"PRINCIPLES OF PHYLOGENETICS: ECOLOGY AND EVOLUTION" Integrative Biology 200B Spring 2011 University of California, Berkeley B.D. Mishler Feb. 1, 2011. Qualitative character evolution (cont.) - comparing two or more characters 1. Correlated evolution of two binary traits under the parsimony criterion Maddison's (1990) concentrated changes test was one of the first tests introduced to test for correlations in the evolution of discrete traits, in a phylogenetic context. The test examines the question: are changes in character B concentrated on portions of the phylogeny where character A has a particular state, more than expected by chance? Examples shown on the following pages: Does larval gregariousness in butterflies evolve more often than expected in lineages with warning coloration? Does dioecy evolve from hermaphroditism more often than expected in lineages that have fleshy (vs. dry) fruits? The test proceeds in several steps: 1) first reconstruct the evolution of character A on the tree. This is considered fixed – an independent factor that may influence evolution of character B, but is not dependent upon it. 2) character B is mapped on the tree, and the total number of evolutionary transitions (gains and losses), and the number of transitions that occur against each background in trait A, are tabulated; 3) by exact calculation, or simulation, the number of possible ways to arrange the same number of changes on the given phylogeny are calculated, along with the number of arrangements which involve as many or more changes against the relevant background of character A. 4) The significance of the observed pattern is calculated as the proportion of possible arrangements with as many or more changes located in the selected background of character A. ≥4 gains (out of 5 gains, 1 loss) on black branches: p = 0.0638 69 ways to arrange 2 gains and 0 losses 15 have 2 gains on black branches III. Correlated evolution of two binary traits! Maddison's (1990) concentrated changes test was one of the first tests introduced to test for correlations in the evolution of discrete traits, in a phylogenetic context. The test examines the question: are changes in character B concentrated on portions of the phylogeny where character A has a particular state, more than expected by chance? For example: does dioecy evolve from hermaphroditism more often than expected in lineages that have fleshy (vs. dry) fruits? Does larval gregariousness in butterflies evolve more often than expected in lineages with warning coloration? ! The test proceeds in several steps: ! 1) first reconstruct the evolution of character A on the tree. This is considered fixed – an independent factor that may influence evolution of character B, but is not dependent upon it. ! 2) character B is mapped on the tree, and the total number of evolutionary transitions (gains and losses), and the number of transitions that occur against each background in trait A, are tabulated; ! 3) by exact calculation, or simulation, the number of possible ways to arrange the same number of changes on the given phylogeny are calculated, along with the number of arrangements which involve as many or more changes against the relevant background of character A. ! 4) The significance of the observed pattern is calculated as the proportion of possible arrangements with as many or more changes located in the selected background of character A."4 gains (out of 5 gains, 1 loss) on! 69 ways to arrange 2 gains and 0 lossesblack branches: p = 0.0638! 15 have 2 gains on black branchesIII. Correlated evolution of two binary traits! Maddison's (1990) concentrated changes test was one of the first tests introduced to test for correlations in the evolution of discrete traits, in a phylogenetic context. The test examines the question: are changes in character B concentrated on portions of the phylogeny where character A has a particular state, more than expected by chance? For example: does dioecy evolve from hermaphroditism more often than expected in lineages that have fleshy (vs. dry) fruits? Does larval gregariousness in butterflies evolve more often than expected in lineages with warning coloration? ! The test proceeds in several steps: ! 1) first reconstruct the evolution of character A on the tree. This is considered fixed – an independent factor that may influence evolution of character B, but is not dependent upon it. ! 2) character B is mapped on the tree, and the total number of evolutionary transitions (gains and losses), and the number of transitions that occur against each background in trait A, are tabulated; ! 3) by exact calculation, or simulation, the number of possible ways to arrange the same number of changes on the given phylogeny are calculated, along with the number of arrangements which involve as many or more changes against the relevant background of character A. ! 4) The significance of the observed pattern is calculated as the proportion of possible arrangements with as many or more changes located in the selected background of character A."4 gains (out of 5 gains, 1 loss) on! 69 ways to arrange 2 gains and 0 lossesblack branches: p = 0.0638! 15 have 2 gains on black branches2. Maximum likelihood principles, and applications to discrete characters Maximum likelihood (ML) principles provide an alternative to parsimony in the reconstruction of phylogenies and estimation of ancestral states. ML also represents an important shift in thinking from standard probabilistic statistics. In standard statistics we focus on the probability of a given observation under a null hypothesis. If the actual observations are considered very unlikely, then we reject the null hypothesis. However, we don't actually accept a particular alternative hypothesis. For example, consider a t-test of the following observations: Treatment A: 5, 8, 10 (mean = 7.7, sd = 2.5) Treatment B: 8, 12, 15 (mean = 11.7, sd = 3.5) Null hypothesis: • Assume that observations represent a finite sample from a normal distribution (in other words, the process in the natural world that generates these data would generate a normal distribution if you collected an infinite sample) • assume that the means and variances of those distributions are equal in the two samples • if these assumptions are true, the probability of drawing two samples that differ by as much or more as the two above is
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