Life Sciences · Ecology · Evolution · Research / Principles and Exploration
Population growth and carrying capacity — principles and investigation
Population growth occurs when there is sufficient food and space and growth occurs differently when resources are limited. Compare exponential growth and logistic growth by adjusting the initial population, growth rate, and environmental capacity. This is an activity that reads a graph by distinguishing between the current number of objects and the number that increases during unit time.
How does it work?
In the logistic model, the increase rate per individual decreases as N increases. Read the time curve and the growth rate according to N together.
N index=N₀eʳᵗ · Nlogistic=K/[1+(K/N₀−1)e⁻ʳᵗ]
Try this investigation
- The green dots in the large petri dish represent entities. As the points increase, we observe whether resource limitations reduce growth.
- Run and record both models with N₀=10, K=1000, and r=0.5 days⁻¹.
- Change K and r one by one in the logistic model. K is not used in the exponential model.
Interpreting your results
Which N has the largest growth rate in the logistic model?
dN/dt=rN(1−N/K) is an open downward quadratic for N. It is maximum at N=K/2 and 0 at N=K.
Assumptions and limitations
It is an analysis formula for the number of consecutive populations in a closed group with a constant r·K. The calculated value may not be an integer. We omit the contingencies of birth and death, immigration and exodus, age structure, delayed resource effects, and actual species-specific figures. The conversion value of one point is fixed for each condition and only a maximum of 1200 points are drawn.