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

Leslie Matrix Population Projection Technique Developed in 1945 Each age class represents a stage F i represents reproductive output at age class i P i represents reproductive output at age class i

Initial Age Distribution Vector vtvt =

The Leslie Matrix L =

Population Projection Lv t v t+1 L2vtL2vt v t+2 L3vtL3vt v t LivtLivt v t+i = = = =

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

New Factors for Lefkovitch Technique F i represents reproductive output at age class i P i represents the probability of not perishing and not changing stages G i represents probability of surviving and moving on to next stage

General Form of the Lefkovitch Matrix

Carreta-Carreta

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

Constructing Our Stage Based Matrix

Our Stage Based Population Projection Matrix A =

Growth Rate Calculation m = e r m = and r = -5.65%

Impact of Various Stages When Their Survival Is 100% Stage NumberAltered Growth Rate

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

The Main Danger Facing Sea Turtles

The Turtle Excluder Device

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