can i insert the outgroup sequence with the input sequences or no, and how we choose the correct outgroup ?
I think your question makes some assumptions about outgroups that I hope the following will make clearer.
Firstly, phylogenetic inference methods output unrooted trees, and assigning an outgroup or the position of the root is an arbitrary decision made by the human, not by the computer. The output might display what looks like a rooted tree, but to the computer, all trees have no polarity.
An outgroup is not inserted into a tree, but data (from a taxon that the experimenter regards as an outgroup) is added to the matrix, and a tree is inferred from that. It is only post-hoc that this outgroup provides polarity (a root) to the tree.
In practical terms, adding an outgroup is a case of adding another (one or more) taxon / species / OTU to your alignment or other matrix. Ideally (but experiment dependent) you would have multiple outgroups of different evolutionary distances from your group of interest, to confirm that they cluster as an outgroup, and to minimise long-branch-attraction biases.
For example, if I was making a phylogeny of cats from some ultra-conserved genes, I could use the sequence from the same gene in an algae as an outgroup. That sounds reasonable, but it would be problematic for two major reasons [1] it would be difficult to convincingly identify a sequence as an ortholog rather than a paralog, and [2] the algae is so distantly related from a cat that any fast-evolving lineages of cats might, through chance, be erroneously identified as being more closely related to the algae than other cats. A better outgroup would be, say, a dog -- or better still multiple dog-like outgroups (say, a wolf, a coyote and a hyena) with a similar spread of variability as your group of interest (say, a lion, a cheetah and a puma). Having phylogenetic proximity allows for easier alignment, stronger inference, and less disruptive influence on your inference methodology (which could be skewed by highly-unrelated outgroup matrix information).
In short, your outgroup should have the same characteristics as your ingroup, and be as closely-related but uncontrovertially-not-ingroup as possible - if that makes sense! Preferably, the outgroup should also be as large as you can make it, not just a single taxon. The same applies for genes, if you are making a gene tree. Your outgroup should be reasonably closely related to your ingroup for all the same reasons.
How to choose a suitable outgroup is entirely experiment dependent - and can be very difficult. For the above trivial example, choosing a dog as outgroup to cats is not problematic because there are several evolutionary reasons to reject the possibility of dogs actually being a type of cat. For genes such clarity is rare. This is especially so for complex situations where horizontal gene transfer, genome duplication, and other reticulating effects may be at play: choosing a suitable outgroup can be extremely difficult and require in-depth experimentation and rationalisation.
Hope that helps :)
I agree with Alastair R Tanner. He has presented a comprehensive answer to this question.
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