 The first concept here is important. Two proteins or two genes, you can use them interchangeably here. Two genes that are evolutionary related are called homologs. And I would even make it clear, I would say that they have a common ancestor. The important part here is this is a binary definition. It's like being pregnant. Either you are pregnant or not pregnant, you can't be a little bit pregnant. Two sequences are either homologs or not homologs. Now we might not be able to detect that two sequences are homologs. But if we knew the answer, the ground truth, we should be able to say there is a common ancestor or there is not a common ancestor. But there are two ways proteins can be related. One of them is that assuming that at some point in the past we had a common ancestor. And then we had a so-called speciation event. Something large happened with the chromosomes so that say that the Neanderthal and the Homo sapiens split. Now if I happen to have a protein here for a gene, let's say it's called G, then I might have G here and G prime here. One of them has changed. Again, they end up in different species. When things are in different species, we call them orthologs. It's due to speciation, but they have the same function. So hemoglobin in llama, hemoglobin in me, hemoglobin in horse, and hemoglobin in whatever, guinea pig. They're orthologs. We're different species but they perform the same function. The other alternative is that I can stick to a single species. But at some point my protein G is duplicated. So I might have both G and G prime. That's how nature ends up reusing things. I'm not sure if we have a great example. Myoglobin and hemoglobin are hemoglobin have four subunits, but the individual gene in hemoglobin is similar to the individual gene of myoglobin, one subunit, but they don't perform exactly the same function. They are so-called paralogs, which comes from gene duplication. So they perform different functions in the same organism. Nature uses both these things, and it can even happen that you first have a so-called gene duplication so that things become paralogs. Then at some point things split off in evolution. Now you have two copies in each species, but then evolution might gradually get rid of one copy. So again, this might not be entirely easy to detect in practice. If there is only one thing you're going to remember from this slide, it is homologs. Homology is an exceptionally important concept, and much of what I'm going to talk about the rest of this lecture relies on ways that we can detect and talk about homology. So homologs have common ancestors. It's not that they are similar because similarity can go from 0 to 100 percent. Homologs is binary. They have a common ancestor.