Why is it that the usual Lotka-Volterra competition equations are not adequate to explain (or model) predator-prey relationships?
Added by Jose Manuel D.
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They focus on how the populations of these species affect each other through competition for limited resources. Show more…
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In 1925 Lotka and Volterra introduced the predator-prey equations, a system of equations that models the populations of two species, one of which preys on the other. Let $x(t)$ represent the number of rabbits living in a region at time $t,$ and $y(t)$ the number of foxes in the same region. As time passes, the number of rabbits increases at a rate proportional to their population, and decreases at a rate proportional to the number of encounters between rabbits and foxes. The foxes, which compete for food, increase in number at a rate proportional to the number of encounters with rabbits but decrease at a rate proportional to the number of foxes. The number of encounters between rabbits and foxes is assumed to be proportional to the product of the two populations. These assumptions lead to the autonomous system $$\begin{aligned}\frac{d x}{d t} &=(a-b y) x \\\frac{d y}{d t} &=(-c+d x) y\end{aligned}$$ where $a, b, c, d$ are positive constants. The values of these constants vary according to the specific situation being modeled. We can study the nature of the population changes without setting these constants to specific values. What happens to the fox population if there are no rabbits present?
Jacob F.
Q2.18. The Lotka-Volterra model produces consistently identical cycles because it is deterministic. The lynx and hare simulation on the right does not, because it is stochastic. Run the simulation again now with the controls below, paying attention to the animals in the enclosure at the top. Given the differences between these two types of models, why would it be difficult to determine accurate values for the four parameters in the Lotka-Volterra predator-prey model (a, rprey, m, b) for animals in the real world? Option A) In the real world, individual predators do not differ in their ability to search for prey. Option B) In the real world, random and unpredictable events occur, so the Lotka-Volterra parameters vary over time. Option C) In the real world, prey population sizes constantly change, and the Lotka-Volterra model fails to account for this. Option D) In the real world, biological interactions are so complex and dynamic that models have no relevance.
Dr. Satish I.
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