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Stage Based Population Projection Matrices and the Power of Linear Algebra

Explore the power of linear algebra in stage-based population projection matrices, with a focus on the Leslie matrix technique developed in 1945 and the Lefkovitch matrix. Learn how these matrices help in calculating growth rates, guiding conservation efforts, and addressing threats like the Turtle Excluder Device for Carreta-Carreta Loggerheads. Discover the nuances of reproductive output, age distribution vectors, stage transitions, and survival probabilities. Unveil the implications of various stages on survival, and evaluate if current conservation strategies need refinement to ensure the well-being of sea turtles.

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Stage Based Population Projection Matrices and the Power of Linear Algebra

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  1. Stage Based Population Projection Matrices and the Power of Linear Algebra Michael Bruce and Emily Shernock

  2. Leslie 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

  3. Initial Age Distribution Vector vt =

  4. The Leslie Matrix L =

  5. Population Projection = = = =

  6. Lefkovitch 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

  7. New 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

  8. General Form of the Lefkovitch Matrix

  9. Carreta-Carreta

  10. Loggerheads in Danger • Listed as “threatened” species in 1978 • Conservation focused on protecting nests • Could this focus be bettered?

  11. Constructing Our Stage Based Matrix

  12. Our Stage Based Population Projection Matrix A =

  13. Growth Rate Calculation • m= er • m= 0.9450 and r = -5.65%

  14. Impact of Various Stages When Their Survival Is 100%

  15. Conservation Efforts Misdirected • Data from Lefkovitch matrix shows where to focus conservation efforts • Egg and nest conservation not the best focus

  16. The Main Danger Facing Sea Turtles

  17. The Turtle Excluder Device

  18. Conclusion • TED’s 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

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