29 From plain English to a matrix model
29.1 Background
This activity is designed for quick in-class practice translating a verbal life-history description into a matrix population model. It connects directly to the workflow in 2_07_matrixModels.Rmd.
Learning outcomes:
- Convert a verbal life-history description into a matrix population model.
- Build and interpret a simple projection from initial stage abundances.
29.2 Worked example
Here is a minimal two-stage example to show the translation from words to a matrix.
Suppose juveniles do not reproduce, adults produce 2 offspring per year, juvenile survival is 0.4, and adult survival is 0.7. A simple stage matrix would be:
\[ A = \begin{bmatrix} 0 & 2 \\ 0.4 & 0.7 \end{bmatrix} \]
The key idea is to map each biological statement to a matrix entry: fecundity goes in the top row, survival and stage transitions go on the sub-diagonal or main diagonal.
29.3 Your task
Use the red-tailed hawk life history description in supplemental/Exercise_Plain_English_To_Matrix_Model_2018.txt.
- Draw a 3-stage life cycle diagram (hatchling, juvenile, adult).
- Translate the verbal description into a 3x3 projection matrix. State any assumptions you make about the juvenile stasis and transition rates.
- Use the initial population sizes given (1000 hatchlings, 150 juveniles, 5 adults) and project the population for 20 time steps.
- Calculate the dominant eigenvalue and interpret whether the population grows or declines.
- Compare your approach with the workflow in
2_07_matrixModels.Rmd.