Stochastic extinction is extinction caused by chance fluctuations (in births and deaths, in gene frequencies, and in the environment, including its rare extremes) rather than by a deterministic decline to zero. The phrase is an umbrella over two classes of randomness: environmental fluctuation, which is external to the population and whose rare extremes (“catastrophes”) are the tail of that same distribution rather than a separate class; and demographic accidents, which are internal and unavoidable in finite numbers, comprising the vagaries of birth and death, and the loss of genetic variability. It also covers a separate palaeontological usage in which “stochastic” instead means extinction non-selective with respect to traits. Most productively it is a population-level idea: even a population with, on average, a positive or stable growth rate can be lost to chance once it becomes small, so that stochastic extinction is best read as a probability: the chance, over a stated horizon, that a self-replacing population completing its full life cycle in the wild is no longer attainable. Whether a given decline is labelled “stochastic” or “deterministic” frequently depends on the scale and time horizon of observation rather than on the biology itself. The term therefore requires four things to be stated: the source of randomness, the biological scale (individual, population, metapopulation or clade), the time horizon and whether the claim concerns an underlying process or an observed pattern.

When describing the status of a species, extant and extinct are well defined: ‘existing’, and ‘no longer in existence’, respectively. What is the appropriate term, however, for a species that is extant, but whose abundance has dropped to an exceptionally low value? In practice, we tend to describe this species as ‘nearly extinct’, or similar. Terms such as ‘rare’ and ‘endangered’ have multiple meanings, but none address ecological functions. Also, in conservation biology, when we ask ‘what drove a species extinct?’, we do not mean ‘what killed the last individual?’ – we mean ‘what drove a species’ population size so low that extinction was likely?’. There is no term for this, so we rely on imprecise wording and assume that the reader knows what we mean. Banks proposed the term ‘extaille’ to fill this void (pronounced ex-tayl). Extaille is the status of a species whose abundance has been reduced so much that it no longer functions as a significant part of its normal ecosystem; “extation” refers to the condition of becoming extaille. These terms have not caught on in the scientific literature, and I recommend against them. Use of this jargon could hurt communication outside the discipline, and a term like “functionally extinct” (or similar) better meets our needs.

Processes of extinction, especially selectivity, can be studied using the distribution of species in morphospace. Random extinction reduces the number of species but has little effect on the range of morphologies or ecological roles in a fauna or flora. In contrast, selective extinction culls species based on their functional relationship to the altered environment and, therefore, to their position within a morphospace. Analysis of the distribution of extinctions within morphospaces can thus help understand whether the drivers of the extinction are linked to functional traits. Current approaches include measuring changes in disparity, mean morphology, or evenness between pre- and post-extinction morphologies. Not all measurements are straightforward, however, because morphospaces may be non-metric or non-linear in ways that can mislead interpretation. Dimension-reduction techniques like principal component analysis – commonly used with highly multivariate geometric morphometric data sets – have properties that can make the center of morphospace falsely appear to be densely populated, can make selective extinctions appear randomly distributed, or can make a group of non-specialized morphologies appear to be extreme outliers. Applying fully multivariate metrics and statistical tests will prevent most misinterpretations, as will making explicit functional connections between morphology and the underlying extinction processes.