What is the Malthusian theory on population?

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According to Malthusian theory of population, population increases in a geometrical ratio, whereas food supply increases in an arithmetic ratio.
This disharmony would lead to widespread poverty and starvation, which would only be checked by natural occurrences such as disease, high infant mortality, famine, war or moral restraint. His main contribution is in the agricultural sector. According to this theory there are two steps to control the population: preventative and positive checks. Preventative means control in birth rate, and uses of different methods to control birth; and positive checks means natural calamities, war, etc.

His theory was wrong because Malthus only considered two factors when he established his basic graph: food supply and population growth. Other factors such as improvements in technology proved him wrong. He was right at his time but development made him wrong. If it wasn't for outside influences on population growth and food supply, his mathematical reasoning which proved his theory and was right.
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Is the drive theory and you theory the same?

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What is neo-malthusians theory on population?

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The official definition for the word theory is "a set of principleson which the practice of an activity is based."