Update Report on Loggerhead Sea Turtle (Caretta caretta) Conservation Monitoring in Fethiye SPA
Loggerhead Sea Turtle Conservation
Transcript of Loggerhead Sea Turtle Conservation
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 02 sm. juveniles 10.1-58 1-7 .7857 03 lg. juveniles 58.1-80 8-15 .6758 04 subadults 80.1-87 16-21 .7425 05 novice breeders > 87 22 .8091 1276 1st-yr remigrants > 87 23 .8091 47 mature breeders > 87 24-54 .8091 80
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Survival and Fecundity
I PiI The probability of survival while in a stage i
I FiI Birth rates for each stage
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Survival and Fecundity
I PiI The probability of survival while in a stage i
I FiI Birth rates for each stage
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 1 Population
I
n(t+1)1 = P1n
(t)1 + F2n
(t)2 · · ·+ F7n
(t)7
I Survivors and hatchlings
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 1 Population
I
n(t+1)1 = P1n
(t)1 + F2n
(t)2 · · ·+ F7n
(t)7
I Survivors and hatchlings
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Matrix Model
I n(t+1)1 = P1n
(t)1 + F2n
(t)2 · · ·+ F7n
(t)7
P1 F2 F3 F4 F5 F6 F7
n(t)1
n(t)2
n(t)3
n(t)4
n(t)5
n(t)6
n(t)7
=
n(t+1)1
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Survival and Fecundity
I PiI The probability of survival while remaining in
same stage
I FiI Birth rates for each stage
I GiI Probability of advancing to the next
stage
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Survival and Fecundity
I PiI The probability of survival while remaining in
same stage
I FiI Birth rates for each stage
I GiI Probability of advancing to the next
stage
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Survival and Fecundity
I PiI The probability of survival while remaining in
same stage
I FiI Birth rates for each stage
I GiI Probability of advancing to the next
stage
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 2 Population
I
n(t+1)2 = G1n
(t)1 + P2n
(t)2
I New stage members and surviving stagemembers
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 2 Population
I
n(t+1)2 = G1n
(t)1 + P2n
(t)2
I New stage members and surviving stagemembers
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Matrix Model cont.
I n(t+1)2 = G1n
(t)1 + P2n
(t)2
I
P1 F2 F3 F4 F5 F6 F7
G1 P2
n(t)1
n(t)2
n(t)3
n(t)4
n(t)5
n(t)6
n(t)7
=
n(t+1)1
n(t+1)2
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Matrix Model cont.
I n(t+1)2 = G1n
(t)1 + P2n
(t)2
I
P1 F2 F3 F4 F5 F6 F7
G1 P2
n(t)1
n(t)2
n(t)3
n(t)4
n(t)5
n(t)6
n(t)7
=
n(t+1)1
n(t+1)2
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Final Matrix Model
I
P1 F2 F3 F4 F5 F6 F7
G1 P2
G2 P3
G3 P4
G4 P5
G5 P6
G6 P7
n(t)1
n(t)2
n(t)3
n(t)4
n(t)5
n(t)6
n(t)7
=
n(t+1)1
n(t+1)2
n(t+1)3
n(t+1)4
n(t+1)5
n(t+1)6
n(t+1)7
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Fi
I Fi is easy.
Table: Stage Based Life Table for Loggerhead Sea Turtles
I
Stage Class Size(cm) Ages(yr) Survival Fec.
1 eggs/hatchlings < 10 < 1 .6747 02 sm. juveniles 10.1-58 1-7 .7857 03 lg. juveniles 58.1-80 8-15 .6758 04 subadults 80.1-87 16-21 .7425 05 novice breeders > 87 22 .8091 1276 1st-yr remigrants > 87 23 .8091 47 mature breeders > 87 24-54 .8091 80
I Found in far right column.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Fi
I Fi is easy.
Table: Stage Based Life Table for Loggerhead Sea Turtles
I
Stage Class Size(cm) Ages(yr) Survival Fec.
1 eggs/hatchlings < 10 < 1 .6747 02 sm. juveniles 10.1-58 1-7 .7857 03 lg. juveniles 58.1-80 8-15 .6758 04 subadults 80.1-87 16-21 .7425 05 novice breeders > 87 22 .8091 1276 1st-yr remigrants > 87 23 .8091 47 mature breeders > 87 24-54 .8091 80
I Found in far right column.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Fi
I Fi is easy.
Table: Stage Based Life Table for Loggerhead Sea Turtles
I
Stage Class Size(cm) Ages(yr) Survival Fec.
1 eggs/hatchlings < 10 < 1 .6747 02 sm. juveniles 10.1-58 1-7 .7857 03 lg. juveniles 58.1-80 8-15 .6758 04 subadults 80.1-87 16-21 .7425 05 novice breeders > 87 22 .8091 1276 1st-yr remigrants > 87 23 .8091 47 mature breeders > 87 24-54 .8091 80
I Found in far right column.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage Specific Survival pi
I Each stage has specific survival rate, found intable
Table: Stage Based Life Table for Loggerhead Sea Turtles
I
Stage Class Size(cm) Ages(yr) Survival Fec.
1 eggs/hatchlings < 10 < 1 .6747 02 sm. juveniles 10.1-58 1-7 .7857 03 lg. juveniles 58.1-80 8-15 .6758 04 subadults 80.1-87 16-21 .7425 05 novice breeders > 87 22 .8091 1276 1st-yr remigrants > 87 23 .8091 47 mature breeders > 87 24-54 .8091 80
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage Specific Survival pi
I Each stage has specific survival rate, found intable
Table: Stage Based Life Table for Loggerhead Sea Turtles
I
Stage Class Size(cm) Ages(yr) Survival Fec.
1 eggs/hatchlings < 10 < 1 .6747 02 sm. juveniles 10.1-58 1-7 .7857 03 lg. juveniles 58.1-80 8-15 .6758 04 subadults 80.1-87 16-21 .7425 05 novice breeders > 87 22 .8091 1276 1st-yr remigrants > 87 23 .8091 47 mature breeders > 87 24-54 .8091 80
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Gi
Table: Population and Survival
I
Pop. Years
M 1Mpi 2Mp2
i 3Mp3
i 4Mp4
i 5Mp5
i 6
Mp6i 7
I Eligible:
Mp5i
M + Mpi + Mp2i + Mp3
i + Mp4i + Mp5
i
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Gi
Table: Population and Survival
I
Pop. Years
M 1Mpi 2Mp2
i 3Mp3
i 4Mp4
i 5Mp5
i 6
Mp6i 7
I Eligible:
Mp5i
M + Mpi + Mp2i + Mp3
i + Mp4i + Mp5
i
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Gi cont.
I Proportion:(p5
i
1 + pi + p2i + p3
i + p4i + p5
i
)
I Hit this again with piI Yields the percentage that actually advance.
I
Gi =
(p6i
1 + pi + p2i + p3
i + p4i + p5
i
)
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Gi cont.
I Proportion:(p5
i
1 + pi + p2i + p3
i + p4i + p5
i
)I Hit this again with pi
I Yields the percentage that actually advance.
I
Gi =
(p6i
1 + pi + p2i + p3
i + p4i + p5
i
)
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Gi cont.
I Proportion:(p5
i
1 + pi + p2i + p3
i + p4i + p5
i
)I Hit this again with pi
I Yields the percentage that actually advance.
I
Gi =
(p6i
1 + pi + p2i + p3
i + p4i + p5
i
)
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Gi
I
Gi =
(p5i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Gi generalized: di represents stage duration.
I
Gi =
(pdi−1
i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Gi =(1− pi)p
di
i
1− pdi
i
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Gi
I
Gi =
(p5i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Gi generalized: di represents stage duration.
I
Gi =
(pdi−1
i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Gi =(1− pi)p
di
i
1− pdi
i
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Gi
I
Gi =
(p5i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Gi generalized: di represents stage duration.
I
Gi =
(pdi−1
i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Gi =(1− pi)p
di
i
1− pdi
i
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Gi
I
Gi =
(p5i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Gi generalized: di represents stage duration.
I
Gi =
(pdi−1
i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Gi =(1− pi)p
di
i
1− pdi
i
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Pi
Table: Population and Survival
I
Pop. Years
M 0Mpi 1Mp2
i 2Mp3
i 3Mp4
i 4Mp5
i 5
Mp6i 6
I Mp5i are eligible to advance
I then M + Mpi + Mp2i + Mp3
i + Mp4i are ineligible.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Pi
Table: Population and Survival
I
Pop. Years
M 0Mpi 1Mp2
i 2Mp3
i 3Mp4
i 4Mp5
i 5
Mp6i 6
I Mp5i are eligible to advance
I then M + Mpi + Mp2i + Mp3
i + Mp4i are ineligible.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Pi
Table: Population and Survival
I
Pop. Years
M 0Mpi 1Mp2
i 2Mp3
i 3Mp4
i 4Mp5
i 5
Mp6i 6
I Mp5i are eligible to advance
I then M + Mpi + Mp2i + Mp3
i + Mp4i are ineligible.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Pi cont.
I M + Mpi + Mp2i + Mp3
i + Mp4i are ineligible to advance
I Only option for survival is remain in class.
I Proportion:
1 + pi + p2i + p3
i + p4i
1 + pi + p2i + p3
i + p4i + p5
i
I Hit this with piI Percentage that actually survive and remain.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Pi cont.
I M + Mpi + Mp2i + Mp3
i + Mp4i are ineligible to advance
I Only option for survival is remain in class.
I Proportion:
1 + pi + p2i + p3
i + p4i
1 + pi + p2i + p3
i + p4i + p5
i
I Hit this with piI Percentage that actually survive and remain.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Calculating Pi cont.
I M + Mpi + Mp2i + Mp3
i + Mp4i are ineligible to advance
I Only option for survival is remain in class.
I Proportion:
1 + pi + p2i + p3
i + p4i
1 + pi + p2i + p3
i + p4i + p5
i
I Hit this with piI Percentage that actually survive and remain.
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Pi
I
Pi =
(1 + pi + p2
i + p3i + p4
i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Pi generalized: di represents stage duration.
I
Pi =
(1 + pi + p2
i + · · ·+ pdi−2i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Pi =
(1− pdi−1
i
1− pdi
i
)pi
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Pi
I
Pi =
(1 + pi + p2
i + p3i + p4
i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Pi generalized: di represents stage duration.
I
Pi =
(1 + pi + p2
i + · · ·+ pdi−2i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Pi =
(1− pdi−1
i
1− pdi
i
)pi
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Pi
I
Pi =
(1 + pi + p2
i + p3i + p4
i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Pi generalized: di represents stage duration.
I
Pi =
(1 + pi + p2
i + · · ·+ pdi−2i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Pi =
(1− pdi−1
i
1− pdi
i
)pi
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Generalizing Pi
I
Pi =
(1 + pi + p2
i + p3i + p4
i
1 + pi + p2i + p3
i + p4i + p5
i
)pi
I Pi generalized: di represents stage duration.
I
Pi =
(1 + pi + p2
i + · · ·+ pdi−2i
1 + pi + p2i + · · ·+ pdi−1
i
)pi
I
Pi =
(1− pdi−1
i
1− pdi
i
)pi
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Final Matrix
0 0 0 0 127 4 80.6747 .7371 0 0 0 0 0
0 .0486 .6611 0 0 0 00 0 .0147 .6907 0 0 00 0 0 .0518 0 0 00 0 0 0 .8091 0 00 0 0 0 0 .8091 .8088
n(t)1
n(t)2
n(t)3
n(t)4
n(t)5
n(t)6
n(t)7
=
n(t+1)1
n(t+1)2
n(t+1)3
n(t+1)4
n(t+1)5
n(t+1)6
n(t+1)7
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Population After 50 Years
I
0 10 20 30 40 5010
−2
100
102
104
106
Time (years)
Pop
ulat
ion
1st2nd3rd4th5th6th7th
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Diagonalizing
I Call matrix model L
I
Lk = V ΛkV−1
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Diagonalizing
I Call matrix model L
I
Lk = V ΛkV−1
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Diagonalizing
I ~xk = Lk ~x0
I ~xk =(V ΛkV−1
)~x0
I V−1~x0 = ~c
I~xk = c1λ
k1 ~v1 + · · · + cnλ
kn ~vn
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Diagonalizing
I ~xk = Lk ~x0
I ~xk =(V ΛkV−1
)~x0
I V−1~x0 = ~c
I~xk = c1λ
k1 ~v1 + · · · + cnλ
kn ~vn
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Diagonalizing
I ~xk = Lk ~x0
I ~xk =(V ΛkV−1
)~x0
I V−1~x0 = ~c
I~xk = c1λ
k1 ~v1 + · · · + cnλ
kn ~vn
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Diagonalizing
I ~xk = Lk ~x0
I ~xk =(V ΛkV−1
)~x0
I V−1~x0 = ~c
I~xk = c1λ
k1 ~v1 + · · · + cnλ
kn ~vn
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Eigenvalues
Table: Eigenvalues
Gi = 1 λ1 λ2 λ3 λ4 λ5 λ6 λ7
Stage 1 −.100 −.100 .317 .317 .750 .750 .963Stage 2 −.230 −.230 .320 .320 1.16 .778 .778Stage 3 −.320 −.320 1.30 .791 .791 .336 .336Stage 4 −.225 −.225 .320 .320 1.15 .775 .775Stage 5 −.090 −.090 .314 .314 .753 .753 .953Stage 6 −.095 −.095 .314 .314 .753 .753 .953
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 3 Eigenvalues
I Using λi for Stage 3 from eigenvalue table
I k = 50
I ~x (50) =c1(−.32)(50)~v1 +c2(−.32)(50)~v2 +c3(1.3)(50)~v3 . . .
I When λi < 1 then λki → 0
I ~x (50) ≈ c3λ503 ~v3
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 3 Eigenvalues
I Using λi for Stage 3 from eigenvalue table
I k = 50
I ~x (50) =c1(−.32)(50)~v1 +c2(−.32)(50)~v2 +c3(1.3)(50)~v3 . . .
I When λi < 1 then λki → 0
I ~x (50) ≈ c3λ503 ~v3
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 3 Eigenvalues
I Using λi for Stage 3 from eigenvalue table
I k = 50
I ~x (50) =c1(−.32)(50)~v1 +c2(−.32)(50)~v2 +c3(1.3)(50)~v3 . . .
I When λi < 1 then λki → 0
I ~x (50) ≈ c3λ503 ~v3
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 3 Eigenvalues
I Using λi for Stage 3 from eigenvalue table
I k = 50
I ~x (50) =c1(−.32)(50)~v1 +c2(−.32)(50)~v2 +c3(1.3)(50)~v3 . . .
I When λi < 1 then λki → 0
I ~x (50) ≈ c3λ503 ~v3
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Stage 3 Eigenvalues
I Using λi for Stage 3 from eigenvalue table
I k = 50
I ~x (50) =c1(−.32)(50)~v1 +c2(−.32)(50)~v2 +c3(1.3)(50)~v3 . . .
I When λi < 1 then λki → 0
I ~x (50) ≈ c3λ503 ~v3
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
G3 Set to 100%
I
0 10 20 30 40 5010
0
102
104
106
108
1010
Time(years)
Pop
ulat
ion
Rat
io
1st2nd3rd4th5th6th7th
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
G3 Set to 4%
I
0 10 20 30 40 5010
0
101
102
103
104
105
Time(years)
Pop
ulat
ion
Rat
io
1st2nd3rd4th5th6th7th
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
G3 Set to 5%
I
0 10 20 30 40 5010
0
101
102
103
104
105
Time(years)
Pop
ulat
ion
Rat
io
1st2nd3rd4th5th6th7th
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
Population After 50 Years
I
0 10 20 30 40 5010
−2
100
102
104
106
Time (years)
Pop
ulat
ion
1st2nd3rd4th5th6th7th
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation
The Bibliography
Deborah Crouse, Larry Crowder, Hal Caswell, 1987 A StageBased Population Model For Loggerhead Sea Turtles AndImplications For Conservation
Wikipedia, Oct. 1, 2009 Loggerhead Sea Turtles
David Arnold, Kevin Yokoyama, The Leslie Matrix
David Arnold, Kevin Yokoyama, The Leslie Matrix Part Two
Ben Marshall and Alex Varner Loggerhead Sea Turtle Conservation