Consider the Ricker population model presented in class, Rt+1 = F(Rt) = aRte aRte-bRt where R...

  

 
 

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Consider the Ricker population model presented in class, Rt+1 = F(Rt) = aRte aRte-bRt where R is the total mass of the recruits in time t. (a) Verify that a is 'proliferation' in the model, that is, verify a = F'(0). (b) What are the equilibria in this model? Derive conditions for when they are stable and unstable. F'(0) (c) Re-write the model, so that it only has parameters a and k, where a = and k is the positive equilibrium. (d) Using your new model, in part (c), and R. plot time series (R, vs. t) given Ro = 2, a = 2, and k = 100, from t = 0 to t = 25. Repeat for a = 10, a = 13 and a = 18. How do your calculations in part (b) help explain the behaviour in these graphs? (e) Generate an orbit diagram for your model in (c), in other words plot R₁, for all t€ [1,000, 1, 500], vs. a, from a = 0 to a = 35. Consider the Ricker population model presented in class, Rt+1 = F(Rt) = aRte aRte-bRt where R is the total mass of the recruits in time t. (a) Verify that a is 'proliferation' in the model, that is, verify a = F'(0). (b) What are the equilibria in this model? Derive conditions for when they are stable and unstable. F'(0) (c) Re-write the model, so that it only has parameters a and k, where a = and k is the positive equilibrium. (d) Using your new model, in part (c), and R. plot time series (R, vs. t) given Ro = 2, a = 2, and k = 100, from t = 0 to t = 25. Repeat for a = 10, a = 13 and a = 18. How do your calculations in part (b) help explain the behaviour in these graphs? (e) Generate an orbit diagram for your model in (c), in other words plot R₁, for all t€ [1,000, 1, 500], vs. a, from a = 0 to a = 35.

Answer rating: 100% (QA)

a To verify that a is proliferation in the model we need to calculate the derivative of FR with respect to R at R0 This gives us F0a Therefore a is in... View the full answer