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

OutlineOutline

Biological background Understanding Nematode Survival

Experimental Setup Survival Analysis Results

Discussion

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

Nematode life cycleNematode life cycle

http://www.bath.ac.uk/bio-sci/clarke.htm

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

Study Site: the Bodega Marine ReserveStudy Site: the Bodega Marine Reserve

The predatory nematode The predatory nematode Heterorhabditis marelatusHeterorhabditis marelatus

neudorff.de/nuetzlinge/img/hmne.jpg

A natural host: the ghost moth A natural host: the ghost moth Hepialus californicusHepialus californicus

Adult Host

Larvae infected by nematodes

Host larvae

Ghost moth caterpillars feed on the Ghost moth caterpillars feed on the roots of bush lupine (roots of bush lupine (Lupinus arboreusLupinus arboreus))

Lupine killed by ghost moth Lupine killed by ghost moth caterpillarscaterpillars

Large-scale ghost moth outbreaks Large-scale ghost moth outbreaks occur, killing 10,000+ mature lupinesoccur, killing 10,000+ mature lupines

20012001

20022002

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

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

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

OutlineOutline

Biological background Understanding Nematode Survival

Experimental Setup Survival Analysis Results

Discussion

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

Survival AnalysisSurvival Analysis

Survival AnalysisSurvival Analysis

HomogeneousDeath Rates

Survival AnalysisSurvival Analysis

HomogeneousDeath Rates

ExponentialDistribution

Survival AnalysisSurvival Analysis

HomogeneousDeath Rates

HeterogeneousDeath Rates

ExponentialDistribution

Survival AnalysisSurvival Analysis

HomogeneousDeath Rates

HeterogeneousDeath Rates

ExponentialDistribution

Mixed ExponentialDistribution

First Step: Exponential FitFirst Step: Exponential Fit

Mixed Exponential DistributionsMixed Exponential Distributions

Individuals have different mortality rates, k.

Mixed Exponential DistributionsMixed Exponential Distributions

Individuals have different mortality rates, k.

Risk of death for each individual is constant over time.

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.

Pareto Distribution:Pareto Distribution:

The mixed exponential you get when you assume k is gamma distributed.

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

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 |

)(

)()|()(

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

The distribution of survival rates shifts over time leading to a decrease in mean mortality rate.

McNolty, Doyle and Hansen, Technometrics, 1980

Improvement: Pareto FitImprovement: Pareto Fit

Improvement: Pareto FitImprovement: Pareto Fit

= 0.29 = 2.77

= 0.73 = 2.77

Why is it an improvement?Why is it an improvement?

1. Akaike says so: AICc = 3.46

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.

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, .

Results:Results:

Survival in soil is heterogeneous.

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)

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)

OutlineOutline

Biological background Understanding Nematode Survival

Experimental Setup Survival Analysis Results

Discussion

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

Alternative Explanations for Alternative Explanations for Observations Observations

Decreasing individual hazards

Alternative Explanations for Alternative Explanations for Observations Observations

Decreasing individual hazards

Density Dependant Survival

Future work:Future work:

Apply this analysis to new experiments to assess survival and heterogeneity in different soil types.

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.

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.

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