BIOL 290 Lecture 12: Continuous Growth

33 views2 pages
9 Nov 2018
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:
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))]
Unlock document

This preview shows half of the first page of the document.
Unlock all 2 pages and 3 million more documents.

Already have an account? Log in

Get OneClass Notes+

Unlimited access to class notes and textbook notes.

YearlyBest Value
75% OFF
$8 USD/m
Monthly
$30 USD/m
You will be charged $96 USD upfront and auto renewed at the end of each cycle. You may cancel anytime under Payment Settings. For more information, see our Terms and Privacy.
Payments are encrypted using 256-bit SSL. Powered by Stripe.