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The broad categories of data included in the repository are summarized in Online-only Table 2 and visualized in Fig. 2. Each category is explained in greater detail below, while full details together with accompanying notes are given in the repository (Database_structure.csv) and in Supplementary File 1. Online-only Table 2 gives an overview of data coverage per category, both across all species and for native species separately. A complete list of data sources is available in Supplementary File 2.Fig. 2Visualization of the attributes presented in the database.Full size imageGeneration of the species listTaxon names listed in the most recent and widely accepted New Flora of the British Isles’ index12 were digitized via the Optical Character Recognition Software ReadirisTM 17 (IRIS). Results from the digitization were transferred into a spreadsheet and obvious recognition errors were fixed. The resulting table contained 5,687 taxa and associated taxonomic authorities. A total of 360 unnamed hybrids were excluded, as well as species noted to have only questionable or unconfirmed records, leaving 5,038 species. Forty-one intergeneric hybrid species, 827 entries relating to (notho)subspecies, (notho)varieties, cultivars and forma were also removed along with 720 named hybrids. Species that were included by Stace12 but which he considered not to be part of the flora (i.e. listed as ‘other species’ and ‘other genera’, e.g. genus Tragus or Coreopsis verticillata) were also excluded. Seven species that were labelled ‘extinct’ in the flora were included as there were indications that the species might be in the process of reintroduction (e.g. Bromus interruptus, Bupleurum falcatum and Schoenoplectus pungens). Extinct native and archaeophyte species without any signs of reintroduction (e.g. Dryopteris remota) are also listed but no additional data are provided and they are not included in calculations of completeness of data (Online-only Table 2). The final number of extant species listed here is therefore 3,209 (comprising 1,468 natives, 1,690 aliens and 51 species with unknown status), plus 18 formally extinct species (natives and archaeophytes not seen in the study region since 1999). Species names and taxonomic authorities were revised according to the 2021 reprint of the New Flora of the British Isles, communicated to us by C.A.S. ahead of publication. Genera with less well-defined species – for example due to apomixis – contain additional information on subgenera, sections, and aggregates, as per Stace12. Since misidentifications are common in these groups, we include a column termed ‘unclear_species_marker’ that allows for these species to be quickly identified and excluded from analyses if appropriate. Such genera are often incompletely listed in our database since most microspecies are not sufficiently well defined.TaxonomyNomenclature of the list was checked by Global Names Resolver in the R package ‘taxize’20,21, using the International Plant Names Index (IPNI)22 as the data source, to remove any digitisation errors. Resolved names were used to determine accepted higher taxonomic hierarchy (family, order) again using taxize, with the National Center for Biotechnology Information (NCBI) database. Species that could not be resolved by the Global Names Resolver or did not yield matches in the NCBI database for their higher taxonomic ranks were manually checked for name matches in the World Checklist of Vascular Plants (WCVP)17. Species within the original species list that were found to be identical to a different spelling in WCVP were retained in the database. In such instances, and when slight spelling differences occurred, the columns ‘taxon_name‘ and ‘taxon_name_WCVP‘ differ. To improve clarity, each species is presented here with its unique identification number according to the WCVP (listed as ‘kew_id’) together with three additional columns (i.e. WCVP.URL, POWO.URL and IPNI.URL) which contain hyperlinks to the freely accessible taxon description websites of the (WCVP)17, Plants of the World Online (POWO)23 and (IPNI)22, respectively. Thus, while the taxon names used in the database correspond to those used by Stace12, changes in the accepted species name since publication can be traced in columns ‘taxonomic_status’ and ‘accepted_kew_id’. The family classification of WCVP follows APG IV24 for angiosperms, Christenhusz et al. (2011)25 for gymnosperms and Christenhusz & Chase (2014)26 for ferns and lycopods.Native statusWe offer three different datasets which describe the status of a species as native or non-native, and its level of establishment in BI. The first is extracted from Stace (2019)12, the second contains the status codes used in PLANTATT10 and the unpublished ALIENATT (pers. comm. author K.J.W.) dataset, and the third is extracted from Alien Plants13. The status from Stace12 and Stace & Crawley13 assigns a species to either native or alien status, with aliens subdivided into archaeophytes and neophytes at different levels of establishment (e.g. denizen, colonist etc., see Online-only Table 1). Status codes from the BSBI can be either AC (alien casual), AN (neophyte), AR (archaeophyte), N (native), NE (native endemic) or NA (native status doubtful).Functional traitsData for five ecologically relevant functional traits (i.e. seed mass, specific leaf area [SLA], leaf area, leaf dry matter content [LDMC] and vegetative height) were downloaded from public data available in the TRY database27 (for specific authors see Supplementary File 1 and Supplementary File 2). Averages were calculated using the available measurements downloaded for each species, excluding rows where the measurement was 0. In addition, the maximum vegetative height for each species is given, where available.Realized niche descriptionRealized niche descriptions based on assessments made on plants living in BI are given in the form of Ellenberg indicator values18, as published in PLANTATT10. Ellenberg indicator values place each species along an environmental gradient (e.g. light or salinity) by assigning a number on an ordinal scale, depending on the species preference for the specific gradient (Online-only Table 2). This information is often used to gain insights into environmental changes based on species occurrences28. For species listed under a previously accepted name in PLANTATT, the information was associated with the accepted synonym in Stace (2019)12. Due to the low coverage of PLANTATT for non-native species included in our list, we additionally include Ellenberg indicator values based on Central European assessments, as made available by Döring29. Each Ellenberg category is listed in a separate column, keeping the information from both data sources separate to avoid confounding of assessments based on two different regions (i.e. Britain and Ireland versus Central Europe).Life strategyTo characterize the life strategy of a species, we used the CSR scheme developed by Grime19, which classifies each species as either a competitor (C), stress tolerator (S), ruderal (R) or a combination of these (e.g. CS, SR). CSR classifications were obtained from the Electronic Comparative Plant Ecology database30. Due to the low coverage of available CSR assessments for species in our database (i.e. data available for just 460 out of 3,209 species) we imputed CSR strategies for a further 981 species using available functional trait data, following the method proposed by Pierce et al.31. The functional leaf traits required for this method – i.e. specific leaf area, leaf area, leaf dry matter content – were obtained from the TRY database27. Pre-existing30 and newly imputed CSR strategies are listed in separate columns.Growth form, succulence and life-formPlant growth form descriptions were obtained from the TRY database27 and filtered for those entries given by specific contributors (Online-only Table 2) to maintain consistent use of growth form categories. Information on whether a species was considered to be a succulent was obtained by screening the entire growth form information obtained from the TRY database for the phrase ‘succulence’ or ‘succulent’.Species life-form categories according to Raunkiaer32 were determined for each species in our dataset with regard to the typical life-form of the species as it grows in BI (pers. comm. M.J.M.C.).Associated biome and originInformation given in the Ecoflora database3 for the biome that each species is associated with was matched to the species names according to Stace12. The recognized biome categories follow Preston & Hill33 and are ‘Arctic montane’, ‘Boreal Montane’, ‘Boreo-Arctic Montane’, ‘Boreo-Temperate’, ‘Mediterranean’, ‘Mediterranean-Atlantic’, ‘Southern Temperate’, ‘Temperate’, ‘Wide Boreal’ and ‘Wide Temperate’.For non-native species, the assumed origin (i.e. the region that plants were most likely to have been introduced to BI from, rather than the full non-BI distribution of a species) was adapted from Stace12 into a brief description of their country or region of origin. In addition, these descriptions were manually allocated to the TDWG level 1 regions listed in the World Geographical Scheme for Recording Plant Distributions (WGSRPD, TDWG)34.Species distributionsDistribution metrics for each species are given as the number of 10-km square hectads in BI with records for the species in question within a specified time window. The data were derived from the BSBI Distribution Database35 and were extracted for each species, dividing the study region into Great Britain (incl. Isle of Man), Ireland and the Channel Islands, as previously partitioned for data available in PLANTATT10. The database was queried using species and hectads for grouping, showing only records ‘matching or within 2 km of county boundary’ and excluding ‘do-not-map-flagged occurrences’. The data were not corrected for sampling bias and should therefore only be used as an indication of trends.Hybrid propensityData on hybridization is provided for 641 species, obtained from the Hybrid flora of the British Isles36 which enumerates every hybrid reported in BI up until 2015 (pers. comm. M.R.B.). Each entry was transcribed manually, and then filtered to exclude (a) hybrids that have been recorded, but not formed in the British Isles, (b) triple hybrids (mainly reported for the genus Salix), (c) doubtful records, (d) hybrids between subspecific ranks, and (e) hybrids where at least one parent is not native (only archaeophytes included). This left 821 hybrid combinations for data aggregation. The metric chosen here is hybrid propensity, which is a per-species metric of how many other species a focal species hybridizes with (sensu Whitney et al., 201037). A scaled hybrid propensity metric is also given which was calculated by weighting the hybrid propensity score by the number of intrageneric combinations for a given genus, to account for the greater opportunities of hybridization in larger genera.DNA barcodesDNA barcode sequences for plant species present in BI are currently available for 1,413 species in our database. The information was derived from a dataset of rbcL, matK and ITS2 sequences compiled for the UK flora generated by the National Botanic Garden of Wales and the Royal Botanic Garden Edinburgh38,39 (pers. comm. L.J. and N.D.V.). The data are given as a hyperlink to the record’s page on the Barcode of Life Data Systems (BOLD40) which includes the DNA barcode sequences as well as scans of the herbarium specimen and information on the sample’s collection. Most species have multiple record pages associated with them, due to the sampling of more than one individual. We include a maximum of three BOLD accessions per species; the full range of individuals sampled can be accessed via the original publications38,39. DNA barcodes are almost exclusively available for native species. Future releases of our database will increase the coverage of the non-native flora significantly. Where species in the BOLD database are attributed to a species name that is considered synonymous with another name in our list, the hyperlink is matched to the latest nomenclature12. 1,421 species have at least one sequence associated with them and 935 species have sequence data for all three sequences (rbcL, matK and ITS2).Genome size and chromosome numbersGenome size data for 2,117 specimens (at least one measurement per species) were obtained from various sources. Measurements for a total of 467 species were newly estimated using plant material of known BI origin, often sourced  from the Millennium Seedbank of the Royal Botanic Gardens, Kew (RBG Kew)41. The measurements were made by flow cytometry using seeds or seedlings and following an established protocol42. Information on the extraction buffers and calibration standard species used are available in the file GS_Kew_BI.csv, along with peak CV values of the measurements as a quality control. Where more than one measurement is reported per species, the measurements were made on plant material from different populations or using different buffers. Previously published data for additional species were obtained from reports on the Czech flora43, the Dutch flora44, and prime values listed in the Plant DNA C-values database45,46. Since significant intraspecific differences in genome size between plant material from different geographical origins have previously been described, predominantly due to cytotype diversity in ploidy level47, genome size measurements from previously published sources were assessed with regard to the origin of the material. The column ‘from_BI_material’ (GS_BI.csv, BI_main.csv) allows users to filter for measurements made on material from BI to exclude a potential bias. The information was obtained from the original publication source of each measurement.Chromosome numbers for 1,410 species (at least one chromosome number per species) determined exclusively from material collected in BI were obtained from an extensive dataset compiled by R.J.G. from various published studies, unpublished theses and personal communications from trusted sources. The counts were made between 1898 and 2017, with a large proportion stemming from efforts to achieve greater coverage of the flora by a team of cytologists based at the University of Leicester and headed by R.J.G. Part of the dataset was previously incorporated into the BSBI’s data catalogue5 but has since undergone revisions to incorporate new information and changes in taxonomy. The dataset contained many measurements at subspecies level which were allocated to the species level taxon in our list. This served to include as much of the often considerable infraspecific variation as possible. Since some species for which chromosome counts have been reported elsewhere are lacking chromosome counts from British or Irish material, they are absent from this dataset. To fill such gaps, we also present chromosome numbers from reports on the Czech flora43, the Dutch flora44, and the Plant DNA C-values database45,46. More

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Species dataSpecies CPUE data were obtained from the National Oceanographic and Atmospheric Administration (NOAA) Northeast Fishery Science Center (NEFSC) U.S. NES bottom trawl survey, which, for almost 50 years, has collected abundance data for over 250 fish species in the spring and fall. The survey employs a stratified random design, with stations allocated proportionally to the stratum area. A 12 mm mesh coded liner is used to retain small-bodied and juvenile fish. All fish caught are weighed and counted18. We downloaded the data from OceanAdapt.com, which calibrates the CPUE for each species depending on survey ship. We cleaned the data for the years from 1998 to 2020, excluding years prior to 1997 due to many missing values for chlorophyll (Chla). We only included strata that were consistently sampled in the spring and fall. To account for the seasonal migrations of many of the studied species, we modeled spring and fall seasons separately. We present the results for the fall CPUE, with the spring results and presence/absence results in the supplemental materials. We selected species that were present in at least 400 tows and with a biomass of at least 0.5 kg/tow (CPUE) in more than 100 tows. Finally, we removed roughly 400 tows per season with missing environmental covariates (see below). In the fall, we selected 30 species with 5217 observations, and in the spring, we selected 24 species with 5935 observations (see Supplemental Tables S1, S2).Environmental dataThe study region includes Southern New England and The Gulf of Maine. We selected environmental covariates known to influence marine fish distributions and abundances. Depth, temperature (bottom and surface) and salinity (bottom and surface) were measured in situ during trawl surveys. Missing values were augmented with the data-assimilative HYbrid Coordinate Ocean Model (HYCOM) daily and then monthly data. HYCOM is an oceanographic model that produces 32 vertical layers including ocean temperature, salinity, sea surface height, and wind stress as well as other 3- and 4-dimensional variables. The system uses the Navy Coupled Ocean Data Assimilation (NCODA) system19 for data assimilation. NCODA uses the model forecast as a first guess in a multivariate optimal interpolation (MVOI) scheme and assimilates available satellite altimeter observations (along track obtained via the Naval Oceanographic Office Altimeter Data Fusion Center satellite) and in situ sea surface temperature as well as available in situ vertical temperature and salinity profiles from expendable bathythermographs, Argo floats, and moored buoys20. Seven HYCOM models (HYCOM + NCODA Global 1/12° Reanalysis GLBu0.08 Expts 19.0, 19.1, 90.9, 91.0, 91.1, 91.2) were temporally concatenated to create a continuous dataset of BT and salinity, ranging from 1992 to 2017. These model runs differed slightly in their configurations (time steps, advection scheme, mixing, vertical structure, slight change in NCODA, and MVOI transition to 3-dimensional analysis in 2013), but the differences are not expected to influence the applicability of the output21. The numbers of filled in missing values were 787 (7.0%) surface salinity (SSAL), 735 (6.5%) surface temperature (SST), 809 (7.2%) bottom temperature (BT), and 850 (7.6%) bottom salinity (BSAL). Chla was obtained from the MODIS satellite (monthly rasters from 2003 to 2019) on a monthly time step22, with missing values filled using the SeaWIFS satellite23 (1998 to 2009). Temperature, salinity and Chla data that were not collected in situ were downloaded using Google Earth Engine (HYCOM and MODIS)24. Benthic substrate (grain size in mm, referred to as SEDSIZE), subregion (Gulf of Maine or Southern New England), benthic land position (high, low, mid), and seabed form data (depression, high flat, high slope, low slope, mid flat, side slope, steep) were obtained from the Nature Conservancy’s Northwest Atlantic Marine Ecoregional Assessment25 (Supplemental Fig. S1).GJAMTo study the influence of the environmental covariates on the joint distribution of marine fish and invertebrate species we use the generalized joint attribute model (GJAM)12 and the corresponding R package (Version 2.5)26. Briefly, this multivariate Bayesian model allows us to jointly model the marine fish community and accounts for responses to the environment that can include combinations of continuous and discrete responses (e.g., CPUE and zeros) and the dependence between species. GJAM returns all parameters on the observation scale, in this case, CPUE and presence-absence. Products of model fitting include a species‐by‐species covariance matrix (Σ), species responses to predictor variables (B), and predicted responses. The species‐by‐species covariance matrix Σ captures residual codependence between species after removing the main structure explained by the model (also referred to as the residual correlation matrix). As a result, Σ allows for conditional prediction of some species under different scenarios for the abundances of others27.CPUE is termed continuous abundance (CA) data in GJAM, meaning that observations are continuous with discrete zeros. Let yis be the CPUE for species s at location i. For CA data GJAM expands the tobit model for (univariate) regression to the multivariate setting, where a latent variable wis is equal to yis when yis is positive and zero otherwise,$$y_{i,s}^{0} = left{ {begin{array}{*{20}l} {w_{is} ,} hfill & {w_{is} > 0quad {text{continuous}}} hfill \ {0,} hfill & {w_{is} le 0quad {text{discrete zero}}} hfill \ end{array} } right.$$
(1)
The length-S vector of all species responses wi is continuous on the real line, and thus can be modeled with a multivariate normal. The model for wi is$$begin{aligned} left. {{mathbf{w}}_{i} } right|{mathbf{x}}_{i, } {mathbf{y}}_{i} & sim ,MVNleft( {{varvec{mu}}_{i} ,{Sigma }} right) times mathop prod limits_{s = 1}^{S} {mathcal{I}}_{is} \ u_{{varvec{i}}} & = {mathbf{B}}^{prime } {mathbf{x}}_{{varvec{i}}} \ {mathcal{I}}_{is} & = mathop prod limits_{k in C} I_{is,k}^{{Ileft( {y_{is} = k} right)}} left( {1 – I_{is,k} } right)^{{Ileft( {y_{is} ne k} right)}} \ end{aligned}$$
(2)
$$begin{aligned} {mathcal{I}}_{is} & = I(w_{is} le 0)^{{Ileft( {y_{is} = 0} right)}} left[ {1 – Ileft( {w_{is} le 0} right)} right]^{{Ileft( {y_{is} > 0} right)}} \ & quad I(w_{is} > 0)^{{Ileft( {y_{is} > 0} right)}} left[ {(1 – I(w_{is} > 0)} right]^{{Ileft( {y_{is} = 0} right)}} \ end{aligned}$$where the indicator function (I(cdot )) is equal to 1 when its argument is true and 0 otherwise. For presence-absence data, ({mathbf{p}}_{{varvec{i}}{varvec{s}}}boldsymbol{ }=boldsymbol{ }left(-boldsymbol{infty },boldsymbol{ }0,boldsymbol{ }boldsymbol{infty }right).) This is equivalent to Chib and Greenberg’s28 probit model which can be written as ({mathcal{I}}_{is}=I({w}_{is} >{0)}^{Ileft({y}_{is} >0right)}I({w}_{is}le {0)}^{1-{y}_{is}}).The mean vector ({varvec{mu}}_{i} = {mathbf{B}}^{prime } {mathbf{x}}_{{varvec{i}}}) contains the Q × S matrix of coefficients B and the length-Q design vector xi. Σ is a S × S covariance matrix. There is a correlation matrix associated with Σ,$${mathbf{R}}_{{S,S^{prime } }} = frac{{{{varvec{Sigma}}}_{{S,S^{prime } }} }}{{sqrt {{{varvec{Sigma}}}_{S,S} {{varvec{Sigma}}}_{{S^{prime } ,S^{prime } }} } }}$$
(3)
The predictive distribution is obtained as$$left[tilde{Y }left| tilde{X }right.right]=int left[ tilde{Y }left| tilde{X }right.,widehat{theta }right]left[widehat{theta } left|X, Yright.right]$$
(4)
The integrand contains the likelihood (Eq. (2)) followed by the posterior distribution for parameters, (widehat{theta }= left{widehat{mathbf{B}},boldsymbol{ }widehat{{varvec{Sigma}}}right}). Input (tilde{X }) can equal X (in-sample prediction) or not (out-of-sample prediction). We fitted both CPUE (continuous abundance) and presence-absence versions of the model. As a Bayesian method, GJAM provides probabilistic estimates of parameters with full dependence in data, including jointly distributed species. Model fitting is performed using Gibbs sampling, which is a Markov chain Monte Carlo (MCMC) technique.The sensitivity of an individual response variable s to an individual predictor q is given by the coefficient βqs (individual coefficients from the B matrix). The sensitivity that applies to the full response matrix is given by$${mathbf{f}} = diagleft( {{mathbf{B}}{Sigma }^{ – 1} {mathbf{B}}^{prime } } right)$$
(5)
The Q × S matrix B contains relationships of each species to the environment, the “signal”, but not to each another. Matrix E summarizes species similarities in terms of their response to an environment (stackrel{sim }{mathbf{x}}) and is given by$${mathbf{E}=mathbf{B}}^{boldsymbol{^{prime}}}mathbf{V}mathbf{B}$$
(6)
where V is a covariance matrix for (stackrel{sim }{mathbf{x}})(a vector of predictors) and contributes the environmental component of variation in (stackrel{sim }{mathbf{y}}). Similar species in E have similar columns in B. Those similarities and differences are amplified for predictors (stackrel{sim }{mathbf{x}}) with large variance. Conversely, species differences in B do not matter for variables in X that do not vary. The covariance in predictors could come from observed data, i.e., the variance of X (see12 for more details).Prior distributions for this study are non-informative. This is particularly helpful for the covariance, lending stability to Gibbs sampling and avoiding dominance by a prior. In cases this particular case, the direction of the prior effect may be known, but the magnitude is not.Variable selectionUnlike the familiar univariate setting, variable selection has to consider which species are included in the model. In a univariate model, there is one response and perhaps a number of potential predictor variables from which to choose. As in a univariate model, variable selection focuses on predictors held in the n by p design matrix X. Rather than a response vector, the multivariate model includes the n by S response matrix Y. Unlike the univariate model, the overall fit and predictive capacity depends not only on what is in X, but also on the species that are included in Y, each of which would be best explained by a different combination of variables. Rare species having no signal will not provide cross-correlations and thus can offer little learning from an analysis. For this reason, there may be no reason to include them in model fitting. Given that many species may be rare, and rare types will not be explained by the model, there will be decisions about what variables to include on both sides of the likelihood (i.e., predictors and responses).These considerations mean that simple rules for variable selection, such as the combination yielding the lowest DIC, may not be sensible. The combination of variables that yields the lowest DIC could miss variables that are important for subsets of species. In principle, one poorly-fitted species could dominate variable selection. The best model for responses ranging from rare to abundant will depend on precisely which species are included, both rare and abundant. Thus, in order to select variables, we utilize inverse prediction—predicting the environment from species – and the overall community sensitivity12.Inverse prediction provides a comprehensive estimate of the environmental importance for the entire community, because it determines the capacity of the community to predict (through the fitted model) the environment; it inverts the model12. A variable predicted by the community explains important variation in one to many species. A variable that is not predicted by the community does not explain important variation in any of them. To look at the importance of environmental variables for the entire community, we started with the saturated model that included the predictors BT, SST, depth, BSAL, SSAL, Chla, SEDSIZE, subregion, benthic position and an interaction between depth and BT, BSAL, SST and SSAL (Fig. 1a). Sensitivity was highest for the interaction between BT and depth and lowest for Chla and sediment size (see right subpanel on Fig. 1a for sensitivity). Inverse prediction confirmed that sediment size and Chla contribute little to community biomass, because the community cannot “predict” them (see left and middle subpanels on Fig. 1a for sensitivity). Inverse prediction results from a second model (Fig. 1b) showed that SSAL and the third model for benthic position also (Fig. 1c) contribute little to the community response. Using the combination of sensitivity and inverse prediction we obtained the final model that includes BT, depth, BSAL, SST, subregion and an interaction between depth and BT, BSAL and SST (Fig. 1d). Inverse prediction indicates that the CPUE predicts the environment well. In the final model, sensitivity is highest for depth. Subregion remains as a two-level factor and there is strong inverse prediction for that variable as well (Fig. 1d). In the variable-selection stage, each model was run on the entire fall dataset for 5000 iterations and a burn-in of 800. Inverse prediction results from the spring model indicated similar patterns; thus, the same variables were used for the spring and fall.Figure 1Inverse prediction and sensitivity for combinations of environmental parameters in GJAM. Starting with the most complicated model (a), sensitivity was highest for the interaction between BT and depth and lowest for Chla and sediment size (a). Inverse prediction confirms that sediment size and Chla contribute little to community biomass (a) and those are removed in the second model (b). SSAL contributes little to community response and are removed in the third model (c), The final model (d) includes terms that have strong inverse prediction and overall sensitivity. Inverse prediction for continuous and factor variables is on the left and center of each box, and overall sensitivity is on the right.Full size imageWe compare the model selected above using inverse prediction to a model selected using the more traditional method of out-of-sample prediction. For out-of-sample prediction, we fitted all combinations of 11 environmental variables (BT, BSAL, SST, SSAL, Chla, depth, sediment size, subregion, position, seabed form) plus interaction terms between depth and SEDSIZE, BT, BSAL, SST, SSAL and chlorophyll. These models were run with 1000 iterations and a burn-in of 400. All models included BT, BSAL, SST, SSAL, chlorophyll A and depth, as these variables have been shown to be important for these species. In total, 1,024 possible models were evaluated by training each potential model on 70% of the data (n = 3652 in the fall, n = 4155 in the spring), evaluating in-sample performance with DIC, and then testing out-of-sample performance on the remaining 30% (n = 1565 in the fall, n = 1780 in the spring). The 10 models with the lowest DIC in-sample were selected, and the final model was selected out of those 10 with the lowest out-of-sample R2. The selected model for fall CPUE had the following terms: ~ BT + depth + BSAL + SST + SSAL + chla + depth*BT + depth*SEDSIZE + depth*SSAL + depth*chla + SEDSIZE + Benthic position. Recall that inverse prediction selected a simpler model including the following terms: BT + depth + BSAL + SST + Subregion + depth*BT + depth*BSAL + depth*SST. The inclusion of SEDSIZE and benthic position in the model selected via out-of-sample prediction is probably a result of these predictor variables being important for a subset of species (i.e. benthic species29), but not the community as a whole. When we have a large number of response variables, as in this study, we need to consider the variables that are more important on a community level, rather than just for a few species. Thus, we use the model selected via inverse prediction for the remainder of the study.We fitted the selected model with 70% of the data for 20,000 iterations with a burn-in of 8,000 iterations (n = 3652 in the fall, n = 4155 in the spring). Out-of-sample prediction was performed on the remaining 30% (n = 1565 in the fall, n = 1780 in the spring) of the dataset and predicted versus observed values were evaluated (Supplemental Figs. S2 and S3) as well as residual versus fitted values (Supplemental Figs. S4 and S5). As has been shown in other research30,31, aggregating noisy predictions based on similar environmental preferences can improve performance, especially for larger datasets. Thus, we generated an aggregated data set that uses a k-means clustering of predictors (Supplemental Figs. S8 and S9). We performed the same analysis for the spring and the fall as well as with the presence absence data and recorded AUC as well as precision for each species (Supplemental Figs. S6 and S7). Precision is defined as the arithmetic mean of precision (proportion of predicted presences actually observed as presences) across all threshold values (at an interval of 0.01).Final modelWe ran the final model on 100% of the data with 20,000 iterations and a burn-in of 8000 iterations for the spring and fall for CPUE as well as presence absence for a total of 4 models. From the final model we obtained coefficients for the species-environment responses, β, covariance between species in how they respond to the environment E, and the residual correlation from the fitted model, R. We subtracted the absolute values from the presence/absence residual correlation matrix from the absolute values of the CPUE residual correlation matrix to observe where these results diverged. For MCMC chains and convergence of the final model as well as example models from both methods of variable selection see Supplemental Figs. S10–S12).Comparison to SSDMsWe built single species distribution models for each species in the form of GAMs using the mgcv package in R32. GAMs are a semiparametric extension of the generalized linear model and are a common modeling technique for species distribution modeling in this ecosystem33. For each species, we ran one GAM with CPUE as the response variable with a log-linked tweedie distribution that had penalized regression splines, a REML smoothing parameter with an outer Newton optimizer, 10 knots, and omitted NAs. We also ran GAMs for each species with a binary response variable indicating species presence with a binomial error distribution and a logit link function, penalized regression splines, a REML smoothing parameter with an outer Newton optimizer, 10 knots, and omitted NAs. We compared the out of sample observed versus predicted values for GAMs versus GJAM using RMSPE, R2, AUC, and precision. Root Mean Squared Prediction Error (RMSPE) is a measure of the average squared difference between the observed and predicted values, measured in the same units as the input data (kg/tow). R2 is a measure of the average squared difference between the observed and predicted values and is unitless. R2 is calculated as (1 − sum((predicted − observed)2)/sum((observed − mean(observed))2)) The ROC curve is a measure of model performance which plots true positive rate versus false positive rate, and the area under the ROC curve (AUC) provides a single measure of accuracy. A pairwise Wilcoxon test was used to compare means. We also compare the significance of predictors in both the GJAM model and GAM models. In this example, significance is defined for GJAM as a credible interval of the beta estimation that does not cross zero, and for the GAM as a p-value less than 0.0534.Spatial and temporal autocorrelationExamining the spatial and temporal autocorrelation of the modeled residuals can help specify missing endogenous (habitat selection or density dependence) and exogenous (covariate) effects that may be missing from the model. Thus, for each species modeled, we plot the spatial autocorrelation of residuals using a semi-variogram for the year 2015 and the temporal autocorrelation of the residuals using a partial autocorrelation function (PACF). We present the results for each species in the fall in the Supplemental materials (Supplemental Figs. S27–S57).All analysis and figure creation was performed in R version 3.6.235. Figures were created using the following R packages: ggplot236, ggpubr37, corrplot38, gridExtra39, cowplot40, lessR41, and ggcorrplot42. More

Study area and study populationData come from a long-term study of a pied flycatcher population breeding in nestboxes in central Spain (ca. 41°N, 3°W, 1200–1300 m.a.s.l.). The longitudinal data cover the period 1990–2016 (no data for 2003) and include records for 1436 males (yearly mean and SD: 107.4 and 34.2) and 1641 females (yearly mean and SD: 119.7 and 28.6). The study area consists of two plots in two different montane habitats separated by 1.1 km, including 237 nestboxes with an average occupancy rate around 54% (SD = 0.11). One habitat is an old deciduous oak (Quercus pyrenaica) forest, and the other one is a managed mixed coniferous (mainly Pinus sylvestris) forest. The nestboxes have remained in the same position since 1988 (pinewood) and 1995 (oakwood) (for details, see42,43).Fieldwork and data collectionNestboxes were regularly (every 3rd–4th day) checked during the breeding season (from mid-April to the beginning of July) to determine the date of the first egg laid, clutch size, hatching date, and the number of fledglings. Parents were captured with a nestbox trap while incubating (females) or feeding 8-day-old nestlings (both sexes; for details, see43 and marked with a numbered metal ring (both sexes). We used a unique combination of colour rings (males only) for individual identification before capture. Many breeding birds (53%) hatched in the nestboxes, and, therefore, their exact age was known44. Unringed breeders were aged as first-year or older based on plumage traits following ageing criteria described in44,]45. All nestlings were ringed at 13 days of age.Polygamous males were detected when captured and/or individually identified while repeatedly feeding young in two nests (see24 for details on capture protocol and mating status classification). We distinguished three classes of females according to their male mating status: (i) monogamous female, i.e. mated with a monogamous male; (ii) primary female, the first mated female of a polygynous male; and (iii) secondary female, the second mated female of a polygynous male. However, in some nests, it was not possible to know with certainty the mating status of the female (14.3% of times) or the male (3.7% of times, see below for how we dealt with this source of uncertainty).Ethics declarationThe study was reviewed by the ethical committees at the Doñana Biological Station and the Consejo Superior de Investigaciones Científicas headquarters (Spain) and adhered to Spain standards. All methods were carried out in accordance with relevant guidelines and regulations. Birds were caught and ringed with permission from the Spanish Ministry of Agriculture, Food, Fisheries, and Environment’s Ringing Office. The study complied with (Animal Research: Reporting of In Vivo Experiments) guidelines46.Multi-event capture-recapture modelsWe used multi-event capture-recapture (MECR hereafter) models47 to test, separately for females and males, how the mating status affected the probability of surviving (and not leaving the area permanently) and the probability of changing, or not, from one mating status to another. The MECR models accommodate uncertainty in state assignment by distinguishing between what is observed (the event) and what is inferred (the state). This approach allows estimating the effects of mating status on the parameters (e.g. probabilities of local survival and change in mating status) while accounting for the uncertainty, as outlined above, due to the unknown mating status of some captured individuals.MECR models are defined by three types of parameters: Initial State probabilities, Transition probabilities and Event probabilities (details in Appendices S5). As these parameter types may be broken into steps, we considered two Transition steps, Local survival and Mating Status Change, and two Event steps, Recapture and Mating Status Assignment. Accordingly, we considered the following parameters of the MECR model: (i) Initial State, the probability of being in a specific mating status at the first encounter (in our case the first known breeding event of an individual); (ii) Local survival, the probability of surviving and not emigrating permanently from the study area between year t and year t + 1; (iii) Mating Status Change, the probability that a live bird changes state between year t and t + 1; (iv) Recapture: the probability of recapture of a live and not permanently emigrated individual; (v) Mating Status Assignment: the probability that the mating status of a captured individual is ascertained in the field (assuming no state misclassification). In this study, we will use the term “parameter” to denote any of the probabilities (see i-v above) estimated in the MECR model. Also, note that, as is often the case, we cannot distinguish the probability of site fidelity from that of surviving. For simplicity, we will often use the term “survival” to refer to “local survival”.We used the encounter histories of all identified birds breeding in the study area at least once between 1990 and 2016. We ran separate analyses for each sex, considering four biological states for females: live monogamous breeder (MBF), live primary breeder (PBF), live secondary breeder (SBF) and dead or permanently emigrated (†); and five events, numbered as they appear in the encounter histories: (0) non-captured, (1) captured as a monogamous breeder, (2) captured as a primary breeder, (3) captured as a secondary breeder and (4) captured in an unknown mating status. Females of unknown mating status were those for which we did not know the mate’s identity after repeated identification attempts at the nestbox (see details in24). These females could be of any mating status, and the mate being absent (e.g. dead after pairing) or very sporadically visiting the nest. For males, however, we considered three biological states: live monogamous breeder (MBM), live polygynous breeder (PBM) and dead or permanently emigrated (†), mediated by four events: (0) non-captured, (1) captured as a monogamous breeder, (2) captured as a polygynous breeder, (3) captured in an unknown mating status. Males of unknown mating status were identified by reading their colour-rings combinations near a nestbox and not captured or seen again during the breeding season. For both sexes, we established two age classes: 1-year-old individuals (1-yo hereafter: 41.74% females; 26.46% males) and individuals older than 1 year ( > 1-yo hereafter: 58.26% females; 73.54% males) that we included as a control variable in our capture-recapture models. This classification allowed the inclusion of non-local breeders (immigrants) in our analyses.Models were built and fitted to the data using E-SURGE 2.2.048. As our data were annually collected and we had no data for 2003, we selected the “Unequal Time Intervals” option to account for the 2002–2004 interval. Details on the probabilistic framework and the limitations of the modelling approach are given in Appendix S4.Goodness of fitBefore running the capture-recapture analysis, we preliminary assessed the goodness of fit (GOF) of a general model to the data. Since GOF tests are not available for multi-event models, we tested the GOF of the Cormack-Jolly-Seber (CJS), a model accounting for just two states, alive and dead, and for temporal variation in survival (Transition) and recapture (Event) probabilities, using U-CARE 2.3.249. This approach is conservative because the CJS is coarser than the MECR model. Thus, if the former fits the data well, the latter will fit them. All the GOF tests were run for males and females separately. The global tests were not significant for both males [c2 = 72.57, df = 103, p = 0.99; N(0,1) statistic for transient ( > 0) =  − 0.49, p = 0.69; N(0,1) signed statistic for trap-dependence = − 0.84, p = 0.99] and females [c2 = 76.13, df = 122, p = 0.99; N(0,1) statistic for transient ( > 0) = − 2.51, p = 0.69; N(0,1) signed statistic for trap-dependence = − 1.22, p = 0.22], indicating acceptable fits of the Cormack-Jolly-Seber models to the data. For the complete results of 3.SR (transience) and 2.CT (trap-dependence) tests, see Appendix S5.Model selectionModel selection was based on Akaike Information Criterion corrected for small sample sizes (AICc)50. For each sex, in a preliminary analysis, we built a global model checking that there were no parameter identifiability issues48. The structure of the global model was: Initial State (mating status × time), Local survival (age + (mating status × time)), Mating Status Change (age × mating status), Recapture (mating status × time), Mating status Assignment (mating status × time).Our modelling approach consisted of two steps. In step one, starting from the global model, we followed a backwards model selection procedure to test various combinations of variables potentially influencing each parameter of the MECR model while simplifying the model’s structure. According to the classic approach for which the recapture part of the model is modelled before that of survival51,52, we followed the following order of model selection: Initial State, Mating Status Assignment, Recapture, Mating Status Change, and Local survival. After testing the model structure (set of effects) for a parameter, we set the best structure (lower AICc) for that parameter, and we then tested the models for the following parameter. Thus, at the end of step one, we examined the effect of mating status on the biologically relevant parameters, that is, on Local survival and Mating Status Change. In step two, we used the simplified model resulting from step one (final model 1) to test whether the frequency of the FSP differentially affected the biologically relevant parameters according to the mating status. First, we tested the effects of FSP on Mating Status Change and then on Local survival (by keeping in MSC the same structure of final model 1). In the Results section, we reported parameter’ estimates from a model that combined the best final structure (lowest AICc) found on all the parameters, when not stated otherwise.Linear regression analysis of FSP and fledging success of hatchlingsWe used a GLM model to test whether the FSP depends on the yearly average proportion of hatchlings that fledged. We used the simulateResiduals function of the DHARMa53 package in R54 to confirm the absence of over-dispersion and the good fit of the model. More