A change in the price of the good in question will cause a movement ALONG the demand curve, not a shift of the entire demand curve.
An increase in the population would cause the demand curve for bagels (and all goods) to shift to the right.
An increase in the supply of bagels will cause a change in the price of the bagels, which will cause a movement ALONG the demand curve, not a shift of the entire demand curve.
Because muffins are a substitute product for bagels, a decrease in the price of muffins will cause the demand curve for bagels to shift to the left. Because muffins are now comparatively cheaper, fewer bagels will be demanded at every level of price.
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