Where does Malthusian collide?

In demography and population dynamics the Malthusian growth model is the law of unchecked exponential (geometric) increase: with constant per-capita birth and death rates a population grows at a fixed proportional rate and doubles over a constant interval. Malthus's 1798 An essay on the principle of population stated the principle that population, left unchecked, increases in a geometric ratio while subsistence increases only arithmetically. The referent is a deterministic growth law for a population's size over time, distinct from an economy's subsistence equilibrium and from a genotype's fitness, though the single rate constant it turns on is the quantity evolutionary biologists later borrowed and renamed the Malthusian parameter.[1]

Unit

The constant proportional growth rate of a population's size

Recovery means

Not applicable

Measured by

Fitted as the exponential rate constant from population size at two or more times, or as the crude birth rate minus the crude death rate

In economic history the Malthusian trap is a self-correcting equilibrium in which any rise in income or productivity is eventually absorbed by population growth, so material living standards return to a subsistence floor. Clark's 2007 A farewell to alms uses the mechanism to characterise the pre-industrial economy, where higher wages raised fertility and lowered mortality until rising numbers pushed wages back down, building on Malthus's 1798 argument. The referent is an economy-wide demographic–economic equilibrium, not a growth rate or a measure of fitness, the two other things the word "Malthusian" labels elsewhere.[2][1]

Unit

The subsistence real wage toward which income reverts

Recovery means

Escape from the trap is the Industrial-Revolution break in the wage–fertility link, not a within-model recovery

Measured by

Traced through long real-wage and population series and the historical correlation of wages with fertility and mortality

In evolutionary biology the Malthusian parameter is the intrinsic per-capita rate of increase of a genotype, taken as its Darwinian fitness: a type with a higher Malthusian parameter grows faster and is favoured by selection. Fisher's 1930 The genetical theory of natural selection made this rate the currency of his fundamental theorem, tying the rate of increase in mean fitness to the genetic variance in fitness. Here "Malthusian" names a property of a competing type measured in inverse time, a different construct from an economy's subsistence trap, even though it is the same exponential rate that Malthus first drew.[3][1]

Unit

The intrinsic per-capita rate of increase of a type, per unit time

Recovery means

Not applicable

Measured by

Estimated from a type's exponential growth rate or from its life-table reproduction over a generation