Contact Info:
Dr. James Peirce
Professor of Applied Mathematics 
Department of Mathematics & Statistics
River Studies Center

The University of Wisconsin - La Crosse (UWL) Mathematics & Statistics Department is proud to offer a 10-week Summer Research Experience for Undergraduates program in the beautiful city of La Crosse, Wisconsin.

Through workshops, seminars, and retention activities we will help 8 students develop the motivation and wide-ranging skills necessary to transition into scientific careers including becoming professional mathematical biologists. Our REU program aims to give the participants as thorough an interdisciplinary research experience as possible with a focus on the model development, analysis, and validation processes of the mathematical modeling cycle. This will be achieved through our mathematics and biology mentors who will provide introductory lectures and tutorials tailored to meet project and student needs. Student experiences will then swiftly transition from classroom sessions to daylong research-level activities and eventually to the preparation of presentations and/or manuscripts for dissemination. Throughout the summer, team-building activities will supplement research and educational activities to develop an environment that places high priority on collaboration and interaction among students and between students and their mentors.

Each group will meet daily with their research advisors, with increasing independence as the summer progresses.  We expect that the summer projects will result in presentations at a national meeting (such as the International Symposium on Biomathematics and Ecology Education and Research or the MAA-AMS Joint Mathematics Meeting).

Students will be given the opportunity to develop their research questions and then share their findings in both academic settings and with resource managers. We will also provide participants with educational and social activities to create an environment that is conducive to collaboration.

Our previous REU Site provided mentoring to 24 students through collaborations among mathematics, statistics, and biology faculty, as well as with federal scientists. Products from these collaborations include multiple research papers that have either been published or are being prepared for publication.  One published paper in particular, "Using a Summer REU to Help Develop the Next Generation of Mathematical Ecologists", was specifically inspired by our 2016-18 REU site and appeared in the Bulletin of Mathematical Biology.

The 2019-2021 REU program will build upon UWL’s successful track record of fostering undergraduate research in mathematical biology from our previous NSF-funded Undergraduate Biology and Mathematics-Group: Collaborations on Riverine Ecology program (2010-13) and our recent REU Site: University of Wisconsin La Crosse REU in Mathematical Ecology (2016-18). The University of Wisconsin - La Crosse has a national reputation for excellence in fostering undergraduate research, which has led to hosting the 2009 and 2013 National Conference on Undergraduate Research.  Additionally, the University of Wisconsin - La Crosse is the host to the biennial Midwest Mathematical Biology Conference and is hosting the International Symposium on Biomathematics and Ecology Education and Research in October 2019.

Program Dates:  June 1, 2021 - August 7, 2021
Stipend:  $5000 and a $75 weekly food allowance. 
Note:  Notification of acceptance may begin as early as February 15th.

Who Should Apply?

Who Should Apply:

Relation Majors/Areas

  • Mathematics
  • Statistics
  • Data Science
  • Biology/Ecology

Students will explore questions in one of the following two working groups:

Application of spatially discrete, integral projection models (IPMs) to fish species in the Upper Mississippi River System.

As part of this program, students will explore how the size distributions of particular fish species influence patterns of growth, movement, and survival at the population level. Recent models have merged individual-based population models with network-node-based spatial models. Students will apply these models to fish species found in the Upper Mississippi River System and investigate how factors such as harvesting, spawning, and competition affect population patterns. After an introduction to general ecological principles and the theoretical components of existing models, students will be encouraged to develop questions that are of interest to them.  Research mentors from the Mathematics & Statistics Department, Biology Department, and U.S. Geological Survey will assist students with modifying existing code (in R or Python) to create simulations that attempt to answer their specific questions. Results from this work will be important for both understanding the basic ecology of particular fish species and developing appropriate strategies aimed at managing their populations. 

Student Qualifications

Students having the following background/experience are ideal:   

  • For a math student (preferred but not required), experience with linear algebra or differential equations
  • For a biology/ecology/natural resource student (preferred but not required), experience with population modeling, population ecology, or population dynamics covering topics such as matrix population models 

  • Coding in R, python, or other programming language(s)

  • Able to work collaboratively and independently

  • And have access to reliable internet (if the REU is virtual, students will be expected to participate online daily)

 We will teach the background on ecology, mathematical modeling, and programming related skills (in R or Python) necessary for this project.  

Mentors: James Peirce (Mathematics & Statistics), Greg Sandland (Biology), Richard Erickson (U.S. Geological Survey)

Application of Topological Data Analysis to Upper Mississippi River Data

Topological Data Analysis (TDA) utilizes Topological tools to understand the “shape” of the underlying space of a given data. Data analysis from Topological perspective is beneficial in visualizing the data, and this is useful especially when the data at hand is high dimensional. USGS has been collecting data from the Upper Mississippi River (UMR) for over 25 years, and these data include water quality, vegetation, fish, time-series, and more. Students will manipulate these datasets, apply TDA to the datasets, and extract topological information. The interpretation of the topological information is used to answer ecological questions such as: “When in time did the Mississippi River experience a regime shift from unvegetated to diverse plant communities? “What is the shape of the Mississippi River from up-river to downriver? What scales predominantly define the shape? What characteristics define the ecological heterogeneity along this upriver to downriver gradient?” And more. Students will gain experience working with large datasets, cluster analysis, and Topological Data Analysis. The outcomes of this project will be used so that resource management of UMR has better understanding of these data.  

Student Qualifications

Students having the following background/experience are ideal: 

  • data preparation, statistical modeling.  

  • topics in ecology or natural resource management. 

  • coding in R, python, or other programming language(s). 

  • topology (preferred, not required), linear algebra (preferred, not required). 

  • able to work Independently, able to Communicate clearly and have access to reliable internet (present weekly virtually if REU is held virtually).  

We will teach the background on ecology, topology, TDA, and TDA related programs in R necessary for this project.  

Mentors: Dr. Wako Bungula (Mathematics & Statistics) Dr. Danelle Larson (U.S. Geological Survey) 

Application Info


Participation in the UWL REU in Ecological Modeling of the Mississippi River Basin is limited to students who meet the following criteria.

  • U.S. Citizen or Permanent Resident
  • Current Undergraduate with at least one semester of coursework remaining before obtaining a Bachelor's degree

Application Materials

Applications can be completed on the NSF Education and Training Application website

Application Timeline

  • December 1, 2020 - Application opens
  • February 15, 2021 - Priority deadline (review of completed applications begins)
  • March 1, 2021 - Application deadline
  • March 15, 2021 - Decisions and offers complete



Events (if REU is not virtual):

  • Campus and department orientation
  • Team-building activities
  • Tour of United States Geological Survey (USGS) facility
  • Visit with the Biostatistics division of Mayo Clinic
  • Guest lectures by area professionals
  • Continuous social interactions with Dean's Distinguished Fellows at UWL
  • Participation in UWL's College of Science and Health Summer Research Celebration in early August



  • Competitive Stipend
  • Suite-style apartments
  • Travel expenses to and from La Crosse and to and from one national meeting
  • Full access to campus recreation and campus library/computing facilities
  • Wireless internet throughout campus

Over the past three summers our REU participants have been trained in modeling techniques ranging from branching process, temperature-dependent disease dynamics, and data science. To date, the inaugural REU Site resulted in two publications in professional journals (Haider et. al (2017), Bennie et. al (2018)) with two more in preparation (Buch et. al (2018), Sandland (2018)), and numerous talks and poster presentation a regional and national conferences. The 2018 summer will likely result in four publications, while the 2019 summer is still writing up results to submit for publication. Select examples from the past 3 years:

[1] Haider*, H. S., Oldfield*, S. C., Tu*, T., Moreno*, R. K., Diffendorfer, J. E., Eager, E. A., & Erickson, R. A.. Incorporating Allee effects into the potential biological removal level. Natural Resource Modeling, 30(3) (2017):  e12133. The group studying the effects of wind energy development, the students derived a new metric for potential biological removal that better accounts for Allee Effects - the effects of low populations on extinction risk.

[2] Bauer*, J., Lieberman*, K., Rouleau*, R., Allen, M, Baines, A. A Model of Virulent and Hypovirulent Strains of Fungus and Survivability of American Chestnut Forests. To be submitted. Target: Letters in Biomathematics (2018). In an attempt to control the spread of a fungal blight that has been infecting American chestnut trees for the past 100 years, students modeled the dynamics of various tree communities over time with the effects of virulent and hypovirulent forms of the blight using an epidemiological model. Their results have been very encouraging thus far for the chestnut community in their efforts to abate the effects of blight in various communities in the Midwest.

[3] Gahm*, K., Budd*, S., Baumann, D., Bennie, B., Haro, R., Erickson, R., Janikowski, K.J., Van Appledorn, M. Analysis of Wood Dynamics in Large River Systems. To be submitted. Target: Geomorphology (2018). In an effort to understand the distribution of large woody structure in large rivers such as the Upper Mississippi River (UMR), students analyzed a long-term dataset of wood occurrence in three UMR navigation pools using random forest models, mixed-effects logistic models, and t-tests. The students found relationships between wood presence and aquatic habitat strata, water depth, and wing dam or revetment presence, indicating that both transport- and source-related variables may be important to understanding wood dynamics in large rivers.

*REU student authors


Our REU has sought to expose under-represented groups to mathematical ecology and its application to natural resources management. As remarked above, we successfully recruited a significant proportion of underrepresented minority and/or first-generation college students and increased their likelihood of attending graduate school. The results of student work have had an impact on natural resource management. We achieved this by using an interdisciplinary team of academic and government researchers who all work closely with natural resource managers. Our students shared their results with the US Geological Survey and US Fish & Wildlife (USWFS) biologists, who incorporated our students' findings into their work. For example, the results from Haider et al. (2017) were used by a USFWS Endangered Species group to help select a type of model used for a species listing decision. Additionally, our students presented their results with state policy makers (representatives for Sen. Baldwin and the Wisconsin Chief of Staff for Rep. Kind). Faculty mentors utilized the invasive species dataset collected during the first REU program as a tangible realistic study for exercises in their upper level multivariate statistics course.

Summary of Results

Objective 1: Training Undergraduate Students in Various Sub-disciplines of Mathematical Ecology. We trained twenty-four undergraduate students in the area of mathematical ecology through research projects ranging from disease ecology to data analytics. During the course of the summer, students learned introductory material in both mathematics and ecology, participated in field sampling in the Upper Mississippi River, and developed and implemented their own research projects.

Survey results: Frequent and direct contact with research mentors was a key factor in successfully training our undergraduates in the sub-disciplines of mathematical ecology. Of the 24 participating undergraduate students, 87.5% were extremely satisfied with the interactions that they had with their research mentors while the remaining 12.5% was satisfied with this relationship. No students reported dissatisfaction with their faculty interactions. In terms of mentor quality, students were either extremely satisfied (62.5%) or satisfied (12.5%) with the backgrounds of their mentors and mentor preparedness.

Research products: Students were required to present their research results at a number of meetings including the UWL College of Science and Health Summer Celebration of Undergraduate Research (August 2016), the International Symposium on Biomathematics, Education and Research (Oct. 2016, Oct. 2017), the Joint Mathematics Meetings (Jan. 2017, Jan. 2018), and to members of various government agencies (e.g., the USGS and the USFWS). Before the end of the program, student pairs were also required to begin writing a formal manuscript of their projects.

Objective 2: Motivating Undergraduate Students, Especially Underrepresented and/or First-Generation College Students with Limited Access to Research at their Home Institution, to Attend Graduate School. A substantial fraction of our 24 students were part of underrepresented minority groups and/or were first-generation college students (45.8%). Additionally, 66.6% of our students were female. The proportion of students that reported that our REU increased their likelihood of attending graduate school contained a representable proportion of the aforementioned students from underrepresented minority groups or students that were first-generation college students (50%).

Survey results 83.3% of all participants reported that the REU increased their likelihood of attending graduate school. Three of the students from 2016 have recently completed their first year in graduate school. In the 2017 cohort, over half of the students are presently in a STEM related graduate program.

Student testimony: A number of students had their perspectives changed through our REU program. One individual stated that the “...REU experience, greatly changed [her/his] view [of] research for the better.” In some cases, the program appeared to convince some of our students to continue on with mathematical biology research. This was exemplified by one of our participants who wrote, “talking with the professors helped me see the benefits of going to grad school, and I haven't talked to many people about their own grad school experience so hearing the stories from the mentors helped convince me it is the right thing to do.”  Another individual stated that “after studying several math models, [she/he was] very interested in doing a Ph.D. in applied math and/or math bio programs.” Based on assessment results and student written comments, it appears as though our REU program was successful in motivating students to pursue positions in STEM-related fields in general, and in mathematical biology Ph.D. programs in particular.

Objective 3: Preparing Participants to be Successful in an Interdisciplinary, Collaborative Setting

Our REU program was based upon student collaborations, which is now an essential skill across interdisciplinary projects and programs. Project ideas, model development, data collection and eventually the written products were all successfully achieved as part of a research team. Moreover, research teams were expected to provide feedback to other groups during our weekly meetings. This included feedback on all parts of the research process including critiques of posters prior to conference presentations.

Student testimony: Students appreciated and genuinely enjoyed being part of a mathematical biology research team. This appeared to enhance student experiences in the program. For example, one students reported that our REU was “a very good research experience for [her/him], because [she/he] was able to collaborate with others who were excited about mathematics.” Another individual stated that “one of the best things about the program was the gratification of working on something as a group; collaboration in mathematics can be very fulfilling.” Finally, at the end of the program, one of our students highlighted that the “being able to work with a group of students with a similar project basis, while also pursuing an unique project individually gave me the confidence to be able to work both in a collaborative and individual environment for the project.”