ecology 8310 population (and community) ecology application of projection matrices sea turtle...
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Ecology 8310Population (and Community) Ecology
• Application of projection matrices
• Sea turtle conservation (Crouse et al.)
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Sea Turtle Conservation:Applying what we’ve learned
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Stage
Class Size (cm)
Age (yr)
Survival
Fecundity
1 Eggs, hatchling <10 <1 0.68 0
2 Small juv. 10-58 1-7 0.79 0
3 Large juv. 58-80 8-15 0.68 0
4 Subadult 80-87 16-21 0.74 0
5 Novice breeders >87 22 0.81 127
6 1st-yr remigrants >87 23 0.81 4
7 Mature breeders >87 24-54 0.81 80
Stage based life table for loggerhead sea turtle
Crouse et al.(1987) Ecology 68: 1412
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2 31
P15
P214 5 6 7
P17P16
P32 P43 P54 P65 P76
P22 P33 P44 P77
Life cyclediagram:
Are we done?
Stage
Class Age (yr)
Survival
1 Eggs, hatchling <1 0.68
2 Small juv. 1-7 0.79
3 Large juv. 8-15 0.68
4 Subadult 16-21 0.74
5 Novice breeders 22 0.81
6 1st-yr remigrants 23 0.81
7 Mature breeders 24-54 0.81
What does “survival represent?
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81.81.00000
0081.0000
00005.000
00069.02.00
000066.05.0
0000074.67.
8041270000
A
2 31
P15
P214 5 6 7
P17P16
P32 P43 P54 P65 P76
P22 P33 P44 P77
TransitionMatrix:
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Long-term behavior of system?
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Use the projection matrix to estimate population growth rates:
= 0.945
r = - 0.0565
Population is declining! (matches empirical observation)
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Stable AgeDistribution:
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Contribution to the future population that a female of age (stage) x will make
Depends on:• Future reproduction• Probability of surviving to realize it• Time for offspring to be produced
ReproductiveValue:
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Life stage Reproductive value
Eggs, hatchlings 1
Small juveniles 1.4
Lg. juveniles 6
subadults 116
Novice breeders 567
1st yr remigrants 507
Mature breeder 588
ReproductiveValue:
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• By convention, scaled to 1 for newborn
• Increases from birth to maturation
• Thereafter, can increase or decrease (usually increase; eventually decrease)
ReproductiveValue:
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But how did we get l, RV, and SSD?
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1) Crank it out (look at long-term results)
2) Characteristic equation
3) Eigenvectors and eigenvalues
1) Dominant eigenvalue gives l
2) Left eigenvector gives v(x) Repro. Value
3) Right eigenvector gives w(x), SSD
Methods:
See Caswell 2001
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What is a manager to do?
• Reproductive value
• Sensitivity analyses
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Life stage Reproductive value
Eggs, hatchlings 1
Small juveniles 1.4
Lg. juveniles 6
subadults 116
Novice breeders 567
1st yr remigrants 507
Mature breeder 588
ReproductiveValue:
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1) "Limitation" or large perturbation
2) Small perturbation:
• Sensitivity: dl/dPij
• Elasticity: d(lnl)/dln(Pij) = (l/Pij)(d /l dPij)= dl/ l / dPij/Pij
= “proportional change”
Sensitivity analyses:
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Increase survival to 100% (or increase fecundity by 50%)
How would that affect population growth rate?
Can we shift it from declining to increasing?
Which stage should we target?
"Limitation":
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Increase survival to 100% (or increase fecundity by 50%)
Results:
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Increase survival to 100% (or increase fecundity by 50%)
Results:Large Juveniles
Subadults
Eggs/hatchlings
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To increase from 0.945 to 1:
Lg. juv. survival from 0.68 0.77
Subadult survival from 0.74 0.88
or smaller in both
Target Juveniles:
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Elasticity:
Persist, Pii
Repro, P1i
Grow, Pi+1,i
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Focusing on eggs and hatchlings alone will
NEVERlead to recovery!
Surprise Conclusion:
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Why is there a greater effect for juveniles and mature adults (vs. eggs)?
Elasticity:
Life stage Stage Duration
Eggs, hatchlings
<1
Small juveniles 6
Lg. juveniles 7
subadults 5
Novice breeders
1
1st yr remigrants
1
Mature breeder
~30
2 31
P15
P214 5 6 7
P17P16
P32 P43 P54 P65 P76
P22 P33 P44 P77
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Change annual Pr(survival) from .7 to 1.
What is effect on through stage survival?
• 1 year: survival increases from .7 to 1.0• 2 years: survival increases from .49 to
1.0• 10 years: survival increases from 0.03 to
1.0
Effect ofStage Duration:
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What can be done to increase survival of juveniles & subadults?
Single biggest factor: incidental capture and drowning by shrimp trawling
> 40,000 sea turtle deaths per year
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Turtle excluder device (TED):
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Do nothing
Seasonal offshoreAll waters,All seasons
Crowder et al. 1994. Ecol. Appl. 4:437
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• Elasticity focuses on very small changes
• All methods ignore economics and feasibility
• Might be better to know Dl/D$
Problems:
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Why might actual recovery be slower (as it has been…)?
1) Non-compliance (i.e., cheaters)
2) Parameter estimates off
3) Transient dynamics
4) Change in parameters (e.g., oil spill)
5) Density-dependence
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Homework #2:
Will be emailed out later today…
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James R. VoneshDept. of Zoology University of Florida (VCU)
Omar De la Cruz Dept. of MathematicsPurdue University