AP Biology: Population Ecology – Exponential vs Logistic Growth, Carrying Capacity, r/K?Selection

Population Ecology – Exponential vs Logistic Growth, Carrying Capacity, r/K?Selection

Concept Summary

• Exponential growth: Unlimited population increase under ideal conditions (J-shaped curve), significant for understanding rapid outbreaks or invasive species.
• Logistic growth: Population growth slows as it approaches carrying capacity (K) (S-shaped curve), modeling real-world resource limits.
• Carrying capacity (K): Maximum population size an environment can sustain indefinitely, determined by limiting factors (e.g., food, space).
• r-selection: Life history strategy favoring high reproductive rates, short lifespans, and minimal parental care (e.g., insects, weeds).
• K-selection: Life history strategy favoring low reproductive rates, long lifespans, and high parental investment (e.g., humans, elephants).

Core Questions

WHAT (definitional)

Q: What is exponential growth? A: Population growth at a constant per capita rate (r) without resource limits, producing a J-shaped curve. Trap/Clarification: Exponential growth cannot continue indefinitely—it assumes unlimited resources, which never exist in nature.

Q: What is carrying capacity (K)? A: The maximum population size an environment can support long-term, set by limiting factors (e.g., food, predation, disease). Trap/Clarification: K is not fixed—it fluctuates with environmental changes (e.g., drought, habitat loss).

WHY (causal/explanatory)

Q: Why does logistic growth slow as N approaches K? A: Density-dependent factors (e.g., competition, disease) reduce birth rates or increase death rates as resources become scarce. Trap/Clarification: The growth rate never reaches zero at K—it oscillates around K due to time lags in feedback.

Q: Why are r-selected species often pioneers in disturbed habitats? A: Their high reproductive output and rapid maturation allow them to exploit temporary resource surges before competitors arrive. Trap/Clarification: r-selection-"better"—it’s a trade-off; K-selected species dominate stable environments.

HOW (process/application)

Q: How do you calculate exponential growth? A: Use the formula N? = N?e, where N? = future population, N? = initial population, r = intrinsic growth rate, t = time. Trap/Clarification: "r" is the per capita growth rate (births – deaths), not the total population growth rate.

Q: How does logistic growth differ mathematically from exponential? A: Logistic growth adds a carrying capacity term: dN/dt = rN[(K – N)/K], where (K – N)/K slows growth as N approaches K. Trap/Clarification: The logistic equation assumes instantaneous feedback—real populations often overshoot K before stabilizing.

CAN (conditions/possibilities)

Q: Can a population exceed carrying capacity? A: Yes, but only temporarily (overshoot), followed by a crash (dieback) due to resource depletion (e.g., reindeer on St. Matthew Island). Trap/Clarification: Overshoot-sustainable growth—it’s a sign of delayed density-dependent effects.

Q: Under what conditions does exponential growth occur in nature? A: Only in short bursts when resources are temporarily unlimited (e.g., invasive species in new habitats, bacterial blooms). Trap/Clarification: "Unlimited resources" is rare—exponential growth is usually a transient phase before logistic constraints kick in.

Quick Facts & Traps

• Fact: r in growth equations = intrinsic rate of increase (births – deaths), not the total population growth rate.
• Trap: "Logistic growth always stabilizes at K"-Reality: Populations often oscillate around K due to time lags in feedback.
• Fact: K-selected species have Type I survivorship curves (low juvenile mortality); r-selected species have Type III (high juvenile mortality).
• Trap: "r-selection = small body size"-Reality: Body size is correlated but not definitive (e.g., some fish are r-selected but large).
• Fact: Density-dependent factors (e.g., competition, disease) regulate populations near K; density-independent factors (e.g., weather) can limit growth at any size.
• Trap: "Carrying capacity is the same for all species in an ecosystem"-Reality: K varies by species (e.g., deer vs. wolves in the same forest).

Rapid-Fire True/False

• Statement: Exponential growth can continue indefinitely if resources are abundant. Answer: FALSE Why the common mistake happens: Confusing temporary resource surges (e.g., seasonal blooms) with permanent unlimited conditions.

• Statement: K-selected species always have fewer offspring than r-selected species. Answer: TRUE Why the common mistake happens: Overlooking that K-selected species invest more per offspring (e.g., elephants have 1 calf vs. frogs’ 1000s of eggs).

• Statement: A population at carrying capacity has a growth rate of zero. Answer: FALSE Why the common mistake happens: Assuming K is a static "ceiling"—real populations fluctuate around K, with growth rates oscillating near zero.