Title: Stage Based Population Projection Matrices and the Power of Linear Algebra
1Stage Based Population Projection Matrices and
the Power of Linear Algebra
Michael Bruce and Emily Shernock
2Leslie Matrix Population Projection Technique
- Developed in 1945
- Each age class represents a stage
- Fi represents reproductive output at age class i
- Pi represents reproductive output at age class i
3Initial Age Distribution Vector
vt
4The Leslie Matrix
L
5Population Projection
6Lefkovitch Stage Based Population Matrix
- The Leslie matrix is only a specific case of a
general matrix - Lefkovitch matrix does not relate age and stage
- Organisms do not always develop at the same rate
- Some animals are not easily identified as to age
7New Factors for Lefkovitch Technique
- Fi represents reproductive output at age class i
- Pi represents the probability of not perishing
and not changing stages - Gi represents probability of surviving and moving
on to next stage
8General Form of the Lefkovitch Matrix
9Carreta-Carreta
10Loggerheads in Danger
- Listed as threatened species in 1978
- Conservation focused on protecting nests
- Could this focus be bettered?
11Constructing Our Stage Based Matrix
12Our Stage Based Population Projection Matrix
A
13Growth Rate Calculation
- ?m er
- ?m 0.9450 and r -5.65
14Impact of Various Stages When Their Survival Is
100
15Conservation Efforts Misdirected
- Data from Lefkovitch matrix shows where to focus
conservation efforts - Egg and nest conservation not the best focus
16The Main Danger Facing Sea Turtles
17The Turtle Excluder Device
18Conclusion
- TEDs required in most U.S. waters of Gulf of
Mexico and South Atlantic - Florida Loggerhead population stable
- Florida home to one third of world Loggerhead
population