1. Ecology 8310 Population (and Community) Ecology Application of projection matrices Sea turtle conservation (Crouse et al.)

2. Sea Turtle Conservation: Applying what we’ve learned

4. StageClassSize (cm)Age (yr)SurvivalFecundity 1 Eggs, hatchling <10<10.680 2 Small juv. 10-581-70.790 3 Large juv. 58-808-150.680 4 Subadult 80-8716-210.740 5 Novice breeders >87220.81127 6 1 st -yr remigrants >87230.814 7 Mature breeders >8724-540.8180 Stage based life table for loggerhead sea turtle Crouse et al.(1987) Ecology 68: 1412

5. 231 P 15 P 21 4567 P 17 P 16 P 32 P 43 P 54 P 65 P 76 P 22 P 33 P 44 P 77 Life cycle diagram: Are we done? StageClassAge (yr)Survival 1 Eggs, hatchling <10.68 2 Small juv. 1-70.79 3 Large juv. 8-150.68 4 Subadult 16-210.74 5 Novice breeders 220.81 6 1 st -yr remigrants 230.81 7 Mature breeders 24-540.81 What does “survival represent?

6. 231 F 5 =P 15 P 21 4567 F 7 =P 17 F 6 =P 16 P 32 P 43 P 54 P 65 P 76 P 22 P 33 P 44 P 77 Transition Matrix:

7. 231 P 15 P 21 4567 P 17 P 16 P 32 P 43 P 54 P 65 P 76 P 22 P 33 P 44 P 77 Transition Matrix:

8. Long-term behavior of system?

9. Use the projection matrix to estimate population growth rates: = 0.945 r = - 0.0565 Population is declining! (matches empirical observation)

10. Stable Age Distribution:

11. 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 Reproductive Value:

12. Life stageReproductive value Eggs, hatchlings1 Small juveniles1.4 Lg. juveniles6 subadults116 Novice breeders567 1 st yr remigrants507 Mature breeder588 Reproductive Value:

13. By convention, scaled to 1 for newborn Increases from birth to maturation Thereafter, can increase or decrease (usually increase; eventually decrease) Reproductive Value:

14. But how did we get , RV, and SSD?

15. 1)Crank it out (look at long-term results) 2)Characteristic equation 3)Eigenvectors and eigenvalues 1)Dominant eigenvalue gives  2)Left eigenvector gives v(x) Repro. Value 3)Right eigenvector gives w(x), SSD Methods: See Caswell 2001

16. What is a manager to do? Reproductive value Sensitivity analyses

17. Life stageReproductive value Eggs, hatchlings1 Small juveniles1.4 Lg. juveniles6 subadults116 Novice breeders567 1 st yr remigrants507 Mature breeder588 Reproductive Value:

18. 1)"Limitation" or large perturbation 2)Small perturbation: Sensitivity: d /dP ij Elasticity: d(ln )/dln(P ij ) = ( /P ij )(d  dP ij ) = d /  /  dP ij /P ij = “proportional change” Sensitivity analyses:

19.   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":

20. Increase survival to 100% (or increase fecundity by 50%) Results:

21. Increase survival to 100% (or increase fecundity by 50%) Results: Large Juveniles Subadults Eggs/hatchlings

22. 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:

23. Elasticity: Persist, P ii Repro, P 1i Grow, P i+1,i

24. Focusing on eggs and hatchlings alone will NEVER lead to recovery! Surprise Conclusion:

25. Why is there a greater effect for juveniles and mature adults (vs. eggs)? Elasticity: Life stageStage Duration Eggs, hatchlings<1 Small juveniles6 Lg. juveniles7 subadults5 Novice breeders 1 1 st yr remigrants 1 Mature breeder~30 231 P 15 P 21 4567 P 17 P 16 P 32 P 43 P 54 P 65 P 76 P 22 P 33 P 44 P 77

26. 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 of Stage Duration:

27. 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

28. Turtle excluder device (TED):

29. Do nothing Seasonal offshore All waters, All seasons Crowder et al. 1994. Ecol. Appl. 4:437

30. Elasticity focuses on very small changes All methods ignore economics and feasibility Might be better to know  /  $ Problems:

31. 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

32. Homework #2: Will be emailed out later today…

33. James R. Vonesh Dept. of Zoology University of Florida (VCU) Omar De la Cruz Dept. of Mathematics Purdue University