Yes you can concatenate them but will no doubt need different models of sequence evolution for each gene. Always separately analyze different genes to determine the information content of each gene. Evaluate them separately to find the respective best models.

Yes, it is possible and recommended. In addition I would recommend to use a species tree approach (such as *BEAST) as it takes into account the unique evolutionary trajectory of each marker.

Thank you so much for providing answers. I greatly appreciate your input, and I will definitely consider your recommendations and suggestions when it comes to concatenating mtCOI and nuclear genes.

Again, thank you so much Denis Copilaș-Ciocianu and Patrice Showers Corneli

Denis Copilaș-Ciocianu

Thank you for your suggestion. Do You mean smth like this? Article STELAR: a statistically consistent coalescent-based species ...

May be You could suggest something to read?

Thank all of You for information and help!

Dear Ulyana Simakova

Here is a great tutorial (with references) for estimating species trees with *BEAST: https://taming-the-beast.org/tutorials/StarBeast-Tutorial/

Denis Copilaș-Ciocianu

Thank You a LOT!!!

I would warn here that there are proved cases of mitochondrial or nuclear introgressions when one species in course of secondary hybridization picks up picks up the other's. As the result they look as a single species on a mitochondrial tree, but may be quite far on a "nuclear" tree. The most famous case is the romantic history of brown and white bears. In case of joining sequences one would obtain weird results while using BEAST or any other software with the merged dataset. On as smaller scale (say, intraspecific) the danger is less, but there is other thing: mitochondrial Ne is 4 times smaller with all strange consequences like "artificial bottlenecks" on a mitochondrial tree. So you may still use the merged data sets, but you are warned.