 Demographic balancing equation

For a fixed territory and interval, the demographic balancing equation is the accounting identitywhere $N_0,N_1$ are initial and final resident counts and $B,D,I,E$ are births, deaths, immigration and emigration during that interval. All quantities must use compatible definitions of territory, residence and reference time. This is conservation of population counts, not an assumed law of population dynamics.

For $N_0=10000$, $B=140$, $D=90$, $I=80$ and $E=110$, the final count is $10020$: natural increase adds 50 and net human migration removes 30. Rearranging yields $I-E=N_1-N_0-B+D$, allowing net migration to be estimated residually. In measured data, that residual also absorbs errors in censuses and vital-event counts, so the identity does not independently establish the accuracy of any measurement.