Continuous Growth
Thursday, November 8, 2018
4:02 PM
• Continuous growth described by differential equations
• dN/dT= f(N)
• The change in population size (dN) over elapsed time (dT) is a function of population size
• dN/dT= f(N)= bN-dN
• Instantaneous Birth and Death Rate: bN-dN= (b-d)N
• B= birth rates
• D= death rates
• rN= (b-d)N
• Little r: Instantaneous Growth Rate
• r>0 when b>d
• The larger r is; population increases faster and faster
• r<0 when b<d
• Exponential decline; fewer individuals slower decline, more individuals faster decline
Continuous growth
• Nt= N(0)e^rt
Discrete Growth
• N(o)lambda^t
• Lambda ~ e^r
• Geometric Growth Rate: when generations are separate from each other
• Continuous Growth Rate:
• Adding Environmental Stochasticity (randomness)
• If lambda varies over time due to weather effects on deaths and births
• If b(t) and d(t) are not constant
• N(t+1)= N(t)Lambda(t)
• Ex: (Grizzly Bear Abundance)
-varies from year to year
• [r(t)=ln(lambda(t))]