Consequences of Heterogeneous Survival Rates of an Entomopathogenic Nematode'

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Consequences of Heterogeneous Survival Rates of
an Entomopathogenic Nematode.

• Chris Dugaw
• Department of Mathematics
• Humboldt State University

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Outline

• Biological background
• Understanding Nematode Survival
• Experimental Setup
• Survival Analysis
• Results
• Discussion

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Entomopathogenic nematodes

• Insect predators, in soil or litter
• Can move gt2 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 cycle
http//www.bath.ac.uk/bio-sci/clarke.htm
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Current Uses of Nematodes as Biocontrol Agents
Source http//www.oardc.ohio-state.edu/nematodes/
biologyecology.htm
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Study Site the Bodega Marine Reserve
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The predatory nematode Heterorhabditis marelatus
neudorff.de/nuetzlinge/img/hmne.jpg
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A natural host the ghost moth Hepialus
californicus
Host larvae
Adult Host
Larvae infected by nematodes
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Ghost moth caterpillars feed on the roots of bush
lupine (Lupinus arboreus)
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Lupine killed by ghost moth caterpillars
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Large-scale ghost moth outbreaks occur, killing
10,000 mature lupines
2001
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2002
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The trophic cascade predators indirectly affect
producers by suppressing herbivores
Strong 1997, Strong et al. 1999
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Seasonal 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 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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Outline

• Biological background
• Understanding Nematode Survival
• Experimental Setup
• Survival Analysis
• Results
• Discussion

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Experimental design
Each tube - 30 g past. soil - 1100 IJ nematodes -
Fine mesh covers

• 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

Sampled 3 times over a Summer
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Survival Analysis
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Survival Analysis
Homogeneous Death Rates
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Survival Analysis
Homogeneous Death Rates
Exponential Distribution
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Survival Analysis
Homogeneous Death Rates
Exponential Distribution
Heterogeneous Death Rates
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Survival Analysis
Homogeneous Death Rates
Exponential Distribution
Heterogeneous Death Rates
Mixed Exponential Distribution
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First Step Exponential Fit
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Mixed Exponential Distributions

• Individuals have different mortality rates, k.

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Mixed Exponential Distributions

• Individuals have different mortality rates, k.
• Risk of death for each individual is constant
  over time.

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Mixed 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

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

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Pareto Distribution

• The mixed exponential you get when you assume k
  is gamma distributed.
• A simple function form can be derived by
  integrating

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Pareto Distribution

• The mixed exponential you get when you assume k
  is gamma distributed.
• A simple function form can be derived by
  integrating

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Pareto Distribution

• The mixed exponential you get when you assume k
  is gamma distributed.
• A simple function form can be derived by
  integrating

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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 Fit
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Improvement Pareto Fit
? 0.29 ? 2.77
? 0.73 ? 2.77
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Why is it an improvement?

• Akaike says so ?AICc 3.46

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Why is it an improvement?

• Akaike says so ?AICc 3.46
• Provides a greater understanding of the
  biological system.

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Why is it an improvement?

• Akaike says so ?AICc 3.46
• Provides a greater understanding of the
  biological system.
• Allows us to quantify heterogeneity using the
  scale parameter, ?.

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Results

• Survival in soil is heterogeneous.

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Results

• Survival in soil is heterogeneous.
• Mean mortality is higher in the grasslands.
  (log ratio test ?2 0.449, df1, p 0.050)

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Results

• Survival in soil is heterogeneous.
• Mean mortality is higher in the grasslands.
  (log ratio test ?2 0.449, df1, p 0.050)
• Heterogeneity same in the two treatments.
  (log ratio test ?2 0.279, df1, p 0.98)

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Outline

• Biological background
• Understanding Nematode Survival
• Experimental Setup
• Survival Analysis
• Results
• Discussion

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Feedback loop in trophic cascade
Preisser, Dugaw, et al., In Review
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Alternative Explanations for Observations

• Decreasing individual hazards

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Alternative Explanations for Observations

• Decreasing individual hazards
• Density Dependant Survival

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Future work

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

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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

• 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

• Evan Preisser
• Mike Eng
• Don Strong
• Brian Dennis
• Support of
• NSF
• UC Davis Dissertation Year Fellowship
• UCD Faculty Fellow