Quite rightly, biodiversity is in the news a lot, but it is still greatly misunderstood. An important reason is that, as with 'information' we have one single word (actually a portamento term: biological diversity) to do many jobs. The term has a political significance where it summarises the living natural environment, especially represented by particular charismatic species, or habitats, especially if they are under threat of destruction. In its political / common language usage, biodiversity means both the significant species and the habitats in which they live; it might even mean beautiful landscapes. Certainly if you ask people on the street what biodiversity means to them (I have tried this), many will say things like "species like tigers and elephants that are going extinct" or "forests and butterflies etc.". Well, I am not going to criticise this, because I think it has an important role in representing the living natural world as people experience and think of it. All that is important.

"The variability among living organisms from all sources including, terrestrial, marine and other aquatic ecosystems and the ecological complexes of which they are part; this includes diversity within species, between species and of ecosystems."  CBD Article 2. UNEP 1992.


But scientists who want to measure the diversity of life and understand what determines it and what it affects, they need to have a more precise definition that is quantitative and unambiguous.



Biodiversity as total Difference

Diversity has become one of those politically loaded words. It is the legal and moral obligation of organisations in many countries of the world to meet a minimum standard of 'diversity' in their workforce. Many organisations say that it is in their best interests to build and maintain a 'diversity of talents' and policy makers might claim to consider a 'diversity of views'. In every case, the word 'diversity' is being used as a sort of euphemism for differences that matter. The reason for the rather tangential language is that for differences to be identified, as a requirement for quantifying them, people have to be categorised and that is considered impolite in modern culture.

Imagine a bag of objects which you can take out one by one and place on the table: what you take out will be a sample of the objects in the bag. Let’s say they differ in colour, shape and size. So your first object might be a large round blue ball and the next might be a small green cube, etc. The sample will contain a set of objects that can differ in three different ways: each of these is an axis of diversity. If the sample contained just two objects, then there can be at most three different ways in which its component parts differ (one for each pair-wise comparison, for each category of difference).
How much information is needed to describe the two-object sample? The answer is three bits (one for each difference). The information content of the sample (in these terms only) is identical, it is three bits. This information content escalates rapidly as we take a larger sample. Suppose there are at least three colours, at least three shapes and at least three sizes. Then with a sample of 3 objects there can be as many as nine differences among the objects, and as few as none (if all the objects extracted from the bag are the same). The probability of the number of differences in the sample depends on the number of categories defined for each dimension of diversity: this is termed the number of levels. Notice now that we are describing a situation that is mathematically equivalent to the one used to explain thermodynamic entropy in terms of the number of ways of arranging the state of the system - termed  the multiplicity - which is expressed as via a probability distribution.