I want to determine the phylogenetic age of the members of the Lepidoptera (Sphingidae) based on mtDNA, using BEAST software; But I do not have a good indicator. Please what is mutation rate in the mitochondrial genomes of the Lepidoptera (in million years)?
This paper has done a very good study of that question:
Papadopoulou A, Anastasiou I, Vogler AP.
Revisiting the insect mitochondrial molecular clock: the mid-Aegean trench calibration.
Mol Biol Evol. 2010 Jul;27(7):1659-72. doi: 10.1093/molbev/msq051.
Epub 2010 Feb 18. PubMed PMID: 20167609.
https://www.ncbi.nlm.nih.gov/pubmed/?term=Revisiting+the+Insect+Mitochondrial+Molecular+Clock%3A+The+Mid-Aegean+Trench+Calibration
It is not a simple answer. Different genes within the mitochondrial genomes evolve at different rates due to selection pressures, and different lineages of insects can also have different rates. But the paper discusses all of this and gives good estimates, and explains methods of getting estimates.
See also:
https://www.hindawi.com/journals/isrn/2013/491636/
Complete Mitogenomes of Euploea mulciber (Nymphalidae: Danainae) and Libythea celtis (Nymphalidae: Libytheinae) and Their Phylogenetic Implications
Keep in mind that all such estimates, if fossil calibrated, are minimums only. There is a lot of misrepresentation (if not actual lying) of these results as maximums or actual clade ages. And priors do not solve this as they are just guesses, not empirical evidence. Tectonic calibrations are estimates of actual dates, but have to be used critically as divergence may be older than a particular geological feature that superficially may seem to be correlated. There is a a good amount of published literature on this which needs to be consulted.
I would highly recommend to anyone interested in tectonic calibration to read 'Molecular Panbiogeography of the Tropics" (2012) and 'Biogeography of Australasia' (2014) as starting points. These books include hundreds of examples of tectonic correlation with extensive integration of phylogeny for an immense range of animal and plant groups, and also presents a critical account of the issues in molecular calibration. This is just the tip of the iceberg. As for molecular rates of divergence, there seem to be all sorts of models so you take your pick - assuming there is a molecular clock in any meaningful sense. Some have objected to tectonic calibration where it provides ages for a subclade that would then push the larger clade back into e.g. the pre-Cambrian. Of course they never consider that perhaps their clock model is erroneous. Primates provide an excellent example for tectonic correlation with group after group of distributions corresponding to major tectonic events of Mesozoic and Cenozoic time. Some molecular researchers fall back on the mystical 'I can't believe it' when tectonic ages considerably predate the oldest fossil, but other molecular researchers are quite happy when their fossil calibrated estimates considerably predate the oldest fossils. There is a lot of waffle thinking out there, but the fact is that the vast array of modern life shows tectonic correspondence with Mesozoic tectonics. That is the great reality. Fossil-calibrated molecular clocks were widely proclaimed to falsify that, but it was all smoke and mirrors.
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