Growth model of L. monocytogenes in RTE seafood including background flora competition
Source:R/sfGrowthJameson.R
sfGrowthJameson.RdThe sfGrowthJameson() function is used to simulate the growth of L. monocytogenes in RTE seafood, as affected by lactic acid bacteria (LAB),
according to the Jameson-effect competition model published in Giménez and Dalgaard (2004)
.
Usage
sfGrowthJameson(
time,
N0Lm,
N0LAB,
q0Lm,
q0LAB,
muLm,
muLAB,
MPDLm,
MPDLAB,
unitSize,
gamma = 1,
lim = 1,
step = 1
)Arguments
- time
(h) Storage time of a pack of RTE seafood
- N0Lm
(CFU) Numbers of L. monocytogenes in RTE seafood at time=0
- N0LAB
(CFU) Numbers of LAB in RTE seafood at time=0
- q0Lm
Initial parameter Q of the Baranyi and Roberts' model related to lag phase for L. monocytogenes at time=0
- q0LAB
Initial parameter Q of the Baranyi and Roberts' model related to lag phase for LAB at time=0
- muLm
(h-1) Growth rate of L. monocytogenes in RTE seafood
- muLAB
(h-1) Growth rate of LAB in RTE seafood
- MPDLm
(log10 CFU/g) Maximum population density of L. monocytogenes in RTE seafood
- MPDLAB
(log10 CFU/g) Maximum population density of LAB in RTE seafood
- unitSize
(g) Weight of the contents of an RTE seafood pack (for MPD)
- gamma
Interaction parameter of the competition model. Note: if gamma=1, population 1 stops when population 2 reaches MPD. If gamma < 1, population 1 still increases when population 2 reaches MPD. If gamma > 1, population 1 decreases when population 2 reaches MPD.
- lim
= 1 A parameter indicating when the competition should be considered as meaningful.
- step
= 1 Integration step.
Value
a list of four elements:
- N1Lm
(CFU) Numbers of L. monocytogenes at the end of storage;
- N1LAB
(CFU) Numbers of LAB at the end of storage;
- lnQtLm
Natural logarithm of q0 for L. monocytogenes at the end of storage;
- lnQtLAB
Natural logarithm of q0 for LAB at the end of storage.
Note
For sake of speed, the function first evaluates a classical Baranyi and Roberts model without interactions. If any of the two population reaches a value greater than \(10^{(MPD - lim)}\) CFU, an expanded version of the Jameson-effect model by Giménez and Dalgaard (2004) is used. This model includes the parameter gamma proposed by Møller et al. (2013) . The function is vectorized for all parameters.
References
Giménez B, Dalgaard P (2004). “Modelling and predicting the simultaneous growth of Listeria monocytogenes and spoilage micro-organisms in cold-smoked salmon.” Journal of Applied Microbiology, 96, 96-109.
Møller COA, Ilg Y, Aabo S, Christensen BB, Dalgaard P, Hansen TB (2013). “Effect of natural microbiota on growth of Salmonella spp. in fresh pork – A predictive microbiology approach.” Food Microbiology, 34(2), 284-295. ISSN 0740-0020, doi:10.1016/j.fm.2012.10.010 .
Author
Regis Pouillot rpouillot.work@gmail.com and Laurent Guillier
Examples
library(qraLm)
iter <- 1000
set.seed(666)
vtime <- 200
vN0Lm <- 10^runif(iter, 0, 3)
vN0LAB <- 10^runif(iter, 0, 3)
vq0Lm <- exp(runif(iter, 0, 1))
vq0LAB <- exp(runif(iter, 0, 1))
vmuLm <- runif(iter, 0, 0.1)
vmuLAB <- runif(iter, 0, 0.1)
sfGrowthJameson(
time = vtime, N0Lm = vN0Lm, N0LAB = vN0LAB,
q0Lm = vq0Lm, q0LAB = vq0LAB,
muLm = vmuLm, muLAB = vmuLAB,
MPDLm = 8, MPDLAB = 7,
unitSize = 100,
gamma = 0.8
)
#> Integrate over 305 portions
#> ================================================================================
#> $N1Lm
#> [1] 47153320 458647888 996 284 2223 34605
#> [7] 8926253951 1997290 4332654 9 659 55409
#> [13] 171037106 387763 728271006 4899 508454 281706
#> [19] 558612 172 2657456 391189136 211560 76621
#> [25] 257372 21176054 28512 661 11694 72828
#> [31] 1428 16019433 5115625513 2494674623 439 226050629
#> [37] 17823470 100671157 1298 2246 271213011 2528655
#> [43] 13942 6023196329 149015 161813099 3967 109
#> [49] 1498504 7675580261 15100 33 20811 296103601
#> [55] 2873764 1928750013 10863639 318087361 8 2
#> [61] 886 12353 245203 12333 49626 19
#> [67] 94555182 774464 3690062316 54099402 5195929792 123
#> [73] 2520975 29021 33009 157658071 9875 3
#> [79] 270831207 571 2292 2079 33136 187079500
#> [85] 3177167 374457 21109122 4 251848071 16229
#> [91] 828176 5583950 215926 159465510 836975 17783413
#> [97] 9143522 1790645 1752427293 769 7923681 43476
#> [103] 2599352804 1514421931 1177163244 24505 73814699 60325
#> [109] 72 1834227693 74096746 15338 7287195 1010815170
#> [115] 29788 19141572 1853830 89175 8077637472 564
#> [121] 229537010 2601884 3020830 15966229 49231 362798
#> [127] 9200016932 22 8352350 347903005 1674992 9513125
#> [133] 71 3134 188 227932955 640875 349
#> [139] 51 13848743 1409170 8 135 776282
#> [145] 4219716919 5 55739909 646 12 12740067
#> [151] 151298017 657169 25574 19098711 46 239032
#> [157] 1179241 3649 951848 2526711 5536659573 191057936
#> [163] 9588097 12020792 6790158 7501609517 20991 393538
#> [169] 10691 67935 1938764011 3482060529 758495 38516435
#> [175] 5336582637 1494636 188846551 4356078235 17 177
#> [181] 102448448 33 220773008 5 120436 183
#> [187] 3397324 7546222 104265 53864 4003808737 9274
#> [193] 59103 54 150133153 9309773 6392 865
#> [199] 1979938 23223 7990 472 30314951 327662258
#> [205] 51468652 251855 3849378 20313078 6895 4595292
#> [211] 37553224 5770761595 2844 6963662369 26415773 27
#> [217] 50293 81 32813 587 6127 2250
#> [223] 189656 13330 240622 71 195 177688
#> [229] 10704 117683644 3806456 11 16810027 792982860
#> [235] 199029 473712 120461 152 19 11152
#> [241] 45563557 3350 6888087495 513 2293741 63262
#> [247] 58518 4978790 383756 2014642738 38404802 20779484
#> [253] 716773429 1719816 207 559472 783814733 2435565306
#> [259] 27864 882 895936 24557 2805951 32907
#> [265] 10 2340938377 2110 2445599981 32600448 48244931
#> [271] 2434443 130 3522115 957 714446 8658607
#> [277] 12419 304 1156770 160104402 4303027341 124517
#> [283] 167 920391600 2310445096 3718239028 390416 419
#> [289] 57410 9562 2253 11277897 7856 161
#> [295] 143518330 1998991 1782717758 303970 56524 7224928630
#> [301] 102351 747 11 27789 63712 34719
#> [307] 514 853911 1412 1332062 2124 2599
#> [313] 1173 7030199729 8758050935 148865007 4167957855 164
#> [319] 35554 1931623 799 22916 1622430758 661595945
#> [325] 9038199 240232 59235 341809 32490099 105459563
#> [331] 3293 82951 30 14354609 5626142218 682296039
#> [337] 3310 501 61135690 227798974 18 2260284
#> [343] 4093 4944752 43893040 118512993 33 817
#> [349] 256421038 26791444 394532 443410 1582866 120095581
#> [355] 94008 345923 1573933595 864 439 205638
#> [361] 495 1226480 90 526 235616 11854
#> [367] 15758 131 72572 2988389146 6510459489 17245046
#> [373] 201550 81364375 7317724 130100 2812811 4549978
#> [379] 921 12972 165565471 24432 43353 51774283
#> [385] 636 889 121684774 62445258 961 21403753
#> [391] 42532061 2639 111633 173365 39008 315609
#> [397] 13536 407786781 622737564 12646 5876 52643
#> [403] 9142320232 3562 583437 31661 1560878794 20452
#> [409] 568433969 15231 1701241196 8226369 227053 124504695
#> [415] 529008043 286964230 270766522 10152218 8652394 10
#> [421] 223 2176587 5232085560 27337 397605 1021511028
#> [427] 1706232 12800065 750160 1130100 452 1269616
#> [433] 160078675 3361879581 577 7233324 70 1972631240
#> [439] 8771720 231240806 2756 21461 741728 24517077
#> [445] 968190 9995401 14028783 5283200 143506498 2501
#> [451] 145650 177251566 87451665 54 10427973 1369
#> [457] 631435964 162752910 12992415 14570622 11675 27505
#> [463] 59463707 5057 7740889216 27 83066 7035
#> [469] 293570325 71810733 46509823 3917672290 4354 778374497
#> [475] 47 65 310 1925 357764888 4587205
#> [481] 273869 14 5842525 1460993997 619836115 18344
#> [487] 787 325 1312429856 30677499 3328 257375911
#> [493] 31926 12637189 7780835534 187877085 79319137 13570
#> [499] 85062 28182 355839356 32566 2649 57095191
#> [505] 12122 948876560 2211 3877 49739822 95915041
#> [511] 20904650 1060582 184558 37 6 34008983
#> [517] 92153677 89777 829209561 3319186 5790 27390939
#> [523] 15582 60642 278 232 9188 17073574
#> [529] 6082 21815 71819 246 49135 126750
#> [535] 4407659797 468993 21 776106320 51 300021
#> [541] 139648 82 7903520 4 15563128 31502451
#> [547] 1492407891 4272527 2 5665217 4661097 41045808
#> [553] 16478 994701528 5026529544 8429969 7983752328 325324
#> [559] 54016710 34822 355168 3579165 277592 149987683
#> [565] 717654 21315 786 32986883 68 81205659
#> [571] 289547848 10515 8232 306549 1333 6698
#> [577] 171401565 147134 4753135 109 639809876 33343
#> [583] 630468470 1120043108 6141 104 67138 3377
#> [589] 288079015 30781 78 94069 84 24027
#> [595] 3657367 2125688 1129 2115310 768208847 2415
#> [601] 432086835 238 302614 510530586 3872 389
#> [607] 2895391 308808592 660 49000 11090 467183
#> [613] 483611833 673439837 218288 1814 5387861 390741
#> [619] 1110771 371626341 4902651 39718 40734986 30404
#> [625] 1569378029 5903817 143591 30742482 10258 147
#> [631] 456226 25897408 5967775392 190596 757755384 3935
#> [637] 2 11129 5741537 7 29 1103
#> [643] 6039790 2283 1990594913 99362 1268236 735511
#> [649] 6411006 9423 4311175 97356 10466546 21979
#> [655] 1528923752 1656118535 16943127 929128164 279 8370877
#> [661] 396822 5276 698444 60534 48125626 10738864
#> [667] 1647987 686 133 4556102561 1035185 62
#> [673] 3489295 643634915 15044014 16631 11371 8925
#> [679] 398 4574 2780 14462 97056 137
#> [685] 356510443 587 1347089995 36256873 5032113 320197
#> [691] 7416018015 446 94521733 430044 22298 69
#> [697] 49 9319620404 3169435874 6884 461776 122072
#> [703] 433 21455 577942 2023 13862 195
#> [709] 31378 12454 14026 476228484 66881239 18311215
#> [715] 127181506 585471841 102176404 435 8692 60926
#> [721] 648 8342413738 629978 2434 3630 6777374400
#> [727] 870 2312277 1448887247 950952 8405470 4995
#> [733] 327 25 32116891 48467096 10344178 104
#> [739] 139 10568 36556211 18199038 8157155322 32
#> [745] 2308995893 6118920395 1990732 32400619 6586732 5614215330
#> [751] 43 1042683 14 104347 8757016 221381
#> [757] 1926124099 7616880058 54 53379593 127436 32113
#> [763] 435 40511 680 161408 12054 32047349
#> [769] 19181760 98218 471440522 81885 951 3755741463
#> [775] 89 257228 1335382664 723 97818381 1594304
#> [781] 1072705849 686 1330726016 3 17006 82
#> [787] 195763 6384 5341 5743276 14623439 32510
#> [793] 4741523 200342650 16 10754 504340132 27
#> [799] 76383364 20 57126 120719 14611210 2330855
#> [805] 248 10969082 43231 4532 15950 66
#> [811] 100226 176695 623936540 1045680 1827 17608
#> [817] 64524 28424157 11531591 748441523 706 7199047054
#> [823] 326648910 8025187 6765439 14337 159968371 66
#> [829] 13168929 997795 572650946 290 501 227016
#> [835] 9147619565 8078757716 50 2596 2792996501 296074236
#> [841] 55 9024830 139911 1150 430283 8711910755
#> [847] 5358739 1825496 2265972 3 2515695672 2020702
#> [853] 16150719 25 810246045 1836695972 388496000 44
#> [859] 8286140 148061262 200 3887221 76824547 9896
#> [865] 158120216 3175 846122524 213 258520 1503939133
#> [871] 787 7183798 81 6540199774 23598 103
#> [877] 38850 86954 398 7272 622594709 275829209
#> [883] 363383953 104 32 34987 1590 1844
#> [889] 178942 3535 82 806383 1475816 563008589
#> [895] 16198669 173441221 8846 1991059 13974 106
#> [901] 65708892 6647453 47 510749 412321964 30860
#> [907] 4932 15 806 162136 9600563 48829
#> [913] 1446821 169328664 324190544 275303 21579 603701
#> [919] 7 25 2307 2937 9526594348 254816639
#> [925] 37393785 453 2994657 5117 23 126844461
#> [931] 26183 150180 513711355 5852 1905512 39094
#> [937] 63 214860388 9 1722676 2059170440 3759609455
#> [943] 1382574 4373 291762 644 93249 107
#> [949] 2334 731 472264 11380 4 917092008
#> [955] 6101150104 50 432 260 5424220 168510
#> [961] 3153 1396 2582481 941120066 200309678 351
#> [967] 117421205 2003 571264 457 7883927834 82508410
#> [973] 395446 3472 4 91 620153226 31923209
#> [979] 6365175680 4713507 403485245 2742923 454488689 4054086
#> [985] 169232 1581031501 15319797 135539657 25 114035187
#> [991] 106 26407 8798812451 2026098372 2687390 18687
#> [997] 1158321147 18475039 76037009 199554
#>
#> $N1LAB
#> [1] 867178660 38323 354438334 599909329 255397299 370 6462366
#> [8] 1206610 3644499 315037 21917858 12822 4056 1400636
#> [15] 2081 869862577 3687104 289942 8332 19200 165162
#> [22] 130647712 749559 562207 3752204 441654674 25088185 443
#> [29] 484207 35016 59 190833202 772095 5914 35338812
#> [36] 4859 4624262 50715333 79308 92 2161874 8028677
#> [43] 94671745 2554 4150 451695 359 756598151 818594729
#> [50] 724744 12021 65011 13177234 154926 193 2
#> [57] 528881 6068357 95940168 1358 5550472 33 2955411
#> [64] 945165268 56877925 1992186 11303999 340625 12525 10910231
#> [71] 63994 859168 25 370241 6262 88046673 34
#> [78] 72 30133 982710498 17304916 59526772 22247 792441
#> [85] 803 281504 996879 6064 713 500646143 97200561
#> [92] 491704 280592869 468245670 1976 157 29666 80696
#> [99] 8930289 3915934 332617 60969 738249000 141 4029671
#> [106] 870241 213187 250836 120686 62890853 301434577 16611762
#> [113] 53674 306 38120322 630965307 22930 3811 9227487
#> [120] 16595 69079793 829853 124 11367679 58328 17129
#> [127] 35376 2815 187825 1094 906782665 1720249 3
#> [134] 35 195870834 569311205 2890976 896 431 30247
#> [141] 361243 2810254 6927 2198196 1076944 79814463 6176626
#> [148] 637294505 11308 1280472 4206 166 618704416 3094223
#> [155] 182 208051814 141954 10367900 164006131 755786787 6260881
#> [162] 180530144 3998127 9717787 10091 17031004 297 209356
#> [169] 44312785 1256 42888 248932022 535484 986031328 12591989
#> [176] 6716021 101284 877209298 12 986270032 140871 26
#> [183] 410427 173511677 119906725 2767499 28 18587 902840214
#> [190] 580474 193403 176027110 36363 31547986 130398963 18233157
#> [197] 10895 63 85859 147 3547 1307303 8433
#> [204] 39779396 378268998 29440679 21584541 16860993 619741859 20446
#> [211] 71260 2836 136134 243118 197497 14291 143209813
#> [218] 905942808 18400374 441704 214171 792901157 906100896 581
#> [225] 189652516 11314 34934648 2981 5416740 29568 30478
#> [232] 2936 1193115 6 522041722 597 265 781939601
#> [239] 86719723 2646 104728909 55255532 993 314890354 147440115
#> [246] 32106208 7029501 5641 266 97 895325969 46001632
#> [253] 356932901 18567431 176758 217679595 36016487 80044 1279
#> [260] 577853391 218242079 7891 788018577 1056782 194893 462990
#> [267] 98495 207598181 973536704 114929090 123248 689885 1122484
#> [274] 355328257 113 112 133970167 220 1308 3
#> [281] 2797 184762885 6135 66 337096946 21628049 62278635
#> [288] 193591 3 972628098 18 18429227 2193591 17725171
#> [295] 2535909 80683 147 972724920 4703817 4122812 562
#> [302] 10799 944529607 1261532 402 54545 726 493673
#> [309] 764 223525198 88 97965299 3953715 3442757 943107
#> [316] 137163171 38 179638 470 900182365 36688 13591136
#> [323] 37 2381198 3549023 1878 108 31680371 1388
#> [330] 34388 2568582 168821222 89833 53340 1169515 124845
#> [337] 18948 9763609 179548 488125340 7656413 19220408 354
#> [344] 4637 310916103 114704969 3203435 167621 36 11761864
#> [351] 267356244 450643 10158222 302 69232 423 1430
#> [358] 303082744 768129 3850392 2612119 22884015 652 21
#> [365] 112312 577718476 43 8475 7600 1327 86208941
#> [372] 16183480 26401849 29189124 1544229 46064 186780 7626058
#> [379] 790908268 68 677849 64944974 59451 4517782 97310
#> [386] 206442 835 18086 98329789 8 1786904 57980926
#> [393] 174655 996 5473099 4827 97502640 18891388 14946
#> [400] 15241011 195 45329 64253805 1412 120543 7219
#> [407] 1889364 23852 500346623 562325352 117806 4078 345847214
#> [414] 917647048 1075 759028641 144775 412698255 344 3
#> [421] 14860 255764979 910905 40065467 174627 2005 1591
#> [428] 39992 256931066 99287 83519423 704 61 2671
#> [435] 110751 408104494 1457 12744793 102818177 24560020 154
#> [442] 24968199 82815753 102453967 1310607 818 9007 119311397
#> [449] 49129 239 1497270 4877 119764 2218 385
#> [456] 23 97990367 47 1592241 37439 103720987 28119
#> [463] 142 174718900 875577 39714 1723 907162483 1486
#> [470] 39245 413 12386 220431261 8808 2067021 575329121
#> [477] 83963 449759382 198107612 450518862 49032 27005232 208869
#> [484] 8663 1101772 56251 62793669 6337469 14421 53554
#> [491] 3550 983426242 196 522156594 756915 68126 315997764
#> [498] 4911 74 1815282 374608 139752971 227671 152844200
#> [505] 881860679 4486290 8 647130007 7093169 11959038 722005376
#> [512] 16256 13957 16333319 3162431 59 4022 54347
#> [519] 2041522 11503 7043 1684608 7284 23569102 33
#> [526] 39 75769934 34032103 23095 924815 633445 7238
#> [533] 391003 14966 3942920 1612 882422156 182339392 4495
#> [540] 631614 2007 44781682 618326799 3268 306 136385
#> [547] 8403 2362404 780208970 755 2404 243447 67043490
#> [554] 4529854 946319 42767 48472635 412007070 2010466 36279977
#> [561] 847 24 1644 922567324 15821624 6682 127240277
#> [568] 170893 98871 921998759 12998 2526494 23578013 980448929
#> [575] 2603 27631 155449 58 446069068 238 38181
#> [582] 824 1499009 395807 20704 17800324 80333251 147349
#> [589] 2384617 189014 1565 383551 366 991636800 11592911
#> [596] 109021 843319 845656 4614 836 79208 568860004
#> [603] 2121666 5762 11193 981450 472822166 3429079 540496192
#> [610] 437 18774222 35722038 84137 92154202 71783608 977448181
#> [617] 1312 1055759 844043 119707004 352 166481129 14275
#> [624] 963829202 1787 77 330855850 780229214 16 1032935
#> [631] 208 972427004 681 23679 113637115 26 2206
#> [638] 73078 88317 14348274 170841 1184 407044113 6
#> [645] 298 314381 229423349 2799038 38991 11901742 280379925
#> [652] 1646 870788734 150 18 4331384 60410 3147669
#> [659] 684359 50041 51292211 726112549 57148140 3216123 354
#> [666] 72623 309 25973436 2078 4186629 1385 225954459
#> [673] 307 468 213188624 27251 1236 827142042 312618050
#> [680] 3846 13888 995961980 6872906 527353744 57416 930032796
#> [687] 181252382 556053200 408765139 60 97128462 41807465 1468
#> [694] 306004342 22985 365270215 14520 2108 8204424 50023337
#> [701] 68803 8 242586 50529 58312 983794286 981713527
#> [708] 35995 1461678 758653620 430 561643724 341255 40103
#> [715] 658717407 169 94469503 1651490 518971005 2031834 84
#> [722] 67712 6 10255 267071482 198920 9414 2111374
#> [729] 584141 182406 1547 17 2963 139635221 1249
#> [736] 529 129045 45 178519165 4 34 23885
#> [743] 21734973 190 25054958 175064759 552872839 6516 982092911
#> [750] 21855 10056 955509083 934892324 59 969051588 8542423
#> [757] 623226463 3488298 154408 98 43 196948 28
#> [764] 4852 1638 12347346 15676657 167 72 46
#> [771] 343 3121 5371 1034173 74685547 577183963 107617
#> [778] 317673005 28722895 6277975 679506 1354210 1978278 902440127
#> [785] 973973919 6 495507573 111581 1107436 37852726 52485
#> [792] 21201032 469115 1136 6087787 12351 676 340
#> [799] 2589 22141780 327669766 6424 9821457 88475301 726942934
#> [806] 1977 98 17836 1527939 701 30714 44367
#> [813] 365928429 33782 4 2543 2283 983743343 39592
#> [820] 800703 991251066 740 37282420 4655550 215366 32559811
#> [827] 607686764 320 125820972 167 223 3758 917223245
#> [834] 110467 690 1727143 1261 934569807 231 1457
#> [841] 224654 7579 18980 926173339 84490 74993996 1710669
#> [848] 9923602 1091177 1087907 590 352 109705 433110
#> [855] 53685303 21663 811901997 63357568 5048148 206902923 41042873
#> [862] 29776579 37047693 277024142 244394310 222081314 51318309 50
#> [869] 926362724 460 207 14230972 19186 23369 885620916
#> [876] 4689 5889123 726854746 18255426 39271026 806398161 2583231
#> [883] 358 36864 689 88104236 778 880627375 946844038
#> [890] 6184 45408 41118071 7867 3662 1748129 3320
#> [897] 521177 859908 3031225 215283091 783618731 17778 69872
#> [904] 490308 2469 393636 6954208 63635263 48415 119931440
#> [911] 3254622 2189162 1401462 3013398 3 112504393 3501
#> [918] 343223218 523 116 991179447 30276 49651 27442
#> [925] 68396215 2154202 846911303 455048 45479 944217303 2835
#> [932] 80 40686497 35449557 4424 273391 241663959 99148184
#> [939] 502984 201636 9971111 21493 2205609 61497 15495923
#> [946] 121 208698 5931 10545917 768 838485574 74333841
#> [953] 348920 69454 1091 254084763 187 222685139 192646535
#> [960] 2293 401 1347203 2051 211258 17747 204274
#> [967] 25986 19724875 353563568 339 20863 4059372 646105513
#> [974] 73299 22090 157951770 254765 860783 17779007 862723991
#> [981] 120325337 755122111 14402810 6695 350444 1017226 783589
#> [988] 141961262 126934662 280 15447 827716027 1201 53221653
#> [995] 747266785 30852 165693771 10479 5688436 510289344
#>
#> $lnQtLm
#> [1] 14.6614016 19.6425165 1.1450465 5.6492883 6.0880500 6.0842393
#> [7] 19.1549147 11.9167138 16.1553593 1.3793510 2.0843358 12.0108844
#> [13] 19.0801774 12.7203284 19.7797397 4.2032246 13.6680141 7.5731478
#> [19] 11.0460894 2.6452037 8.7469348 16.5176127 13.0294551 11.2331571
#> [25] 7.6257261 16.7026391 10.9748259 3.0894123 6.3288348 6.4823871
#> [31] 5.2570711 14.8469359 18.2937542 19.7191208 2.4164290 16.6561960
#> [37] 15.6779784 12.8630579 2.5529049 4.6820093 19.0189305 12.3472133
#> [43] 9.8806188 17.8215398 6.7533894 14.5650840 6.6298980 1.0132094
#> [49] 12.7977386 18.5672897 9.9726108 3.9804609 10.0604636 15.3768356
#> [55] 15.5998669 17.6080040 16.3422687 14.7004533 2.1465444 1.1487332
#> [61] 2.4346686 4.7112446 11.5922852 6.6675122 5.6157424 1.9753737
#> [67] 17.3156161 8.2285742 19.3038581 12.1779846 19.8684102 3.5617064
#> [73] 10.9004266 5.1114688 10.7416642 14.3305998 6.0714437 1.4361964
#> [79] 13.5895339 0.3718896 3.3108965 3.2275558 9.2571442 14.0444689
#> [85] 13.9058895 8.4629581 11.3239042 0.7255456 15.6916636 4.9795515
#> [91] 13.8447099 15.8423556 10.8422822 16.0452632 10.7779574 16.7586495
#> [97] 11.8449052 12.5273150 17.9415408 2.1170245 12.8341027 9.4222398
#> [103] 18.4223950 17.9634530 20.3454061 4.5131810 17.5210213 10.1904791
#> [109] 3.2513621 17.2583962 17.7306361 8.9689227 14.1586519 18.9186858
#> [115] 9.6487124 12.3633035 10.2423348 10.9116205 19.3043418 1.5522469
#> [121] 19.3715597 11.9004798 14.3847405 11.5045558 11.1212169 9.4563833
#> [127] 19.9760043 3.9609528 11.7924419 19.9660263 14.3505350 13.1370858
#> [133] 0.5976553 2.1937909 1.6825225 18.4364643 7.6603991 2.8697896
#> [139] 1.4325846 15.5915484 12.5575254 2.8105146 2.8239356 9.4731375
#> [145] 18.2648587 1.7670889 14.7037800 6.8790873 2.7952258 16.8035603
#> [151] 16.3993542 11.7481207 10.2174231 13.8253087 4.9661849 8.7755385
#> [157] 12.9328979 8.4079325 12.9010668 16.0309113 18.0702731 19.2549226
#> [163] 11.4995831 11.9564288 14.3227980 18.3562982 10.0981596 11.9673496
#> [169] 6.5617097 6.5894906 16.7767485 19.5580167 10.0738418 20.5934258
#> [175] 17.6244628 11.9042599 16.0982128 20.3414492 2.9787823 0.9122315
#> [181] 17.2015285 3.5977875 19.1711572 0.5148154 8.1864177 2.8982975
#> [187] 11.8436384 13.1166657 12.8836851 8.1807021 18.9391278 5.6570755
#> [193] 6.2774281 4.3380558 18.2165399 15.3411964 5.8914249 6.2790920
#> [199] 11.8035450 6.0444523 8.8507534 5.0277167 18.0466727 17.8471768
#> [205] 12.2614816 9.3892727 10.9264995 13.9440917 9.1701781 13.8427208
#> [211] 13.5889778 20.0491562 7.3257070 19.0127523 12.5992310 3.7421698
#> [217] 10.6167927 4.3510472 9.7728969 4.0381311 8.7565295 4.9100280
#> [223] 11.2875779 4.8790533 7.3696912 4.4890481 5.7741659 11.0408818
#> [229] 7.7582225 17.1649123 10.0503146 1.8958079 17.0580079 15.7631990
#> [235] 11.5568325 9.5938675 9.6106014 1.4176281 3.5398610 6.6633476
#> [241] 17.1644487 4.1736311 18.9050999 2.0649938 10.9141687 7.0534485
#> [247] 6.3693187 11.6227541 10.8532868 18.0972225 13.7930663 11.5145901
#> [253] 18.0408709 8.8554305 4.0883135 10.3452381 17.3540360 16.2277283
#> [259] 10.6080209 7.4108562 9.3829546 7.9444276 11.1212874 10.7779019
#> [265] 1.0866728 18.5058110 7.5390860 17.9537248 18.9245594 12.9036812
#> [271] 11.1233873 3.1520820 12.9021498 1.5162828 14.2099162 11.3391518
#> [277] 9.5804131 4.8223189 9.1441469 14.4862120 16.6549180 9.1850594
#> [283] 5.1502569 15.3914767 17.9361103 18.2154305 7.7232643 3.5315776
#> [289] 7.2471127 8.7801885 7.8836515 15.0196989 4.8301725 3.5603053
#> [295] 13.1063583 9.0851047 18.8663034 9.2688950 7.9703440 19.9263275
#> [301] 11.8407986 6.7826914 3.6587323 8.2586780 8.8819126 5.6232486
#> [307] 3.4727734 8.2238816 8.1503829 10.5523480 3.7725452 5.5988191
#> [313] 1.9738689 19.1273189 19.5903468 16.4321722 18.6076221 0.5208504
#> [319] 10.5010193 9.3056252 4.8073723 7.4917500 16.0776748 15.9658364
#> [325] 14.6461234 11.3756239 5.1211574 10.2048672 17.4416922 13.1048316
#> [331] 3.7725607 7.4001332 3.7097530 13.5866043 17.7455799 14.8286712
#> [337] 3.9529762 6.8383274 17.2570923 17.6211196 1.0009147 12.0755092
#> [343] 6.5992076 12.3061609 12.3592209 18.4879621 1.7928627 4.8024264
#> [349] 18.1737273 16.8219605 12.0395785 9.1023082 12.9897829 14.5125606
#> [355] 12.3298987 7.4965263 15.7322547 7.5443396 3.0061517 10.7163775
#> [361] 3.4553596 9.3016872 5.3696136 5.4719058 13.0018382 7.8396938
#> [367] 4.9103649 0.7532398 8.2580359 18.6750813 18.3791130 12.4254826
#> [373] 10.2437600 13.9563439 12.4750651 11.3212974 10.4036219 16.5014332
#> [379] 6.1808602 5.7577231 13.9075827 4.2760547 11.7761374 15.5566676
#> [385] 7.3304430 4.2388926 13.9088340 15.0076981 2.0157129 16.3226372
#> [391] 12.8340537 2.4719075 11.3568400 6.4165272 10.4731477 10.7160477
#> [397] 7.5430921 19.0275430 16.4679358 8.1327016 2.8157765 5.9938898
#> [403] 20.1802817 7.1217928 11.3551265 9.2544910 16.2510656 5.1208558
#> [409] 16.7376840 5.9649665 19.1684452 14.1958925 6.5692369 14.4983679
#> [415] 14.7895785 15.7089763 14.3720400 15.5015170 13.1988054 1.7113188
#> [421] 1.8337346 12.1754336 19.3158949 8.8011499 8.9822977 18.5912329
#> [427] 13.2904963 16.3122521 13.0732978 13.7086513 1.2942987 14.0262555
#> [433] 17.1944327 17.7187122 1.8494120 14.7355056 3.7781215 19.2544608
#> [439] 15.2287124 18.7236391 8.1836240 7.4378011 10.4246623 17.2753974
#> [445] 8.5971967 11.6189425 17.0616624 11.0344733 13.6268229 2.0021960
#> [451] 9.3349451 14.7113686 12.6184355 2.2431588 13.3460685 3.0353373
#> [457] 17.6255542 17.8866626 14.1826802 11.0341526 6.1199173 5.9437610
#> [463] 16.4064825 7.0124231 20.1295254 0.7152532 6.9575394 10.7077788
#> [469] 15.7474211 18.4360866 15.1045281 19.7503159 9.3978462 15.4484087
#> [475] 0.6260657 3.8743305 5.9682042 5.9944998 19.3192313 11.1172644
#> [481] 8.6054678 1.3698814 16.5043902 17.3783076 20.6139625 7.8430678
#> [487] 5.6863298 4.1577310 19.4387749 14.5487297 4.9144396 16.8234630
#> [493] 6.4249081 15.8511022 20.3066753 18.0303224 18.7146199 9.6472846
#> [499] 6.8274507 9.0401721 18.6682275 10.7684237 4.4170020 15.7704605
#> [505] 7.4935664 17.5407541 6.4118956 5.4965740 13.0704784 16.8518795
#> [511] 17.4790650 9.5964478 6.6127092 2.6814776 1.9801505 13.6935782
#> [517] 17.0029126 8.1487617 17.2770389 9.6575374 9.4755521 12.5015743
#> [523] 4.1588680 10.5555283 4.1896795 3.7876087 5.6461769 15.7745466
#> [529] 8.3432545 7.8662334 11.8566426 1.3258665 7.0969902 9.0023902
#> [535] 17.8775483 10.8451317 2.4085767 15.9682443 2.5406907 12.9656713
#> [541] 10.2703083 3.3891890 17.8070322 0.5507621 16.8038006 16.0873313
#> [547] 19.2160345 11.7725019 1.5156556 14.0893197 14.2280994 13.9105927
#> [553] 7.1273810 16.2020783 18.7247717 14.0437068 18.7032653 7.5429086
#> [559] 15.9963444 9.0121287 7.3967169 15.4590888 12.1967527 17.1187249
#> [565] 11.5109599 9.2185593 2.7139674 11.4556223 4.9129810 16.5151724
#> [571] 17.2577310 4.0574073 8.9136133 8.6830894 7.5593474 3.7182646
#> [577] 14.3168482 9.0714069 14.4983556 1.5670438 19.3157922 4.3850758
#> [583] 19.3528986 18.4435627 8.9250234 1.8182418 11.5919921 8.0941306
#> [589] 18.7737030 6.5062377 4.3595267 5.9565170 1.9347916 10.1093965
#> [595] 9.8065718 11.4005040 7.9090929 12.5843466 19.9785680 6.6915878
#> [601] 16.4983855 2.1199551 10.0279132 18.8706018 7.0662829 1.3147974
#> [607] 13.9802866 17.7285749 7.3063054 10.6576304 7.0801580 10.9408437
#> [613] 17.0323243 14.7563722 6.6633856 9.7172096 13.0601658 11.6127573
#> [619] 8.4094231 18.1291547 14.6298961 6.4277630 18.2592351 11.7031179
#> [625] 20.0271052 11.6957039 11.9050846 15.0566884 8.6682458 5.7011343
#> [631] 8.2062152 16.9977143 18.0800653 10.6491815 19.4734065 3.4300350
#> [637] 1.2399396 8.8241915 15.9953466 2.0493302 3.8501051 3.3328769
#> [643] 12.8339906 4.8063587 20.2981995 9.0555189 13.8996113 13.0063236
#> [649] 10.0042371 10.0236458 13.8777185 8.6840676 12.9855733 9.7149622
#> [655] 17.3417700 16.4526360 15.5519560 18.9315539 0.9235515 16.3290614
#> [661] 7.9448061 4.6652867 7.8249188 7.5652639 15.7893490 12.4051329
#> [667] 9.1966675 5.4221777 4.0877494 17.7131308 11.5916402 0.9952755
#> [673] 9.9249743 19.4881955 17.5490438 9.5032229 4.2251259 4.8630506
#> [679] 3.9793076 6.9303030 7.2598487 7.3275849 11.5803355 2.2891877
#> [685] 14.3577250 2.4410009 17.3629745 17.8976461 11.5337963 7.4652998
#> [691] 20.3915215 5.9662382 14.2599328 8.0089696 4.8627343 0.8438574
#> [697] 2.9888945 19.9241470 19.5660683 8.3611746 10.0477786 11.4386618
#> [703] 3.5746153 4.8458164 11.1382103 3.9582218 11.4007904 3.3546180
#> [709] 7.1389060 7.5637666 9.0347097 20.3089974 15.7895093 13.8212917
#> [715] 13.6289801 16.1982571 16.8825841 3.3801592 9.1587655 8.2884623
#> [721] 6.1715051 19.4197964 9.2184080 6.5752530 3.8467270 18.2654025
#> [727] 5.1089965 12.9116897 20.0797978 8.1027153 13.9825787 3.5922294
#> [733] 6.6569297 3.0153387 11.4263710 15.7186190 16.1868283 4.6220535
#> [739] 0.3508151 3.3867336 14.5406019 11.1804180 20.0614615 1.6007267
#> [745] 18.4784942 19.3670523 11.2618226 15.5451124 14.6129430 18.5959352
#> [751] 2.6215015 12.1984770 2.0562705 11.2427565 19.4006847 10.8529978
#> [757] 18.3686246 20.0622000 4.6875452 16.7830287 10.1556461 7.2281831
#> [763] 5.6084364 9.4876997 3.7614703 11.2706980 9.4008638 14.8434910
#> [769] 17.9021655 8.3338380 18.7568537 5.7985417 3.4619696 18.2298557
#> [775] 3.5215356 12.0670104 19.4685350 4.1482285 12.7909022 13.5526201
#> [781] 18.2057995 2.4571727 18.8593118 1.3681825 12.3132636 4.1378648
#> [787] 8.0173580 5.2777578 3.6829761 16.3603785 11.8848148 7.0555198
#> [793] 10.3845910 13.7886128 2.9329486 4.3985277 18.3359416 1.0282492
#> [799] 12.6423370 3.6511557 10.1485103 6.6759045 11.9121684 12.6812791
#> [805] 1.1068133 10.9346503 11.2460309 7.1625923 8.2380908 1.5051634
#> [811] 6.9957191 9.1958459 16.2686768 9.3022245 7.3233880 6.8440822
#> [817] 6.1182486 15.4673360 14.4744656 16.4290903 6.4932434 19.2707831
#> [823] 16.2738181 15.9850012 14.0266582 8.4070056 14.8772111 4.0801209
#> [829] 13.2990614 9.9782604 15.8996474 2.5393851 1.3283344 12.5866405
#> [835] 19.3656014 19.6167798 4.1793582 3.8117606 18.7482951 14.7271255
#> [841] 0.5556000 11.3689843 10.6699524 1.7180414 9.3883573 20.3684556
#> [847] 14.8510992 13.7909021 9.9194850 1.4987546 17.3137090 14.6159555
#> [853] 15.7195026 3.2188067 18.9176954 19.9144131 19.3533238 4.4026529
#> [859] 10.9421493 17.5730000 0.6969685 10.9853019 16.1054403 8.9204471
#> [865] 17.1909578 4.7959846 18.0785752 5.0703673 13.1310182 18.6509442
#> [871] 6.2255774 16.1239850 0.7506049 18.6049609 11.5521062 2.9917801
#> [877] 5.9775154 5.9061096 3.8689143 5.8917429 18.2142145 18.2122008
#> [883] 15.9896663 1.4865307 3.2239355 5.2968552 6.3604669 7.6699028
#> [889] 10.7939089 4.5332496 0.8838174 7.8538803 12.1275254 16.7594468
#> [895] 11.6451412 17.1796185 3.5446492 10.0910746 9.4066805 3.9428202
#> [901] 19.8239450 13.9645208 3.3596842 13.1679243 15.6695711 7.1053106
#> [907] 5.8709440 3.5451055 5.1432765 11.6400498 14.9518533 4.8576186
#> [913] 8.3707050 16.0912965 13.6283575 8.5709977 8.4360156 8.7152334
#> [919] 0.7376680 3.7527401 7.1411917 4.5386926 20.3458805 20.5275735
#> [925] 13.2412936 2.3988245 12.4410519 7.5360912 1.4022209 18.5259448
#> [931] 10.2495203 11.4836977 15.0111709 6.1542305 14.2703115 8.6190238
#> [937] 4.1546765 19.7262264 1.1117062 15.0949171 16.5044586 16.8762559
#> [943] 14.1238818 4.7804392 9.7607796 5.0266471 12.0708242 4.6573922
#> [949] 6.3595376 2.3871371 14.5354358 4.6472171 0.5889250 17.8382120
#> [955] 20.4499258 4.8022397 3.3945855 5.2994101 14.4445455 9.6355504
#> [961] 4.6132386 7.5211307 11.0105564 18.6822151 15.4568458 2.2126617
#> [967] 14.1146609 8.0143024 14.4992158 7.1154468 19.5072905 18.3167042
#> [973] 12.4800987 8.3691068 0.3573986 5.2095570 17.9611438 17.4580122
#> [979] 18.6906405 13.3103523 14.3618384 12.2742062 15.5960343 14.6046702
#> [985] 8.8959367 16.6441571 13.9661701 16.7514745 0.9445045 18.4257783
#> [991] 4.6144808 5.5233523 20.0347501 19.2848938 12.6592139 8.0938583
#> [997] 15.3644721 11.0992854 12.6902746 11.8401108
#>
#> $lnQtLAB
#> [1] 18.0969578 10.4957968 16.9667394 17.8391576 15.8897401 3.1818114
#> [7] 18.4073930 14.8040125 12.4507145 13.4009788 11.0660416 8.8018878
#> [13] 5.9976209 14.4951547 7.7262111 18.3190717 11.2574786 7.8863612
#> [19] 8.5896702 5.7635803 11.8853261 13.0401781 12.2440135 9.1589086
#> [25] 11.4427987 20.1237035 15.0032962 5.4015440 10.6054428 9.3508214
#> [31] 3.5644061 17.5932091 12.0146547 7.6999259 14.2852120 2.7187815
#> [37] 15.0210067 18.0538819 12.0275255 4.6994227 13.9809045 14.5169931
#> [43] 12.9375897 9.0224673 6.0762796 10.2792636 2.8499281 19.2908894
#> [49] 18.4821010 14.5950543 5.0995827 9.9225782 15.3653520 10.3038080
#> [55] 5.6920740 1.6421620 9.1738130 12.7792463 14.9925685 1.4644642
#> [61] 12.1409859 3.4664842 9.6203823 19.9744248 17.5180924 12.2528693
#> [67] 11.3807289 9.8248373 6.1013704 16.0770798 8.4923633 8.1951766
#> [73] 0.7166274 12.5337019 9.8674141 13.4765577 1.2512005 1.2972649
#> [79] 5.2217089 19.6227440 15.6798097 14.7078594 10.4834558 10.7348655
#> [85] 5.6565865 12.2103933 13.4073528 3.5878232 0.7619888 17.3936936
#> [91] 19.2114241 9.5341399 16.9506457 20.3763312 1.5390011 4.8128812
#> [97] 6.0613810 9.8229633 12.3940630 14.3689409 12.9758582 9.2525648
#> [103] 16.8235719 5.3581293 15.8931797 10.5014364 12.6169915 11.7487221
#> [109] 7.9196076 15.1801864 17.6680555 14.4835351 7.8805017 1.3718410
#> [115] 16.6296289 20.5608168 8.7841460 8.9924273 12.2031371 4.7806679
#> [121] 13.3934861 7.9002192 1.3470059 14.8365826 12.0396948 10.4276471
#> [127] 6.8208300 3.3753407 8.8036906 7.0576118 18.9862797 14.2366825
#> [133] 0.6185780 4.2588680 14.0197996 16.5453150 10.9668860 0.1982030
#> [139] 5.9236664 10.5860122 8.1149929 10.9817308 3.6255073 13.4966904
#> [145] 9.3403471 13.7088330 16.3193772 17.5111417 9.2338985 8.4673472
#> [151] 5.5780444 1.7604951 18.1046526 11.8828396 6.0704218 15.5995533
#> [157] 6.9692494 13.8695916 19.2064695 19.7799537 10.8325509 17.8822384
#> [163] 11.2610226 10.6879612 6.2716361 14.4709546 0.8530939 12.1153037
#> [169] 14.9976683 3.1013982 6.2871540 14.2705490 7.2072713 19.1744605
#> [175] 12.7174569 15.6575238 8.6811496 18.5699564 1.7237517 20.2592226
#> [181] 9.3135555 1.4340298 12.1184971 19.5290614 16.7326095 9.8410836
#> [187] 2.1569570 6.6237416 18.4175361 7.7500196 9.1995263 14.7186944
#> [193] 7.8069762 11.6545753 18.3964201 12.3148831 8.4028517 4.1554062
#> [199] 10.0632769 5.0998180 4.8839144 8.5540569 4.2190434 17.3812885
#> [205] 19.5950593 16.1545155 13.7891531 13.3877585 18.3396778 9.5291755
#> [211] 8.4949814 2.8137313 7.7528808 8.5517576 6.7188991 5.4511274
#> [217] 19.1846792 20.2689254 11.0611786 12.3527102 9.4878987 18.1197295
#> [223] 20.6602816 4.0927147 14.9328176 7.7092615 15.1757159 1.9555749
#> [229] 14.8833497 7.0718042 9.4823326 4.4384476 13.5089402 1.6771936
#> [235] 19.6175175 7.1467312 1.4341562 20.0159798 18.3609576 2.1879103
#> [241] 17.9908448 11.8563541 1.5837774 20.4119252 17.8232238 14.3948176
#> [247] 11.2063669 7.4730048 3.5427418 3.7785844 20.2499057 15.0541222
#> [253] 15.2837752 12.5962749 12.4364009 15.4851928 17.3909454 10.6936815
#> [259] 1.7738022 17.9416989 15.0427509 7.0061617 17.0413718 13.4285410
#> [265] 10.9813510 9.5444215 9.9645202 18.4253877 18.9423338 19.4371686
#> [271] 11.8529364 11.2815997 10.8427185 20.1366463 4.6695947 4.6715339
#> [277] 19.4199335 1.6654108 7.5337630 1.8541856 3.1067761 20.2219330
#> [283] 4.6139246 3.2151865 19.2939036 18.0771443 17.6338653 11.1336344
#> [289] 1.9089952 19.9653869 2.6858852 11.3866101 14.1293675 12.8806732
#> [295] 14.2735382 9.1993886 2.5394781 18.6067114 12.1244346 15.4582030
#> [301] 7.5123151 3.6479297 18.1100322 15.0251710 6.9902505 6.3712658
#> [307] 5.0244580 10.4652340 4.0137253 15.7495070 2.8087753 16.5704071
#> [313] 11.8800676 16.4626259 14.2776591 14.7276583 2.9327592 10.8641107
#> [319] 0.1286579 19.1149416 7.3832453 16.6010254 3.5020915 9.2829846
#> [325] 10.4229751 2.1157656 0.6497861 16.2524244 6.1427340 9.1973175
#> [331] 10.4466985 13.4083658 5.7925374 7.6841576 9.5298593 7.6300345
#> [337] 8.3583285 11.8352736 12.4460828 17.7267371 15.4241047 14.4878579
#> [343] 5.0744326 6.9908379 20.4007655 14.3926067 10.6215449 8.7487360
#> [349] 3.4499111 14.4790159 16.7256380 8.8767398 12.7728678 3.3137009
#> [355] 5.7938540 6.3864166 6.2106944 17.5551920 12.9469461 15.0723383
#> [361] 10.7443303 11.3774305 4.3851835 3.1818833 9.4712178 15.7270652
#> [367] 0.7470970 6.3214076 6.6954416 6.7479097 16.2688264 14.4080355
#> [373] 15.1129615 11.5365143 9.7123332 10.7783404 9.8451227 11.5077700
#> [379] 16.8667085 0.4970448 9.2954479 15.1184947 11.6824580 9.7551316
#> [385] 8.1831644 9.8174224 6.0298631 7.8702916 16.2673640 1.2013391
#> [391] 9.0565646 15.6154102 12.9177066 5.2219545 14.0520508 7.4499653
#> [397] 15.2641521 13.4941889 5.3712505 10.8436760 4.5558672 6.0755048
#> [403] 18.2068348 1.7463498 10.1116563 7.1803577 11.5662860 9.8436304
#> [409] 15.8356341 20.0280791 9.0262670 4.5606001 18.5585033 19.1370198
#> [415] 2.5393679 18.9463946 9.3369876 16.1185310 2.6779555 1.4282348
#> [421] 6.2734312 20.4700717 13.1726871 16.9568336 10.3595960 8.2600453
#> [427] 2.4871920 7.6352015 15.6989045 7.4006503 16.1776258 3.9347295
#> [433] 2.7518081 2.3292139 8.2998895 15.8690035 2.6473627 14.7399281
#> [439] 14.4133872 16.6256916 5.7683011 15.8756145 16.0682711 16.0243764
#> [445] 11.5841584 3.7832572 5.7324016 18.9892163 8.8190134 1.1584312
#> [451] 13.1243745 4.6135615 7.6635691 1.6517765 0.3865012 1.9776688
#> [457] 18.4999408 1.2350006 15.0117262 9.7732207 18.3947654 10.0267559
#> [463] 1.8837776 17.4405130 12.0000053 8.0875415 3.9452774 18.4575308
#> [469] 3.6916702 10.1926820 1.7433288 6.6879850 17.3484090 7.2595434
#> [475] 13.6311401 15.9977287 9.9349933 16.6512971 15.9299987 18.5477569
#> [481] 6.0000365 15.7760990 11.1921765 4.1577918 10.8927758 4.9712544
#> [487] 16.6245583 15.8456496 5.7792480 5.8930123 4.6404402 19.4497146
#> [493] 2.5899324 19.8731086 13.1292820 9.1876019 16.7062063 6.0718754
#> [499] 2.8654242 14.9464903 8.5764794 16.8052076 7.9002892 14.6209110
#> [505] 18.3800218 12.7086298 2.9117032 15.9955052 13.6530820 13.7702891
#> [511] 17.4502667 9.0319780 7.9761523 13.2552471 12.5973978 0.9670243
#> [517] 8.8481221 10.4371969 11.8931281 5.0490275 4.6965673 9.5006850
#> [523] 5.2557144 11.4883450 2.4053038 3.3517133 17.0805453 18.4846158
#> [529] 9.2794570 10.0477221 10.4507690 4.9513241 9.1354476 6.2694932
#> [535] 13.6334720 5.8826193 19.6356868 20.3329109 4.8336695 12.4279557
#> [541] 6.4993426 15.8070461 17.5031854 6.8594479 1.4036910 7.4005354
#> [547] 9.6568018 9.6485683 18.0309373 6.1894798 4.0203829 8.1491596
#> [553] 12.4000210 10.2638782 10.6630451 7.4389046 14.7628454 17.3502162
#> [559] 12.2763369 15.0854110 1.0994616 1.2072239 5.9407714 19.1588392
#> [565] 11.6533726 8.4652859 13.8746343 6.6705660 6.3856162 18.1348550
#> [571] 4.5616830 12.1572060 14.4832746 20.7089902 5.3981485 6.2589368
#> [577] 9.8042900 1.7509918 19.3617288 3.5775129 8.1425285 1.7773578
#> [583] 11.6495283 11.5232206 6.1249824 13.7341400 12.9446435 6.2895803
#> [589] 13.9418204 8.8686463 3.3166397 9.7892510 5.3582861 20.3583464
#> [595] 13.7481067 7.9544306 9.4141920 10.1399851 8.9437657 3.2654714
#> [601] 10.2169219 17.6489846 13.7539338 3.9425811 3.3688531 13.2024005
#> [607] 17.7037044 9.8610595 19.3511253 4.5123314 13.0822664 12.2706324
#> [613] 7.4272571 18.7206978 16.7259884 19.0256729 2.5968920 8.3172500
#> [619] 12.8260135 13.5343508 0.8717103 14.5098947 5.5332577 20.3734559
#> [625] 2.4263178 2.0793923 19.4442036 18.3583986 3.1893962 9.1359271
#> [631] 2.3483341 19.9312019 6.3602858 5.0080816 12.9154590 2.6503250
#> [637] 2.4698376 10.4106951 6.5878573 12.4061287 11.7234912 1.9055486
#> [643] 19.2540729 1.0154632 1.1055556 7.3375783 17.2004028 9.4272237
#> [649] 7.6145798 16.3934988 18.6294198 5.3616741 18.9917679 1.0772582
#> [655] 3.9580521 9.4980068 9.7456161 15.1769502 10.5609363 6.5685912
#> [661] 15.8308973 19.5049011 18.5532146 12.1878656 3.6171605 5.7916201
#> [667] 3.0715164 14.9055437 7.6605496 15.3782060 8.0804647 14.2190199
#> [673] 4.2129658 4.3082546 16.5152046 4.7592834 3.3157833 18.0386586
#> [679] 16.0868172 7.7474854 9.7119815 20.7087042 14.9836926 19.8151356
#> [685] 4.9456605 17.6773085 19.8514972 20.4375978 17.1062756 0.8608649
#> [691] 16.1011602 12.5148679 7.0869019 16.9482589 7.5845438 19.6328880
#> [697] 5.9218616 2.9518830 14.8587465 17.0718255 7.3815843 1.6491079
#> [703] 13.2706330 9.7655862 9.5373924 19.5608342 19.9749951 9.3938453
#> [709] 8.4820671 18.7202219 6.6538870 17.2087470 12.6297456 9.0562729
#> [715] 19.3592731 4.6638616 17.3971421 11.1185484 14.9423516 11.5053690
#> [721] 1.8709236 8.6653689 1.2002944 5.4464230 14.7165376 9.4769833
#> [727] 8.8538557 9.1133748 14.0987139 12.3911370 2.0877969 0.3877024
#> [733] 7.1839500 19.5434024 2.8715368 6.6285761 10.3556048 2.1482215
#> [739] 16.0102549 0.7098235 2.5704149 5.2946449 12.7411709 2.1646909
#> [745] 17.8506371 15.8771771 15.3383226 3.0702245 19.4519814 6.7545003
#> [751] 5.4613447 18.9960705 19.9972868 4.6850481 19.1594290 10.8269721
#> [757] 16.3954899 13.8971921 12.5731054 5.1669733 1.1377731 6.9953191
#> [763] 3.5996025 7.3300491 3.1694344 13.4654029 13.6892058 0.5039242
#> [769] 4.1726754 3.8266851 0.8424392 2.3540590 7.2218536 14.9786272
#> [775] 18.1785852 20.3118944 8.4972706 18.3983029 18.1411419 10.2219790
#> [781] 11.4752552 14.0265029 13.3149883 17.0515631 20.4399233 1.8827390
#> [787] 19.9978282 11.5089552 8.8694692 16.2067993 10.4845180 15.1256095
#> [793] 12.9806202 0.6662317 10.7229020 7.8654992 2.2364335 6.5393795
#> [799] 3.4759878 13.0125043 14.4382397 5.0022187 14.5100555 18.1370078
#> [805] 17.1436697 1.3389284 4.2432549 6.8985267 14.1838001 5.1108484
#> [811] 4.6158682 11.5953558 14.6488462 5.9228073 1.3699617 4.9900764
#> [817] 1.9075140 19.9883487 8.4626062 8.2916595 20.3261064 6.7752717
#> [823] 16.5700682 14.0641262 10.1247231 11.5236927 17.1559936 6.0473110
#> [829] 16.8180167 4.6327506 2.5999511 7.3666697 18.4447957 8.8484084
#> [835] 7.5232062 15.1346911 7.0018273 18.1775788 2.1904468 6.8548415
#> [841] 13.4049046 3.5027484 5.4144805 19.7452153 10.9137063 17.5397251
#> [847] 13.4258339 16.4659308 10.0638878 10.5166003 1.9373509 1.5734079
#> [853] 9.1141106 13.5724250 15.0514711 6.2659172 18.1385600 14.4646442
#> [859] 11.0874064 16.4929631 16.3160711 12.8236295 11.9408403 20.4286826
#> [865] 15.4999648 17.2908540 16.9854802 0.9639673 18.5532911 5.7626419
#> [871] 5.3558960 13.0448864 10.5203416 9.8628599 20.7951638 3.4542610
#> [877] 10.5672260 20.5472053 13.0212862 14.9901759 16.7730276 15.6592266
#> [883] 3.8764749 5.5081399 7.3315200 15.7305530 4.5464975 16.9944386
#> [889] 18.0944609 6.5766037 6.0232170 18.4302875 3.4261239 3.8350676
#> [895] 12.0721527 8.5847641 9.8007578 13.6145669 13.9255582 19.7602007
#> [901] 19.1355383 4.2378774 9.2294392 10.9434824 7.7628117 9.0243564
#> [907] 12.8414736 15.8146285 9.4867973 14.8761921 13.6459202 13.8990744
#> [913] 11.6516027 9.3900772 1.5395077 19.2048153 7.4146941 15.9516564
#> [919] 2.8232933 2.5004838 20.2751722 6.5412574 13.1650126 10.2373133
#> [925] 13.2370687 14.2132982 19.0428809 7.0701079 8.3507756 18.2741083
#> [931] 7.9384774 2.1802433 13.5780281 17.0734627 8.9037486 10.3377581
#> [937] 20.3924106 14.1528308 7.6553776 9.0305734 13.8165727 8.1691337
#> [943] 10.2771624 10.2372239 16.1828577 2.5490518 7.2477243 6.7564011
#> [949] 16.0245747 5.5401740 20.0191265 15.5145930 9.9643963 9.4179650
#> [955] 2.4601550 17.4322711 3.0221913 16.8900313 18.5815412 7.4146692
#> [961] 4.9562972 12.9152875 8.5709987 7.5296453 4.7225711 12.9685293
#> [967] 9.2981187 17.0536567 15.8604446 4.1529987 4.4904015 13.3814312
#> [973] 18.9983004 7.8991209 4.5288300 18.3787785 12.3656238 10.3207370
#> [979] 17.3862961 17.9054515 18.8208475 15.9234916 13.8846128 8.5512994
#> [985] 8.9563736 14.7588306 9.2431561 15.4035021 15.2263957 4.8531087
#> [991] 4.7953162 17.3918226 7.5838731 17.3380569 19.7865393 9.3864614
#> [997] 18.1580031 5.2146874 14.1651314 19.2570181
#>
# This is not very efficient (201 integrations), but it works.
Res <- sfGrowthJameson(
time = 0:200, N0Lm = rep(1, 201), N0LAB = rep(100, 201),
q0Lm = rep(1, 201), q0LAB = rep(1, 201),
muLm = rep(.1, 201), muLAB = rep(.3, 201),
MPDLm = rep(8, 201), MPDLAB = rep(7, 201),
unitSize = rep(100, 201),
gamma = rep(0.8, 201)
)
#> Integrate over 152 portions
#> ================================================================================
plot(0:200, log10(Res$N1Lm), type = "l", ylim = c(0, 9), xlab = "time", ylab = "log10 cfu")
points(0:200, log10(Res$N1LAB), type = "l", col = "blue")
legend(x = 0, y = 8.5, legend = c("Listeria", "Food flora"), col = c("black", "blue"), lty = 1)
