8.1.4 Population Growth

Exponential growth formula

dN/dT = r_maxN

r = per capita rate of increase, stays constant

unconstrained growth

r = r_max

Birth/Death Growth formula

dN/dT = B - D = rN

B = birth RATE

D = death RATE

Logistic growth

dN/dT = r_max((K-N)/K)*N

growth that slows as population reaches carrying capacity (K)

K = max pop size

r = rmax ( (K-N)/K ), gets smaller towards K

Density-Dependent Limiting Factors

• create logistic growth pattern and determines K

• factors are mostly biotic

1. Competition w/n population

2. Predation

3. Disease and parasites

4. Waste accumulation

Competition w/n population

• population grows but resources do not

  • food, water, shelter are limited

• Responses

  1. Slow down breeding

  2. Migrate

  3. Die

Predation

predators focus on HIGH density prey areas and avoid low density prey areas

Disease and parasites

• diseases and parasites spread easier in HIGH density populations

• have their own growth curves

Density-independent factors

• affect growth rates, not dependent on density

• mostly abiotic

• Natural disasters

Cyclic oscillations

populations that rise and fall over time

1. Seasonal changes

2. Overshooting carrying capacity

3. Predator-prey interactions