Population growth
For a population over an interval, births and immigration add individuals while deaths and emigration remove them. In exponential growth, equal proportional growth produces increasing absolute additions as N rises. In the simple logistic model, per-capita growth declines as N approaches K; total growth is greatest near K/2 when r and K are constant. Real populations can overshoot, fluctuate, and experience changing K, so a model is a prediction framework rather than a guarantee.
MAKE IT CONCRETE
With r=0.4 per year, N=300, and K=1,000, logistic growth is 0.4×300×(1−0.3)=84 individuals per year at that moment.
DON’T FALL FOR THIS
Carrying capacity is not a permanent species characteristic. Resources, habitat, climate, and interactions can change it.