Bigger populations don't always grow faster
- The idea
- Predict
- See it
- Why
- Check
The idea
“The bigger a population gets, the more it adds, so it grows fastest right before its limit.”
While a population is small, more parents do mean more offspring. It's easy to assume that holds all the way up.
The short version
The mistake: The bigger a population gets, the more it adds, so it grows fastest right before its limit.
What's actually true: Crowding lowers growth per individual, so a population adds the most at half its carrying capacity, K, and none at K.
- Growth per individual falls as a population grows. Each one gets less food and space, so it has fewer offspring and is more likely to die. That's density dependence.
- In the logistic model, dN/dt is rN times the share of room left, K minus N over K. r is the top growth rate per individual. K is the most the habitat can hold.
- Few breeders or no room both mean few added. The peak is in between, at half of K, where the S-shaped curve of N over time is steepest.
On the exam: A population adds the most at half of K. Near K there are lots of breeders but almost no room.