Lecture 22+23-cwo - Roadm ap Population Ecology A Dynam ics...

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Population Ecology A. Dynamics a. Context: sea turtles b. Approaches i. Life cycle diagram ii. Age-structure iii. Projection matrices iv. Projections v. Population growth vi. More flexible approaches Roadmap : Photo by CW Osenberg
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What is population abundance? What is population density? How do we measure them? How do they change? Dynamics :
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Population Structure : From vianica.com
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Life Cycle Diagram? Approach : Age 1 Age 2 Age 0 Age 3 Age-based approach. What now?
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More transitions? Approach : Age 1 Age 2 Age 0 Age 3 Dead Are we done?
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Add values? P ij = Per capita transition from group j to i Approach : Group 2, Age 1 Group 3, Age 2 Group 1, Age 0 Group 4, Age 3 Dead Now what? P 21 P 14 P 32 P 43 P 13 1-P 21
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Projection matrix approach (lecture) Vs. Life table approach (textbook) Caveat :
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Project from time t to time t+1…. Approach : Group 2, Age 1 Group 3, Age 2 Group 1, Age 0 Group 4, Age 3 Dead Project what? P 21 P 14 P 32 P 43 P 13 1-P 21
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n x,t = abundance (or density) of class x at time t. So, given that we know n 1,t , n 2,t , n 3,t , etc. …. What is n 1,t+1 , n 2,t+1 , n 3,t+1 , etc? Approach :
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n 2,t+1 = ?? = P 21 x n 1,t Approach : Group 2, Age 1 Group 3, Age 2 Group 1, Age 0 Group 4, Age 3 Dead Project what? P 21 P 14 P 32 P 43 P 13 1-P 21
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n 1,t+1 = ?? = (P 14 x n 4,t ) + (P 13 x n 3,t ) Approach : Group 2, Age 1 Group 3, Age 2 Group 1, Age 0 Group 4, Age 3 Dead Project what? P 21 P 14 P 32 P 43 P 13 1-P 21
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More generally: Approach : = + = + + + = n j t j j i t i t i t i t i n P n P n P n P n 1 , , , 3 3 , , 2 2 , , 1 1 , 1 , ... Group 2 Group 3 Group 1 Group 4 P 21 P 24 P 23 P 22
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Matrix algebra : t t An n = + 1 n is a vector of abundances for the groups; A is a matrix of transitions
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algebra : = = 44
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Lecture 22+23-cwo - Roadm ap Population Ecology A Dynam ics...

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