1. Context dependent pollinator limitation
Evolutionary Ecology of Multispecific Interactions in Changing Environments ATBC 2007, Morelia, Michoacan, MEXICO
Context dependent pollinator limitation
Carol C. Horvitz1, Johan Ehrlén2 and David Matlaga1
1University of Miami, Coral Gables, FL USA
2Stockholm University, SE Stockholm, SWEDEN

2. Supplemental pollination = higher plant fitness?
Issue
Supplemental pollination = higher plant fitness?

3. Demographic, biotic, abiotic variability in the environment
Contexts
Demographic, biotic, abiotic variability in the environment
Ecological, evolutionary and conservation consequences of pollen limitation
e.g. Ashman et al. 2004

4. Candidate currencies for measuring fitness
Fitness components
Reproduction
Survival
Growth
Population growth rate
Stochastic growth rate

5. Demographic transitions and fitness in a constant world
N(t+1) = A N(t)
A is a population projection matrix
Transitions and contributions between stages, aij = fitness components
λ = population growth rate

6. Demographic transitions and fitness in a variable world
N(t+1) = X(t) N(t)
X(t) is a random variable
A1, A2, A3…AK , K environmental states
Transitions and contributions in each environment, aijβ
λS = stochastic growth rate
Tuljapurkar 1982, 1990

7. In a variable world: sequences, frequencies and new sensitivities
Environmental dynamics
sequences along sample paths
an expected long run stationary distribution
λs is sensitive to perturbations of means, variances, and transitions in particular environmental states
Eδ, Eμ, Eβ and others…
Tuljapurkar et al Am Nat
Horvitz et al Ecology

8. Lathyrus vernus Long lived perennial forest herb
Ranges from central and northern Europe to Siberia
Particularly well-studied example

9. not exactly tropical… Deciduous forest Quercus, Fraxinus, Betula
Tullgarnsnäset
SW of Stockholm 58º6’ N, 17º4’ E
Deciduous forest
Quercus, Fraxinus, Betula

10. Bruchus (seed predator) Demographic costs of seeds and beetles
Players
Bombus (pollinator)
Bruchus (seed predator)
Demographic costs of seeds and beetles

11. Field experiment λ was negatively affected
Supplemental pollen increased seed set
within the year
BUT
Next year’s flower production and growth reduced
λ was negatively affected
Ehrlen and Eriksson 1995, Ecology 69:

12. End of story? NO!
Changing the demographic context can offset costs to λ
In variable environments
the currency for measuring the effects is λs
frequency and sequence of high pollination years relative to other kinds of years determine outcome

13. Stages seeds seedlings small intermediate large vegetative
large flowering
dormant rhizome
Ehrlen and Eriksson 1995, Ecology 69:

14. Open-pollinated
Ehrlen and Eriksson 1995, Ecology 69:

15. Hand-pollinated
Ehrlen and Eriksson 1995, Ecology 69:

16. Costs to fates of large flowering plants and to λ
More seeds
Shrink
Go Dormant
Flower Less
Data in Ehrlen and Eriksson 1995, Ecology 69:

17. But 53% of seeds had been lost to beetles
(both open and hand pollinated plants)
Observed seeds = “Gross Seeds” - Beetles
Beetles cost as much as seeds…
Observed fates really for “Gross Seeds”
Data in Ehrlen and Eriksson 1995, Ecology 69:

18. Elimination of seed predators lessens negative effect on λ
Data in Ehrlen and Eriksson 1995, Ecology 69:

19. Demographic context: single constant environment
Using λ to measure fitness
Δ Seed survival
Δ Germination
Δ Seedling survival
Using λs to measure fitness
Some years High Pollination
Some years Low Pollination
High germination year added
Δ Frequency
Δ Sequence
(All simulations that follow use the predator-absent scenario)

20. Higher seed survival can compensate for cost

21. Higher germination can compensate for cost

22. Higher seedling survival can NOT compensate for cost

23. Demographic context: multiple environmental states
Using λ to measure fitness
Δ Seed survival
Δ Germination
Δ Seedling survival
Using λs to measure fitness
Some years High Pollination
Some years Low Pollination
High germination year added
Δ Frequency
Δ Sequence
(All simulations that follow use the predator-absent scenario)

24. 2-state model for variable environment
Probability rules that generate environmental sequences
Columns sum to 1
Dot size indicates probability
Color coded for environmental state to which the system transitions
Env at time t+1
Env at time t

25. 2-state IID models Increasing probability of going to a
high pollination year

26. Variable environments: Increasing frequency of high pollination year decreases fitness

27. Focus on world with 70% high, 30% low pollination
What is the outcome of adding some high germination
years among the low pollination years?

28. Now there are three environments
Low pollination (as before)
High pollination (as before)
Low pollination accompanied by High (9x) germination
λ = 1.063
λ = 1.055
λ = 1.157

29. 3-state IID models
High germination
any time

30. 3-state Markov models
High germination
only after high pollination

31. Variable environments: increasing frequency of high germination years increases fitness
Sequence
matters

32. Changing the demographic context can offset costs to λ
Conclusions
Changing the demographic context can offset costs to λ
In variable environments
the currency for measuring the effects is λs
frequency and sequence of high pollination years relative to other kinds of years determine outcome

33. Thanks Rodolfo and John 2006-08 NSF OPUS Uppsala University
Stockholm University