====================================================================================================================== EVERYTHING A SMALL FOUNDING GROUP LOSES ON THE WAY Monte Carlo study of the founder effect: sampling, recovery and detectability Science Journaling Club, Volume 1 Issue 1, Fall 2024 ====================================================================================================================== This output is generated entirely by simulation. No organism, population, island, field site or laboratory measurement is involved anywhere in it. numpy version : 2.4.2 python version : 3.12.3 master seed : 20241108 generator : numpy PCG64, one spawned stream per experiment allele states per locus : 20 (K-allele mutation model) mutation rate mu : 4.000e-04 per copy per generation carrying capacity K : 1,000 diploids theta = 4 K mu : 1.6000 loci in source spectrum : 20 Founding: 2k gametes drawn from the source pool, Multinomial(2k, p). Growth: N_{t+1} = min(K, round(N_t (1 + r))). Breeding: gametes mutate under the K-allele model, then Multinomial(2N, q). ====================================================================================================================== SECTION 1. THE SOURCE POPULATION ====================================================================================================================== The spectrum below is drawn once, from stream 0, and then held fixed for the rest of the study. It is the known quantity the founding groups sample from. locus alleles gene diversity commonest rarest -------------------------------------------------------- 0 12 0.740583 0.37806 0.000572 1 12 0.687268 0.46527 0.000770 2 14 0.710348 0.47084 0.000534 3 14 0.820341 0.27707 0.000877 4 6 0.271237 0.84939 0.003959 5 9 0.563791 0.56984 0.002055 6 16 0.727218 0.41731 0.000524 7 10 0.816421 0.29513 0.001769 8 14 0.848131 0.24448 0.001031 9 12 0.633356 0.52319 0.000718 10 11 0.756402 0.35858 0.000695 11 9 0.186247 0.90063 0.001097 12 13 0.621723 0.51426 0.001271 13 16 0.523646 0.67223 0.000590 14 9 0.706682 0.44396 0.000642 15 10 0.285275 0.84273 0.000780 16 15 0.459482 0.72052 0.000520 17 9 0.593216 0.55040 0.000522 18 11 0.536494 0.66398 0.001234 19 9 0.600783 0.59341 0.000971 -------------------------------------------------------- mean 11.55 0.604432 H_source over all 20 loci : 0.604432 H_source over the 20 founding-sweep loci : 0.604432 H_source over the 5 recovery-grid loci : 0.645955 H_source over the 15 detection loci : 0.640893 mean alleles per locus in the source : 11.550 total distinct alleles across all loci : 231 Allele frequency classes in the source, mean count per locus class alleles/locus 0.00 to 0.01 5.050 0.01 to 0.02 1.250 0.02 to 0.05 1.500 0.05 to 0.10 1.100 0.10 to 0.20 1.100 0.20 to 0.40 0.800 0.40 to 1.00 0.750 ====================================================================================================================== SECTION 2. THE FOUNDING DRAW, AND THE CLOSED FORM ====================================================================================================================== Prediction, exact for this model and not an approximation: E[H_new] = H_old (1 - 1/(2k)). H_old here is 0.604432, the mean gene diversity of the 20 source loci. Replicates per founding size: 20,000. k retention predicted diff SE z verdict H_new sim H_new pred --------------------------------------------------------------------------------------------------- 2 0.749731 0.750000 -0.000269 0.000482 -0.56 agree 0.453161 0.453324 3 0.834208 0.833333 +0.000875 0.000411 +2.13 agree 0.504222 0.503693 5 0.900022 0.900000 +0.000022 0.000323 +0.07 agree 0.544002 0.543989 8 0.937180 0.937500 -0.000320 0.000258 -1.24 agree 0.566462 0.566655 10 0.950393 0.950000 +0.000393 0.000231 +1.70 agree 0.574448 0.574211 12 0.958510 0.958333 +0.000177 0.000212 +0.83 agree 0.579354 0.579247 20 0.975032 0.975000 +0.000032 0.000165 +0.19 agree 0.589341 0.589321 30 0.983445 0.983333 +0.000112 0.000135 +0.83 agree 0.594426 0.594358 50 0.990020 0.990000 +0.000020 0.000104 +0.19 agree 0.598400 0.598388 75 0.993297 0.993333 -0.000036 0.000085 -0.42 agree 0.600381 0.600403 100 0.994976 0.995000 -0.000024 0.000075 -0.32 agree 0.601396 0.601410 150 0.996625 0.996667 -0.000042 0.000061 -0.69 agree 0.602392 0.602417 200 0.997532 0.997500 +0.000032 0.000052 +0.61 agree 0.602940 0.602921 350 0.998594 0.998571 +0.000023 0.000040 +0.57 agree 0.603582 0.603569 500 0.998990 0.999000 -0.000010 0.000033 -0.30 agree 0.603822 0.603828 --------------------------------------------------------------------------------------------------- largest |z| over the 15 founding sizes: 2.13 mean z: +0.239 (expected near 0, SD near 1; realised SD 0.904) Every founding size agrees with H_old(1 - 1/(2k)) inside three standard errors. There is no free parameter in that comparison. ====================================================================================================================== SECTION 3. ALLELES LOST AT THE MOMENT OF FOUNDING ====================================================================================================================== Allele i survives the draw unless all 2k gametes miss it, so P(lost) = (1 - p_i)^{2k}, E[alleles lost] = sum_i (1 - p_i)^{2k}. The 20 source loci carry 231 distinct alleles between them. k lost sim SE lost pred diff z verdict alleles/locus % of source -------------------------------------------------------------------------------------------------- 2 183.2095 0.0224 183.1935 +0.0159 +0.71 agree 2.3895 20.69 3 172.4461 0.0261 172.4861 -0.0400 -1.54 agree 2.9277 25.35 5 157.6531 0.0293 157.6512 +0.0018 +0.06 agree 3.6673 31.75 8 142.9695 0.0315 142.9601 +0.0094 +0.30 agree 4.4015 38.11 10 135.7292 0.0317 135.7451 -0.0159 -0.50 agree 4.7635 41.24 12 129.7398 0.0320 129.7811 -0.0413 -1.29 agree 5.0630 43.84 20 112.9313 0.0326 112.9654 -0.0340 -1.04 agree 5.9034 51.11 30 99.7105 0.0324 99.7291 -0.0186 -0.57 agree 6.5645 56.84 50 83.4518 0.0322 83.4330 +0.0188 +0.59 agree 7.3774 63.87 75 70.9252 0.0321 70.8834 +0.0418 +1.30 agree 8.0037 69.30 100 62.1842 0.0319 62.1840 +0.0002 +0.01 agree 8.4408 73.08 150 50.1800 0.0312 50.1878 -0.0078 -0.25 agree 9.0410 78.28 200 41.8978 0.0301 41.9132 -0.0154 -0.51 agree 9.4551 81.86 350 26.9724 0.0270 26.9434 +0.0291 +1.08 agree 10.2014 88.32 500 18.6943 0.0242 18.7112 -0.0170 -0.70 agree 10.6153 91.91 -------------------------------------------------------------------------------------------------- largest |z| on allele loss: 1.54 Allele by allele, at k = 2 and k = 50. Only the rarest and commonest few are printed; the full set behaves the same way. p is the source frequency, P(lost) the binomial prediction, and the last column the simulated rate. k = 2 p P(lost) pred P(lost) sim diff z ---------------------------------------------------------- 0.000520 0.997922 0.997650 -0.000272 -0.84 0.000522 0.997915 0.998100 +0.000185 +0.57 0.000524 0.997907 0.998150 +0.000243 +0.75 0.000534 0.997868 0.997100 -0.000768 -2.35 0.000572 0.997714 0.997800 +0.000086 +0.25 0.000590 0.997641 0.997100 -0.000541 -1.58 0.016164 0.936896 0.938800 +0.001904 +1.11 0.016360 0.936150 0.936050 -0.000100 -0.06 0.016802 0.934467 0.936700 +0.002233 +1.28 0.016930 0.933980 0.934050 +0.000070 +0.04 0.720523 0.006101 0.006000 -0.000101 -0.18 0.842728 0.000612 0.000650 +0.000038 +0.22 0.849386 0.000515 0.000500 -0.000015 -0.09 0.900629 0.000098 0.000050 -0.000048 -0.68 across all 231 alleles: mean predicted 0.793046, mean simulated 0.793115, mean |diff| 0.001289 k = 50 p P(lost) pred P(lost) sim diff z ---------------------------------------------------------- 0.000520 0.949314 0.948050 -0.001264 -0.81 0.000522 0.949157 0.946800 -0.002357 -1.52 0.000524 0.948970 0.951800 +0.002830 +1.82 0.000534 0.948033 0.948300 +0.000267 +0.17 0.000572 0.944397 0.941850 -0.002547 -1.57 0.000590 0.942671 0.943900 +0.001229 +0.75 0.016164 0.196015 0.194400 -0.001615 -0.58 0.016360 0.192148 0.189900 -0.002248 -0.81 0.016802 0.183696 0.183250 -0.000446 -0.16 0.016930 0.181315 0.183400 +0.002085 +0.77 0.720523 0.000000 0.000000 -0.000000 -0.00 0.842728 0.000000 0.000000 -0.000000 -0.00 0.849386 0.000000 0.000000 -0.000000 -0.00 0.900629 0.000000 0.000000 -0.000000 -0.00 across all 231 alleles: mean predicted 0.361182, mean simulated 0.361263, mean |diff| 0.001408 ====================================================================================================================== SECTION 4. A FINITE SOURCE, AND THE CASE k = N ====================================================================================================================== The source is now a real population of N = 60 diploids, 120 gene copies, whose composition is drawn once from the spectrum of Section 1. Founder gametes are taken without replacement, so E[H_new] = H_old [1 - (1/(2k)) (2N - 2k)/(2N - 1)]. At k = N the bracket is exactly 1 and the founding group is the source. realised finite source: H_old = 0.603764, 145 distinct alleles over 20 loci k H sim SE H pred infinite H pred finite diff z verdict alleles lost -------------------------------------------------------------------------------------------------------- 2 0.456188 0.000288 0.452823 0.456628 -0.000440 -1.53 agree 96.9729 5 0.547892 0.000184 0.543387 0.547954 -0.000061 -0.33 agree 71.5337 10 0.578457 0.000126 0.573576 0.578396 +0.000061 +0.48 agree 50.8241 20 0.593817 0.000081 0.588670 0.593617 +0.000201 +2.49 agree 30.4082 30 0.598670 0.000057 0.593701 0.598690 -0.000021 -0.36 agree 18.8868 45 0.602100 0.000033 0.597055 0.602073 +0.000028 +0.84 agree 7.6707 60 0.603764 0.000000 0.598733 0.603764 -0.000000 +nan exact 0.0000 -------------------------------------------------------------------------------------------------------- At k = N = 60: simulated H = 0.6037638889, source H = 0.6037638889, difference -1.11e-16. Alleles lost: mean 0.0000, maximum over 20,000 replicates 0. Nothing is lost, in any replicate, exactly as the hypergeometric variance says. Note the fourth column. Using the infinite-source formula on a finite source overstates the loss badly once k approaches N: at k = 30 it predicts 0.593701 where the right answer is 0.598690. The club got this wrong once. ====================================================================================================================== SECTION 5. CONVERGENCE OF THE MONTE CARLO ESTIMATE ====================================================================================================================== Running mean of the retention ratio H_new / H_old against replicate count, for three founding sizes, with the analytic value it is converging on. reps k=2 running k=2 target k=10 running k=10 target k=50 running k=50 target -------------------------------------------------------------------------------------------------------- 50 0.756909 0.750000 0.947865 0.950000 0.988083 0.990000 100 0.759494 0.750000 0.947939 0.950000 0.990191 0.990000 200 0.751894 0.750000 0.949277 0.950000 0.989609 0.990000 500 0.751759 0.750000 0.949767 0.950000 0.989950 0.990000 1000 0.748637 0.750000 0.949210 0.950000 0.990280 0.990000 2000 0.748776 0.750000 0.950330 0.950000 0.990369 0.990000 5000 0.749404 0.750000 0.950804 0.950000 0.990067 0.990000 10000 0.749135 0.750000 0.950728 0.950000 0.990024 0.990000 20000 0.749731 0.750000 0.950393 0.950000 0.990020 0.990000 -------------------------------------------------------------------------------------------------------- k = 2: final 0.749731, target 0.750000, SE 0.000482, |final - target| / SE = 0.56 k = 10: final 0.950393, target 0.950000, SE 0.000231, |final - target| / SE = 1.70 k = 50: final 0.990020, target 0.990000, SE 0.000104, |final - target| / SE = 0.19 ====================================================================================================================== SECTION 6. THE RECOVERY GRID ====================================================================================================================== 8 founding sizes x 4 growth rates = 32 cells, 5,000 replicates each, 5 loci per replicate, carrying capacity 1,000. Each cell runs until the population has sat at carrying capacity for 20 generations, with a floor of 50 and a ceiling of 170. H_end is gene diversity at the last simulated generation. The 'recursion' column is the exact expectation from the two-line recursion in the docstring, run along the same size path. No fitting of any kind. k r gens N_end H_found H_end recursion diff z verdict A_found A_end % H kept % A kept ------------------------------------------------------------------------------------------------------------------------------- 2 0.05 147 1000 0.483685 0.079757 0.079539 +0.000217 +0.34 agree 2.517 5.812 12.35 50.32 2 0.15 64 1000 0.486170 0.116041 0.116385 -0.000344 -0.34 agree 2.533 5.456 17.96 47.23 2 0.40 50 1000 0.484320 0.278571 0.276409 +0.002162 +1.68 agree 2.523 6.059 43.13 52.46 2 1.00 50 1000 0.484140 0.388537 0.388960 -0.000423 -0.36 agree 2.524 6.576 60.15 56.93 5 0.05 128 1000 0.581808 0.143415 0.144113 -0.000697 -0.65 agree 3.952 5.967 22.20 51.66 5 0.15 57 1000 0.580274 0.321402 0.323051 -0.001649 -1.29 agree 3.945 6.067 49.76 52.53 5 0.40 50 1000 0.580795 0.462799 0.463838 -0.001039 -0.94 agree 3.952 7.000 71.65 60.61 5 1.00 50 1000 0.582063 0.532121 0.531705 +0.000415 +0.46 agree 3.954 7.556 82.38 65.42 10 0.05 114 1000 0.613956 0.277356 0.277188 +0.000168 +0.13 agree 5.135 6.317 42.94 54.69 10 0.15 52 1000 0.613986 0.454534 0.455386 -0.000852 -0.78 agree 5.133 6.714 70.37 58.13 10 0.40 50 1000 0.614591 0.549051 0.548285 +0.000766 +0.89 agree 5.133 7.793 85.00 67.47 10 1.00 50 1000 0.615137 0.587589 0.586295 +0.001294 +1.80 agree 5.150 8.351 90.96 72.30 25 0.05 95 1000 0.633048 0.458914 0.458588 +0.000327 +0.29 agree 6.719 7.139 71.04 61.81 25 0.15 50 1000 0.633183 0.565298 0.564594 +0.000704 +0.87 agree 6.715 7.911 87.51 68.50 25 0.40 50 1000 0.633109 0.605787 0.605365 +0.000423 +0.68 agree 6.705 8.842 93.78 76.56 25 1.00 50 1000 0.632863 0.619834 0.620662 -0.000828 -1.58 agree 6.702 9.318 95.96 80.68 50 0.05 81 1000 0.639320 0.546357 0.548587 -0.002230 -2.52 agree 7.802 7.870 84.58 68.14 50 0.15 50 1000 0.639794 0.606536 0.605662 +0.000874 +1.41 agree 7.798 8.808 93.90 76.26 50 0.40 50 1000 0.639774 0.624766 0.625161 -0.000395 -0.78 agree 7.810 9.524 96.72 82.45 50 1.00 50 1000 0.639456 0.632044 0.632255 -0.000211 -0.47 agree 7.805 9.850 97.85 85.28 100 0.05 67 1000 0.642871 0.599505 0.600307 -0.000803 -1.20 agree 8.749 8.728 92.81 75.57 100 0.15 50 1000 0.642832 0.626909 0.626640 +0.000269 +0.54 agree 8.754 9.573 97.05 82.88 100 0.40 50 1000 0.642994 0.635397 0.634972 +0.000425 +1.01 agree 8.746 10.001 98.37 86.59 100 1.00 50 1000 0.642899 0.637870 0.637956 -0.000087 -0.22 agree 8.751 10.171 98.75 88.06 250 0.05 50 1000 0.644642 0.631971 0.631938 +0.000033 +0.07 agree 9.871 9.784 97.84 84.71 250 0.15 50 1000 0.644555 0.638008 0.638453 -0.000446 -1.12 agree 9.873 10.186 98.77 88.19 250 0.40 50 1000 0.644688 0.640340 0.640473 -0.000133 -0.36 agree 9.873 10.340 99.13 89.52 250 1.00 50 1000 0.644662 0.641413 0.641197 +0.000216 +0.59 agree 9.876 10.409 99.30 90.12 500 0.05 50 1000 0.645398 0.640734 0.640345 +0.000388 +1.02 agree 10.632 10.323 99.19 89.38 500 0.15 50 1000 0.645318 0.641495 0.641586 -0.000090 -0.25 agree 10.639 10.422 99.31 90.24 500 0.40 50 1000 0.645329 0.642374 0.641967 +0.000406 +1.11 agree 10.648 10.460 99.45 90.56 500 1.00 50 1000 0.645196 0.642054 0.642103 -0.000049 -0.14 agree 10.644 10.461 99.40 90.57 ------------------------------------------------------------------------------------------------------------------------------- largest |z| against the exact recursion over 32 cells: 2.52 mean z -0.004, SD 0.998 ====================================================================================================================== SECTION 7. HOW LONG UNTIL IT COMES BACK ====================================================================================================================== The recursion is exact and costs nothing to run, so once Section 6 has shown it tracks the simulation we can push it far past what we can afford to simulate. Below, a population founded by k individuals grows at r = 0.40 to K = 1,000 and then sits there. Gene diversity as a percentage of the source, at generations we could never reach by Monte Carlo. k 0 1 5 10 25 50 100 250 500 1000 2000 5000 10000 20000 -------------------------------------------------------------------------------------------------------------------------------------- 2 75.00 62.55 44.35 40.72 41.10 42.79 46.00 54.44 65.22 78.44 88.64 92.19 92.25 92.25 5 90.00 83.62 73.42 71.00 71.11 71.81 73.13 76.62 81.08 86.54 90.76 92.23 92.25 92.25 10 95.00 91.65 85.94 84.58 84.63 84.88 85.36 86.62 88.22 90.19 91.72 92.24 92.25 92.25 25 98.00 96.64 94.29 93.80 93.77 93.72 93.62 93.37 93.05 92.66 92.36 92.26 92.25 92.25 50 99.00 98.33 97.20 97.03 96.94 96.78 96.49 95.72 94.73 93.52 92.58 92.26 92.25 92.25 100 99.50 99.18 98.69 98.63 98.51 98.30 97.91 96.88 95.56 93.94 92.70 92.26 92.25 92.25 250 99.80 99.70 99.58 99.53 99.39 99.15 98.70 97.53 96.02 94.18 92.76 92.26 92.25 92.25 500 99.90 99.87 99.83 99.78 99.63 99.38 98.92 97.70 96.15 94.25 92.77 92.26 92.25 92.25 -------------------------------------------------------------------------------------------------------------------------------------- mutation-drift equilibrium of this model at N = K: H = 0.595921, 92.25% of the source The source spectrum itself sits slightly above that equilibrium, which is why even the unbottlenecked ceiling in the table is below 100 per cent. Approach to the model's own equilibrium. The last column is the first generation from which expected gene diversity stays inside one per cent of H_eq for good, coming from whichever side it started on. k H at founding minimum H at gen half the climb back within 1% ---------------------------------------------------------------------------------- 2 0.484466 0.261155 14 532 3017 5 0.581360 0.457361 13 531 2359 10 0.613657 0.545859 13 530 1599 25 0.633036 0.595921 - never dips below 394 50 0.639496 0.595921 - never dips below 1235 100 0.642725 0.595921 - never dips below 1451 250 0.644663 0.595921 - never dips below 1549 500 0.645309 0.595921 - never dips below 1574 ---------------------------------------------------------------------------------- ====================================================================================================================== SECTION 8. WHERE A DIFFERENT MODELLING CHOICE CHANGES THE ANSWER ====================================================================================================================== Two choices we made are arbitrary. Both are re-run here for k = 5, r = 0.15, 5,000 replicates, and all three variants are run for exactly 120 generations so that only the choice under test differs. capped geometric growth, mutation on gens 120 H_end 0.343596 +/- 0.001238 recursion 0.345179 A_end 7.187 discrete logistic growth, mutation on gens 120 H_end 0.339325 +/- 0.001247 recursion 0.339647 A_end 7.163 capped geometric growth, mutation off gens 120 H_end 0.287117 +/- 0.001322 recursion 0.286769 A_end 1.988 Individual-generations lived over the 120 generations: 89,715 under capped geometric growth against 83,553 under discrete logistic growth. Logistic growth holds the population below capacity for longer, and its final gene diversity differs from the geometric case by -1.24%, which is -0.004270 against a standard error of 0.001757 on the difference. Switching mutation off changes final gene diversity by -16.44% and the final allele count by -72.34%, over the same 120 generations. ====================================================================================================================== SECTION 9. HOW LONG THE SIGNATURE STAYS VISIBLE ====================================================================================================================== A new population on an island of carrying capacity 400, growth rate 0.25. 5,000 replicates per cell, 15 loci, and at each checkpoint a genetic sample of 60 gene copies (30 diploids) per locus, drawn with replacement from the population. Checkpoints start at generation 10 because before that the smaller founding groups hold fewer than 30 individuals, and a 30-individual sample is not something anybody could take. The control is a population founded by the full island capacity. It lost essentially nothing at the founding, but it lives in the same small place and drifts at the same rate afterwards. The test therefore measures the extra signature left by a SMALL founding group, over and above the signature left by living somewhere small. That is a harder test than comparing against the source. The statistic is the heterozygosity excess of Cornuet & Luikart (1996). A bottleneck kills rare alleles faster than it kills heterozygosity, so the population carries more diversity than its own allele count implies. We calibrate 'implies' from the controls, which were founded by the full 400 individuals and so lost essentially nothing, then count how many of the 15 loci sit above that control curve. The critical value is the smallest count whose control tail probability is at or below 0.05, so the false positive rate is 5 per cent by construction. Control null: distribution of the number of loci above the control curve. gen N k=5 crit false pos power k=5 power k=25 H k=5 H ctrl A k=5 A ctrl ------------------------------------------------------------------------------------------------------ 10 47 12 0.0212 0.6708 0.7096 0.4023 0.6345 2.551 6.377 13 91 12 0.0220 0.5978 0.6312 0.3954 0.6331 2.545 6.288 17 222 12 0.0224 0.4892 0.5500 0.3925 0.6307 2.578 6.172 22 400 12 0.0242 0.4098 0.4476 0.3921 0.6284 2.642 6.047 28 400 12 0.0340 0.3250 0.3764 0.3920 0.6252 2.718 5.911 36 400 12 0.0352 0.2050 0.2808 0.3913 0.6211 2.794 5.759 46 400 12 0.0410 0.1348 0.2090 0.3910 0.6163 2.869 5.593 60 400 12 0.0424 0.0648 0.1360 0.3906 0.6093 2.949 5.390 78 400 12 0.0494 0.0348 0.1060 0.3908 0.6014 3.029 5.192 100 400 13 0.0118 0.0016 0.0156 0.3896 0.5910 3.098 4.990 128 400 12 0.0494 0.0046 0.0478 0.3889 0.5794 3.157 4.787 160 400 13 0.0114 0.0004 0.0072 0.3889 0.5666 3.208 4.604 200 400 13 0.0136 0.0004 0.0080 0.3884 0.5514 3.248 4.424 ------------------------------------------------------------------------------------------------------ k = 5: power stays at or above 0.80 through generation never reached, and at or above 0.50 through generation 13. At generation 200 the power is 0.000. Binomial standard error on that last figure: 0.0003. k = 25: power stays at or above 0.80 through generation never reached, and at or above 0.50 through generation 17. At generation 200 the power is 0.008. Binomial standard error on that last figure: 0.0013. ====================================================================================================================== SECTION 10. THE NUMBERS THE ARTICLE QUOTES ====================================================================================================================== H retained by 2 founders : 74.973% +/- 0.048% (closed form 75.000%) H retained by 50 founders : 99.002% +/- 0.010% (closed form 99.000%) H retained by 500 founders : 99.899% +/- 0.003% (closed form 99.900%) alleles retained by 2 founders : 2.3895 of 11.550 per locus = 20.69% alleles retained by 50 founders : 7.3774 of 11.550 per locus = 63.87% alleles lost by 2 founders : 183.209 of 231 = 79.31% H after growth back to K, k=2 : 43.125% of source, after 50 generations at r = 0.40 H after growth back to K, k=50 : 96.720% of source, after 50 generations at r = 0.40 alleles after growth back, k=2 : 6.059 per locus = 52.46% of source generations for k=2 to climb half : 532 largest |z|, closed form : 2.13 over 15 founding sizes largest |z|, allele loss : 1.54 largest |z|, exact recursion : 2.52 over 32 cells k = N loses nothing : max alleles lost over 20,000 replicates = 0 total replicates in this file : 630,000 ====================================================================================================================== SECTION 11. FIGURE DATA ====================================================================================================================== Blocks below are the exact numbers plotted in the article's figures. Each block begins with FIGDATA and ends with ENDDATA, one record per line. FIGDATA source_spectrum locus p0 p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 0 0.378057224 0.307934238 0.094813188 0.081809309 0.062994670 0.035992884 0.025748709 0.006873495 0.002116868 0.002113869 0.000973626 0.000571920 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 1 0.465269403 0.263891933 0.152593893 0.047801741 0.019582497 0.018895693 0.014792612 0.007512265 0.004077458 0.003697293 0.001114923 0.000770290 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 2 0.470836039 0.205052826 0.126329677 0.086034365 0.035527274 0.022740974 0.016359582 0.016163569 0.015580713 0.001584687 0.001423007 0.000957594 0.000876176 0.000533517 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 3 0.277071285 0.230304053 0.156588340 0.107231033 0.097462946 0.051105969 0.029896568 0.024941953 0.012579501 0.005370520 0.003499911 0.001899450 0.001171568 0.000876904 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 4 0.849386241 0.068951722 0.039628846 0.030018519 0.008055383 0.003959289 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 5 0.569844415 0.328203715 0.054134242 0.027011100 0.007089156 0.006295085 0.003186906 0.002180098 0.002055284 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 6 0.417309331 0.288767698 0.082300297 0.055668656 0.047681011 0.043548086 0.028434428 0.018558377 0.004327601 0.003800195 0.003093716 0.001988774 0.001855221 0.001186821 0.000956139 0.000523648 0.000000000 0.000000000 0.000000000 0.000000000 7 0.295134449 0.186601808 0.175713453 0.141846570 0.070563127 0.050543130 0.049079662 0.026626444 0.002122605 0.001768752 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 8 0.244477394 0.162791261 0.157241697 0.116737911 0.113062758 0.101414354 0.060101243 0.020376694 0.009019491 0.006972795 0.003992567 0.001704193 0.001076806 0.001030837 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 9 0.523189580 0.282970658 0.106100741 0.026218175 0.017938657 0.017820163 0.015085178 0.004315211 0.003121754 0.001446741 0.001074817 0.000718324 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 10 0.358583190 0.262183414 0.172768220 0.105345212 0.069576561 0.021454826 0.003834836 0.003242172 0.001246683 0.001069754 0.000695131 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 11 0.900628807 0.042675224 0.023503620 0.010572699 0.008752783 0.005282166 0.004506022 0.002982074 0.001096605 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 12 0.514258288 0.331424839 0.040119594 0.027983871 0.027858068 0.021757510 0.014294994 0.009193325 0.004910082 0.002661161 0.002607991 0.001659134 0.001271142 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 13 0.672230568 0.126247651 0.077455163 0.038905138 0.016930236 0.015063026 0.012639990 0.011230750 0.011046023 0.007592185 0.003863438 0.003338927 0.001258005 0.000829393 0.000779298 0.000590208 0.000000000 0.000000000 0.000000000 0.000000000 14 0.443955662 0.229030008 0.190818390 0.071172424 0.045054478 0.015903063 0.001766680 0.001657687 0.000641608 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 15 0.842727525 0.040858001 0.036215253 0.028483852 0.018839147 0.017086052 0.008728107 0.003327835 0.002954648 0.000779579 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 16 0.720522651 0.114970555 0.064815470 0.060001518 0.015719799 0.007141333 0.004866187 0.002958800 0.002683796 0.001779444 0.001227451 0.001063439 0.001063340 0.000666198 0.000520020 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 17 0.550397189 0.310365933 0.072067718 0.046955878 0.008481178 0.004992129 0.004733103 0.001485196 0.000521676 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 18 0.663979626 0.103367586 0.072259730 0.054777743 0.054595132 0.019803822 0.016801992 0.006994098 0.004713221 0.001472790 0.001234262 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 19 0.593407875 0.135306670 0.119117946 0.118984503 0.018955105 0.006919671 0.004089894 0.002247028 0.000971308 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 ENDDATA The block above is the complete source spectrum, every allele frequency at every locus, so that the interactive companion and any re-analysis start from the same numbers this run did. FIGDATA fig1_retention k retention se predicted alleles alleles_se 2 0.74973056 0.00048159 0.75000000 2.389528 0.001119 3 0.83420838 0.00041055 0.83333333 2.927695 0.001303 5 0.90002170 0.00032322 0.90000000 3.667347 0.001464 8 0.93717987 0.00025843 0.93750000 4.401525 0.001575 10 0.95039272 0.00023053 0.95000000 4.763540 0.001585 12 0.95851008 0.00021210 0.95833333 5.063007 0.001601 20 0.97503182 0.00016474 0.97500000 5.903433 0.001632 30 0.98344518 0.00013495 0.98333333 6.564475 0.001621 50 0.99002019 0.00010406 0.99000000 7.377410 0.001611 75 0.99329730 0.00008505 0.99333333 8.003740 0.001604 100 0.99497615 0.00007460 0.99500000 8.440790 0.001593 150 0.99662467 0.00006052 0.99666667 9.041000 0.001558 200 0.99753165 0.00005223 0.99750000 9.455110 0.001507 350 0.99859414 0.00003963 0.99857143 10.201377 0.001350 500 0.99898998 0.00003302 0.99900000 10.615288 0.001208 ENDDATA FIGDATA fig2_loss k lost lost_se predicted frac_alleles_kept 2 183.209450 0.022379 183.193547 0.20688550 3 172.446100 0.026053 172.486105 0.25348009 5 157.653050 0.029285 157.651241 0.31751926 8 142.969500 0.031498 142.960055 0.38108442 10 135.729200 0.031701 135.745090 0.41242771 12 129.739850 0.032021 129.781100 0.43835563 20 112.931350 0.032643 112.965394 0.51111970 30 99.710500 0.032416 99.729050 0.56835281 50 83.451800 0.032213 83.432950 0.63873680 75 70.925200 0.032079 70.883365 0.69296450 100 62.184200 0.031861 62.183967 0.73080433 150 50.180000 0.031151 50.187770 0.78277056 200 41.897800 0.030132 41.913230 0.81862424 350 26.972450 0.027003 26.943368 0.88323615 500 18.694250 0.024160 18.711204 0.91907251 ENDDATA FIGDATA fig2b_perallele_k2 p pred_lost sim_lost 0.37805722 0.14962416 0.14770000 0.30793424 0.22939791 0.23045000 0.09481319 0.67135600 0.67220000 0.08180931 0.71077401 0.70990000 0.06299467 0.77084710 0.76855000 0.03599288 0.86361656 0.86290000 0.02574871 0.90091529 0.90505000 0.00687349 0.97278819 0.97295000 0.00211687 0.99155938 0.99220000 0.00211387 0.99157130 0.99225000 0.00097363 0.99611118 0.99650000 0.00057192 0.99771428 0.99780000 0.46526940 0.08175986 0.08270000 0.26389193 0.29360693 0.29300000 0.15259389 0.51566346 0.51710000 0.04780174 0.82207139 0.82100000 0.01958250 0.92394097 0.92360000 0.01889569 0.92653265 0.92655000 0.01479261 0.94212958 0.94050000 0.00751226 0.97028785 0.97160000 0.00407746 0.98378965 0.98435000 0.00369729 0.98529265 0.98470000 0.00111492 0.99554776 0.99590000 0.00077029 0.99692240 0.99700000 0.47083604 0.07840812 0.07645000 0.20505283 0.39934944 0.39595000 0.12632968 0.58262664 0.58725000 0.08603436 0.69778153 0.69450000 0.03552727 0.86528625 0.86225000 0.02274097 0.91209224 0.91290000 0.01635958 0.93615004 0.93605000 0.01616357 0.93689647 0.93880000 0.01558071 0.93911863 0.93940000 0.00158469 0.99367630 0.99315000 0.00142301 0.99432011 0.99305000 0.00095759 0.99617512 0.99650000 0.00087618 0.99649990 0.99645000 0.00053352 0.99786764 0.99710000 0.27707128 0.27313786 0.27550000 0.23030405 0.35097550 0.34745000 0.15658834 0.50600919 0.50985000 0.10723103 0.63526707 0.63475000 0.09746295 0.66352939 0.65900000 0.05110597 0.81071995 0.80970000 0.02989657 0.88567047 0.88445000 0.02494195 0.90390312 0.90165000 0.01257950 0.95062352 0.95160000 0.00537052 0.97869036 0.97840000 0.00349991 0.98607368 0.98590000 0.00189945 0.99242382 0.99255000 0.00117157 0.99532196 0.99565000 0.00087690 0.99649700 0.99615000 0.84938624 0.00051459 0.00050000 0.06895172 0.75143048 0.75140000 0.03962885 0.85066082 0.85185000 0.03001852 0.88522521 0.88705000 0.00805538 0.96816571 0.96915000 0.00395929 0.98425665 0.98460000 0.56984441 0.03423752 0.03300000 0.32820371 0.20368094 0.20665000 0.05413424 0.80042015 0.79950000 0.02701110 0.89625490 0.89680000 0.00708916 0.97194349 0.97095000 0.00629508 0.97505643 0.97505000 0.00318691 0.98731318 0.98860000 0.00218010 0.99130808 0.99220000 0.00205528 0.99180417 0.99035000 0.41730933 0.11527955 0.11590000 0.28876770 0.25588563 0.25255000 0.08230030 0.70925493 0.71020000 0.05566866 0.79523891 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0.00901949 0.96440721 0.96515000 0.00697279 0.97239919 0.97450000 0.00399257 0.98412512 0.98525000 0.00170419 0.99320063 0.99385000 0.00107681 0.99569973 0.99640000 0.00103084 0.99588303 0.99685000 0.52318958 0.05168719 0.05100000 0.28297066 0.26433076 0.26325000 0.10610074 0.63849031 0.63035000 0.02621818 0.89918004 0.90100000 0.01793866 0.93015316 0.93220000 0.01782016 0.93060216 0.93435000 0.01508518 0.94101098 0.94025000 0.00431521 0.98285056 0.98375000 0.00312175 0.98757134 0.98835000 0.00144674 0.99422558 0.99480000 0.00107482 0.99570766 0.99560000 0.00071832 0.99712980 0.99735000 0.35858319 0.16926273 0.17065000 0.26218341 0.29634231 0.29450000 0.17276822 0.46828348 0.45970000 0.10534521 0.64065167 0.64705000 0.06957656 0.74941533 0.75130000 0.02145483 0.91690326 0.91800000 0.00383484 0.98474867 0.98505000 0.00324217 0.98709424 0.98630000 0.00124668 0.99502258 0.99565000 0.00106975 0.99572785 0.99555000 0.00069513 0.99722237 0.99730000 0.90062881 0.00009751 0.00005000 0.04267522 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0.96945000 0.00386344 0.98463558 0.98395000 0.00333893 0.98671103 0.98625000 0.00125800 0.99497747 0.99465000 0.00082939 0.99668655 0.99590000 0.00077930 0.99688645 0.99675000 0.00059021 0.99764126 0.99710000 0.44395566 0.09559555 0.09670000 0.22903001 0.35330509 0.35200000 0.19081839 0.42873014 0.42900000 0.07117242 0.74428695 0.74660000 0.04505448 0.83159982 0.82915000 0.01590306 0.93788917 0.93685000 0.00176668 0.99295199 0.99255000 0.00165769 0.99338572 0.99360000 0.00064161 0.99743604 0.99770000 0.84272752 0.00061180 0.00065000 0.04085800 0.84631421 0.84485000 0.03621525 0.86281998 0.86180000 0.02848385 0.89084079 0.89280000 0.01883915 0.92674627 0.92465000 0.01708605 0.93338752 0.93490000 0.00872811 0.96554200 0.96640000 0.00332783 0.98675496 0.98675000 0.00295465 0.98823368 0.98810000 0.00077958 0.99688533 0.99650000 0.72052265 0.00610080 0.00600000 0.11497056 0.61352304 0.61740000 0.06481547 0.76487287 0.76810000 0.06000152 0.78074392 0.78185000 0.01571980 0.93858800 0.93985000 0.00714133 0.97173921 0.97445000 0.00486619 0.98067687 0.97995000 0.00295880 0.98821722 0.98855000 0.00268380 0.98930796 0.98760000 0.00177944 0.99290120 0.99280000 0.00122745 0.99509923 0.99445000 0.00106344 0.99575302 0.99560000 0.00106334 0.99575342 0.99650000 0.00066620 0.99733787 0.99750000 0.00052002 0.99792154 0.99765000 0.55039719 0.04086167 0.04425000 0.31036593 0.22619074 0.22815000 0.07206772 0.74142143 0.73935000 0.04695588 0.82499635 0.82245000 0.00848118 0.96650444 0.96745000 0.00499213 0.98018052 0.98015000 0.00473310 0.98120158 0.98060000 0.00148520 0.99407244 0.99345000 0.00052168 0.99791493 0.99810000 0.66397963 0.01274860 0.01265000 0.10336759 0.64633510 0.64975000 0.07225973 0.74080795 0.74025000 0.05477774 0.79824417 0.80100000 0.05459513 0.79886121 0.79915000 0.01980382 0.92310695 0.92345000 0.01680199 0.93446698 0.93670000 0.00699410 0.97231575 0.97260000 0.00471322 0.98127999 0.98015000 0.00147279 0.99412184 0.99470000 0.00123426 0.99507209 0.99560000 0.59340787 0.02732976 0.02510000 0.13530667 0.55904715 0.55885000 0.11911795 0.60210336 0.59815000 0.11898450 0.60246829 0.60160000 0.01895511 0.92630824 0.92735000 0.00691967 0.97260729 0.97195000 0.00408989 0.98374052 0.98480000 0.00224703 0.99104214 0.99120000 0.00097131 0.99612043 0.99725000 ENDDATA FIGDATA fig3_traj_k2_r0.05 t N h h_recursion a 0 2 0.48368500 0.48446644 2.516960 1 2 0.36215500 0.36364379 1.989280 2 2 0.27195000 0.27310310 1.693200 3 2 0.20374000 0.20525475 1.502280 4 2 0.15260000 0.15441133 1.369800 5 3 0.12799333 0.12923430 1.325680 6 3 0.10655778 0.10827110 1.273320 7 3 0.08866444 0.09081648 1.227440 8 3 0.07500889 0.07628321 1.191760 9 3 0.06372000 0.06418235 1.162600 10 3 0.05342667 0.05410678 1.136720 11 3 0.04520889 0.04571755 1.114720 12 4 0.04055625 0.04066903 1.106320 13 4 0.03625625 0.03625529 1.095880 14 4 0.03223750 0.03239653 1.086040 15 4 0.02928875 0.02902295 1.078360 16 4 0.02655125 0.02607355 1.070920 17 5 0.02450400 0.02416629 1.066760 18 5 0.02306960 0.02245119 1.064200 19 5 0.02162320 0.02090891 1.060640 20 5 0.02023920 0.01952203 1.057240 21 6 0.01924389 0.01861330 1.055960 22 6 0.01823722 0.01778101 1.054080 23 6 0.01746611 0.01701871 1.051800 24 6 0.01694944 0.01632053 1.050600 25 7 0.01663143 0.01588472 1.052200 26 7 0.01611714 0.01548038 1.051040 27 7 0.01554980 0.01510524 1.050360 28 8 0.01507250 0.01489908 1.051400 29 8 0.01490125 0.01470597 1.050400 30 9 0.01476765 0.01463267 1.051040 31 9 0.01460938 0.01456351 1.051280 32 10 0.01477460 0.01458352 1.054200 33 10 0.01484460 0.01460252 1.055360 34 11 0.01505521 0.01469051 1.058160 35 11 0.01532248 0.01477443 1.060040 36 12 0.01542806 0.01491342 1.062040 37 12 0.01533056 0.01504650 1.063400 38 13 0.01532071 0.01522467 1.063960 39 13 0.01539136 0.01539585 1.065120 40 14 0.01547378 0.01560477 1.067280 41 15 0.01571093 0.01584508 1.071680 42 16 0.01586820 0.01611183 1.073960 43 16 0.01602406 0.01637003 1.074640 44 17 0.01630976 0.01665149 1.079200 45 18 0.01669469 0.01695293 1.082600 46 19 0.01701873 0.01727169 1.086200 47 20 0.01731270 0.01760556 1.091640 48 21 0.01784204 0.01795269 1.095920 49 22 0.01824368 0.01831156 1.100680 50 23 0.01867879 0.01868085 1.106800 51 24 0.01911635 0.01905943 1.111760 52 25 0.01952554 0.01944635 1.116360 53 27 0.02008933 0.01985518 1.122080 54 28 0.02057227 0.02026976 1.128000 55 29 0.02096647 0.02068955 1.132000 56 31 0.02156445 0.02112564 1.142800 57 32 0.02203596 0.02156538 1.147760 58 34 0.02254777 0.02201842 1.155800 59 36 0.02284131 0.02248305 1.164840 60 37 0.02334729 0.02294957 1.169920 61 39 0.02365738 0.02342585 1.178080 62 41 0.02397362 0.02391077 1.184400 63 43 0.02457950 0.02440337 1.193120 64 45 0.02521327 0.02490285 1.202720 65 48 0.02560753 0.02541419 1.213520 66 50 0.02606150 0.02593070 1.222640 67 53 0.02663564 0.02645673 1.234000 68 55 0.02732083 0.02698671 1.244520 69 58 0.02778343 0.02752447 1.255720 70 61 0.02834334 0.02806915 1.268120 71 64 0.02885552 0.02862000 1.279000 72 67 0.02943317 0.02917636 1.291520 73 70 0.02990785 0.02973769 1.303320 74 74 0.03048417 0.03030632 1.322200 75 78 0.03093088 0.03088140 1.334080 76 82 0.03166292 0.03146221 1.353520 77 86 0.03224191 0.03204814 1.368680 78 90 0.03276021 0.03263865 1.385880 79 94 0.03333337 0.03323328 1.408080 80 99 0.03386268 0.03383339 1.422840 81 104 0.03446237 0.03443837 1.442400 82 109 0.03503637 0.03504770 1.469520 83 115 0.03570112 0.03566229 1.489960 84 120 0.03618077 0.03628030 1.510520 85 127 0.03668722 0.03690372 1.533080 86 133 0.03736274 0.03753085 1.564120 87 139 0.03799135 0.03816132 1.593280 88 146 0.03858936 0.03879570 1.619240 89 154 0.03912738 0.03943442 1.646880 90 161 0.03984580 0.04007620 1.675960 91 170 0.04052632 0.04072217 1.711040 92 178 0.04112710 0.04137118 1.745680 93 187 0.04184420 0.04202352 1.784680 94 196 0.04247521 0.04267881 1.825680 95 206 0.04318928 0.04333727 1.871600 96 216 0.04388814 0.04399853 1.914440 97 227 0.04450524 0.04466272 1.958320 98 239 0.04523119 0.04532992 2.002320 99 250 0.04590972 0.04599940 2.045280 100 263 0.04665562 0.04667161 2.099200 101 276 0.04731384 0.04734622 2.149160 102 290 0.04792648 0.04802325 2.202080 103 304 0.04861709 0.04870241 2.268080 104 320 0.04941382 0.04938396 2.334000 105 336 0.05009345 0.05006759 2.391480 106 352 0.05083251 0.05075308 2.461280 107 370 0.05145640 0.05144057 2.534000 108 389 0.05217999 0.05213000 2.608880 109 408 0.05295352 0.05282113 2.682200 110 428 0.05358613 0.05351390 2.764440 111 450 0.05425093 0.05420838 2.844080 112 472 0.05495891 0.05490435 2.924760 113 496 0.05576176 0.05560185 3.028040 114 521 0.05655249 0.05630078 3.128160 115 547 0.05727258 0.05700106 3.220960 116 574 0.05799099 0.05770260 3.332960 117 603 0.05866431 0.05840538 3.434520 118 633 0.05937196 0.05910931 3.548080 119 665 0.06005467 0.05981437 3.666920 120 698 0.06067788 0.06052046 3.787480 121 733 0.06138039 0.06122754 3.910240 122 769 0.06207811 0.06193553 4.035960 123 808 0.06270381 0.06264442 4.180240 124 848 0.06345480 0.06335414 4.319200 125 891 0.06419424 0.06406466 4.462920 126 935 0.06492216 0.06477589 4.628960 127 982 0.06560429 0.06548783 4.793880 128 1000 0.06635122 0.06619941 4.914680 129 1000 0.06708346 0.06691003 5.022080 130 1000 0.06782692 0.06761970 5.102200 131 1000 0.06848821 0.06832842 5.164480 132 1000 0.06919390 0.06903619 5.224400 133 1000 0.06994025 0.06974301 5.285240 134 1000 0.07060429 0.07044888 5.337840 135 1000 0.07130735 0.07115380 5.376000 136 1000 0.07198815 0.07185778 5.432040 137 1000 0.07276410 0.07256082 5.481960 138 1000 0.07346810 0.07326291 5.518480 139 1000 0.07414692 0.07396406 5.560480 140 1000 0.07485675 0.07466426 5.603280 141 1000 0.07552341 0.07536353 5.634640 142 1000 0.07618342 0.07606186 5.678360 143 1000 0.07698401 0.07675926 5.717720 144 1000 0.07767243 0.07745572 5.737360 145 1000 0.07833183 0.07815124 5.765240 146 1000 0.07908879 0.07884583 5.789880 147 1000 0.07975685 0.07953949 5.811760 ENDDATA FIGDATA fig3_traj_k2_r0.15 t N h h_recursion a 0 2 0.48617000 0.48446644 2.533280 1 2 0.36606000 0.36364379 1.999480 2 3 0.30492000 0.30344789 1.846040 3 3 0.25551556 0.25332686 1.692080 4 3 0.21366667 0.21159451 1.565520 5 4 0.18869500 0.18568917 1.509400 6 5 0.17001280 0.16769940 1.467640 7 5 0.15442480 0.15152223 1.423680 8 6 0.14222111 0.13951162 1.393680 9 7 0.13233837 0.13018014 1.371800 10 8 0.12418500 0.12269097 1.354880 11 9 0.11794691 0.11653264 1.340160 12 11 0.11302711 0.11190553 1.332560 13 12 0.10869292 0.10791901 1.324800 14 14 0.10542061 0.10474841 1.320880 15 16 0.10264422 0.10216443 1.318880 16 19 0.10040183 0.10017092 1.322080 17 22 0.09857740 0.09859354 1.326560 18 25 0.09712358 0.09732416 1.330680 19 28 0.09595431 0.09629130 1.336840 20 33 0.09529537 0.09554021 1.346800 21 38 0.09468368 0.09499303 1.359080 22 43 0.09438628 0.09459994 1.373920 23 50 0.09420559 0.09436693 1.391280 24 57 0.09403775 0.09425321 1.410400 25 66 0.09398780 0.09425419 1.433720 26 76 0.09409398 0.09434983 1.459800 27 87 0.09448686 0.09452385 1.492560 28 100 0.09469218 0.09476788 1.530160 29 115 0.09505496 0.09507276 1.566600 30 132 0.09527679 0.09542969 1.618720 31 152 0.09578872 0.09583290 1.672520 32 175 0.09631396 0.09627618 1.740520 33 201 0.09667199 0.09675368 1.819160 34 232 0.09709346 0.09726198 1.907800 35 266 0.09765102 0.09779575 2.005480 36 306 0.09815663 0.09835228 2.110760 37 352 0.09883137 0.09892858 2.238600 38 405 0.09936482 0.09952210 2.376640 39 466 0.09999209 0.10013059 2.547840 40 536 0.10063715 0.10075205 2.741760 41 616 0.10126760 0.10138469 2.959320 42 708 0.10188852 0.10202706 3.211400 43 815 0.10256596 0.10267796 3.485240 44 937 0.10323382 0.10333617 3.791600 45 1000 0.10391308 0.10399698 4.061680 46 1000 0.10453354 0.10465690 4.232200 47 1000 0.10519732 0.10531593 4.366560 48 1000 0.10584979 0.10597408 4.488440 49 1000 0.10656829 0.10663135 4.592320 50 1000 0.10717451 0.10728773 4.677920 51 1000 0.10784712 0.10794324 4.771720 52 1000 0.10851264 0.10859786 4.849600 53 1000 0.10915416 0.10925161 4.922280 54 1000 0.10980774 0.10990448 4.993360 55 1000 0.11044317 0.11055647 5.039840 56 1000 0.11101555 0.11120759 5.092160 57 1000 0.11165565 0.11185784 5.148600 58 1000 0.11228184 0.11250721 5.194400 59 1000 0.11291721 0.11315572 5.247640 60 1000 0.11354365 0.11380335 5.294160 61 1000 0.11424250 0.11445011 5.337160 62 1000 0.11481787 0.11509601 5.379640 63 1000 0.11542501 0.11574104 5.418880 64 1000 0.11604089 0.11638520 5.455640 ENDDATA FIGDATA fig3_traj_k2_r0.40 t N h h_recursion a 0 2 0.48432000 0.48446644 2.522920 1 3 0.40451778 0.40404866 2.240680 2 4 0.35473500 0.35394477 2.076120 3 5 0.32028240 0.31900195 1.967000 4 8 0.30118312 0.29956238 1.925720 5 11 0.28856711 0.28646863 1.898880 6 15 0.27968649 0.27745970 1.884600 7 21 0.27347084 0.27140627 1.881280 8 30 0.26918767 0.26744464 1.887400 9 41 0.26670984 0.26475077 1.904800 10 58 0.26527226 0.26304039 1.931200 11 81 0.26443454 0.26199149 1.972520 12 113 0.26388570 0.26140892 2.034480 13 159 0.26353008 0.26116480 2.122920 14 222 0.26363350 0.26115524 2.249120 15 311 0.26386539 0.26131440 2.416760 16 436 0.26404637 0.26159389 2.646720 17 610 0.26438395 0.26195858 2.983640 18 854 0.26480033 0.26238415 3.434600 19 1000 0.26531414 0.26283159 3.847680 20 1000 0.26575536 0.26327843 4.105640 21 1000 0.26613952 0.26372467 4.297520 22 1000 0.26660674 0.26417032 4.451000 23 1000 0.26706450 0.26461536 4.599040 24 1000 0.26754254 0.26505981 4.704400 25 1000 0.26796752 0.26550366 4.811560 26 1000 0.26845613 0.26594692 4.907720 27 1000 0.26893709 0.26638958 5.004240 28 1000 0.26941105 0.26683165 5.076000 29 1000 0.26973761 0.26727312 5.140280 30 1000 0.27016898 0.26771401 5.202760 31 1000 0.27061089 0.26815430 5.276040 32 1000 0.27093837 0.26859400 5.332120 33 1000 0.27142227 0.26903311 5.396920 34 1000 0.27183754 0.26947163 5.445400 35 1000 0.27232042 0.26990957 5.493600 36 1000 0.27275206 0.27034691 5.548800 37 1000 0.27322065 0.27078367 5.597360 38 1000 0.27361684 0.27121984 5.642480 39 1000 0.27405706 0.27165543 5.688640 40 1000 0.27444899 0.27209044 5.725800 41 1000 0.27488267 0.27252486 5.760040 42 1000 0.27525417 0.27295870 5.795160 43 1000 0.27576987 0.27339195 5.840280 44 1000 0.27620375 0.27382463 5.872000 45 1000 0.27661655 0.27425672 5.909200 46 1000 0.27699439 0.27468823 5.933680 47 1000 0.27743680 0.27511917 5.964880 48 1000 0.27783840 0.27554953 5.993520 49 1000 0.27825726 0.27597931 6.017000 50 1000 0.27857099 0.27640851 6.059160 ENDDATA FIGDATA fig3_traj_k2_r1.00 t N h h_recursion a 0 2 0.48414000 0.48446644 2.523560 1 4 0.42456375 0.42425109 2.370000 2 8 0.39722469 0.39815038 2.316240 3 16 0.38592313 0.38615827 2.304400 4 32 0.37994617 0.38059185 2.318840 5 64 0.37771991 0.37809413 2.359600 6 128 0.37666691 0.37709682 2.444720 7 256 0.37648492 0.37684171 2.618120 8 512 0.37667592 0.37695578 2.961280 9 1000 0.37692192 0.37724953 3.605720 10 1000 0.37726985 0.37754288 3.977520 11 1000 0.37751789 0.37783583 4.240360 12 1000 0.37775481 0.37812839 4.439880 13 1000 0.37798722 0.37842056 4.600000 14 1000 0.37827224 0.37871234 4.753360 15 1000 0.37852470 0.37900373 4.880320 16 1000 0.37880225 0.37929472 4.989000 17 1000 0.37911305 0.37958533 5.094240 18 1000 0.37942803 0.37987554 5.179200 19 1000 0.37963973 0.38016537 5.273320 20 1000 0.37993657 0.38045481 5.355680 21 1000 0.38026124 0.38074385 5.417040 22 1000 0.38051652 0.38103252 5.490480 23 1000 0.38073656 0.38132079 5.559520 24 1000 0.38101211 0.38160868 5.621280 25 1000 0.38133275 0.38189618 5.681520 26 1000 0.38164499 0.38218329 5.732680 27 1000 0.38183712 0.38247002 5.793320 28 1000 0.38210997 0.38275637 5.836960 29 1000 0.38240173 0.38304233 5.884920 30 1000 0.38272098 0.38332791 5.922400 31 1000 0.38303427 0.38361310 5.970400 32 1000 0.38332142 0.38389791 6.015800 33 1000 0.38358533 0.38418234 6.053080 34 1000 0.38382642 0.38446639 6.081440 35 1000 0.38411347 0.38475006 6.118760 36 1000 0.38440656 0.38503335 6.156720 37 1000 0.38470302 0.38531625 6.196240 38 1000 0.38496986 0.38559878 6.243400 39 1000 0.38530058 0.38588093 6.268880 40 1000 0.38560497 0.38616270 6.301840 41 1000 0.38587525 0.38644409 6.335800 42 1000 0.38615071 0.38672510 6.369960 43 1000 0.38647571 0.38700574 6.406160 44 1000 0.38680843 0.38728600 6.432680 45 1000 0.38713607 0.38756589 6.449920 46 1000 0.38749057 0.38784540 6.473280 47 1000 0.38766949 0.38812453 6.498440 48 1000 0.38788707 0.38840329 6.528040 49 1000 0.38822390 0.38868168 6.554880 50 1000 0.38853665 0.38895969 6.575720 ENDDATA FIGDATA fig3_traj_k25_r0.05 t N h h_recursion a 0 25 0.63304762 0.63303615 6.719200 1 26 0.62170648 0.62112411 5.999760 2 28 0.61064704 0.61030455 5.549560 3 29 0.60040908 0.60006313 5.220640 4 30 0.59078967 0.59035179 4.955600 5 32 0.58205779 0.58142561 4.746480 6 34 0.57426419 0.57318098 4.575880 7 35 0.56590811 0.56530540 4.428680 8 37 0.55875860 0.55798565 4.307960 9 39 0.55172135 0.55115780 4.198400 10 41 0.54556253 0.54476807 4.104360 11 43 0.53976281 0.53877077 4.023320 12 45 0.53388621 0.53312680 3.947520 13 47 0.52818217 0.52780248 3.883840 14 49 0.52348288 0.52276858 3.825280 15 52 0.51850643 0.51809820 3.780680 16 55 0.51378033 0.51374854 3.738240 17 57 0.50995966 0.50960604 3.697400 18 60 0.50624592 0.50572701 3.663320 19 63 0.50276458 0.50208439 3.632960 20 66 0.49919988 0.49865497 3.602720 21 70 0.49601141 0.49547044 3.585200 22 73 0.49305658 0.49245686 3.569320 23 77 0.49044419 0.48964181 3.553240 24 81 0.48773927 0.48700452 3.533760 25 85 0.48553221 0.48452731 3.521200 26 89 0.48309020 0.48219494 3.511600 27 93 0.48092367 0.47999423 3.506480 28 98 0.47910378 0.47793897 3.503920 29 103 0.47680796 0.47601439 3.501160 30 108 0.47499521 0.47420784 3.505840 31 113 0.47313591 0.47250838 3.512360 32 119 0.47151867 0.47092338 3.517480 33 125 0.46990819 0.46944142 3.522960 34 131 0.46826400 0.46805271 3.530320 35 138 0.46686019 0.46676116 3.544320 36 145 0.46559941 0.46555709 3.554520 37 152 0.46458099 0.46443217 3.570320 38 160 0.46348992 0.46338836 3.588800 39 168 0.46252646 0.46241770 3.605840 40 176 0.46168504 0.46151336 3.624920 41 185 0.46104325 0.46067618 3.647440 42 194 0.46030592 0.45989979 3.675120 43 204 0.45959011 0.45918420 3.705120 44 214 0.45884801 0.45852360 3.729720 45 225 0.45831953 0.45791753 3.761120 46 236 0.45772171 0.45736079 3.801520 47 248 0.45709989 0.45685262 3.839600 48 260 0.45673790 0.45638845 3.878880 49 273 0.45612041 0.45596740 3.916920 50 287 0.45570045 0.45558825 3.965960 51 301 0.45547076 0.45524702 4.009440 52 316 0.45517354 0.45494258 4.055840 53 332 0.45490976 0.45467360 4.113320 54 348 0.45463349 0.45443677 4.171760 55 366 0.45452569 0.45423261 4.234080 56 384 0.45446813 0.45405802 4.288360 57 403 0.45429970 0.45391170 4.348560 58 424 0.45415803 0.45379361 4.419640 59 445 0.45408767 0.45370103 4.487840 60 467 0.45408995 0.45363267 4.565360 61 490 0.45397696 0.45358725 4.645480 62 515 0.45402282 0.45356442 4.726560 63 541 0.45403019 0.45356280 4.813960 64 568 0.45408236 0.45358114 4.902680 65 596 0.45414070 0.45361821 4.998280 66 626 0.45408081 0.45367348 5.086600 67 657 0.45405679 0.45374577 5.187400 68 690 0.45417510 0.45383448 5.297200 69 724 0.45418762 0.45393851 5.414800 70 761 0.45427428 0.45405763 5.522280 71 799 0.45441439 0.45419077 5.643640 72 839 0.45457416 0.45433729 5.772320 73 881 0.45481061 0.45449651 5.908120 74 925 0.45496781 0.45466779 6.043280 75 971 0.45511556 0.45485048 6.190520 76 1000 0.45530436 0.45503973 6.331080 77 1000 0.45548481 0.45522872 6.414840 78 1000 0.45566148 0.45541746 6.495920 79 1000 0.45580073 0.45560595 6.556520 80 1000 0.45614987 0.45579418 6.620400 81 1000 0.45638287 0.45598216 6.665840 82 1000 0.45649082 0.45616989 6.718080 83 1000 0.45664952 0.45635737 6.770760 84 1000 0.45684152 0.45654459 6.810640 85 1000 0.45704780 0.45673157 6.843640 86 1000 0.45719004 0.45691829 6.873040 87 1000 0.45739610 0.45710476 6.908520 88 1000 0.45763844 0.45729098 6.947560 89 1000 0.45779435 0.45747696 6.972280 90 1000 0.45797521 0.45766268 7.005920 91 1000 0.45823263 0.45784815 7.034840 92 1000 0.45840916 0.45803338 7.064600 93 1000 0.45856512 0.45821835 7.088480 94 1000 0.45869763 0.45840308 7.106040 95 1000 0.45891449 0.45858756 7.139440 ENDDATA FIGDATA fig3_traj_k25_r0.15 t N h h_recursion a 0 25 0.63318291 0.63303615 6.714640 1 29 0.62279239 0.62238400 6.098040 2 33 0.61369150 0.61322559 5.717440 3 38 0.60624140 0.60543664 5.464840 4 44 0.59972583 0.59884348 5.287600 5 50 0.59412523 0.59314773 5.147240 6 58 0.58923719 0.58833225 5.047240 7 67 0.58503367 0.58424393 4.973920 8 76 0.58139331 0.58070614 4.915200 9 88 0.57849668 0.57771582 4.883040 10 101 0.57571194 0.57516773 4.860160 11 116 0.57376023 0.57300278 4.849520 12 134 0.57180662 0.57118093 4.853280 13 154 0.57028140 0.56964435 4.870840 14 177 0.56898412 0.56835451 4.895000 15 203 0.56789926 0.56727515 4.934000 16 234 0.56694885 0.56638456 4.986520 17 269 0.56624699 0.56565418 5.054960 18 309 0.56567079 0.56506195 5.132080 19 356 0.56529945 0.56459196 5.233720 20 409 0.56501324 0.56422583 5.347480 21 471 0.56470604 0.56395132 5.479560 22 541 0.56451152 0.56375483 5.644120 23 622 0.56431795 0.56362658 5.822680 24 716 0.56429230 0.56355806 6.027520 25 823 0.56421216 0.56354084 6.250400 26 946 0.56423639 0.56356818 6.505640 27 1000 0.56425884 0.56361158 6.714120 28 1000 0.56437866 0.56365492 6.855440 29 1000 0.56450035 0.56369821 6.971440 30 1000 0.56455989 0.56374144 7.065960 31 1000 0.56457912 0.56378460 7.144200 32 1000 0.56452536 0.56382772 7.222840 33 1000 0.56452953 0.56387077 7.289520 34 1000 0.56454066 0.56391376 7.347000 35 1000 0.56462581 0.56395670 7.401280 36 1000 0.56472763 0.56399958 7.446760 37 1000 0.56481409 0.56404240 7.491440 38 1000 0.56486502 0.56408517 7.534280 39 1000 0.56487270 0.56412787 7.577640 40 1000 0.56486498 0.56417052 7.608080 41 1000 0.56487850 0.56421312 7.643920 42 1000 0.56498665 0.56425565 7.682120 43 1000 0.56498742 0.56429813 7.710920 44 1000 0.56511619 0.56434055 7.740960 45 1000 0.56507415 0.56438292 7.767160 46 1000 0.56509439 0.56442523 7.797840 47 1000 0.56514403 0.56446748 7.831800 48 1000 0.56522928 0.56450967 7.855760 49 1000 0.56531761 0.56455181 7.881320 50 1000 0.56529827 0.56459389 7.911280 ENDDATA FIGDATA fig3_traj_k25_r0.40 t N h h_recursion a 0 25 0.63310899 0.63303615 6.704520 1 35 0.62452335 0.62425583 6.251320 2 49 0.61870655 0.61815733 6.034840 3 69 0.61485973 0.61395529 5.918280 4 96 0.61194425 0.61103906 5.869440 5 134 0.60982244 0.60904338 5.872640 6 188 0.60852392 0.60770988 5.914200 7 264 0.60776650 0.60684655 6.007560 8 369 0.60726019 0.60631278 6.151360 9 517 0.60700999 0.60601549 6.359920 10 723 0.60691042 0.60588580 6.656080 11 1000 0.60696867 0.60587243 7.061680 12 1000 0.60699628 0.60585908 7.284920 13 1000 0.60696081 0.60584575 7.440280 14 1000 0.60692248 0.60583243 7.583040 15 1000 0.60691017 0.60581914 7.681320 16 1000 0.60690435 0.60580586 7.771920 17 1000 0.60683144 0.60579260 7.859200 18 1000 0.60687869 0.60577935 7.937480 19 1000 0.60703513 0.60576613 8.002480 20 1000 0.60696585 0.60575292 8.065520 21 1000 0.60689140 0.60573973 8.117320 22 1000 0.60684270 0.60572656 8.157760 23 1000 0.60688402 0.60571340 8.201520 24 1000 0.60682947 0.60570026 8.243920 25 1000 0.60673898 0.60568715 8.289480 26 1000 0.60664221 0.60567404 8.338560 27 1000 0.60658235 0.60566096 8.369120 28 1000 0.60657066 0.60564789 8.407560 29 1000 0.60650457 0.60563484 8.435920 30 1000 0.60639427 0.60562181 8.464520 31 1000 0.60633477 0.60560880 8.491760 32 1000 0.60629877 0.60559580 8.521520 33 1000 0.60626589 0.60558282 8.546080 34 1000 0.60626888 0.60556986 8.569880 35 1000 0.60625527 0.60555691 8.596680 36 1000 0.60617571 0.60554399 8.629640 37 1000 0.60610888 0.60553108 8.649640 38 1000 0.60612845 0.60551818 8.659640 39 1000 0.60606191 0.60550531 8.677040 40 1000 0.60595177 0.60549245 8.696240 41 1000 0.60583499 0.60547961 8.710200 42 1000 0.60585794 0.60546679 8.730560 43 1000 0.60579471 0.60545398 8.742040 44 1000 0.60587713 0.60544119 8.754960 45 1000 0.60573283 0.60542842 8.764720 46 1000 0.60576531 0.60541567 8.777040 47 1000 0.60569386 0.60540293 8.785320 48 1000 0.60572621 0.60539021 8.801400 49 1000 0.60573960 0.60537750 8.818480 50 1000 0.60578732 0.60536482 8.842160 ENDDATA FIGDATA fig3_traj_k25_r1.00 t N h h_recursion a 0 25 0.63286307 0.63303615 6.702480 1 50 0.62658720 0.62696998 6.488320 2 100 0.62383190 0.62410574 6.458880 3 200 0.62231211 0.62281917 6.528280 4 400 0.62177591 0.62231577 6.727360 5 800 0.62164109 0.62220253 7.128920 6 1000 0.62158007 0.62216728 7.505600 7 1000 0.62158310 0.62213207 7.732680 8 1000 0.62158132 0.62209690 7.901680 9 1000 0.62152297 0.62206179 8.041960 10 1000 0.62147542 0.62202672 8.152120 11 1000 0.62134886 0.62199170 8.247840 12 1000 0.62131778 0.62195672 8.334960 13 1000 0.62131285 0.62192179 8.409080 14 1000 0.62124689 0.62188691 8.468880 15 1000 0.62111034 0.62185208 8.544760 16 1000 0.62103037 0.62181729 8.602040 17 1000 0.62096107 0.62178255 8.639600 18 1000 0.62095409 0.62174786 8.679560 19 1000 0.62093413 0.62171321 8.713120 20 1000 0.62087345 0.62167861 8.754680 21 1000 0.62077860 0.62164406 8.791640 22 1000 0.62073206 0.62160955 8.830720 23 1000 0.62075206 0.62157509 8.867800 24 1000 0.62085090 0.62154067 8.902960 25 1000 0.62083509 0.62150630 8.925240 26 1000 0.62079998 0.62147198 8.954560 27 1000 0.62074736 0.62143770 8.979680 28 1000 0.62067699 0.62140347 9.002360 29 1000 0.62066839 0.62136928 9.020680 30 1000 0.62059771 0.62133514 9.048400 31 1000 0.62057553 0.62130105 9.062960 32 1000 0.62054180 0.62126700 9.080640 33 1000 0.62056346 0.62123300 9.101040 34 1000 0.62051550 0.62119904 9.123320 35 1000 0.62052952 0.62116513 9.141520 36 1000 0.62046653 0.62113126 9.156920 37 1000 0.62041155 0.62109744 9.174680 38 1000 0.62040536 0.62106367 9.188760 39 1000 0.62037516 0.62102994 9.214320 40 1000 0.62033614 0.62099626 9.216920 41 1000 0.62032305 0.62096262 9.226440 42 1000 0.62033292 0.62092902 9.242160 43 1000 0.62025870 0.62089547 9.252000 44 1000 0.62025102 0.62086197 9.263880 45 1000 0.62015797 0.62082851 9.278640 46 1000 0.62012083 0.62079510 9.284400 47 1000 0.62004740 0.62076173 9.289240 48 1000 0.61992084 0.62072840 9.302560 49 1000 0.61989545 0.62069512 9.310080 50 1000 0.61983419 0.62066189 9.318400 ENDDATA FIGDATA fig3_traj_k250_r0.05 t N h h_recursion a 0 250 0.64464244 0.64466335 9.870720 1 262 0.64357799 0.64368966 9.472040 2 276 0.64243254 0.64278098 9.224840 3 289 0.64146524 0.64192711 9.045520 4 304 0.64061439 0.64113025 8.911760 5 319 0.63986406 0.64038499 8.812760 6 335 0.63925836 0.63968947 8.722440 7 352 0.63860432 0.63904171 8.661800 8 369 0.63807139 0.63843725 8.607320 9 388 0.63753051 0.63787650 8.569840 10 407 0.63717295 0.63735533 8.542440 11 428 0.63679751 0.63687367 8.532800 12 449 0.63632241 0.63642779 8.520120 13 471 0.63591514 0.63601590 8.525320 14 495 0.63558268 0.63563755 8.537520 15 520 0.63527213 0.63529078 8.562520 16 546 0.63496005 0.63497373 8.582080 17 573 0.63464061 0.63468465 8.611600 18 602 0.63434832 0.63442275 8.643960 19 632 0.63412593 0.63418632 8.690680 20 663 0.63386977 0.63397374 8.741240 21 696 0.63378168 0.63378418 8.794920 22 731 0.63374409 0.63361672 8.859200 23 768 0.63358135 0.63347041 8.930200 24 806 0.63341429 0.63334377 9.002400 25 847 0.63325316 0.63323634 9.082720 26 889 0.63310113 0.63314673 9.160640 27 933 0.63303450 0.63307405 9.256520 28 980 0.63291387 0.63301774 9.358560 29 1000 0.63288091 0.63296798 9.422720 30 1000 0.63280392 0.63291828 9.462800 31 1000 0.63274166 0.63286865 9.503960 32 1000 0.63268000 0.63281908 9.533000 33 1000 0.63274277 0.63276958 9.561960 34 1000 0.63272391 0.63272015 9.591160 35 1000 0.63275449 0.63267078 9.613680 36 1000 0.63271364 0.63262148 9.634400 37 1000 0.63267965 0.63257224 9.653640 38 1000 0.63257629 0.63252308 9.667400 39 1000 0.63260468 0.63247397 9.684880 40 1000 0.63255937 0.63242494 9.704960 41 1000 0.63247709 0.63237597 9.712200 42 1000 0.63233967 0.63232706 9.727120 43 1000 0.63217410 0.63227822 9.739240 44 1000 0.63219192 0.63222945 9.740960 45 1000 0.63212924 0.63218074 9.754040 46 1000 0.63208069 0.63213210 9.762520 47 1000 0.63210409 0.63208352 9.765000 48 1000 0.63213189 0.63203501 9.772160 49 1000 0.63201416 0.63198656 9.776320 50 1000 0.63197101 0.63193817 9.784120 ENDDATA FIGDATA fig3_traj_k250_r0.15 t N h h_recursion a 0 250 0.64455465 0.64466335 9.872600 1 288 0.64359458 0.64380077 9.548600 2 331 0.64292133 0.64308567 9.380480 3 380 0.64234115 0.64249756 9.297040 4 437 0.64198138 0.64202104 9.267320 5 503 0.64159157 0.64164188 9.290120 6 578 0.64131209 0.64134622 9.335480 7 665 0.64119077 0.64112367 9.411920 8 765 0.64098098 0.64096452 9.526760 9 879 0.64084375 0.64085996 9.678520 10 1000 0.64080202 0.64079967 9.844240 11 1000 0.64075193 0.64073947 9.934360 12 1000 0.64065987 0.64067934 9.991440 13 1000 0.64059055 0.64061930 10.038200 14 1000 0.64060805 0.64055933 10.073320 15 1000 0.64057979 0.64049945 10.103200 16 1000 0.64046521 0.64043965 10.127480 17 1000 0.64035230 0.64037993 10.139920 18 1000 0.64030354 0.64032028 10.147960 19 1000 0.64027229 0.64026072 10.169800 20 1000 0.64020827 0.64020124 10.183920 21 1000 0.64007224 0.64014184 10.190800 22 1000 0.64002878 0.64008251 10.196520 23 1000 0.63992336 0.64002327 10.198160 24 1000 0.63987323 0.63996410 10.207120 25 1000 0.63980988 0.63990502 10.218280 26 1000 0.63967390 0.63984601 10.223440 27 1000 0.63948879 0.63978709 10.225920 28 1000 0.63938544 0.63972824 10.216280 29 1000 0.63934034 0.63966947 10.216960 30 1000 0.63931246 0.63961078 10.220000 31 1000 0.63925845 0.63955217 10.219800 32 1000 0.63914968 0.63949364 10.224000 33 1000 0.63907794 0.63943519 10.215040 34 1000 0.63906274 0.63937681 10.220720 35 1000 0.63891482 0.63931852 10.224280 36 1000 0.63876981 0.63926030 10.223240 37 1000 0.63867667 0.63920216 10.221800 38 1000 0.63852027 0.63914409 10.214920 39 1000 0.63839471 0.63908611 10.208840 40 1000 0.63825484 0.63902820 10.204520 41 1000 0.63827677 0.63897037 10.211720 42 1000 0.63827888 0.63891262 10.213360 43 1000 0.63827637 0.63885495 10.208080 44 1000 0.63821775 0.63879735 10.207080 45 1000 0.63812798 0.63873983 10.204880 46 1000 0.63815617 0.63868239 10.192400 47 1000 0.63802845 0.63862502 10.189040 48 1000 0.63800995 0.63856774 10.182800 49 1000 0.63804472 0.63851052 10.190960 50 1000 0.63800776 0.63845339 10.185960 ENDDATA FIGDATA fig3_traj_k250_r0.40 t N h h_recursion a 0 250 0.64468829 0.64466335 9.873280 1 350 0.64392045 0.64399911 9.686240 2 490 0.64359056 0.64359933 9.690000 3 686 0.64335109 0.64338801 9.811720 4 960 0.64321250 0.64331093 10.056040 5 1000 0.64309472 0.64324735 10.208480 6 1000 0.64311792 0.64318386 10.290640 7 1000 0.64301469 0.64312046 10.345240 8 1000 0.64296850 0.64305714 10.371680 9 1000 0.64294119 0.64299391 10.400320 10 1000 0.64288846 0.64293076 10.415920 11 1000 0.64282095 0.64286769 10.435320 12 1000 0.64285544 0.64280471 10.451560 13 1000 0.64285317 0.64274182 10.464080 14 1000 0.64278052 0.64267901 10.463440 15 1000 0.64263699 0.64261628 10.473400 16 1000 0.64254063 0.64255364 10.473320 17 1000 0.64244495 0.64249108 10.478160 18 1000 0.64243290 0.64242860 10.494360 19 1000 0.64237108 0.64236621 10.490080 20 1000 0.64234261 0.64230391 10.484760 21 1000 0.64219841 0.64224168 10.477400 22 1000 0.64211958 0.64217954 10.481520 23 1000 0.64209931 0.64211749 10.482680 24 1000 0.64211339 0.64205551 10.481600 25 1000 0.64198587 0.64199362 10.474080 26 1000 0.64197908 0.64193182 10.460480 27 1000 0.64193364 0.64187009 10.459200 28 1000 0.64194281 0.64180845 10.458080 29 1000 0.64186924 0.64174689 10.452600 30 1000 0.64182237 0.64168541 10.445920 31 1000 0.64174135 0.64162402 10.440840 32 1000 0.64165516 0.64156271 10.431520 33 1000 0.64155469 0.64150148 10.433560 34 1000 0.64148340 0.64144033 10.424560 35 1000 0.64138724 0.64137927 10.420640 36 1000 0.64127999 0.64131828 10.422120 37 1000 0.64114887 0.64125738 10.419080 38 1000 0.64115452 0.64119656 10.406320 39 1000 0.64109635 0.64113583 10.400480 40 1000 0.64101530 0.64107517 10.390960 41 1000 0.64093161 0.64101459 10.387640 42 1000 0.64099912 0.64095410 10.384560 43 1000 0.64088793 0.64089369 10.383880 44 1000 0.64077731 0.64083336 10.374600 45 1000 0.64070626 0.64077310 10.367160 46 1000 0.64065043 0.64071293 10.371680 47 1000 0.64054193 0.64065285 10.361080 48 1000 0.64039472 0.64059284 10.350760 49 1000 0.64036788 0.64053291 10.349240 50 1000 0.64033968 0.64047306 10.339840 ENDDATA FIGDATA fig3_traj_k250_r1.00 t N h h_recursion a 0 250 0.64466228 0.64466335 9.876080 1 500 0.64425401 0.64427550 9.926520 2 1000 0.64422388 0.64421063 10.252880 3 1000 0.64415405 0.64414585 10.393560 4 1000 0.64412956 0.64408116 10.473240 5 1000 0.64408699 0.64401655 10.515440 6 1000 0.64400304 0.64395203 10.551560 7 1000 0.64400747 0.64388759 10.577240 8 1000 0.64392226 0.64382324 10.580960 9 1000 0.64389357 0.64375898 10.596720 10 1000 0.64380802 0.64369481 10.603360 11 1000 0.64372092 0.64363072 10.613320 12 1000 0.64373814 0.64356671 10.609040 13 1000 0.64366443 0.64350280 10.615040 14 1000 0.64367423 0.64343896 10.616480 15 1000 0.64355893 0.64337522 10.616280 16 1000 0.64341986 0.64331156 10.611040 17 1000 0.64334722 0.64324798 10.610320 18 1000 0.64327756 0.64318449 10.603160 19 1000 0.64311035 0.64312109 10.594120 20 1000 0.64305461 0.64305777 10.588960 21 1000 0.64297628 0.64299453 10.574600 22 1000 0.64289280 0.64293138 10.566200 23 1000 0.64291497 0.64286832 10.554680 24 1000 0.64276529 0.64280534 10.557280 25 1000 0.64263274 0.64274244 10.552480 26 1000 0.64254363 0.64267963 10.550640 27 1000 0.64245412 0.64261690 10.538320 28 1000 0.64250879 0.64255426 10.541040 29 1000 0.64241385 0.64249170 10.531760 30 1000 0.64250077 0.64242922 10.530040 31 1000 0.64244387 0.64236683 10.528240 32 1000 0.64243271 0.64230452 10.514640 33 1000 0.64235494 0.64224230 10.507320 34 1000 0.64238112 0.64218016 10.499000 35 1000 0.64230061 0.64211810 10.494520 36 1000 0.64219888 0.64205613 10.490440 37 1000 0.64217809 0.64199424 10.485480 38 1000 0.64215550 0.64193243 10.481280 39 1000 0.64207433 0.64187070 10.477640 40 1000 0.64206163 0.64180906 10.469480 41 1000 0.64195882 0.64174750 10.463880 42 1000 0.64183843 0.64168602 10.443760 43 1000 0.64177926 0.64162463 10.439000 44 1000 0.64175097 0.64156332 10.433920 45 1000 0.64170462 0.64150209 10.434280 46 1000 0.64156210 0.64144094 10.426280 47 1000 0.64149965 0.64137987 10.422960 48 1000 0.64140962 0.64131889 10.418480 49 1000 0.64135008 0.64125799 10.413000 50 1000 0.64141289 0.64119717 10.408720 ENDDATA FIGDATA fig3b_longrun k 0 1 5 10 25 50 100 250 500 1000 2000 5000 10000 20000 2 75.000000 62.550564 44.348061 40.721147 41.102485 42.790659 46.001699 54.437357 65.218639 78.436496 88.644765 92.189827 92.254082 92.254160 5 90.000000 83.616045 73.416955 71.001983 71.108714 71.806584 73.133986 76.621179 81.078023 86.542115 90.762083 92.227566 92.254128 92.254160 10 95.000000 91.649416 85.937423 84.578551 84.628022 84.879710 85.358440 86.616101 88.223469 90.194102 91.716040 92.244569 92.254148 92.254160 25 98.000000 96.640722 94.285690 93.796868 93.766114 93.716215 93.621302 93.371959 93.053283 92.662586 92.360847 92.256062 92.254162 92.254160 50 99.000000 98.333039 97.204610 97.030613 96.935396 96.780900 96.487036 95.715032 94.728364 93.518708 92.584480 92.260048 92.254167 92.254160 100 99.500000 99.184550 98.692308 98.633133 98.505970 98.299639 97.907183 96.876168 95.558469 93.942969 92.695304 92.262023 92.254170 92.254160 250 99.800000 99.697169 99.580790 99.531778 99.386701 99.151304 98.703559 97.527299 96.023968 94.180882 92.757451 92.263131 92.254171 92.254160 500 99.900000 99.868327 99.826536 99.775880 99.625937 99.382644 98.919882 97.704168 96.150412 94.245507 92.774332 92.263432 92.254171 92.254160 ENDDATA FIGDATA fig4_power gen power_k5 power_k25 h_k5 h_ctrl a_k5 a_ctrl 10 0.670800 0.709600 0.402257 0.634510 2.551307 6.377240 13 0.597800 0.631200 0.395448 0.633096 2.544613 6.288480 17 0.489200 0.550000 0.392494 0.630731 2.577853 6.172160 22 0.409800 0.447600 0.392140 0.628437 2.642067 6.046653 28 0.325000 0.376400 0.391981 0.625249 2.717840 5.911320 36 0.205000 0.280800 0.391272 0.621116 2.794213 5.758733 46 0.134800 0.209000 0.391006 0.616342 2.868693 5.593187 60 0.064800 0.136000 0.390642 0.609327 2.949400 5.389560 78 0.034800 0.106000 0.390767 0.601444 3.028640 5.191547 100 0.001600 0.015600 0.389575 0.591008 3.098307 4.990200 128 0.004600 0.047800 0.388871 0.579404 3.157160 4.786520 160 0.000400 0.007200 0.388896 0.566559 3.208467 4.603653 200 0.000400 0.008000 0.388351 0.551370 3.247600 4.423933 ENDDATA FIGDATA fig5_convergence reps k2 k10 k50 25 0.75359989 0.94477106 0.99052971 50 0.75690878 0.94786487 0.98808312 75 0.76090703 0.94587403 0.98918498 100 0.75949385 0.94793932 0.99019088 125 0.75624701 0.94963513 0.98935876 150 0.75546114 0.94917464 0.98886777 175 0.75259541 0.95072234 0.98917212 200 0.75189375 0.94927736 0.98960885 225 0.75401350 0.94821047 0.98930814 250 0.75314492 0.94862427 0.98938504 275 0.75472792 0.94819276 0.98931517 300 0.75515094 0.94762774 0.98908610 325 0.75496799 0.94771216 0.98932619 350 0.75342263 0.94846638 0.98972334 375 0.75304841 0.94820348 0.98946729 400 0.75217810 0.94862902 0.98994214 425 0.75252937 0.94928575 0.99001399 450 0.75171566 0.94925001 0.99027669 475 0.75183660 0.94940786 0.98993895 500 0.75175932 0.94976666 0.98995046 525 0.75141366 0.94982500 0.99001948 550 0.75040380 0.94998106 0.99003335 575 0.75144192 0.94938265 0.99014309 600 0.75110099 0.94917120 0.99025728 625 0.75002629 0.94895879 0.99038714 650 0.75060916 0.94929915 0.99050332 675 0.75062802 0.94930179 0.99041927 700 0.75061598 0.94952818 0.99047535 725 0.75067609 0.94943831 0.99049275 750 0.75044266 0.94947465 0.99062355 775 0.75014424 0.94941845 0.99059843 800 0.74968351 0.94935129 0.99053402 825 0.74952645 0.94900995 0.99045772 850 0.74971924 0.94916215 0.99052051 875 0.74889654 0.94905229 0.99062664 900 0.74851018 0.94891131 0.99039681 925 0.74808880 0.94887811 0.99039484 950 0.74831002 0.94901907 0.99044633 975 0.74824416 0.94923552 0.99030081 1000 0.74863656 0.94920953 0.99028016 1025 0.74822295 0.94940875 0.99032932 1050 0.74837066 0.94955202 0.99020521 1075 0.74859808 0.94945507 0.99030814 1100 0.74901257 0.94934297 0.99028523 1125 0.74866413 0.94929910 0.99035725 1150 0.74838479 0.94938373 0.99038520 1175 0.74827575 0.94955311 0.99031640 1200 0.74827465 0.94934940 0.99021702 1225 0.74802036 0.94940655 0.99022843 1250 0.74826431 0.94937737 0.99026050 1275 0.74845003 0.94929256 0.99027959 1300 0.74820704 0.94934688 0.99036478 1325 0.74841024 0.94937354 0.99034297 1350 0.74844507 0.94936797 0.99035701 1375 0.74881704 0.94948473 0.99037669 1400 0.74860701 0.94951075 0.99034785 1425 0.74878168 0.94962933 0.99030222 1450 0.74907156 0.94965339 0.99026913 1475 0.74894501 0.94947866 0.99020854 1500 0.74919493 0.94940737 0.99019525 1525 0.74919256 0.94943144 0.99022176 1550 0.74915024 0.94930771 0.99026389 1575 0.74947034 0.94924516 0.99024516 1600 0.74931514 0.94919722 0.99022366 1625 0.74896745 0.94932359 0.99023487 1650 0.74888723 0.94935312 0.99022534 1675 0.74893288 0.94930622 0.99026640 1700 0.74911708 0.94928454 0.99032901 1725 0.74919403 0.94932055 0.99029030 1750 0.74933970 0.94949947 0.99033692 1775 0.74916085 0.94952818 0.99031915 1800 0.74930867 0.94967810 0.99028823 1825 0.74944678 0.94968839 0.99022191 1850 0.74953644 0.94981354 0.99019434 1875 0.74897848 0.94983433 0.99026620 1900 0.74914813 0.94990137 0.99025803 1925 0.74900182 0.95005132 0.99032791 1950 0.74885927 0.95016901 0.99033315 1975 0.74887216 0.95021105 0.99036132 2000 0.74877615 0.95032979 0.99036934 2025 0.74878975 0.95024748 0.99038230 2050 0.74896946 0.95028299 0.99042083 2075 0.74916977 0.95027120 0.99036650 2100 0.74917327 0.95025161 0.99029226 2125 0.74924481 0.95018168 0.99028321 2150 0.74939164 0.95021457 0.99019848 2175 0.74952083 0.95037906 0.99018728 2200 0.74957188 0.95041686 0.99018935 2225 0.74971009 0.95040305 0.99016220 2250 0.74978088 0.95040941 0.99010498 2275 0.75001829 0.95048599 0.99018115 2300 0.75005273 0.95056252 0.99010149 2325 0.74984181 0.95059097 0.99010102 2350 0.74989499 0.95065790 0.99005996 2375 0.74990351 0.95059279 0.99006549 2400 0.74982569 0.95053594 0.99008204 2425 0.74991577 0.95050721 0.99009963 2450 0.74994914 0.95055774 0.99008974 2475 0.74981890 0.95062663 0.99009450 2500 0.74981121 0.95050206 0.99011202 2525 0.75011491 0.95046743 0.99010448 2550 0.74993011 0.95049496 0.99010289 2575 0.75000589 0.95048564 0.99005569 2600 0.74990523 0.95045392 0.99007711 2625 0.74980255 0.95036514 0.99010161 2650 0.75001396 0.95026382 0.99010018 2675 0.74998563 0.95021589 0.99014461 2700 0.74991952 0.95026872 0.99014495 2725 0.74995708 0.95017579 0.99012408 2750 0.74996763 0.95012981 0.99010584 2775 0.75001899 0.95019019 0.99008578 2800 0.75016175 0.95013132 0.99008472 2825 0.75014825 0.95005123 0.99007648 2850 0.74998624 0.95015454 0.99007912 2875 0.75010757 0.95017736 0.99003695 2900 0.75008420 0.95023173 0.99002821 2925 0.75009657 0.95020980 0.99007446 2950 0.74990193 0.95023227 0.99008088 2975 0.74994691 0.95022114 0.99012513 3000 0.74984982 0.95022191 0.99012446 3025 0.74971331 0.95017754 0.99013212 3050 0.74965363 0.95026409 0.99006011 3075 0.74958484 0.95037035 0.99006960 3100 0.74950714 0.95039111 0.99006556 3125 0.74964246 0.95039194 0.99009733 3150 0.74965417 0.95040616 0.99010297 3175 0.74962662 0.95043161 0.99014881 3200 0.74968351 0.95034990 0.99014337 3225 0.74983250 0.95036642 0.99016616 3250 0.74978512 0.95040432 0.99013641 3275 0.74973215 0.95038771 0.99013153 3300 0.74972072 0.95033739 0.99009584 3325 0.74987117 0.95028273 0.99009116 3350 0.74996382 0.95020616 0.99011656 3375 0.74991722 0.95022877 0.99013749 3400 0.74998992 0.95013390 0.99014411 3425 0.74979286 0.95012458 0.99013688 3450 0.74988938 0.95001266 0.99013480 3475 0.74992500 0.94998149 0.99012542 3500 0.74994239 0.95002724 0.99012604 3525 0.74990086 0.95008817 0.99013711 3550 0.74995603 0.95009838 0.99014762 3575 0.75000466 0.95013262 0.99015747 3600 0.75014739 0.95023866 0.99016750 3625 0.75010844 0.95019285 0.99017625 3650 0.75014652 0.95018540 0.99017942 3675 0.75001807 0.95019562 0.99016986 3700 0.74996123 0.95023934 0.99015897 3725 0.75010224 0.95027381 0.99015735 3750 0.74995460 0.95030154 0.99013481 3775 0.74992943 0.95032463 0.99014132 3800 0.75013318 0.95032815 0.99013428 3825 0.75018016 0.95025701 0.99011176 3850 0.75018626 0.95030045 0.99013800 3875 0.75004017 0.95033534 0.99011346 3900 0.75003382 0.95038483 0.99011878 3925 0.75003019 0.95042020 0.99010641 3950 0.74990095 0.95046738 0.99009949 3975 0.74975773 0.95048171 0.99009657 4000 0.74977399 0.95041737 0.99009661 4025 0.74972068 0.95043944 0.99014405 4050 0.74961697 0.95047726 0.99013073 4075 0.74948915 0.95051828 0.99011151 4100 0.74955962 0.95047083 0.99007451 4125 0.74954399 0.95050487 0.99006723 4150 0.74953853 0.95044262 0.99007944 4175 0.74948359 0.95043144 0.99003379 4200 0.74944162 0.95047486 0.99000376 4225 0.74942462 0.95051013 0.99000217 4250 0.74940539 0.95051354 0.99000884 4275 0.74935977 0.95052795 0.99002245 4300 0.74938442 0.95054017 0.99002753 4325 0.74954029 0.95056286 0.99001488 4350 0.74950181 0.95058473 0.99003046 4375 0.74944251 0.95062014 0.99002969 4400 0.74941208 0.95066220 0.99002673 4425 0.74935629 0.95071099 0.98999502 4450 0.74938942 0.95073933 0.99000576 4475 0.74941757 0.95071699 0.99000943 4500 0.74949595 0.95075620 0.99002123 4525 0.74941808 0.95075723 0.99003314 4550 0.74949332 0.95080842 0.99003710 4575 0.74946604 0.95077037 0.99002108 4600 0.74951998 0.95075080 0.99003394 4625 0.74950849 0.95075524 0.99005833 4650 0.74956162 0.95078897 0.99006537 4675 0.74959207 0.95076378 0.99007561 4700 0.74965078 0.95075980 0.99007135 4725 0.74967606 0.95072768 0.99006684 4750 0.74952691 0.95072724 0.99006759 4775 0.74956339 0.95071347 0.99005937 4800 0.74957580 0.95073094 0.99005378 4825 0.74959665 0.95071404 0.99005300 4850 0.74951282 0.95070941 0.99006486 4875 0.74945529 0.95068218 0.99008780 4900 0.74952709 0.95068056 0.99008651 4925 0.74956456 0.95070414 0.99008370 4950 0.74947631 0.95072681 0.99006942 4975 0.74944299 0.95077129 0.99005841 5000 0.74940381 0.95080416 0.99006683 5025 0.74945966 0.95083432 0.99005404 5050 0.74943921 0.95084263 0.99008020 5075 0.74955139 0.95083456 0.99006194 5100 0.74949825 0.95088497 0.99004920 5125 0.74937500 0.95086104 0.99003557 5150 0.74939551 0.95085436 0.99004039 5175 0.74941383 0.95083808 0.99003767 5200 0.74953735 0.95079388 0.99003469 5225 0.74950534 0.95076680 0.99005053 5250 0.74952681 0.95074062 0.99005701 5275 0.74952651 0.95075467 0.99005684 5300 0.74953206 0.95071356 0.99004303 5325 0.74954534 0.95071433 0.99004104 5350 0.74957201 0.95072962 0.99005560 5375 0.74939645 0.95072907 0.99004869 5400 0.74931250 0.95074966 0.99005109 5425 0.74937420 0.95073736 0.99002389 5450 0.74942773 0.95071614 0.99002491 5475 0.74940901 0.95068091 0.99002606 5500 0.74943558 0.95068781 0.99002100 5525 0.74956110 0.95071367 0.99001458 5550 0.74956625 0.95068891 0.99001127 5575 0.74953241 0.95067543 0.99000686 5600 0.74941023 0.95067477 0.99002945 5625 0.74937738 0.95066545 0.99002517 5650 0.74930090 0.95065181 0.99003412 5675 0.74940001 0.95069959 0.99004505 5700 0.74937307 0.95070515 0.99004413 5725 0.74937347 0.95070481 0.99002638 5750 0.74937027 0.95073440 0.99002048 5775 0.74922743 0.95075478 0.99002802 5800 0.74930689 0.95075374 0.99002348 5825 0.74932354 0.95073033 0.99003185 5850 0.74927465 0.95077762 0.99003000 5875 0.74927721 0.95080317 0.99001487 5900 0.74917635 0.95079100 0.99000065 5925 0.74915139 0.95078759 0.98997669 5950 0.74917877 0.95075869 0.98995234 5975 0.74918342 0.95073738 0.98995913 6000 0.74923974 0.95076264 0.98995704 6025 0.74925097 0.95077800 0.98996029 6050 0.74921595 0.95076303 0.98997933 6075 0.74924931 0.95077009 0.98999333 6100 0.74933834 0.95075859 0.98998416 6125 0.74938612 0.95075685 0.98997990 6150 0.74936962 0.95079566 0.98997906 6175 0.74929298 0.95079478 0.98999426 6200 0.74934203 0.95075829 0.98998925 6225 0.74935249 0.95078088 0.98998403 6250 0.74942242 0.95077180 0.98999522 6275 0.74939786 0.95078243 0.99001661 6300 0.74933904 0.95076501 0.99002562 6325 0.74939348 0.95077585 0.98999099 6350 0.74932374 0.95080601 0.98998908 6375 0.74931131 0.95081452 0.98997782 6400 0.74931191 0.95079809 0.98997793 6425 0.74935273 0.95078990 0.98998282 6450 0.74936919 0.95079959 0.98999496 6475 0.74935838 0.95084435 0.99000161 6500 0.74932379 0.95084428 0.99001656 6525 0.74930848 0.95082595 0.99002579 6550 0.74931538 0.95083688 0.99000437 6575 0.74924675 0.95084539 0.99000783 6600 0.74932591 0.95085090 0.99000338 6625 0.74939198 0.95085205 0.98999702 6650 0.74942024 0.95084008 0.98998628 6675 0.74949321 0.95083414 0.98999029 6700 0.74952397 0.95081195 0.98998978 6725 0.74954066 0.95082024 0.98999893 6750 0.74951280 0.95081837 0.99001157 6775 0.74950651 0.95083689 0.99000941 6800 0.74956718 0.95080875 0.99000391 6825 0.74952741 0.95077621 0.99001426 6850 0.74957096 0.95076360 0.99003147 6875 0.74953748 0.95075474 0.99003529 6900 0.74969756 0.95072994 0.99003074 6925 0.74961907 0.95074140 0.99001879 6950 0.74953817 0.95072558 0.99002367 6975 0.74953642 0.95072119 0.99000738 7000 0.74957014 0.95069740 0.98999319 7025 0.74954915 0.95073802 0.99001201 7050 0.74943591 0.95068512 0.99000641 7075 0.74949009 0.95065791 0.99000635 7100 0.74954679 0.95065524 0.99001592 7125 0.74956392 0.95062374 0.99002359 7150 0.74962286 0.95059789 0.99002052 7175 0.74961942 0.95056312 0.99001536 7200 0.74959160 0.95060488 0.99000794 7225 0.74964411 0.95058149 0.99001059 7250 0.74965917 0.95055483 0.99001284 7275 0.74965140 0.95057413 0.99000397 7300 0.74967908 0.95056797 0.98999242 7325 0.74966564 0.95058059 0.99000367 7350 0.74969731 0.95059420 0.99000668 7375 0.74970353 0.95061081 0.99000442 7400 0.74971949 0.95059611 0.99000365 7425 0.74973256 0.95062613 0.99001104 7450 0.74960396 0.95066816 0.99002107 7475 0.74961179 0.95068850 0.99001995 7500 0.74967334 0.95070688 0.99002126 7525 0.74969188 0.95067958 0.99003559 7550 0.74964867 0.95068943 0.99001974 7575 0.74960574 0.95065608 0.99000483 7600 0.74959167 0.95064010 0.99001535 7625 0.74954243 0.95063236 0.99002121 7650 0.74953001 0.95059974 0.99003117 7675 0.74954462 0.95059099 0.99002256 7700 0.74951884 0.95060255 0.99002208 7725 0.74948787 0.95060724 0.99002685 7750 0.74943443 0.95060240 0.99002390 7775 0.74947974 0.95059684 0.99002631 7800 0.74949692 0.95055457 0.99003553 7825 0.74951796 0.95057235 0.99003677 7850 0.74944270 0.95053522 0.99002524 7875 0.74940994 0.95053074 0.99004633 7900 0.74941273 0.95053869 0.99003825 7925 0.74942594 0.95058657 0.99004969 7950 0.74940915 0.95058826 0.99005324 7975 0.74939636 0.95057132 0.99006351 8000 0.74942759 0.95056343 0.99007687 8025 0.74937616 0.95053430 0.99007492 8050 0.74937129 0.95057036 0.99007156 8075 0.74941640 0.95052940 0.99007393 8100 0.74935655 0.95051546 0.99006546 8125 0.74940524 0.95049473 0.99007010 8150 0.74941810 0.95046723 0.99007007 8175 0.74943975 0.95044227 0.99006248 8200 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0.99001307 19100 0.74985953 0.95040241 0.99001516 19125 0.74985685 0.95039635 0.99002022 19150 0.74985849 0.95040566 0.99002167 19175 0.74984935 0.95042210 0.99002148 19200 0.74983000 0.95041774 0.99002638 19225 0.74983167 0.95041492 0.99002119 19250 0.74980810 0.95041132 0.99001975 19275 0.74977546 0.95041442 0.99001756 19300 0.74980881 0.95041041 0.99001804 19325 0.74979766 0.95041219 0.99001883 19350 0.74978067 0.95041967 0.99002407 19375 0.74977599 0.95040787 0.99002014 19400 0.74978571 0.95040895 0.99002092 19425 0.74978423 0.95041523 0.99001987 19450 0.74976415 0.95040732 0.99002708 19475 0.74975474 0.95040087 0.99002523 19500 0.74974641 0.95039760 0.99002446 19525 0.74974076 0.95040151 0.99003163 19550 0.74973617 0.95040189 0.99002578 19575 0.74976223 0.95039261 0.99003049 19600 0.74976977 0.95040401 0.99003367 19625 0.74975831 0.95040652 0.99003116 19650 0.74971531 0.95039401 0.99003158 19675 0.74973129 0.95039014 0.99002894 19700 0.74971258 0.95039078 0.99003311 19725 0.74970545 0.95037816 0.99003225 19750 0.74969729 0.95036158 0.99002946 19775 0.74970222 0.95037204 0.99002073 19800 0.74973430 0.95036768 0.99002750 19825 0.74974647 0.95036912 0.99002886 19850 0.74973674 0.95037990 0.99002081 19875 0.74973224 0.95039842 0.99002158 19900 0.74972618 0.95040195 0.99002048 19925 0.74972326 0.95039261 0.99002178 19950 0.74973019 0.95038786 0.99002314 19975 0.74971433 0.95039276 0.99002424 20000 0.74973056 0.95039272 0.99002019 ENDDATA FIGDATA grid_table k r gens h0 h0_se h_end h_se h_pred z a0 a_end 2 0.05 147 0.48368500 0.00107894 0.07975685 0.00064263 0.07953949 0.3382 2.516960 5.811760 2 0.15 64 0.48617000 0.00108622 0.11604089 0.00101463 0.11638520 -0.3393 2.533280 5.455640 2 0.40 50 0.48432000 0.00108125 0.27857099 0.00129047 0.27640851 1.6757 2.522920 6.059160 2 1.00 50 0.48414000 0.00109496 0.38853665 0.00118664 0.38895969 -0.3565 2.523560 6.575720 5 0.05 128 0.58180800 0.00071923 0.14341517 0.00106706 0.14411255 -0.6536 3.951880 5.967040 5 0.15 57 0.58027440 0.00070858 0.32140201 0.00127467 0.32305062 -1.2934 3.944840 6.066880 5 0.40 50 0.58079520 0.00072837 0.46279931 0.00110013 0.46383840 -0.9445 3.952280 7.000400 5 1.00 50 0.58206320 0.00070561 0.53212072 0.00091028 0.53170532 0.4563 3.953880 7.556120 10 0.05 114 0.61395640 0.00049857 0.27735579 0.00130868 0.27718762 0.1285 5.134560 6.316720 10 0.15 52 0.61398560 0.00051088 0.45453377 0.00109541 0.45538595 -0.7780 5.132960 6.713880 10 0.40 50 0.61459120 0.00051753 0.54905120 0.00086056 0.54828495 0.8904 5.133160 7.792560 10 1.00 50 0.61513740 0.00050714 0.58758922 0.00071800 0.58629548 1.8019 5.150000 8.351200 25 0.05 95 0.63304762 0.00032543 0.45891449 0.00110912 0.45858756 0.2948 6.719200 7.139440 25 0.15 50 0.63318291 0.00032511 0.56529827 0.00081196 0.56459389 0.8675 6.714640 7.911280 25 0.40 50 0.63310899 0.00032663 0.60578732 0.00062588 0.60536482 0.6751 6.704520 8.842160 25 1.00 50 0.63286307 0.00032249 0.61983419 0.00052277 0.62066189 -1.5833 6.702480 9.318400 50 0.05 81 0.63932018 0.00023480 0.54635728 0.00088412 0.54858708 -2.5221 7.801840 7.870440 50 0.15 50 0.63979387 0.00022370 0.60653590 0.00062082 0.60566153 1.4084 7.797760 8.808200 50 0.40 50 0.63977450 0.00022857 0.62476594 0.00050677 0.62516131 -0.7802 7.810120 9.523520 50 1.00 50 0.63945608 0.00022996 0.63204366 0.00045031 0.63225503 -0.4694 7.805400 9.849640 100 0.05 67 0.64287140 0.00016238 0.59950453 0.00066707 0.60030706 -1.2031 8.748520 8.728160 100 0.15 50 0.64283235 0.00016331 0.62690853 0.00049661 0.62663976 0.5412 8.754400 9.573040 100 0.40 50 0.64299371 0.00015971 0.63539714 0.00041922 0.63497169 1.0148 8.746280 10.001440 100 1.00 50 0.64289923 0.00016235 0.63786968 0.00040089 0.63795650 -0.2166 8.750680 10.170760 250 0.05 50 0.64464244 0.00010235 0.63197101 0.00044323 0.63193817 0.0741 9.870720 9.784120 250 0.15 50 0.64455465 0.00010263 0.63800776 0.00039620 0.63845339 -1.1247 9.872600 10.185960 250 0.40 50 0.64468829 0.00010195 0.64033968 0.00037209 0.64047306 -0.3585 9.873280 10.339840 250 1.00 50 0.64466228 0.00010258 0.64141289 0.00036691 0.64119717 0.5879 9.876080 10.408720 500 0.05 50 0.64539762 0.00007207 0.64073354 0.00038187 0.64034535 1.0166 10.632200 10.323480 500 0.15 50 0.64531830 0.00007242 0.64149523 0.00035734 0.64158567 -0.2531 10.639400 10.422240 500 0.40 50 0.64532947 0.00007203 0.64237363 0.00036690 0.64196742 1.1071 10.647880 10.460080 500 1.00 50 0.64519597 0.00007310 0.64205439 0.00035979 0.64210312 -0.1354 10.644280 10.460560 ENDDATA FIGDATA spectrum_shift class_lo class_hi source founders_k5 recovered_k5 0.0000 0.0100 4.933333 0.000000 3.685533 0.0100 0.0200 1.266667 0.000000 0.352900 0.0200 0.0500 1.733333 0.000000 0.284000 0.0500 0.1000 1.066667 0.000000 0.299400 0.1000 0.2000 1.133333 1.652267 0.533700 0.2000 0.4000 1.000000 1.263933 0.779367 0.4000 1.0000 0.666667 0.945000 0.996800 ENDDATA Spectrum note: the source carries 4.933 alleles per locus below 1% frequency. Five founders keep 0.000 of them, and after 50 generations back at carrying capacity the population has 3.686 in that class, nearly all of them new mutations rather than survivors. ====================================================================================================================== total wall clock: 276.4 s ======================================================================================================================