topic 3- exponential pop growth Flashcards Preview

pop. ecology > topic 3- exponential pop growth > Flashcards

Flashcards in topic 3- exponential pop growth Deck (12)
Loading flashcards...
1
Q

what is the exponential (cont) pop growth model

A
Nt=N0e^rt  
-dN/dt for this one is integrated 
- pop size at time 
dN/dt=rN
- cont. differential equation pop growth rate
2
Q

what are we interested with? assumptions?

A

Interested in continuous growth

Assume time interval is infinitely small (t approaches 0)

3
Q

discrete time model vs exponential

A

deltaN/deltat=(b-d)N from discrete model is replaced with dN/dt=(b-d)N
it is derivative - describes how a function changes as input changes

4
Q

what is pop growth now descirbed by? variables?

A

population growth is now described by the change in population size (dN) occurring
during an infinitely small time interval (dt)
b & d are now “instantaneous” rates
b-d=r
r = instantaneous rate Of increase
(aka: intrinsic rate of increase, finite rate of increase, Malthusian parameter

5
Q

solve differential equation?

A

dN/dt=rN - differential equation, output = instantaneous pop growth rate
solve by integration ->
Nt=N0e^rt

6
Q

geometric vs exponential model? look at the graphs

A

geometric
- pop size in intervals
-pop growth rate (slope) deltaN/deltaT is the same from (t) to (t+1)
exponential
-smooth line
pop cont. reproducing/increasing
-cont changing slope/ pop growth rate (dN/dt)

7
Q

how do geometric and exponential behave similarly?

A

follow same curve
λ=e^r
r= loge(λ)= In(λ)

8
Q

how is the pop growth rate approximated? how does it change?

A
• Population growth rate 
	Population growth rate (dN/dt) is 
	approximated by the slope of the 
	line tangent to the curve at any point 
	in time (t) 
	Population growth rate changes 
	continually over time 
	Populations increase at an 
	accelerating rate for the exponential 
model
9
Q

pop growth for different values of r or λ

A

r>0 or λ>1 = pop grows
r=0 or λ=1 = pop constant
r<0 or λ<1 = pop decline

10
Q

convert exponential model to linear model

A

Nt=N0e^rt becomes In(Nt)=In(N0) +rt
In(No) is y intercept
r is slope
if r is contant, the log of N will be a linear function of ti,e

11
Q

exponential doubling time?

A

In(2)/r=t
if r is 0 = undefined
if d>b, r is negative

12
Q

assumptions?

A

• Closed population
• Unlimited resources & constant
environment (b, d, r constant)
• All individuals identical (b & d) or average b
& d is constant throughout time (stable age-
class distribution)
• Continuous growth with no time lags