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

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Nematode Population Dynamics and Economic Thresholds

Dinâmica das Populações de Nematóides e Níveis de Dano Econômico

23o CONGRESSO BRASILEIRO DE NEMATOLOGIA

March 14, 2001

Howard FerrisDepartment 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

Sex Ratios and Multiple Mating Effects

0 50 100Pi

1:1 F:M

0.3:0.7 F:M

0.7:0.3 F:M

•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

Rhabditis pellio

150200

3 5 7 9Male Age

zed Total sperm = 884

Female produces 600 oocytesOnly 150 fertilized at a single mating

3 4 5 6 7 8 9 10Age (days)

Caenorhabditis elegans

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

0 8 16 24 32 40 48

Lifetime egg production

wild type

0 8 16 24 32 40 48LIFESPAN (days)

Death Rates

• Intrinsic factors– natural longevity– relationships of fecundity and longevity

• Extrinsic factors– resource availability– environmental extremes– predation– management

8 1 6 2 4 3 2 4 0 4 8 0A G E ( d a y s )

80 eggs/day40-79 eggs/day1-39 eggs/day0 eggs/day

C. elegans wild type

0 8 1 6 2 4 3 2 4 0 4 8

A G E ( d a y s )

l xw i l d t y p ec l k - 1a g e - 1

IVE 24

0 8 16 24 32 40 48 0

AGE (days)

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 Nt=N0ert, Nt=N0 t

dN/dt=rN

r=dNt/Ntdt (growth rate/indiv.)

=er (pop. growth/unit time)

0 200 400 600 800N0

0 20 40 60 80 100Time

Continuous time models Nt=N0ert, Nt=N0 t

dN/dt=rN

r=dNt/Ntdt (growth rate/indiv.)

=er (pop. growth/unit time)

0 200 400 600 800N0

0 20 40 60 80 100Time

0 200 400 600N0

Seasonal Multiplication:

Nt/N0=ert

Nt/N0=aN0b, Nt=aN0

0 2 4 6 8 10Ln Initial Population (Pi) Sep 99

Pf=(75/-Ln0.993)(1-0.993Pi)

0 2 4 6 8 10Ln(Pi) Sep 99

tiplic

Pf/Pi=1018 Pi-0.71, r2=0.71

Pf/Pi=(400/-Ln0.90)(1-0.90Pi)/Pi

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 RatePf/Pi=((a/-Lnq)(1-qPi))/Pi

0 2 4 6 8 10

Ln(Pi) Sep 99

tiplic

for PiPf/Pi=325, else

Pf/Pi=1018 Pi-0.71, r2=0.71

Kim and Ferris (2001)

Meloidogyne arenaria - oriental melon

Seasonal population change

Discrete time models

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

Soil Moisture (bars)

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

10 C 15 C 20 C 25 C 30 C 35 C

Temperature

0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84

10 C 15 C 20 C 25 C 30 C 35 C

Soil Temperature

0 10 20 30 40 50

EggsJ2J3J4Ad

0 10 20 30 40 50

EggsJ2J3J4Ad

0 10 20 30 40 50

s)Statistical Models

Crop Yield in Relation to Nematode Population Density

Total harvest

0.60.8

0 2 4 6 8 10Ln (Pi+1)

Late season

0.20.4

0 2 4 6 8 10Ln (Pi+1)

Early season

00.20.40.60.8

0 2 4 6 8 10Ln (Pi+1)

A: Early seasonY = 0.43+0.57*0.998Pi, ym=19743

B: Late seasonY = 0.03+0.97*0.998Pi, ym=10170

C: Total harvestY = 0.50+0.50*0.999Pi, ym=12312

Oriental melon - Meloidogyne arenaria

050000

100000150000200000250000300000

0 10 20 30 40 50 60Pi Sep 99

100000

200000

300000

400000

0 10 20 30 40 50 60Pi Sep 99

Crop Value Panel A Panel BEarly Harvest 2019 won/kg 967 won/kgLate Harvest 967 won/kg 2019 won/kg

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

Management Efficacy = 90%

7.055.54.3

0 2 4 6 8Ln (Pi+1)

s ET = 74PL1 = 245PL2 = 1153

Management Efficacy = 100%

4.15 5.5

0 2 4 6 8

Ln (Pi+1)

ET = 63PL1 = 245

Fixed Cost Economic Threshold

0 2 4 6 8 10Nematode Population (Ln)

Continuous Model Optimization

0 2 4 6 8 10log2 Pi

a = 15b = 50

Pi = 550m = 0.1T = 50z = 0.999

$max = 1000E.T. = 110

Discrete Model

0 2 4 6 8 10log2 Pi

a = 600Pi = 200m = 0.1T = 20z = 0.99

$max = 1000E.T. = 78.48428

Optimized Discrete Model

Seasonal Multiplication Rates (Host Crop)

0 500 1000 1500 2000

ia = 500b = -0.2

amax = 500p = 1q = -0.1s = 0.65

Overwinter Survival Rates

0 500 1000 1500 2000Pf1

a = 500b = -0.2

amax = 500p = 1q = -0.1s = 0.65

Annual Population Change (Host Crop)

100000

120000

0 500 1000 1500 2000Pi1

)a = 500b = -0.2

amax = 500p = 1q = -0.1s = 0.65

Annual Population Change (Non-host)

0 500 1000 1500 2000Pi(t)

Pi3a = 500b = -0.2

amax = 500p = 1q = -0.1s = 0.65

0 1 2 3 4 5 6 7 8

Years After Planting Host Crop

a = 300b = 0.6s = 0.4

Pi(0) = 70

Population Convergence

0 5 10 15Year

Optimum Rotation Length

0 1 2 3 4 5 6 7 8 9 10

Years of Non-host

Perennial Crop Considerations

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

Lovell

Nemaguard

0 2000 4000 6000 8000 10000 12000 14000

Degree-Days

Year 1

0 1000 2000 3000DD

Year 2

02000400060008000

1000012000

0 1000 2000 3000DD

Year 3

1000015000200002500030000

0 1000 2000 3000DD

Year 4

1000015000200002500030000

0 1000 2000 3000DD

Year 1

0 1000 2000 3000DD

Year 2

02000400060008000

1000012000

0 1000 2000 3000DD

Year 3

1000015000200002500030000

0 1000 2000 3000DD

Year 2 Year 3 Year 4 Year 5

LT-Full

LT-S/F

LU-Full

LU-S/F

NT-Full

NT-S/F

NU-Full

NU-S/F

0 20 40 60 80 100AUC

oss y=1.15+0.37x, r2=0.89

0 2000 4000DD

Pi2170

Noling and Ferris(1987)

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

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

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