Where does viability collide?

In cell biology, viability is the proportion of cells in a sample that are alive and intact. Pappenheimer's 1917 Experimental studies upon lymphocytes reported that living cells keep the dye trypan blue out while dead cells let it in, which turned staining into a count of the living. Strober's 1997 Trypan blue exclusion test of cell viability set out the standard bench protocol still used to report a percentage of live cells. Here the referent is the fraction of a cell population that is alive at one moment, not a firm that survives, a wildlife population that persists, or a path that stays inside a mathematical boundary.[1][2]

Unit

A fraction of live cells in a sample, usually a percentage

Recovery means

Not applicable

Measured by

Counted by dye exclusion (trypan blue), or by assays of membrane integrity, metabolism, or replication

In applied mathematics and control theory, viability describes whether a system's path can stay inside a set of allowed states for all time. Nagumo's 1942 theorem on the position of integral curves gave the condition under which a trajectory that starts in a closed set remains in it, and this result is the foundation of the idea. Aubin's 1991 book Viability theory named and built out the field, defining the viability kernel as the states from which a viable path exists. The referent is a property of trajectories under constraints, worked out from the dynamics and the boundary, and it is unrelated to counting live cells, to a firm's survival, or to a wildlife population's odds of persisting.[3][4]

Unit

A property of a trajectory, or the set of viable initial states

Recovery means

Not applicable

Measured by

Established by the viability condition at the boundary, and computed as viability kernels using set-valued analysis

In management cybernetics, viability is an organization's capacity to maintain a separate existence and keep functioning as its environment changes. Beer's 1972 Brain of the firm introduced the viable system model, which sets out the parts an enterprise needs to stay self-regulating and independent. Beer's 1984 paper The viable system model consolidated its structure and its use as a diagnostic tool. The referent is a whole organization judged by whether it can go on existing and adapting, not the share of live cells in a dish, a wildlife population's persistence, or a trajectory obeying a mathematical constraint.[5][6]

Unit

An organization judged viable or not by its capacity to persist

Recovery means

The model's regulatory and adaptive channels restore balance after a disturbance

Measured by

Diagnosed by mapping an organization against the five subsystems of the viable system model

In conservation biology, viability is the probability that a population will persist rather than go extinct over a chosen span of time. Shaffer's 1981 Minimum population sizes for species conservation defined a minimum viable population as the smallest number able to survive a given period with high probability, given the random threats it faces. Boyce's 1992 review Population viability analysis gathered the modeling methods used to estimate that persistence. The referent is the survival prospect of a whole wildlife population over time, not the live fraction of cells, a firm's continued existence, or a mathematical trajectory staying in bounds.[7][8]

Unit

A population's probability of persistence over a set time horizon

Recovery means

Not applicable

Measured by

Estimated by population viability analysis from demographic rates, variability, and extinction-risk models