Stage Based Population Projection Matrices and the Power of Linear Algebra

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

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Initial Age Distribution Vector
vt

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The Leslie Matrix
L
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Population Projection




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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

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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

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General Form of the Lefkovitch Matrix
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Carreta-Carreta
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Loggerheads in Danger

• Listed as threatened species in 1978
• Conservation focused on protecting nests
• Could this focus be bettered?

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Constructing Our Stage Based Matrix
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Our Stage Based Population Projection Matrix
A
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Growth Rate Calculation

• ?m er
• ?m 0.9450 and r -5.65

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Impact of Various Stages When Their Survival Is
100
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Conservation Efforts Misdirected

• Data from Lefkovitch matrix shows where to focus
  conservation efforts
• Egg and nest conservation not the best focus

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The Main Danger Facing Sea Turtles
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The Turtle Excluder Device
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Conclusion

• 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