Monday, 12 October 2015

Natural sorting

You may have heard about natural selection. There's also natural sorting.

Sorting is a process which involves creating order out of disorder by rearrangement.

Sorting is ubiquitous in nature. There are pecking orders, lek rankings and dominance hierarchies. Rocks sort themselves by size on beaches and gasses sort themselves by density in the atmosphere.

In computer science, filtering and sorting get similar space on bookshelves. Knuth's epic volume 3 of The Art of Computer Programming is devoted to Sorting and Searching. This equal billing seems fairly reasonable to me.

However, sorting is rarely mentioned by physicists, biologists or evolutionary theorists. In evolutionary theory in particular, filtering seems to get all the limelight - while sorting is largely ignored.

I think the neglect of sorting is probably a case of terminology influencing thought. Selection is regarded as a central concept in evolutionary theory - while sorting doesn't enjoy the same status.

Whatever the reason for its neglect, sorting is a pretty important phenomenon. Environmental gradients are common (e.g. depth and altitude). Often organisms get sorted along the gradients - with the most competent organisms getting the best niches. For humans proximity to city centers results in an important gradient. The poorest humans get sorted to the outskirts by property prices - while a lot of courtship of the most desirable mates takes place in central locations.

Sorting and filtering are often combined in biological systems. Sorting is fairly often followed by filtering. In some cases the filtering is performed by mates - who choose the best partners they can find. In other cases, filtering is done by predators. For example, when a cheetah chases gazelles, the prey naturally sort themselves from fastest to slowest. The cheetah then filters out the slowest one.

It is worth noting that sorting has other effects on evolutionary dynamics that aren't much to do with sorting being a prelude to filtering. Consider assortative mating, for example. That's not really sorting followed by filtering - the sort itself is what affects the evolutionary dynamics.

It is possible to classify natural sorting into two main types based on the mechanism involved. Some types of sorting involve direct comparisons between neighbors. Others do not - and instead rely on different entities having different speeds or trajectories. Examples of sorts that do not involve direct comparisons between neighbors include the gazelle example above, electrophoresis and the ink diffusion spectrum phenomenon.

Sorting processes that involve neighbour copmparisons are dissipative: they create order and they need a power supply and generate heat. Sorting processes that don't compare the entities they are sorting tend to be more reversible. For example, a prism sorts light rays. However it isn't dissipative: the effect of a prism can be reversed by another prism. This observation suggests the names 'dissipative sort' and 'reversible sort' for the two categories of sorting processes.

Sorting is usually thought of as being a one dimensional phenomenon. However natural sorting also takes place in two and three dimensions. Here's a two-dimensional sort of ink pigments:

The dimensionality involved is not a defining characteristic of sorting processes.

It is sometimes possible to describe dissipative sorting operations in terms of selection. For example, when you shake your breakfast cereal, and the largest lumps rise to the top that process could be described as a series of many individual "selections" in which layers of the cereal act as porus sieves that allow small particles to fall through and select against large particles. This sort of re-description is possible for sorts that involve neighbor comparisons. It is usually less helpful to describe sorts that do not involve neighbor comparisons in terms of selection. Even where re-description in terms of selection is possible, describing sorting as a series of filtering operations is often long-winded and obtuse. It is best to simply describe sorting processes using the term "sorting".

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