Wednesday, Sep. 7
|Time||14:00 - 15:00, Sep. 7|
Department of Animal and Plant Sciences, Sheffield University, England
Integral projection models (IPMs) project a continuously structured population, where say individuals are characterized by their size, in discrete time. An overview of the application of IPMs to field populations will be given covering 1) model parameterization in both constant and stochastic environments, 2) populations where multiple traits influence an individual’s fate (e.g. size and age), and 3) density dependence. The use IPMs to understand the evolution of traits in natural populations will then be explored. In these IPMs individuals are characterized by traits that vary over the organism’s life, such as size and age, and invariant traits, such as genotype or breeding value. Methods of approximating the dynamics of both the mean and variance of the genotype/breeding value distribution will be presented. Methods for embedding quantitative genetics models into IPMs will be presented and used to explore the timing of reproduction in two plant populations. These models will be used to explore the maintenance of genetic variability in natural populations.
|Time||15:00 - 16:00, Sep. 7|
Centre for Vascular Research, University of New South Wales, Sydney, Australia
When we think of infection, we usually think of active replication of a virus or parasite, causing illness. However, some infections can lie sleeping (latent) for many years before they re-activate to cause a new active infection. Understanding how infections become latent, and how they reactivate from latency, is important to controlling infection. Because it is not easy to measure the latent (sleeping) infection, modeling is needed to study how infection reactivates. This talk will discuss modeling applied to experimental data from patient and animal studies to better understand the dynamics of latency in HIV infection.
Thursday, Sep. 8
|Time||15:45 - 17:15, Sep.8|
Research Institute of Electrical Communication
In this presentation, I talk about my research activities up to now, mainly focusing on the decentralized control mechanism underlying animal locomotion.
Animals exhibit adaptive, versatile, and resilient locomotion under unpredictable and unstructured real- world constraints. They achieve such movements by successfully coordinating many points along their bodies, each of which has some degrees of freedom, even though their computational resources are limited. A key mechanism for the coordination of many body points is an autonomous decentralized control, whereby the non-trivial macroscopic behavior or functionality of an entire system emerges through the coordination of simple individual components. In fact, several biological findings indicate that animal locomotion depends on autonomous decentralized control mechanisms such as biochemical oscillators in true slime molds  and central pattern generators (CPGs) found in many animals .
We are trying to understand the decentralized control mechanism of various animals by using a synthetic approach: we propose a mathematical model based on the observation of real animals, and then we implement the propose mechanism in a robot to reproduce the locomotion of real animals. I introduce our recent results based on this approach, particularly focusing on the locomotion of snakes and ophiuroids [3,4].
|Time||16:15 - 16:45, Sep.8|
Department of Mathematics, Shimane University
Mathematical description of disease transmission dynamics often yields a nonlinear infinite- dimensional dynamical system (). Many important mathematical theories for infectious diseases dynamics have been developed . However, the waning immunity is a major challenge for mathematical modeling and analysis. We present our recent studies for epidemiological models with waning immunity . Here we also discuss delay equation formulation in the spirit of Lotka’s renewal equation. We then introduce an application of delay differential equations for modeling periodical outbreak of a childhood disease .
|Time||16:45 - 17:15, Sep.8|
Institute of Oceanography, National Taiwan University. Research Center for Environmental Changes, Academia Sinica
Microbial diversity in natural environments had been not observable for long time but microbial ecology and environmental microbiology have identified microbial diversity in the last two decades. General ecology also has just started investigating in-situ roles of microbial diversity, not only for using microbial community as model system. Major research interests include the roles of microbial community and diversity as the determinant of fitness of other organisms and their diversity through interactions, e.g, those between microbes and plants, their impacts on ecosystem functions (i.e. biogeochemical processes such as carbon and nutrient cycling), and community and ecoststem stability. In this presentation, after briefly summarizing my past studies on the roles of microbial community (bacteria and fungi) in plant-soil feedback in terrestrial ecosystems, I’m going to talk on recent achievements and developing ideas for better understanding the roles of bacterial diversity in ecosystem functions and their stability.
With a series of mathematical models, we have investigated the roles of microbes in the plant-soil feedback system where plant community alters soil abiotic and biotic environment that in turn affects plant growth, competition, and thus community and ecosystem dynamics. A model of two plant-two microbe species coupled with nutrient cycling demonstrated the roles of microbial diversity in buffering species- specific plant control on soil environments, and thus maintaining plant coexistence . The buffering effect was later supported by the microcosm experiment. A model of the stage-structured plant population coupled with two distinct microbial functional groups (parasitic and mutualistic ones) demonstrated that different plant traits are the key determinants of plant fitness under the dominance of parasitic or mutualistic microbes, which could also explain the empirical pattern . We have also reviewed the past achievement in the field of plant-soil feedback from the point of mathematical modeling .
For better understanding the roles of bacterial diversity in the maintenance of ecosystem functioning in aquatic ecosystems, we are developing an integrated framework that combines comparative genomic analysis, microcosm experiments, and model simulations . The key index to predict the decline of ecosystem functionality due to species loss is called ‘functional redundancy’, i.e., how many functions are shared by coexisting species within a community. Our new approach succeeded in evaluating the functional redundancy through species loss simulation using whole genome information of bacteria, which can quantitatively explain the results from microcosm experiments. On-going study extends this framework for developing new indices to predict functional stability of ecosystem, as well as the magnitude of ecosystem functions. Finally, I will briefly address the importance of developing new statistical methods to quantify microbial functions, which will be the main topic in my presentation at the mini symposium “Mathematical and statistical modeling to bridge the gap between empirical and theoretical research in ecology” on Sep. 9.