For many, classification is shrouded in mystery and questions such as ‘How do taxonomists find all those species?’ have led philosophers of science to discuss species concepts rather than how taxonomists actually discover natural entities. The same is true for monophyletic taxa in general: much is made of defining monophyletic taxa rather than discovering them. Ask a room full of systematists to define monophyly and there will probably be at least five different definitions (see Vanderlaan et al. 2013). Yet, every single one of those individuals will most likely be able to identify the same monophyletic taxon. All that said, it seems what systematists say they do is often not what they do (sensu Medawar [1967] 1968, epigraph above; see also Winsor 2001), discovering monophyly being a case in point.

We will treat the terms monophyly and monophyletic group in more detail in Chapter 7. Briefly, it refers to a taxon characterised by at least one synapomorphy (also further discussed in Chapter 7). Many recent definitions of monophyly have been based on ancestry. This book is focused on classification, so here monophyly is considered to be an empirical concept, matching evidence to conclusions. Monophyletic groups are taxa; but not all taxa are monophyletic – they are, for the most part, assumed to be so.

In Chapter 2 we noted some differences between natural and artificial classifications. To recap: artificial classifications are created or imposed and often constructed so that those who do not know a particular organism are able to identify it. Natural classification is about discovery; discovering something about the natural world (of which more later). The usual kinds of artificial classifications are keys and field guides (see Chapter 2), but here we extend the term to include classifications found by using any specific method, or any specific algorithm, or any specific kind of data, even a combination of the above. This may seem an extreme position to take, one that would eliminate all methods of analysis as having any merit. This is not what we are stating and we will expand on this below, but first we begin by considering ‘sets’ of numerical methods and discussing what we understand to be their underlying philosophy. We do not intend to discuss in detail the technical workings of all those methods. As we have already noted, we are not writing a cookbook.

Our first example is from the Australian Richard Flanagan’s novel The Narrow Road to the Deep North, which won the Man Booker Prize in 2014. Flanagan’s novel is primarily about suffering and survival, surviving the enforced building of the Thailand–Burma Railway (the ‘Death Railway’) during World War II; the survival of the Australian prisoners of war who built it.

The phrase in the title above – ‘carving nature at its joints’ – comes from Plato’s Phaedrus asking how and why people ‘carve-up’ and partition the organic world in the way they do. In short: “How do we classify the world?” There are, of course, many ways to classify, but the central question for biology is why are some groups of organisms, such as birds, recognised as real groups, when others, such as invertebrates, are rejected as such? This, of course, begs an additional question as to what ‘real’ might mean in terms of classification.

In 1972, Edward N. Adams III published what might be the first paper on consensus techniques for use in biological classification. He addressed the following question: ‘… can we combine the information from rival classifications into a new, hopefully more accurate classification? Such a consensus of the rivals is useful both in tree comparison and tree discovery’ (Adams 1972, p. 390). Since Adams’ paper, nearly half a century ago, numerous consensus tree techniques have been proposed, numerous critiques of each have been published and an almost infinite number of suggestions have been made as to how to use one of them, some of them, any of them, all of them, or none of them (Bininda-Emonds 2004a, 2004b). Alongside this avalanche of technical detail are discussions concerning supertrees (which are a form of consensus analysis) and supermatrices, the latter being an extension of the ‘combining data’ debate (Sanderson et al. 1998, see the following Chapter 10). Again, as with the methods of data analysis described in Chapter 8, we do not intend to discuss each and every consensus technique in detail but deal with what we understand to be the basic issues (on the details of consensus methods, we make some suggestions in the Further Reading section below).

A cladogram is simply a branching diagram (the word is derived from the Greek klados meaning branch); it is non-reticulate; it summarises current knowledge about organisms (Nelson 1979). A cladogram relates all taxa, fossil and Recent, based on evidence derived from organisms and their parts (homologues) and, ultimately, their interrelationships (monophyly, homology). The branching aspect (the specific relationship) is referred to as its cladistic parameter (Nelson 1979, p. 12; Williams & Ebach 2008).

Part of the problem of species delineation is the fact that morphology, as an approach for delimiting species, has some limits. Traditional morphology-based taxonomy only discriminates what Cain (1954) called ‘morphospecies’, i.e. species exclusively established on morphology … Traditional morphology-based taxonomy is not the study of life’s diversity per se, but rather the study of one of its multiple facets, morphological diversity, which I refer to as ‘morphodiversity’.

A significant debate in systematics that began in the late-1970s, developed in the mid-1980s and still with us today is the discussion on the use of what was initially called the ‘Total evidence versus Consensus’ debate. The essence of the debate can be captured with two contrasting approaches to systematics, whether to combine evidence or keep it partitioned.

From the preceding chapters – and the wealth of literature on the subject – one thing seems clear: different solutions to systematic problems are possible from different methods, whether those methods are directed toward the analysis of raw data or the analysis of cladograms (consensus). Once again the issue is whether the solutions found (by whatever means, data or method, or combination thereof) represent aspects of the natural world or include artefacts of the methods used.

In the preceding chapters we discussed the classification and relationships of a few animals and plants. We discussed these in relation to what can be referred to as derivative cladograms sensu Nelson: ‘a graphic representation of a hierarchical classification’ (Nelson 1979, p. 5; see Chapter 7). In some we provided a written classification. For the box jellyfish Malo kingi (see Chapter 2), for example, an indented written classification, with ranks, would look something like this

Haeckel’s genealogical project began in 1866 with his monumental two-volume Generelle Morphologie der Organismen (Haeckel 1866), written partly under the influence of Darwin’s Origin of Species (Darwin 1859), terminating some 30 years later with another equally exhaustive survey – this time in three volumes: Systematische Phylogenie: Entwurf eines natürlichen Systems der Organismen auf Grund ihrer Stammesgeschichte (Haeckel 1894–18961).