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Predation is one of the prime movers of energy through food chains. It is an important factor in the ecology of populations, and is also an important evolutionary force: natural selection favors more effective predators and more evasive prey. Holling (1959) described three different functional responses curves that describes the relationship between the number of prey eaten by a predator, and the prey density, which are used when modeling predator-prey interactions. Problem 1. The first type of functional response is a simple linear relationship between the num- ber of prey eaten per predator, and the prey density. The equation that represents this type of response is V ( N ) = CN + a a) What would be the rate of predation for this type of functional response? b) What is this model assuming? Give an example in where this response could be apply. Problem 2. The second type of functional response is an hyperbolic function that saturates, because it take in account the time it takes to handle the prey (catch, subdue, and consume an individual prey). The equation that represents this type of response is: V ( N ) = - CN a +N where a represents the "handling time". (a) What does c represent in this equation? (analyze the limit of this function when N -+ 0o). (b) Write the equation for the instantaneous rate of predation for this model when c = 50 and a = 40. (c) Give an example where this type of response could be apply.

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Subject: Calculus, Math
Predation is one of the prime movers of energy through food chains. It is an important factor in the ecology of populations, and is also an important...
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