(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:
Faculty: 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
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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.
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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).