Equation 4 · Demography, Migration, and Urban Futures in Practice: An Advanced Technical Guide
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol P_a+1,s,t+1
+1,s,t+1 is part of the quantity the equation computes from the expression on the right.
Symbol P_a,s,t
,s,t is one of the signed contributions combined to compute the quantity on the left.
Symbol S_a,s,t
,s,t is one of the signed contributions combined to compute the quantity on the left.
Symbol M_a,s,t
,s,t is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
Aging the cohort forward. For each one-year (or five-year) step, every age-sex cohort is advanced by applying an age-specific survival ratio — the probability of surviving from one age to the next, derived from a life table built out of registered deaths and mortality schedules — and then subtracting deaths and adding net migrants assigned to that same age and sex [ 1 ] . Symbolically, for a cohort of age a and sex s in year t : . where P is the population count, S is the age-and-sex-specific survival ratio for that interval, and M is net migration assigned to that cohort during the interval. The youngest cohort in each step is not aged forward from an existing cohort; it…
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Aging the cohort forward. For each one-year (or five-year) step, every age-sex cohort is advanced by applying an age-specific survival ratio — the probability of surviving from one age to the next, derived from a life table built out of registered deaths and mortality schedules — and then subtracting deaths and adding net migrants assigned to that same age and sex [ 1 ] . Symbolically, for a cohort of age a and sex s in year t : . where P is the population count, S is the age-and-sex-specific survival ratio for that interval, and M is net migration assigned to that cohort during the interval. The youngest cohort in each step is not aged forward from an existing cohort; it is generated fresh from the number of births, which is itself the product of age-specific fertility rates applied to the female population of childbearing age, by convention ages 15 to 49 [ 1 ] .
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