ECOLOGY MATH
ECOLOGY MATH
1) Population density
= # of members/unit of area
ECOLOGY MATH
2) Growth rate (per capita)
= change in number of members/time
r = N/ t
( N = births –deaths)
FYI
• Per capita = per person
ECOLOGY MATH
3) ZPG = Zero Population Growth
birth rate = death rate
r=0
ECOLOGY MATH
4) Change in population at any one instant
N/ t = rN
Ex 1. A population of 500 experiences 55 births and 5
deaths during a one year period. What was the
reproductive rate during this year?
ECOLOGY MATH
Ex. 1 A population of 500 experiences 55 births
and 5 deaths during a one year period.
What was the reproductive rate during this
year?
Ans. N/ t =rN
50/1 = r(500) = .1 or 10%
ECOLOGY MATH
5) Intrinsic Rate of Increase (rmax)
-Fastest rate of growth possible
-Pop. Reproducing w/out limits
-Resources abundant
dN/dt= rmaxN
ECOLOGY MATH
dN/dt= rmaxN
Ex. 2 A population of bacteria with a rmax= .7
per day has a current population of 15,000
cells. How many bacteria will exist in 15
days if resources remain readily available?
ECOLOGY MATH
dN/dt= rmaxN
dN/15 = .7(15,000)
N = 157,500 cells
ECOLOGY MATH
6) Logistical growth model
- availability of resources limits growth
- carry capacity (K) – max # of individuals of a
pop. Supported
dN/dt = rmaxN (K-N/K)
ECOLOGY MATH
Logistical growth model
dN/dt = rmaxN (K-N/K)
Note: As N = K then r = zero
Ex 3. K is estimated at 500, the population size is
currently 400 and r is .01. What is the
growth rate?
ECOLOGY MATH
Logistical growth model
dN/dt = rmaxN (K-N/K
dN/dt = (.01)(400)(100/500)
dN/dt = .8
What does this actually mean?
.8 births per year
ECOLOGY MATH
Logistical growth model
dN/dt = rmaxN (K-N/K
dN/dt = (.01)(400)(100/500)
dN/dt = .8
What does this actually mean?
.8 births per year
This applies to…
•
•
•
•
Age structures
K – resources available
The trophic level that provides the resources
Primary productivity impacts pop. growth for
all levels above
• Cause and effect for food chains/webs