4. Population Dynamics and Carrying Capacity

A population grows when births (and immigration) exceed deaths (and emigration). The four factors:
\[ \Delta \text{Population} = (\text{Birth rate} + \text{Immigration}) - (\text{Death rate} + \text{Emigration}) \]

Two patterns of population growth:

Exponential growth (J-curve): occurs when resources are unlimited. A population doubles repeatedly at a constant rate. In reality, this cannot continue — it leads to resource exhaustion.

Logistic growth (S-curve): more realistic. A population grows exponentially at first, then slows as it approaches the carrying capacity (K) — the maximum population size an environment can sustainably support. At K, birth rate equals death rate and the population stabilizes.

Limiting factors prevent a population from exceeding K:

• Density-dependent: stronger when population is larger. Examples: food competition, disease, predation, waste accumulation. These create negative feedback — a larger population suffers more, which reduces growth.
• Density-independent: affect population regardless of size. Examples: drought, wildfire, frost, floods. A hard freeze kills 40% of a population whether it is 100 or 10,000.

Overshoot and crash: if a population briefly exceeds K (due to a temporary resource boom), it rapidly exhausts resources and crashes — sometimes below the original stable population size. This pattern is common when populations have no natural predators or when resources are suddenly increased then removed.

r-selected vs. K-selected species:

• r-selected species (rabbits, insects, weeds): many small offspring, short lifespan, rapid reproduction. Good at colonizing new areas. High variability in population size.
• K-selected species (elephants, whales, humans): few large offspring, long parental care, slow reproduction. Live near K; more sensitive to environmental disruption.