Life Table Analysis - REBECCA DALTONrebeccadalt.weebly.com/uploads/6/2/1/1/62112287/... · Survivorship curve graph in the assessment. ii. The teacher version has the blank copy of

SciREN Lesson Plan High school biology and math lesson plan In this lesson plan, students are introduced to central topics in population ecology through a mathematical lens. They perform a life table analysis using pre-formatted Microsoft Excel worksheets and a publicly available dataset on seven non-human primate species.

R e b e c c a D a l t o n D u k e U n i v e r s i t y

Data from: Bronikowski, Anne M., et al. "Female and male life tables for

Life Table Analysis

SciREN Lesson Plan Biology and Math 2016

Life Table Analysis Lesson Plan Author(s): Designed and written by Rebecca Dalton

Assistance with lesson plan by Marie Perkins (STEM/MAT Program) Author Affiliation and Location: University Program in Ecology

Duke University Optional Author Website http://rebeccadalt.weebly.com Optional Author Contact [email protected] Summary of Lesson Plan (max. 100 Words) Include aspects of the lesson that are unique and innovative.

In this lesson plan, students are introduced to central topics in population ecology through a mathematical lens. They perform a life table analysis using pre-formatted Microsoft Excel worksheets and a publicly available dataset on seven non-human primate species. This lesson is unique because it can be used for either for a high school math or biology course. The lesson plan contains separate math and biology assessments.

List of Standards Addressed Common Core, NC Essential Science, Next Gen, etc. (This should be list of all full standards addressed by the lesson)

K-12 NC Essential Science Standards: Bio. 2.1 Analyze the interdependent relationships of living organisms within their environments.

• Bio.2.1.2 Analyze the survival and reproductive success of organisms in terms of behavioral, structural, and reproductive adaptations. 5F/H3

Common Core Math Standards: CCSS.MATH.CONTENT.HSA.CED.A.1

• Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CCSS.MATH.CONTENT.HSA.CED.A.2

• Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

*Please note, the follow-up discussion questions for math and biology meet different standards.

Learning Objectives using Measurable Verbs (what students will be able to do)

(1) Students will become familiar with foundational concepts in

population biology. (2) Students will calculate a variety of statistics using publically

available data. (3) Students will assess population outcomes based on statistics

(math) and make conservation recommendations (biology).


Appropriate Grade Levels High school students Group Size/# of students activities are designed for

This lesson plan can be used in any sized classroom, but it will be easier to answer questions if class size is smaller and/or students work in pairs.

Setting (e.g. indoors, outdoors, lab, etc.)

Indoors and a computer or tablet is necessary for each student or group of students

Approximate Time of Lesson (Break down into 20-50 minute periods)

• Introductory lecture: 20 minutes • Students working on analysis and answering assessment: 20

minutes • Review of assessment: 10-20 minutes

Resources Needed for Students

Computers or tablets with Microsoft Excel Printed out copies of assessment

Resources Needed for Educators (e.g. blackboard, PowerPoint capabilities, etc.)

Computer with Microsoft Excel and ability to access internet to download data file, Projector for introductory PowerPoint

Apps/Websites Needed

Original data and research article: http://www.nature.com/articles/sdata20166 Documents for lesson plan: Student excel file: SCIREN_LifeTable_STUDENT_2016.xlsx Teacher excel file: SCIREN_LifeTable_TEACHER_ AnswerKey_2016.xlsx Original data excel file (supplemental, not necessary): OriginalData_Bronikowski.LifeTables.SciData2016.xlsx

Lesson Activity (step by step description of activity)

Engage:

1. Ask students to read the abstract from the original research article prior to coming to class. The abstract can be found: http://www.nature.com/articles/sdata20166. Students are not expected to understand most of the abstract. They should take away that the authors used math to understand non-human primate populations.


2. Download the Powerpoint presentation titled

“SciREN_PowerPoint_LifeTable_2016.pptx.” Feel free to change the presentation as you see fit for your students.

3. Project and use PowerPoint presentation to explain topics

necessary for completion of this lesson plan. Explore & Explain:

1. Ask students to form pairs (or work alone if there are enough computers available).

2. Students will open the Microsoft Excel sheet titled “SCIREN_LifeTable_STUDENT_2016.xlsx.” If you have a projector, project this data file on the front of the room. Please note that the teacher version, “SCIREN_LifeTable_TEACHER_AnswerKey_2016.xlsx” does have answers in it, so do not project this up on the screen until the end of the class.

3. Once open, ask the students to click through all of the tabs and explain to the class what they are viewing. The tabs are colored according to the following categories:

• Orange: Primate species life table data i. Sheet names: Baboon, Blue, Capuchin,

Chimpanzee, Gorilla, Muriqi, Sifaka ii. There are seven non-human primate species with

life table data available online. Each tab represents the life table data for the females of one species.

iii. Teacher file has answers in blue and the excel formula for statistic calculation. In the student file, these boxes are blank and highlighted yellow.

• Blue: Metadata file i. This file has extra information about each primate

species (such as location), a link to the original data file, and supplemental information on life table statistics. Both student and teacher file has this sheet.

• Red: Assessment i. The student file has an extra blank copy of the

Survivorship curve graph in the assessment. ii. The teacher version has the blank copy of the

Survivorship curve, a completed Survivorship curve complete with all seven species, and a sheet with data used to create the answer key.


4. Ask each student or student pair to pick one of the species and calculate the statistics that are missing. The formulas used to calculate all of the statistics are located in the excel sheet. Please see Appendix 1 for supplemental information.

Elaborate: After students have had time to calculate statistics for one of the species, walk through the steps in the front of the room. Ask for volunteers to help you and explain to the class how they completed the activity. Evaluate: Students will complete the worksheet in Appendix 3 using the statistics they calculated. This document can either be assigned as homework or completed as an in-class activity. There are two separate assignments in Appendix 2 (one for math class and one for biology).

Final Product/Assessment

Completion of attached worksheet (separate worksheets if used for a math or biology course)

Appendices

• Appendix 1: Formulas and calculation of life table statistics • Appendix 2: Blank in-class follow up assessments and answer

keys for math and biology lesson plans • Appendix 3: PowerPoint presentation for start of class (math and

biology slides included) • Appendix 4: Resources used to create this lesson plan

Background Reading for Teachers (ranked in order of most useful)

• https://www.britannica.com/science/population-

ecology/Calculating-population-growth • Florida International University life table experiment:

http://www2.fiu.edu/~troxlert/PCB3043L/manual/03-Life_Tables.pdf

• Lab experiment from MIT: http://web.mit.edu/7.01x/7.014/documents/populations.pdf

• Study.com survivorship curve video: http://study.com/academy/lesson/survivorship-curve-types-examples-quiz.html

• Wolfram Alpha survivorship curve: http://mathworld.wolfram.com/SurvivorshipCurve.html


• **Research article for non-human primate data: http://www.nature.com/articles/sdata20166

• Information on life table analysis: http://www.tiem.utk.edu/~gross/bioed/bealsmodules/lifetables.html

• Information on biology of some of the primate species in this lesson plan: http://www.monkeyworlds.com/types-of-monkeys/

Appendix 1:

Formulas and calculation of life table statistics

Symbol Name Definition Formula Units

𝒙 Age interval Age or category of a structured population From dataset Time

𝑺(𝒙) Cohort survival

The total number of individuals that are alive at the beginning of age interval x.

From dataset Number of individuals

𝒃(𝒙) Fecundity schedule

Average number of female offspring born per unity time to an individual female of a particular age

From dataset Number of individuals

𝒍(𝒙) Survivorship schedule

Proportion of the original cohort that survives to the start of age x or the probability that an individual survives from birth to the beginning of age x.

𝑙 𝑥 =𝑆(𝑥)𝑆 0

Proportion

𝒈(𝒙) Survival probability

Probability that an individual survives from age x to age x+1

𝑔 𝑥 =𝑙 𝑥 + 1𝑙 𝑥 No units,

probability

𝑮 Generation time

Average age of the parents of all the offspring produced by a single cohort (Caughley, 1977)

𝐺 =𝑙 𝑥 𝑏(𝑥)𝑥!

!!!

𝑙 𝑥 𝑏(𝑥)!!!!

Time

𝑹𝟎 Net

reproductive rate

The mean number of female offspring produced per female over her lifetime

𝑅! = 𝑙 𝑥 𝑏(𝑥)!

!!!

Number of offspring

𝒓 Intrinsic rate of increase

The rate at which a population increases in size if there is no competition for resources with other animals

𝑟 =ln (𝑅! )𝐺

r=0 population size stay stays the same r>0 population declines r<0 population declines


Net Reproductive Rate, 𝑹𝟎

The net reproductive rate (𝑹𝟎) is the mean number of female offspring produced per female over her entire lifetime. Remember that 𝒃(𝒙) is just the mean number of female offspring produced per female in a given age interval. The net reproductive rate is the reproductive potential of a female over her entire lifetime and is adjusted for the mortality in each age category.

𝑅! = 𝑙 𝑥 𝑏(𝑥)!

!!!

• 𝐼𝑓 𝑅! > 1, 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑎 𝑛𝑒𝑡 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 𝑜𝑓 𝑜𝑓𝑓𝑠𝑝𝑟𝑖𝑛𝑔 𝑒𝑎𝑐ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑠 𝑔𝑟𝑜𝑤𝑖𝑛𝑔 • 𝐼𝑓 𝑅! < 1, 𝑡ℎ𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑤𝑖𝑙𝑙 𝑑𝑒𝑐𝑙𝑖𝑛𝑒 𝑡𝑜 𝑒𝑥𝑡𝑖𝑛𝑐𝑡𝑖𝑜𝑛 • 𝐼𝑓 𝑅! = 1, 𝑡ℎ𝑒 𝑚𝑜𝑟𝑡𝑎𝑙𝑖𝑡𝑦 𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑠 𝑓𝑒𝑐𝑢𝑛𝑑𝑖𝑡𝑦 𝑎𝑛𝑑 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑛𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑖𝑧𝑒

Generation Time, G

Generation time is the average age of the parents of all offspring produced by a single cohort (Caughley 1977). Unless newborns have a really large fecundity (b(0) would have to be much larger than 0), the numerator will always be larger than the denominator and will typically be larger than one.

𝐺 =𝑙 𝑥 𝑏(𝑥)𝑥!

!!!

𝑙 𝑥 𝑏(𝑥)!!!!

Intrinsic rate of increase, r

The intrinsic rate of increase is the rate at which a population increases in size if there are no density-dependent forces (competition for resources). This is how fast a population would grow or decline if they were in a vacuum with unlimited resources.

𝑁! = 𝑁! 𝑒!"

𝑁!𝑁!

= 𝑒!"

𝑅! ≈ 𝑒!"

ln (𝑅! ) ≈ 𝑟𝐺

𝑟 ≈ln (𝑅!)𝐺

• 𝐼𝑓 𝑟 > 0, 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑎 𝑛𝑒𝑡 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 𝑜𝑓 𝑜𝑓𝑓𝑠𝑝𝑟𝑖𝑛𝑔 𝑒𝑎𝑐ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑠 𝑔𝑟𝑜𝑤𝑖𝑛𝑔 • 𝐼𝑓 𝑟 < 0, 𝑡ℎ𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑤𝑖𝑙𝑙 𝑑𝑒𝑐𝑙𝑖𝑛𝑒 𝑡𝑜 𝑒𝑥𝑡𝑖𝑛𝑐𝑡𝑖𝑜𝑛 • 𝐼𝑓 𝑟 = 0, 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑛𝑜 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑖𝑧𝑒

Appendix 2

Name: __________________

Species: ________________

Biology Lesson: Life Table Analysis

1. Fill in the following table using data from other classmates.

Statistic Baboon Blue Capuchin Chimpanzee Gorilla Muriqi Sifaka

R0

G

r

2. Which species has the highest intrinsic growth rate? Which has the lowest?

3. What does a low r-value suggest?

4. What are some reasons why Blue Monkeys might have a lower population growth rate than their counterparts in the same ecological region, Baboons? There is no right answer!

5. Plot the fecundity and survivorship schedule of the species you chose to analyze and choose one other species. Compare and contrast the two lines


Name: __________________

Species: ________________

Math Lesson: Life Table Analysis



R0

G

r

2. Which species has the intrinsic rate of increase? Which has the lowest?

3. Plot the fecundity and survivorship schedule of the species you chose to analyze and choose one other species. Compare and contrast the two lines.

4. Why might r be a good value to compare between different species? What does it take into consideration in its formula?


Appendix 2: Answer Key

Name: __________________

Species: ________________

Biology Lesson: Life Table Analysis



R0 1.622 2.049 1.511 0.745 1.918 2.369 1.919

G 11.228 13.678 12.513 22.428 20.335 19.993 12.533

r 0.043 0.052 0.033 -0.013 0.032 0.043 0.052

2. Which species has the highest intrinsic rate of increase? Which has the lowest? Highest: Blue and Sifaka (0.052) Lowest: Chimpanzee (-0.013)

3. What does a low r-value suggest?

A low r-value (below 0) suggests that the population is declining in size. The lower the value, the faster the population is declining in size.

4. What are some reasons why Blue Monkeys might have a lower intrinsic rate of increase than their counterparts in the same ecological region, Baboons? There is no right answer! Blue Monkeys might have to compete more for food or shelter than Baboons.

5. Plot the fecundity and survivorship schedule of the species you chose to analyze and choose one other species. Compare and contrast the two lines See the answer key in the Excel sheet for teachers.


Name: __________________

Species: ________________

Math Lesson: Life Table Analysis



R0 1.622 2.049 1.511 0.745 1.918 2.369 1.919

G 11.228 13.678 12.513 22.428 20.335 19.993 12.533

r 0.043 0.052 0.033 -0.013 0.032 0.043 0.052

6. Which species has the highest intrinsic rate of increase? Which has the lowest? Highest: Blue and Sifaka (0.052) Lowest: Chimpanzee (-0.013)

7. Plot the fecundity and survivorship schedule of the species you chose to analyze and choose one other species. Compare and contrast the two lines.

See answer key in teacher’s Excel file.

8. Why might r be a good value to compare between different species? What does it take into consideration in its formula? The intrinsic rate of natural increase can be used to compare growth rates of populations of a species that have different generation times. Some human populations have higher intrinsic rates of natural increase partially because individuals in those groups begin reproducing earlier than those in other groups. Mice have higher intrinsic rates of natural increase than elephants because they reproduce at a much earlier age and have a much shorter mean generation time (from Britannica).


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 10 20 30 40 50

Pro

porti

on s

urvi

vng

l(x)

Age in years (x)

Survivorship curves for non-human primates


Appendix 3:

SciREN_Math+Biology_Appendix 3.pptx


Appendix 4: Bronikowski, A. M., Cords, M., Alberts, S. C., Altmann, J., Brockman, D. K., Fedigan, L. M., ... & Morris, W. F. (2016). Female and male life tables for seven wild primate species. Scientific data, 3.

Gotelli, N. J. (2001). A primer of ecology. Sunderland, Massachusetts. Sinauer Associates, Inc, 385, 386.

Mittelbach, G. G. (2012). Community ecology. Sinauer Associates.

Morris, W. F., & Doak, D. F. (2002). Quantitative conservation biology. Sinauer, Sunderland, Massachusetts, USA.