Considering that the available studies on sexual dichromatism have used methods that can create a bias in estimates (Maia & White, 2018), here we address the possibility of finding non-equivalent results between the different methodological approaches now available for comparing colour among sexes in monochromatic bird species for the human vision, and whether the distribution of sexual dichromatism in passerine bird species, as revealed by novel methods, is related to the evolution of different colour plumage patterns (e.g., conspicuous and camouflaged). Since conspicuous traits are thought to be sexually selected, it has been suggested that colorful plumages are often under directional selection for greater elaboration in response to male competition for access to mates (intrasexual selection) or mate choice (i.e., intersexual selection) (Kirkpatrick, 1982; Prum, 2012).

Are you sure that ALL studies have used biased methods? If not, it is better to say "Considering that most studies on..." OR "Considering that the available studies on s.d. have, in general, used methods..."

Studies on [not "of" The study of medicine is okay. But for specific studies, it is better to say The study on sexual dichromatism or plural There have been many studies on...]

between the different methodological approaches now available for comparing colour among sexes in monochromatic bird species for  the human vision: Unclear. Not sure what you are trying to say here. If you say "between" then the reader is expecting two things: "Between this and that". 

As revealed by novel methods: added this between commas to give structure to the sentence.

You first use "Colour" but then you use "colorful". To remain consistent you should use Colour and Colourful (British) or Color and Colorful (American)