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Correlated trait evolution

Correlated trait evolution. Maximum likelihood approach (Pagel and Milligan). Procedure. Estimate the set of rates in the q-matrix that maximize the likelihood of the data and calculate that likelihood

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Correlated trait evolution

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  1. Correlated trait evolution

  2. Maximum likelihood approach(Pagel and Milligan)

  3. Procedure • Estimate the set of rates in the q-matrix that maximize the likelihood of the data and calculate that likelihood • Constrain the matrix so that it represents independence (q12 = q34; q13 = q24; q21 = q43; q31 = q42) and repeat the calculation • Use a likelihood ratio test to evaluate significance

  4. Fruit color/size in figsLomascolo et al. (2008) OECOLOGIAlikelihood ratio = 4.889; P value = 0.027

  5. Wind-pollination correlated with….? Friedman and Barrett (2008) IJPS

  6. Wind-pollination correlated with….? Friedman and Barrett (2008) IJPS

  7. Issues to consider • Rejection of independence does not tell you what kind of non-independence you have • You need reasonable branch lengths • Sampling matters (if perhaps less than parsimony)

  8. Continuous traits • All morphological traits can be treated as continuous variables • Often people have wanted to look at the correlation of such variables across species

  9. Sperm competition in primates But, species are not independent!

  10. Why phylogeny should be considered

  11. Major Available Methods • Linear/square-change Parsimony • Independent contrasts • Phylogenetic Generalized Least Squares

  12. e f g Linear/Square-change parsimony b c d a Tips = n Branches = 2n-2

  13. Linear Parsimony • Find the set of ancestral states such that the absolute amount of change summed across branches is minimized • Each internal node is the average of the three surrounding nodes

  14. e f g Graph the changes b c d a 10 4 2 6 5 3 5 3 6 Change in y 0 2 4 1 1 -10 -10 0 10 Change in x

  15. e f g Independent contrasts b c d a Tips = n Contrasts = n-1

  16. Independent Contrasts value of x value of y 7 9 14 20 20 24 30 40 22 35 8 17

  17. Independent Contrasts • Calculations: • by convention, contrasts for independent variable are positive • contrasts for dependent variable may be positive or negative • correlate contrasts • no correlation = no causal relationship • significant correlation = causal relationship (negative or positive)

  18. Independent Contrasts value of x value of y 30 40 20 24 20 7 9 14 22 35 8 17 x y d1 2 4 d2 6 10 d3 9 13

  19. Independent Contrasts 10 x y d1 2 4 d2 6 10 d3 9 13 y contrast 0 15 x contrast

  20. Assumptions of independent contrasts • We know branch lengths • We know tip values with certainty • Traits values evolve by Brownian motion • Needed to calculate ancestral states • Needed to accommodate error in the estimation of ancestral states

  21. Expected change in time, t, is 0 with var. t

  22. Assumptions of independent contrasts • We know branch lengths • Traits values evolve by Brownian motion • Strength of correlation is the same across the tree

  23. Broader objections • The tip correlation may be what we care about • No characters evolve by Brownian motion • The assumption of a constant “correlation” is biologically unrealistic

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