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 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
Consequences of Multiple Mating
•C. elegans produces 4x more
eggs when multiple-mated than
by hermaproditism.
Sex Ratios and Multiple Mating Effects
4000
Pf
•Females of Heterodera attract
and are mated by several males
2000
Eggs fertilized
•R. pellio male does not supply
sufficient sperm to fertilize all
oocytes from a single female
0
Rhabditis pellio
400
350
300
250
200
150
100
50
0
Total sperm = 884
Female produces 600 oocytes
Only 150 fertilized at a single mating
3
5
7
Male Age
1:1 F:M
0
9
50
0.3:0.7 F:M
Pi
0.7:0.3 F:M
100
•Probability that female
genes are perpetuated is
increased
•Population may increase at
a greater rate when there are
fewer females and more
males
120
Caenorhabditis elegans
Age-specific Reproduction
N2
100
clk-1
age-1
80
60
40
20
0
3
4
5
6
7
Age (days)
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
8
9
10
wild type
400
300
200
Lifetime egg production
100
0
0
8
16
24
32
40
48
age-1
400
300
200
100
0
0
8
16
24
32
LIFESPAN (days)
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
40
48
Death Rates
• Intrinsic factors
– natural longevity
– relationships of fecundity and longevity
• Extrinsic factors
– resource availability
– environmental extremes
– predation
– management
NUMBER
ALIVE
48
C. elegans wild type
³80 eggs/day
40-79 eggs/day
1-39 eggs/day
0 eggs/day
24
lx
1 .0
w i l d ty p e
c lk -1
age-1
0 .8
0 .6
0 .4
0 .2
0 .0
0
0
0
8
16
24
AGE (days)
Chen, Carey and Ferris (2001), Expt. Gerontology 36:431-440
32
8
16
24
32
A G E (d ays )
40
40
48
48
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=N0  t
Nt=N0ert,
dN/dt=rN
6000
r=dNt/Ntdt (growth rate/indiv.)
4000
Nt
=er (pop. growth/unit time)
2000
0
0
800
Nt
600
400
200
0
0
20
40
60
Time
80
100
200
400
N0
600
800
Continuous time models
Nt=N0  t
Nt=N0ert,
dN/dt=rN
6000
r=dNt/Ntdt (growth rate/indiv.)
4000
Nt
=er (pop. growth/unit time)
2000
Seasonal Multiplication:
0
Nt/N0=ert
0
Nt=aN0(b+1)
800
10
600
8
Nt/N0
Nt
Nt/N0=aN0b,
400
4
0
2
20
40
60
Time
80
100
400
N0
600
800
6
200
0
200
0
200
N0
400
600
Ln Final Population (Pf)
10
dN/dt=rN(1-N/K)
Nt=K/(1+((K/N0-1)(e-rt))
5
dP/dt=aP(1-P/E)
Pf=aEPi/((a-1)Pi+E)
Pf=(75/-Ln0.993)(1-0.993Pi)
0
0
2
4
6
8
Ln Initial Population (Pi) Sep 99
10
Pf=(a/-Lnq)(1-qPi)
500
Multiplication Rate
Pf/Pi=((a/-Lnq)(1-qPi))/Pi
Multiplication Rate (Pf/Pi)
450
400
350
Pf/Pi=1018 Pi-0.71, r2=0.71
Pf/Pi=(400/-Ln0.90)(1-0.90Pi)/Pi
300
250
200
150
100
50
0
0
2
4
6
Ln(Pi) Sep 99
8
10
Multiplication Rate (Pf/Pi)
Seasonal population change
500
Meloidogyne arenaria - oriental melon
400
for Pi<5, Pf/Pi=325, else:
Pf/Pi=1018 Pi
300
-0.71
2
, r =0.71
200
100
0
0
2
4
6
Ln(Pi) Sep 99
Kim and Ferris (2001)
8
10
Discrete time models
1.2
1
0.8
0.6
0.4
0.2
1.2
0
1
10 C
15 C
20 C
25 C
30 C
35 C
0.8
Soil Temperature
Rate
Rate
Discrete time models
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
Soil Moisture (bars)
0.96
1.92
3.84
1.2
1
0.8
0.6
0.4
0.2
1.2
0
1
20 C
25 C
30 C
35 C
0.8
Soil Temperature
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
0.96
1.92
3.84
Soil Moisture (bars)
1.2
1
0.8
Rate
15 C
0.6
0.4
0.2
0
10 C
15 C
20 C
25 C
30 C
35 C
Soil Temperature
1.2
1
0.8
Rate
10 C
Rate
Rate
Discrete time models
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
Soil Moisture (bars)
0.96
1.92
3.84
1.2
1
0.8
Rate
Discrete time models
0.6
0.4
0.2
1.2
0
1
10 C
15 C
20 C
25 C
30 C
35 C
0.8
Rate
Soil Temperature
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
0.96
1.92
3.84
Soil Moisture (bars)
1.2
1
Rate
0.8
0.6
0.4
0.2
0
10 C
15 C
20 C
25 C
30 C
35 C
Soil Temperature
1.2
1
Rate
0.8
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
Soil Moisture (bars)
1.2
1
Rate
0.8
0.6
0.4
0.2
0
10 C
15 C
20 C
25 C
Temperature
30 C
35 C
0.96
1.92
3.84
1.2
1
0.8
Rate
Discrete time models
0.6
0.4
0.2
1.2
0
1
10 C
15 C
20 C
25 C
30 C
35 C
0.8
Rate
Soil Temperature
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
0.96
1.92
3.84
Soil Moisture (bars)
1.2
1
Rate
0.8
1.2
0.6
0.4
1
0.2
0.8
0
0.6
10 C
15 C
0.4
20 C
25 C
30 C
35 C
Soil Temperature
0.2
1.2
0
1
20 C
25 C
30 C
35 C
0.8
Temperature
Rate
15 C
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
Soil Moisture (bars)
1.2
1
0.8
Rate
10 C
0.6
0.4
0.2
0
10 C
15 C
20 C
25 C
Temperature
30 C
35 C
0.96
1.92
3.84
1.2
1.2
0.6
0.4
1
0.2
0.8
Rate
1
0.8
Rate
Discrete time models
1.2
0
1
10 C
0.6
15 C
20 C
25 C
30 C
35 C
0.8
Soil Temperature
Rate
0.4
0.6
0.2
0.4
0
10 C
15 C
20 C
25 C
30 C
0.2
35 C
Temperature
0
0.015
0.03
0.06
0.12
0.24
0.48
0.96
1.92
3.84
Soil Moisture (bars)
1.2
1
Rate
0.8
1.2
0.6
0.4
1
0.2
0.8
0
0.6
10 C
15 C
0.4
20 C
25 C
30 C
35 C
Soil Temperature
0.2
1.2
0
1
20 C
25 C
30 C
35 C
0.8
Temperature
Rate
15 C
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
Soil Moisture (bars)
1.2
1
0.8
Rate
10 C
0.6
0.4
0.2
0
10 C
15 C
20 C
25 C
Temperature
30 C
35 C
0.96
1.92
3.84
1.2
Discrete time models
1
Rate
0.8
1.2
0.4
1
0.2
0.8
Rate
0.6
1.2
0
1
10 C
0.6
15 C
20 C
25 C
30 C
35 C
0.8
Soil Temperature
Rate
0.4
0.6
0.2
0.4
0
10 C
15 C
20 C
25 C
30 C
0.2
35 C
Temperature
0
0.015
0.03
0.06
0.12
0.24
0.48
0.96
1.92
3.84
Soil Moisture (bars)
250
1.2
1
200
150
1
0.8
100
0.6
0.4
0.2
Rate
Eggs
J2
J3
J4
Ad
1.2
0.8
0.6
0.4
0.2
0
10 C
15 C
20 C
25 C
30 C
35 C
Soil Temperature
50
1.2
0
1
20 C
25 C
30 C
35 C
Temperature
0.8
0
Rate
15 C
0
10
20
30
Days
40
50
0.6
0.4
0.2
0
0.015
0.03
0.06
0.12
0.24
0.48
Soil Moisture (bars)
1.2
1
0.8
Rate
10 C
0.6
0.4
0.2
0
10 C
15 C
20 C
25 C
Temperature
30 C
35 C
0.96
1.92
3.84
250
200
Eggs
J2
J3
J4
Ad
150
100
50
0
0
10
20
30
Days
40
50
Total (all stages)
600
500
400
300
200
100
0
0
10
20
30
Days
40
50
Statistical Models
Total (all stages)
600
500
400
300
200
100
0
0
10
20
30
Days
40
50
Crop Yield in Relation to
Nematode Population Density
Oriental melon - Meloidogyne arenaria
1.2
1
0.8
0.6
0.4
0.2
0
0
2
C
Relative Yield
B
Early season
Relative Yield
Relative Yield
A
4
6
Ln (Pi+1)
8
10
Total harvest
Late season
1.2
1
0.8
0.6
0.4
0.2
0
0
2
4
6
Ln (Pi+1)
8
A: Early season
Y = 0.43+0.57*0.998Pi, ym=19743
1.2
1
0.8
0.6
0.4
0.2
0
B: Late season
Y = 0.03+0.97*0.998Pi, ym=10170
0
2
Kim and Ferris (2001)
4
6
Ln (Pi+1)
8
10
C: Total harvest
Y = 0.50+0.50*0.999Pi, ym=12312
10
Value Loss (WON)
Early
Late
Total
Crop Value
Early Harvest
Late Harvest
Panel A
2019 won/kg
967 won/kg
Panel B
967 won/kg
2019 won/kg
0 10 20 30 40 50 60
Pi Sep 99
Value Loss (WON)
A
300000
250000
200000
150000
100000
50000
0
B
Kim and Ferris (2001)
400000
300000
Early
Late
200000
Total
100000
0
0 10 20 30 40 50 60
Pi Sep 99
The Economic Threshold
That initial population at which the loss in value due
to nematode damage is equal to the cost of
nematode management
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
Profitability Limit constraint
That initial population level at which net returns
become zero
Management Efficacy = 100%
ET = 63
PL1 = 245
600
400
200
4.15
5.5
0
0
2
4
Ln (Pi+1)
6
8
Management Efficacy = 90%
800
Net Returns
Net Returns
800
ET = 74
PL1 = 245
PL2 = 1153
600
400
200
4.3
5.5
7.05
0
0
2
4
Ln (Pi+1)
6
8
Fixed Cost Economic Threshold
Net Returns ($)
600
500
400
300
200
100
0
0
2
4
6
Nematode Population (Ln)
8
10
Continuous Model Optimization
1600
1400
1200
a
b
Pi
m
T
z
$max
E.T.
=
=
=
=
=
=
=
=
15
50
550
0.1
50
0.999
1000
110
1000
$ 800
600
400
200
0
0
2
4
6
log2 Pi
8
10
a=
600
Pi =
200
m=
0.1
T=
20
z=
0.99
$max =
1000
E.T. = 78.48428
Discrete Model
1200
1000
800
$ 600
400
200
0
0
2
4
log2 Pi
6
8
10
Optimized Discrete Model
Seasonal Multiplication Rates (Host Crop)
500
Pf/Pi
400
a=
b=
amax =
p=
q=
s=
500
-0.2
500
1
-0.1
0.65
300
200
100
0
0
500
1000
Pi
1500
2000
Overwinter Survival Rates
1
Pi2/Pf1
0.8
a=
b=
amax =
p=
q=
s=
500
-0.2
500
1
-0.1
0.65
0.6
0.4
0.2
0
0
500
1000
Pf1
1500
2000
Annual Population Change (Host Crop)
120000
a=
b=
amax =
p=
q=
s=
500
-0.2
500
1
-0.1
0.65
Pi1 * (Pi2/Pi1)
100000
80000
60000
40000
20000
0
0
500
1000
Pi1
1500
2000
Annual Population Change (Non-host)
1400
1200
Pi(t+x)
1000
800
Pi1
Pi2
a=
b=
amax =
p=
q=
s=
500
-0.2
500
1
-0.1
0.65
Pi3
600
400
200
0
0
500
1000
Pi(t)
1500
2000
1600
a=
b=
s=
Pi(0) =
1400
Pi(t+x)
1200
300
0.6
0.4
70
1000
800
600
400
200
0
0
1
2
3
4
5
6
7
Years After Planting Host Crop
8
0NHR
Population Convergence
Population Level
3000
2NHR
4NHR
6NHR
2000
1000
0
0
5
Year
10
15
Ave. Annual Returns
($)
Optim um Rotation Length
300
200
100
0
-100
-200
0
1
2
3
4
5
6
7
Years of Non-host
8
9
10
Perennial Crop Considerations
12000
Mesocriconema xenoplax
10000
Lovell
Nemaguard
8000
6000
4000
2000
0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Days
12000
Mesocriconema xenoplax
10000
8000
6000
4000
2000
0
0
2000
4000
6000
8000
Degree-Days
10000
12000
14000
2200
Year 1
Year 2
100
60
LU
40
LT
20
NU
0
NT
0
1000
DD
2000
AUC
AUC
80
12000
10000
8000
6000
4000
2000
0
3000
LT
NU
NT
1000
2000
DD
3000
AUC
AUC
LU
0
LT
NU
NT
0
Year 3
30000
25000
20000
15000
10000
5000
0
LU
1000 DD 2000
3000
Year 4
30000
25000
20000
15000
10000
5000
0
LU
LT
NU
NT
0
1000
DD
2000
3000
Year 1
Year 2
100
60
LU
40
LT
20
NU
0
NT
0
1000
DD
2000
3000
AUC
LU
LT
NU
NT
0
1000
2000
DD
3000
LU
LT
NU
NT
0
Year 3
30000
25000
20000
15000
10000
5000
0
AUC
AUC
80
12000
10000
8000
6000
4000
2000
0
1000
DD
2000
3000
Coefficient
12
LT-Full
10
LT-S/F
8
LU-Full
6
LU-S/F
4
NT-Full
2
NT-S/F
0
NU-Full
Year 2 Year 3 Year 4 Year 5
NU-S/F
Area Under Curve
80
60
Pi2170
40
Pi4
20
Pi43
Pi434
0
0
2000
4000
DD
Noling and Ferris
(1987)
Alflafa Yield Loss
40
y=1.15+0.37x, r2=0.89
30
20
10
0
0
20
40
60
AUC
80
100
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