Where does density collide?

The amount of mass contained in a unit of volume of a substance, written as mass divided by volume and reported in kilograms per cubic metre. It is an intensive property, meaning a small chip of a pure material has the same value as a large block of it, so it identifies the material rather than the size of the sample, as set out in standard treatments such as Serway and Jewett's Physics for Scientists and Engineers (2018). The referent here is a physical ratio of matter to space, always carried in units of mass over volume, and it is unrelated to a curve whose area is a probability, a count of organisms over ground, or a fraction of possible links in a network.[1]

Unit

Kilograms per cubic metre, mass divided by the volume it occupies

Recovery means

Not applicable

Measured by

Found by weighing a sample and dividing by its measured or displaced volume, as in Archimedes' displacement method, or by pycnometry

A function attached to a continuous random quantity whose integral over any region gives the probability of landing in that region, so its area, not its height, is the probability, and its value at a point can even exceed one. Built on Kolmogorov's 1933 axioms and made precise as a Radon and Nikodym derivative by Nikodym's 1930 theorem, it is a density of one measure with respect to another reference measure, most often length or volume, so it is defined only relative to that chosen measure. The referent is a rate of probability per unit of the reference measure, and it is emphatically not a mass per volume, a headcount over an area, or a share of realised ties.[2][3]

Unit

Probability per unit of the reference measure, so it integrates to one over the whole space

Recovery means

Not applicable

Measured by

Estimated from data by histograms or kernel density estimation, or derived analytically by differentiating the cumulative distribution

The number of individuals of a population living in a unit of area or volume, a core demographic parameter that governs competition, resource use, and the rates at which a population grows or declines. Sibly and colleagues' 2005 study in Science showed across mammals, birds, fish, and insects that growth rate depends on this density, the signature of density dependence in population regulation. The referent is a count of living things scaled by the ground or water they occupy, a biological quantity, and it has nothing in common with a material's mass over volume, a probability curve's area, or the wiring fraction of a graph.[4]

Unit

Individuals per unit area or volume, for example animals per square kilometre

Recovery means

Density dependence can pull an over-crowded population back toward a carrying capacity as births fall and deaths rise

Measured by

Estimated by direct counts, quadrat sampling, mark and recapture, or distance sampling scaled to the area surveyed

The proportion of the ties that could possibly exist among a set of actors that are actually present, computed as the number of observed links divided by the number of pairs, giving a number between zero and one. Wasserman and Faust's 1994 Social Network Analysis defines it as a basic measure of how knit together a whole network is, and Newman's 2003 review places the same ratio at the centre of complex network structure. The referent is a dimensionless fraction of realised connections in a graph, and it is a different thing from a mass over a volume, a probability spread over a line, or a headcount over a field.[5][6]

Unit

A dimensionless ratio from zero to one, observed ties divided by possible ties

Recovery means

Not applicable

Measured by

Computed from an adjacency matrix as edges divided by the maximum possible edges for the number of nodes