File S1: Appendices

نویسندگان

  • Elizabeth C. Elliott
  • Stephen J. Cornell
چکیده

We wish to reduce the number of parameters in the model and make it so that the model is more easily comparable to our previous work [1]. To do this we first look at the nonspatial single morph model which is given by: Ni(t+ 1) = (1 + b)Ni(t) exp(−mi −mi (1 + b)Nt) For the purpose of this model we want the carrying capacity K to be fixed by the equilibrium population density. We therefore calculate the equilibrium density N∗ i by setting Ni(t + 1) = N(t) which gives the equilibrium to be N∗ i = log(1+b)−m0i mi (1+b) and then set K = N∗ i . The nonspatial version of the continuous model in [1] is given by dNi dt = riNi(1 − Ni K ). To relate the population growth rate term to the parameters in the discrete model we assume that when Ni is small we get exponential growth in one time step. We can therefore assume that when Ni << K we have Nt = N0e rit where N0 is the initial population size and t is time. In the discrete model when Ni << K we have that Nt = RtN0 where R = (1 + b)e −m0i . We can therefore relate the continuous and discrete models by R = ei , which gives ri = log(1 + b)−mi . In the full spatial model the parameter Di is defined in the same way as in [1] and so parameter values used in the two models are directly comparable.

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تاریخ انتشار 2013