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Optimality

Optimality. Studying Evolution. Evolution is a process that creates patterns As evolutionary biologists we wish to understand the process Since most of us were not there to observe the process, we require models. Adaptation and optimality.

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Optimality

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  1. Optimality

  2. Studying Evolution • Evolution is a process that creates patterns • As evolutionary biologists we wish to understand the process • Since most of us were not there to observe the process, we require models

  3. Adaptation and optimality • Orzack & Sober (1994) provide a useful way to think about where optimality modelling fits into evolutionary biology: • Selection played some role in a traits evolution • Selection played a major role in a traits evolution • Selection alone is sufficient to explain a traits evolution

  4. Optimality modelling • The optimization approach to studying adaptation assumes that natural selection produces phenotypes, that subject to constraints, are optimal in a sense that they maximize fitness. (Parker & Maynard Smith) • An adaptation is a phenotypic variant that results in the highest fitness amongst a set of variants in a given environment (Reeve & Sherman, 1993).

  5. The phenotypic gambit (Grafen, 1984) • The dynamic biological entities of interest in an optimality model are phenotypes (strategies), not genes • Thus genes will evolve as necessary in order to obtain the optimal phenotype • Negative correlations • Etc.

  6. A lizard thermoregulation example benefit Benefit-cost Huey & Slatkin, 1978

  7. Core assumptions (Mitchell & Valone, 1990) • Random mutations generate new strategies each generation • Different strategies have different fitness • Current Populations of strategies reside near a locally stable equilibrium • Relative fitness of strategies is not influenced by their mode of transmission

  8. Just So Stories? • Lewontin, Gould etc. Assuming optimality in the first place? • Genetic models often show that with more than one locus, selection will not always achieve fitness maximization • Transmission of strategies from one generation to the next is definitely genetics dependent BUT, recent modelling of long term selection on genetic systems is extremely promising (Eshel, Hammerstein, Hurst, Johnstone)

  9. How can we test such model’s • First, we need to generate testable predictions • E.g. Comparative biology is one way to do this • E.g. different species, or individuals in different situations might have different cost functions, therefore different optima. • Do the data fit their predicted optima? How valid are the model assumptions? • i.e. model testing involves examining the predictive power of the model (See Orzack & Sober, 1994)

  10. Optimality modelling when fitness depends on other strategies • Game theory (von Neumann, Nash, Maynard Smith, Parker) • A strategy’s fitness depends on what others in the population are doing • A strategy is a Nash Equilibrium if it is a best reply to itself:For all y, E(x,x)≥E(y,x) • A strategy is an ESS if it is a Nash Equilibrium and for all equal best replies y≠x, E(x,y)>E(y,y) • Alternatively, an ESS is the population strategy that cannot be invaded

  11. Sex allocation (The flagship of optimality theory)

  12. Fig wasps = haplodiploid Fertilized eggs = diploid females, unfertilized eggs = haploid males Selective fertilization = sex ratio control Mothers and offspring are easy to count Fitness = obvious Patch structured populations Few mothers contribute offspring to a given patch Most matings are between siblings 0.5 Sex ratio 0 mothers Fig pollinators are model organisms for testing sex ratio theory under LMC e.g. Hamilton (1967) extraordinary sex ratios. Science

  13. Offspring allocation

  14. One egg per fig Observation & data Random patch use 9/10 Poisson fits Dispersers can mate in natal figs Direct observation Females only mate once Direct observation Mothers determine offspring sex & male morphology Model assumption Modelling assumptions r2 = 0.82

  15. The model 4th 2nd 3rd Mothers determine how many others used The patch before them Mean density = mean expected mothers Fitness Wix = qi wfi + ri wri + si wdi 0 truncated Poisson or Actual density Optimize qi, ri si ESS = when mutant strategies can no longer replace Population strategy

  16. Predictions ? = • Should a species have a dispersing male? = =

  17. ± 20 figs from 6, 4, and 3 crops for study species respectively Offspring, sexed, morphed and counted Mothers density distributions estimated Used to seed model Specific Model predictions 1st mother = female egg 2nd mother = disperser / female 3rd etc = fighter / female Testing predictions: Male dimorphism

  18. Results • Morph ratios decrease with increasing male density (across crops and individual figs) • E vs O dispersers Figs containing 1 disperser 72%, 80%, 70%

  19. Complete knowledge Mistakes (Mean no. of mothers) Sex ratio predictions

  20. Sex ratio model results Data = 11 crops ± 20 figs per crop º = mistakes • = no mistakes R = 0.935, P< 0.01 R = 0.642, P < 0.05

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