In this graph "grain" is the world's annual production of rice, wheat and corn, "oil" is the global production of all petroleum liquids, and people are people. I normalized the numbers so that they all start off from an index of 100 in 1985. This is a standard technique that makes the relationsip between the three elements visible.
It's obvious at a glance that food, oil and population are tightly related, but the nature of their relationship is open to interpretation. If you were an economist you could say that as the number of people grows, we go out and grow more food and find more oil to meet our growing needs. Conversely if you were an ecologist you might say that increasing supplies of oil and food allow our population to grow. Or you could say (as I do) that they all exist in a complex feedback loop.
If they are all components of a feedback loop, that means that anything that influences one will influence the others, at least to some extent. Oil is essential in our modern system of industrial agriculture to grow and distribute food. Without enough food populations don't grow - food shortages tend to lower womens' fertility, increase infant mortality and decrease life expectancy.
The correlation shown above between oil and grain production implies that that any significant hiccup in the world's oil supply is going to affect food production. And the virtually 100% correlation between grain and population implies that any hiccup in the food supply is going to impact our numbers sooner or later.
And we've already hit the Peak Oil plateau:
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