Who published the logistic equation model of population growth in 1838?

Correct — D. The logistic equation of population growth was published in 1838 by Pierre François Verhulst, a Belgian mathematician → option (d).

What he added was a ceiling. Malthus had described population rising exponentially without limit. Verhulst kept that growth for small populations but made the rate fall away as numbers approach the resources available.

In modern notation the model is dN⁄dt = rN(1 − N⁄K), where K is the carrying capacity. The bracket is close to 1 while N is small and shrinks to 0 as N approaches K.

The curve that results is an S-shape (sigmoid): slow, then steep, then flattening at K.

Why the others are wrong

• (a)
  Alfred Russel Wallace — Alfred Russel Wallace was a British naturalist who arrived independently at natural selection, in a paper read jointly with Darwin's, and who mapped the faunal divide named after him. He wrote no population growth equation.
• (b)
  Howard Thomas Odum — Howard Thomas Odum was a twentieth-century American ecologist known for systems ecology and for tracing energy flow through ecosystems — a full century after 1838.
• (c)
  George Evelyn Hutchinson — George Evelyn Hutchinson was a twentieth-century ecologist and limnologist, remembered above all for formalising the ecological niche. He too is far too late for an 1838 publication.

Two models of population growth are worth holding apart.

Exponential (Malthusian) growth assumes unlimited resources: the population multiplies by the same factor each interval and the curve is J-shaped, rising without limit.

Logistic (Verhulst) growth assumes a finite environment: growth is fastest in the middle, then slows as the population nears the carrying capacity K, giving the S-shaped curve.

Real populations start out looking exponential, which is why the logistic model is described as a correction rather than a replacement.

Key facts

• Pierre François Verhulst, a Belgian mathematician, published the logistic model of population growth in 1838.
• The logistic model is written dN⁄dt = rN(1 − N⁄K), with K the carrying capacity.
• Its graph is sigmoid, or S-shaped, flattening as the population approaches K.
• It was framed as a correction to Malthus's unchecked exponential growth.

Common traps

• Answering Malthus by reflex because the topic is population — his model is the unlimited exponential one.
• Picking a famous ecologist on name recognition alone, when both Odum and Hutchinson belong to the twentieth century.
• Confusing Wallace's work on evolution and biogeography with population mathematics.

No directly related past PYQ was found.