The transformations are intended to map parameters that should only take
on restricted values to the full scale of real numbers. For kinetic rate
constants and other paramters that can only take on positive values, a
simple log transformation is used. For compositional parameters, such as
the formations fractions that should always sum up to 1 and can not be
negative, the ilr transformation is used.
The transformation of sets of formation fractions is fragile, as it supposes
the same ordering of the components in forward and backward transformation.
This is no problem for the internal use in mkinfit.
transform_odeparms(parms, mkinmod, transform_rates = TRUE, transform_fractions = TRUE) backtransform_odeparms(transparms, mkinmod, transform_rates = TRUE, transform_fractions = TRUE)
mkinmod, containing the names of
the model variables that are needed for grouping the formation fractions
before ilr transformation, the parameter names and
the information if the pathway to sink is included in the model.
ilr
transformation.
A vector of transformed or backtransformed parameters with the same names as the original parameters.
#># Fit the model to the FOCUS example dataset D using defaults fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE) summary(fit, data=FALSE) # See transformed and backtransformed parameters#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:20:49 2016 #> Date of summary: Fri Nov 18 15:20:49 2016 #> #> Equations: #> d_parent/dt = - k_parent_sink * parent - k_parent_m1 * parent #> d_m1/dt = + k_parent_m1 * parent - k_m1_sink * m1 #> #> Model predictions using solution type deSolve #> #> Fitted with method Port using 153 model solutions performed in 0.681 s #> #> Weighting: none #> #> Starting values for parameters to be optimised: #> value type #> parent_0 100.7500 state #> k_parent_sink 0.1000 deparm #> k_parent_m1 0.1001 deparm #> k_m1_sink 0.1002 deparm #> #> Starting values for the transformed parameters actually optimised: #> value lower upper #> parent_0 100.750000 -Inf Inf #> log_k_parent_sink -2.302585 -Inf Inf #> log_k_parent_m1 -2.301586 -Inf Inf #> log_k_m1_sink -2.300587 -Inf Inf #> #> Fixed parameter values: #> value type #> m1_0 0 state #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.600 1.61400 96.330 102.900 #> log_k_parent_sink -3.038 0.07826 -3.197 -2.879 #> log_k_parent_m1 -2.980 0.04124 -3.064 -2.897 #> log_k_m1_sink -5.248 0.13610 -5.523 -4.972 #> #> Parameter correlation: #> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> parent_0 1.00000 0.6075 -0.06625 -0.1701 #> log_k_parent_sink 0.60752 1.0000 -0.08740 -0.6253 #> log_k_parent_m1 -0.06625 -0.0874 1.00000 0.4716 #> log_k_m1_sink -0.17006 -0.6253 0.47163 1.0000 #> #> Residual standard error: 3.211 on 36 degrees of freedom #> #> Backtransformed parameters: #> Confidence intervals for internally transformed parameters are asymmetric. #> t-test (unrealistically) based on the assumption of normal distribution #> for estimators of untransformed parameters. #> Estimate t value Pr(>t) Lower Upper #> parent_0 99.600000 61.720 2.024e-38 96.330000 1.029e+02 #> k_parent_sink 0.047920 12.780 3.050e-15 0.040890 5.616e-02 #> k_parent_m1 0.050780 24.250 3.407e-24 0.046700 5.521e-02 #> k_m1_sink 0.005261 7.349 5.758e-09 0.003992 6.933e-03 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.398 4 15 #> parent 6.827 3 6 #> m1 4.490 1 9 #> #> Resulting formation fractions: #> ff #> parent_sink 0.4855 #> parent_m1 0.5145 #> m1_sink 1.0000 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 7.023 23.33 #> m1 131.761 437.70#> Model cost at call 1 : 18915.53 #> Model cost at call 2 : 18915.53 #> Model cost at call 7 : 10205.88 #> Model cost at call 10 : 10205.05 #> Model cost at call 13 : 8136.609 #> Model cost at call 18 : 2504.352 #> Model cost at call 20 : 2504.35 #> Model cost at call 22 : 2504.285 #> Model cost at call 25 : 1747.542 #> Model cost at call 27 : 1745.941 #> Model cost at call 29 : 1745.431 #> Model cost at call 30 : 1341.034 #> Model cost at call 34 : 1341.034 #> Model cost at call 35 : 1032.65 #> Model cost at call 39 : 1032.649 #> Model cost at call 40 : 919.9522 #> Model cost at call 42 : 919.952 #> Model cost at call 44 : 919.9518 #> Model cost at call 45 : 903.8272 #> Model cost at call 47 : 903.827 #> Model cost at call 49 : 903.8268 #> Model cost at call 50 : 780.8699 #> Model cost at call 52 : 780.8698 #> Model cost at call 54 : 780.8697 #> Model cost at call 55 : 734.3043 #> Model cost at call 57 : 734.3036 #> Model cost at call 60 : 717.8438 #> Model cost at call 67 : 676.3908 #> Model cost at call 68 : 676.3907 #> Model cost at call 69 : 676.3906 #> Model cost at call 71 : 676.3885 #> Model cost at call 72 : 642.2738 #> Model cost at call 73 : 642.2738 #> Model cost at call 76 : 642.2738 #> Model cost at call 77 : 604.7128 #> Model cost at call 78 : 604.7126 #> Model cost at call 82 : 560.1285 #> Model cost at call 83 : 560.1285 #> Model cost at call 86 : 560.1285 #> Model cost at call 87 : 521.6932 #> Model cost at call 88 : 521.6932 #> Model cost at call 91 : 521.6931 #> Model cost at call 92 : 453.6483 #> Model cost at call 93 : 453.6483 #> Model cost at call 96 : 453.6483 #> Model cost at call 98 : 422.5498 #> Model cost at call 102 : 422.5497 #> Model cost at call 106 : 413.6426 #> Model cost at call 108 : 413.6416 #> Model cost at call 111 : 407.4639 #> Model cost at call 113 : 407.4639 #> Model cost at call 115 : 407.4639 #> Model cost at call 116 : 403.6974 #> Model cost at call 118 : 403.6973 #> Model cost at call 120 : 403.6973 #> Model cost at call 121 : 396.004 #> Model cost at call 123 : 396.004 #> Model cost at call 126 : 391.2533 #> Model cost at call 128 : 391.2533 #> Model cost at call 130 : 391.2533 #> Model cost at call 131 : 388.4056 #> Model cost at call 133 : 388.4056 #> Model cost at call 135 : 388.4055 #> Model cost at call 137 : 384.0739 #> Model cost at call 139 : 384.0734 #> Model cost at call 143 : 383.6352 #> Model cost at call 145 : 383.635 #> Model cost at call 148 : 381.1342 #> Model cost at call 152 : 381.1342 #> Model cost at call 153 : 380.1443 #> Model cost at call 157 : 380.1443 #> Model cost at call 158 : 378.5615 #> Model cost at call 162 : 378.5614 #> Model cost at call 164 : 378.4583 #> Model cost at call 168 : 378.4583 #> Model cost at call 169 : 377.7047 #> Model cost at call 173 : 377.7047 #> Model cost at call 175 : 377.7042 #> Model cost at call 178 : 377.7042 #> Model cost at call 179 : 377.7042 #> Model cost at call 180 : 377.1553 #> Model cost at call 182 : 377.1553 #> Model cost at call 183 : 377.1553 #> Model cost at call 185 : 377.0866 #> Model cost at call 187 : 377.0866 #> Model cost at call 190 : 377.0288 #> Model cost at call 194 : 377.0288 #> Model cost at call 196 : 376.9814 #> Model cost at call 200 : 376.9814 #> Model cost at call 201 : 376.9488 #> Model cost at call 203 : 376.9488 #> Model cost at call 205 : 376.9488 #> Model cost at call 206 : 376.9184 #> Model cost at call 208 : 376.9184 #> Model cost at call 211 : 376.9095 #> Model cost at call 213 : 376.9095 #> Model cost at call 215 : 376.9095 #> Model cost at call 216 : 376.901 #> Model cost at call 218 : 376.901 #> Model cost at call 221 : 376.8936 #> Model cost at call 225 : 376.8936 #> Model cost at call 226 : 376.8848 #> Model cost at call 227 : 376.8608 #> Model cost at call 228 : 376.7665 #> Model cost at call 229 : 376.4162 #> Model cost at call 230 : 375.4439 #> Model cost at call 235 : 375.4439 #> Model cost at call 237 : 375.2281 #> Model cost at call 241 : 375.2281 #> Model cost at call 242 : 374.3381 #> Model cost at call 244 : 374.3381 #> Model cost at call 251 : 374.2632 #> Model cost at call 253 : 374.2632 #> Model cost at call 256 : 374.2391 #> Model cost at call 257 : 374.2247 #> Model cost at call 259 : 374.2247 #> Model cost at call 261 : 374.2247 #> Model cost at call 263 : 374.2024 #> Model cost at call 266 : 374.2024 #> Model cost at call 270 : 374.1952 #> Model cost at call 274 : 374.1952 #> Model cost at call 275 : 374.186 #> Model cost at call 279 : 374.186 #> Model cost at call 280 : 374.1724 #> Model cost at call 281 : 374.156 #> Model cost at call 282 : 374.0763 #> Model cost at call 283 : 373.7692 #> Model cost at call 284 : 372.729 #> Model cost at call 285 : 371.4251 #> Model cost at call 287 : 371.4251 #> Model cost at call 290 : 371.2142 #> Model cost at call 291 : 371.2142 #> Model cost at call 292 : 371.2142 #> Model cost at call 295 : 371.2134 #> Model cost at call 298 : 371.2134 #> Model cost at call 300 : 371.2134 #> Model cost at call 309 : 371.2134 #> Model cost at call 320 : 371.2134 #> Optimisation by method Port successfully terminated.summary(fit.2, data=FALSE)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:20:51 2016 #> Date of summary: Fri Nov 18 15:20:51 2016 #> #> Equations: #> d_parent/dt = - k_parent_sink * parent - k_parent_m1 * parent #> d_m1/dt = + k_parent_m1 * parent - k_m1_sink * m1 #> #> Model predictions using solution type deSolve #> #> Fitted with method Port using 327 model solutions performed in 1.34 s #> #> Weighting: none #> #> Starting values for parameters to be optimised: #> value type #> parent_0 100.7500 state #> k_parent_sink 0.1000 deparm #> k_parent_m1 0.1001 deparm #> k_m1_sink 0.1002 deparm #> #> Starting values for the transformed parameters actually optimised: #> value lower upper #> parent_0 100.7500 -Inf Inf #> k_parent_sink 0.1000 0 Inf #> k_parent_m1 0.1001 0 Inf #> k_m1_sink 0.1002 0 Inf #> #> Fixed parameter values: #> value type #> m1_0 0 state #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.600000 1.6140000 96.330000 1.029e+02 #> k_parent_sink 0.047920 0.0037500 0.040310 5.553e-02 #> k_parent_m1 0.050780 0.0020940 0.046530 5.502e-02 #> k_m1_sink 0.005261 0.0007159 0.003809 6.713e-03 #> #> Parameter correlation: #> parent_0 k_parent_sink k_parent_m1 k_m1_sink #> parent_0 1.00000 0.6075 -0.06625 -0.1701 #> k_parent_sink 0.60752 1.0000 -0.08740 -0.6253 #> k_parent_m1 -0.06625 -0.0874 1.00000 0.4716 #> k_m1_sink -0.17006 -0.6253 0.47164 1.0000 #> #> Residual standard error: 3.211 on 36 degrees of freedom #> #> Backtransformed parameters: #> Confidence intervals for internally transformed parameters are asymmetric. #> t-test (unrealistically) based on the assumption of normal distribution #> for estimators of untransformed parameters. #> Estimate t value Pr(>t) Lower Upper #> parent_0 99.600000 61.720 2.024e-38 96.330000 1.029e+02 #> k_parent_sink 0.047920 12.780 3.050e-15 0.040310 5.553e-02 #> k_parent_m1 0.050780 24.250 3.407e-24 0.046530 5.502e-02 #> k_m1_sink 0.005261 7.349 5.758e-09 0.003809 6.713e-03 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.398 4 15 #> parent 6.827 3 6 #> m1 4.490 1 9 #> #> Resulting formation fractions: #> ff #> parent_sink 0.4855 #> parent_m1 0.5145 #> m1_sink 1.0000 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 7.023 23.33 #> m1 131.761 437.70initials <- fit$start$value names(initials) <- rownames(fit$start) transformed <- fit$start_transformed$value names(transformed) <- rownames(fit$start_transformed) transform_odeparms(initials, SFO_SFO)#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 100.750000 -2.302585 -2.301586 -2.300587backtransform_odeparms(transformed, SFO_SFO)#> parent_0 k_parent_sink k_parent_m1 k_m1_sink #> 100.7500 0.1000 0.1001 0.1002# The case of formation fractions SFO_SFO.ff <- mkinmod( parent = list(type = "SFO", to = "m1", sink = TRUE), m1 = list(type = "SFO"), use_of_ff = "max")#>#> Model cost at call 1 : 15156.12 #> Model cost at call 2 : 15156.12 #> Model cost at call 6 : 8243.644 #> Model cost at call 12 : 6290.714 #> Model cost at call 13 : 6290.684 #> Model cost at call 15 : 6290.453 #> Model cost at call 18 : 1700.75 #> Model cost at call 20 : 1700.612 #> Model cost at call 24 : 1190.923 #> Model cost at call 26 : 1190.922 #> Model cost at call 29 : 1017.417 #> Model cost at call 31 : 1017.417 #> Model cost at call 33 : 1017.416 #> Model cost at call 34 : 644.0471 #> Model cost at call 36 : 644.0469 #> Model cost at call 38 : 644.0468 #> Model cost at call 39 : 590.5024 #> Model cost at call 41 : 590.5021 #> Model cost at call 43 : 590.5015 #> Model cost at call 44 : 543.2187 #> Model cost at call 45 : 543.2183 #> Model cost at call 46 : 543.2182 #> Model cost at call 50 : 391.348 #> Model cost at call 51 : 391.3479 #> Model cost at call 56 : 386.4789 #> Model cost at call 58 : 386.4789 #> Model cost at call 60 : 386.4779 #> Model cost at call 61 : 384.0686 #> Model cost at call 63 : 384.0686 #> Model cost at call 66 : 382.7812 #> Model cost at call 68 : 382.7812 #> Model cost at call 70 : 382.7812 #> Model cost at call 71 : 378.9272 #> Model cost at call 73 : 378.9272 #> Model cost at call 75 : 378.9272 #> Model cost at call 76 : 377.4846 #> Model cost at call 78 : 377.4846 #> Model cost at call 81 : 375.9738 #> Model cost at call 83 : 375.9738 #> Model cost at call 86 : 375.3387 #> Model cost at call 88 : 375.3387 #> Model cost at call 91 : 374.5774 #> Model cost at call 93 : 374.5774 #> Model cost at call 95 : 374.5774 #> Model cost at call 96 : 373.5447 #> Model cost at call 100 : 373.5446 #> Model cost at call 102 : 373.2643 #> Model cost at call 104 : 373.2643 #> Model cost at call 107 : 372.6799 #> Model cost at call 111 : 372.6798 #> Model cost at call 114 : 372.6325 #> Model cost at call 116 : 372.6325 #> Model cost at call 119 : 372.6159 #> Model cost at call 121 : 372.6159 #> Model cost at call 123 : 372.6159 #> Model cost at call 124 : 372.5845 #> Model cost at call 126 : 372.5845 #> Model cost at call 129 : 372.5375 #> Model cost at call 130 : 372.4771 #> Model cost at call 131 : 372.2008 #> Model cost at call 132 : 371.4923 #> Model cost at call 134 : 371.4923 #> Model cost at call 137 : 371.3022 #> Model cost at call 139 : 371.3022 #> Model cost at call 143 : 371.2271 #> Model cost at call 144 : 371.2271 #> Model cost at call 148 : 371.2202 #> Model cost at call 149 : 371.215 #> Model cost at call 152 : 371.215 #> Model cost at call 154 : 371.2136 #> Model cost at call 155 : 371.2136 #> Model cost at call 156 : 371.2136 #> Model cost at call 160 : 371.2134 #> Model cost at call 164 : 371.2134 #> Model cost at call 167 : 371.2134 #> Optimisation by method Port successfully terminated.summary(fit.ff, data = FALSE)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:20:52 2016 #> Date of summary: Fri Nov 18 15:20:52 2016 #> #> Equations: #> d_parent/dt = - k_parent * parent #> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1 #> #> Model predictions using solution type deSolve #> #> Fitted with method Port using 185 model solutions performed in 0.764 s #> #> Weighting: none #> #> Starting values for parameters to be optimised: #> value type #> parent_0 100.7500 state #> k_parent 0.1000 deparm #> k_m1 0.1001 deparm #> f_parent_to_m1 0.5000 deparm #> #> Starting values for the transformed parameters actually optimised: #> value lower upper #> parent_0 100.750000 -Inf Inf #> log_k_parent -2.302585 -Inf Inf #> log_k_m1 -2.301586 -Inf Inf #> f_parent_ilr_1 0.000000 -Inf Inf #> #> Fixed parameter values: #> value type #> m1_0 0 state #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.60000 1.61400 96.3300 102.9000 #> log_k_parent -2.31600 0.04187 -2.4010 -2.2310 #> log_k_m1 -5.24800 0.13610 -5.5230 -4.9720 #> f_parent_ilr_1 0.04096 0.06477 -0.0904 0.1723 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> parent_0 1.0000 0.5178 -0.1701 -0.5489 #> log_k_parent 0.5178 1.0000 -0.3285 -0.5451 #> log_k_m1 -0.1701 -0.3285 1.0000 0.7466 #> f_parent_ilr_1 -0.5489 -0.5451 0.7466 1.0000 #> #> Residual standard error: 3.211 on 36 degrees of freedom #> #> Backtransformed parameters: #> Confidence intervals for internally transformed parameters are asymmetric. #> t-test (unrealistically) based on the assumption of normal distribution #> for estimators of untransformed parameters. #> Estimate t value Pr(>t) Lower Upper #> parent_0 99.600000 61.720 2.024e-38 96.330000 1.029e+02 #> k_parent 0.098700 23.880 5.701e-24 0.090660 1.074e-01 #> k_m1 0.005261 7.349 5.758e-09 0.003992 6.933e-03 #> f_parent_to_m1 0.514500 22.490 4.374e-23 0.468100 5.606e-01 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.398 4 15 #> parent 6.459 2 7 #> m1 4.690 2 8 #> #> Resulting formation fractions: #> ff #> parent_m1 0.5145 #> parent_sink 0.4855 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 7.023 23.33 #> m1 131.761 437.70initials <- c("f_parent_to_m1" = 0.5) transformed <- transform_odeparms(initials, SFO_SFO.ff) backtransform_odeparms(transformed, SFO_SFO.ff)#> f_parent_to_m1 #> 0.5# And without sink SFO_SFO.ff.2 <- mkinmod( parent = list(type = "SFO", to = "m1", sink = FALSE), m1 = list(type = "SFO"), use_of_ff = "max")#>#> Model cost at call 1 : 12435.14 #> Model cost at call 2 : 12435.14 #> Model cost at call 5 : 8276.306 #> Model cost at call 6 : 8276.294 #> Model cost at call 7 : 8275.676 #> Model cost at call 9 : 5256.953 #> Model cost at call 11 : 5256.951 #> Model cost at call 12 : 5256.943 #> Model cost at call 14 : 4469.745 #> Model cost at call 18 : 4462.927 #> Model cost at call 21 : 4462.925 #> Model cost at call 22 : 4376.059 #> Model cost at call 24 : 4376.058 #> Model cost at call 27 : 4366.956 #> Model cost at call 29 : 4366.956 #> Model cost at call 31 : 4365.275 #> Model cost at call 33 : 4365.275 #> Model cost at call 35 : 4351.877 #> Model cost at call 37 : 4351.877 #> Model cost at call 39 : 4338.109 #> Model cost at call 41 : 4338.109 #> Model cost at call 43 : 4297.053 #> Model cost at call 44 : 4218.591 #> Model cost at call 45 : 3940.397 #> Model cost at call 46 : 3690.395 #> Model cost at call 48 : 3690.395 #> Model cost at call 49 : 3690.385 #> Model cost at call 50 : 3038.366 #> Model cost at call 53 : 3038.365 #> Model cost at call 54 : 2637.866 #> Model cost at call 57 : 2637.865 #> Model cost at call 59 : 2588.01 #> Model cost at call 60 : 2588.009 #> Model cost at call 63 : 2576.742 #> Model cost at call 66 : 2576.742 #> Model cost at call 67 : 2574 #> Model cost at call 68 : 2574 #> Model cost at call 69 : 2574 #> Model cost at call 71 : 2569.76 #> Model cost at call 73 : 2569.76 #> Model cost at call 74 : 2569.76 #> Model cost at call 75 : 2569.403 #> Model cost at call 76 : 2569.403 #> Model cost at call 79 : 2569.4 #> Model cost at call 80 : 2569.4 #> Model cost at call 81 : 2569.4 #> Model cost at call 83 : 2569.4 #> Model cost at call 86 : 2569.4 #> Model cost at call 90 : 2569.4 #> Model cost at call 99 : 2569.4 #> Model cost at call 100 : 2569.4 #> Optimisation by method Port successfully terminated.summary(fit.ff.2, data = FALSE)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:20:52 2016 #> Date of summary: Fri Nov 18 15:20:52 2016 #> #> Equations: #> d_parent/dt = - k_parent * parent #> d_m1/dt = + k_parent * parent - k_m1 * m1 #> #> Model predictions using solution type deSolve #> #> Fitted with method Port using 104 model solutions performed in 0.44 s #> #> Weighting: none #> #> Starting values for parameters to be optimised: #> value type #> parent_0 100.7500 state #> k_parent 0.1000 deparm #> k_m1 0.1001 deparm #> #> Starting values for the transformed parameters actually optimised: #> value lower upper #> parent_0 100.750000 -Inf Inf #> log_k_parent -2.302585 -Inf Inf #> log_k_m1 -2.301586 -Inf Inf #> #> Fixed parameter values: #> value type #> m1_0 0 state #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 84.790 2.96500 78.78 90.800 #> log_k_parent -2.756 0.08088 -2.92 -2.593 #> log_k_m1 -4.214 0.11150 -4.44 -3.988 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 #> parent_0 1.0000 0.11059 0.46156 #> log_k_parent 0.1106 1.00000 0.06274 #> log_k_m1 0.4616 0.06274 1.00000 #> #> Residual standard error: 8.333 on 37 degrees of freedom #> #> Backtransformed parameters: #> Confidence intervals for internally transformed parameters are asymmetric. #> t-test (unrealistically) based on the assumption of normal distribution #> for estimators of untransformed parameters. #> Estimate t value Pr(>t) Lower Upper #> parent_0 84.79000 28.600 3.939e-27 78.78000 90.80000 #> k_parent 0.06352 12.360 5.237e-15 0.05392 0.07483 #> k_m1 0.01478 8.966 4.114e-11 0.01179 0.01853 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 19.66 3 16 #> parent 17.56 2 7 #> m1 18.71 1 9 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 10.91 36.25 #> m1 46.89 155.75