Introduction

The expansion and intensification of agriculture are major drivers of biodiversity loss globally (Foley et al. 2011; Kehoe et al. 2015; Davison et al. 2021). Recent decades saw a considerable increase in land-based production per unit of area, made possible by increases in the use of fertilisers, pesticides, irrigation, and technical improvements in the mechanisation of the production operations (Erb et al. 2013). All these often co-occurring processes are collectively understood as agricultural intensification (Erb et al. 2013; Kuemmerle et al. 2013). However, describing the relationship between agricultural land-use intensity (LUI) and farmland biodiversity is a challenging task (Batáry et al. 2015; Le Provost et al. 2021). This is because LUI is a multifaceted phenomenon that is notoriously difficult to clearly define and to quantify in a one-dimensional way (Erb et al. 2013; Kuemmerle et al. 2013; Dullinger et al. 2021). Indeed, while certain definitions of LUI focus on inputs and outputs of agricultural systems (e.g. “the combined effect of agricultural inputs (e.g., fertiliser, pesticide, ploughing) and biomass outputs (e.g., grazing, mowing, harvest)”; Meier et al. 2020), others reflect farmers’ practices of varying intensities (e.g. “the degree of yield amplification caused by human activities”; Dietrich et al. 2012). We here adopt the definition by Kehoe et al. (2015), that defined LUI as “the degree of adoption of land management practices enabling yield increases from a given area of agricultural land”, and highlighted that, in order to thoroughly assess LUI impacts on biodiversity, a wide spectrum of relevant LUI metrics needs to be adopted. The impacts of (positive or negative) changes in LUI are similarly hard to assess as they depend on highly context- and scale-specific processes that vary across regions, and which have cascading direct and indirect effects on the ecosystem (Diogo et al. 2022).

The efforts in trying to conceptualise and adequately quantify LUI for applications in biodiversity modelling have increased recently (Beckmann et al. 2019; Dullinger et al. 2021; Semenchuk et al. 2022). Nonetheless, a consensus on the conceptualisation and integration of LUI dimensions is yet to be reached: Dullinger et al. (2021) performed an exploratory literature assessment on the different metrics used to measure LUI in recent biodiversity research and found that a wide variety of metrics exist. These metrics are often used independently and interchangeably in biodiversity studies, while only few studies combine several LUI metrics (Dullinger et al. 2021). The use of different LUI metrics can lead to variable and sometimes contrasting results in biodiversity studies, thus multiplying the uncertainties in our understanding of the LUI-biodiversity relationship.

Another important source of uncertainty in LUI-related analyses is the spatial unit of aggregation of LUI metrics, which often varies across studies. While the challenges of modelling and predicting biodiversity responses to environmental factors across spatial scales have been widely investigated (Azaele et al. 2015; McGarigal et al. 2016; Graham et al. 2019; Spake et al. 2021), there has been much less focus on the implications of using different geometrical shapes as units of aggregation of biodiversity and environmental measurements (but see Birch et al. 2007 and Le Ber et al. 2009). Square grids are the most common aggregation units in spatially-explicit biodiversity studies, because the vast majority of spatial data used in ecology is generated or collected in the form of square grids (Birch et al. 2007). This is true not only for remote sensing-derived products like land use/land cover, topography and climate rasters, but also for many biodiversity monitoring schemes that employ square plots for animal and plant surveys, like national butterfly and breeding bird monitoring schemes (Zingg et al. 2019; Harris et al. 2021) and the High Nature Value farmland monitoring (Aue et al. 2014). Moreover, the symmetrical, orthogonal coordinate system of square grids allows a supposedly simple change of data resolution by aggregation or disaggregation to different spatial scales.

Hexagonal grids are becoming more popular in recent years, especially in camera trap, connectivity and movement ecology studies (Broadley et al. 2019; Naidoo and Burton 2020) as the nearest neighbour concept is less ambiguous in hexagonal than in square grids, where one needs to choose between the rook’s case (where neighbouring grid-cells are defined based on a common edge) and the queen’s case (where neighbouring grid-cells are defined based on a common edge or a common vertex) contiguity. The hexagonal tessellation can also be applied to spherical surfaces without incurring distortion problems, making it ideal for global studies (Stough et al. 2020).

Irregular tessellation methods with units of variable shape and area are rarely used in ecology (but see Stewart and van der Ree 2010; Galpern et al. 2012; Prates et al. 2019; Santos-Fernandez et al. 2021), although simulating discontinuity and patchiness in spatial phenomena could be advantageous for certain applications (Le Ber et al. 2009; Bełej and Figurska 2020). For example, agroecosystems consist of a mosaic of crops and semi-natural land cover types, which might be better represented through irregular tessellation methods like the voronoi polygons than by regular grids (Le Ber et al. 2009). When the precise geometries of agricultural fields and of the surrounding land-cover patches are not available or accessible, the voronoi tessellation based on, for example, remotely-sensed land-cover products can provide a fair approximation.

In this study, we computed commonly used LUI metrics and compared their spatial patterns to identify divergences across metrics and grid types over an agricultural region in Germany, the Mulde River Basin. We employed three different spatial aggregation methods, i.e. square, hexagonal and voronoi tessellation, and we showed that the choice of LUI metric and of the spatial aggregation unit can lead to significant variations in LUI values sampled at given point locations. We further tested how these differences affect the estimation of species-environment relationships through a practical example using virtual species with known response curves to specific LUI metrics. This allowed us to exemplify that not taking into account multiple LUI dimensions can lead to erroneous conclusions on LUI-biodiversity associations.

Materials and methods

Study area

The Mulde River Basin is a traditionally agricultural region in the federal state of Saxony, Germany. It covers an area of 5814 km2 and the elevation ranges from 24 to 1214 m asl (Staatsbetrieb Geobasisinformation und Vermessung Sachsen 2016). The climate is predominantly continental; total annual precipitation ranges between 570 and 1260 mm and mean annual temperatures between 7.4 and 14.1 °C (Deutscher Wetterdienst, www.dwd.de). Land use is predominantly agricultural, with 38% of the study area covered by cropland and 13% by grasslands (SMEKUL 2020).

Calculation of LUI metrics

We calculated ten LUI metrics that have been used in recent spatially-explicit biodiversity models, such as species distribution models (SDMs) and analyses relating local- and landscape-level LUI to species richness or abundance (Table 1). To facilitate comparability, we chose all variables to indicate a higher LUI with increasing values. For this purpose, we computed the “conventionally farmed utilised agricultural area (UAA)” metric as a complementary variable to the organically farmed area, which was used in the cited studies in Table 1. Similarly, we calculated three landscape homogeneity metrics based on the opposite of the commonly used crop- and landscape-diversity measures. We categorised each metric based on the conceptual model for the description of agricultural systems proposed by Firbank et al. (2008), which identifies three dimensions: 1. (large-scale) land use, 2: crop or grassland management at the field level (i.e. land management), and 3. landscape structure. All metrics were calculated in R (R Core Team 2022, version 4.1.3) using the packages sf (Pebesma 2018), raster (Hijmans 2022a), terra (Hijmans 2022b), and dplyr (Wickham et al. 2022). Packages ggplot2 (Wickham 2016), mapview (Appelhans et al. 2021) and tmap (Tennekes 2018) were used for visualisation purposes.

Table 1 LUI metrics and their units of measure used in this study, with references to previous studies employing them as LUI proxies in biodiversity models
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Spatial aggregation methods: preparation of the different grids

The square and the hexagonal grids were created with the function sf::st_make_grid() (Pebesma 2018) by setting the cell size to 1000 × 1000 m. This resulted in a square grid with 6158 cells of 1 km2 and a hexagonal grid with 7070 hexagons with an area of 0.87 km2. For these two regular tessellation methods, we preferred spatially aligned grids (Fig. S1) over grid cells of equal size, as the spatial position of each grid is likely to strongly influence many of the calculated metrics. We computed voronoi polygons to simulate the mosaic-like nature of agricultural landscapes, which are composed of different land-use/land-cover patches of irregular shape. We cropped the land-cover map by Preidl et al. (2020, at 20 × 20 m resolution) to the study area extent and converted it to polygons in QGIS (https://www.qgis.org) using the Polygonize (Raster to vector) function to obtain one polygon for each land cover patch. To reduce the number of polygons and eliminate overly small ones, polygons with an area of less than 12.5 ha were removed. This threshold was chosen to reduce the number of remaining polygons to 6708, a comparable number to that of the other two grids. We computed the centroids of the polygons (if centroids fell outside of the polygon, we picked a random point within it), calculated the voronoi tessellation with the sf::st_voronoi() function, and then intersected it with the study area boundary. The resulting voronoi polygons had an area ranging between 0.13 and 17.4 km2, with a mean of 0.88 km2.

Virtual species simulation

To illustrate how different LUI metrics and grids can affect biodiversity models, we created three virtual species with varying habitat requirements (an arable land, a grassland, and a wetland species) using the package virtualspecies (Leroy et al. 2015). As this package requires raster data as environmental input data, we used the 1 km2 square grid created earlier and converted the LUI metrics from shapefile to raster. We defined the niche of the arable land species through positive response functions to the LUI metrics Arable and Field_size, and a negative linear relationship with N_input. The grassland species had negative relationships with Arable_UAA, Intens_f and LULC_homog. The wetland species had negative response functions to Arable_UAA, Conv_farm and LC_homog. For each virtual species, the three response functions were multiplied to obtain the environmental suitability raster, which was then converted into a probability of occurrence of the virtual species using a logistic conversion. The probability of occurrence equals the chance of sampling a presence point, so that presence-absence data can be randomly drawn from the probability of occurrence raster using a probabilistic approach (Leroy 2018). For example, a pixel with probability of occurrence of 0.8 has a probability of 80% of being sampled as a presence. For each virtual species, we sampled 500 random points and extracted their presence/absence information to be used for the comparative analysis across metrics and grids and in the species distribution model. Grid cells with UAA = 0 were masked out of the sampling area.

Comparative analysis of LUI values across metrics and grids

To ease comparisons across metrics and grids, we scaled all metrics such that they had values between 0 and 1. To identify the areas with highest disagreement across metrics in a spatially-explicit way, we calculated the standard deviation across the ten metrics at the grid-cell level, for each of the three grids. To investigate how different spatial aggregation units affect LUI values, we calculated, separately for each metric, the absolute difference between LUI values calculated using the square grid (used as basis of comparison as it is the most common one) and those of the hexagonal and the voronoi grid, for 20,000 randomly sampled points within the study area. This number of points was chosen to adequately cover the entire study area, making sure that all grid cells, irrespective of the grid type, were sampled at least once. We visualised these cross-grid differences though bivariate choropleth maps using the package biscale (Prener et al. 2022). To compare LUI values across metrics and grids at specific point locations (e.g. at biodiversity monitoring sites), we extracted the values from each metric and grid at the sampled presence points of the virtual species and compared their density distributions via ridgeline plots constructed using the packages ggridges (Wilke 2021) and ggplot2 (Wickham 2016). For each pair of metrics, within and across different grids, we calculated the symmetrical Kullback-Leibler divergence (KLD; a divergence measure to compare two probability distributions) using the philentropy::kullback_leibler_distance() function (Drost 2018). To study the correlation structure across LUI metrics and compare it across grids, we produced pairplots (scatterplots for each pair of metrics) of the values extracted at the 500 randomly sampled presence/absence points of each virtual species using the package psych (Revelle 2022) and calculated the Spearman correlation coefficient for each pair of metrics.

Species distribution models of the virtual species using LUI metrics

To exemplify how the choice of LUI metric(s) can affect the outcomes of biodiversity models, we modelled the occurrence of the three virtual species using the LUI metrics as explanatory variables. As the virtual species were built based on gridded data, we employed the square grid in this modelling step, as using hexagonal or voronoi grids would introduce an additional bias in the explanatory power of the model. We extracted the values of the LUI metrics from the square grid at the 500 randomly sampled presence-absence points of each virtual species, and we fitted Generalised Additive Models (GAMs) with binomial distribution using the package mgcv (Wood 2011). GAMs enabled us to model nonlinear relationships between the predictors and the response variable, and to test for their statistical significance. We set the smoothing basis dimension (k) of the smoothing functions to five to avoid overfitting (Zingg et al. 2018). Starting from a global model including all ten LUI metrics as predictors, we performed automatic model selection using the MuMIn::dredge() function (Barton 2022), which ranks all nested models of the global model by their Akaike Information Criterion score corrected for small sample size (AICc). Highly correlated metrics, i.e. with Spearman’s |R| ≥ 0.7, were excluded from the same model (Dormann et al. 2013). From the model selection table, we extracted the best (with lowest AICc) overall model as well as the best models when one of the three LUI dimensions was not represented, i.e. when all metrics related to one LUI dimension were excluded from the model. The goodness of fit of the models was checked via diagnostic plots of the model residuals using the DHARMa package (Hartig 2022). We checked that model residuals were not spatially autocorrelated via spline correlograms using the ncf package (Bjornstad 2022).

Results

Spatial disagreement of LUI values across metrics and grids

The computed LUI maps were very different across metrics (Fig. S2–S4). The standard deviation across the values of the ten LUI metrics revealed large areas with high disagreement across metrics (Fig. 1, upper panel): grid-cells with standard deviation ≥ 0.3 constituted 35% of all grid-cells in the square grid, 34% in the hexagonal, and 24% in the voronoi grid. However, no clear spatial pattern in the hotspots of cross-metric divergence emerged. High standard deviation values were found in the more intensively used areas in the north and centre of the study region, as also in the southern part, which consists of a mix of managed and semi-natural (mostly forested) lands, and at the outer borders of urban agglomerations (Fig. 1, upper panel). The bivariate choropleth maps of the absolute difference in LUI values across different grid types showed great divergences in the values of the same LUI metric depending on the choice of spatial aggregation method (Fig. 1, lower panel; Fig. S5). Spatial patterns of cross-grid divergence varied depending on the LUI metric: UAA, Arable_UAA, and N_input had low cross-grid disagreement in the central area of the region, where intensive agriculture prevails (Fig. 1; Fig. S5). In turn, LULC_homog values were highly variable across grids throughout the study area (Fig. 1), indicating a particularly strong effect of the type of grid on the calculation of this metric.

Fig. 1
figure 1

Upper panel: standard deviation across the values of the ten LUI metrics, calculated at the grid-cell level for each of the three grids. Lower panel: bivariate choropleth maps of the absolute difference between LUI values calculated using the square (SQ) and the hexagonal (HX) grids, and between the square and the voronoi (VO) grids, extracted at randomly sampled point locations, for three exemplary LUI metrics (see Fig. S5 for the other seven LUI metrics). The nine colour classes of the bivariate choropleths are based on equally-sized intervals in the range of values of the absolute cross-grid differences. Grid-cells with utilised agricultural area equal to zero, or points falling therein, were masked out

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Comparison of LUI values across metrics and grids at the sampling points of the virtual species

The random sampling of the virtual species’ occurrence returned 215,99 and 204 presences for the arable land, the grassland and the wetland species, respectively, out of 500 sampled grid-cells. The density distributions of the values of different LUI metrics at the presence points of the three virtual species showed significant differences (Fig. 2, Fig. S6). For example, Arable and Field_size peaked at low intensity levels (close to zero), whereas ALU_homog encompassed generally higher values (above 0.4) at the presence points of the virtual grassland species (Fig. 2). Cross-grid differences were also evident, as the shapes of the density distributions varied importantly across grids for certain metrics (e.g. Arable_UAA, ALU_homog, LULC_homog). The density distribution of values for Field_size is extremely skewed towards zero: this is because only a few grid-cells in the study area had very high values of the metric (Figs. S2–S4), and neither of those were randomly sampled among the presence points of the virtual species. Similar considerations apply to the density distributions of LUI values at the presence points of the other two virtual species, though with less marked cross-grid variations in the case of the arable land species (Fig. S6).

These differences were reflected also by the symmetrical KLD, which varied greatly across pairs of metrics and grids (Tables S1–S3). Differences were generally larger across metrics within the same grid than across different spatial aggregations of the same metric. The four metrics related to landscape structure scored comparatively high KLD values at the presence points of the grassland and the wetland species (Tables S2–S3), while for the arable land species Field_size scored consistently high KLD values (Table S1), indicating that density distributions of landscape structure metrics diverged more from the other LUI metrics.

Fig. 2
figure 2

Density distributions of the LUI metrics extracted at the 99 presence points of the virtual grassland species, shown by grid type. The x-axis indicates the value of each metric (with higher values indicating higher LUI); the y-axis indicates the density (frequency) of data points along the LUI gradient. All metrics were scaled between 0 and 1 to ease cross-metric comparisons. Different colours define the different quantiles in the distribution of the sampled values. True sampled values are shown by red dots along the x-axis and fall within the value range [0,1], while the estimated density distribution may exceed these range limits

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The pairplots of the LUI values extracted at the 500 randomly sampled locations revealed highly-varying rank correlation structures across LUI metrics, including both positive and negative correlations (Fig. S7–S15). However, only few pairs of metrics had a very high absolute Spearman correlation coefficient with absolute values > 0.7, which is the most commonly used threshold for excluding highly correlated variables from the same model to avoid distortions in the model evaluation and subsequent interpretation of the effects of each predictor variable (Dormann et al. 2013).

Species distribution models of the virtual species

For each of the three virtual species, the overall best model (with lowest AICc) correctly identified the true drivers of the species’ distribution (Table 2) and described the shapes of the underlying species-environment relationships with fair accuracy (Fig. 3; Figs. S16–S17). The best overall model for the wetland species also included a fourth predictor (Field_size, not utilised in the virtual species’ design), but this was not statistically significant. The exclusion of LUI metrics describing land management from the modelling framework did not affect the correct identification of the other drivers of the species occurrence and led to minor decreases in the adjusted R² for all virtual species (Table 2). When excluding landscape-structure metrics, the best models for the grassland and the wetland species failed to detect the effect of the land-management metrics (Intens_f and Conv_farm, respectively) that were used in the construction of the two species (Table 2). Excluding land-use metrics deteriorated the explanatory power of the models of the grassland and wetland species the most, with a large decrease in adjusted R2. For all three species, the models without land-use metrics included the true drivers of each species’ distribution relating to land management and landscape structure, although the depiction of certain species-environment relationships by the smooth functions were less accurate (e.g. modelled hump-shaped effect of LULC_homog on the grassland species’ occurrence, Fig. 3).

Table 2 Best GAM models explaining the occurrence of the three virtual species, constructed using metrics from all (“best overall”) LUI dimensions, or by omitting metrics related to one LUI dimension (“no land management”, “no landscape structure”, “no land use”)
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Fig. 3
figure 3

Plots of the true response curves of the virtual grassland species, and of the component smooth functions of the top-ranking GAM models constructed using metrics describing all (best overall) LUI dimensions, or by leaving out metrics related to one LUI dimension. Shading shows the confidence interval of the smooth functions. The y-axes are labelled s(pred, edf) where pred is the predictor name, and edf are the estimated degrees of freedom of the smooth. The range of the y-axes is kept constant to ease cross-model comparisons. Statistical significance of the predictors is shown at the 0.05 (∗) and 0.001 (∗∗∗) levels

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Discussion

A better understanding of the relationship between biodiversity and agricultural LUI is urgently needed in order to reduce the trade-offs between food production and nature conservation (Semenchuk et al. 2022). Here, we addressed one of the main challenges in this context, namely quantifying LUI in a spatially-explicit and continuous manner across heterogeneous agricultural regions for applications in biodiversity modelling. We focused on agricultural systems (though similar caveats likely apply also to forestry systems) and used established metrics to map LUI in a typical agricultural region in Germany. Our aim was to test how the choice of metric and spatial aggregation unit affects the quantification of LUI across space, and ultimately the outputs of biodiversity models. Our results showed that the different LUI metrics varied considerably in terms of estimated intensity levels for the same spatial units (Figs. S2–S4). We found large spatial variability in LUI values across metrics and across grids (Fig. 1), showing that the disagreement among LUI metrics is not constant in space. We also showed that LUI values at the sampling locations of (virtual) biodiversity data varied significantly depending on the chosen metric and spatial unit (Fig. 2 and S5; Tables S1–S3), with correlation structures between metrics encompassing both positive and negative associations (Figs. S7–S15). Finally, we exemplified that the lack of representation of certain LUI dimensions in biodiversity models can lead to erroneous conclusions regarding the strength, significance, and shape of the investigated LUI-biodiversity relationships, as was the case for two out of the three virtual species that we modelled (Fig. 3 and S17). As already stated by other researchers (e.g. Dullinger et al. 2021), the LUI concept is complex and multidimensional, and thus needs to be fully represented in biodiversity models. Our findings confirmed that metrics related to different characteristics of agricultural landscapes (e.g., land use, land management, and landscape structure) can vary almost independently of each other: while agricultural intensification is generally leading towards larger monoculture fields, more intensively used (higher inputs and outputs) land, and more homogenised landscapes, the three processes are not always co-occurring (Kuemmerle et al. 2016). Moreover, these processes may act at different spatial scales (Azaele et al. 2015; Spake et al. 2021) and may have interactive effects on biodiversity (Spake et al. 2023). Failure to take into account this multitude of intercorrelated processes can distort our conclusions about the impacts of LUI on biodiversity, with potentially serious consequences if wrong conclusions are translated into policy recommendations.

LUI conceptualisations in the context of biodiversity modelling

Many of the challenges outlined in this study are associated with the multidimensionality of LUI and its different existing conceptualisations (Dullinger et al. 2021). In this study, we referred to the framework presented by Firbank et al. (2008), as we found this to be a particularly useful conceptualisation for biodiversity research in agricultural landscapes. This framework identifies land use, land management, and landscape structure as the most important classes of drivers of species distribution in farmland, each of which describing different aspects of LUI. Strictly speaking, land use and landscape structure are not direct proxies of LUI according to the definition by Kehoe et al. (2015). While several studies attempted to precisely quantify LUI in comprehensive ways, e.g. by including multiple land-management factors describing input and harvest intensity (Billeter et al. 2008; Felipe-Lucia et al. 2020; Le Provost et al. 2021; Semenchuk et al. 2022), many others, especially when they cover large regions, as in continental or global analyses, employed simple land-use metrics to quantify LUI (e.g. Pekin and Pijanowski 2012). On the other hand, certain studies quantified LUI based solely on landscape-structure metrics (e.g. Breitbach et al. 2010; Li et al. 2023). In this context, the Firbank framework effectively integrates management-related variables with landscape characteristics (land use and landscape structure), both of which shape habitat availability and quality for a given species.

Output metrics, such as agricultural yield and net primary productivity (NPP), and system-level metrics, such as human appropriation of NPP, are also popular LUI indicators (Dullinger et al. 2021). We did not include them here as, from a biodiversity perspective, agricultural outputs, or human consumption thereof, are not directly affecting biodiversity in any way, but it is rather the management actions undertaken to achieve them that impact ecological processes and species distributions (Kleijn et al. 2012). Ultimately, the choice of LUI conceptualisation, and therefore of representative LUI dimensions and metrics, depends on the research question at hand, but we encourage researchers to explore different LUI conceptualisations, which should help guiding their choice of relevant metrics, and to ultimately adopt a more comprehensive view of LUI.

Differences between grid types for representing spatial LUI patterns

We explored how the use of different grids for aggregating spatially continuous LUI metrics led to significant differences in the quantification of LUI values at specific locations, like the occurrence points of the virtual species (Fig. 1 and S6). These differences will likely translate into differences in modelled LUI-biodiversity relationships. Unfortunately, as the virtual species was built on raster (square) data, modelling it using the hexagonal or the voronoi grid would add another level of uncertainty to the models, which could confound our results. This meant that we could not compare modelling results across different grid types, as the modelling step was performed solely using LUI metrics from the square grid. As in our example, oftentimes the choice of grid depends on the nature of the available biodiversity data, as response and explanatory variables should, whenever possible, match in their spatial unit of measure. The square grid, most frequently used in ecology, is a logical choice when the biodiversity data have been collected in square plots, as is often the case (Birch et al. 2007). However, in other situations, researchers should carefully consider which grid type is to be preferred (and whether a grid system is a sensible choice at all). For example, the hexagonal grid offers advantages over square cells in terms of neighbourhood distances (Noori et al. 2021), and is thus preferable for connectivity studies and movement path applications (Birch et al. 2007). Moreover, the hexagonal grid minimises geographical distortions in distances, shapes and areas caused by map projection, making it suitable for global analyses (Barreto et al. 2019). Irregular tessellation methods like the voronoi grid are generally unpopular in ecology, but can offer a more realistic representation of the mosaic structure of agricultural landscapes compared to regular grids (Langhammer et al. 2019; Thiele et al. 2023). Even when the exact geometries of field parcels are available, the voronoi tessellation is a practical solution for large-scale studies, where a more simplified and spatially continuous representation of the landscape (which includes non-agricultural areas between fields) can reduce computational effort by generalising complex field geometries to simple polygons (e.g. Beltran et al. 2022). These considerations apply not only to the estimation of LUI spatial patterns, but have broad applications in landscape ecology studies especially when designing new monitoring schemes. For example, hexagonal grids have been used to decide where to deploy camera traps (Naidoo and Burton 2020) and bioacoustic devices (Smith et al. 2021). Voronoi grids have been used to test alternative spatial sampling designs for insect monitoring in agricultural settings (Thiele et al. 2023), to estimate the total cultivated land per farmhouse, when such data is not available or accessible from cadastral sources (Ibrahim and Johansson 2022), and also to approximate the territory size and density of breeding birds from known locations of their nests (Fernández-Gil et al. 2023).

Towards an improved representation of LUI patterns in biodiversity research

We found great divergences among commonly used LUI metrics (Figs. 1 and 2), underlining that using a single metric of LUI is often inappropriate to advance our understanding of complex biodiversity-LUI relationships. Even studies that use multiple LUI metrics but do not consider different LUI dimensions may ultimately provide a biased picture of land-use related drivers of biodiversity patterns. In our virtual species examples, not taking the landscape structure metrics into account in the SDM masked the negative effect of Intens_f and of Conv_farm on two (grassland and wetland species) out of the three modelled species (Table 2). This type of omission (i.e. not accounting for landscape structure when investigating land-use and land-management effects) is not infrequent in biodiversity studies (e.g. Vermaat et al. 2007; Diekötter et al. 2014; Oliver et al. 2016; Zingg et al. 2018), which motivated us to exemplify potential consequences of omitting important confounding variables in such models. The SDMs of the arable land species, which was designed to select for large arable fields with low nitrogen input, on the other hand were not as strongly affected by the omission of landscape structure metrics (nor other LUI dimensions). Their exclusion from the models led to only minor decreases in adjusted R2 and did not impair the identification of the other drivers of the species occurrence (Table 2). Indeed, certain open-land species may be less strongly affected by landscape simplification, as woody features and hedges do not provide suitable habitat for them (Gayer et al. 2019). Such cross-species variations in our findings shows that relevant explanatory variables in biodiversity models should be grounded in ecological knowledge of the focal organism.

Based on our results, we recommend biodiversity researchers to include multiple metrics reflecting different LUI dimensions in their analyses, especially when their primary aim is to understand LUI-biodiversity relationships. One option towards a more inclusive representation of LUI is using composite indices. For example, a tool to obtain a composite LUI index based on information from land owners on mowing, grazing and fertilisation was recently developed for the German Biodiversity Exploratories (Ostrowski et al. 2020). However, such detailed information from farmers is not always available or accessible, especially when modelling larger regions encompassing multiple farms. Moreover, aggregated indices can be difficult to interpret: biodiversity, as exemplified in our analysis, can show contrasting responses to different dimensions of LUI, and a composite index is likely to blur causal relationships between components of intensity (Herzog et al. 2006). In this sense, using multiple separate metrics, whenever available, is a more transparent and readily interpretable approach.

Life-cycle assessment (LCA) methods are an alternative way to estimate agricultural impacts on biodiversity. Expert-based LCA approaches are based on inventory data on crops, semi-natural habitats and management practices, whose effects on biodiversity are estimated from the literature and expert knowledge (Jeanneret et al. 2014). Such methods have also been extended by adding habitats and practices specific to vegetable production systems for crop-specific impact assessments (Pépin et al. 2023). However, these methods also rely on the availability of detailed information on employed management practices and on-farm activities, which is often not the case.

Challenges and solutions in compiling field-level LUI data across large areas

We here compiled a short, non-exhaustive list of commonly used LUI metrics (Table 1). While land-use and landscape-stucture information can be compiled through field-work or by using one of the many available land-use/land-cover products (e.g. Preidl et al. 2020; Malinowski et al. 2020), the selection and use of land-management metrics are instead often limited by data availability. Detailed information on e.g. fertiliser input, irrigation, livestock density, ploughing and mowing frequencies are often lacking or subject to stringent data sharing agreements. Spatially explicit, detailed management data is collected at the farm level through the Integrated Administration and Control System (IACS; European Commission 2023), the Farm Structure Survey (FSS; Eurostat 2022) and the Farm Accountancy Data Network (FADN; European Commission 2020) across the European Union. Getting access to this data, however, is difficult and time consuming due to stringent privacy and data sharing policies. This data is a very valuable resource for researchers, as it allows them to precisely quantify certain LUI components.

Recent developments in the fields of remote sensing and artificial intelligence can help in bridging this data gap: for example, maps of mowing frequency, grazing intensity and fertiliser application based on satellite data are now available (Schwieder et al. 2022; Lange et al. 2022), similar products may be developed for estimating time and frequency of ploughing events (Voormansik et al. 2020), and new methodologies for irrigation mapping using Synthetic Aperture Radar data have been proposed (Gao et al. 2018). Additionally, remote sensing is a valuable source of data for the development of metrics related to vegetation structure (Moudrý et al. 2023). For example, an index of temporal variation in vegetation height during the growing season was recently used as LUI index by Li et al. (2023), while Josefsson et al. (2017) suggested that crop structural diversity may be a better predictor of biodiversity patterns than the typically used crop diversity (equivalent to ALU_homog in our study).

Our study included four metrics pertaining to landscape structure, ALU_homog, LULC_homog, LC_homog and Field_size. The differences in correlation structures, describing both positive and negative relationships (Figs. S7–S15), and in spatial patterns (Figs. S2-S4) among the three homogeneity metrics shows that the choice of land-use/land-cover product used as basis for their calculation can dramatically influence the quantification of landscape homogeneity. Indeed, crop diversity and land cover diversity are different aspects of landscape structure that can affect biodiversity in different ways. Interestingly, we found many studies including measures of crop diversity (Sirami et al. 2019; Stjernamn et al. 2019; Martin et al. 2020) and of land-cover heterogeneity (treating cropland as a single land-cover class; Tuck et al. 2014; Le Provost et al. 2021). On the contrary, only few studies measured the diversity of both crop and semi-natural cover, either in a single metric (as in Gaba et al. 2010) or in multiple ones (as in Billeter et al. 2008). Since different crops and semi-natural covers can provide species with spatially- and temporally-varying resources, this often overlooked landscape diversity measure could be an important factor to consider in future biodiversity models.

Conclusion

Understanding and modelling the effects of LUI metrics on farmland biodiversity is a very current research topic that has important policy consequences in the progress towards a more sustainable development of the agricultural sector. A realistic and reliable representation of LUI spatial patterns across large heterogeneous regions is one of the main present challenges. In this study, we showed how different LUI metrics can dramatically affect the quantification of LUI, with cascading consequences on biodiversity modelling results. We also highlight that the choice of spatial aggregation unit, which often receives little attention, can importantly affect LUI estimation. We thus recommend that future studies carefully evaluate alternative spatial aggregation units when designing and conducting spatially-explicit studies and include multiple LUI metrics, describing different dimensions, in their analyses. Borrowing from already established conceptualisations of LUI, or designing new ones, may prove useful in adopting a more comprehensive representation of LUI in biodiversity models and in supporting the selection of LUI metrics to be included in a particular study. Improved access to detailed farm-level management and land-use data as well as advances in remote sensing-derived products are important tools to improve our understanding of the complex relationship between biodiversity and LUI, which will ultimately help to design more targeted and effective conservation policies for agroecosystems.