successions

Successions is a term used in several disciplines to describe ordered progressions or transfers that unfold over time. In everyday use it often refers to sequences in mathematics, but it also appears in ecology and law, among other fields.

In mathematics, a succession (or sequence) is an ordered list of elements, usually numbers, indexed by natural numbers. The nth term is denoted a_n, and a rule or formula determines each term. A succession can be finite, having a last term, or infinite, continuing without end. Common examples include arithmetic progressions, where a_n = a_1 + (n−1)d, and geometric progressions, where a_n = a_1 r^{n−1}. Many properties of successions concern their behavior as n grows large, such as monotonicity, boundedness, and convergence, where a_n approaches a limit L. Subsequence refers to a new succession formed by choosing certain terms in order of increasing indices.

In ecology, ecological succession describes the gradual change in species composition and ecosystem structure after a disturbance or the creation of a new habitat. Primary succession begins on substrate devoid of life, such as bare rock, while secondary succession occurs where soil remains after a disturbance. Early stages typically feature pioneer species like lichens or grasses, followed by intermediate communities and eventually a more stable climax community. The process is influenced by climate, soil development, and disturbances such as fire or inundation.

In law, succession concerns the transfer of property, titles, and duties upon a person’s death. It includes mechanisms of testate succession (according to a will) and intestate succession (without a will), and may involve executors or administrators who manage estate distribution. Dynastic or institutional contexts may also describe forms of succession.