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# Predator when that prey is more abundant numerical

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predator when that prey is more abundant Numerical responses are increases in the predator population in response to an increase in prey population. We will only develop models for numerical responses here

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Numerical Response Modeled using the assumption that the prey population is limited by predation (not by its own equilibrium population size), and that predator is limited by food supply. So we can write an equation for prey population growth as: dN/dt = rN a NP where N is the prey population, P the predator population, NP is the interactions between prey and predators, a is a coefficient expressing what fraction of those interactions leads to predation. Note prey grows exponentially in the absence of the predator, and there is an equilibrium point (dN/dt = 0) at which rN = a NP
Numerical Response (cont.) The equation for predator population growth can be written as: dP/dt = b a NP mP where b is a coefficient translating prey consumed into predators born (numerical response!), m is the death rate of predators. Equilibrium where b a NP = mP. Note that the equilibrium population size for the prey is dependent only on the predator population (not prey), and the predator is dependent only on the prey population (not predator)

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Mutualism Positive interactions among species are extremely widespread for example most plants take up nutrients through a symbiosis with fungi, and many reproduce through positive interactions with pollinators and with agents of dispersal.

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