1. Consequences of Heterogeneous Survival Rates of an Entomopathogenic Nematode. Chris Dugaw Department of Mathematics Humboldt State University

2. Outline  Biological background  Understanding Nematode Survival  Experimental Setup  Survival Analysis  Results  Discussion

3. Entomopathogenic nematodes Insect predators, in soil or litter Can move >2 cm/day following volatiles Kills prey with symbiotic bacteria injected into host One nematode in  800K+ emerge Images courtesy of Ed Lewis, Virginia Tech

4. Nematode life cycle Nematode life cycle http://www.bath.ac.uk/bio-sci/clarke.htm

5. Current Uses of Nematodes as Biocontrol Agents CommodityInsect Pests Artichokes Artichoke plume moth Berries Root weevils Citrus Root weevils Cranberries Root Weevils Cranberry girdler MushroomsFungus gnats Ornamentals Root Weevils Wood borers Fungus gnats Turf Scarabs Mole crickets Billbugs Armyworm, Cutworm, Webworm Source: http://www.oardc.ohio-state.edu/nematodes/biologyecology.htm

6. Study Site: the Bodega Marine Reserve

7. The predatory nematode Heterorhabditis marelatus neudorff.de/nuetzlinge/img/hmne.jpg

8. A natural host: the ghost moth Hepialus californicus Adult Host Larvae infected by nematodes Host larvae

9. Ghost moth caterpillars feed on the roots of bush lupine (Lupinus arboreus)

10. Lupine killed by ghost moth caterpillars

11. Large-scale ghost moth outbreaks occur, killing 10,000+ mature lupines 2001

12. 2002

13. The trophic cascade: predators indirectly affect producers by suppressing herbivores Strong 1997, Strong et al. 1999

14. Seasonal Dynamics Wet Winter Nematodes search for hosts Nematode reproduction occurs Hosts are in larval stage Dry Summer Nematodes are inactive Nematodes must survive Host become adults and disperse Host eggs are deposited on bush

15. Seasonal Dynamics Wet Winter Nematodes search for hosts Nematode reproduction occurs Hosts are in larval stage Dry Summer Nematodes are inactive Nematodes must survive Host become adults and disperse Host eggs are deposited on bush

16. Outline  Biological background  Understanding Nematode Survival  Experimental Setup  Survival Analysis  Results  Discussion

17. Experimental design 2 treatments = Lupine, Grasslands 4 replicates/treatment = 8 total replicates 50 tubes/replicate = 400 total tubes Each sampling date, removed 10 tubes/replicate = 80 total tubes/sampling date Assessed nematodes using ‘bait’ insects Each tube - 30 g past. soil - 1100 IJ nematodes - Fine mesh covers Sampled 3 times over a Summer

18. Survival Analysis

19. Homogeneous Death Rates

20. Survival Analysis Homogeneous Death Rates Exponential Distribution

21. Survival Analysis Homogeneous Death Rates Heterogeneous Death Rates Exponential Distribution

22. Survival Analysis Homogeneous Death Rates Heterogeneous Death Rates Exponential Distribution Mixed Exponential Distribution

23. First Step: Exponential Fit

24. Mixed Exponential Distributions Individuals have different mortality rates, k.

25. Mixed Exponential Distributions Individuals have different mortality rates, k. Risk of death for each individual is constant over time.

26. Mixed Exponential Distributions Individuals have different mortality rates, k. Risk of death for each individual is constant over time. The conditional distribution for individual lifespan, T, given k is exponential.

27. Pareto Distribution: The mixed exponential you get when you assume k is gamma distributed.

28. Pareto Distribution: The mixed exponential you get when you assume k is gamma distributed. A simple function form can be derived by integrating:

29. Pareto Distribution: The mixed exponential you get when you assume k is gamma distributed. A simple function form can be derived by integrating:

30. Pareto Distribution: The mixed exponential you get when you assume k is gamma distributed. A simple function form can be derived by integrating:

31. The distribution of survival rates shifts over time leading to a decrease in mean mortality rate. McNolty, Doyle and Hansen, Technometrics, 1980

32. Improvement: Pareto Fit

33.  = 0.29  = 2.77  = 0.73  = 2.77

34. Why is it an improvement? 1.Akaike says so:  AIC c = 3.46

35. Why is it an improvement? 1.Akaike says so:  AIC c = 3.46 2.Provides a greater understanding of the biological system.

36. Why is it an improvement? 1.Akaike says so:  AIC c = 3.46 2.Provides a greater understanding of the biological system. 3.Allows us to quantify heterogeneity using the scale parameter, .

37. Results: Survival in soil is heterogeneous.

38. Results: Mean mortality is higher in the grasslands. (log ratio test:  2 = 0.449, df=1, p = 0.050)

39. Results: Survival in soil is heterogeneous. Mean mortality is higher in the grasslands. (log ratio test:  2 = 0.449, df=1, p = 0.050) Heterogeneity same in the two treatments. (log ratio test:  2 = 0.279, df=1, p = 0.98)

40. Outline  Biological background  Understanding Nematode Survival  Experimental Setup  Survival Analysis  Results  Discussion

41. Feedback loop in trophic cascade Preisser, Dugaw, et al., In Review

42. Alternative Explanations for Observations Decreasing individual hazards

43. Alternative Explanations for Observations Decreasing individual hazards Density Dependant Survival

44. Future work: Apply this analysis to new experiments to assess survival and heterogeneity in different soil types.

45. Future work: Apply this analysis to new experiments to assess survival and heterogeneity in different soil types. Compare fitted shape parameter  to physical soil properties.

46. Future work: Apply this analysis to new experiments to assess survival and heterogeneity in different soil types. Compare fitted shape parameter  to physical soil properties. Incorporate heterogeneous survival into a stochastic model that includes nematode reproduction.

47. Thanks to: Evan Preisser Mike Eng Don Strong Brian Dennis Support of: NSF UC Davis Dissertation Year Fellowship UCD Faculty Fellow