Loggerhead Sea Turtle Conservation Ben Marshall and Alex Varner - PowerPoint PPT Presentation

Loggerhead Sea Turtle Conservation Ben Marshall and Alex Varner December 16, 2009 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Table: Stage Based Life Table for Loggerhead Sea Turtles Stage Class Size(cm) Ages(yr) Survival Fec. 1 eggs/hatchlings < 10 < 1 .6747 0 2 sm. juveniles 10.1-58 1-7 .7857 0 3 lg. juveniles 58.1-80 8-15 .6758 0 4 subadults 80.1-87 16-21 .7425 0 5 novice breeders > 87 22 .8091 127 6 1st-yr remigrants > 87 23 .8091 4 7 mature breeders > 87 24-54 .8091 80 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Survival and Fecundity ◮ P i ◮ The probability of survival while in a stage i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Survival and Fecundity ◮ P i ◮ The probability of survival while in a stage i ◮ F i ◮ Birth rates for each stage Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Stage 1 Population ◮ n ( t +1) = P 1 n ( t ) 1 + F 2 n ( t ) 2 · · · + F 7 n ( t ) 1 7 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Stage 1 Population ◮ n ( t +1) = P 1 n ( t ) 1 + F 2 n ( t ) 2 · · · + F 7 n ( t ) 1 7 ◮ Survivors and hatchlings Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Matrix Model ◮ n ( t +1) = P 1 n ( t ) 1 + F 2 n ( t ) 2 · · · + F 7 n ( t ) 1 7   n ( t )   n ( t +1) P 1 F 2 F 3 F 4 F 5 F 6 F 7  1  n ( t ) 1   2       n ( t )       3        n ( t )    =       4       n ( t )         5     n ( t )       6   n ( t ) 7 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Survival and Fecundity ◮ P i ◮ The probability of survival while remaining in same stage Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Survival and Fecundity ◮ P i ◮ The probability of survival while remaining in same stage ◮ F i ◮ Birth rates for each stage Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Survival and Fecundity ◮ P i ◮ The probability of survival while remaining in same stage ◮ F i ◮ Birth rates for each stage ◮ G i ◮ Probability of advancing to the next stage Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Stage 2 Population ◮ n ( t +1) = G 1 n ( t ) 1 + P 2 n ( t ) 2 2 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Stage 2 Population ◮ n ( t +1) = G 1 n ( t ) 1 + P 2 n ( t ) 2 2 ◮ New stage members and surviving stage members Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Matrix Model cont. ◮ n ( t +1) = G 1 n ( t ) 1 + P 2 n ( t ) 2 2 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Matrix Model cont. ◮ n ( t +1) = G 1 n ( t ) 1 + P 2 n ( t ) 2 2 ◮   n ( t ) n ( t +1)    P 1 F 2 F 3 F 4 F 5 F 6 F 7  1 1 n ( t )   n ( t + 1 ) G 1 P 2 2       n ( t ) 2           3       n ( t )   =       4       n ( t )           5       n ( t )       6   n ( t ) 7 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Final Matrix Model ◮     n ( t ) n ( t +1)  P 1 F 2 F 3 F 4 F 5 F 6 F 7  1 1 n ( t ) n ( t +1)     G 1 P 2 2 2        n ( t )   n ( t +1)    G 2 P 3     3 3       n ( t ) n ( t +1)   = G 3 P 4       4 4       G 4 P 5 n ( t ) n ( t +1)           5 5   G 5 P 6     n ( t ) n ( t +1)       6 6 G 6 P 7     n ( t ) n ( t +1) 7 7 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating F i ◮ F i is easy. Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating F i ◮ F i is easy. Table: Stage Based Life Table for Loggerhead Sea Turtles ◮ Stage Class Size(cm) Ages(yr) Survival Fec. 1 eggs/hatchlings < 10 < 1 .6747 0 2 sm. juveniles 10.1-58 1-7 .7857 0 3 lg. juveniles 58.1-80 8-15 .6758 0 4 subadults 80.1-87 16-21 .7425 0 5 novice breeders > 87 22 .8091 127 6 1st-yr remigrants > 87 23 .8091 4 7 mature breeders > 87 24-54 .8091 80 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating F i ◮ F i is easy. Table: Stage Based Life Table for Loggerhead Sea Turtles ◮ Stage Class Size(cm) Ages(yr) Survival Fec. 1 eggs/hatchlings < 10 < 1 .6747 0 2 sm. juveniles 10.1-58 1-7 .7857 0 3 lg. juveniles 58.1-80 8-15 .6758 0 4 subadults 80.1-87 16-21 .7425 0 5 novice breeders > 87 22 .8091 127 6 1st-yr remigrants > 87 23 .8091 4 7 mature breeders > 87 24-54 .8091 80 ◮ Found in far right column. Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Stage Specific Survival p i ◮ Each stage has specific survival rate, found in table Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Stage Specific Survival p i ◮ Each stage has specific survival rate, found in table Table: Stage Based Life Table for Loggerhead Sea Turtles ◮ Stage Class Size(cm) Ages(yr) Survival Fec. 1 eggs/hatchlings < 10 < 1 0 .6747 2 sm. juveniles 10.1-58 1-7 .7857 0 3 lg. juveniles 58.1-80 8-15 0 .6758 4 subadults 80.1-87 16-21 .7425 0 5 novice breeders > 87 22 .8091 127 6 1st-yr remigrants > 87 23 .8091 4 7 mature breeders > 87 24-54 .8091 80 Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating G i Table: Population and Survival Pop. Years M 1 Mp i 2 Mp 2 3 i ◮ Mp 3 4 i Mp 4 5 i Mp 5 6 i Mp 6 7 i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating G i Table: Population and Survival Pop. Years M 1 Mp i 2 Mp 2 3 i ◮ Mp 3 4 i Mp 4 5 i Mp 5 6 i Mp 6 7 i ◮ Eligible: Mp 5 i M + Mp i + Mp 2 i + Mp 3 i + Mp 4 i + Mp 5 i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating G i cont. ◮ Proportion: p 5 � � i 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating G i cont. ◮ Proportion: p 5 � � i 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i ◮ Hit this again with p i ◮ Yields the percentage that actually advance. Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating G i cont. ◮ Proportion: p 5 � � i 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i ◮ Hit this again with p i ◮ Yields the percentage that actually advance. ◮ p 6 � � i G i = 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Generalizing G i ◮ p 5 � � i G i = p i 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Generalizing G i ◮ p 5 � � i G i = p i 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i ◮ G i generalized: d i represents stage duration. Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Generalizing G i ◮ p 5 � � i G i = p i 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i ◮ G i generalized: d i represents stage duration. ◮ � � p d i − 1 i G i = p i i + · · · + p d i − 1 1 + p i + p 2 i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Generalizing G i ◮ p 5 � � i G i = p i 1 + p i + p 2 i + p 3 i + p 4 i + p 5 i ◮ G i generalized: d i represents stage duration. ◮ � � p d i − 1 i G i = p i i + · · · + p d i − 1 1 + p i + p 2 i ◮ G i = (1 − p i ) p d i i 1 − p d i i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating P i Table: Population and Survival Pop. Years M 0 Mp i 1 Mp 2 2 i ◮ Mp 3 3 i Mp 4 4 i Mp 5 5 i Mp 6 6 i Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating P i Table: Population and Survival Pop. Years M 0 Mp i 1 Mp 2 2 i ◮ Mp 3 3 i Mp 4 4 i Mp 5 5 i Mp 6 6 i ◮ Mp 5 i are eligible to advance Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating P i Table: Population and Survival Pop. Years M 0 Mp i 1 Mp 2 2 i ◮ Mp 3 3 i Mp 4 4 i Mp 5 5 i Mp 6 6 i ◮ Mp 5 i are eligible to advance ◮ then M + Mp i + Mp 2 i + Mp 3 i + Mp 4 i are ineligible. Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation

Calculating P i cont. ◮ M + Mp i + Mp 2 i + Mp 3 i + Mp 4 i are ineligible to advance ◮ Only option for survival is remain in class. Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation