Dr. Yun Kang, Professor
Science and Mathematics Faculty
College of Integrative Sciences and Arts
7001 E. Williams Field Road,
Mesa, AZ 85212, USA
Office at Poly: Wanner Hall 301G
Phone number at Poly: 480-727-5004

Email: yun.kang@asu.edu

Area of Research: Dynamical system
theory and Mathematical biology
Curriculum Vitae

My greatest achievement in 2008,2013

Current Research Program in Our Team:

    (1) Mathematical Modeling of Honeybee Populations in Heterogenous Environments: Linking Disease, Parasite, Nutrition, and Behavior.

    The honeybee, Apis mellifera, is not only crucial in maintaining biodiversity by pollinating 85% plant species but also is the most economically valuable pollinator of agricultural crops worldwide with value between $15 and $20 billion annually as commercial pollinators in the U.S. Unfortunately, the recent sharp declines in honeybee population have been considered a global crisis. The primary cause of colony losses is the parasitic Varroa mites (Varroa destructor Anderson and Trueman). The study to unfold the mystery of the dramatic decline in honeybee populations and for developing control strategies for Varroa that reduce colony losses presents both challenges and opportunities for research and education.

    This collaborative research between Arizona State University and Carl Hayden Bee Research Center fosters a culture of theory-experiment collaboration with aims to develop realistic and mathematically tractable models that will be validated and parameterized via using field data. Our interdisciplinary collaboration will enable us to study the integrated effects of disease, parasitism, nutrition and behavior in changing environments and the effects on honeybee colony mortality across multiscale in time and space. Rigorous mathematics will be integrated with extensive field and lab data to investigate:

    1. How parasite migration into colonies via foragers from other hives located at different landscape structures could affect the honeybee-parasite population dynamics with stage structures.
    2. How the honeybee-parasite-virus interactions with the honeybee foraging behavior in seasonal environments cause colony losses.
    3. How the crucial feedback mechanisms linking disease, parasitism, nutrient and honeybee foraging behavior might be responsible for the colony growth dynamics and survival in a dynamical environment with multilevel spatial components.
    Nonlinear nonautonomous differential equations within metapopulation frameworks and individual based models will be used to model the honeybee population with spatial scales ranging from the individual, the colony, to the regional level and timescale spanning from seconds, days, to months.

    This research project has been recommended for funding from NSF DMS 1716802. Our ecologist collaborator is Dr. Gloria DeGrandi-Hoffman

    (2) Research Program on Complex Adaptive Systems of Social Insect Colonies. This is partially supported by The James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Scholar Award.

    Social insect colonies show a decentralized system of the division of labor and its related task allocation. Both are resulting from multi-level interactions among members of the colony and between the colony and the environment, as the size of colony increases. Social insect biologists face the challenge of integrating the individual and colony levels of organization. Mathematical models have begun to show how colony-level patterns of division of labor result from simple individual behavioral rules. However, these models do not integrate the different levels of interactions in a colony nor do they consider the influence of a dynamically changing environment. In addition they lack validation and parameterization through data. We are developing multi-scale ecological and evolutionary models to explore important and interconnected questions like: 1. How do task organization and work performance scale with colony size? 2. How does the scaling of work organization affect colony metabolism and growth? 3. How do social interaction network structure and the related information flow scale with colony size? 4. What are the emergent dynamics inherent in early social group formation? 5.How are social phenotypes shaped by the transition to cooperative associations? 6. How do costs and benefits of cooperation balance across colony founding and reproduction?

    As part of this research program, we are collaborating with behavior and evolutionary biologist Dr. Fewell Jennifer to develop dynamical network models of divison of labor in social insects to investigate questions like (a). How the underlying topology of the interaction network of a colony evolves and adapts at different scales of the organization. (b). How to characterize the crucial feedback mechanisms linking both structure and dynamics of the division of labor in a dynamical environment. And (c). How the decentralized social insect system based on many independent and simple individual interactions leads to highly complex dynamics with great network properties such as scalability, robustness/ flexibility and simplicity. This research project has been supported by NSF DMS 1313312. Please check our website on the related modeling work of social insects Modeling Lab for Social Insects.
    (3) The Impact of Positive Interactions, Disease and Dispersal on Ecological Communities in Heterogeneous Environments: Both positive and interspecific interactions have essential roles in community structure and diversity. The combinations of positive interactions and competition or predation can lead to Allee/Allee-like effects that may generate a critical threshold below which at least one species goes extinct. Allee effects are believed to be strong regulators of coexistence, disease, extinction, and invasion of alien species, which have been detected in natural populations of a wide array of taxa. During the past 3 years, I have been developing mathematical models and the related dynamical system theory to study population dynamics in the presence of Allee effects. In particular, I study discrete-time models on the interactions of Allee effects and interspecific interactions as well as continuous-time models on the interplay among the Allee effects, disease and dispersal. These preliminary studies result more than 11 publications (see our publication page for more detailed work. ). Some highlights of our work include i) Allee effects may promote the coexistence of species in both prey-predator and competition systems when species have scramble competition; ii) Susceptible-Infective models with Allee effects and disease-modified fitness have rich dynamics with implications that the quantification of management or general intervention measures cannot be measured exclusively by the disease's basic reproduction number R0; iii) Allee/Allee-like effects with dispersal may save species from extinction.

    This study has provided a foundation to seek a framework that can integrate community ecology (species interactions), population dynamics (Allee/Allee-like effects), animal (including human) behavior (e.g., dispersal as well as the theory of predations in different environments) and epidemiology (disease) as a whole through strong understanding of mathematical tools. My current work has focused on eco-epidemiological models through collaboration with Professor Weiming Wang, Professor Carlos Castillo-Chaves, and Ph.D students from the Simon A. Levin Mathematical, Computational & Modeling Sciences Center at ASU. Our long-term goal is to introduce a framework that incorporates the following features: (a) disease-modified fitness; (b) positive interactions that can lead to Allee/Allee-like effects; and (c) topological structures of landscape involving a number of patches. My recent graduated Ph.D student Sourav Kumar Sasmal (Indian Statistical Institute, Kolkata, India) worked on this project as part of his dissertation.

    (4) Global Dynamics of Discrete-time Biological Systems: Coexistence of interacting species in nature is a central theme in theoretical ecology. For deterministic models, the idea of permanent coexistence, which guarantees convergence to an interior attractor from any strictly positive initial conditions, is regarded as a strong form of coexistence. Permanence, however, has not been widely used in discrete-time ecological models due to its complicated boundary attractors (e.g., the standard quadratic map). To ameliorate this problem, we apply the relative nonlinearity concept to give an easy-to-check criterion to imply permanence for general multiple-species-interacting discrete time population models. The work on classical two-species-interacting discrete time population models has been done with Peter Chesson in Theoretical Population Biology (2010). Recently, I have extended this work to a general two-species-interacting discrete time population models that is published in Discrete and Continuous Dynamical Systems-B (2013). Now we are working on general n-species models.

    The traditional concept of permanence, which would fail due to exceptional behavior on sets of measure zero is unlikely to be broadly useful, because the noise in nature implies that the system would not stay in such sets. For this reason, I have developed a new concept of coexistence, relative permanence. This new concept is a generalization of permanence that excludes sets of measure zero. By proving the traditional permanence theory in a proper new space and deriving key properties of critical curves of non-invertible maps, we can expect to identify the conditions under which discrete-time two species population dynamics are relatively permanent. I have shown the concept of relative permanence through a simple discrete competition model in two publications: one is in the Journal of Difference Equations & Applications (2012) and the second one with Hal Smith is in the Journal of Biological Dynamics (2012).

    (5) Mathematical modeling on mutualistic symbiosis: Mutualistic symbiosis is a type of mutualism in which individuals interact physically, or even live within the body of the other mutualist. Frequently, the relationship is essential for the survival of at least one member. In general, there are two types of mutualistic symbiosis: facultative and obligate mutualisms. Facultative mutualisms are not essential for the survival of either species. Individuals of each species engage in mutualism when the other species is present. Obligate mutualisms are esstential for the survivial of one or both species.
  • Obligate Mutualisim: Leaf-cutting ants cannot eat leaves. Instead, they carry the cut pieces back to the nest and use it as compost to cultivate the fungus. The fungus cannot survive outside the nest or reproduce without the ants help. Here is an article that may give you a general view of the interaction between leave cutter ants and its fungus-ants. According to data, the division of labor is a very important factor that determines whether the cololy can survive at its early stage (one of the supporting evidences is the poster by Leah Drake, Rebecca Clark and Jennifer Fewell). We have developed a mathematical model to study the interaction between leaves cutter ants and fungus growth during early colony expansion, which is able to address the functional/numerical responses between ants and fungus, and the importance of the labor division at the early stage of colony expansion. This is an ongoing collaboration with Fewell Jennifer and her former Ph.D student Clark Rebecca . See our publication on this topic in 2011.

  • Facultative Mutualisim: Mycorrhizal fungi form symbiotic associations with roots of plants that benefit plants primarily by improving uptake of soil nutrients and increasing stress tolerance. Most plants are colonized by one functional type of mycorrhizal fungi, but some plants such as the important riparian tree Populus fremontii (cottonwood) are colonized by 3 different functional fungal groups; ectomycorrhizal (EM), arbuscular mycorrhizal (AM) and dark septate endophyte fungi (DSE) each contributing different benefits. Shifts in colonization patterns are known to occur and various factors such as life stage and environmental variables. Our current ongoing project (with Jean Stutz) is to develop a mathematical model to examine these fungal colonization patterns over time in heterogenous enviornment.

Some Interesting Problems in Discrete Systems (Click here)