01Growth models
Exponential growth: dN/dt = rₘₐₓN — J-shaped curve when resources are unlimited.
Logistic growth: dN/dt = rₘₐₓN((K − N)/K) — S-shaped curve leveling at carrying capacity (K). Growth is fastest at N = K/2.
02Life histories
r-selected species: many small offspring, little care, short lives (insects, weeds). K-selected: few offspring, lots of care, long lives (elephants, humans).
Survivorship curves: Type I (most die old — humans), Type II (constant risk — birds), Type III (most die young — fish, oysters).
03Notebook box
Worked example: r = 0.1, N = 500, K = 1,000. dN/dt = 0.1 × 500 × (500/1,000) = 25 individuals per time unit.
Population growth rate = (births − deaths) / time.