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Settlement vs. Post-settlement

Density-dependence in Reef Fishes. Settlement vs. Post-settlement. Growth Survival Reproduction Movement. Literature Review. 20 Journals 30 Years (1970 - 1999) plus: electronic search. Settlement 32% Survival 68% Growth 25% Reproduction 7% Behavior 8% Migration 5%

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Settlement vs. Post-settlement

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  1. Density-dependence in Reef Fishes Settlement vs. Post-settlement • Growth • Survival • Reproduction • Movement

  2. Literature Review • 20 Journals • 30 Years (1970 - 1999) • plus: electronic search

  3. Settlement 32% Survival 68% Growth 25% Reproduction 7% Behavior 8% Migration 5% >1 response 31% 59 Papers:

  4. Density-dependent survival Experimental only 48% Observational only 40% Both 12%

  5. Conceptual Problem What quantitative framework facilitates comparison among studies?

  6. Relative Importance:Basic Approach • Model for Recruitment: • Settlers  Adults (A) • Estimate of Relative Importance • Limitation = Aw/o limit - Aambient • Elasticity: ep = (lnA) / (lnp) = (A/A) / (p/p)

  7. Beverton-Holt Recruitment Function: Supply: S number of settlers Density-dep. b  asymptotic number of adults Density-indep. a  density-independent survival

  8. Dascyllus trimaculatus 12 8 SUB-ADULT DENSITY (No. per 0.1m2 anemone) 4 50 100 150 200 250 300 SETTLER DENSITY (No. per 0.1m2 anemone)

  9. No D-D mortality No mortality SLOPE = a SLOPE = 1 ADD AS = b No Supply limitation DENSITY OF SURVIVORS No D-I mortality ADI Observed AAMB SAmb SETTLER DENSITY

  10. No D-D mortality SLOPE = a ADD AS = b No Supply limitation LDD DENSITY OF SURVIVORS LS Observed AAMB SAmb SETTLER DENSITY

  11. 15 LDD LS 10 LIMITATION (ABSOLUTE CHANGE) 5 LDi 20 40 60 80 100 SETTLER DENSITY LS = LDD at S=b/a ( A=b/2)

  12. a = 0.7 (70% survival) 12 b = 9.8 sub-adults 8 SUB-ADULT DENSITY (No. per 0.1m2 anemone) 4 50 100 150 200 250 300 SETTLER DENSITY (No. per 0.1m2 anemone)

  13. 1st QUARTILE 100 MEDIAN 80 MEAN FREQUENCY 60 3rd QUARTILE 40 20 0 0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 196 >200 SETTLER DENSITY CATEGORY (No. per 0.1m2 anemone)

  14. RELATIVE IMPORTANCE FOR DASCYLLUS • (using ambient settlement rates) • LIMITATION (number of new adults) • Density-dependence 12.8 • Supply 5.7 • Density-independence 0.6

  15. An Even Simpler Approach LDD / LS = aS / b

  16. Is this a good metric? Answer: NO (it’s time-dependent) Solution: reformulate the model

  17. Beverton-Holt Model: b  per capita effect of conspecifics a density-indendent mortality rate

  18. Integrated form of model: N0 initial density (i.e., settlers, S) Nt  “final” density (i.e., recruits or adults, A)

  19. Dascyllus trimaculatus 12 8 SUB-ADULT DENSITY (No. per 0.1m2 anemone) 4 50 100 150 200 250 300 SETTLER DENSITY (No. per 0.1m2 anemone)

  20. From Steele (1997)

  21. Is the Beverton-Holt a good model?

  22. a = 0.7 (70% survival) 12 b = 9.8 sub-adults 8 SUB-ADULT DENSITY (No. per 0.1m2 anemone) 4 50 100 150 200 250 300 SETTLER DENSITY (No. per 0.1m2 anemone)

  23. Dascyllus trimaculatus 35 30 25 Number of survivors after 1-week 20 15 10 5 0 50 100 150 200 250 300 Settlers

  24. Dascyllus trimaculatus 10 8 6 Number of survivors at 6 months 4 2 0 5 10 15 20 25 1-wk old fish

  25. start

  26. Density-dependence in Reef Fishes • Post-settlement survival • Variation in the strength of density-dependence

  27. Meta-analysis: • Effect size • Var (effect size)

  28. Beverton-Holt Model: b per capita effect of conspecifics a density-indendent mortality rate

  29. Integrated form of model: N0 initial density (e.g., settlers) Nt  “final” density (e.g., recruits or adults)

  30. Dascyllus trimaculatus a = -0.00201 (day-1) b = -0.0000471 (m2 fish-1 day-1) 12 8 SUB-ADULT DENSITY (No. per 0.1m2 anemone) 4 50 100 150 200 250 300 SETTLER DENSITY (No. per 0.1m2 anemone) Ambient

  31. Meta-analysis: Effect size:a) Per capita effect (b ) b) Total effect (b x ambient density)Var(Effect size): used to weight estimatesMixed model and bootstrapped CI’s

  32. Overall effect of density • = -.0000826 m2 fish-1 day-1(CI: -.00014 to -.000043)[BUT extremely heterogeneous]

  33. Sources of variation? • Conclusion (den-dep vs. den-indep.) • Experimental vs. Observational • Taxonomic groups • Geographic regions • Predators and Age-class

  34. Den-dep. Den-indep.

  35. Den-dep. Den-indep.

  36. Den-dep. Den-indep.

  37. Do experimental and observational studies yield different results? Only 12% of studies reported experimental and observation results.

  38. Gobiosoma Expt: b = - 0.051 +/- 0.01Observ: b = - 0.00008 +/- 0.001 (Wilson and Osenberg, in press)

  39. Exp Obs

  40. Exp Obs

  41. Does “range of density” drive these results? e.g., if doing an experiment, jack up densities to extraordinary levels (insure P<.05 and publication)

  42. Exp Obs Exp Obs Den-dep. Den-indep.

  43. Exp Obs Exp Obs Den-dep. Den-indep.

  44. Exp Obs Exp Obs Den-dep. Den-indep.

  45. Sources of variation? • Conclusion (den-dep vs. den-indep.) • Experimental vs. Observational • Taxonomic groups • Geographic regions • Predators and Age-class

  46. Labrid Gobiid Acanthurid Pomacentrid

  47. Australia California Caribbean Indo-Pacific

  48. Beverton-Holt Model: b per capita effect of conspecifics a density-indendent mortality rate

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