1. Nematode Population Dynamics and Economic Thresholds Dinâmica das Populações de Nematóides e Níveis de Dano Econômico 23 o 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. 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 Consequences of Multiple Mating 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

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 N t =N 0 e rt, N t =N 0 t dN/dt=rN r=dN t /N t dt (growth rate/indiv.) =e r (pop. growth/unit time)

11. Continuous time models N t =N 0 e rt, N t =N 0 t dN/dt=rN r=dN t /N t dt (growth rate/indiv.) =e r (pop. growth/unit time) Seasonal Multiplication: N t /N 0 =e rt N t /N 0 =aN 0 b, N t =aN 0 (b+1)

12. dN/dt=rN(1-N/K) N t =K/(1+((K/N 0 -1)(e -rt )) dP/dt=aP(1-P/E) P f =aEP i /((a-1)P i +E) P f =(a/-Lnq)(1-q Pi ) Multiplication Rate P f /P i =((a/-Lnq)(1-q Pi ))/P i

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

14. Discrete time models

23. Statistical Models

24. Crop Yield in Relation to Nematode Population Density

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

26. A B Kim and Ferris (2001)

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

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

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

32. Continuous Model Optimization 0 200 400 600 800 1000 1200 1400 1600 0246810 log 2 Pi $

33. Discrete Model 0 200 400 600 800 1000 1200 0246810 log 2 Pi $

34. Optimized Discrete Model

35. Seasonal Multiplication Rates (Host Crop) 0 100 200 300 400 500 0 100015002000 Pi Pf/Pi

36. Overwinter Survival Rates 0 0.2 0.4 0.6 0.8 1 0500100015002000 Pf1 Pi2/Pf1

37. Annual Population Change (Host Crop) 0 20000 40000 60000 80000 100000 120000 0500100015002000 Pi1 Pi1 * (Pi2/Pi1)

39. 0 200 400 600 800 1000 1200 1400 1600 012345678 Years After Planting Host Crop Pi(t+x)

41. Perennial Crop Considerations

44. Year 1 0 20 40 60 80 100 0100020003000 DD AUC LU LT NU NT Year 2 0 2000 4000 6000 8000 10000 12000 0100020003000 DD AUC LU LT NU NT Year 3 0 5000 10000 15000 20000 25000 30000 0100020003000 DD AUC LU LT NU NT

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