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Consequences of Consequences of Heterogeneous Survival Rates Heterogeneous Survival Rates
of an Entomopathogenic of an Entomopathogenic Nematode.Nematode.
Chris DugawChris DugawDepartment of MathematicsDepartment of MathematicsHumboldt State UniversityHumboldt State University
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OutlineOutline
Biological background Understanding Nematode Survival
Experimental Setup Survival Analysis Results
Discussion
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Entomopathogenic nematodesEntomopathogenic nematodes
Insect predators, in soil or litter
Can move >2 cm/day following volatiles
Kills prey with symbiotic bacteria injected into host
One nematode in 800K+ emerge
Images courtesy of Ed Lewis, Virginia Tech
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Nematode life cycleNematode life cycle
http://www.bath.ac.uk/bio-sci/clarke.htm
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Current Uses of Nematodes as Biocontrol AgentsCurrent Uses of Nematodes as Biocontrol AgentsCommodity Insect Pests
Artichokes Artichoke plume moth
Berries Root weevils
Citrus Root weevils
Cranberries Root Weevils
Cranberry girdler
Mushrooms Fungus gnats
Ornamentals Root Weevils
Wood borers
Fungus gnats
Turf Scarabs
Mole crickets
Billbugs
Armyworm, Cutworm,
Webworm
Source: http://www.oardc.ohio-state.edu/nematodes/biologyecology.htm
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Study Site: the Bodega Marine ReserveStudy Site: the Bodega Marine Reserve
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The predatory nematode The predatory nematode Heterorhabditis marelatusHeterorhabditis marelatus
neudorff.de/nuetzlinge/img/hmne.jpg
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A natural host: the ghost moth A natural host: the ghost moth Hepialus californicusHepialus californicus
Adult Host
Larvae infected by nematodes
Host larvae
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Ghost moth caterpillars feed on the Ghost moth caterpillars feed on the roots of bush lupine (roots of bush lupine (Lupinus arboreusLupinus arboreus))
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Lupine killed by ghost moth Lupine killed by ghost moth caterpillarscaterpillars
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Large-scale ghost moth outbreaks Large-scale ghost moth outbreaks occur, killing 10,000+ mature lupinesoccur, killing 10,000+ mature lupines
20012001
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The trophic cascade: The trophic cascade: predators predators indirectly affect producers by indirectly affect producers by
suppressing herbivoressuppressing herbivores
B u s h lu p in eL u p i n u s a rbo reu s
G h o s t m o thH ep i a lu s ca li fo rn i cu s
E n to m o p a th o gen ic n em a to d eH et ero rh a bd i t i s m a re la t u s
+
Strong 1997, Strong et al. 1999
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Seasonal DynamicsSeasonal Dynamics
Wet Winter •Nematodes search for hosts •Nematode reproduction occurs•Hosts are in larval stage
Dry Summer• Nematodes are inactive• Nematodes must survive • Host become adults and disperse• Host eggs are deposited on bush
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Seasonal DynamicsSeasonal Dynamics
Wet Winter •Nematodes search for hosts •Nematode reproduction occurs•Hosts are in larval stage
Dry Summer• Nematodes are inactive• Nematodes must survive • Host become adults and disperse• Host eggs are deposited on bush
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OutlineOutline
Biological background Understanding Nematode Survival
Experimental Setup Survival Analysis Results
Discussion
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Experimental designExperimental design 2 treatments =
Lupine, Grasslands 4 replicates/treatment =
8 total replicates 50 tubes/replicate =
400 total tubes Each sampling date, removed
10 tubes/replicate = 80 total tubes/sampling date
Assessed nematodes using ‘bait’ insects
Each tube- 30 g past. soil- 1100 IJ nematodes- Fine mesh covers
Sampled 3 times over a Summer
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Survival AnalysisSurvival Analysis
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Survival AnalysisSurvival Analysis
HomogeneousDeath Rates
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Survival AnalysisSurvival Analysis
HomogeneousDeath Rates
ExponentialDistribution
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Survival AnalysisSurvival Analysis
HomogeneousDeath Rates
HeterogeneousDeath Rates
ExponentialDistribution
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Survival AnalysisSurvival Analysis
HomogeneousDeath Rates
HeterogeneousDeath Rates
ExponentialDistribution
Mixed ExponentialDistribution
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First Step: Exponential FitFirst Step: Exponential Fit
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Mixed Exponential DistributionsMixed Exponential Distributions
Individuals have different mortality rates, k.
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Mixed Exponential DistributionsMixed Exponential Distributions
Individuals have different mortality rates, k.
Risk of death for each individual is constant over time.
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Mixed Exponential DistributionsMixed Exponential Distributions
Individuals have different mortality rates, k.
Risk of death for each individual is constant over time.
The conditional distribution for individual lifespan, T, given k is exponential.
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Pareto Distribution:Pareto Distribution:
The mixed exponential you get when you assume k is gamma distributed.
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Pareto Distribution:Pareto Distribution:
The mixed exponential you get when you assume k is gamma distributed.
A simple function form can be derived by integrating:
0 | )()|()( dkkfktftf KKTT
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Pareto Distribution:Pareto Distribution:
The mixed exponential you get when you assume k is gamma distributed.
A simple function form can be derived by integrating:
dkekke
dkkfktftf
kkt
KKTT
0
1
0 |
)(
)()|()(
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Pareto Distribution:Pareto Distribution:
The mixed exponential you get when you assume k is gamma distributed.
A simple function form can be derived by integrating:
,)(
)(
)()|()(
1
0
1
0 |
t
dkekke
dkkfktftf
kkt
KKTT
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The distribution of survival rates shifts over time leading to a decrease in mean mortality rate.
McNolty, Doyle and Hansen, Technometrics, 1980
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Improvement: Pareto FitImprovement: Pareto Fit
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Improvement: Pareto FitImprovement: Pareto Fit
= 0.29 = 2.77
= 0.73 = 2.77
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Why is it an improvement?Why is it an improvement?
1. Akaike says so: AICc = 3.46
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Why is it an improvement?Why is it an improvement?
1. Akaike says so: AICc = 3.46
2. Provides a greater understanding of the biological system.
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Why is it an improvement?Why is it an improvement?
1. Akaike says so: AICc = 3.46
2. Provides a greater understanding of the biological system.
3. Allows us to quantify heterogeneity using the scale parameter, .
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Results:Results:
Survival in soil is heterogeneous.
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Results:Results:
Survival in soil is heterogeneous.Mean mortality is higher in the grasslands.
(log ratio test: 2 = 0.449, df=1, p = 0.050)
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Results:Results:
Survival in soil is heterogeneous.Mean mortality is higher in the grasslands.
(log ratio test: 2 = 0.449, df=1, p = 0.050)Heterogeneity same in the two treatments.
(log ratio test: 2 = 0.279, df=1, p = 0.98)
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OutlineOutline
Biological background Understanding Nematode Survival
Experimental Setup Survival Analysis Results
Discussion
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Feedback loop in trophic cascadeFeedback loop in trophic cascade
B u s h lu p in eL u p i n u s a rbo reu s
G h o s t m o thH ep i a lu s ca li fo rn i cu s
E n to m o p a th o gen ic n em a to d eH et ero rh a bd i t i s m a re la t u s
++
n o n -tro p h icd ry s ea s o n
tro p h icw e t s ea s o n
+
Preisser, Dugaw, et al., In Review
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Alternative Explanations for Alternative Explanations for Observations Observations
Decreasing individual hazards
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Alternative Explanations for Alternative Explanations for Observations Observations
Decreasing individual hazards
Density Dependant Survival
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Future work:Future work:
Apply this analysis to new experiments to assess survival and heterogeneity in different soil types.
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Future work:Future work:
Apply this analysis to new experiments to assess survival and heterogeneity in different soil types.
Compare fitted shape parameter to physical soil properties.
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Future work:Future work:
Apply this analysis to new experiments to assess survival and heterogeneity in different soil types.
Compare fitted shape parameter to physical soil properties.
Incorporate heterogeneous survival into a stochastic model that includes nematode reproduction.
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Thanks to:Thanks to:Evan Preisser
Mike Eng
Don Strong
Brian Dennis
Support of:Support of:NSF
UC Davis Dissertation Year Fellowship
UCD Faculty Fellow