A Scheme for Adaptive Selection of Population Sizes 1410 10000
Distance0. 00. 51. 0Empirical density× 10 −^3
True
MAP
1.03.0
divLTrue-3.0-1.0
divkmax-5.00.0
degke-5.00.0
dive-5.00.0
proke-5.00.0
initq1.0Ldiv 3.00.01.2
L
init-3.0kmaxdiv -1.0-5.0kdege 0.0-5.0ediv 0.0-5.0kproe 0.0-5.0qinit 0.00.0Linit 1.2Generationt=40Generationt=13 log 10 parameterslog10parametersa0 10 20
Timet(d)250500750Spheroid
radius (μm)0 500
Distance to
spheroid rim (μm)0. 00. 20. 4Fraction ofproliferatingcells0 500
Distance to
spheroid rim (μm)01Extracellularmatrixintensityb c0 40
Generationt102104106108Acceptancethreshold0 40
Generationt0200Population sizen neffd 1d 2Fig. 4. Multiscale tumor growth model. (a)Tumor growth data. 100 samples
from the reference parameters listed in [ 9 ]. The data were: (1) the spheroid radius
over time, (2) the fraction of proliferating cells over distance to the spheroid rim, and
(3) the extracellular matrix intensity over distance to the spheroid rim.(b)Posterior
distributions obtained from an adaptive population size ABC-SMC run withECV=
0 .25. Axis limits correspond to the support of the uniform prior. The purple crosses
and dashed lines “True” indicate the reference parameters. Lower triangle: distribution
of generationt= 13. Upper triangle: distribution of generationt= 40. Diagonal:
distributions across the generations: light to dark: earlier to later generations.(c)
Distribution of distances to the observed datasdatawhich was obtained as average
of 100 samples from the reference parameter values [ 9 ]. True (black): Distances of
the same 100 samples which were used to generate the observed datasdata.MAP
(orange): Distances of 100 samples from the maximum a posteriori parameters.(d)
(d 1 ) Acceptance threshold;(d 2 ) Population sizenand effective population sizeneff
for (b). At generationt,is set to the median of the observation–particle distances of
generationt−1. (Color figure online)