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Dividuals per deme fluctuates weakly around its equilibrium value. This approach, also employed in e.g. [23], has the advantage of realism. Alternatively, we could impose a continual number of folks per deme. (i) 1st, we could opt for a dividing person inside the whole metaSKI II biological activity population with probability proportional to its fitness, and simultaneously suppress a different person, selected at random in the similar deme. Even so, within this case, individuals in demes of greater fitness would exhibit shorter lifespans, which can be not realistic and may perhaps introduce a bias. A second possibility could be to select a dividing individual (in accordance with fitness) in every on the demes, and to simultaneously suppress an additional individual, chosen at random, in every single deme. However, in this case, unless migration events are far much less frequent than these collective division-death events (i.e., these D division-death events), the time interval among them becomes artificially discretized. This introduces biases unless the total migration rate mDN is a lot smaller sized than Nd, i.e. unless m d=D.Methods 1 Simulation methodsOur simulations are primarily based on a Gillespie algorithm [48,49] that we coded within the C language. Here we’ll describe our algorithm for the case of a metapopulation of D demes of identical size, which can be the main scenario discussed in our perform. In our simulations, every single deme has a fixed carrying capacity K e talk about this option further within this section. 1.1 Algorithm. Many distinctive events happen in our simulations, each with an independent rate: (ii)NN N NEach individual divides at rate fg (1{Ni =K), where fg is the fitness associated with the genotype g [ f0,1,2g of the individual, and Ni is the current total number of individuals in the deme i [ ,D to which the individual belongs. This corresponds to logistic growth. If a dividing cell has gv2, upon division, its offspring (i.e., one of the two individuals resulting from the division) mutates with probability m, to have genotype gz1 instead of g. Each individual dies at rate d. Hence, at steady-state, Ni K(1{d=fi ), where fi is the average fitness of deme i. In practice, we choose d 0:1, and fitnesses of order one, thus Ni 0:9K. P Migration occurs at total rate m D Ni . Two different demes i 1 are chosen at random, an individual is chosen at random from each of these two demes, and the two individuals are exchanged. There is no geographic structure in our model, i.e. exchange between any two demes is equally likely.Consequently, while imposing a constant number of individuals is a good simulation approach for a non-subdivided population (see e.g. [28]), it tends to introduce biases in the study of metapopulations. While we chose to perform simulations with fixed carrying capacities in order to avoid any of these biases, we checked that, for small enough migration rates, our results are completely consistent with simulation scheme (ii) described above. This consistency check also demonstrates that it is legitimate to compare our simulation results obtained with fixed carrying capacities to our analytical work carried out with constant population size per deme.2 Crossing PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/20170881 time of the champion demeIn this section, we give more details on the calculation of the average valley or plateau crossing time tc by the champion deme amongst D independent ones. We show in the Results section that, in the best scenario, the crossing time of the whole metapopulation is determined by this time.In practice, the number.