Population Dynamics and Mutualism: Functional Responses of Benefits and Costs

1. Population Dynamics and Mutualism:Functional Responses of Benefits and Costs J. Nathaniel Holland, Donald L. DeAngelis, Judith L. Bronstein Presented by Kate Buenau

2. Generalizations for Mutualism • Benefits—can’t be obtained in absence of partner: nutrients, transport, protection • Costs—investments 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

3. 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

4. Potential Functional Responses • Net Effect = Gross Benefit - Cost

5. Some Basic Models • General model: • Functional responses: linear: saturating: unimodal:

6. 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)

7. 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

8. Building the equation II… • Costs (larval infestation) also saturate • (1-a) represents fraction of flowers potentially setting fruit •  = fraction of fruit  cacti

9. The Other Side… • Moth benefits: number of flowers effectively oviposited • Costs: fruit abortion (-a)

11. Variation Correlates pollination and oviposition Less likelihood of extinction

12. Some simulations…