The problem of measuring complexity in nature is not a well defined problem. We can, at most, define and measure complexity of our descriptions of nature which are always incomplete and, in consequence, I don't think we have any hope to come out with a complete theory of complexity in nature. Considering that any description can always be seen as a sequence of symbols of a given alphabet, Kolmogorov's not computable measure of complexity (Kolmogorov A.K. (1958)., Dolk. Akad. Sci USSR 119: 861) can be used to, at least, define a mathematical measure of the complexity of those descriptions. A simplified approach to measure complexity was given by Chaitin G.J. (1990) Information, Ramdomness & Incompleteness (Papers on Algorithmic Information Theory), World Scientific, Singapore, which has been used by some authors to measure complexity of DNA sequences and proteins. I find both approaches to be unsatisfactory: the first because Kolmogorov's measure is not computable (http://www.cs.princeton.edu/courses/archive/fall11/cos597D/L10.pdf) and the second because Chaitin's approach is based on a simplification, where a context free grammar that generates the given sequence and only the given sequence is used to measure complexity. At this point the most reliable measure of complexity might be entropy, but there is a degree of conceptual difficulty in defining the entropy of an individual sequence see for example http://www.newton.ac.uk/programmes/SAS/ccr2012_booklet.pdf.