Answering Biological Questions Using Circular Data and Analysis in R

Project Summary

This Data Expedition introduced hypothesis-driven data analysis in R and the concept of circular data, while providing some tools for importing it and analyzing it in R.

Themes and Categories

After exploring a simple dataset to learn these tools, we applied what we learned to two real examples of circular datasets: one testing for magnetoreception in salmon (based on Putman et al. 2014), and the other testing for visual orientation in deep-sea squids (Thomas et al. 2017). The lesson was designed to be a code after me, step-by-step journey through data analysis for undergraduate students.

Graduate Students: Julia Notar and Katie Thomas

Faculty: Tom Mitchell-Olds

Course: Bio 304, Biological Data Analysis

This lesson was done entirely in R, an open-source, free programming environment, and provided a rich opportunity for teaching students to explore, manipulate, and statistically analyze data using R and connect it to biological principles and questions. We did this through the introduction and analysis of circular datasets. Circular data is data that indicates an angular orientation (for example, which way an animal is facing or moving, which can be measured in degrees or radians) or a periodic event (for example, circadian rhythms). We took students from raw biological data to publication-quality figures and statistical analyses to demonstrate the broad applications of computing software and the benefits of learning a flexible, open-source programming language.

After an introduction to circular data, students were presented with two different datasets to address two different biological questions using similar circular data analyses.

  1. Do salmon use an inherited magnetic map to navigate using the Earth’s magnetic field?
  2. Do cockeyed squids orient their different sized eyes in different directions to look at different light sources?

See the full lesson.


The first dataset is a transformation (for copyright purposes) of the results of an experiment testing the effect of varying magnetic fields on juvenile salmon orientation (Putman et al. 2014). It contains the results of two experimental treatments and one control treatment, each in a column, with rows indicating the circular orientation (in degrees) of each juvenile salmon in the experiment. The data are from a published study on how naïve juvenile salmon navigate hundreds to thousands of kilometers to feeding areas, and support the hypothesis that salmon use magneto-reception to help in migrations.

The second dataset is raw data on in situ visual orientation among deep-sea cockeyed squids (Thomas et al. 2017). The measurements come from 30 years of deep-sea video data that were analyzed for squid eye orientations. Columns indicate the species, left eye orientation, and right eye orientation for each individual squid measured. The data are from a published study on the functions of different sized eyes in cockeyed squids, and support the hypothesis that the larger left eye looks upward toward dim, downwelling sunlight and the smaller right eye looks downward for flashes of bioluminescence.

Class Format

We designed this to be a first introduction to circular data analysis in R. We chose to use two different datasets so that students could first be led through data import, sub-setting, transformation, plotting, and statistical analysis by the instructors. Students are given only the data files at the beginning of class, and then are walked through coding and structuring analyses by the instructor. Then, we ask them to apply these methods and skills to a different dataset answering a completely different biological question on their own.

Student Feedback

“Very clear explanations of why circular data needed to be treated differently”

“They were really understanding of our knowledge of R, but also really helped out in letting us know other features of R and Data Analysis that the class may not have explored”

“The explanations were very thorough and helped me truly understand what I was doing when I started to write the code on my own”

“The pace was good! Really appreciated both lecturers who repeated things over and over so we could follow along!”

“It was helpful getting to use some of the programming language in a different style of questions”

“Very interesting to learn about circular data”

“I thought the lectures were very interesting, applicable, and well-taught!”


Putman, N. F., M. M. Scanlan, E. J. Billman, J. P. O’Neil, R. B. Couture, T. P. Quinn, K. J. Lohmann, and D. L. G. Noakes. 2014. An inherited magnetic map guides ocean navigation in juvenile pacific salmon. Curr. Biol. 24:446–450. Elsevier Ltd.

Thomas, K., B. Robison, and S. Johnsen. 2017. Two eyes for two purposes: in situ evidence for asymmetric vision in the cockeyed squids Histioteuthis heteropsis and Stigmatoteuthis dofleini. Philos. Trans. R. Soc. B-Biological Sci. 372:20160069.

Related Projects

In this two-day, virtual data expedition project, students were introduced to the APIM in the context of stress proliferation, linked lives, the spousal relationship, and mental and physical health outcomes.

Stress proliferation is a concept within the stress process paradigm that explains how one person’s stressors can influence others (Thoits 2010). Combining this with the life course principle of linked lives explains that because people are embedded in social networks, stress not only can impact the individual but can also proliferate to people close to them (Elder Jr, Shanahan and Jennings 2015). For example, one spouse’s chronic health condition may lead to stress-provoking strain in the marital relationship, eventually spilling over to affect the other spouse’s mental health. Additionally, because partners share an environment, experiences, and resources (e.g., money and information), as well as exert social control over each other, they can monitor and influence each other’s health and health behaviors. This often leads to health concordance within couples; in other words, because individuals within the couple influence each other’s health and well-being, their health tends to become more similar or more alike (Kiecolt-Glaser and Wilson 2017, Polenick, Renn and Birditt 2018). Thus, a spouse’s current health condition may influence their partner’s future health and spouses may contemporaneously exhibit similar health conditions or behaviors.

However, how spouses influence each other may be patterned by the gender of the spouse with the health condition or exhibiting the health behaviors. Recent evidence suggests that a wife’s health condition may have little influence on her husband’s future health conditions, but that a husband’s health condition will most likely influence his wife’s future health (Kiecolt-Glaser and Wilson 2017).

Fluid mechanics is the study of how fluids (e.g., air, water) move and the forces on them. Scientists and engineers have developed mathematical equations to model the motions of fluid and inertial particles. However, these equations are often computationally expensive, meaning they take a long time for the computer to solve.


To reduce the computation time, we can use machine learning techniques to develop statistical models of fluid behavior. Statistical models do not actually represent the physics of fluids; rather, they learn trends and relationships from the results of previous simulation experiments. Statistical models allow us to leverage the findings of long, expensive simulations to obtain results in a fraction of the time. 


In this project, we provide students with the results of direct numerical simulations (DNS), which took many weeks for the computer to solve. We ask students to use machine learning techniques to develop statistical models of the results of the DNS.

Female baboons occasionally exhibit large swellings on their behinds. Although these ‘sexual swellings’ may evoke disgust from human on-lookers, they provide important information to group members about a female’s reproductive state. To figure out what these sexual swellings mean and whether male baboons notice, we need to look at the data.