Calculates the number of fragment ends and the Windowed Protection Score (WPS) in genomic tiles within targets
analyze_fragmentation(bam, targets, tag = "", window_size = 120, step_size = 5, min_size = 120, max_size = 180, ...)
| bam | the input bam file |
|---|---|
| targets | The targets to restrict the windows within. Must have the columns chr, start and end. In case of whole-genome, specify full chromosomes targets. |
| tag | the RG tag if the bam has more than one sample. |
| window_size | The window (bin) size to use within the targets |
| step_size | The step size to use in case of overlapping bins. |
| min_size | Restrict fragments to this minimum size. |
| max_size | Restrict fragments to this maximum size. |
| ... | Other parameters passed to get_fragment_size |
a data frame with the first three columns having the bins coordinates and other columns having the WPS (raw and adjusted by coverage) and number of fragment ends (raw and adjusted by coverage).
Fragment length will extracted from the bam file according to the parameters passed to get_fragment_size, and the number of fragment ends,
and the Windowed Protection Score (WPS) will be computed in the binned input targets. Binning is done according to the window_size and step_size parameters.
WPS is defined as the number of fragments completely spanning a window (bin) minus the number of fragments with an endpoint within the same window as reported by Snyder et al., Cell 2016.
The output include both the fragment end counts and the WPS in their raw format as well as after adjustment by coverage in the bin.
Minimum and maximum bounds of the fragment size are applied before computing WPS and fragment ends counts.
get_fragment_size bin_fragment_size summarize_fragment_size
# \donttest{ data("targets", package = "ctDNAtools") bamN1 <- system.file("extdata", "N1.bam", package = "ctDNAtools") ## basic usage analyze_fragmentation(bam = bamN1, targets = targets)#> chr start end WPS WPS_adjusted n_fragment_ends #> 1 chr14 106327303 106327423 -155 -1.0000000 155 #> 2 chr14 106327308 106327428 -165 -1.0000000 165 #> 3 chr14 106327313 106327433 -170 -1.0000000 170 #> 4 chr14 106327318 106327438 -176 -1.0000000 176 #> 5 chr14 106327323 106327443 -171 -0.9661017 174 #> 6 chr14 106327328 106327448 -172 -0.9347826 179 #> 7 chr14 106327333 106327453 -170 -0.9239130 177 #> 8 chr14 106327338 106327458 -157 -0.8395722 172 #> 9 chr14 106327343 106327463 -155 -0.8288770 171 #> 10 chr14 106327348 106327468 -145 -0.7591623 172 #> 11 chr14 106327353 106327473 -139 -0.7202073 168 #> 12 chr14 106327358 106327478 -137 -0.7025641 166 #> 13 chr14 106327363 106327483 -134 -0.6836735 171 #> 14 chr14 106327368 106327488 -133 -0.6751269 165 #> 15 chr14 106327373 106327493 -119 -0.5804878 164 #> 16 chr14 106327378 106327498 -119 -0.5693780 167 #> 17 chr14 106327383 106327503 -127 -0.6018957 169 #> 18 chr14 106327388 106327508 -65 -0.3080569 138 #> 19 chr14 106327393 106327513 -47 -0.2165899 135 #> 20 chr14 106327398 106327518 -35 -0.1583710 133 #> 21 chr14 106327403 106327523 -41 -0.1744681 138 #> 22 chr14 106327408 106327528 -62 -0.2605042 151 #> 23 chr14 106327413 106327533 -64 -0.2644628 165 #> 24 chr14 106327418 106327538 -85 -0.3281853 175 #> 25 chr14 106327423 106327543 -109 -0.4113208 187 #> 26 chr14 106327428 106327548 -140 -0.5263158 206 #> 27 chr14 106327433 106327553 -157 -0.5709091 217 #> 28 chr14 106327438 106327558 -178 -0.6312057 233 #> 29 chr14 106327443 106327563 -190 -0.6643357 239 #> 30 chr14 106327448 106327568 -213 -0.7123746 256 #> 31 chr14 106327453 106327573 -227 -0.7541528 264 #> 32 chr14 106327458 106327578 -228 -0.7402597 270 #> 33 chr14 106327463 106327583 -250 -0.7812500 287 #> 34 chr14 106327468 106327588 -270 -0.8035714 304 #> 35 chr14 106327473 106327593 -304 -0.8735632 328 #> 36 chr14 106327478 106327598 -312 -0.8813559 333 #> 37 chr14 106327483 106327603 -320 -0.8888889 343 #> 38 chr14 106327488 106327608 -337 -0.9335180 350 #> 39 chr14 106327493 106327613 -323 -0.8947368 343 #> 40 chr14 106327498 106327618 -325 -0.8904110 349 #> 41 chr14 106327503 106327623 -321 -0.8891967 341 #> 42 chr14 106327508 106327628 -327 -0.9008264 345 #> 43 chr14 106327513 106327633 -323 -0.8753388 346 #> 44 chr14 106327518 106327638 -316 -0.8586957 343 #> 45 chr14 106327523 106327643 -292 -0.8021978 334 #> 46 chr14 106327528 106327648 -279 -0.7859155 317 #> 47 chr14 106327533 106327653 -268 -0.7613636 310 #> 48 chr14 106327538 106327658 -262 -0.7616279 310 #> 49 chr14 106327543 106327663 -235 -0.7142857 285 #> 50 chr14 106327548 106327668 -217 -0.7114754 261 #> 51 chr14 106327553 106327673 -194 -0.6466667 249 #> 52 chr14 106327558 106327678 -173 -0.5945017 233 #> 53 chr14 106327563 106327683 -166 -0.5763889 228 #> 54 chr14 106327568 106327688 -136 -0.4892086 207 #> 55 chr14 106327573 106327693 -144 -0.5217391 216 #> 56 chr14 106327578 106327698 -160 -0.5755396 222 #> 57 chr14 106327583 106327703 -154 -0.5422535 223 #> 58 chr14 106327588 106327708 -154 -0.5422535 226 #> 59 chr14 106327593 106327713 -121 -0.4464945 199 #> 60 chr14 106327598 106327718 -114 -0.4253731 192 #> 61 chr14 106327603 106327723 -103 -0.3857678 188 #> 62 chr14 106327608 106327728 -117 -0.4448669 191 #> 63 chr14 106327613 106327733 -145 -0.5272727 211 #> 64 chr14 106327618 106327738 -140 -0.5109489 207 #> 65 chr14 106327623 106327743 -137 -0.4981818 207 #> 66 chr14 106327628 106327748 -143 -0.5238095 209 #> 67 chr14 106327633 106327753 -147 -0.5384615 214 #> 68 chr14 106327638 106327758 -190 -0.6834532 235 #> 69 chr14 106327643 106327763 -193 -0.6868327 238 #> 70 chr14 106327648 106327768 -222 -0.7655172 258 #> 71 chr14 106327653 106327773 -234 -0.7905405 265 #> 72 chr14 106327658 106327778 -231 -0.7938144 262 #> 73 chr14 106327663 106327783 -246 -0.8092105 276 #> 74 chr14 106327668 106327788 -251 -0.8283828 278 #> 75 chr14 106327673 106327793 -256 -0.8152866 285 #> 76 chr14 106327678 106327798 -263 -0.8349206 289 #> 77 chr14 106327683 106327803 -259 -0.8222222 287 #> 78 chr14 106327688 106327808 -268 -0.8589744 290 #> 79 chr14 106327693 106327813 -258 -0.8376623 284 #> 80 chr14 106327698 106327818 -246 -0.8310811 271 #> 81 chr14 106327703 106327823 -235 -0.8020478 268 #> 82 chr14 106327708 106327828 -224 -0.7777778 256 #> 83 chr14 106327713 106327833 -228 -0.7916667 258 #> 84 chr14 106327718 106327838 -227 -0.7964912 257 #> 85 chr14 106327723 106327843 -234 -0.8239437 259 #> 86 chr14 106327728 106327848 -225 -0.8064516 256 #> 87 chr14 106327733 106327853 -198 -0.7333333 235 #> 88 chr14 106327738 106327858 -202 -0.7481481 239 #> 89 chr14 106327743 106327863 -204 -0.7555556 237 #> 90 chr14 106327748 106327868 -198 -0.7500000 234 #> 91 chr14 106327753 106327873 -195 -0.7647059 225 #> 92 chr14 106327758 106327878 -179 -0.7489540 209 #> 93 chr14 106327763 106327883 -168 -0.7118644 202 #> 94 chr14 106327768 106327888 -140 -0.6140351 188 #> 95 chr14 106327773 106327893 -132 -0.5789474 180 #> 96 chr14 106327778 106327898 -109 -0.4844444 173 #> 97 chr14 106327783 106327903 -93 -0.4096916 166 #> 98 chr14 106327788 106327908 -106 -0.4732143 166 #> 99 chr14 106327793 106327913 -87 -0.3866667 156 #> 100 chr14 106327798 106327918 -90 -0.4054054 156 #> 101 chr14 106327803 106327923 -88 -0.3963964 156 #> 102 chr14 106327808 106327928 -96 -0.4444444 157 #> 103 chr14 106327813 106327933 -122 -0.5495495 174 #> 104 chr14 106327818 106327938 -136 -0.6181818 187 #> 105 chr14 106327823 106327943 -170 -0.7657658 197 #> 106 chr14 106327828 106327948 -160 -0.7017544 198 #> 107 chr14 106327833 106327953 -172 -0.7413793 202 #> 108 chr14 106327838 106327958 -186 -0.7622951 217 #> 109 chr14 106327843 106327963 -197 -0.7975709 224 #> 110 chr14 106327848 106327968 -187 -0.7391304 224 #> 111 chr14 106327853 106327973 -190 -0.7600000 220 #> 112 chr14 106327858 106327978 -180 -0.7200000 220 #> 113 chr14 106327863 106327983 -181 -0.7269076 216 #> 114 chr14 106327868 106327988 -187 -0.7510040 218 #> 115 chr14 106327873 106327993 -206 -0.8373984 228 #> 116 chr14 106327878 106327998 -205 -0.8367347 226 #> 117 chr14 106327883 106328003 -204 -0.8429752 223 #> 118 chr14 106327888 106328008 -200 -0.8264463 228 #> 119 chr14 106327893 106328013 -196 -0.8166667 218 #> 120 chr14 106327898 106328018 -193 -0.8143460 216 #> 121 chr14 106327903 106328023 -185 -0.7939914 214 #> 122 chr14 106327908 106328028 -188 -0.8468468 206 #> 123 chr14 106327913 106328033 -185 -0.8371041 205 #> 124 chr14 106327918 106328038 -176 -0.8148148 199 #> 125 chr14 106327923 106328043 -181 -0.8418605 198 #> 126 chr14 106327928 106328048 -170 -0.8173077 190 #> 127 chr14 106327933 106328053 -145 -0.7435897 173 #> 128 chr14 106327938 106328058 -143 -0.7729730 164 #> 129 chr14 106327943 106328063 -108 -0.6506024 139 #> 130 chr14 106327948 106328068 -95 -0.5828221 133 #> 131 chr14 106327953 106328073 -79 -0.5031847 123 #> 132 chr14 106327958 106328078 -56 -0.3636364 107 #> 133 chr14 106327963 106328083 -36 -0.2465753 91 #> 134 chr14 106327968 106328088 -22 -0.1506849 93 #> 135 chr14 106327973 106328093 -25 -0.1748252 84 #> 136 chr14 106327978 106328098 -24 -0.1690141 83 #> 137 chr14 106327983 106328103 -20 -0.1428571 80 #> 138 chr14 106327988 106328108 -48 -0.3529412 95 #> 139 chr14 106327993 106328113 -43 -0.3440000 86 #> 140 chr14 106327998 106328118 -58 -0.4833333 89 #> 141 chr14 106328003 106328123 -77 -0.6470588 98 #> 142 chr14 106328008 106328128 -85 -0.7264957 101 #> 143 chr14 106328013 106328133 -84 -0.7636364 97 #> 144 chr14 106328018 106328138 -87 -0.7981651 99 #> 145 chr14 106328023 106328143 -100 -0.9259259 106 #> 146 chr14 106328028 106328148 -100 -1.0000000 100 #> 147 chr14 106328033 106328153 -99 -1.0000000 99 #> 148 chr14 106328038 106328158 -97 -1.0000000 97 #> 149 chr14 106328043 106328163 -94 -1.0000000 94 #> 150 chr14 106328048 106328168 -94 -1.0000000 94 #> 151 chr14 106328053 106328173 -93 -1.0000000 93 #> 152 chr14 106328058 106328178 -89 -1.0000000 89 #> 153 chr14 106328063 106328183 -88 -1.0000000 88 #> 154 chr14 106328068 106328188 -84 -1.0000000 84 #> 155 chr14 106328073 106328193 -83 -1.0000000 83 #> 156 chr14 106328078 106328198 -80 -1.0000000 80 #> 157 chr14 106328083 106328203 -78 -1.0000000 78 #> 158 chr14 106328088 106328208 -76 -1.0000000 76 #> 159 chr14 106328093 106328213 -72 -1.0000000 72 #> 160 chr14 106328098 106328218 -68 -1.0000000 68 #> 161 chr14 106328103 106328223 -66 -1.0000000 66 #> 162 chr14 106328108 106328228 -50 -1.0000000 50 #> 163 chr14 106328113 106328233 -46 -1.0000000 46 #> 164 chr14 106328118 106328238 -31 -1.0000000 31 #> 165 chr14 106328123 106328243 -21 -1.0000000 21 #> 166 chr14 106328128 106328248 -16 -1.0000000 16 #> 167 chr14 106328133 106328253 -13 -1.0000000 13 #> 168 chr14 106328138 106328258 -11 -1.0000000 11 #> 169 chr14 106328143 106328263 -4 -1.0000000 4 #> 170 chr14 106328148 106328268 0 0.0000000 0 #> 171 chr14 106328153 106328273 0 0.0000000 0 #> 172 chr14 106328158 106328278 0 0.0000000 0 #> 173 chr14 106328163 106328283 0 0.0000000 0 #> 174 chr14 106328168 106328288 0 0.0000000 0 #> n_fragment_ends_adjusted n_reads #> 1 1.0000000 155 #> 2 1.0000000 165 #> 3 1.0000000 170 #> 4 1.0000000 176 #> 5 0.9830508 177 #> 6 0.9728261 184 #> 7 0.9619565 184 #> 8 0.9197861 187 #> 9 0.9144385 187 #> 10 0.9005236 191 #> 11 0.8704663 193 #> 12 0.8512821 195 #> 13 0.8724490 196 #> 14 0.8375635 197 #> 15 0.8000000 205 #> 16 0.7990431 209 #> 17 0.8009479 211 #> 18 0.6540284 211 #> 19 0.6221198 217 #> 20 0.6018100 221 #> 21 0.5872340 235 #> 22 0.6344538 238 #> 23 0.6818182 242 #> 24 0.6756757 259 #> 25 0.7056604 265 #> 26 0.7744361 266 #> 27 0.7890909 275 #> 28 0.8262411 282 #> 29 0.8356643 286 #> 30 0.8561873 299 #> 31 0.8770764 301 #> 32 0.8766234 308 #> 33 0.8968750 320 #> 34 0.9047619 336 #> 35 0.9425287 348 #> 36 0.9406780 354 #> 37 0.9527778 360 #> 38 0.9695291 361 #> 39 0.9501385 361 #> 40 0.9561644 365 #> 41 0.9445983 361 #> 42 0.9504132 363 #> 43 0.9376694 369 #> 44 0.9320652 368 #> 45 0.9175824 364 #> 46 0.8929577 355 #> 47 0.8806818 352 #> 48 0.9011628 344 #> 49 0.8662614 329 #> 50 0.8557377 305 #> 51 0.8300000 300 #> 52 0.8006873 291 #> 53 0.7916667 288 #> 54 0.7446043 278 #> 55 0.7826087 276 #> 56 0.7985612 278 #> 57 0.7852113 284 #> 58 0.7957746 284 #> 59 0.7343173 271 #> 60 0.7164179 268 #> 61 0.7041199 267 #> 62 0.7262357 263 #> 63 0.7672727 275 #> 64 0.7554745 274 #> 65 0.7527273 275 #> 66 0.7655678 273 #> 67 0.7838828 273 #> 68 0.8453237 278 #> 69 0.8469751 281 #> 70 0.8896552 290 #> 71 0.8952703 296 #> 72 0.9003436 291 #> 73 0.9078947 304 #> 74 0.9174917 303 #> 75 0.9076433 314 #> 76 0.9174603 315 #> 77 0.9111111 315 #> 78 0.9294872 312 #> 79 0.9220779 308 #> 80 0.9155405 296 #> 81 0.9146758 293 #> 82 0.8888889 288 #> 83 0.8958333 288 #> 84 0.9017544 285 #> 85 0.9119718 284 #> 86 0.9175627 279 #> 87 0.8703704 270 #> 88 0.8851852 270 #> 89 0.8777778 270 #> 90 0.8863636 264 #> 91 0.8823529 255 #> 92 0.8744770 239 #> 93 0.8559322 236 #> 94 0.8245614 228 #> 95 0.7894737 228 #> 96 0.7688889 225 #> 97 0.7312775 227 #> 98 0.7410714 224 #> 99 0.6933333 225 #> 100 0.7027027 222 #> 101 0.7027027 222 #> 102 0.7268519 216 #> 103 0.7837838 222 #> 104 0.8500000 220 #> 105 0.8873874 222 #> 106 0.8684211 228 #> 107 0.8706897 232 #> 108 0.8893443 244 #> 109 0.9068826 247 #> 110 0.8853755 253 #> 111 0.8800000 250 #> 112 0.8800000 250 #> 113 0.8674699 249 #> 114 0.8755020 249 #> 115 0.9268293 246 #> 116 0.9224490 245 #> 117 0.9214876 242 #> 118 0.9421488 242 #> 119 0.9083333 240 #> 120 0.9113924 237 #> 121 0.9184549 233 #> 122 0.9279279 222 #> 123 0.9276018 221 #> 124 0.9212963 216 #> 125 0.9209302 215 #> 126 0.9134615 208 #> 127 0.8871795 195 #> 128 0.8864865 185 #> 129 0.8373494 166 #> 130 0.8159509 163 #> 131 0.7834395 157 #> 132 0.6948052 154 #> 133 0.6232877 146 #> 134 0.6369863 146 #> 135 0.5874126 143 #> 136 0.5845070 142 #> 137 0.5714286 140 #> 138 0.6985294 136 #> 139 0.6880000 125 #> 140 0.7416667 120 #> 141 0.8235294 119 #> 142 0.8632479 117 #> 143 0.8818182 110 #> 144 0.9082569 109 #> 145 0.9814815 108 #> 146 1.0000000 100 #> 147 1.0000000 99 #> 148 1.0000000 97 #> 149 1.0000000 94 #> 150 1.0000000 94 #> 151 1.0000000 93 #> 152 1.0000000 89 #> 153 1.0000000 88 #> 154 1.0000000 84 #> 155 1.0000000 83 #> 156 1.0000000 80 #> 157 1.0000000 78 #> 158 1.0000000 76 #> 159 1.0000000 72 #> 160 1.0000000 68 #> 161 1.0000000 66 #> 162 1.0000000 50 #> 163 1.0000000 46 #> 164 1.0000000 31 #> 165 1.0000000 21 #> 166 1.0000000 16 #> 167 1.0000000 13 #> 168 1.0000000 11 #> 169 1.0000000 4 #> 170 0.0000000 0 #> 171 0.0000000 0 #> 172 0.0000000 0 #> 173 0.0000000 0 #> 174 0.0000000 0## more options analyze_fragmentation( bam = bamN1, targets = targets, step_size = 10, window_size = 50 )#> chr start end WPS WPS_adjusted n_fragment_ends #> 1 chr14 106327373 106327423 -51 -0.32903226 104 #> 2 chr14 106327383 106327433 -46 -0.27058824 108 #> 3 chr14 106327393 106327443 37 0.20903955 71 #> 4 chr14 106327403 106327453 74 0.40217391 55 #> 5 chr14 106327413 106327463 93 0.49732620 54 #> 6 chr14 106327423 106327473 117 0.60621762 38 #> 7 chr14 106327433 106327483 134 0.68367347 33 #> 8 chr14 106327443 106327493 131 0.63902439 38 #> 9 chr14 106327453 106327503 117 0.55450237 47 #> 10 chr14 106327463 106327513 113 0.52073733 54 #> 11 chr14 106327473 106327523 87 0.37021277 76 #> 12 chr14 106327483 106327533 53 0.22362869 97 #> 13 chr14 106327493 106327543 0 0.00000000 129 #> 14 chr14 106327503 106327553 -55 -0.21568627 156 #> 15 chr14 106327513 106327563 -88 -0.33333333 177 #> 16 chr14 106327523 106327573 -93 -0.34572491 187 #> 17 chr14 106327533 106327583 -89 -0.33085502 181 #> 18 chr14 106327543 106327593 -83 -0.30627306 179 #> 19 chr14 106327553 106327603 -56 -0.22047244 160 #> 20 chr14 106327563 106327613 -41 -0.17012448 141 #> 21 chr14 106327573 106327623 -14 -0.05982906 125 #> 22 chr14 106327583 106327633 13 0.05439331 114 #> 23 chr14 106327593 106327643 73 0.32444444 78 #> 24 chr14 106327603 106327653 103 0.45374449 62 #> 25 chr14 106327613 106327663 84 0.38181818 69 #> 26 chr14 106327623 106327673 98 0.44545455 61 #> 27 chr14 106327633 106327683 109 0.48878924 58 #> 28 chr14 106327643 106327693 98 0.43750000 68 #> 29 chr14 106327653 106327703 60 0.25423729 91 #> 30 chr14 106327663 106327713 42 0.18750000 92 #> 31 chr14 106327673 106327723 35 0.15837104 96 #> 32 chr14 106327683 106327733 -12 -0.05084746 125 #> 33 chr14 106327693 106327743 -9 -0.03896104 122 #> 34 chr14 106327703 106327753 4 0.01886792 112 #> 35 chr14 106327713 106327763 -27 -0.13043478 118 #> 36 chr14 106327723 106327773 -71 -0.33333333 142 #> 37 chr14 106327733 106327783 -49 -0.22580645 135 #> 38 chr14 106327743 106327793 -56 -0.25000000 140 #> 39 chr14 106327753 106327803 -56 -0.26415094 134 #> 40 chr14 106327763 106327813 -27 -0.14136126 109 #> 41 chr14 106327773 106327823 2 0.01136364 87 #> 42 chr14 106327783 106327833 36 0.19565217 76 #> 43 chr14 106327793 106327843 51 0.27567568 67 #> 44 chr14 106327803 106327853 44 0.23655914 72 #> 45 chr14 106327813 106327863 36 0.19565217 74 #> 46 chr14 106327823 106327873 46 0.26136364 65 #> 47 chr14 106327833 106327883 54 0.30681818 61 #> 48 chr14 106327843 106327893 56 0.30769231 65 #> 49 chr14 106327853 106327903 61 0.34078212 63 #> 50 chr14 106327863 106327913 56 0.32183908 59 #> 51 chr14 106327873 106327923 46 0.26436782 64 #> 52 chr14 106327883 106327933 16 0.09195402 81 #> 53 chr14 106327893 106327943 -25 -0.13812155 104 #> 54 chr14 106327903 106327953 -43 -0.22751323 118 #> 55 chr14 106327913 106327963 -68 -0.34343434 135 #> 56 chr14 106327923 106327973 -70 -0.34653465 136 #> 57 chr14 106327933 106327983 -45 -0.23809524 120 #> 58 chr14 106327943 106327993 -29 -0.18012422 99 #> 59 chr14 106327953 106328003 -7 -0.04458599 85 #> 60 chr14 106327963 106328013 28 0.19178082 59 #> 61 chr14 106327973 106328023 47 0.32867133 51 #> 62 chr14 106327983 106328033 46 0.32857143 47 #> 63 chr14 106327993 106328043 53 0.42400000 37 #> 64 chr14 106328003 106328053 67 0.56302521 27 #> 65 chr14 106328013 106328063 66 0.60000000 22 #> 66 chr14 106328023 106328073 58 0.53703704 27 #> 67 chr14 106328033 106328083 57 0.57575758 21 #> 68 chr14 106328043 106328093 50 0.53191489 22 #> 69 chr14 106328053 106328103 39 0.41935484 27 #> 70 chr14 106328063 106328113 4 0.04545455 43 #> 71 chr14 106328073 106328123 -41 -0.49397590 62 #> 72 chr14 106328083 106328133 -52 -0.66666667 65 #> 73 chr14 106328093 106328143 -64 -0.88888889 70 #> n_fragment_ends_adjusted n_reads #> 1 0.6709677 155 #> 2 0.6352941 170 #> 3 0.4011299 177 #> 4 0.2989130 184 #> 5 0.2887701 187 #> 6 0.1968912 193 #> 7 0.1683673 196 #> 8 0.1853659 205 #> 9 0.2227488 211 #> 10 0.2488479 217 #> 11 0.3234043 235 #> 12 0.4092827 237 #> 13 0.5039062 256 #> 14 0.6117647 255 #> 15 0.6704545 264 #> 16 0.6951673 269 #> 17 0.6728625 269 #> 18 0.6605166 271 #> 19 0.6299213 254 #> 20 0.5850622 241 #> 21 0.5341880 234 #> 22 0.4769874 239 #> 23 0.3466667 225 #> 24 0.2731278 227 #> 25 0.3136364 220 #> 26 0.2772727 220 #> 27 0.2600897 223 #> 28 0.3035714 224 #> 29 0.3855932 236 #> 30 0.4107143 224 #> 31 0.4343891 221 #> 32 0.5296610 236 #> 33 0.5281385 231 #> 34 0.5283019 212 #> 35 0.5700483 207 #> 36 0.6666667 213 #> 37 0.6221198 217 #> 38 0.6250000 224 #> 39 0.6320755 212 #> 40 0.5706806 191 #> 41 0.4943182 176 #> 42 0.4130435 184 #> 43 0.3621622 185 #> 44 0.3870968 186 #> 45 0.4021739 184 #> 46 0.3693182 176 #> 47 0.3465909 176 #> 48 0.3571429 182 #> 49 0.3519553 179 #> 50 0.3390805 174 #> 51 0.3678161 174 #> 52 0.4655172 174 #> 53 0.5745856 181 #> 54 0.6243386 189 #> 55 0.6818182 198 #> 56 0.6732673 202 #> 57 0.6349206 189 #> 58 0.6149068 161 #> 59 0.5414013 157 #> 60 0.4041096 146 #> 61 0.3566434 143 #> 62 0.3357143 140 #> 63 0.2960000 125 #> 64 0.2268908 119 #> 65 0.2000000 110 #> 66 0.2500000 108 #> 67 0.2121212 99 #> 68 0.2340426 94 #> 69 0.2903226 93 #> 70 0.4886364 88 #> 71 0.7469880 83 #> 72 0.8333333 78 #> 73 0.9722222 72# }