Modeling with Math for Teachers

Associate Director for Education & Outreach Suzanne Lenhart illustrates the concepts in the “Modeling with Math” teacher workshop. Sixteen teachers from Knoxville area high schools attended.

A new resource for teachers, “Modeling with Mathematics,” with examples and exercises to illustrate modeling concepts using mathematics from Algebra I and II is now available on the NIMBioS website.

Simple models with discrete time steps are included, as well as functions with continuous variables, such as time or number of dollars. Open-ended scenarios to practice creating models are also available.

Additionally, two presentations demonstrate the construction of functions to fit data and the use of probability in biology models. An Excel file is provided to iterate and to illustrate discrete models with sequences.

The teacher workshop for which these materials were developed was conducted in cooperation with Lynn Hodge, associate professor of mathematics education at the UT-Knoxville, and was partially supported by the East TN STEM Hub and the Center for Enhancement Education in Mathematics and Sciences.

The unit is another addition to NIMBioS’ growing list of educational resources, which includes nine educational modules, geared to different grade levels, from K-12. The modules cover a variety of topics, from measuring biodiversity to modeling predator-prey relationships in soil and more.

For more information about NIMBioS Education & Outreach offerings, contact Associate Director of Education & Outreach Suzanne Lenhart ( or Education & Outreach Coordinator Greg Wiggins (

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NIMBioS Extracurriculars & the Mathematics of Dance

“It may be possible to do without dancing entirely. Instances have been known of young people passing many, many months successively, without being at any ball of any description, and no material injury accrue either to body or mind;–but when a beginning is made– when the felicities of rapid motion have once been, though slightly, felt–it must be a very heavy set that does not ask for more.” — Jane Austen in “Emma”

No, this is the not the first interdisciplinary workshop on the mathematics of English country dance, but perhaps it could be.

A man of many talents, NIMBioS Director Louis Gross donned his Elizabethan attire last week to join other local English country dancers in teaching a few steps to students in a 200-level English class at UT that includes the works of Jane Austen. The dancing was very popular at the turn of the 19th century during Austen’s time and featured in her novels, not to mention a good number of modern Austen movie adaptations.

Gross has danced with the local group, Lark in the Moon, for about 15 years. Weekly dances to live music are held every Sunday at the Laurel Theater. Newcomers are always welcome.

“It’s a wonderful group of folks, good exercise, and has participants from elementary school to retired folks,” Gross said.

With their weaving and whirling, the dances reveal a formal mathematical structure akin to abstract algebra, Gross observed, making his visit to the classroom yet another NIMBioS contribution to foster interdisciplinary connections across campus.

Who ever said that college English class is not interesting?!

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New in Science: Working Group Takes on Transient Dynamics

Long Transients Working Group Meeting 2 from October 2017: Ying-Cheng Lai, Alan Hastings, Andrew Morozov, Karen Abbott, Sergei Petrovskii, Katherine Scranton, Tessa Francis, Mary Lou Zeeman, Kim Cuddington, Gabriel Gellner

A review paper published this week in Science by the NIMBioS Working Group on Long Transients and Ecological Forecasting is generating buzz on social media.

The paper proposes a classification system for ecological dynamics that persist over ecologically relevant time scales—dozens of generations or longer. These “long transient dynamics” are applicable to many questions in ecology, such as how to explain species distributions or population changes over broad timescales. Previous research has treated transient phenomena separately, which the authors write, makes instances of transient dynamics appear “novel and idiosyncratic.” In this review, the authors turn to dynamical systems theory to develop a classification scheme that categorizes the mechanisms underlying transients. The study also links empirical observations to simple prototypical models. The systematic framework described in the review could be useful for ecosystem management.

The Working Group has met twice at NIMBioS since 2017 and is scheduled to meet for a third time later this month. It is co-organized by Alan Hastings (Environmental Science and Policy, Univ. of California, Davis); Kim Cuddington (Biology, Univ. of Waterloo, Canada); Andrew Morozov (Mathematics, Univ. of Leicester, UK); and Sergei Petrovskii (Mathematics, Univ. of Leicester, UK).

Citation: Hastings A et al. 07 Sep 2018. Transient phenomena in ecology. Science. Science 361:6406, DOI: 10.1126/science.aat6412


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Happy Birthday to a Great Mentor

(L to R): NIMBioS visitor and seminar speaker Shandelle Henson, UT Math Graduate Coordinator Pam Armentrout, Suzanne Lenhart, and Tom Hallam

Birthday celebration for Tom Hallam (center) in Hallam Auditorium

Professor Emeritus and NIMBioS progenitor Thomas Guy Hallam was feted yesterday in the very room of his namesake Hallam Auditorium before the seminar talk of one of his many former advisees.

Friends, colleagues and former students joined NIMBioS visitor and seminar speaker Shandelle Henson, a math and biology professor at Andrews University in Michigan, to celebrate Hallam’s birthday in a pre-talk reception.

Many of Hallam’s former students have now gone on to have successful research careers at institutions around the country, and quite a few have been involved in NIMBioS, like board member Linda J. S. Allen, a professor of mathematics and statistics at Texas Tech University.

“Tom was really the progenitor of NIMBioS,” explained NIMBioS Director Louis J. Gross.

Hallam joined UT in 1977 as a joint professor in mathematics and ecology. During the next several decades, Hallam’s research group integrated ecotoxicology and population dynamics into a watershed quality assessment tool for the U.S. Environmental Protection Agency. His research in using mathematical models to solve problems in ecotoxicology and ecology inspired him to begin an interdisciplinary program at the university that combines mathematics and biology, the progenitor to NIMBioS.

Happy Birthday Dr. Hallam!



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Major Accomplishments: The 10th Annual Report from NIMBioS

NIMBioS’ 10th annual reporting period to the National Science Foundation, which largely supports the institute, recently concluded, and the 173-page report has been submitted to NSF. 

NSF requires its funded institutes to provide a variety of data as well as answering questions (see boxes at right) about our accomplishments and the impact of our activities. 

Some highlights from this year’s reporting period, which runs from September 2017 to August 2018, include:

  • NIMBioS hosted 10 Working Groups, two Investigative Workshops, two Tutorials, monthly XSEDE HPC workshops, five INCLUDES webinars, and many Education and Outreach activities.
  • There are projected to be more than 400 participants in NIMBioS-hosted activities during this period with 7 Postdoctoral Fellows in residence and 21 Short-term Visitors.
  • Participants from 15 countries and 40 U.S. states representing 181 different institutions.
  • International participants amounted to 10% of all participants.
  • Most participants were college or university faculty (46%), but undergraduates (13%), post-doctoral researchers (13%), and graduate students (8%) accounted for a significant fraction of participants.
  • Across all events female representation was 48%, and minority representation was 12%, which falls within ranges for doctoral recipients in the biological and mathematical sciences.
  • While the majority of participants identify themselves as being in fields of biological/biomedical sciences and mathematical sciences, there are a number of participants from the agricultural sciences/natural resources, health sciences, computer/information sciences, and others.
  • Activities at NIMBioS have led to 896 published journal articles on a range of subjects from January 2009-June 2018. Of those, 819 articles are indexed in the Institute for Scientific Information’s (ISI) Web of Science (WOS), span 104 discipline areas, and involve 2,355 researchers from 919 unique institutions spanning 61 countries. The WOS articles have appeared in 303 different journals, many of which are considered high-impact. The articles have been collectively cited 14,602 times, with an average of 17.92 cites per article and an h-index of 51. The cites per article is greater than either of the two major research fields of the publications during the last 10 years; mathematics (4.17 citers/paper) and biology (16.08 cites/paper). Ninety-eight participants have authored five or more papers each as a result of NIMBioS affiliated collaborations.

The full report can be found here.


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Save the Salamander: Epidemiological Modeling Deployed to Halt Killer Fungus

Fire salamanders in parts of Europe are almost extinct due to the Bsal skin fungus. (Photo: Frank Pasmans)

We like to hear what former NIMBioS postdocs are up to, so we were happy to learn from UT professor Matt Gray that his mentee Angie Peace was recently awarded part of a large $2.5 million grant from the National Science Foundation.

The award will fund research to investigate Batrachochytrium salamandrivorans (Bsal), a flesh-eating fungal pathogen that affects salamanders. Researchers will characterize the  fungus’ epidemiology, host immune responses, and pathogenesis in the red-spotted newt, one of the most widely distributed salamander species in North America. Researchers hope to head off an outbreak of Bsal in North America, which holds the world’s greatest diversity of salamanders. Tennessee alone has 57 species.

Originating from Asia, Basl was first discovered in Europe in the Netherlands in 2008 where it caused mass mortality and drove the infected populations to local extinction. Subsequent laboratory trials showed most European salamander and newt species die within two weeks after infection.

Peace, now an assistant professor of mathematics and statistics at Texas Tech University, was awarded $165,000 to lead the epidemiological modeling associated with the research.

As a NIMBioS postdoc from August 2014 to July 2015, Peace developed mathematical models of essential elements and their interactions under the framework of ecological stoichiometry.

If you have some news about a former NIMBioS postdoc, drop us a line!

ICYMI recent news from NIMBioS postdocs:

Team Science at NIMBioS Produces Top Paper

A Predator-Prey Model of Poverty Traps, New Paper from Ngonghala

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How Will Species Adapt to Climate Change? g2p2pop Seeks Answers

What is g2p2pop? The catchy abbreviation describes a new effort to model genomes to phenomes to populations in a changing climate.

The project grew out of activities of the NIMBioS Working Group on Modeling Organisms-to-Ecosystems, and received a $500,000 Research Coordination Network (RCN) award from the National Science Foundation.

Nika Galic, who works in environmental safety and ecological modeling at Syngenta Crop Protection, was a participant in the Working Group and is co-PI on the grant.

The goal of the RCN is “to assemble a diverse, interdisciplinary, multi-institutional, multinational network of scientists to tackle the urgent challenge of predicting how populations and species of vertebrates will respond to a changing climate by integrating knowledge across levels of biological organization.”

Through up to ten laboratory exchanges and five planned workshops, g2p2pop aims to serve as a platform for building interdisciplinary collaborations. They hope to develop new mechanistic models to extrapolate key processes across levels of organization.

Working Group co-organizer Valery Forbes is co-organizing one of the g2p2pop workshops next summer on “Modeling from Genomes to Phenomes to Populations” at the University of Minnesota.

Membership in the g2p2pop RCN is open to university faculty, students, and postdoctoral scholars, those working in industry, and anyone with an interest in the topic.

PI is Loren Buck, professor of biology at Arizona State University. Along with Galic, the other co-PI is Allyson Hindle, assistant professor of anesthesia at Massachusetts General Hospital/Harvard Medical School.

You can read more about g2p2pop at

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Team Science at NIMBioS Produces Top Paper

The last meeting of the Working Group in May 2015. (L to R): James Bever, Jonathan Bauer, Katharine Suding, Allan Strand, Dan Johnson, Kerri Crawford, James Umbanhower, Karen Abbott, Jiang Jiang, Maarten Eppinga, Liza Comita, Keenan Mack. Not Pictured: Mara Baudena.

This is the story of how researchers from different corners of the scientific universe can come together to create new synthesis — it involves two former NIMBioS postdocs, a former sabbatical fellow and the special alchemy of a NIMBioS Working Group.

From 2013 to 2015, empiricists and theoreticians studying plant-soil feedback met at NIMBioS with the goal of better understanding the potential role of the soil community organisms that drive diversity patterns within plant communities. They formed the NIMBioS Working Group on Plant-Soil Feedback.

Biologist Allan Strand from the College of Charleston was on sabbatical at NIMBioS; Jiang Jiang and Keenan Mack were in residence as postdoctoral fellows. All three joined the Working Group.

The efforts of the Working Group were rewarded this week with a paper in Nature Ecology & Evolution. The study, “Frequency-dependent feedback constrains plant community coexistence,” outlines a new way to mathematically describe the social network that creates and maintains biodiversity in forests. The equation can be applied to plant communities of any number of species, whereas previously, only predictions of pairwise species interaction were possible.

The authors, which included Jiang, Mack and Strand, tested their theory using observations of tree species diversity on more than 200,000 locations in North America.

“We had previously found spatial patterns of seedlings consistent with strong plant-soil feedback in the data. Our new theory enables us to demonstrate that these feedbacks can explain the high diversity of tree species in warm, moist forests in the South East of the United States and the decline in tree diversity in colder and drier forests,” said senior author of the study and Working Group co-organizer James Bever in a press release. Bever is a professor of ecology and evolutionary biology at the University of Kansas.

“To be able to meet with Working Group participants in Knoxville not just once, but four times between 2013 and 2015 was crucial to getting to the bottom of the intriguing problem of how to quantify community-level plant-soil feedback, ” writes lead author and Working Group co-organizer Maarten Eppinga, in a blog post about the paper. Eppinga is an assistant professor of environmental sciences at Utrecht University.

The other authors on the paper—all from the Working Group—are Mara Baudena, an assistant professor of geosciences at Utrecht University, and Daniel J. Johnson, an assistant professor of forest resources and conservation at the University of Florida.

NIMBioS Working Groups are relatively small with no more than 15 participants, focus on a well-defined topic and have well-defined goals and metrics of success. Since 2008 when the institute was established, NIMBioS has hosted 58 Working Groups.

Jiang, who is now a professor in the Department of Soil and Water Conservation at Nanjing Forestry University, China, joined the Working Group during its second meeting. “It was a really good experience with exciting discussions among top scientists in their areas,” he wrote in an email.

For Strand, his sabbatical at NIMBioS changed the way he approaches research, for the better. “I do research differently now after my sabbatical at NIMBioS. Now when I begin a research project, I always think about what team can I assemble to work on this and what data already exists. Before I tended to do this on my own,” Strand said in an interview.

The result? “All of a sudden my publication rate doubled, my funding is better than it was,” he said. “It made me more collaborative and more willing to think about existing data and modeling that.”

Congratulations to the Plant-Soil Feedback Working Group!

Eppinga MB et al. 2018. Frequency-dependent feedback and plant community coexistence. Nature Ecology and Evolution.

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A Decade of Summer Undergrad Research Underway

Undergraduates take the NIMBioS grand tour on the first day of SRE 2018. This year’s program marks the 10th year of SRE.

The NIMBioS Summer Research Experience (SRE) program kicked off yesterday, celebrating a decade of providing students with opportunities to conduct research at the interface of mathematics and biology.

Fifteen undergraduate students from around the country arrived at NIMBioS to begin the program, which runs for eight weeks. With NIMBioS postdocs and UT faculty, they will work on teams tackling a variety of topics, from modeling thousand cankers disease, management of feral cats, to topics related to hunting in tropical forests, using phylogenetics to understand cancer tumor evolution, and predicting mosquito abundance levels in response to the environment.

To mark the first day, students and their mentors met to begin discussing their projects and what they will aim to get accomplished in the eight short weeks.

Although the main focus is research, the students also receive training on mathematical modeling and software, careers, and graduate school, as well as experience working with the media. They also make time for field trips, dinner parties and other social gatherings.

Nationally competitive, the NIMBioS SRE program typically receives more than 100 applicants. Participants have gone on to do amazing things, from publishing their research in academic journals, to winning competitions with their research, to pursuing doctoral studies in at the interface of math and biology. Participants receive a stipend, apartment-style housing, and travel support to Knoxville.

More photos in our SRE Photo Album.

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Nature Paper Sheds Light on Human Brain Evolution

Why did the human brain evolved to its unusually large size? Former NIMBioS GRA Mauricio González-Forero has some answers in a new Nature publication that develops a mechanistic model showing brain expansion was likely driven by ecological, not social, processes.

Roughly six size times larger than expected for its body size, the human brain consumes 20 percent of the body’s energy yet accounts for only 4 percent of its mass. The dominant hypothesis as to why the human brain has evolved this way suggests that challenging social interactions, such as cooperation and competition, were the driving force.

In their model, González-Forero and co-author Andy Gardner found evidence instead that environmental challenges, such as finding food, are key in driving brain-size evolution.

A Marie Curie Fellow of Evolutionary Biology at the University of St Andrews, González-Forero was a NIMBioS GRA from 2010 to 2012. He earned a Ph.D. in ecology and evolutionary biology in 2013, conducting research in the lab of Sergey Gavrilets focused on mathematical modeling of the evolution of sociality.

González-Forero wrote a detailed article for The Conservation about the Nature paper, which can be found here. The paper has already received widespread attention in mainstream media.

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