BIOL 290 Lecture 12: Continuous Growth

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9 Nov 2018
School
Department
Course
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:
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))]
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