresholds and characterizing other critical phenomena in spatial and stochastic models is highly challenging, with few mathematically rigorous results being available for discrete-space models such as the contact process. For continuous-space models of interacting agents, to our knowledge no analytical results are available concerning critical phenomena, even if continuous-space models can arguably be considered to be more natural descriptions of many ecological systems than lattice-based models. Here we present both mathematical and simulation-based methods for deriving extinction thresholds and other critical phenomena in a broad class of agent-based models called spatiotemporal point processes. The mathematical methods are based on a perturbation expansion around the so-called mean-field model, which is obtained at the limit of large-scale interactions. The simulation methods are based on examining how the mean time to extinction scales with the domain size used in the simulation. By utilizing a constrained Gaussian process fitted to the simulated data, the critical parameter value can be identified by asking when the scaling between logarithms of the time to extinction and the domain size switches from sublinear to superlinear. As a case study, we derive the extinction threshold for the spatial and stochastic logistic model. The mathematical technique yields rigorous approximation of the extinction threshold at the limit of long-ranged interactions. The asymptotic validity of the approximation is illustrated by comparing it to simulation experiments. In particular, we show that species persistence is facilitated by either short or long spatial scale of the competition kernel, whereas an intermediate scale makes the species vulnerable to extinction. Both the mathematical and simulation methods developed here are of very general nature, and thus we expect them to be valuable for predicting many kinds of critical phenomena in continuous-space stochastic models of interacting agents, and thus to be of broad interest for research in theoretical ecology and evolutionary biology.