Nestedness is a measure of order in an ecological system, referring to the order in which the number of species is related to area or other factors. The more a system is "nested" the more it is organized.
Imagine island communities at different distances from the mainland. Then we would expect islands farther away to contain fewer species, and these species to be present on all islands that are closer to the mainland. In this case, the species-island-matrix would be highly nested (the matrix has a lowest nestedness temperature: it is 'cold'). If, on the other hand, all species have the same dispersal ability, population size etc. on the mainland, then island communities might simply be random draws from the mainland pool, and the species-island-matrix would not display any significant nestedness (it is 'hot', i.e. in maximum entropy).
One measurement unit for nestedness is a system's 'temperature' offered by Atmar and Patterson in 1993.[1] This measures the order in which species' extinctions would occur in the system (or from the other side - the order of colonizing a system). The 'colder' the system is, the more fixed the order of extinction would be. In a warmer system, extinctions will take a more random order. Temperatures go from 0°, coldest and absolutely fixed, to 100° absolutely random.
For various reasons, the Nestedness Temperature Calculator is not mathematically satisfying (no unique solution, not conservative enough.[2][3] A software (BINMATNEST) is available from the authors on request and from the Journal of Biogeography to correct these deficits [4] In addition, ANINHADO resolves problems of large matrix size and processing of a large number of randomized matrices; in addition it implements several null models to estimate the significance of nestedness [5] and [6]