He optimal value shifts towards greater migration prices. This impact, which may be observed in Fig. 3A, is studied much more precisely in Fig. 3B: at fixed migration rate m, theminimum of tm =tns for d 0:035 (strong line in Fig. 2B), which agrees quite well using the benefits of our numerical simulations. pffiffiffiffiffi (Note that this value of d satisfies d two ms, and is such that the non-subdivided population is within the tunneling regime. These conditions have been used in our derivation of Eq. 8.)Discussion Limits on the parameter range exactly where subdivision maximally accelerates crossingIn the outcomes section, we’ve got shown that getting isolated demes within the sequential fixation regime can be a vital condition for subdivision to significantly accelerate crossing. This requirement limits the interval of your ratio m=(md) over which the highest speedups by subdivision are obtained. The extent of this interval is often characterized by the ratio, R, on the upper to lower bound in Eq. 14. Let us express the bound on R imposed by the requirement of sequential fixation in isolated demes. pffiffiffiffiffi If two ms d 1, the threshold worth N| below which an isolated deme is inside the sequential fixation regime satisfies eN| d d2 =(ms) [28]. Let us also assume that Nd 1, and that s 1 though Ns 1, to be within the domain of validity of Eqs. 15 and 16. Combining the situation NvN| with the expression of R in Eq. 16 yieldsPLOS Computational Biology | www.ploscompbiol.orgPopulation Subdivision and Rugged LandscapesFigure three. Varying the degree of subdivision of a metapopulation. A. Valley crossing time tm of a metapopulation with total carrying capacity DK 2500, versus migration-to-mutation price ratio m=(md), for four diverse numbers D of demes. Dots are simulation final results, averaged over 1000 runs for each and every value of m=(md) (500 runs for any handful of points far from the minima); error bars represent 95 CI. Vertical lines represent the limits of your interval of m=(md) in Eq. 14 in each case, except for D 125, exactly where this interval does not exist. Black horizontal line: plateau crossing time for a nonsubdivided population with K 2500 for precisely the same parameter values, averaged over 1000 runs; shaded regions: 95 CI. Dashed line: Sodium tauroursodeoxycholate corresponding theoretical prediction from Ref. [28]. Parameter values: d 0:1, m eight|10{6 , s 0:3 and d 6|10{3 (same as in Fig. 1C ); m is varied. B. Valley crossing time tm of a metapopulation with total carrying capacity DK 2500, versus the number D of demes, for m 10{5 (i.e. m=(md) 12:5). Dots are simulation results, averaged over 1000 runs for each value of D; error bars represent 95 CI. Parameter values: same as in A. C. Valley crossing time tmin , minimized over m for each value of D, of a metapopulation with total carrying capacity DK 2500, versus the number D of demes. For each value of D, the valley crossing time of the metapopulation was computed for several values of m, different by factors of 100:25 or 100:5 in the vicinity of the minimum (see A): tmin corresponds to the smallest value obtained in this process. Results obtained for the actual metapopulation (blue) are compared to the best-scenario limit (red) where tmin tid =D, PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/20170881 calculated using the value of tid obtained from our simulations. Dots are simulation results, averaged over 1000 runs for each value of D; error bars represent 95 CI. Dashed line: value of D such that R 100. Dotted line: value of D above which the deleterious mutation is effectively neutral in the isolated demes. Solid line: value o.
