If you add a few plants, or remove a few plants each year (by fixing the supplemental matrix with positive or negative numbers), a

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If you add a few plants, or remove a few plants each year (by fixing the supplemental matrix with positive or negative numbers), at which stage does adding/removing plants have the biggest impact on the populations?

Today you will build a population viability analysis (PVA) for wild carrot (Apiaceae: Daucus carota), using data from Fall 2015.  This plant is an escaped cultivated plant and an invasive perennial, spreading by seed.  Flowers appear in mid summer; fruit heads appearing by early fall.  A single umbel can contain hundreds of seeds.

1. Our first goal is to construct a transition matrix for wild carrot using the 2015 data.  You will have access to an Excel spreadsheet with that year’s plants and stages (note that each stem is treated as a plant for this model) and next year’s population has been estimated for you. (Your estimate for year 2 will be unique to you and not shared with anyone else in the class.) 

1. Fill in the tables on the next page. You can ignore the transitions in the grey boxes (those won’t go into the model). 

1. Enter Transition Probabilities (divide cells in table above by column sums):

1. Estimate Recruitment by comparing the number of Stage 3 plants to this year’s new recruits:
   1. Given high seed mortality, start with a fertility value of 3.0. When you model in R, try a few different values (remember that only plants with seeds can produce offspring!).

1. Fill in the transition matrix below, incorporating fertility/recruitment into the first row, and try projecting the population forward two years using matrix multiplication.

NOW WE ARE READY TO MODEL IN R!!

1. Start up RStudio on your own computer.

1. Go to “file” à “Open file” à then navigate to the “PVA_Source.R” file you just downloaded from the PVA folder in the Content area.                           

This file has pre-written code for some of the functions needed. Note that you might need to add a package to R (popbio) to be able to run it! (Go to Tools/Install Packages to add it.) Once popbio is installed, select all of the text in the PVA_Source.R file and run it.

Now open the file “PVA_student_script.R”. This file has pre-written code for you to run.  To run a line of code, put your cursor on that line, and hit the “Ctrl” key and then the “R” key (or “Enter” key for Macintosh or RStudio) while still holding down “Ctrl.”  The code will execute in the R console window.  Anything with a “#” in front of it is just a note, and won’t run.

1. Follow the instructions in the script to set up and run a simulation.  When you get to step # 5 in the script, answer the following questions. You will have to play with the model for a while to be able to answer these fully.

You will not need to write a paper for this lab. Instead of a results paper, you will need to submit answers to these questions. Your answers will need to show effort taken in working through this model to answer the questions using R. You may include screen shots of graphs if this would help you in answering the questions. Your answers should be written in complete sentences, and the standard of writing will be more like that of a results paper than of the exercises earlier in the semester. (Copy these questions to a new Word file, fill in your answers, and submit to the Dropbox on D2L by your deadline.)

How do you interpret the jagged lines plotted on the graphs?

What is “quasi-extinction,” and why do we use that instead of regular extinction?

Which transition probability is the population trajectory most sensitive to?  Explain your process for reaching this conclusion.

If you add a few plants, or remove a few plants each year (by fixing the supplemental matrix with positive or negative numbers), at which stage does adding/removing plants have the biggest impact on the populations?

If you were to harvest five flowering plants each year, how long would the population persist?

What if you were to sprinkle seed capsules into the forest, how many would you need to put out there each year to offset the harvest?  Note, you’ll need the germination rate – unless otherwise instructed, let’s assume one plant establishes for each capsule put out there.

What assumptions went into this model?  Are there any simplifications we made that might not match reality well?  How is reality different from the model, and how would it affect the predictions?