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

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

Birth Rates Intrinsic factors –oocytes and sperm –age effects Extrinsic factors –resource availability –mate availability –temperature

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

Chen, Carey and Ferris (2001), Expt. Gerontology 36:

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

Chen, Carey and Ferris (2001), Expt. Gerontology 36:

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

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)

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)

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

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

Discrete time models

Statistical Models

Crop Yield in Relation to Nematode Population Density

Kim and Ferris (2001) A: Early season Y = *0.998 Pi, ym=19743 B: Late season Y = *0.998 Pi, ym=10170 C: Total harvest Y = *0.999 Pi, ym=12312 A B C Oriental melon - Meloidogyne arenaria

A B Kim and Ferris (2001)

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

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

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

Continuous Model Optimization log 2 Pi $

Discrete Model log 2 Pi $

Optimized Discrete Model

Seasonal Multiplication Rates (Host Crop) Pi Pf/Pi

Overwinter Survival Rates Pf1 Pi2/Pf1

Annual Population Change (Host Crop) Pi1 Pi1 * (Pi2/Pi1)

Years After Planting Host Crop Pi(t+x)

Perennial Crop Considerations

Year DD AUC LU LT NU NT Year DD AUC LU LT NU NT Year DD AUC LU LT NU NT

Noling and Ferris (1987)

References Burt, O. R. and H. Ferris Sequential decision rules for managing nematodes with crop rotations. J. Nematology 28: Chen, J., J.R. Carey and H. Ferris Comparative demography of isogenic populations of Caenorhabditis elegans Expt. Gerontology 36: Ferris, H Nematode economic thresholds: derivation, requirements and theoretical considerations. J. Nematology 10: Ferris, H Density-dependent nematode seasonal multiplication and overwinter survivorship: a critical point model. J. Nematology 17: Hsin, H. and C. Kenyon Signals from the reproductive system regulate the lifespan of C. elegans. Nature 399: Kim D.G. and H. Ferris 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 Nematode-degree days, a density-time model for relating epidemiology and crop losses in perennials. J. Nematology 19: Seinhorst, J.W The relationship between nematode density and damage to plants. Nematologica 11: Seinhorst, J.W The relationship between population increase and population density in plant parasitic nematodes. II. Sedentary nematodes. Nematologica 13: Somers, J.A., H.H. Shorey and L.K. Gaston Reproductive biology and behavior of Rhabditis pellio (Schneider) (Rhabditida:Rhabditidae). J. Nematology 9: More information: