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Populations and Life Cycles
What is a population? Population – a group of the same species
that occupies the same geographical space
What is a community? Community- a group
of interacting populations occupying the same area
How do populations grow?1. Linear Growth
- population grows by set increments (for example 2 feet per year)
#
time
How do populations grow?2. Exponential Growth (J Curve)
- Doubling of population by each time increment
#
time
Where is the…
Lag Phase?
Exponential Phase?
What is biotic potential?
How do populations grow?3. Logistic Growth Curve (S-Curve)
- the population grows exponentially up to a point, then levels off due to resource availability
Where is the…
Lag Phase?
Exponential Phase?
Stationary Phase?
What is the carrying capacity?
So…how do populations actually grow?
BIDE Model
(Births + Immigration) – (Deaths + Emigration) =
Example: A population of chimpanzees has 150 births a year and 10 immigrants per year. During the same year 25 chimpanzees died and 15 left the population. Is this population growing or declining?
(150 + 10) – (25 +15) = +120 chimpanzees
Population Growth or Decline
Terms to know when talking about populations Biotic factors – A factor created by a
living thing or any living component within an environment that effects the action of another organism, for example a predator consuming its prey.
Abiotic factors – A factor that is non-living in an environment that effects the action of another organism, for example rain or soil
Nt+1 = R x Nt
Nt = number individuals nowNt+1 = number of individuals next yearwhere R is the finite rate of increaseIf R > 1 the population growsIf R < 1 the population declines
A More Sophisticated Look: Exponential growth
In problems you may be asked to figure out what R is.
The general equation is R = 1 (+/-) ___ % (in decimal form)
You would use a + sign when the population is increasing
You would use a – sign when the population is declining
Examples of the Exponential Growth Model Example 1: A population of humans has 50
individuals. If the rate of increase is 4% (R = 1 + .04), what will the population be next year?
Nt+1 = 50 x 1.0452 people next year!
Example 2: A population of lemmings is currently at 100. If the rate of decline is 15% (so R = 1 - .15) in the current year, how many will be present next year in the population?
Nt+1 = 100 X .8585 lemmings next year!
What factors influence population growth?• Density Independent
Factors - abiotic factors that effect each member of the population, no matter how many are present
•Density Dependent Factors - biotic factors that influence population size that is influenced by the number of individuals
One other factor that has not been accounted for….
Assumption for exponential growth model was that all individuals are equal.
That is, the population is unstructured
Is the human population unstructured??
Most organisms have structured populations
Stage and Size predict survival and fecundity
Plants- seed, seedling, adult
Invertebrates- number of molts, larva-pupa-adult
Amphibians- egg-tadpole-adult
Birds- egg-chick-adult
Mammals- newborn, juvenile, adult
Exponential growth with structure
N0(t+1)
N2(t+1)
N1(t+1) =F0
0
S0
F1
S1
0
F2
0
0
N0(t)
N2(t)
N1(t)
Nt+1 = R x Nt
Nt+1 = R x Nt
Unstructured exponential growth model
Structured growth model
Management of the pest plant, Garlic mustard
Exotic plant (from Europe)- highly invasive weed in USABiennial life cycle- seed, rosette, adult…also has seed dormancy
Life cycle graph for garlic mustard
Seed Rosette Adult
Life cycle graph for garlic mustard
Seed Rosette Adult
0.09
0.01 0.50
80
Drayton and Primack 1999 Biological Invasions
920
Transition matrix for garlic mustard
Seed Rosette Adult
0.09
0.01 0.50
80
920
seed ros adult
seed
ros
adult
0.09
0.01
0
0
0
0.50
80
920
0
Now
Nex
t Y
ear
NS(t+1)
NA(t+1)
NR(t+1)
=10
0
0
Nt+1 = A x Nt
Ten seeds are introduced to Fullersburg Woods in 2000. How many plants will be there in 2001?
0.09
0.01
0
0
0
0.50
80
920
0
=(0.09*10) + (0*0) + (80*0)
(0.01*10) + (0*0) + (920*0)
(0*10) + (0.50*0) + (0*0)
Pattern to multiply by: Each number in the column labeled “1” must be multiplied by the number beside the letter “A”. Each number in the column labeled “2” must be multiplied by the number beside the letter “B”. Repeat for column “3”. All rows must be added at the end.
The Results for 2001!
It may look like the population is dying, but looks can be deceiving…let’s do it another year!
NS(t+1)
NR(t+1)
NA(t+1)
.9
0
.1
NS(t+1)
NA(t+1)
NR(t+1)
=.9
0
.1
Nt+1 = A x Nt
2001 to 2002
0.09
0.01
0
0
0
0.50
80
920
0
=(0.09*.9) + (0*.1) + (80*0)
(0.01*.9) + (0*.1) + (920*0)
(0*.9) + (0.50*.1) + (0*0)
Notice that the matrix is the same, but this is from our results from 2001!
The Results for 2002!
Hmmm…look adults!...1 more year!
NS(t+1)
NR(t+1)
NA(t+1)
.081
.05
.009
NS(t+1)
NA(t+1)
NR(t+1)
=.081
.05
.009
Nt+1 = A x Nt
2002 to 2003
0.09
0.01
0
0
0
0.50
80
920
0
=(0.09*.081) + (0*.009) + (80*.05)
(0.01*.081) + (0*.009) + (920*.05)
(0*.081) + (0.50*.009) + (0*0)
Notice that the matrix is the same, but this is from our results from 2002!
The Results for 2003!
Ummm we have a problem here….
NS(t+1)
NR(t+1)
NA(t+1)
4.00729
.00045
46.00081
0.001
0.1
10
1000
100000
1E+07
1E+09
1E+11
1 32 4 5 6 7 8 9 10 11
Seed
Rosette
Adult
Po
pu
lati
on
Siz
e (l
og
sca
le)
Time
A BIG Problem…..
We see cycles between rosette and adult years in the field
How do we manage Garlic mustard?
Seed Rosette Adult
0.09
0.01 0.50
80
920
Explore effects of management
Turning over the seed bank = reduce number of seeds present
Spray rosettes with herbicide = reduce rosettes (R) by some amount
Pull adults = Reduce adults (A) by some amount
Managing Only Rosettes
Look at the end of the graph. Why does killing rosettes increase the total number? What information are we missing?
Managing Only Adults
How much do we need to eliminate to make an impact?
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