Ecology 8310Population (and Community) Ecology

• Application of projection matrices

• Sea turtle conservation (Crouse et al.)

Sea Turtle Conservation:Applying what we’ve learned

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

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?

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:

Long-term behavior of system?

Use the projection matrix to estimate population growth rates:

= 0.945

r = - 0.0565

Population is declining! (matches empirical observation)

Stable AgeDistribution:

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:

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:

• By convention, scaled to 1 for newborn

• Increases from birth to maturation

• Thereafter, can increase or decrease (usually increase; eventually decrease)

ReproductiveValue:

But how did we get l, RV, and SSD?

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

What is a manager to do?

• Reproductive value

• Sensitivity analyses

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:

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:

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":

Increase survival to 100% (or increase fecundity by 50%)

Results:

Increase survival to 100% (or increase fecundity by 50%)

Results:Large Juveniles

Subadults

Eggs/hatchlings

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:

Elasticity:

Persist, Pii

Repro, P1i

Grow, Pi+1,i

Focusing on eggs and hatchlings alone will

NEVERlead to recovery!

Surprise Conclusion:

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

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:

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

Turtle excluder device (TED):

Do nothing

Seasonal offshoreAll waters,All seasons

Crowder et al. 1994. Ecol. Appl. 4:437

• Elasticity focuses on very small changes

• All methods ignore economics and feasibility

• Might be better to know Dl/D$

Problems:

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

Homework #2:

Will be emailed out later today…

James R. VoneshDept. of Zoology University of Florida (VCU)

Omar De la Cruz Dept. of MathematicsPurdue University