The operator theory has various practical application in biology. Firstly, it identifies levels of organisation that can be linked to properties of organisms. Secondly, it offers a clear definition of a -unitary- organism. This facilitates the analysis of 'cooperations' between organisms (e.g. colonies, symbioses, etc.). Thirdly, by offering a definition of life, the operator theory assists biologists with the description of their discipline (the 'bio' part of 'biology'). A description of what falls under biology is practical when it comes to the answering of questions such as: "do viruses belong to biology?".


The pursuit of complexity. The utility of biodiversity from an evolutionary perspective.
Jagers op Akkerhuis G.A.J.M. (2012). KNNV Publisher, 120 pp.And as E-book: Filosofieboeken XXL
Towards a hierarchical definition of life, the organism, and death.
Jagers op Akkerhuis G.A.J.M. (2010). Foundations of Science 15: 245-262.
Analysing hierarchy in the organisation of biological and physical systems.
Jagers op Akkerhuis G.A.J.M. (2008). Biological reviews 83: 1-12

1: The layered construction of organisms
A property of the operator theory is that if identifies different levels of organisation of organisms. Accordingly one can identify: 1. bacteria (the 'prokaryote unicellulars'), 2. the singel celled endosymbiont cells (the 'unicellular eukaryotes'), 3a. the multicellulars (e.g. the bluegreen algae), 3b. the endosymbiont multicellulars (e.g. plants, fungi, algae, non-neural animals), and 4. the organisms with a neural network. Every next level of organisation in this sequence inherits most properties of the lower level organisations that take part in its construction. New, cooperative properties are added with every next higher level organism.

Levels of operators in organisms.jpg
Figure 1: Levels in the internal organisation in organisms. Levels that correspond with the operator types are indicated in yellow.

Figure 1 shows that every organism has many internal parts. Certain types of these parts (as well as the types of the organisms) correspond with types in the operator hierarchy (in yellow).Other parts (in white) are relevant aspects of the internal organisation as well, but do not correspond with operator types.

The information in Figure 1 offers a useful tool for the study of stress ecology. This is because every internal aspect can be viewed as a target for a stressor. Such a viewpoint is relevant for example in ecotoxicology, where toxicants either affect targets directly (a toxicant molecule can for example bind to an enzyme) or indirectly, via chain reactions that affect other targets in the organism. It is noteworty that the information in Figure 1 contributes to the science of ecotoxicology, because it adds extra information and structure to the analysis of levels of internal organisation. For this reason, Figure 1 extends the standard one-dimensional 'ecological hierarchy', which is much used in eco(toxico)logy handbooks (e.g. from atoms, to molecules, cells, organs, organisms, population, communities, ecosystems, planets, etc.)

2: A contribution to the understanding of interactions between organisms, such as colonies and symbiosis
The operator hierarchy allows the identification of organisms with different kinds of organisation. Such information can be used to get a clear picture of what is a (unitary) organism, and how unitary organisms can cooperate. This may assist in solving problems with the demarcation of the moment when a group of interacting organisms leads to a new organism, to a colony of attached organisms of the same species, or to a coloy of 'attached' organisms of different species (e.g. a symbiosis). From the viewpoint of the operator theory, a group of non-attached organisms always remains a group, and does not become an organism. People sometimes use the word "superorganism" for forms of interaction such as a bee colony, or plants with mycorriza. Yet in the viewpoint of the operator theory, the concept of (unitary) organism shows a one-to-one relationship with the concept of an operator. All other forms of organisation are viewed as different forms of interactions between organisms.

3: What is biology?
The operator theory assists in definig what is biology. Biology means 'bios-logeia', or "the discipline that studies life". To define life from the ground up, the operator theory suggests to first define the operators and their hierarchy, then select all the operator types that are viewed as organisms, and finally define life as the presence of the typical closure in organisms (hereby excluding closures in lower level operators from the considerations). Following this definition of life, biology becomes the science that studies properties of organisms (defined from the ground up), regardless whether these are active (alive, living) or inactive (frozen, dissicated). From this point of view, an organism cannot 'be dead', because a 'dead organism' no longer classifies as an operator (it is a 'corpse'), and hence does not represent life. Using this basis, one can now define related disciplines, such as ecology, toxicology or ecotoxicology.

The position of viruses in biology is a long discussed topic. Do viruses belong to biology? Or are they 'just molecules'? When discussing this matter one can distinguis two subjects. The first subject is whether or not viruses should be studied in biology. Because biology studies all aspects of organisms, and because viruses do invade organisms and affect their physiology, it seems reasonable to answer this first question affirmative. The second topic is whether or not viruses belong to the realm of biology because they are organisms. Now one may like to distinguish two extremes of viral complexity: 1. a 'bare' virus and 2. a virion. A bare virus is nothing more than an RNA or DNA molecule. And according to the viewpoint of the operator theory, such a molecule lacks the required closures for being classified as an organism. Accordingly it does not belong to the realm of biology. A much more complex example is that of a virion. A virion is a bare virus that is 'packed in'. It consists of a DNA or RNA molecule, which is surrounded by a protein coat (the capsid), which can be surrounded by a membrane (the envelope). Even with capsid and envelope, however, a virion still lacks the required closures (that is, if we apply the viewpoint of the operator hierarchy), for which reason it does not classify as an organism. This implies that while viruses play an important role in biology, and are relevant for biology because they affect organisms, the operator theory suggests that they fall outside the conceptual limits of biology as a scientific discipline, because viruses fail to classify as organisms and as life.