An Example Cohort Analysis:
Phlox drummondii
Complex survivorship pattern in Euterpe globosa
III
II
I
Fecundity
Total number of
seeds produced
by the population
Fx
Fecundity
Total number of
seeds produced
per individual
Fx
fx
Fx
fx 
Nx
Phlox fecundity
fx
Phlox survivorship and fecundity
lx
fx
Predicting population growth
Fx
fx
f
X
Average number of offspring
produced per individual in
absence of mortality
x
 25.3953
Phlox predicting population growth
Fx
lxfx =
fx
lxfx
Net Reproductive Value (R0)
lxfx
R0
Net Reproductive Value (R0)
R0 is the number of offspring produced
over the lifetime of the average plant, as
adjusted by survivorship
R0   lx f x
Phlox: putting it all together
• For the Phlox study R0=2.42 and N0 = 996
• Since Phlox is an annual plant l = R0
• Recall Nt+1 = Ntl
• N1 = N0 x 2.42 = 996 x 2.42 = 2407.92
N1 = 2407.92
Life-table approach to cohort analysis
The same life table approach can be
applied to cohorts of longer lived
plants.
Cohort Analysis
Advantage
• Precise knowledge of birth and death rates
• Precise knowledge of age
Disadvantages
• Individuals may live too long to track
• Different histories among cohorts may
influence birth and death rates
Differences among Cohorts:
Fecundity in a Desert Winter Annual
El Niño Events
Differences among Cohorts:
Population Size in a Desert Winter Annual
Static or Vertical Analysis
The Method
• Locate a large number of individuals
• Classify individuals
-- Age
-- Size
Vertical Analysis of Eastern Hemlock
(Heck and Loucks 1976)
Size classification
Age
Classification
Size vs. Age in Larrea Tridentata (creosote bush)
Size
Predict age
from size
Age
Size vs. Age in Larrea Tridentata (creosote bush)
Sources of error in
estimate
• Environmental heterogeneity
• Genetic variability
• Random events
Size as a predictor of fecundity
Size as demographic predictor
for plants
• Often a better predictor than age
• Easier to estimate than age
Static or Vertical Analysis
The Method
• Locate a large number of individuals
• Classify individuals
• Infer rates of mortality and fecundity
Models of Mortality for Eastern Hemlock
Constant rate of mortality over time
Explains 36% of Variance
y is the number of plants in each age class
Models of Mortality for Eastern Hemlock
Declining
mortality
over time
Explains 49% of Variance
y is the number of plants in each age class
Models of Mortality for Eastern Hemlock
Declining mortality with an underlying periodicity
Explains 81% of Variance
y is the number of plants in each age class
Static/Vertical Analysis
Advantage (vs. cohort analysis)
• Study can be conducted in one fell swoop
Disadvantage (vs. cohort analysis)
• A large number of assumptions must be
made in calculating fecundity or mortality
as a function of size or age
Stage Based Approaches to
Demographic Analysis
Phlox: a simple example
Step #1: Determine stages to include
Seed
Juvenile
Adult
Phlox: a simple example
Step #2: Determine transitions to include
Seed
Juvenile
Adult
Phlox: a simple example
Step #3: Determine parameters to calculate
F13
Seed1
P21
Juvenile2
P32
Adult3
Phlox: a simple example
Step #4: Collect raw data
F13
Seed1
P21
Juvenile2
P32
Adult3
Source of stage data
Seed stage
Juvenile stage
Adult stage
Source of stage data
Seed stage
Juvenile stage
Adult stage
Phlox: a simple example
Step #4: Collect raw data
Total number of seeds produced by adults
F13
2407.92
Seed1
996
Raw data
P21
Juvenile2
190
P32
Adult3
158
Number of individuals in the next generation
N0
Seeds produced = R0N0 = 2407.92
R0
Phlox: a simple example
Step #4: Calculate transition values
P32 
F13
2407.92
Seed1
996
190
P21 
 .19
996
P21
Juvenile2
P32
190
2407.92
 15.24
158
Adult3
158
P32 
158
 .83
190
Phlox: a simple example
Step #5: Test and use model
15.24
2407.92
Seed1
.19
996
Juvenile2
.83
190
R0 
2407.92
 2.417  0.19 * 0.83 *15.24
996
Adult3
158
Complex Life Histories: Argyroxiphium sandwicense
A Long-lived Perennial
Complex Life Histories: Argyroxiphium sandwicense
A Long-lived Perennial
Complex Life Histories: A Cryptic Orchid as an Example
Cypripedium acaule