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imagine in a given area or an ecosystem ,bear hunting is totally banned, but there is a scarcity of food for the bears. i want know what would be the future of the bear population?. and want to derive a model.

bear populations normally show a logistic type growth curve from the verhulst-pearl logistic growth equation $\frac{dN}{dt}=rN\left ( \frac{K-N}{K} \right )$ BUT i want to know what changes do i need to apply when there is a scarcity of food in order to predict the future population and how would be the graph when there is a scarcity of food?

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closed as off-topic by fileunderwater, The Last Word, Chris, Bez, leonardo Jul 4 at 14:38

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Please add details to your post, specifically explain what the parameters mean. –  WYSIWYG Jul 4 at 5:05
    
Well, intuitively I would think that a change in food availability will mainly influence $K$ rather than $r$. Therefore, your maximum population size is lowered but the steepness of the curve to reach this maximum is essentially the same than before. –  Remi.b Jul 4 at 8:43