The Lotka-Volterra predatory-prey model includes K for both predators and prey. True False
Added by Jason B.
Close
Step 1
The equations are: $\frac{dx}{dt} = \alpha x - \beta xy$ $\frac{dy}{dt} = \delta xy - \gamma y$ where: $x$ is the prey population $y$ is the predator population $\alpha$ is the prey growth rate $\beta$ is the predation rate Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 69 other Biology educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The population of prey is denoted x(t) (in millions) and the population of predators is denoted y(t) (in millions). We assume that: In the absence of predators, the prey population satisfies the logistic growth model with a carrying capacity K (in millions). In the absence of prey, the predator population decays at a rate proportional to the predator population. The prey population decays at a rate proportional to the product of prey and predators. The predator population grows at a rate proportional to the product of prey and predators. These assumptions lead to the following nonlinear system of differential equations: x' = αx(1 - x/K) - βxy, y' = γxy - δy where α, β, γ, and δ are positive constants. Assume that K > δ/γ. The equilibrium ye = [K; 0] is locally asymptotically stable. True False
Adi S.
The following is a prey x(t) -predator y(t) system of equations. Prey equation: dx/dt=ax−pxy Predator equation: dy/dt=−by+qxy where t is time and a,b,p,q are constants. State whether the following statement is True or False. In the absence of y(t) , the population of x(t) would decline at natural rate. True or False
Breanna O.
(2) One model of predator-prey interaction, called Lotka-Volterra, is based on the assumptions that - in the absence of predation, prey increase exponentially - in the absence of predation, predators decrease exponentially, - predator-prey interactions increase the predator population and decrease the prey population. If the two populations are given by the dependent variables x and y, a system of equations describing this is dx/dt = -αx + βxy dy/dt = γy - δxy where α, β, γ and δ are nonnegative constants. (a) Based on the described assumptions and the given equations, which variable (x or y) is the prey population and which is the predator population? (Why?) (b) Suppose x and y are given in hundreds of animals (e.g. if x are moths, then x = 1 would mean there are 100 moths). Let α = 3, β = 1, γ = 1/4 and δ = 1/2. There are two possible constant population scenarios such that x = const. and y = const. What are they? (Hint: constant functions have derivative zero.) (c) Suppose there is no predation β = 0 and α = 3. Solve the first equation for x if x(0) = x0.
Madhur L.
Recommended Textbooks
Biology for AP Courses
Objective Biology for NEET
Introduction to General, Organic and Biochemistry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD