Safety and evidence boundary
Use supplied long-term ecological datasets and low-risk simulations. Do not manipulate wild populations, introduce species, enter unsafe field sites, or infer a single cause from correlation alone. Population models are approximations with explicit scale and boundary assumptions.
Explicit science instruction
The logistic model reduces per-capita growth as N approaches a modeled carrying capacity K. One form is dN/dt=rN(1−N/K). K summarizes resource and environmental constraints under stated conditions.
Real populations can overshoot, oscillate, migrate, experience time lags, or face changing K.
Worked example with reasoning
If K=1,000 and N=500, the density factor (1−N/K)=0.5, so modeled growth is half the low-density rN rate. At N near K, net modeled growth approaches zero.
Guided question
Why can carrying capacity change from one decade to another?
Independent work
- Calculate density factors for N/K=.1,.5,.9,1.1.
- Sketch exponential vs logistic curves.
- Name four factors that alter K.
- Explain overshoot.
Misconception check
K is not a morally desirable target and is not always directly measurable; it is a model parameter that can vary.
Formative understanding check
At N=K, what is 1−N/K?
Worked response
0.
Open-book formative practice only; not an official mastery attempt or grade.
Mentor evidence conference
Ask Archaemenes to challenge your systems model, quantitative interpretation, alternative explanations, and boundary conditions.
Open ArchaemenesTeacher guidance
Foundation: use normalized N/K values. Core: interpret logistic terms. Extended: analyze time-lag and variable-K models.
Preserve learning evidence
Keep models, calculations, graphs, corrections and uncertainty notes in the matching Week 33 evidence field.