dataesr/scientific-paragraphs-categorization huggingface dataset:
Our parameterisation cannot capture situations where the modal growth rate is 0, however all of our fits had support well away from 0. For each population, the imposed environment is given by E i in generation i. We only analysed data where information on the grandparental environment was available (i. e. we did not analyse the first two generations in each population). We added indicator variables to the data frame to indicate the location and light cue, such that L i = 1 for Paris, L i = À1 for Lisbon, C i = 1 for light cue, and C i = À1 for no light cue. The mode of the Gamma distribution for the data from generation i is given by h i ¼ e logðfðEiÀ1;EiÞÞ þ dLLi þ dCCiÀ1 ; ð1Þ where f is a function that determines how offspring production depends on the environmental history. The parameter d L is the location effect while d C is the effect of the light cue given in the maternal generation, and these are both considered fixed effects.
Model validation We performed two types of model validation, both employing posterior predictive fitting (c. f. Gelman et al. , 2013). First, we performed posterior predictive plot analysis using the aggregate statistic of geometric mean population growth over the experimental sequences. We used this method to compare the alternative models to the data from which the parameters were inferred. This method allows one to identify models that miss key features of the dataset, but does not assess the sensitivity of the fit to the specific data used. We generated distribution plots of the population geometric mean fitness and compared them to the empirically observed geometric mean population growth. Our second approach employed cross-validation to ensure that the fit is not overly sensitive to the specific data used to fit the parameters.
ACKNOWLEDGEMENTS We thank  T. Vale ,  P. Sandner ,  I. M. Chelo ,  P. Ibañez ,  H. Gendrot ,  J. Nedli ,  S. Nunes  and  S. Santos  for help with worm handling, and  L. -M. Chevin ,  V. Colot , M. -A. F elix, L. Fr ezal,  G. Lep  ere and  L. Noble  for discussion. Several anonymous reviewers provided helpful suggestions that improved the manuscript. Data analysis was done at the  Center for Scientific Computing at UC Santa Barbara , a  National Science Foundation (NSF)  supported facility ( DMR-1121053 ,  CNS-0960316 ). SD was a fellow of the  Labex MemoLife program  ( ANR-10-LBX-54   MEMO LIFE  and  ANR-IDEX-0001-02-PSL ). The project was funded by grants from the  NSF  ( EF-1137835 ) to SRP, and the  European Research Council  ( FP7/ 2007-2013/243285 ) and  Agence Nationale de la Recherche  ( ANR-14-ACHN-0032-01 ) to HT.
In both fields, pH was neutral and the total soil N content, which was determined with the Dumas method (elemental analyzer NA 1500, Carlo Erba, IT), was 1. 76 and 2. 26 g N kg -1 , respectively in the two experimental fields. Meteorological data were collected by a standard weather station from the Lombardy Region meteorological service (ARPA) in a nearby location three km away from the experimental fields.
Statistical Analysis A bootstrap-based method, proposed by Reference  [50] , was applied to estimate the standard deviation of the cumulated N 2 O emissions for each plot. A repeated measure mixed model was used to test the effect of the treatments on the daily N 2 O-N emissions, bulk density, NO 3 -N content, and WFPS over the two monitoring campaigns, splitting the dataset by year and using the repeated measures for considering the correlation between data measured in consecutive dates. The mean comparison was performed with the Tukey post-hoc test. The statistical analysis was executed with IBM SPSS 24. 0.
Results Table  1  shows the values of the summary statistics obtained from the observed population dataset consisting in two unstructured pooled samples of the subspecies S. g. gregaria and S. g. flaviventris. A total of 170 individuals (i. e. , 80 and 90 individuals for S. g. gregaria and S. g. flaviventris, respectively) were genotyped at 23 microsatellite markers derived from either genomic DNA (14 loci) or messenger RNA (9 loci) resources (hereafter referred to as untranscribed and transcribed microsatellite markers, respectively). The level of differentiation between the two subspecies (as measured by the parameter F ST ) was 0. 04 and 0. 12 for untranscribed and transcribed microsatellite markers, respectively. The level of genetic diversity was higher within the northern subspecies S.
ABC-RF analyses supported the same group of scenarios or the same best individual scenario for all ten replicate analyses (Table  2 ). The classification votes and posterior probabilities estimated for the observed microsatellite dataset were the highest for the groups of scenarios in which (i) S. g. flaviventris experienced a bottleneck event at the time of the split (scenarios SB+SCB+SBA U +SBA B +SCBA U +SCBA B in Figure  2 ; average of 2,829 votes out of 3,000 RF-trees; posterior probability = 0. 926), (ii) the ancestral population experienced a population size contraction (scenarios SC+SCB+SCA U +SCA B +SCBA U +SCBA B ; 2,035 of 3,000 RF-trees; posterior probability = 0. 682), and (iii) no admixture event occurred between populations after the split (scenarios S+SC+SB+SCB; 2,013 of 3,000 RF-trees; posterior probability = 0.
g. gregaria into S. g. flaviventris (mean of 10. 8% of votes). All other scenarios obtained less than 5% of the votes and were hence even more weakly supported. We found that the posterior error rates (i. e. , 1 minus the posterior probabilities) were lower than the prior error rates for the analyses considering either groups of scenarios based on the presence (or not) of a bottleneck in S. g. flaviventris (i. e. , 7. 4% versus 19. 0%) or the scenarios separately (i. e. , 43. 6% versus 58. 4%). For other groups of scenarios, the discrimination power was similar at both the global (prior error rates) and local (posterior error rates) scales, with values ranging from 26. 1% to 32. 1% (Table  2 ). Altogether, these results indicate that the observed dataset belongs to a region of the data space where the power to discriminate among scenarios is higher than the global power computed over the whole prior data space, and that the presence or absence of a bottleneck in S.
g. flaviventris is the demographic event with the most robust prediction in our ABC-RF treatments. These results can be visually illustrated by the projection of the reference table datasets and the observed one on a single (when analyzing pairwise groups of scenarios) or on the first two linear discriminant analysis (LDA) axes (when analyzing the twelve scenarios considered separately) (Figure  S1. 1, Supplementary Material S1). Figure  S1. 2, Supplementary Material S1, illustrates how RFs automatically rank the summary statistics according to their level of information. It shows that the number and set of most informative statistics is different depending on the comparisons (groups of scenarios or individual scenarios). Two sample statistics that measure the amount of genetic variation shared between populations (F ST , DM2 and LIK) were among the most informative when discriminating among groups of scenarios including or not an admixture event.
We thus evaluated the accuracy of ABC-RF estimation of the population divergence time as a function of the time scale, under scenario SCB. Analyses of simulated pseudo-observed datasets showed that the ABC-RF median estimate of divergence time reached a plateau for time scales ≥ 100,000 generations (Figure  4 ). Thus, the divergence time between S. g. flaviventris and S. g. gregaria estimated on our real microsatellite dataset (~10,000 generations) is positioned within the period of linearity with time, well before reaching a plateau reflecting a saturation of genetic information at microsatellite markers. It is hence expected to represent a sensible estimation of the actual divergence time. Using the median as a point estimate, we estimated that the population size contraction in the ancestor could have occurred at a time approximately three times older than the divergence time between the subspecies (cf.
Statistical advances by means of ABC Random Forest To our knowledge, the present study is the first one using recently developed ABC-RF algorithms  (Raynal et al. 2019)  to carry out inferences about parameter estimation on a real multi-locus microsatellite dataset (for scenario choice see for example  Rougemont et al. 2016 and Fraimout et al. 2017 ). When compared with various ABC solutions, this new RF method offers several advantages: a significant gain in terms of robustness to the choice of the summary statistics, independence from any type of tolerance level, and a good trade-off in terms of quality of point estimator precision of parameters and credible interval estimations for a given computing time  (Raynal et al. 2019). The RF approach that we used here includes three novelties in statistical analyses that were particularly useful for reconstructing the evolutionary history of the divergence between S.
g. gregaria and S. g. flaviventris subspecies. First, our ABC-RF statistical treatments benefited from the incorporation of previous estimations of mutation rates and allele size constraints for the microsatellite loci used in this study (for details see the Materials and methods section Microsatellite dataset, mutation rate and mutational model). Microsatellite mutation rate and pattern of most eukaryotes remains to a large extent unknown, and, to our knowledge, the present study is a rare one where independent information on mutational features was incorporated into the microsatellite prior distributions. Second, given the low RF computing time, we could simulate large pseudo-observed datasets to compute error measures conditionally to a subset of fixed divergence time values chosen to cover the entire prior interval.
In this way, we showed that posterior distributions for estimation of divergence time between the two subspecies accurately reflected true divergence time values. Third, because error levels may differ depending on the location of an observed dataset in the prior data space (e. g. ,  Pudlo et al. 2016) , priorbased indicators are poorly relevant, aside from their use to select the best classification method and set of predictors, here our summary statistics. Therefore, in addition to global prior errors, we computed local posterior errors, conditionally to the observed dataset. The latter errors measure prediction quality exactly at the position of the observed dataset. For parameter estimation accuracy, we propose an innovative way to approximate local posterior errors, relying partly on out-of-bag predictions and implemented in a new version of the R library abcrf (version 1.
g. , + 50% when considering the twelve scenarios separately; Table  S4. 1, Supplementary Material S4). Analyses of simulated pseudo-observed datasets (pods) showed that assuming a uniform prior rather than a log-uniform prior for time period parameters would have also biased positively the median estimate of the divergence time and substantially increased its 90% credibility interval (Figure  S4. 1 and Table  S4. 2, Supplementary Material S4). Using a log-uniform distribution remains a sensible choice for parameters with ranges of values covering several if not many log-intervals, as doing so allows assigning equal probabilities to each of the log-intervals. We used uniform prior distributions bounded between 1x10 4 and 1x10 6 diploid individuals for the different stable effective population sizes N f , N g and N a  (Chapuis et al.
Microsatellite dataset, mutation rate and mutational model We carried out our statistical inference on the microsatellite dataset previously published in  Chapuis et al. (2016). The 23 microsatellite loci genotyped in that dataset were derived from either genomic DNA (14 loci) or messenger RNA (9 loci) resources, and were hereafter referred to as untranscribed and transcribed microsatellite markers  (following Blondin et al. 2013). These microsatellites were shown to be genetically independent, free of null alleles and at selective neutrality  (Chapuis et al. 2016). Previous levels of F ST  (Weir 1996)  and Bayesian clustering analyses  (Pritchard et al. 2000)  among populations showed a weak genetic structuring within each subspecies  (Chapuis et al. 2014 (Chapuis et al. , 2017)). For each subspecies, we selected and pooled three population samples in order to ensure both a large sample size (i.
Analyses using ABC Random Forest We used the software DIYABC v. 2. 1. 0 (Cornuet et al. 2014)  to simulate datasets constituting the so-called reference tables (i. e. , records of a given number of datasets simulated using the scenario ID and the evolutionary parameter values sampled from prior distributions and summarized with a pool of statistics). Random-forest computations were then performed using a new version of the R library abcrf (version 1. 8) available on the CRAN. This version includes all ABC-RF algorithms detailed in  Pudlo et al. (2016) ,  Raynal et al. (2019)  and  Estoup et al. (2018a)  for scenario choice and parameter estimation, as well as several statistical novelties allowing to compute error rates in scenario choice and accuracy measures for parameter estimation (see details below).
An overview of the ABC-RF methods used in the present paper is provided in Supplementary Material S3. Readers can also consult  Pudlo et al. (2016) ,  Rougemont et al. (2016) ,  Fraimout et al. (2017) ,  Estoup et al. (2018a,b)  and  Marin et al. (2018)  for scenario choice, and  Raynal et al. (2019)  for parameter estimation to access to further detailed statistical descriptions, testing and applications of ABC-RF algorithms. For scenario choice, the outcome of the first step of the ABC-RF statistical treatment applied to a given target dataset is a classification vote for each scenario which represents the number of times a scenario is selected in a forest of n trees. The scenario with the highest classification vote corresponds to the scenario best suited to the target dataset among the set of compared scenarios.
This step also provides an error rate relevant to the entire prior sampling space, the global prior error. See the section Global prior errors in Supplementary Material S3 for details. The second RF analytical step provides a reliable estimation of the posterior probability of the best supported scenario. One minus such posterior probability yields the local posterior error associated to the observed dataset (see the section Local posterior errors in Supplementary Material S3). In practice, ABC-RF analyses were processed by drawing parameter values into the prior distributions described in the two previous sections and by summarizing microsatellite data using a set of 32 statistics (see Table  1  for details about such summary statistics) and the one LDA axis or eleven LDA axes (i. e. number of scenarios minus 1;  Pudlo et al.
2016 ) computed when considering pairwise groups of scenarios or individual scenarios, respectively. We processed ABC-RF treatments on reference tables including 150,000 simulated datasets (i. e. , 12,500 per scenario). Following  Pudlo et al. (2016) , we checked that 150,000 datasets was sufficient by evaluating the stability of prior error rates and posterior probabilities estimations of the best scenario on 50,000, 80,000 and 100,000 and 130,000 simulated datasets (Table  S1. 3, Supplementary Material S1). The number of trees in the constructed random forests was fixed to n = 3,000, as this number turned out to be large enough to ensure a stable estimation of the prior error rate (Figure  S1. 5, Supplementary Material S1). We predicted the best scenario and estimated its posterior probability and prior error rate over ten replicate analyses based on ten different reference tables.
For parameter estimation, we conducted ten independent replicate RF treatments based on ten different reference tables for each parameter of interest  (Raynal et al. 2019) : the time since divergence, the ratio of the time of the contraction event into the ancestral population on the time since divergence, the intensity of the bottleneck event in the sampled S. g. flaviventris population (defined as the ratio of the bottleneck event of duration d B on the effective population size N B ) and the ratio of the stable effective population size of the two sampled populations. For each RF treatment, we simulated a total of 100,000 datasets for the selected scenario PEER COMMUNITY IN EVOLUTIONARY BIOLOGY 20 (drawing parameter values into the prior distributions described in the two previous sections and using the same 32 summary statistics).
Following  Raynal et al. (2019) , we checked that 100,000 datasets was sufficient by evaluating the stability of the measure of accuracy on divergence time estimation using 50,000, 80,000 and 90,000 simulated datasets (Table  S1. 4, Supplementary Material S1). The number of trees in the constructed random forests was fixed to n = 2,000, as such number turned out to be large enough to ensure a stable estimation of the measure of divergence time estimation accuracy (Figure  S1. 6, Supplementary Material S1). For each RF treatment, we estimated the median value and the 5% and 95% quantiles of the posterior distributions. It is worth noting that we considered median values as the later provided more accurate estimations (according to out-of-bag predictions) than when considering mean values (results not shown).
Accuracy of parameter estimation was measured using out-of-bag predictions and the normalized mean absolute error (NMAE). NMAE corresponds to the mean of the absolute difference between the point estimate (here the median) and the (true) simulated value divided by the simulated value (formula detailed in Supplementary Material S3). Finally, because microsatellite markers tend to underestimate divergence time for large time scales due to allele size constraints, we evaluated how the accuracy of ABC-RF estimation of the time of divergence between the two subspecies was sensitive to the time scale. To this aim, we used DIYABC to produce simulated pseudo-observed datasets assuming fixed divergence time values chosen to cover the prior interval (100 ; 250 ; 500; 1,000 ; 2,500; 5,000 ; 10,000 ; 25,000 ; 50,000; 100,000; 250,000 generations) and using the best scenario.
We simulated 5,000 of such test datasets for each of the eleven divergence time values. Each of these test dataset was treated using ABC-RF in the same way as the above target observed dataset. (a-b) Distribution range and winds are adapted from  Sword et al. (2010)  and  Nicholson (1996) , respectively. (c-f) Vegetation habitats are adapted from  Adams and Faure (1997). Open vegetation habitats suitable for the desert locust correspond to deserts (dark orange), xeric shrublands (light orange) and tropical -Mediterranean grasslands (pink). Other unsuitable habitat classes (white) are forests, woodlands and temperate shrublands and savannas.
g. , pollen or insect fossils assemblages) from marine cores or terrestrial lakes. References are  Bond et al. (1997) ,  Guo et al. (2000) ,  Kröpelin et al. (2008) ,  Roberts et al. (1993)  and  van Andel and Tzedakis (1996)  for northern Africa, and  Talma and Vogel (1992) ,  Stokes et al. (1997), and Shi et al. (1998)  for southern Africa. See also  Gasse (2000)  for a review. Simulated pseudo-observed datasets (5,000 per divergence time) were generated for fixed divergence time values of 100 ; 250 ; 500; 1,000 ; 2,500; 5,000 ; 10,000 ; 25,000 ; 50,000; 100,000; and 250,000 generations (cf. x-axis with a log-scale). a) The estimated median (plain lines) and 90% credibility interval (90% CI; dashed lines), averaged over the 5,000 datasets, are represented (y-axis). b) The local accuracy is measured using out-of-bag predictions and the normalized mean absolute error (NMAE).
See Supplementary Material S3 for details. Table 1. The names of summary statistics are those given in the program DIYABC  (Cornuet et al. 2014). NAL: mean number of alleles; HET: mean expected heterozygosity; VAR: variance of allele sizes in base pairs; MGW: M index of  Garza and Williamson (2001) ; FST: pairwise differentiation estimator of  Weir (1996) ; DAS: shared allele distance  (Chakraborty and Jin 1993) ; LIK: the mean index of classification  (Rannala and Moutain, 1997; Pascual et al. 2007 ); DM2: distance of  Golstein et al. (1995). N2P, H2P and V2P: NAL, HET and VAR statistics computed after pooling the two population samples. Note that five "noise variables", randomly drawn into uniform distributions bounded between 0 and 1, and denoted NOISE1 to NOISE5 in the concerned illustrations, were added to the set of summary statistics processed by RF, in order to evaluate which summary statistics of our genetic datasets were informative in our different inferential ABC-RF settings, when conducting scenario choice or parameter estimation.
The number of records for each reference datasets simulated from DIYABC was set to 150,000 and the number of RF-trees was 3,000. For each evolutionary parameter, we reported posterior point estimates averaged over ten replicate analyses. CI: credibility interval. The number of records for each reference datasets simulated from DIYABC was set to 100,000 and the number of RF-trees was 2,000. Accuracy has been measured with the normalized mean absolute error (NMAE) which corresponds to the mean of the absolute difference between the point estimate of the parameter (here the median) and the (true) simulated value divided by the (true) simulated value. NMAE measures were computed using out-of-bag predictions either on the whole data space defined by the prior distributions (prior NMAE) or conditionally to the observed dataset (posterior NMAE); see Supplementary material S3 for details.
We report values for the proportion of votes, prior error rates and posterior probabilities of the best scenario on ten replicate analyses based on ten different reference tables. Scenarios are depicted in Figure  2. For each reference table, the number of datasets simulated using DIYABC was set to 150,000 and the number of RF-trees was 3,000. The scenario SCB was the best supported for all replicate analyses: it involves a bottleneck event in S. g. flaviventris right after divergence, a population size contraction in the ancestral population and not any genetic admixture event. Replicate analyses have been processed on different reference tables. For each reference table, the number of datasets simulated using DIYABC was set to 100,000 and the number of RF-trees was 2,000. Divergence times are given in number of generations (G).
SD stands for standard deviations computed from the ten values of median, 5% quantile and 95% quantile estimated from the ten replicate analyses. 2. The number of records in the reference datasets (n ref ) simulated from DIYABC varied from 50,000 to 150,000. We report mean and standard deviation values for the proportion of votes for each scenario, and for prior error rates and posterior probabilities of the best scenario for ten replicate analyses.
j for two population statistics, with k=1 for the set of untranscribed microsatellites or k=2 for the set of transcribed microsatellites, and i(j)=1 for the S. g. flaviventris subspecies or and i(j)=2 for the S. g. gregaria subspecies. See Table  S1  for details on the summary statistics abbreviations. Five noise variables, randomly drawn into uniform distributions bounded between 0 and 1, and denoted NOISE1 to NOISE5 were added to the set of summary statistics processed by RF, in order to evaluate from which amount of decrease in the Gini criterion the summary statistics computed from our genetic datasets were not The contribution of each 32 summary statistics and eleven LDA axes is evaluated as the total amount of decrease in the Gini criterion (variable importance on the x-axis). The higher the contribution of the statistics, the more informative it is in the inferential process.