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
2000
4000
0 50 100Pi
Pf
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
0
50
100
150200
250
300
350
400
3 5 7 9Male Age
Egg
s fe
rtili
zed Total sperm = 884
Female produces 600 oocytesOnly 150 fertilized at a single mating
0
20
40
60
80
100
120
3 4 5 6 7 8 9 10Age (days)
Ag
e-s
pe
cifi
c R
ep
rod
uct
ion
N2
clk-1
age-1
Caenorhabditis elegans
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
0
100
200
300
400
0 8 16 24 32 40 48
Lifetime egg production
wild type
0
100
200
300
400
0 8 16 24 32 40 48LIFESPAN (days)
age-1
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
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 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0
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
NU
MB
ER
AL
IVE 24
48
0 8 16 24 32 40 48 0
AGE (days)
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
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
2000
4000
6000
0 200 400 600 800N0
Nt
0
200
400
600
800
0 20 40 60 80 100Time
Nt
Continuous time models Nt=N0ert, Nt=N0 t
dN/dt=rN
r=dNt/Ntdt (growth rate/indiv.)
=er (pop. growth/unit time)
0
2000
4000
6000
0 200 400 600 800N0
Nt
0
200
400
600
800
0 20 40 60 80 100Time
Nt
2
4
6
8
10
0 200 400 600N0
Nt /N
0
Seasonal Multiplication:
Nt/N0=ert
Nt/N0=aN0b, Nt=aN0
(b+1)
0
5
10
0 2 4 6 8 10Ln Initial Population (Pi) Sep 99
Ln F
inal
Pop
ulat
ion
(Pf)
Pf=(75/-Ln0.993)(1-0.993Pi)
0
50
100
150
200
250
300
350
400
450
500
0 2 4 6 8 10Ln(Pi) Sep 99
Mul
tiplic
atio
n R
ate
(Pf/
Pi)
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
100
200
300
400
500
0 2 4 6 8 10
Ln(Pi) Sep 99
Mul
tiplic
atio
n R
ate
(Pf/
Pi)
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
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
Discrete time models
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
Discrete time models
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
Discrete time models
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
Discrete time models
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
Discrete time models
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Temperature
Rat
e
0
0.2
0.4
0.6
0.8
1
1.2
0.015 0.03 0.06 0.12 0.24 0.48 0.96 1.92 3.84
Soil Moisture (bars)
Ra
te
0
0.2
0.4
0.6
0.8
1
1.2
10 C 15 C 20 C 25 C 30 C 35 C
Soil Temperature
Rat
e
0
50
100
150
200
250
0 10 20 30 40 50
Days
EggsJ2J3J4Ad
Discrete time models
0
50
100
150
200
250
0 10 20 30 40 50
Days
EggsJ2J3J4Ad
0
100
200
300
400
500
600
0 10 20 30 40 50
Days
Tot
al (
all s
tage
s)
0
100
200
300
400
500
600
0 10 20 30 40 50
Days
Tot
al (
all s
tage
s)Statistical Models
Crop Yield in Relation to Nematode Population Density
Total harvest
0
0.2
0.4
0.60.8
1
1.2
0 2 4 6 8 10Ln (Pi+1)
Rel
ativ
e Y
ield
Late season
0
0.20.4
0.6
0.81
1.2
0 2 4 6 8 10Ln (Pi+1)
Rel
ativ
e Y
ield
Early season
00.20.40.60.8
11.2
0 2 4 6 8 10Ln (Pi+1)
Re
lativ
e Y
ield
Kim and Ferris (2001)
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
A B
C
Oriental melon - Meloidogyne arenaria
050000
100000150000200000250000300000
0 10 20 30 40 50 60Pi Sep 99
Val
ue L
oss
(WO
N)
Early
Late
Total
0
100000
200000
300000
400000
0 10 20 30 40 50 60Pi Sep 99
Val
ue L
oss
(WO
N)
Early
Late
Total
Crop Value Panel A Panel BEarly Harvest 2019 won/kg 967 won/kgLate Harvest 967 won/kg 2019 won/kg
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
Management Efficacy = 90%
7.055.54.3
0
200
400
600
800
0 2 4 6 8Ln (Pi+1)
Ne
t Re
turn
s ET = 74PL1 = 245PL2 = 1153
Management Efficacy = 100%
4.15 5.5
0
200
400
600
800
0 2 4 6 8
Ln (Pi+1)
Net
Ret
urns
ET = 63PL1 = 245
Fixed Cost Economic Threshold
0
100
200
300
400
500
600
0 2 4 6 8 10Nematode Population (Ln)
Net
Ret
urns
($)
Continuous Model Optimization
0
200
400
600
800
1000
1200
1400
1600
0 2 4 6 8 10log2 Pi
$
a = 15b = 50
Pi = 550m = 0.1T = 50z = 0.999
$max = 1000E.T. = 110
Discrete Model
0
200
400
600
800
1000
1200
0 2 4 6 8 10log2 Pi
$
a = 600Pi = 200m = 0.1T = 20z = 0.99
$max = 1000E.T. = 78.48428
Optimized Discrete Model
Seasonal Multiplication Rates (Host Crop)
0
100
200
300
400
500
0 500 1000 1500 2000
Pi
Pf/P
ia = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
Overwinter Survival Rates
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000Pf1
Pi2
/Pf1
a = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
Annual Population Change (Host Crop)
0
20000
40000
60000
80000
100000
120000
0 500 1000 1500 2000Pi1
Pi1
* (
Pi2
/Pi1
)a = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
Annual Population Change (Non-host)
0
200
400
600
800
1000
1200
1400
0 500 1000 1500 2000Pi(t)
Pi(t
+x)
Pi1
Pi2
Pi3a = 500b = -0.2
amax = 500p = 1q = -0.1s = 0.65
0
200
400
600
800
1000
1200
1400
1600
0 1 2 3 4 5 6 7 8
Years After Planting Host Crop
Pi(t
+x)
a = 300b = 0.6s = 0.4
Pi(0) = 70
Population Convergence
0
1000
2000
3000
0 5 10 15Year
Po
pu
lati
on
Le
vel
0NHR
2NHR
4NHR
6NHR
Optimum Rotation Length
-200
-100
0
100
200
300
0 1 2 3 4 5 6 7 8 9 10
Years of Non-host
Ave
. An
nu
al R
etu
rns
($
)
Perennial Crop Considerations
0
2000
4000
6000
8000
10000
12000
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Days
Mes
ocric
onem
a xe
nopl
ax
Lovell
Nemaguard
0
2000
4000
6000
8000
10000
12000
0 2000 4000 6000 8000 10000 12000 14000
Degree-Days
Mes
ocric
onem
a xe
nopl
ax
Year 1
0
20
40
60
80
100
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 2
02000400060008000
1000012000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 3
05000
1000015000200002500030000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 4
05000
1000015000200002500030000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 1
0
20
40
60
80
100
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 2
02000400060008000
1000012000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
Year 3
05000
1000015000200002500030000
0 1000 2000 3000DD
AU
C LU
LT
NU
NT
0
2
4
6
8
10
12
Year 2 Year 3 Year 4 Year 5
Co
eff
icie
nt
LT-Full
LT-S/F
LU-Full
LU-S/F
NT-Full
NT-S/F
NU-Full
NU-S/F
0
10
20
30
40
0 20 40 60 80 100AUC
Alfl
afa
Yie
ld L
oss y=1.15+0.37x, r2=0.89
0
20
40
60
80
0 2000 4000DD
Are
a U
nder
Cur
ve
Pi2170
Pi4
Pi43
Pi434
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
