1. Population-Projection Models

2. Individuals in a pop. are not
created equal.

4. Age classes
Stage classes
<1.5 (calves)
Fawns
1.5
Button bucks
2.5
Spikes
3.5
Branch-antlered
≥4.5

5. Common frog (Rana temporaria)

7. Anatomy of a population-projection matrix (M)
The reproductive contribution of each stage to the next time step.
PJUV
JUV AD
PJUV JUV AD
Stage-specific survival rates.
A female-based matrix model for the common frog with 3 stage classes: pre-juvenile (PJUV), juvenile (JUV), and adult (AD).

8. Mean number of eggs a female frog produces annually = 650.
PJUV
JUV AD
PJUV JUV AD
Mean number of eggs a female frog produces annually = 650.
0.08 x 650 = 52
0.43 x 650 = 279.5

9. Annual survival of JUV females = 0.25 + 0.08 = 0.33.
PJUV
JUV AD
PJUV JUV AD
Annual survival of JUV females = = 0.33.

10. Population-size vector (n)
n(t) =

11. Multiplying M by n(t) x =
M x n(t) = n(t+1) = Resultant vector

12. Projecting a matrix through time
n(t)
n(t+1)
N2013= 3848 x =
N2014= 2093 x =
N2015= 5812 x =

13. Projecting the matrix for 25 years

14. Change the y-axis to a logarithmic scale

15. Now you do it
Consider a population with 4 age cohorts (0-3) and age-specific survival rates of 0.50, 0.65, 0.85, and 0.40, respectively. Assume that the age 0 cohort consists of immature (non-breeding) individuals and that reproductive rates for the other 3 cohorts are age specific: 0.1, 20, and Using a population-projection matrix, project and graph each cohort in the population for 10 years starting with an initial age-specific population size of 1000, 500, 200, and 85 for age cohorts 0-3, respectively.

16. Project and graph each cohort in the population for 10 years.
1000
500
200 85 X = ?
Project and graph each cohort in the population for 10 years.