23 o CONGRESSO BRASILEIRO DE NEMATOLOGIA March 14, 2001 Howard Ferris Department of Nematology

1. Nematode Population Dynamics and Economic ThresholdsDinâmica das Populações de Nematóides e Níveis de Dano Econômico 23o CONGRESSO BRASILEIRO DE NEMATOLOGIA March 14, 2001 Howard Ferris Department of Nematology University of California, Davis

2. Basic components of the dynamics of populations: • Birth and death rates • Development and senescence rates • Population size • Density dependence • resource availability • Predator pressure

3. Birth Rates • Intrinsic factors • oocytes and sperm • age effects • Extrinsic factors • resource availability • mate availability • temperature

4. Consequences of Multiple Mating • C. elegans produces 4x more eggs when multiple-mated than by hermaproditism. • Females of Heterodera attract and are mated by several males • R. pellio male does not supply sufficient sperm to fertilize all oocytes from a single female • Probability that female genes are perpetuated is increased • Population may increase at a greater rate when there are fewer females and more males

5. Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440

6. Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440

7. Death Rates • Intrinsic factors • natural longevity • relationships of fecundity and longevity • Extrinsic factors • resource availability • environmental extremes • predation • management

8. Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440

9. Many types of models represent our understanding of the dynamics of populations…. • Continuous and discrete time models • differential equations and time steps • understand behavior through calculus or sensitivity analysis • Age and stage structured models • Deterministic and stochastic models • Individual and event-based models • time steps or event steps Models with parameters related to properties of the organisms are usually more satisfying to biologists than equations that draw lines through points on a graph

10. Continuous time models Nt=N0ert, Nt=N0  t dN/dt=rN r=dNt/Ntdt (growth rate/indiv.) =er (pop. growth/unit time)

11. Continuous time models Nt=N0ert, Nt=N0  t dN/dt=rN r=dNt/Ntdt (growth rate/indiv.) =er (pop. growth/unit time) Seasonal Multiplication: Nt/N0=ert Nt/N0=aN0b, Nt=aN0(b+1)

12. dN/dt=rN(1-N/K) Nt=K/(1+((K/N0-1)(e-rt)) dP/dt=aP(1-P/E) Pf=aEPi/((a-1)Pi+E) Pf=(a/-Lnq)(1-qPi) Multiplication Rate Pf/Pi=((a/-Lnq)(1-qPi))/Pi

13. Seasonal population change Meloidogyne arenaria - oriental melon Kim and Ferris (2001)

14. Discrete time models

15. Discrete time models

16. Discrete time models

17. Discrete time models

18. Discrete time models

19. Discrete time models

20. Discrete time models

23. Statistical Models

24. Crop Yield in Relation to Nematode Population Density

25. Oriental melon - Meloidogyne arenaria B A C A: Early season Y = 0.43+0.57*0.998Pi, ym=19743 B: Late season Y = 0.03+0.97*0.998Pi, ym=10170 C: Total harvest Y = 0.50+0.50*0.999Pi, ym=12312 Kim and Ferris (2001)

26. A B Kim and Ferris (2001)

27. The Economic Threshold That initial population at which the loss in value due to nematode damage is equal to the cost of nematode management

28. The Economic Threshold amended That initial population at which the difference in crop value with and without management is equal to the cost of the management

29. Profitability Limit constraint That initial population level at which net returns become zero

32. Continuous Model Optimization 1600 1400 1200 1000 $ 800 600 400 200 0 0 2 4 6 8 10 log Pi 2

33. Discrete Model 1200 1000 800 $ 600 400 200 0 0 2 4 6 8 10 log Pi 2

34. Optimized Discrete Model

35. Seasonal Multiplication Rates (Host Crop) 500 400 300 Pf/Pi 200 100 0 0 500 1000 1500 2000 Pi

36. Overwinter Survival Rates 1 0.8 0.6 Pi2/Pf1 0.4 0.2 0 0 500 1000 1500 2000 Pf1

37. Annual Population Change (Host Crop) 120000 100000 80000 60000 Pi1 * (Pi2/Pi1) 40000 20000 0 0 500 1000 1500 2000 Pi1

38. Pi1 Annual Population Change (Non-host) Pi2 1400 Pi3 1200 1000 800 Pi(t+x) 600 400 200 0 0 500 1000 1500 2000 Pi(t)

39. 1600 1400 1200 1000 800 Pi(t+x) 600 400 200 0 0 1 2 3 4 5 6 7 8 Years After Planting Host Crop

41. Perennial Crop Considerations

44. Year 1 Year 2 100 12000 10000 80 8000 60 LU LU AUC AUC 6000 40 LT LT 4000 20 NU NU 2000 0 NT NT 0 0 1000 2000 3000 0 1000 2000 3000 DD DD Year 3 30000 25000 20000 LU AUC 15000 LT 10000 NU 5000 0 NT 0 1000 2000 3000 DD

46. Noling and Ferris (1987)

47. References Burt, O. R. and H. Ferris. 1996. Sequential decision rules for managing nematodes with crop rotations. J. Nematology 28:457-474. Chen, J., J.R. Carey and H. Ferris. 2001. Comparative demography of isogenic populations of Caenorhabditis elegans Expt. Gerontology 36:431-440. Ferris, H. 1978. Nematode economic thresholds: derivation, requirements and theoretical considerations. J. Nematology 10:341-350. Ferris, H. 1985. Density-dependent nematode seasonal multiplication and overwinter survivorship: a critical point model. J. Nematology 17:93-100. Hsin, H. and C. Kenyon. 1999. Signals from the reproductive system regulate the lifespan of C. elegans. Nature 399:362-366. Kim D.G. and H. Ferris. 2001. Relationship between crop losses and initial population densities of Meloidogyne arenaria in winter-grown oriental melon in Korea. J. Nematology (subm.) Noling, J.W. and H. Ferris. 1987. Nematode-degree days, a density-time model for relating epidemiology and crop losses in perennials. J. Nematology 19:108-118. Seinhorst, J.W. 1965. The relationship between nematode density and damage to plants. Nematologica 11:137-154. Seinhorst, J.W. 1967. The relationship between population increase and population density in plant parasitic nematodes. II. Sedentary nematodes. Nematologica 13:157-171. Somers, J.A., H.H. Shorey and L.K. Gaston. 1977. Reproductive biology and behavior of Rhabditis pellio (Schneider) (Rhabditida:Rhabditidae). J. Nematology 9:143-148. More information: http://plpnemweb.ucdavis.edu/nemaplex/nemaplex.htm