Population Dynamics and Mutualism: Functional Responses of Benefits and Costs

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Population Dynamics and MutualismFunctional
Responses of Benefits and Costs
J. Nathaniel Holland, Donald L. DeAngelis, Judith
L. Bronstein
Presented by Kate Buenau
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Generalizations for Mutualism

• Benefitscant be obtained in absence of partner
  nutrients, transport, protection
• Costsinvestments in attracting mutualists,
  substances to reward them, energy and time to
  obtain rewards
• Both affect reproduction and survival
• Benefits and costs tend to be density dependent
• Positive feedback between mutualists
• Negative feedback needed for stability

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The Goal

• Develop functional responses in terms of benefits
  and costs as a function of the population of the
  mutualist partner
• General model
• Case study of senita cactus

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Potential Functional Responses

• Net Effect Gross Benefit - Cost

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Some Basic Models

• General model
• Functional responses
• linear
• saturating
• unimodal

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Senita Cacti and Moths

• Flowers must be pollinated by moths
• Moths lay eggs in flowers
• Not all flowers have fruit, and moth larvae eats
  some immature fruit
• Fruit with larvae cannot produce seeds
• Fruit may abort, and eggs and larvae die
  (negative feedback)

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The Model

• Benefits and costs to cacti depends upon
  abundance of moths compared to flower production
  (M/FP) unimodal net effect
• Benefit Flowers are pollinated with a saturating
  function, using a Poisson searching process

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Building the equation II

• Costs (larval infestation) also saturate
• (1-a) represents fraction of flowers potentially
  setting fruit
• ? fraction of fruit ? cacti

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The Other Side

• Moth benefits number of flowers effectively
  oviposited
• Costs fruit abortion (-a)

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Variation

• Correlates pollination and oviposition
  
• Less likelihood of extinction

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Some simulations