= Population density
{title2=$n(\mathbf x,t)$}
<Population density> is the number of organisms per specified habitat area or volume. A region with $N$ individuals and area $A$ has mean <population density> $N/A$; the spatial scale, counted organisms and usable habitat must be stated. Ten animals per square kilometre of an entire landscape is not the same quantity as ten per square kilometre of its occupied habitat.
A spatially varying <population density> $n(\mathbf x,t)$ satisfies
$$
N_D(t)=\int_D n(\mathbf x,t)\,d\mathbf x,
$$
with the integral taken over area or volume as appropriate. Integrating restores an abundance count, so the units check the definition. For example, a uniform density of three plants per square metre over a ten-square-metre plot gives thirty plants.
The distinction is useful in <population dynamics>: movement can change local <population density> without any birth or death, while expanding habitat can lower average <population density> even when total abundance stays fixed. Sampling quadrats estimates a local or spatially averaged density; extrapolation requires the sampled habitat and sampling design to represent the intended region.
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