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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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These authors contributed equally: Claire R. Peart, Sergio Tusso, Saurabh D. Pophaly.Science of Life Laboratories and Department of Evolutionary Biology, Uppsala University, Uppsala, SwedenClaire R. Peart, Sergio Tusso, Chi-Chih Wu, Aaron B. A. Shafer & Jochen B. W. WolfDivision of Evolutionary Biology, Faculty of Biology, LMU Munich, Planegg-Martinsried, GermanyClaire R. Peart, Sergio Tusso, Saurabh D. Pophaly, Fidel Botero-Castro & Jochen B. W. WolfMax Planck Institute for Plant Breeding Research, Cologne, GermanySaurabh D. PophalyLaboratorio de Ecología de Pinnípedos ‘Burney J. Le Boeuf’, Centro Interdisciplinario de Ciencias Marinas, Instituto Politécnico Nacional, Baja California Sur, MéxicoDavid Aurioles-GamboaDepartment of Natural Sciences, University of Houston-Downtown, Houston, TX, USAAmy B. BairdDepartment of Ecology and Conservation Biology, Texas A&M University, College Station, TX, USAJohn W. BickhamBritish Antarctic Survey, Natural Environment Research Council, Cambridge, UKJaume Forcada & Joseph I. HoffmanElephant Seal Research Group, Sea Lion Island, Falkland IslandsFilippo Galimberti & Simona SanvitoDepartment of Anatomy, University of Otago, Dunedin, New ZealandNeil J. GemmellDepartment of Animal Behaviour, Bielefeld University, Bielefeld, GermanyJoseph I. HoffmanNorwegian Polar Institute, Fram Centre, Tromsø, NorwayKit M. Kovacs & Christian LydersenDepartment of Environmental and Biological Sciences, University of Eastern Finland, Joensuu, FinlandMervi Kunnasranta & Tommi NymanNatural Resources Institute Finland (Luke), Joensuu, FinlandMervi KunnasrantaDepartment of Ecosystems in the Barents Region, Norwegian Institute of Bioeconomy Research, Svanhovd Research Station, Svanvik, NorwayTommi NymanLaboratory of Mammal Ecology, Universidade do Vale do Rio dos Sinos, São Leopoldo, BrazilLarissa Rosa de OliveiraNational Oceanic and Atmospheric Administration, National Marine Fisheries Service, Alaska Fisheries Science Center, Marine Mammal Laboratory, Seattle, WA, USAAnthony J. OrrThe Saimaa Ringed Seal Genome Project, Institute of Biotechnology, University of Helsinki, Helsinki, FinlandMia ValtonenForensic Science & Environmental Life Sciences, Trent University, Peterborough, Ontario, CanadaAaron B. A. Shafer More

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Case dataMedically attended influenza B cases in New Zealand were identified from samples taken from patients with influenza-like illness (ILI) attended by a network of general practitioners recruited for surveillance (2430 cases with an identified influenza B lineage) and from non-surveillance hospital samples (1606 cases with an identified lineage) analyzed by regional diagnostic laboratories and by the World Health Organization (WHO) National Influenza Centre at the Institute for Environmental Science and Research (ESR). Briefly, general practice surveillance operates from May to September, with participating practices collecting nasopharyngeal or throat swabs from the first ILI patient examined on each Monday, Tuesday, and Wednesday. ILI is defined as an “acute respiratory tract infection characterized by an abrupt onset of at least two of the following: fever, chills, headache, and myalgia”38. A subset of the New Zealand data (cases from 2002 to 2013) was previously compiled by Vijaykrishna et al.28 along with cases from Australia reported to the WHO Collaborating Centre for Reference and Research on Influenza in Melbourne.Statistical model of influenza B susceptibility based on infection historyFor lineage V (B/Victoria), we modeled the number of cases in people born in birth year b observed in season y as a multinomial draw with probabilities given by:$${theta }_{V}(b,y)=D(b,y)beta (b,y){Z}_{V}(b,y)rho (b,y)$$
(1)
with an analogous equation defining the multinomial distribution θY(b, y) for lineage Y (B/Yamagata). D(b, y) is the fraction of the population that was born in year b as of observation season y. Z(b, y) is the susceptibility to lineage V during season y of a person born in year b relative to that of an unexposed person. β(b, y) is a baseline probability of infection with influenza B that captures differences in transmission associated with age (thus depending on b and y) and is equal to β1 if people born in year b are in preschool during season y (0–5 years old), β2 if they are school-age children or teenagers (6–17 years old), or β3 if they are 18 or older. ρ(b,y) is an age-specific factor equal to a parameter ρ if people are  0. Letting α1 and α2 be the instantaneous attack rates for preschoolers and school-age children:$${P}_{mathrm{N}}(A)=left{begin{array}{ll}{e}^{-{alpha }_{1}(A-m)}frac{(1-{e}^{-{alpha }_{1}})}{{alpha }_{1}},hfill&,{text{if}},A; le; {A}_{mathrm{s}}\ {e}^{-{alpha }_{1}({A}_{mathrm{s}}-m)}{e}^{-{alpha }_{2}(A-{A}_{mathrm{s}})}frac{(1-{e}^{-{alpha }_{2}})}{{alpha }_{2}},&,{text{if}},A; > ; {A}_{mathrm{s}}end{array}right.$$
(26)
where As is the age at which children start going to school (4 years old in the Netherlands69). It is noteworthy that for school-age children (the equation for A  > As on the bottom), the correction term for uncertainty in sampling is not necessary for the time spent in preschool (assumed to be exactly As years), only for the time after preschool (A − As).Handling cases with missing lineage informationWe assumed cases with missing lineage information in 2002 (n = 61), 2011 (n = 312), and 2019 (n = 206) belonged to B/Victoria, as 99% or more of identified cases in those seasons were B/Victoria (86/87 cases in 2002, 276/280 cases in 2011, and 552/552 cases in 2019) as were 94%, 92%, and 92%, respectively, of isolates from sequence databases (for Australia and New Zealand combined). We assumed cases with missing lineage information belonged to B/Yamagata in 2013 (n = 37), 2014 (n = 77), and 2017 (n = 87), when the majority of identified cases were B/Yamagata (268/272, 131/138, and 473/489, respectively), as were 99%, 94%, and 84%, respectively, of isolates in sequence databases. Unidentified cases in other seasons were disregarded, because both lineages were present at higher frequencies among identified cases. Removing unidentified cases altogether in all seasons led to similar parameter estimates.Sequence divergence analysisTo estimate the amount of evolution within and between lineages, we analyzed all complete HA and NA sequences from human influenza B isolates available on GISAID in July 2019. The set of isolates used in this analysis differs from the set used to estimate lineage frequencies, because we required isolates to have complete sequences (although not all sequences listed as complete on GISAID were in fact complete). Two isolates collected in 2000 (B/Hong Kong/548/2000 and B/Victoria/504/2000) were deposited as B/Victoria but our BLAST assignment indicated they were in fact B/Yamagata (their low divergence from B/Yamagata strains was a clear outlier). NA sequences from isolates B/Kanagawa/73 and B/Ann Arbor/1994 were only small fragments (99 and 100 amino acids long) poorly aligned with other sequences and were thus excluded. We also excluded NA sequences from B/Yamagata isolates B/Catalonia/NSVH100773835/2018 and B/Catalonia/NSVH100750997/2018, because they were extremely diverged (60% and 38%) from the reference strain B/Yamagata/16/88 and aligned poorly with other sequences.To compare sequence diversity within and between lineages over time, we aligned sequences using MAFFT v. 7.31070 and calculated percent amino acid differences in pairs of sequences from the same lineage and in pairs with one sequence from each. For each year, we sampled 100 sequences from each lineage (or used all sequences if 100 or fewer were available) to limit the number of pairwise calculations. To estimate how much B/Yamagata and B/Victoria evolved since the late 1980s, we calculated percent amino acid differences between each B/Yamagata and B/Victoria sequence, and the corresponding HA and NA sequences of reference strains B/Yamagata/16/88 and B/Victoria/2/87. Unlike in the analysis of pairwise divergence within each time point, we used all sequences from each lineage in each year. We excluded sites in which one or both sequences had gaps or ambiguous amino acids.To compare HA and NA divergence between influenza B lineages with divergence between influenza A subtypes, we downloaded complete HA and NA sequences from H3N2 and H1N1 isolated since 1977 and available on GISAID in August 2019. Homologous sites in the HA of H3N2 and H1N1 are difficult to identify by conventional sequence alignment, and instead we used the algorithm by Burke and Smith71 implemented on the Influenza Research Database website72. Both H3N2 and H1N1 sequences were aligned with the reference H3N2 sequence A/Aichi/2/68. We verified that this method matched sites on the stalk and head of the H1N1 HA with sites on the stalk and head of H3N2 HA by comparing the resulting alignment with the alignment in Supplementary Fig. S2 of Kirkpatrick et al.73. To limit the total number of influenza A sequences analyzed, we randomly selected 100 H3N2 and 100 H1N1 sequences for years in which more than 100 sequences were available, and used all available sequences for the remaining years. Isolates A/Canterbury/58/2000, A/Canterbury/87/2000, and A/Canterbury/55/2000 were excluded, because both H1N1-like and H3N2-like sequences were available under the same isolate name on GISAID.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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