1. Age and Stage Structure
N t+1 = Noert
N(t+1) = N(t)
These assume that all
individuals have the
same demographic rates

2. Sometimes, this assumption isn’t appropriate…
We may have more information that we can
use: stage/age specific demographic rates
The stage/age classes may be so different from
each other that using a general average
is not accurate enough
We may have a question that requires a stage/
age structured model

3. Which stage is the most important to protect to preserve the species?
An example-
Sea turtle conservation strategies
Which stage is the most important
to protect to preserve the species?
Crouse et al. 1987, Crowder et al. 1994

4. Setting up the equation:
N(t+1) = N(t)
N(t+1) =  (N1(t) + N2(t) + … + Nx(t)
N(t+1) =  (Nx(t))
We are still going to ignore immigration
and emigration…

5. The components of N(t+1)
The total number of individuals in the
population is the sum of individuals
in each age/stage.
Individuals in t+1 come from two sources
(assuming no immigration):
Survival
Birth

6. This should be n1, not n0

7. The components of N(t+1)
Let’s assume N(t+1) = N1(t+1) + N2(t+1)
an age-structured model
Addition of new individuals:
N1(t+1) = N1(t)*b1*S0 + N2(t)*b2*S0
New first stage individuals are born to both
stages at stage-specific reproductive rates,
then must survive to t+1 to be counted.

8. The components of N(t+1)
Still assuming N(t+1) = N1(t+1) + N2(t+1)
Survival of existing individuals:
N2(t+1) = N1(t)*S1
Note: all N1(t+1) individuals came from
birth processes

9. The components of N(t+1)
Putting it all together….
N(t+1) = N1(t)*b1*S0 + N2(t)*b2*S0
Reproduction
+N1(t)*S1
Survival

10. The remainder of this lecture…
Form of a matrix
The transition matrix
Translating a life history graph into
a transition matrix
Get the notes from someone if you
missed class!!!