Introduction to Social Insects:

Social insects such as ants, bees, wasps, and termites, have been extraordinarily successful ecologically and evolutionarily, dominating the environment in most terrestrial habitats. These species live in intricately governed societies that rival our own complexity and internal cohesion. They exhibit consistent patterns of task allocation, division of labor and associated resource exploitation, produced proximately by nonlinear social dynamics and ultimately by multilevel selection effects. Social insect colonies present an excellent system in which to model the organizational challenges for complex societies, because (i). they scale from small groups of a few individuals to large-scale societies of thousands to millions; (ii). their life cycle can be divided into discrete stages, including colony founding, ergonomic growth, and colony reproduction, paralleling in many ways the organisma stages of early development, adult growth and reproduction; and (iii). each colony stage is shaped by a distinctive blend of multi-level nonlinear social interactions with potential multi-level fitness effects from gene level, to individual level, and to colony level.

Aims of Mathematical Modeling:

The goal of our work is to develop a quantitative and realistic modeling approach that can (a). integrate across different ecological scales and stages; (b). incorporate selection and thus evolutionary effects; and (c). incorporate directly measurable parameters, including metabolic costs, efficiency of energy flow, individual mass, and group size. We aim to apply these integrated multiscale multistage models to address central themes in behavior ecology and sociobiology, including: 1. How does selection act on social systems across levels from the individual to the collective group as a whole? 2. How does the organization of complex social groups scale relative to environmental conditions and constraints? 3. How do patterns of social interactions at different colony stages influence fitness and how are they shaped by selection?

Modeling Classes Relatd to Social Insects:

-Introduction of mathematical modeling of social and life sciences
-Adaptive complex systems

Current Research Projects Related to Social Insects:

(1) Social Network of Social Insects and Applications in Disease Spreading:    The colony network consists of two scales: (a) Individual scale: defines individual workers as nodes, (b) Colony scale: collapses the individual scale network so that the tasks themselves become nodes.  When the individual level network collapses, it becomes apparent that communication edges between tasks are extremely strong. This may suggest that what are normally considered weak ties in social networks become unusually strong in social insect colonies. We are developing individual based models (IBM) to explore how these weak ties allow colonies to adjust flexibly and resiliently to external changes to disrupt the network and to changes in colony size and associated work requirements; and we use the mean-field approximations from  IBM to address how network topology at the level of task groups interactions connects with colony function. Then can we integrate these two scales modeling approaches to address the central questions of how social insect colonies structure their networks around work, and how information within colonies contributes to efficiency and flexibility. 

Living in societies affects disease transmission, and understanding how infectious diseases transmit in social settings is a crucial area of research for humans directly.  Social ant colonies provide a novel experimental approach to manipulate infection and measure disease transmission. Social ants have a highly evolved social systems and they are able to effectively control many diseases as are known to optimize the transmission of resources like sugar and protein while reducing pathogen spread. Through understanding social network interactions across different scales, we will develop novel dynamic multiscale network models including spatial movements to understand the role of group size, group complexity, and individual contact patterns in driving infectious disease transmission; and therefore explore the important components of social living that promote disease transmission, and those that reduce its spread. Our mathematical modeling studies are expected to provide useful insights into the mechanisms behind social immunity and disease control in humans and other social species.
Involved Research Members:

 Faculty: Dr. Yun Kang; Dr. Carlos Castillo-Chavez;Dr. Gloria DeGrandi-Hoffman; Dr. Jennifer Fewell
 Graduate students:  Ioulia Bespalova (Ph.D student of Dr. Fewell); John McKay; Xiaohui Guo.
 Undergraduate students: Alyssa Holmes; Benjamin Krako; Jose Valenzuela; Karishma Thakkar; Heather Lyon; Talia Davis.

(2) Division of Labor for Social Insects: Social insect colonies show a decentralized system of the division of labor and its related task allocation. Both are resulting from multilevel 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 parametrization through data. We are developing multiscale models to explore: (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 and simplicity. This is an ongoing collaboration with Behavior Ecologists-Dr. Fewell Jennifer. This research has been supported by NSF DMS 1313312.

Involved Research Members:

 Faculty: Dr. Yun Kang; Dr. Jennifer Fewell; Dr. Jon Harrison; and Dr. Dieter Armbruster
 Graduate students: Oyita Udiani; Marisabel Rodriguez; Xiaohui Guo; Stephen Evilsizor;     Komi Messan; Sourav Kumar Sasmal (International graduate student from India).
 Undergraduate students: Benjamin Krako; Jared Scolaro; Jose Valenzuela; Mitchell Anhoury; Heather Lyon; Karishma Thakkar; Talia Davis.

(3) Ecological and Evolutionary Dynamics of Social Insects: Evolutionary and game theoretical models have been developed to show that social interactions can have profound effects on trait expression, patterns of selection, and the evolution of social groups. However, these models do not adequately capture the complexity of the internal dynamics within social groups. This is often due to simplifying assumptions about group dynamics that include: limiting the range of possible social options to be modeled, assuming that cooperation generates a negative pay-off gain when matched with a non-cooperative strategy, assuming that specialization consistently increases efficiency or gain over a generalist strategy (and by extension that individual efficiency always translates to group efficiency) and, importantly, that expression of a given behavioral trait is independent of the group's social and interaction structure.

To understand the interface between social dynamical processes and selection requires a new and more sophisticated modeling approach that captures these interaction effects, with better alignment between experimental biology and its mathematical assumptions. We will use different types of nonlinear differential equations (e.g., ODEs, delay differential equations, and integral differential equations) and individual based models to model complex adaptive dynamics in: (i) The link between gene regulation and social behavior to understand the evolution of sociality, and of particular interest in eusocial insects with their rich behavioral repertoires and diversity of social interactions; (ii) The founding stage, by comparing the alternate strategies of queens founding nests alone or in cooperative groups, with the aim of understanding how the interplay between proximate emergent mechanisms of social behavior and their fitness consequences may generate cooperative social groups; (iii) The ergonomic stage of colony growth (via producing more workers), with the aim of understanding how variation in foraging behavior around resource availability and colony nutrient demands affect colony growth and survival outcomes; (iv) The integrated multiscale and multistage models to obtain a full picture of how social interactions may affect selection patterns and evolutionary dynamics of social groups
Involved Research Members:

Dr. Yun Kang; Dr. Jennifer Fewell; and Dr. Jürgen Gadau
Postdocs: Martin Helmkampf, Sasha Mikheyev
Graduate students: Oyita Udiani; Marisabel Rodriguez; Stephen Evilsizor; Sourav Kumar Sasmal (International graduate student from India).
Undergraduate students: Jared Scolaro; Mitchell Anhoury

(4) Mathematical Modeling on Honeybees:
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 as a global crisis. The exact causes and triggering factors for the increased mortality of honeybees have not been completely understood yet, but several possible causes have been proposed including nutritional stress, harsh winter conditions, diseases, and parasitic mites particularly Varroa destructor that can vector pathogenic viruses. Mathematical models have begun to provide insights on ecological processes and important factors that contribute to the mortality of honeybees. However, the existing models are either detailed simulation models that are mathematically untrackable or over simplified models lacking essential biological components. In addition, they lack validation and parameterization with field data.

In order to understand the intertwined effects from disease, parasites, nutrition, climate changes, and foraging behavior on colony populations, there is a need to develop novel, realistic and mathematically tractable models that have a better alignment with data. This this collaborative research is to use both deterministic and stochastic spatial modeling approaches to develop realistic and mathematically tractable models to study the integrated effects of disease, parasitism, nutrition and behavior in changing environments on colony mortality. Specifically, we would like to address: 1. How parasite migration into colonies on foragers from other hives could affect the honeybee-parasite population dynamics with stage structures. 2. How the three way honeybee-parasite-pathogen 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.

Involved Research Members:

Faculty: Dr. Yun Kang; Dr. Carlos Castillo-Chavez; Dr. Rob Page; Dr. Gloria DeGrandi-Hoffman; Dr. Gro Adam
Graduate students: Krystal Blanco; Komi Messan; Marisabel Rodriguez.
Undergraduate students: Talia Davies and Karishma Thakkar.

(5) Mathematical Modeling on Obligated Mutualistic Interactions between Leaf-cutting Ants and Their Fungus Garden:
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 colony 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.

Involved Research Members:

Faculty: Dr. Yun Kang; Dr. Jennifer Fewell
Postdocs: Dr. Clark Rebecca (Prior Ph.D student of Dr. Fewell)
Graduate students: Marisabel Rodriguez.
Undergraduate students: Jonny Woodbury; Tin Phan; and Michael Makiyama (currently a M.S. student at OSU).