Unit 8 · 8.4 — Effect of Density on Populations [cite: 50, 52, 55]

Everything to learn here

• Concept: Logistic growth models accurately reflect populations actively approaching their hard environmental carrying capacity, resulting in a flattening S-shaped curve as environmental resistance increases [cite: 13, 53].
• Equation: Equation/Process: Logistic Growth Equation: $\frac{dN}{dt} = r_{max}N \frac{K-N}{K}$ (where $K$ represents the exact mathematical carrying capacity) [cite: 31, 54].
• Vocabulary: Carrying Capacity ($K$) — the absolute maximum sustainable population size a highly specific environment can support long-term based heavily on available, finite resources [cite: 14, 53].
• Vocabulary: Density-Dependent Factor — a biological limiting factor (e.g., food competition, disease outbreak, severe predation) whose severity strongly increases exactly as population density increases [cite: 53].
• Vocabulary: Density-Independent Factor — an abiotic limiting factor (e.g., natural disasters, extreme weather shifts) that catastrophically affects a population regardless of its actual density [cite: 53].
• Concept: Population density is regulated by resource availability, leading to logistic growth as the population approaches its carrying capacity.
• Equation: $$\frac{dN}{dt}=r_{max}\cdot N\cdot (\frac{K-N}{K})$$

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