dataesr/scientific-paragraphs-categorization huggingface dataset:
Thus, in the comparison Expansion versus Constant versus Contraction (algorithm 1), each model was simulated 10, 000 times under the homogeneous Ne model, and 10, 000 times under the heterogeneous Ne model. To test the performance of DILS in model comparisons (among demographic models and among genomic models), we simulated 30, 000 pseudo-observed datasets of 100 loci by using random combinations of parameters. Throughout the manuscript, pseudoobserved datasets are used to evaluate the performance of the random forest and do not contribute to its training. These simulated datasets are equally distributed between the demographic models (10, 000 for each of the three Expansion/Constant/Contraction models) and between the genomic models (5, 000 for each of the two homo/hetero Ne alternative genomic models for a given demographic model).
Then, for each of these pseudo-observed datasets, we apply step 1 and step 2 of the algorithm 1 in order to obtain for each model M, the proportion of pseudo-observed datasets that is i) correctly and strongly captured by the random forest approach, ii)falsely and strongly captured and Data: A single fasta containing all genes sequenced in all individuals sampled in the studied population Result: Posterior probabilities for the best 1) demographic and 2) genomic models  Conversely, the Isolation with Migration (IM) and Secondary Contact (SC) models describe two populations that are currently connected by introgression events at rate N. m. The two-population models shown here are of constant size, but DILS optionally incorporates alternative versions of the same four models where effective size can change independently in both daughter populations between the present time and T split.
Each of these 10,000 simulated datasets are evenly distributed between the two genomic models, homo and hetero Ne. The parameters used for the simulated datasets are randomly drawn from uniform laws, with N e in [1-1,000,000] individuals and T dem in [1-2,000,000] generations. Each simulated dataset consists of 100 loci of length 1, 000 nucleotides. For a given dataset, the model comparison will provide two pieces of information: i) What is the best model among all those arbitrarily proposed in the analysis? ii) With which posterior probability is the best model supported? It is from the latter probability that we determine whether an inference is strong or ambiguous. For this we use a probability threshold beyond which an inference is considered strong. This threshold is determined recursively on the basis of the false positive rate which decreases monotonically by increasing the value of the threshold.
From datasets randomly simulated under different models, we establish a threshold value such that the false positive rate is less than or equal to 1%. With this approach, the falsepositive rate remains consistently low, but the relative proportions of true positives versus ambiguous cases vary according to the power of the ABC to discriminate among an arbitrary set of models. Thus, among the 30, 000 pseudo-observed datasets simulated under the Expansion, Constant and Contraction models, if a threshold is applied that keeps the error rate below 1%, the proportions that are correctly supported by our approach are 86%, 89% and 99% respectively, while the proportions that are ambiguous are 13%, 10% and 0. 2% (figure  2 ). The second step of the hierarchical comparison, which classifies models with genomic variation in effective size (hetero) or without variation (homo), is evaluated using the same procedure as step 1 (figure  2 ).
For this purpose, the proportion of ambiguous, correct and false inferences are measured among 5, 000 pseudo-observed datasets simulated for each of the 6 combinations [demographic models] x [genomic models]. For the Expansion and Constant demographic models, the correct recapture rates of homo and hetero Ne genomic models range from 75% (Expansion + hetero Ne; 24% of ambiguity) to 86% (Constant + homo Ne; 13% of ambiguity). Finally, while recovering the Contraction demographic model is a very robust analysis with 99% of inferences that are both correct and associated with a high posterior probability, it is more complicated to distinguish "Contraction + homo Ne" from "Contraction + hetero Ne". About 41% of the pseudo-observed datasets simulated in the "Contraction + homo Ne" model are correctly captured by the random forest, and only 26% for the "Contraction + hetero Ne" model.
1. 1 is performed here. We evaluated the performance of DILS for 60, 000 pseudo-observed datasets simulated under the "isolation" supermodel (10, 000 for each combination of [SI; AM], [homo-Ne; hetero-Ne] and [homo-N. m; hetero-N. m] for the AM model only) and 80, 000 under the "migration" supermodel (10, 000 for each combination of [IM; SC], [homo-Ne; hetero-Ne] and [homo-N. m; hetero-N. m]). As shown in figure  3 , 95% of the datasets simulated under the supermodel "isolation" with random combinations of parameters from large priors are correctly recaptured by the random forest approach with a high probability (4% ambiguity and 1% error if we apply a posterior probability threshold of 0. 84; table  S1 )). Similarly, 98% of the pseudo observed datasets under the "migration" supermodel are strongly recaptured (with 1% of ambiguity and 1% of error for a threshold of 0.
665). Models with migration are globally more efficiently recaptured by DILS, relying on a lower threshold probability to be robustly supported. The second step of the hierarchical model comparisons is to classify the demographic models described in figure  1-B , within the supermodel that was best supported in the previous step (figure  3-B ). The results of the performance analyses first show that a pseudo-observed dataset simulated under an SI model (homo-Ne and hetero-Ne) is very unlikely to be strongly supported in an SI versus AM comparison. Out of 20, 000 simulations, only 1% are correctly recaptured by DILS (98% ambiguity and 1% error for a threshold of 0. 845). The AM model is more robustly supported than SI (56%), but the 10, 000 inferences made under each of the AM sub-models lead to weak support (43% ambiguity, 1% error for a threshold of 0.
Data On the contrary, the two models making the "migration" supermodel (IM and SC) are more efficiently distinguished by DILS. The 40, 000 pseudo-observed datasets randomly simulated under the IM model are captured at 79% with a high probability in the IM versus SC comparison (20% ambiguity, 1% error for a threshold of 0. 885). Similarly, 70% of the 40, 000 pseudo-observed datasets from the SC model are correctly recaptured by DILS (29% ambiguity, 1% error for a threshold of 0. 915). We then evaluate DILS performance for discriminating among alternative models of genomic distribution for the Ne (figure  3-B ; table  S2 ) and N. m (figure  3-C ). Concerning the effective population size, DILS systematically recaptures the homogeneous model more easily than the heterogeneous model for each of the four demographic models tested.
Detection of barriers to gene flow One additional purpose of DILS is to identify genomic regions which are associated to a local reduction in the introgression rate N. m. This analysis will only be carried out by DILS if the observed dataset is better explained by 1) a demographic model with ongoing migration (IM or SC) and 2) a genomic model with gene flow heterogeneity (hetero-N. m). To achieve this purpose, DILS will infer the parameters under the model that best explains the data. Then, for each gene, DILS performs a comparison between two models that differ only for the parameter N. m: 1) the migration model corresponds to the whole set of parameters estimated under the best supported model; 2) the isolation model corresponds to the previous model whose N. m has been set to zero, because a barrier gene impedes gene flow locally along the chromosome.
Therefore, such a gene should be supported by the isolation model if the barrier effect is strong. This approach therefore seeks to approximate a continuous variable, N. m, by a dichotomous choice of model: region with a local-isolation versus local-migration. In order to evaluate the performance of DILS, the locus-specific model comparison was applied for locus simulated under an IM model with different values of N. m in [0, 1] (figure  4 ). A value of zero means no exchange during the divergence process from one population to another. A value of 1 means that there is one immigrant individual on average every genera-tion. We simulated genes 10, 000 times for different combinations of N. m and T split under an IM model. Then, for each simulated dataset, we applied the locusspecific model comparison to finally record for each locus which model is the best between local-migration and local-isolation.
Parameter estimates In this section, we describe performance tests for estimating the parameters of different demographic models. The same procedure was applied for single and twopopulation models: first, simulating pseudo-observed datasets (10, 000 for the three single-population models, 2, 000 for the 14 two-population models) and then ABC estimation of the parameters to test DILS ability to recapture the parameter values used. We only detail here the results obtained for the demographic parameters, i. e. , those describing the mean effective population size (N e current and N e past ), time of split (T split ), the date for the cessation of gene flow (T AM ), the age of the secondary contact (T SC ) and the migration rates (N. m).
Single-population models The current effective population size is by far the parameter that is most accurately recaptured, especially in a constant and homogeneous model with a meansquared error (MSE) close to zero (MSE≈ 0. 005; figure  5-A ; table  S2 ). The introduction of a recent demographic change reduces the quality of inferences for N e current , more for the expansion model than for the contraction model. The inference of ancestral size conducted for 4 x 10, 000 pseudo-observed datasets shows globally a low error rate on the raw values of N e past with a M SE max ≈ 0. 09 (table  S2 ). Errors depend very closely on the relative values between N e current and N e past (figure  5-B ). Hence, while the estimate of a N e past is reliable for a change in size by a factor of 10, it becomes less accurate as the contrast with N e current is increasingly sharp.
Two-population models To estimate the accuracy of DILS in recapturing model parameters, we followed the same procedure based on the analysis of simulated datasets as in the previous paragraph. Note that the two-population models comprise two additional parameters that affect patterns of divergence: the time of split (T split ) and the migration rate (N. m). The error rate in the estimation of the parameter N e current is of the same order of magnitude as in models with a single population (figure  6-A ; table  S3 ). However, the imprecision increases with ongoing migration and tends to underestimate N e current. Estimates of N e current are thus more accurate for the SI model, than for the AM model, and the worst for IM and/or SC. This negative effect of ongoing migration on the accuracy of parameter estimation is more pronounced for the ancestral population size N e past (figure  6-B ).
Illustration of DILS with RNA-seq data from 28 pairs of Mytilus populations We now illustrate the potential of DILS to contribute to the study of speciation among 8 populations of a complex of four Mytilus mussels species (figure  7-A ;  Bierne et al. , 2003; Popovic et al. , 2019). The relationship between molecular divergence and genetic isolation was established over 28 pairs of Mytilus populations using DILS. The aim was to identify which pairs of populations, characterized by different levels of molecular divergence (net synonymous divergence between 0. 003% and 6. 705%), are inferred to be currently connected by ongoing gene flow (figure  7-B ). This large scale analysis within the same genus was made possible by the use of a large RNA-seq dataset recently published by  Popovic et al.
e. broadcast spawning, high-dispersal larvae, large effective population sizes and living in a highly connected marine environment). DILS offers the possibility for the users to participate to this enterprise, and record on the web-platform where their biological model falls within this global speciation picture. Such a global picture of transition from gene flow to no gene flow is necessary for the central problem of species delineation  (Hey and Pinho, 2012). Although a universal criterion for delineating species seems impossible, as exemplified by the mussel dataset, the idea of defining a grey zone by taxonomic system is promising  (Galtier, 2019). Thus, our collaborative approach option included in DILS will allow in the future to establish a relationship between molecular divergence and genetic isolation for different taxa, i.
, 2008; Cornuet et al. , 2014. DILS also provides values for each locus of: 1) each summary statistic; 2) the approximated recombination rate calculated based on the four-gamete rule  (Galtier et al. , 2017; Hudson and Kaplan, 1985) ; and 3) the posterior probability of being genetically linked to a barrier to gene flow (for two-population models only). These results are outputted as interactive graphics on the web-platform. Our method is implemented in a user-friendly webplatform allowing the configuration of the ABC analysis via a graphical interface, its execution and the visualization of the results. Detailed information for how to use DILS is provided in the manual. The released version of DILS is currently hosted by the French Institute of Bioinformatics (XXX). To ensure full reproducibility and portability on any server, DILS is packaged in a singularity container freely available at https://github.
Summary statistics Since ABC is a category of inferential method based on the comparison between statistics summarizing simulated and observed datasets, we first describe here the statistics computed in our framework. We assume that users are interested in carrying out inferences from multilocus datasets. For single population models, DILS calculates for each locus: i) the pairwise nucleotide diversity (π)  (Tajima, 1983) ; ii) Watterson's θ  (Watterson, 1975)  and iii) Tajima's D  (Tajima, 1989). In addition to these three statistics, the sitefrequency spectrum (SFS;  Fischer, 1930; Wright, 1931; Wright, 1938)  is also used to summarize the data, i. e, the number of single-nucleotide polymorphism (SNP) where the derived allele is present in [2,. , nseq -1] copies in the studied population/species, where nseq represents the number of copies sampled for a given locus.
Simulations In the current version of DILS, all simulations are performed using the msnsam coalescent simulator  (Hudson, 2002; Ross-Ibarra et al. , 2008). Each simulated multilocus dataset takes properties from the observed datasets (same number of genes, lengths and sample size). Since the summary statistics used to perform the ABC inferences are averages and standard deviations measured over all the surveyed genes, then for model comparisons and parameter estimations we randomly subsample 1, 000 genes if more loci are present in the total dataset. The purpose of this subsampling is to avoid unnecessarily long simulation times because the values of statistics for a given locus will not impact the used summary statistics over 1, 000 loci. If an outgroup is specified by the user, then it will be used for each locus (or contig, or gene) to correct its mutation rate µ i to µ.
Model comparisons Here, when used alone, the term model means a given combination between a demographic and a genomic model. All comparisons are performed by using the abcrf function of the eponymous R package  (Pudlo et al. , 2015). The comparison is a two-step process. First, grow the random forest with the abcrf function. This requires one reference table per model for the training. The reference table of each model is produced by 10, 000 multilocus simulations whose parameters correspond to random combinations sampled from priors. They are composed of one row per multilocus simulation and one column for each summary statistic described in section 4. 1. 1. When categories of models are compared following the hierarchical approaches (figures 2 and 3), the reference tables of the different models in the same category are merged together.
Parameter estimates Two strategies are applied simultaneously to estimate the parameters describing the best-supported model among those compared: 1) a joint estimation of the set of parameters using a rejection/regression method  (Csilléry, François, and Blum, 2012). Estimation is based on the 5, 000 multilocus simulations producing the statistics closest to the observed dataset among 1, 000, 000 simulations. We then correct for imperfect matches between observed and retained values of statistics. The parameter values of the selected simulations are weighted by their Euclidean distance and corrected according to a nonlinear regression method using a neural network. 10 trained neural networks with 10 hidden networks are used in the regression. 2) an individual estimation of each parameter by constructing a random forest of 1, 000 trees per parameter  (Raynal et al.
, 2019). The results from both approaches are returned to the user. There is no evidence to further support a method over the other in terms of estimation accuracy. Within the framework of the models currently compared in DILS, both approaches produce similar estimates when tested on pseudo-observed datasets. However, joint parameter estimation has the advantages of including parameter co-variations as well as providing a probability density. This is achieved at a computational cost that is ≈ 100 times greater regarding the number of multilocus simulations, since 10, 000 are required for a parameter estimation using random forest versus 1, 000, 000 when using the rejection/regression algorithm.
Locus-specific model comparison To identify barriers to gene flow among a set of sequenced DNA fragments (genes for instance), we adopt the same procedure as in Ciona intestinalis  (Roux et al. , 2013)  and Mytilus  (Roux et al. , 2014)  but by replacing the neural network with a random forest to divide the computational cost by 100. This step is performed by DILS only if 1) observed data better fits models with ongoing migration (IM or SC; figure  1 ) and 2) genomic models of N. m. variation explain the data better than homogeneous models. We first estimate the parameters of the best model from the multilocus dataset. Based on this estimation, two models are compared at each locus: 1) local-migration: the multilocus estimated model with the non-zero migration rate estimated over the whole genome.
Pseudo-observed datasets In this study we distinguish two types of simulations. Simulations carried out to build reference tables used to train a random forest, or from which a small proportion will be sub-sampled in a rejection/regression algorithm based on the Euclidean distance with the observed data. Then a second type of simulations produces pseudo-observed datasets. These are not used for training, but to evaluate the inferential power of the ABC approach, and test whether it can recapture the parameters used to simulate the pseudo-observed datasets. To assess the reliability of model comparisons ( θ i -θ i ) 2 , where θ i and θ i represent the estimated and the true parameter values respectively.
For each model, 10, 000 sets of pseudo-observed data were analysed. These datasets were simulated by taking random combinations of parameters from large prior distributions. The table reports for each model comparison the proportions among these simulations that lead to correct, ambiguous or wrong inferences according to a threshold set to keep the rate of wrong inferences below 1%. Estimation errors are calculated on N = 2, 000 simulated datasets for each model, by using random combination of parameter values. The reported values are measured as follows 1 N * variance(θ i ).
simulations to train the random-forest: 10 • Data cleaning: forall genes i making the dataset do. discard from the alignment of gene i the individuals with too many Ns;. discard gene i if there are not enough retained individuals;. discard gene i if it doesn't contain enough positions without an aligned null allele carried out to build reference tables used to train a random forest, or from which a small proportion will be sub-sampled in a rejection/regression algorithm based on the Euclidean distance with the observed data. Then a second type of simulations produces pseudo-observed datasetitN; end • Reference , 000 multilocus datasets under each combination of [demographic models] x [genomic models]; • Model comparisons: Random Forest (RF) comparisons of: step 1. Expansion [homo + hetero] versus Constant [homo + hetero] versus Contraction [homo + hetero]; step 2.
: A single fasta containing all genes sequenced in all individuals sampled in the two studied populations Result: Posterior probabilities for 1) ongoing hetero-Ne IM + hetero-Ne SC]; step 4. if migration then [homo-N. m IM + homo-N. m SC] versus [hetero-N. m IM + hetero-N. m SC]; Algorithm 2: Two-population hierarchical model comparisons migration, 2) [SI, AM] (in case of current isolation) or [IM, SC] (in case of ongoing migration), 3) Ne and N. m (in case of ongoing migration) • data cleaning: forall genes i do forall population/species j do. discard from the alignment of gene i the individuals with too many Ns;. discard gene i if there are not enough retained individuals in population j;. discard gene i if it doesn't contain enough positions without an aligned null allele N; end end • Reference simulations to train the random-forest: 20, 000 multilocus datasets under each combination of [demographic models] x [genomic models]; • Model comparisons:; Random Forest (RF) comparisons of:; step 1.
Supplementary Table 1: Performance of DILS model comparisons For each model, 10, 000 sets of pseudo-observed data were analysed. These datasets were simulated by taking random combinations of parameters from large prior distributions. The table reports for each model comparison the proportions among these simulations that lead to correct, ambiguous or wrong inferences according to a threshold set to keep the rate of wrong inferences below 1%. Estimation errors are calculated on N = 2, 000 simulated datasets for each model, by using random combination of parameter values. The reported values are measured as follows 1 N * variance(θ i ) comparison target correct ambiguous wrong threshold Single-population models Expansion versus Constant versus Contraction Expansion 0. 8627 0. 1275 0. 0098 0.
Several conflicts also arise on the growth of the stellar masses of the BCGs:  Collins & Mann (1998) ;  Collins et al. (2009) ;  Stott et al. (2010)  found little to no evolution. On the other hand, other studies found a strong evolution in the stellar masses of BCGs since redshift z = 2  (Aragon-Salamanca et al. 1998; Lidman et al. 2012; Lin et al. 2013; Bellstedt et al. 2016; Zhang et al. 2016 ). In the present paper, we will try to characterize how the properties of BCGs have evolved since z = 1. 80, based on HST data to have the best possible spatial resolution, which is particularly necessary at high redshift. When dealing with a large amount of data, identifying individually the BCG of a cluster to build a sample can be a long task to do. This is why we present here a method based on several photometric properties of the BCGs, that will allow to detect BCGs automatically.