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Extracting Meaning from a Tree • Rooted and Unrooted Trees •Comparing Trees: Tree Compatibility 03‐327/727 Lecture 2 •Next Up: Trait Evolution

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Extracting Meaning from a Tree • Rooted and Unrooted Trees •Comparing Trees: Tree Compatibility 03‐327/727 Lecture 2 •Next Up: Trait Evolution Outline •Tree terminology revisited Extracting meaning from a tree • Rooted and unrooted trees •Comparing trees: tree compatibility 03‐327/727 Lecture 2 •Next up: Trait evolution 1 2 Tree terminology reading Ultrametric trees • Understanding Evolutionary Trees Gregory, 2008. • Page and Holmes Ch. 2.1.1 ‐ 2.1.4, 2.4 2 •The rate of change is the same in all lineages 2 3 • Gregory •Page •The distance from the root to leaf is the same for all leaves 1 1 –Cladograms –Cladograms •The root is at the midpoint Warthog Pig Sheep –Phylograms – Additive trees between the two most distant – Chronograms – Ultrametric trees taxa. 3 4 1 Chronogram Ultrametric trees Root Ultrametric •The rate of change is the same in Branch lengths are proportional to time. all lineages 2 3 •The distance from the root to leaf The distance from root to leaf is the is the same for all leaves 1 1 same for every leaf. •The root is at the midpoint Warthog Pig Sheep Explicit time scale (typically in between the two most distant millions or billions of years) taxa. •Same rate in all lineages → branches are proporonal to me The rectangular shape makes it easy to align divergences with • Chronograms are ultrametric trees • chronological milestones • other points on the tree 5 6 Brady, S.G., S. Sipes, A Pearson, B. Danforth. 2006. Cladograms Cladograms versus Chronograms • Chronograms •Cladograms All branches are the same length – Branch lengths are –Branch lengths are proportional to time meaningless –All leaves end at the same –All leaves end at the same point point Each level is the same length Note that each level is the same length 7 8 2 Accurate time estimates can be difficult to obtain, even when fossils Cladogram evidence is available: Chronogram Data from timetree.org Capra, et al, 2014 9 10 Tzika & Milinkovitch 2008 Phylograms Phylograms are not ultrametric Branches are proportional to the amount of change (typically in substitutions per site). 2 3 Different rates in different lineages Distance from root to leaves is not uniform Pig 1 1 Horse Warthog Pig Sheep Tips, Leaves, Tapir Teriminal nodes Ultrametric Root Whale Phylogram tree (Page calls this an additive tree.) 11 12 3 Taxa that share more common ancestors are more closely related Similarity versus common ancestry •The pig is more closely related to the whale than to the horse 8 7 6 •The pig is more similar to the horse 5 4 than to the whale. Humans and chimps • share 8 common ancestors Pig 3 Horse • are most closely related 2 1 Humans and Lemurs Tapir • share 1 common ancestor • are most distantly related Whale 13 Similarity versus common ancestry Rooted and unrooted trees More closely related taxa are not guaranteed to be more similar unless the rate of change is • Midpoint rooting proportional to time. 2 3 •Outgroup rooting •The warthog is more closely related to the •The position of the root can have a big impact on pig than to the sheep 1 1 interpretation. •The warthog is more similar to the pig Warthog Pig Sheep •Visual representation of rooted and unrooted trees than to the sheep 16 17 4 Outline Unrooted trees versus rooted trees A rooted gene tree gives information •Tree terminology about the order of events. Rooted and unrooted trees •Comparing trees •Trait evolution An unrooted tree gives information about the relationships between taxa. 18 19 •There are as many possible roots as there are edges in the tree. •There are as many possible roots as there are edges in the tree. •Each of these is a different hypothesis about the order of events. •Each of these is a different hypothesis about the order of events. Baboon Marmoset Baboon Marmoset Tamarin Tamarin A different hypothesis Chimp One Hypothesis Chimp Human Human Lemur Lemur Humans are more closely related to Humans are more closely related to Marmosets than to Lemurs Lemurs than to Marmosets 20 21 5 How to root an unrooted tree How to root an unrooted tree 1. Midpoint rooting 2. Outgroup rooting When the rate of change is constant, the distance from root to leaf is the same for all leaves, • Ingroup: A set of taxa under study. → the root is the point that is equidistant from all leaves. • Outgroup: A taxon such that the relationship I between the outgroup and every member of the O If the rate of change is roughly the same in all lineages, place ingroup is more distant than the relationship the root at the point that is roughly equidistant from all leaves. between any pair of ingroup taxa. A good outgroup should be outside the ingroup, 23 but still close enough so you can compare them. 24 Outgroup rooting Outgroup rooting • Add 2+ outgroup taxa to the data set prior to inferring • Add 2+ outgroup taxa to the data set the tree. shark ray prior to inferring the tree. • The root is the node that connects the outgroup to the trout • The root is the node that connects ingroup. eagle the outgroup to the ingroup. shark ray ray • A good outgroup should be outside the ingroup, but still close enough so trout shark you can compare them. eagle trout eagle bat mouse • For example, sharks and rays are cartilaginous, not bony,fish. bat • Other good choices of outgroups mouse could be jawless fish or invertebrates. bat mouse A good outgroup should be outside the ingroup, 26 but still close enough so you can compare them. 27 6 Ingroup: dogs, Two representations of unrooted trees foxes The little pigtail at the top is just a drawing artifact. Outgroup: bears Radial trees Rectangular trees with a trichotomy at the top Frequently, unrooted trees that are drawn as though they were rooted appear in published 29 articles. Read the fine print! 31 American Why do unrooted trees have a trichotomy at the top? One of these trees is not like the others If we draw the same tree in rectangular A form, B ABDEF C R C D F E R A •the node at the top will have three B children (and three adjacent edges) A R •all other nodes have a parent and B D two children (and three adjacent In an unrooted tree, each internal edges). D node is adjacent to three edges. R E E C 33 F 35 C F 7 Outline Merging and Pruning •Tree terminology • Rooted and unrooted trees Comparing trees: tree compatibility •Next up: Trait evolution Prune 37 38 Compatibility Merge Two trees, T1 and T2, are compatible if there exists a tree that such that •some combination of pruning and merging operations will yield T1 and •some combination of pruning and merging operations will yield T2. 39 40 8 Trees A and B are compatible because both can be obtained from Tree C through merging and/or pruning Outline A •Tree terminology • Rooted and unrooted trees • Comparing trees: tree compatibility Next up: Trait evolution C B 41 42 Traits evolving on a tree A character is a heritable trait or “well defined feature that … can assume one or more mutually exclusive states”* * Graur and Li, Molecular Evolution, 2000 Introduction to characters & character state matrices States can be •Reconstructing ancestral states and evolutionary transitions –binary (yes/no) or multistate (blood type: A, B, O) •Why is it useful to know the ancestral state? – quantitative (weight) or qualitative (spotted) –Examples of questions we can address with ancestral –discrete (number of legs) or continuous (weight) state reconstruction • Properties of characters Examples: –Ancestral (basal) and derived states Character States – Monophyletic states eye color blue, brown, green •Why is it useful to know the ancestral state? mammary glands present, absent – Cladistics and classification number of legs 0, 2, 4, 6, 8, etc. 43 44 9 Character‐state table Character‐state table Example: Darwin’s finches Taxon 1 Taxon 2 Taxon 3 … Character 1 G. fuliginosa G. fortis C. parvulus … Character 2 Body size small medium small … Character 3 Diet seeds seeds insects … … Bill shape crushing crushing grasping … edge edge Bill tip biting … crushing crushing ……….… … 45 46 Another example Traits evolving on a tree • Introduction to characters & character state matrices Reconstructing ancestral states and evolutionary transitions •Why is it useful to know the ancestral state? –Examples of questions we can address with ancestral state reconstruction • Properties of characters – Ancestral (basal) and derived states Gorilla Chimp Human – Monophyletic states Fur Yes Yes No •Why is it useful to know the ancestral state? Weight (kg) Heavy Light Light – Cladistics and classification Tool use No Yes Yes 47 48 * Graur and Li, Molecular Evolution, 2000 10 Evolutionary change on a tree Evolutionary change on a tree •Given •Given –a tree –a tree –a set of characters that are variable for these taxa, –a set of characters that are variable for these taxa, –a character state matrix for the leaf taxa –a character state matrix for the leaf taxa •infer •infer –the character states of each ancestral node and –the character states of each ancestral node and –the state changes along each branch –the state changes along each branch • such the number of changes required is minimal Parsimony * Graur and Li, Molecular Evolution,51 2000 * Graur and Li, Molecular Evolution,52 2000 Use parsimony to infer ? • The ancestor was furry furry • Ancestral character states • (states on internal nodes) Fur was lost on the lineage leading to humans • Character state transitions ? (on branches) furry loss: fur Parsimony: Thrifty, stingy Assumption: The hypothesis that requires the fewest changes to explain the data is the best hypothesis. Gorilla Chimp Human Fur Yes Yes No Gorilla Chimp Human Wt Heavy Light Light Fur Yes Yes No Tool No Yes Yes use 54 56 11 • The ancestor was light (~50kg) light • The ancestor was heavy (~175kg) heavy • Increase in body mass on the loss: • Loss in body mass on the lineage body mass lineage leading to Gorilla leading to the common ancestor gain: body mass light of Chimpanzee and Human light … or … There may be more than one most parsimonious solution.
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