Species are biologically complex. The Merriam-Webster Online Dictionary define Complex as "a whole made up of complicated or interrelated parts", that is 'interrelated parts' that are "consisting of parts intricately combined". Species on the other hand are harder to define.
I will not define a species here. There are enough species concepts to go around and adding another one will not aid the growing problem of understanding species. The difficulty that many have with species is that they do not classify well. This presents us with a problem: if classification makes sense of complexity, then why can't we classify species? Why, for instance, do some claim species are never monophyletic? If species are presented by genealogical and therefore reticulated lineages that include ancestors and descendants, it will be impossible for us to classify them - to divided up related individuals into separate groups. The same argument can be made of genera and families too, but we are able to classify them. Why do species present us with this problem. The answer lies in what we mean by pattern and process.
A pattern is a repeating relationship. The character-states 0(11) for instance represent a relationship or homolog that relate the taxa A, B and C. If A = 0, B= 1 and C = 1, the relationship can be expressed as A(BC). If this taxic relationship occurs many times in different characters, it forms a pattern or homology. Process however is harder to define.
Returning to the Merriam-Webster dictionary we find the process means "a natural phenomenon marked by gradual changes that lead toward a particular result". For example, ontogeny is a process. What of the processes we are unable to see or measure? These processes can be discovered through patterns. The homology A(BC) is a discovery of evolution. That is a common and shared history. A 'hidden' process, such as the sexual behavioral traits of hadrosaurs is completely unknown to us (if they had any at all). We are able to model these traits based on assumptions, wild guesses or on the behavior of related living taxa such as birds. What ever result is generated (artificially produced) will never represent a discovery. We will never see such behavioral traits, so our models are merely speculations. The same is true for genealogical relationships. We only know who we are related to simply by observation, written documentation or by word-of-mouth. Through our DNA we are able to discover how similar we are to other people, either dead or alive, but we will never know if they are our direct descendants. Genealogy, as an unobserved process, is therefore often hypothesized. In order to make that process consistent we assign a rational hypothesis or explanatory mechanism. Genealogical relationships that move beyond our understanding (i.e., observation, recorded history etc.) rely on this hypothesized explanatory mechanism.
Explanatory mechanisms (unobserved processes) do not discover patterns. They generate artificial and ad hoc hypotheses. Observed processes however do. They provide a more robust explanation, but offer little in the way of a direct or trivial narrative (e.g., who begot whom).
Let us return to species. We assume that they are interbreeding classificatory 'units' real or otherwise. Species that are defined on an unobserved 'process' are mechanical. For some this helps conceptualize a species, for others it has little to do with classification.
Biological classification is based on patterns and the observed processes that help to uncover them. We may infer explanatory mechanism from patterns, but we will never be able to discover patterns from explanatory mechanisms. Species, as defined by explanatory mechanisms, have no place in classification. As arbitrary taxa (like genera or families), however, they make perfect sense.