Some sticky issues Short branches and ortholog/paralog inference Short branches and rearrangement Species tree Multiple roots Let’s first review how unrooted trees lead to uncertainty.

Very short branches imply non-binary nodes FA HA1 MA1 HA2 CA2 CA1 Sometimes, the sequence data does not provide enough information to be able to determine what the true, binary branch pattern is at some node and so the reconstruction program will produce such a node to represent uncertainty. FA HA1 MA1 HA2 CA2 CA1

Alternate Hypotheses FA HA1 MA1 HA2 CA2 CA1 FA CA1 MA1 HA1 CA2 HA2 FA Here is what I mean by the true, binary branching pattern. With this tree, the sequence data does not provide enough information on exactly how chicken, mouse, and human A1 are related. The non-binary node that joins these three actually represents three different binary trees. (Click) In the first case, the Chicken and Mouse A1 gene are more closely related than either is to the Human A1 gene. Can anyone guess another possibility? (Yes/no. click). It is also possible that the Chicken and Human A1 genes are more closely related; or that the Human and Mouse are more closely related. Thus, a non-binary node indicates uncertainty in which possible series events occurred. This example showed a trifurcation (or non-binary node with 3 children) and had only 3 distinct possibilities. But this node could have had 4 or even 5 children. How many different hypotheses would that non-binary node then represent? CA1 MA1 HA1 CA2 HA2 FA HA1 MA1 HA2 CA2 CA1 FA HA1 MA1 HA2 CA2 CA1

Each alternate hypothesis yields a different set of orthologs FA HA1 MA1 HA2 CA2 CA1 D Orthologs: (MA1,CA1) Paralogs: (HA1,CA1), (HA1,MA1) Orthologs: (HA1,CA1) Paralogs: (MA1,CA1), (HA1,MA1) Here is what I mean by the true, binary branching pattern. With this tree, the sequence data does not provide enough information on exactly how chicken, mouse, and human A1 are related. The non-binary node that joins these three actually represents three different binary trees. (Click) In the first case, the Chicken and Mouse A1 gene are more closely related than either is to the Human A1 gene. Can anyone guess another possibility? (Yes/no. click). It is also possible that the Chicken and Human A1 genes are more closely related; or that the Human and Mouse are more closely related. Thus, a non-binary node indicates uncertainty in which possible series events occurred. This example showed a trifurcation (or non-binary node with 3 children) and had only 3 distinct possibilities. But this node could have had 4 or even 5 children. How many different hypotheses would that non-binary node then represent? All three are orthologs FA HA1 MA1 HA2 CA2 CA1 D FA HA1 MA1 HA2 CA2 CA1

Some sticky issues Short branches and ortholog/paralog inference Short branches and rearrangement Species tree Multiple roots Let’s first review how unrooted trees lead to uncertainty.

Rearrangement will prefer hypothesis 1, but is that a better choice? CA1 HA2 CA2 HA1 FA CA1 HA2 CA2 HA1 FA Rearrangement will prefer hypothesis 1, but is that a better choice? In this case, the rooted gene would be this. Notice that this rooting dramatically changes the interpretation of the data; however, the rooted tree still has the same relationships between the genes as the unrooted tree. For example, the A1 subfamily still groups together in both trees. So how many different rooted trees are there? (Get answer from audience). D D Hypothesis 1: FA HA1 HA2 CA2 CA1 Hypothesis 2: FA HA1 HA2 CA2 CA1

Some sticky issues Short branches and ortholog/paralog inference Short branches and rearrangement Species tree Multiple roots Let’s first review how unrooted trees lead to uncertainty.

Baldauf, Science 2003

General agreement on unrooted Eukaryotic tree Dictyostelium Animals Fungi Plasmodium Plants Here again is the gene tree created from the multiple alignment of those 6 genes – one from fish and mouse, two from chicken in human. If we knew what really happened, we’d know where the root is, we’d know the real order of events. There are many possible locations for the root in this gene tree. One hypothesis is that the root is located somewhere along this edge, leading to the Fish A gene. If so, This would be the rooted gene tree. However, another hypothesis may be that the root is really located along this edge, leading to the chicken A2 gene.

Cavalier-Smith’s root

Arisue’s root

Some sticky issues Short branches and ortholog/paralog inference Short branches and rearrangement Species tree Multiple roots Let’s first review how unrooted trees lead to uncertainty.

Beta Crystalin family CrybB2 Notung: All bold branches have the same score CrybA2 Crybb2 CrybA4 CrybA3 CrybB1 CrybA1 Ruvinsky and Silver, Genomics, 1997

Beta Crystalin family acidic basic Ruvinsky and Silver: Root provided by biochemical information acidic basic A2 A3 A1 B3 B1 A4 B2 This example suggests that we can devise a mathematical cost function for scoring possible rootings based on this notion of duplication and loss.