Ecology 8310 Population (and Community) Ecology Application of projection matrices Sea turtle conservation (Crouse et al.) Other applications exist (plentiful, e.g., Doak et al. 1994 and desert tortoises), but Crouse et al. is a classic, so no need to belabor the point; approaches are fairly similar.

Sea Turtle Conservation: Applying what we’ve learned

Stage based life table for loggerhead sea turtle Class Size (cm) Age (yr) Survival Fecundity 1 Eggs, hatchling <10 <1 0.68 2 Small juv. 10-58 1-7 0.79 3 Large juv. 58-80 8-15 4 Subadult 80-87 16-21 0.74 5 Novice breeders >87 22 0.81 127 6 1st-yr remigrants 23 7 Mature breeders 24-54 80 Crouse et al.(1987) Ecology 68: 1412

Transition Matrix: P17 P16 P15 P21 P32 P43 P54 P65 P76 P22 P33 P44 P77

Long-term behavior of system? i.e.how to take this information, target your actions, and get the best increase in pop growth. Management action should affect one or more elements in the matrix, but the response of lambda won't be the same. So, to inform our decision, we'd like i..,e how senstive is lambda to changes in the elements of A.

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

Stable Stage Distribution: Why are there 2’s than 1’s and more 7’s than 6’s?

Reproductive Value: 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: Eggs, hatchlings 1 Small juveniles 1.4 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

What is a manager to base policy on? Reproductive value Sensitivity analyses Limitation Elasticity i.e.how to take this information, target your actions, and get the best increase in pop growth. Management action should affect one or more elements in the matrix, but the response of lambda won't be the same. So, to inform our decision, we'd like i..,e how senstive is lambda to changes in the elements of A.

Reproductive Value i.e.how to take this information, target your actions, and get the best increase in pop growth. Management action should affect one or more elements in the matrix, but the response of lambda won't be the same. So, to inform our decision, we'd like i..,e how senstive is lambda to changes in the elements of A.

Reproductive Value: Eggs, hatchlings 1 Small juveniles 1.4 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

Sensitivity Analyses i.e.how to take this information, target your actions, and get the best increase in pop growth. Management action should affect one or more elements in the matrix, but the response of lambda won't be the same. So, to inform our decision, we'd like i..,e how senstive is lambda to changes in the elements of A.

Sensitivity analyses: "Limitation" or large perturbation Small perturbation: Sensitivity: dλ/dPij Elasticity: d(lnλ)/d(lnPij) = (λ/Pij)(dλ/dPij) = dλ/λ / dPij/Pij = “proportional changes”

Limitation i.e.how to take this information, target your actions, and get the best increase in pop growth. Management action should affect one or more elements in the matrix, but the response of lambda won't be the same. So, to inform our decision, we'd like i..,e how senstive is lambda to changes in the elements of A.

Limitation:  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?

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

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

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

Target Juveniles: To increase λ from 0.945 to 1:   Lg. juv. survival from 0.68  0.77   Subadult survival from 0.74  0.88 or smaller  in both

Elasticity i.e.how to take this information, target your actions, and get the best increase in pop growth. Management action should affect one or more elements in the matrix, but the response of lambda won't be the same. So, to inform our decision, we'd like i..,e how senstive is lambda to changes in the elements of A.

Elasticity: Largest effects are associated with "persistence" of juvenile stages and mature breeders… Persist, Pii Grow, Pi+1,i Repro, P1i

Policy Implications: Incidental capture and drowning by shrimp trawling was the single biggest source of mortality for juveniles and subadults… Turtle excluder device (TED):

Discussion 1: Why did RV "miss" the importance of juveniles? In other words, articulate the essential difference between the focus of RV vs. sensitivity analyses.

Discussion 2: Why did the sensitivity analyses indicate that large juveniles (and to a lesser extent small juveniles, subadults, and mature breeders) were so much more important than other stages? i.e., what's the problem with protecting novice breeders (which have the highest fecundity!)

Effect of Stage Duration: 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

Discussion 3: Do these measures of response (even if the underlying math and biology are accurate) tell us what we need to know to set policy? Enforcement? Feasibility? Economics? might be better to know d(lambda)/d$

Why might recovery be slower (or different) than projected Discussion 4: Why might recovery be slower (or different) than projected (as it was)? Transient dynamics Cheaters (noncompliance) Parameter estimates incorrect Environment changed (so parameters no longer apply): e.g., oil spill Density Dependence

James R. Vonesh Dept. of Zoology University of Florida (now Assoc. Prof. at VCU) Omar De la Cruz Dept. of Mathematics Purdue University (now at Case Western)