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Notes on implementing the cemetery module in a mathematical modeling course for Life Sciences majors

After many essential conversations with members of my QUBES Faculty Mentoring Network, I implemented the Demography from Cemeteries module in my course MAT 1314 Modeling for the Life Sciences, a new course offered for the first time in the spring 2016 semester. This new course was designed at the request of the Department of Biology and the Program in Cognitive and Behavioral Neurosciences, to complement redesigned courses in Biocalculus and Statistics for the Life Sciences. The class was in lecture-discussion format, meeting twice per week for 75 minutes each. We did not have a long lab session time available to us. Since this was a quantitative course designed for life sciences students rather than a quantitative module in what is otherwise a life sciences course, the focus was on the quantitative skills. The primary objectives were to acquire some understanding of and facility with using and interpreting life tables. Other objectives included familiarity with Excel in a scientific context, experience in selecting a data set, formulating and addressing questions that are both on topic for the classroom discussion and appropriate for the data set available. Finally, the broader objective was to place the questions and tools of the module within the context of the remainder of the course, since this module came at the end of the semester.

Since the students arrived with some experience with Excel and data, I was able to present the module as follows. I introduced the concepts for the module in the final portion of one class period and handed out a subset of the Lanza paper for the students to read for the next class, along with a couple of brief handouts on cohort vs. static life tables. In the next class, I spent part of the class period talking through the planned exercise and addressed any student questions from the reading. I also talked briefly about several online references to life tables (links included above) as we looked through them together in class, projected on the screen. I asked the students to search for an appropriate data set online, download it, and bring it to the next class in Excel, ready to work. In the next class, I took questions and went on to other material, leaving them several days to complete their assignment and submit it to me online.  We did not take the time for oral presentations to the class as suggested in the Lanza paper.

Because this was a Math course rather than a Science course, the quantitative focus pervaded the entire semester, so there was inherent scaffolding in some sense. On the other hand, I tried throughout the semester when dealing with seemingly more theoretical structures such as differential equations and difference equations to talk about how data could inform, validate, and verify the models, so a module specifically on data was a natural follow-on by the end of the semester.​

In my next version of the course, I would place the module earlier in the mix of the course topics, spend more time on other uses of life tables, and be a little more explicit in constructing examples rather than simply talking through finished examples.

​Douglas Norton

Villanova University

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Using the virtual cemetery option to fit this into a single three hour lab session

Institution/institution type: Augustana College (residential liberal arts college)

Course/Course format: General Ecology (Junior and senior biology and environmental studies majors, does not count towards general education requirements so it is a majors only course). The course had 36 enrolled students. Lab met once a week for three hours.

What I hoped to accomplish with this module was to give students an opportunity to test their own hypotheses about human survivorship, and strengthen their ability to understand survivorship curves.

I introduced the module during a broader unit on population ecology. By the time students were working on this module, we had already covered survivorship curves and basic life table parameters in lecture (Molles 6th edition, chapter 10). Students had already worked simple, deterministic, problems in class, for example, determining which survivorship curve a population has given lx values, and given sx, mx, and nx, values predict nt+1.  I used this module along with the plant population viability analysis module to form a lab unit on populations.  This module is also good for reinforcing the distinction between static and cohort life table approaches.

I have used this module many times, and before that I used this module’s predecessor from the 1993 Experiments to Teach Ecology (Nancy Flood’s Cemetery Demography)

I used example problems, as stated above, and assessed these by using clickers in lecture. I use clickers to provide a low stakes, immediate feedback atmosphere for quantitative work in class (questions are worth participation credit, and all responses receive credit), and we continued working example problems until a significant majority of the class was consistently getting correct answers.  These skills were also assessed on an exam.

I use selected parts of this module, because I want the experience to fit into a single, three-hour, lab session.

1) We do virtual, rather than physical cemeteries.  This is a trade-off, as the physical cemetery opens up nice liberal arts connections to local history and changing trends in funerary art. Further, students always enjoyed the field trip. However, with the physical cemetery, students were constrained to exploring a hypothesis I knew would work with the data they would find there (male vs female and/or 1860s vs 1890s cohorts). We tended to spend the whole three hours collecting data. Switching to virtual cemeteries cuts out travel time and permits students come up with their own hypotheses, and this makes this much more of an open inquiry experience. Since one of my primary objectives for this experience is that students explore hypotheses of their own choosing, the virtual cemetery simply works better.

2) We eliminate the oral presentation.  The Lanza module calls for an oral presentation of the data. This is another trade-off, of course. Oral presentations are important, but at the end of a three-hour session, students would not be ready to do that. Instead, I ask students to submit a more traditional lab report.

Here is the way I run the session.

1) Students break into pairs and come up with a hypothesis. Students clear their hypothesis with me before they begin looking for data, so I can steer them away from hypotheses that are too specific and would therefore take too long to find enough data to address. I also need to steer students away from hypotheses that can’t be addressed using survivorship curves inferred from census or cemetery data.  For example, some students will want to address something very contemporary, like zika virus, and I have to remind them that most of the affected individuals are still alive (so will not be represented in any cemetery) and that the event can’t possibly be represented in the US census. It takes some groups a few tries to come up with a hypothesis that is a good match for their interest and for the technique we want to practice.

2) Students collect data and generate survivorship curves as per the module. Students doing method 1 take longer to collect the data, but usually need less support on the calculations and graphing (steps 7-10). Students doing method 2 tend to find the data they need more quickly, but need lots of support getting through steps 5 and 6 (the calculation of lx).This is exactly what Lanza predicts in the module.  Most of the middle hour of my class is spent circulating around the computer lab helping students with the analyses.

By the end of the lab session, most groups will have generated survivorship curves and some groups will actually have the lab report ready to submit. Groups that do not leave with their curves finished tend to be groups that did method 2 (the census method) and who really struggled with the calculations.  If I really needed every student to finish the session with graphs in hand, I might be tempted to limit them to method 1 (ages at death). 

For the lab report itself, I ask the following (lab reports in my class are always excel spreadsheets):

1) The names of all group members.

2) (5 points) a brief statement of the hypothesis you are testing and the methods you chose to test it. Why did you choose this hypothesis?

3) (5 points) Tables of the raw data and calculations used to generate graphs. Please put these tables one or more tabs and don’t put them on the main report tab. Name all tabs in the spreadsheet for easy reference.

4) (45 points) Clearly labeled survivorship curves formatted to make it easy to see if your hypothesis is supported by the data. Format your curves as survivorship per 1000, just as Lanza indicates.  You will probably find it useful to plot your curves on the same set of axes so you can see differences in the curves.

5) (40 points) Do the data support your hypothesis?  We are not using a statistical test to answer this question, but make careful reference to the figures you generated in item 4 to justify your answer.  What historical trends or events may explain any observed difference or lack of difference? You do NOT need to answer questions 1-9 in the Lanza article. However, these questions (especially 1-8) will give you some good ideas to consider as you try to explain the trends in your graph or graphs).

6) (5 points) A bibliography of any data sources consulted or references used.

This module works very well for me. While I am still not totally at peace about abandoning the physical cemetery work, I do feel that the trade-off in favor of more open inquiry for students is worth it.   I anticipate continuing to use this module. Students are often surprised by the outcomes. For example, one group this year compared survivorship in urban Chicago vs a more rural area in downstate Illinois for individuals born in the 1890s. They assumed that urban would beat rural due to access to healthcare, but were astounded to find a large difference in the other direction. This prompted a good discussion on public health, the industrial revolution, and student’s assumptions about the costs and benefits of different lifestyles.  Another group compared survivorship from a Mexican cemetery to a Californian one from the same era. The students correctly predicted higher Californian survivorship, but were surprised how large the observed difference was. Again, this was a springboard for a good discussion about public health trends and social justice.  Of all the labs I do, this one connects most easily and fully to the larger liberal arts context of the school.    

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Instructor notes from an only partly successful implementation attempt

Institution/institution type: Augustana College (residential liberal arts college)

 

Course/Course format: General Ecology (Junior and senior biology and environmental studies majors, does not count towards general education requirements so it is a majors only course). The course had 36 enrolled students. Lab met once a week for three hours.

Module synopsis: In this module, students collect demographic data for a local plant population, and then use a stochastic model in R to look at the impact of changing survivorship and fecundity on the population.  

Instructor notes:

What I hoped to accomplish with this module was to give students an opportunity to apply demographic models in a more real world setting, and see how those models can inform management decisions. As a secondary objective, I wanted to give students a chance to work with a stochastic model, rather than the deterministic models I have traditionally used in this class.

I introduced the module during a broader unit on population ecology. By the time students were working on this module, we had already covered survivorship curves and basic life table parameters in lecture (Molles 6th edition, chapter 10). Students had already worked simple, deterministic, problems in class, for example, determining which survivorship curve a population has given lx values, and given sx, mx, and nx, values predict nt+1.  I had not used matrix-based models in this class before, so I also spent about a half hour at the beginning of lab working through the example on page 6 of the Charney and Record module.

I also used the cemetery demography module, which I have used before, in this same unit. As Charney and Record note, these two modules together serve as a good unit on populations.  

The lab report was modified from the set of questions in the TIEE module. I used questions 3-6, and 9 as the basis for the lab report.

Unfortunately, my experience with the viability analysis module was mixed. The module states that no prior experience with R is needed, however, my lack of experience with R proved to be a barrier to effective implementation of this activity. 

The students loved the fieldwork aspects of the lab, and collecting the data and getting students to enter the data on google docs was straightforward, with only the minor and expected difficulty of a few students miscoding things or entering redundant data.  Further, the students noticed lots of variation in petal number in the population we were working on, and this got them thinking about the possible fitness impact of petal number as well as asking good ecological questions about this trait, for example, do large plants also have more petals? The module was very successful on that level.

However, I was not able to get the R script I was supposed to run to simulate next year’s data to run (PVA_instructor_script-singleyear.R).  The sample data the module authors provided ran just fine, but I just could not get my file to work. More familiarity with R would have helped here, as it is likely that some small format issue was the problem.

The students were still excited about the project, though, so I came up with some simulated data for next year based on crude back-of-the–envelope calculations assuming that the current data represented a stable stage distribution.  I practiced using the student R scripts in my office, and the simulations ran perfectly.  I scheduled our next class meeting for one of the computer labs on campus, after making sure R was installed on these machines.

Unfortunately, during class, only two or three stations were able to run the student scripts successfully. Error messages popped up across the room, and without R experience, I was not able to troubleshoot the simulation. Sometimes if students just exited R and started over, the script worked, which suggested user error on our part, but mostly we would just hit the same errors repeatedly.

Wanting to salvage more from the experience, I created an excel spreadsheet that used the data we collected in a deterministic matrix model (Chapter 14 in Donovan and Welden Spreadsheet exercises in Ecology and Evolution, 2002 Sinauer and associates press), and I asked students to prepare a lab report using our data and entering different parameter values in this excel based model.  I did not ask students to create the spreadsheet. Rather, I used a template, and write-protected the formulas, so students could only change the parameters I wanted them to manipulate. This worked reasonably well, but lacked the more realistic element of the stochastic model in the R based module. I was pleased with most of the lab reports, but a few students took a very cursory approach to the simulation (changing very few parameters in the model and changing them only a little). If I were to do this again, I would be more explicit about this aspect of the report.

The module does not give details about how to collect fecundity data, admittedly a big task that would have added another layer of complexity to the student directions, but this is a critical step if the module is to be successfully implemented across years. One issue I did not anticipate here is setting aside class time for seed collection/germination.

On the plus side, the variation in petal numbers became the basis for a good, engaging, student project. Further, the lab reports based on the excel-based, deterministic, model showed that students successfully got the connection between stage based survival, fecundity, and the viability of the population. While students were initially surprised that changing the fecundity of different stages by the same amount had different population impacts, most reasoned out the connection with survivorship and the potential conservation applications of this connection. 

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Human demography for undergraduate Ecology course for majors

I used this module in a small (12 students) introductory Ecology course for undergraduate Biology majors. We met once a week for three hours. I used this module because it was possible to adapt using local (Puerto Rico) data, making it more relevant. It also involved several major learning objectives like formulating hypotheses, designing experiments, collecting and analyzing data, and interpreting data. I have included Instructor Notes that describe how I modified and supplemented the module with additional assignments to introduce the terminology as well as to extend and relate the discussion to broader concepts previously covered (like climate change). 

Included here are:

  1. Instructor notes on what I modified, followed, and what I will change in future implementations of this module.
  2. Pre-exercise assignment
  3. Short introductory presentation reviewing terminology
  4. Modified data entry excel file and modified data analysis file. 
  5. Post-exercise assignment

 

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Adaptation to: Global Temperature Change in the 21st Century

I used this module in a large (i.e., 150 students) introductory Biology course for non-majors that ran for 7 weeks and had no laboratory component. I used this module because it met several learning objectives for this class including the ability to quantify, analyze, and interpret biological data. In this posting I have included Instructor Notes that describe how I modified and supplemented the module to create 5 assignments that students worked on in teams of 4-5 students. This class met 4 days per week and students were provided 1 day per week to work on their group project assignments. I also included several assignments that were supplemental to the module.

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Phenology in the Majors Introductory Biology Lab

This TIEE Phenology module was used in a majors introductory biology lecture/laboratory course.  Before implementing this module, students had done a lab earlier in the semester introducing them to quantitative analyses and so should have at least been familiar with the use of EXCEL and basic statistics.  I slightly modified the student handout part of the module to include student learning objectives, hyperlinks to the data and a section on the use of EXCEL.  Before lab, students printed out and read the lab activity. During lab, I briefly introduced phenology and shared two videos highlighting the topic.  Then students worked in pairs and as groups to complete the activity.  At the end of the 3-hour lab, students handed in their completed labs for assessment.

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Phenology Introduction

This module was implemented in a 1st year course (lab) designed for majors, but is also an option for non-majors to fulfill general education requirements. Before we started the lab, a PPT on linear regression and basic statistical analyses in Excel was presented (that PPT is available in this Collection). I then gave this brief PPT on phenology and I introduced the module. The entire module fit in a single 4 hour lab period with most students taking 3.5 hours to finish.

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Printout Eagle Lab (condensed)

This is the "condensed" version of the Eagle Lab that was done in a single lab period (~3 hours). We focused just on:

Part I: How does the bald eagle population at a winter stopover change over three decades?

Part II: How do salmon abundance and December temperatures influence bald eagle numbers?

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Bald Eagle Introduction

This module was implemented in a 1st year course (lab) designed for majors, but is also an option for non-majors to fulfill general education requirements. Before we started the lab, a PPT on quadratic regression and basic statistical analyses in Excel was presented (that PPT is available in this Collection). I then gave this brief PPT on Bald Eagles and I introduced the module. I cut the module to only the guided exercises and to work on the questions:

Part I: How does the bald eagle population at a winter stopover change over three decades?

Part II: How do salmon abundance and December temperatures influence bald eagle numbers?

The module still took about 3 hours and 15 minutes to complete, but it all fit in the single lab period we had allotted for this particular module. 

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The “Global Temperature Change in the 21st Century” was used in the majors introductory non-lab biology course. The purpose of this course was to introduce potential biology majors to the process of science and to understand that all the science information they read in their textbooks comes from people doing work and analyzing information. The class met for 90 minutes twice a week. I used the module near the beginning of the semester, week 4, and it was their first experience using Excel in my course. The module took two 90 minute class periods and I included a take-home summative assignment at the end.

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Instructor notes from an introductory biology course

This module was used in the majors introductory non-lab biology course at the end of the semester as a culminating experience to track their Excel and data interpretation skills. The purpose of this course is to introduce potential biology majors to the process of science and to understand that all the science information they read in their textbooks comes from people doing work and analyzing information. The class meets for 90 minutes twice a week. The module was done in class with class discussions of the results interspersed throughout the module. 

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Adaptation to: Investigating the footprint of climate change on phenology and ecological interactions in north-central North America

I used this module for group work in an introductory Biology course for majors that ran for 7 weeks and had no laboratory component. In this posting I have included Instructor Notes that describe how I modified and supplemented the module to create 6 assignments that students worked on in a group of 4-5 students. In addition, I’ve added assignment instructions and rubrics that are supplemental to the module.

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Supplemental Instruction Handout Noel Resources

I launched a Supplemental Instruction session using modified resources in March 2016. Everything seemed to go smoothly, aside from our computers all deciding to randomly shut down and install updates halfway through the activity. Honestly, some computers did appear to work and students seemed to complete the activity. The way I have it all streamlined should have helped these non-major students. I have three master Excel files (these sheets are not locked) and can be manipulated. The three city Excel files have the first two sheets locked/protected to minimize students accidentally erasing data. Please let me know if you have any questions as the last file is the word document each group of students had in front of them to turn in. Hopefully you find it useful if you choose to use pieces of this.

Brandon

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EREN PFPP Complete Protocol

This pdf file contains all of the Protocols for PFPP. The datasheets and all of the appendices need to be downloaded separately.

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Gabriela Hamerlinck onto Permanent Forest Plot Project

Quadratic Regression

This is a PowerPoint presentation that I put together to get our freshman Biological Diversity Lab (4 hours) students up to speed for the bald eagle lab.  It covers how to determine which models and variables are statistically significant as well as quadratic regression.  This is a 30 minute presentation to be used in the 1 hour of lecture and 3 hours of lab (4 hours total) course that a biologist and I (mathematician) co-taught.  We have about 15 students in each of two lab sections.  Feel free to modify in any way to suit your needs.    

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Linear Regression PowerPoint Presentation

This is a PowerPoint presentation that I put together to get our freshman Biological Diversity Lab students up to speed for the phenology lab.  It includes an introduction to graphing, rates of change, total change, lines, and simple linear regression.  This is a 30 minute presentation to be used in the 1 hour of lecture and 3 hours of lab (4 hours total) course that a biologist and I (mathematician) co-taught.  We have about 15 students in each of two lab sections.  Feel free to modify in any way to suit your needs.    

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Favorites

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Erich Huebner onto new collection

To P or not to P?

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Drew LaMar onto Timeline

Multiple explanatory variables (cont'd)

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Drew LaMar onto Timeline

Example Post

This is an example post. In this description I could include the following:

“This is a modified activity from the TIEE materials. I had my students use data from Wisconsin to ask their own questions about phenology that was turned in as a lab report (rubric included). This was in a 3-hour lab of 30 senior level undergraduates. I also had my students read the information on this website as a pre-lab exercise (www.qubeshub.org/groups/esa)”

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Chapter 18: Multiple explanatory variables (cont'd)

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Drew LaMar onto Timeline

Data Processing with dplyr & tidyr, by Brad Boehmke

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Drew LaMar onto Data Manipulation

Mixed-effects models for repeated-measures ANOVA

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Drew LaMar onto Statistics and Data Analysis