Biological diversity is not a continuous cloud of variation, but rather appears strongly bundled into clusters of organisms notably alike in their genes, structures and ecology. This is enough to justify the working taxonomist's pragmatic approximations of species, but to play fruitful and precise roles in biology, these units need to match important components in our evolutionary or ecological models — they need to be actors in, or notable products of, nature's processes. For example, in our models of evolutionary process, a genetic community (e.g., an interbreeding population) acts as a unit, having stochastically-predictable behaviour that produces particular patterns of genetic diversity. In phylogenetic biology, minimal monophyletic groups are products of evolution that serve as building blocks for our historical reconstruction. These (and other process-relevant units) yield concepts of species that can each play a central role in our understanding of how life functions or is structured, but each might lead to different delimitations of groups of individuals. The degree of this discordance is poorly characterized, but to the extent that it arises from differing interests of biologists, it is not easily resolved.
There is a second sense of discordance: contradictions among patterns pertinent to a single species concept. This is especially evident in concepts that define species as outcomes of an evolutionary process, either as fragments of a realized history (e.g., minimal monophyletic groups), or stepping even further toward operationalism, as sets of individuals sharing features. Incomplete lineage sorting can cause different genetic loci to show contradictory patterns as they descend within genetic communities, yielding a discordance among genes that makes simple pattern-based species concepts either ambiguous or arbitrary. Under alternative concepts that view species as actors in a model of process, such tangled outcomes may complicate our inference, but they do not necessarily compromise the discreteness of the species themselves — discrete evolutionary actors can produce tangled patterns.
Should species be actors in a model of process (i.e., the causes), helping to explain our observations of phenotypic diversity, or should they be the products (i.e., the effects), to be explained by our models? Regardless of our decision, the varied (and important) concepts can be used regardless, with different labels, in their respective domains. Applying the taxonomist's pragmatism to the theorists' modelling, one could seek a single umbrella species concept with the largesse to accommodate several more precise ones, but the units so defined would likely not serve precisely enough in models and explanations, either as actors or products.