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Assumptions for the space-for-time substitutionThe main methodological concept in this study is the notion of a space-for-time substitution. Such approach has previously been used in various studies to estimate the effect of land cover change on temperature20,22 or on the surface energy balance22,72. The overarching assumption behind the method is that the difference in properties of neighbouring patches of land can serve as a surrogate for changes in time. While this main assumption largely holds for land surface properties, such as skin temperature, it requires a more detailed articulation into several underlying assumptions in order to apply the approach to atmospheric properties such as cloud cover. This is because atmospheric properties are prone to lateral movements, partially decoupling them from the land cover directly below them, and thus adding considerable complexity to the analysis.The first underlying assumption is that the method will be mostly sensitive to low-level convective clouds generated in the boundary layer (i.e. cumulus clouds). These are typically formed under stable conditions of high pressure and low wind, and are thus expected to have a higher spatial correlation with the underlying landscape elements. Other types of low-level clouds, such as stratus clouds, are typically much more uniformly spread across the landscape, which would result in no difference in CFrC when comparing two distinct and neighbouring vegetation classes. For medium- or high-level clouds, their position will be determined mostly by the state of the atmosphere rather than by the land surface, resulting in a very low correlation with vegetation spatial patterns. The space-for-time substitution approach would thus similarly result in white noise.The second assumption is that the boundary layer cumulus clouds will see very limited lateral advection between the moment of their formation and the satellite observation. Cumulus clouds over land show a very stable climatology where the peak formation is largely confined to the early afternoon (around 14:00), timing which remains very stable across space and season43. Therefore this assumption should largely hold if the observations are made at this time.The third assumption is that if we consider topographically flat terrain that is away from a coastline, general weather conditions are essentially the same at a local scale (i.e. a region of radius circa 25 km around a given point). Within such an area, we then assume that variations in low cloud cover are mostly determined by local differences in surface properties, themselves determined by the type and condition of the present land cover.Preparation of input datasetsThis study requires gridded geospatial datasets for two variables: cloud fractional cover and land fractional cover. Both datasets used here have been prepared in the frame of the European Space Agency’s (ESA) Climate Change Initiative (CCI)73.The Cloud CCI55 provides a series of cloud properties derived from distinct satellite Earth observation platforms in a harmonized way. Here we use their cloud fractional cover variable (henceforth CFrC), which describes the fraction of a 0.05° × 0.05° pixel covered by clouds based on observations made at a finer spatial resolution at the given time of the satellite overpass. We chose to use Cloud CCI dataset based on the MODIS instrument on-board of the Aqua platform for two reasons. First, the timing of overpass of the Aqua platform (circa 13:30 local time at the Equator) coincides very well with the timing of peak of cumulus cloud formation43, thus greatly limiting the extent of possible cloud advection between the moment of cloud formation and observation. Second, native spatial resolution of the MODIS instrument is superior to the alternative (AVHRR), and should result in a better sensitivity to the presence of small cumulus clouds. More specifically, out of the 5 spectral bands of the MODIS instrument used by the Cloud CCI to characterize cloud properties (bands 1, 2, 20, 31 and 32), two of them (bands 1 and 2) have a native spatial resolution of 250 m. While these are aggregated to 1 km (the spatial resolution of the other MODIS bands) prior to their ingestion in the cloud retrieval algorithm, their finer native granularity and quality should prove to be an asset for small cumulus cloud detection. The CCI MODIS-AQUA CFrC data is available for the period 2004–2014. The values are first averaged from daily to monthly scale, and then a single monthly value is calculated for every pixel over the period 2004–2014. The results are 12 layers each representing the multi-annual average CFrC for a given month.The second type of data needed for the analysis is the fraction of the 0.05° × 0.05° pixels that are covered by distinct vegetation types (essentially trees and grasses) and by other land cover classes (urban areas, bare soil, etc.). These are derived from the Land Cover CCI54, a set of consistent annual maps describing, with a spatial resolution of 300 m, how the terrestrial surface is covered based on The United Nations Land Cover Classification Scheme74. This information is aggregated both spatially and thematically using a specifically designed framework75 to produce maps of general land fractional cover with a spatial resolution of 0.05° to match that of the cloud fractional cover data. The procedure is very similar to that done in a previous study22. For the context of this study, which has a focus on afforestation, the interest lies on transitions among three main vegetated classes, namely: deciduous forest, evergreen forests and herbaceous vegetation. Herbaceous vegetation is composed of both grasses and crops, irrespective of management practice such as irrigation. While irrigation has a clear biophysical effect of its own60, we deemed the land cover product was not consistent enough for this specific class. For reasons that are explained in the respective methodological section below, the full compositional description of the landscape is necessary (i.e. beyond the classes of interest), and therefore land cover fractions of the following classes are also generated: shrublands, savannas, wetlands, water, bare or sparsely vegetated, snow or ice, and urban.Retrieving potential cloud fractional cover changeUnder the above-mentioned assumptions, we apply a space-for-time substitution algorithm developed in a previous study22 to the cloud fractional cover and land fractional cover datasets. We summarize the main aspects of the methodology, along with the few necessary adaptations, but the reader requiring more detail is redirected to the original papers22,76. The approach consists in applying an un-mixing operation over a spatially moving window containing n pixels. Over each window we apply a linear regression based on a matrix X containing the explanatory variables, in which each column of X represents the fractional cover of a given land cover type for each of the n pixels. The response variable is a vector y containing the n values of CFrC for the n pixels, while the vector β represents the regression coefficients:$${bf{y}}={bf{X}}beta$$
(1)
This is equivalent to solving the following system of equations:$$left{begin{array}{ll}{y}_{1}=&{beta }_{1}{x}_{11}+{beta }_{2}{x}_{12}+…+{beta }_{m}{x}_{1m}\ {y}_{2}=&{beta }_{1}{x}_{21}+{beta }_{2}{x}_{22}+…+{beta }_{m}{x}_{2m}\ vdots &\ {y}_{n}=&{beta }_{1}{x}_{n1}+{beta }_{2}{x}_{n2}+…+{beta }_{m}{x}_{nm}end{array}right.$$
(2)
in which the digits of the subscript of x, e.g. xij, represent the land cover fraction j in pixel i, for the n pixels in the moving window and the m classes that are considered. Once identified, we can use the β coefficients to predict the local y value corresponding to a given composition x, including that composed of a single land cover j by setting xj = 1 and all other x values to zero. However, applying a regression directly on X carries a risk due to the compositional nature of the data (i.e. the sum of each row adds up to one), as the analysis of any given subset of compositional components can lead to very different patterns, results and conclusions77. To avoid this, we reduce the dimensionality of X through singular value decomposition (SVD) after removing the mean of each column:$$({bf{X}}-{bf{M}})={bf{U}}{bf{D}}{{bf{V}}}^{t}$$
(3)
where M is the appropriate matrix of column means, U and V are the matrices containing, respectively, the left-hand and right-hand singular vectors, and D is a diagonal matrix containing the singular values representing the standard deviations of the ensuing dimensions. The squared values of D represent the variance explained by each dimension, and can thus serve to define z, a reduced subset of dimensions that conserves 100% of the original matrix’s variation. The corresponding z right-hand singular vectors, Vz, can then be used to find the appropriately transformed predictor matrix of reduced dimension Z as follows:$${bf{Z}}=({bf{X}}-{bf{M}}){{bf{V}}}_{z}$$
(4)
which can now be regressed onto the CFrC y:$$y={bf{Z}}{beta }_{z}+varepsilon$$
(5)
where Z has been augmented with a leading column of 1s to accommodate an intercept term in the regression. We then use the standard method to obtain an estimate of βz:$${beta }_{z}={left({{bf{Z}}}^{t}{bf{Z}}right)}^{-1}{{bf{Z}}}^{t}y$$
(6)
However, because of the matrix transformation from X to Z, the regression coefficients βz do not provide direct information on the relationship between land fractional cover and cloud fractional cover (as in a normal regression). To identify the z values associated with a particular vegetation or land cover type (within the local analysis defined by the moving window), we define a ‘dummy pixel’ whose composition contains only a single class, with all other classes in its composition set to zero. This pixel’s composition is then transformed, and its y value predicted. This is the y associated with that vegetation type. To generalize this for all compositional components of interest, we define a matrix P with as many rows as these compositional components that we wish to predict. P is centred on the same column means as above (M, specific to each local analysis), and then multiplied by the correct number of transposed right-hand singular vectors (Vz, again, specific to each local analysis).$${{bf{Z}}}_{{rm{p}}}=({bf{P}}-{bf{M}}){{bf{V}}}_{z}$$
(7)
Predicted yp values for each vegetation or land cover type (identified by predicting the appropriately transformed ‘dummy pixels’) are then calculated as:$${y}_{{rm{p}}}={{bf{Z}}}_{{rm{p}}}{beta }_{z}$$
(8)
The expected change in variable y associated with a transition from vegetation type A (e.g. herbaceous vegetation) to vegetation type B (e.g. deciduous forest) at the centre of the local window is then the difference between the yp predicted for each ‘pure’ vegetation type:$${{Delta }}{y}_{{rm{A}}to {rm{B}}}={y}_{rm{B}}-{y}_{rm{A}}$$
(9)
The uncertainty in the estimation of ΔyA→B can be expressed as a standard deviation using the following expression:$${sigma }_{{rm{A}}to {rm{B}}}=sqrt{{sigma }_{rm{A}}^{2}+{sigma }_{rm{B}}^{2}-2{sigma }_{rm{AB}}}$$
(10)
where ({sigma }_{rm{A}}^{2}) and ({sigma }_{rm{B}}^{2}) are the variances in the estimates of yA and yB, and σAB is their covariance. These variances and covariances are in turn obtained from the covariance matrix, defined from the regression as:$${mathbf{Sigma }}={{bf{Z}}}_{{rm{p}}}{rm{Var}}[beta ]{{bf{Z}}}_{{rm{p}}}^{t}$$
(11)
The diagonal terms in Σ are the variances of individual predictions of (individual) classes. The off-diagonal parts of Σ hold the covariances between these predictions. As a reminder, the uncertainty σA→B calculated in this way is related to the methodological uncertainty and does not include the uncertainty in the input variables of land cover or cloud fractional cover.In the default set-up for this study, we concentrate on two transitions: herbaceous vegetation to deciduous forest and herbaceous vegetation to evergreen forest. These are calculated using a spatial window of 7 × 7 pixels, each pixel being of 0.05°, resulting in a squared spatial window of circa 35 km in size. To ensure there are enough values to do the un-mixing over each window, we established that there must be a minimum of 60% of valid values in each window, and that at least 40% must have distinct compositions. The operation is applied to all 12 monthly layers of CFrC, resulting in 12 maps of Δy with a 0.05° spatial resolution for each of the two vegetation cover transitions.Post-processingA series of post-processing steps are required to ensure the results of the Δy maps can be used to evaluate the effect of land on cloud cover. The first step is to mask all pixels in which there is insufficient co-occurrence of the two vegetation classes involved in the transition. This co-occurrence is quantified by an index of vegetation co-occurrence76, Ic, calculated from the land fractional cover layers using the same spatial moving window of 7 × 7 pixels as used before. This index is calculated pairwise, i.e. for 2 vegetation classes of interest A and B, using two vectors pA and pB, describing the presence of these two vegetation classes in each of the i pixels in the moving window. It also requires the definition of another i point evenly distributed along a hypothetical line B = 1 − A in the two-dimensional space describing the presences of vegetation class A and vegetation class B. These points, whose position in the 2-D space are labelled qA and qB, represent an ideal situation of maximum co-occurrence that serves as a reference to establish the index. The formal definition of the index is thus:$${I}_{{rm{c}}}=1-frac{{sum }_{i}min {sqrt{{left({q}_{A}-{p}_{A}right)}^{2}+{left({q}_{B}-{p}_{B}right)}^{2}}}}{{sum }_{i}sqrt{{q}_{A}^{2}+{q}_{B}^{2}}}$$
(12)
The minimum operator in the numerator selects the smallest distance that a given point p can have to any of the q points. The sum relates to the sum of this distance for all i points in the spatial moving window. The denominator characterizes the maximum distance that the point p can encounter. Ic will range from 0 to 1 corresponding to a gradient of ‘no presence of either class’ to ‘full and evenly balanced presence of both classes’. As in76, we retain only pixels with Ic ≥ 0.5 where we consider that there is sufficient information at local scale concerning both vegetation types to derive meaningful information about the target land cover transition.The second step is to remove the potential orographical effects, which can be especially problematic given that forests are more likely to be located over mountainous areas due to human action56. Here we mask the areas where considerable topographical variation occurs within the 7 × 7 pixel moving window of interest using the same implementation described in76. This involves using 3 different indicators, v1, v2 and v3, calculated over the moving window based on μh and σh, which are, respectively, the mean and the standard deviation of elevation over each grid cell of the input cloud dataset. These are defined as follows:$${v}_{1}=frac{1}{n}mathop{sum }limits_{i=1}^{n}{sigma }_{h,i}$$
(13)
$${v}_{2}=| {mu }_{h}-frac{1}{n}mathop{sum }limits_{i=1}^{n}{mu }_{h,i}|$$
(14)
$${v}_{3}=| {sigma }_{h}-{v}_{1}|$$
(15)
For an interpretation of these metrics, readers are invited to read76. These three indicators are combined together in a single layer depicting all pixels satisfying all of the following conditions: v1  More

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Study systemWe studied a D. magna population (OHZ) from a small, shallow man-made pond in Oud-Heverlee, Belgium (50°50´ N– 4°39′ E). This pond was constructed for pisciculture in 1970 and has a detailed record of fish-stocking densities for 16 years (Fig. 1a). Dormant stages of D. magna were sampled from three depths of a sediment core, corresponding to three time periods that varied in the level of fish-predation pressure: (1) the pre-fish period (1970–1972), during which no fish were stocked in the pond; (2) the high-fish period (1976–1979), a period with high fish-predation pressure due to intensive fish stocking; (3) the reduced-fish period (1988–1990), with relaxed fish predation pressure due to a reduction in fish stocking (Fig. 1a)9,10,37. This archive was previously sampled using a standard Plexiglas corer with inner diameter of 5.2 cm10. Dating of the sedimentary archive could not be completed with traditional radioisotope analysis, but was based on dry weight and organic matter content under the assumption of a constant sedimentation rate since the establishment of the pond10. The cores contained the full sediment archive, including the transition to the mineral sediment. Sediment cores were aligned using the patterns of Daphnia dormant egg abundance and changes in size of the dormant egg cases as described in Cousyn et al.10. The dormant stages were hatched in the laboratory and taking advantage of the parthenogenetic reproduction mode of D. magna as long as conditions are favorable, we started up clonal lines. The resulting clonal lines are each genetically unique, as dormant stages in D. magna are the result of sexual reproduction. Our approach was thus to sequence the full genome of a random sample of 12 individuals from each of three depth layers of a sediment core representing populations that occurred in three periods with distinct fish-predation pressure.In addition to the reconstruction of temporal genome dynamics, we used twelve regional populations of D. magna distributed along strong environmental gradients of fish-predation pressure in the region. Six populations (DANA, U2, TER1, MO, KNO15, and TER2) were sampled from fishless ponds, while six populations (ZW4, LRV, ZW3, OHN, OM2, and OM3) were sampled from ponds that harbored fish (Supplementary Table 1). These genotypes were hatched from dormant eggs isolated from the upper 2–3 cm of sediment of the study ponds.Whole-genome sequencingTo reconstruct the genomic history, we resequenced the 36 D. magna lines resurrected from the OHZ pond and validated it with additional whole-genome resequencing of 144 D. magna genotypes spread across twelve spatial populations along a fish gradient in the region (Supplementary Table 1). Twelve individuals from each temporal subpopulation of the sediment core and 8–17 individuals per population in the spatial survey were used for genomic DNA extraction using the Nucleo Spin Tissue extraction kit (Macherey-Nagel, Germany), with overnight incubation at 56 °C and following the manufacturer’s instructions. We quantified DNA using PicoGreen reagent (Life Technologies) on a DTX 880 spectrofluorometer (Beckman Coulter). For each sample, 1 µg of gDNA was normalized in a final volume of 50 µl of Tris Buffer, pH 8.5, and sheared using an E220 Focused Ultrasonicator in conjunction with a microTube plate (Covaris) in accordance with the manufacturer’s recommendations. Sheared genomic DNA was assayed on a 2200 TapeStation (Agilent) with High Sensitivity DNA Screentapes to determine the distribution of sheared fragments. The sheared genomic DNA was then prepared into Illumina compatible DNA Sequencing (DNASeq) 100-bp paired-end libraries utilizing NextFlex chemistry (Bio Scientific). Following library construction, libraries were assayed on a 2200 TapeStation (Agilent) with High Sensitivity DNA Screentapes to determine the final library size. Libraries were quantified using the Illumina Library Quantification Kit (Kapa Biosystems) and normalized to an average concentration of 2 nM prior to pooling. Genomic DNA quantification and normalization, shearing setup, library construction, library quantification, library normalization, and library pooling were performed utilizing a Biomek FXP dual-hybrid automated liquid handler (Beckman Coulter). C-Bot (TruSeq PE Cluster Kit v3, Illumina) was used for cluster generation and the Illumina HiSeq2500 platform (TruSeq SBS Kit v3 reagent kit) for paired-end sequencing with 100-bp read length following the manufacturer’s instructions.Short-read mapping and variant callingThe paired end reads (100 × 2) of each individual were first analyzed using FASTQC (http://www.bioinformatics.babraham.ac.uk/projects/fastqc/) for quality checks. Subsequently, low-quality base trimming and adapter cleaning was performed using the Trimmomatic software38. Here, parameter values to remove adapter sequences were chosen for seedMismatches (2), palindromeClipThreshold (30), and simpleClipThreshold (10). The minimum phred quality required to keep a base was set to 28, and the minimum read length to 50 bp. Furthermore, the cleaned reads were mapped to the D. magna genome version 2.439 using Bowtie240 software with very-sensitive parameter settings (-D 20 -R 3 -N 0 -L 20 -i S,1,0.50) and insert size between 200 and 700 bp. The mapped reads were then marked for duplicates using the MarkDuplicates feature of Picard tools (http://broadinstitute.github.io/picard/) to avoid PCR duplicates. The resulting sorted BAM files were then used for variant calling using FreeBayes41. FreeBayes41 is a haplotype-based variant caller that calls SNPs, indel, and complex variants. Minimum base quality was set to 30 with minimum coverage of four reads. We obtained more than 3 × 106 raw variants (3 441 615) for the OHZ temporal subpopulations and 6 × 106 raw variants for the spatial populations.Only biallelic SNPs supported by at least four reads and sequenced in at least 90% of individuals were retained after filtering. The draft genome of Daphnia magna consists of thousands of scaffolds and contigs. To remove repetitive and paralogous regions in the genome, we used the 293 scaffolds greater than 5 kb that altogether represent 84% of the sequenced genome. Further SNP filtering was performed based on D. magna gene models, such that each polymorphic SNP contained within genic regions could be unambiguously assigned to only one gene locus, thereby removing uncertainties attributed to sequence reads mapping to paralogs and to overlapping genes coding on alternative strands of DNA. Finally, SNPs at frequencies below 5% (pooled subpopulations) were removed retaining a total of 724,321 SNPs (mean coverage 20 reads per SNP/individual; 99.6% SNPs with missing values less than 5%) for the temporal analysis of the OHZ population and 748,511 SNPs for the spatial populations. These SNPs were used for downstream analyses.Population differentiationWe calculated both genome-wide and locus-specific levels of genetic differentiation (FST; Weir & Cockerham 198442) using the diffCalc function of the diveRsity43 package in R44. These calculations were performed for each pair of temporal subpopulations (i.e., pairwise FST) in the temporal setting (OHZ) and for six random pairs of nonfish and fish populations in the spatial survey.To calculate allele frequencies in the temporal analysis, we used vcfglxgt function of vcflib (https://github.com/vcflib/vcflib) to set genotypes that are most likely to be true based on maximum genotype likelihood. We then identified the significant differences in allele frequencies between temporal subpopulations over time (P value < 0.01) using a modified chi-square test developed by RS Waples (Waples 1989)11 and implemented in the TAFT software45 (hereafter referred to as Waples test) that accounts for effective population size (Ne), yielding 30,669 significant SNPs (4.23% of total OHZ SNPs) by comparing the prefish and high-fish temporal subpopulation and yielding 11,257 SNPs (1.55% of total OHZ SNPs) for the high-fish and reduced-fish temporal subpopulation comparison; 1771 SNPs showed significant allele-frequency changes in both transitions, most of them also showing a significant reversal in the second transition. To determine whether the observed number of SNPs that showed a significant reversal in allele frequencies is higher than expected by chance, we estimated the null distribution by randomly permuting the temporal subpopulation labels (i.e., prefish, high fish, and reduced fish) and alleles per locus (724,321 SNPs), and recalculating the number of reversals based on Buffalo and Coop 202012.Estimation of effective population size (N e)Effective population sizes (Ne) were calculated from θ = 4Neµ, across the whole genome and with a mutation rate per generation of 4 × 10−946 and a generation time of one year (Daphnia undergoes 10–15 asexual generations and one sexual generation per year), where Ɵ is Watterson’s diversity index and µ is mutation rate. Watterson Ɵ was calculated using the folded SFS option in ANGSD software47 and found to be stable, i.e., near 0.03 across the three subpopulations (prefish, high fish, and reduced fish). The calculated Ne was found to be ~1.66 million in the prefish temporal subpopulation and ~1.72 million for the high-fish and reduced-fish temporal subpopulations. Similarly, for spatial populations, the value ranges from ~1.06 to 1.45 million (Supplementary Table 2).Detecting genomic islands of differentiationFor each scaffold, and for each pairwise comparison among temporal subpopulations and six independent fish and no-fish replicate pairs in the spatial survey, a hidden Markov model (HMM) was used to distinguish genomic regions of high, moderate, or low differentiation among (sub)populations. We used a similar approach as used earlier by Soria-Carrasco et al. (2014)48. In brief, for each of these three levels of genetic differentiation (i.e., the hidden states), a Gaussian distribution of log10(FST + 1) was assumed with the mean and variance initialized as those of the log10(FST + 1) values within each respective level. We then used the Baum–Welch algorithm49 to refine the Gaussian model for each state and the transition matrix among the states. Direct transition from the low to the high state was not allowed. Hidden states were then estimated from the data and we estimated the parameters by the Viterbi algorithm using the R package HiddenMarkov50. A high differentiating island between genomes is defined to contain at least three consecutive SNPs categorized as high-state SNPs by HMM, yielding 6111 and 2879 islands of genomic differentiation between the prefish vs high-fish (mean length: 2428 bp) and the high-fish vs reduced-fish comparison (mean length: 1713 bp), respectively. Similarly, for six independent spatial fish vs no-fish comparisons, the number of islands of differentiation ranged between 4136 and 7493 (with range of mean length 1879–3290 bp), depending upon the comparison (Supplementary Table 3).Functional annotation and enrichment analysisWe investigated the function of the outlier SNPs (P values smaller than 0.01) in the comparison among temporal subpopulations (prefish vs high fish and high fish vs reduced fish) and in HMM-based high-differentiation islands in spatial comparisons. Transcriptome-based functional annotation was performed using the Daphnia magna genome version 2.439. The pathway enrichment analysis was performed using the orthologous genes of D. magna in the D. pulex genome51 based on OrthoDB gene families52 and the KEGG pathway database53. Out of ~29,000 annotated genes of D. magna, 17,400 genes have 17,832 orthologs in D. pulex. However, due to the fragmented status of the D. magna genome assembly, manual curation for high-quality gene models resulted in a total of 12,264 D. magna genes used in our study, of which 2402 genes are annotated to KEGG pathways. Ortholog mapping is not unique. A given gene from the source species, here D. magna, can map to a single, multiple, or no ortholog in the target species, here D. pulex. This can bias statistical tests when referencing to D. pulex genomics resources. We used the number of nonunique mappings for each D. magna gene on the KEGG pathways of D. pulex to weight-adjust the confusion matrix for Fisher’s exact test to obtain the correct P values. Significant pathways are defined as those with FDR corrected (Benjamini–Hochberg method) P values smaller than 0.05. The data analysis was performed using Python packages (NumPy v1.17.454, SciPy v1.4.155, statsmodels v0.11.1, and plotly v4.8.1).Rarefaction analysisRarefaction analyses were used to determine the rate at which outlier SNPs accumulate in the temporal subpopulation or in the set of regional populations as a function of sample size, i.e., the number of individuals sampled from a given population or group of populations. These analyses were performed separately for the prefish as well as for the reduced-fish temporal subpopulation, in both cases to assess the number of individuals needed to accumulate a given percentage of the SNPs that were suggested to be important for the evolution in response to fish through an outlier analysis of the prefish to high-fish transition. With the rarefaction analysis on the prefish population, we estimate the minimum number of individuals that are needed to reach sufficient genetic variation to enable the observed level of adaptation to fish in this population. The rarefaction analysis on the reduced-fish temporal subpopulation was to assess whether the level of genetic polymorphism declined or increased following the period of strong selection by fish. We thus aimed to evaluate how much evolutionary potential a certain number of individuals from the oldest (i.e., before the introduction of fish) as well as the youngest temporal subpopulation (i.e., after a wave of selection) represent. In the first set of analyses, we used the 1109 SNPs belonging to the divergent SNPs that showed significant changes in allele frequencies in the prefish to high-fish transition and also a significant reversal during the high-fish to reduced-fish and were potentially under positive selection (i.e. excluding hitchhiked SNPs) in the OHZ population. This group of SNPs represent polymorphisms that are presumably adaptive or at least contribute to adaptive allelic variants and hence contribute to the adaptive potential of the temporal subpopulations. The analyses were performed by rarefying the genotype matrix of all 12 individuals from either the prefish or the reduced-fish population to all possible (i.e., 4095) subsets of samples of 1–12 genotypes. For each of these subsets we then calculated the average proportion of polymorphic SNPs. These values were plotted against sample size to generate rarefaction curves. Similarly, rarefaction analyses were performed for the 1003 SNPs belonging to the outlier SNPs that were potentially under positive selection (i.e., excluding hitchhiked SNPs) in the OHZ population and that were also present as SNPs in the full spatial dataset (90.4% of the total number of 1109 SNPs). In this case, rarefaction curves were plotted by randomly resampling (1000 times) 1–30 individuals from the total of the 111 individuals of the Leuven regional populations in the spatial data set (i.e., the cluster of populations that represents a sample of nearby populations (within a radius of 10 km) to the focal OHZ population).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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