Anne Mcleod

Shawn Leroux

Chelsea L Little

François Massol

Eric Vander Wal

Yolanda F Wiersma

Isabelle Gounand

Loeuille Nicolas

Eric Harvey
email: eric.harvey@uqtr.ca

Nicolas Loeuille

Eric Harvey

Studying the spatial structuring of chemical elements through the prism of community and landscape ecology

Keywords: meta-ecosystem, zoogeochemistry, biogeochemistry, distribution models, ecological stoichiometry, beta-diversity, elemental hotspots

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Introduction

Approximatively 25 chemical elements are essential for the maintenance, growth and reproduction of all living organisms [START_REF] Elser | Organism Size, Life History, and N:P Stoichiometry[END_REF][START_REF] Kaspari | Biogeochemistry and Geographical Ecology: Embracing All Twenty-Five Elements Required to Build Organisms[END_REF]. The field of ecological stoichiometry has made great progress in understanding how some elements (mainly C, N and P) influence biotic community structure and stability through resource competition and stoichiometric imbalance [START_REF] Leroux | Predator-driven elemental cycling: The impact of predation and risk effects on ecosystem stoichiometry[END_REF][START_REF] Sterner | Ecological stoichiometry[END_REF][START_REF] Sentis | Stoichiometric constraints modulate temperature and nutrient effects on biomass distribution and community stability[END_REF].

Most of this research, however, has been conducted at small spatial extents (e.g., lab, mesocosm, field sites; [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF]. Consequently, our basic expectations for the spatial distribution of elements and the drivers of those patterns at larger extents are limited to abiotic components (e.g. bedrock; [START_REF] Kaspari | Biogeochemistry and Geographical Ecology: Embracing All Twenty-Five Elements Required to Build Organisms[END_REF]. To address this gap, researchers in marine (e.g., [START_REF] Galbraith | A simple nutrient-dependence mechanism for predicting the stoichiometry of marine ecosystems[END_REF], freshwater (e.g., [START_REF] Collins | Lake nutrient stoichiometry is less predictable than nutrient concentrations at regional and sub-continental scales[END_REF], and terrestrial (e.g., [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF] ecosystems are developing spatially explicit tools and methods for predicting spatial patterns in elements at landscape/seascape extents.

Patterns of elemental abundance in geographic space are the result of the combined feedbacks of passive abiotic flows and biotic ecosystem components (e.g., animal transport and deposition of materials). Biotic influences on a landscape are expected to generate a patchy elemental distribution characterized by areas with elemental hotspots and coldspots [START_REF] Bernhardt | Control points in ecosystems: moving beyond the hot spot hot moment concept[END_REF][START_REF] Mcinturf | Vectors with autonomy: what distinguishes animal-mediated nutrient transport from abiotic vectors?[END_REF]. For example, [START_REF] Mcintyre | Fish distributions and nutrient cycling in streams: can fish create biogeochemical hotspots[END_REF] demonstrated that the spatial distribution and nutrient excretion of a diverse neotropical fish community can influence the elemental distribution of N and P availability in streams and that these neotropical fish communities can influence the distributions of N and P very differently. To scale up the study of elemental distribution to regional extents, [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF] proposed stoichiometric distribution models (StDMs) -statistical models akin to species distribution models that make spatially explicit predictions of elemental patterns. Stoichiometric distribution models generate spatial maps of elements based on the measured relationship between elements and environmental parameters (e.g., elevation, land cover), thus filling an important gap in measuring elements across a whole landscape. Such elemental maps can then be used readily to study spatial patterns of specific elements (e.g., percent C or N) or their ratios and can be linked to patterns of resource quality (e.g., [START_REF] Heckford | Spatially explicit correlates of plant functional traits inform landscape patterns of resource quality[END_REF].

Building expectations on what spatial patterns in elements should look like, how they relate to landscape features, and how they relate to the other biotic components of ecosystems is not trivial. There is considerable variation in how different plant and animal species respond to and consequently affect their environment -the scale of these effects is species-specific (see review in [START_REF] Doherty | Coupling movement and landscape ecology for animal conservation in production landscapes[END_REF] and demonstrate hierarchical patterns within a species (e.g. [START_REF] Mayor | The spatial structure of habitat selection: a caribou's-eye-view[END_REF]. For example, small mammals, such as snowshoe hares or meadow voles have a relatively small home range and short daily movements (e.g., [START_REF] Rizzuto | Forage stoichiometry predicts the home range size of a small terrestrial herbivore[END_REF]. Thus, these smaller mammals interact with their environment at smaller scales than larger mammals (e.g., [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF]. The consequences of this smaller environmental footprint mean they may contribute to more localized hotspots of nutrients. Larger mammals, such as moose, use an environment several orders of magnitude larger than hares or voles in boreal forests (e.g., [START_REF] Balluffi-Fry | Quantity-quality trade-offs revealed using a multiscale test of herbivore resource selection on elemental landscapes[END_REF]. Through a larger home range and longer daily movements, these larger animals can potentially create larger hotspots of nutrients or more dispersed nutrient hotspots than animals with small home-ranges (e.g., around den sites; [START_REF] Gharajehdaghipour | Arctic foxes as ecosystem engineers: increased soil nutrients lead to increased plant productivity on fox dens[END_REF]. Movement is just one example of how a biotic component of an ecosystem may impact elemental distributions across spatial scales, another example is demographic processes such as the aggregation or over-dispersion of individuals. A tree (e.g., balsam fir) seedling may extract water and limiting nutrients from a small area of soil surrounding its shallow roots whereas an adult tree will extract these resources and affect a much larger area [START_REF] Olesinski | Effects of soil moisture manipulations on fine root dynamics in a mature balsam fir (Abies balsamea L. Mill.) forest[END_REF].

Alternatively, these plants and animals could be homogenizing resource distributions across their home ranges by depleting hotspots that arise from abiotic influences.

The effects of these biotic ecosystem components on elemental distribution can have a temporal component as well -foraging for resources whether by the root systems of plants or daily movements of animals, are on a shorter temporal scale then dispersal and migration (e.g., [START_REF] Massol | How life-history traits affect ecosystem properties: effects of dispersal in meta-ecosystems[END_REF]. In this way a feedback develops both temporally and spatially, further complicating spatial elemental patterns. For example, Pacific salmon spawning creates a pulse of nutrients every fall (hotspot), which is subsequently used by plants and gradually depleted (cold spot) until the next nutrient pulse [START_REF] Helfield | Effects of salmon-derived nitrogen on riparian forest growth and implications for stream productivity[END_REF]. Meanwhile, abiotic features of ecosystems can also lead to patterns that depend on scale. At a broad spatial and temporal extent, weathering of bedrock contributes to the elemental pool, which then get distributed via abiotic and biotic mechanisms. For example, local hotspots of inorganic nitrogen in soils may develop beside streams and rivers where ground and surface water mix, converging chemically distinct flow paths [START_REF] Edwards | The hyporheic zone[END_REF]. Human activities are significantly modifying both biotic [START_REF] Díaz | The global assessment report on biodiversity and ecosystem services: Summary for policy makers[END_REF] and abiotic [START_REF] Pörtner | Climate change 2022: Impacts, adaptation and vulnerability[END_REF]) components of ecosystems with potential knock-on effects on the distribution and flux of elements (see [START_REF] Tucker | Moving in the Anthropocene: Global reductions in terrestrial mammalian movements[END_REF] for examples of how human activities have modified the movement of biotic ecosystem components). Consequently, developing tools or methods to measure and quantify how spatial patterns in elements vary across spatial grains is critical to diagnose how ecosystems are being shaped by the current era of rapid change.

Here, we apply tools from community and landscape ecology to study spatial patterns in elements (Fig. 1). We aim to explore how spatial grain and spatial dissimilarity of elements interact, leading to predictable patterns in elemental distributions at various spatial scales. In particular, because the distribution of elements across the landscape are the result of combined element-specific feedbacks of passive abiotic flows and biotic ecosystem components, we demonstrate how dissimilarity metrics offer a unique way to synthesize how multiple elements vary independently across spatial gradients. We illustrate this framework with an empirical proof of concept in the boreal forest. This proof of concept integrates models of the distribution of elements in birch foliage across two landscapes [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF] with macro-ecological smoothing techniques [START_REF] Patrick | The challenges that spatial context present for synthesizing community ecology across scales[END_REF] and dissimilarity analyses to investigate the elemental diversity and variation across spatial grains. We first a) generate stoichiometric distribution predictions for N, P, Ca, K, and Mg in birch foliage for our two landscapes. We then b) use community ecology approaches to explore elemental dissimilarity in elemental content across spatial scales, and c) identify potential elemental hotspots/coldspots including d) the critical elements contributing to landscape uniqueness, i.e., hotspots or coldspots. Specifically, we would expect dissimilarity to increase and asymptote at a landscape level dissimilarity value as it is broadly driven by geological processes. We would expect hotspots/coldspots to become more homogeneous across the landscape as spatial grain increases and geological processes dominate biotic processes paralleled with a decrease in amount of core area for critical elements contributing to landscape uniqueness.

Using community and landscape ecology to study spatial patterns in elements: conceptual underpinning

We outline our empirical framework and proof of concept in three steps. We begin with a brief description of our study system and stoichiometric distribution models (sensu [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF] as applied to this system. Next, we outline our application of tools from community ecology to quantify different components of beta diversity applied to our proof of concept [START_REF] Anderson | Navigating the multiple meanings of β diversity: a roadmap for the practicing ecologist[END_REF][START_REF] Legendre | Beta diversity as the variance of community data: dissimilarity coefficients and partitioning[END_REF]. Finally, we borrow metrics from landscape ecology (e.g., [START_REF] Wang | Measuring habitat fragmentation: An evaluation of landscape pattern metrics[END_REF] to measure how dissimilarity of elements varies across spatial grains in our proof of concept.

Proof of concept and stoichiometric distribution models

For our proof of concept, we focused on two boreal forest landscapes (i.e., study areas), hereafter called Plum Point and Old Man!s Pond, on the island of Newfoundland, Canada (see Supplementary Information 1, Fig A1 for map of study area locations). We clipped foliage samples from the browse height available to boreal forest herbivores (i.e., leaves and small stems from between 0.3 and 2 m) of 1 to 6 small trees (i.e., < 3 m) within 10 m radius plots across 106 plots at Plum Point between June 30 and July 7, 2015 (see [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF][START_REF] Balluffi-Fry | Quantity-quality trade-offs revealed using a multiscale test of herbivore resource selection on elemental landscapes[END_REF] for more details on field sampling). We used birch trees (Betula papyrifera) < 3 m as part of these data were originally designed to ask questions about moose foraging and moose only forage on trees < 3 m. We expect these foliage samples to be indicative of bioavailable elements for herbivores. In particular, white birch is the primary summer forage for moose and snowshoe hares [START_REF] Dodds | Food competition and range relationships of moose and snowshoe hare in Newfoundland[END_REF], some of the major herbivores in this system, and thus white birch foliage serves as a proxy for bioavailable elements on the landscape. Focusing on this tree size, also allows us to control for the possibility that trees of different sizes may differ in their elemental composition. Foliage samples were pooled at the plot level and analysed for N, P, Ca, K, Mg (see [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF] for further details on sampling design and Supplementary Information 1 for details on chemical analysis). We focused on these five elements because they are part of the twenty-five elements essential for life and are among the most studied elements in ecological stoichiometry [START_REF] Jeyasingh | Testing the ecological consequences of evolutionary change using elements[END_REF], are critical for metabolic activity [START_REF] Kaspari | Biogeochemistry and Geographical Ecology: Embracing All Twenty-Five Elements Required to Build Organisms[END_REF], and frequently reported in studies of the ionome (or the mineral nutrient and trace element composition of organisms; [START_REF] Parent | The plant ionome revisited by the nutrient balance concept[END_REF]. We omit carbon in our analyses because the stoichiometric distribution models for Carbon had a poor fit (see Fig A2 andTable A1(a) for model fit details). We focus only on N, P, Ca, K, and Mg, however, the approach presented here could be applied to a broader suite of elements. Further, while we demonstrate the utility of this approach in a focused proof of concept on the bioavailable elements in foliage samples, a similar approach to the one presented here could be applied to elements in the soil, other important forage, and other animals and would improve insights into the generality of the patterns observed here. The emergence of synthetic databases of the elemental composition of soils and diverse organisms (e.g., https://stoichproject.wordpress.com/stoich/the-stoich-project/about-thedatabase/)) may facilitate applications of our approach to different case studies.

Using this white birch foliage chemical composition and methods described in [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF], we fit StDMs to each element from the Plum Point study area. These StDMs are statistical models that describe foliar elemental composition using environmental and biotic covariates aimed at predicting correlations in organismal stoichiometry. We then extrapolate elemental composition across Plum Point and Old Man!s Pond landscapes from the correlations in sampled sites of elemental composition with environmental covariates [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF].

Composition of white birch foliar proportions of mass of N, P, K, Ca, and Mg (i.e., elemental composition; %) were the response variables. Predictor variables included three continuous landscape covariates (i.e., normalized aspect or orientation of slope, slope and elevation), and three categorical landscape covariates (i.e., landcover [coniferous, deciduous or mixedwood], stand (canopy) height, and dominant tree species). For more details on StDM model fits, sample design, and chemical analysis see Supplementary Information 1. We retained the full model for each stoichiometric response to predict white birch across the landscape (R 2 for full models were 0.31, 0.42, 0.39, 0.13, and 0.27 for N, P, K, Mg, and Ca, respectively; see Table A1 and Fig. A3 -A7 in Supplementary Information 1 for specific details on StDM model fits). Using a raster for each discrete covariate, we then developed stoichiometric composition predictions for foliage in each cell. We then transformed the elemental compositions using a chord transformation [START_REF] Legendre | Ecologically meaningful transformations for ordination of species data[END_REF] based on the guidelines by [START_REF] Legendre | Beta diversity as the variance of community data: dissimilarity coefficients and partitioning[END_REF] for community composition data, of which our elemental composition data is akin (see Fig. A10 for scaled elemental composition in the two study areas). In particular, this means that we can calculate elemental dissimilarity using the techniques described in [START_REF] Legendre | Beta diversity as the variance of community data: dissimilarity coefficients and partitioning[END_REF] without violating any assumption of these approaches.

Elemental dissimilarity across the landscape

An important concept in community ecology is how species diversity is organized across spacea concept for which many metrics have been developed including alpha and beta diversity. By applying species diversity concepts to elemental composition across space, we can determine if elemental composition varies across space in a predictable fashion. Despite many alpha-diversity metrics incorporating both species richness and evenness, the constraints on both elemental diversity and evenness mean that alpha-diversity is too coarse a metric to describe elemental distributions appropriately across the landscape. As an explicit metric of variation, however, Bray-Curtis dissimilarity (or variation in elemental composition between cells across the landscape) is sensitive to deviations in evenness. Therefore, we applied dissimilarity metrics to the transformed StDMs to examine stoichiometric variability across landscapes.

Before computing dissimilarities, we applied a macroecological spatial smoothing approach (MESS), described in [START_REF] Patrick | The challenges that spatial context present for synthesizing community ecology across scales[END_REF]. This approach consists of applying a sliding window across a landscape wherein each spatial window resampling and summarizing of local observations occurs. To apply the MESS approach, a spatial grain (s) for the sampling regions is selected, the number of random subsamples (n) of a given sample size (ss) of local cells within that sampling region is specified, along with the minimum number (mn) of local cells in a given sampling region (see Fig. 1). Using the inset in Fig. 1 as an example we would sample 6 subsamples (ss) of each window of size s and do this 3 times (n). By resampling the sub-samples in this way we remove the impact of outliers (see [START_REF] Patrick | The challenges that spatial context present for synthesizing community ecology across scales[END_REF]. Similar to [START_REF] Patrick | The challenges that spatial context present for synthesizing community ecology across scales[END_REF], we employed a series of analyses to optimize the sample size (ss) and number of random sub-samples (n) required to ensure sufficient sampling is done to determine the value of the dissimilarity metric with appropriate accuracy (essentially where the changepoint in variation around the Bray-Curtis dissimilarity metric occurred was deemed sufficient sampling; see Fig. A8 and A9 in Supplementary Information 2 for results). Our optimal sample size was 11 (mn = 1.5×ss as per Patrick & Yuan 2019), a n of 7, and a spatial grain increasing sequentially from a grain size of 500 m to 5000 m in intervals of 200 m. Dissimilarity metrics are then computed for each random subsample of the region, typically averaged within each region. We calculated total community composition variance as proposed by [START_REF] Legendre | Beta diversity as the variance of community data: dissimilarity coefficients and partitioning[END_REF] as our dissimilarity metric which returns values between 0 (completely similar cells) and 1 (very dissimilar cells). In this way, we would expect Bray-Curtis dissimilarity to be unaffected by grain size if there is no underlying pattern in elemental distributions, increasing if there is an underlying gradient in elemental distributions, and increasing much more rapidly if elements are aggregated in large patches (see Fig. 2a). Finally, we compared the empirical patterns qualitatively to a null model by randomly shuffling longitude and latitude couplets across elemental percentages and then re-running all analyses on the random data set (100 iterations).

Identifying hotspots and coldspots of elemental dissimilarity across the landscape

We can extend our proof of concept to characterize cell uniqueness per study area in terms of elemental contributions by applying the approach presented by [START_REF] Legendre | Beta diversity as the variance of community data: dissimilarity coefficients and partitioning[END_REF] and extended by [START_REF] Laliberté | Partitioning plant spectral diversity into alpha and beta components[END_REF] (termed local contributions to beta diversity; LCBD). This approach uses sum of squared deviations to characterize individual cells'"contributions to elemental beta diversity:

𝐿𝐶𝐵𝐷 = ∑ " !" # "$% ## &'()* (1)
where

𝑠 $% = '𝑦 $% -𝑦 % ¯*' (2)
and

𝑆𝑆 ()*+, = ∑ ∑ 𝑠 $% - %./ 0 $./ (3)
Where i is cell and j is element, and y is elemental percentage. As such, this metric identifies the cells that contribute more or less than the mean to beta diversity, acting as a comparative indicator of cell uniqueness with larger LCBD values indicating cells that are more different in terms of elemental composition. Importantly, this metric has been used to identify hotspots, or cells which have unusually rich species compositions, and coldspots, or cells which are species poor, but does not distinguish between the two [START_REF] Legendre | Beta diversity as the variance of community data: dissimilarity coefficients and partitioning[END_REF][START_REF] Poisot | Hosts, parasites and their interactions respond to different climatic variables[END_REF][START_REF] Laliberté | Partitioning plant spectral diversity into alpha and beta components[END_REF]. We apply this approach to elements to identify unique cells on the landscape -or cells that have unusually high elemental evenness and cells which have unusually low elemental evenness.

Identifying critical elements contributing to landscape uniqueness

By applying the framework presented in [START_REF] Legendre | Beta diversity as the variance of community data: dissimilarity coefficients and partitioning[END_REF] we can tease out site uniqueness across the landscape, and can determine the individual contributions of each element to each site across the landscape. In particular, we can identify patches where a specific element is the most important contributor to elemental diversity (i.e., elemental contributions to beta diversity; ECBD), and explore how the size of these patches change with grain size. For example, if small foraging movements dominate the transport of elements around the landscape at small grain sizes, we may expect a random configuration of very small patches for each element, while if geochemical processes dominate the distribution of elements at larger grain sizes then we may expect much larger patches for each element.

Similar to LCBD, our novel application we term, ECBD, uses a sum of squared deviations approach:

𝐸𝐶𝐵𝐷 = ∑ " !" + !$% ## &'()* (4)
Where sij and SStotal are defined as above. To determine patchiness of elemental contributions, we then applied landscape pattern metrics to determine how patches of elemental contributions vary with grain size, and compared these values to the null model randomizations generated earlier in the analysis.

We applied three spatial pattern metrics -mean core area, perimeter area fractal dimension, and normalized landscape shape index -at the landscape level (see Fig. 2b for examples). These metrics were identified by [START_REF] Wang | Measuring habitat fragmentation: An evaluation of landscape pattern metrics[END_REF] as suitable metrics to differentiate spatial aggregations of landscapes.

Mean core area index is defined as the mean of the core areas of all patches belonging to each landscape class (i.e. N, P, K, Ca, and Mg) where core area is defined as all cells that have no neighbours (queen's case) with a landscape class different from their own. If geochemical processes dominated the distribution patterns of elements at larger spatial grains, we would expect the mean core area to increase with spatial grain whereas if mean core decreases with spatial grain biotic ecosystem components (e.g., foraging) may be the drivers.

The perimeter area fractal dimension is a shape metric describing patch complexity, but is scale independent, and has values between 1 and 2, with values closer to 1 denoting simple shapes and values closer to 2 denoting irregular shapes. If biotic drivers (e.g., foraging movements) were dominating the distribution pattern of elements at finer spatial grains, we may expect shapes with higher overall irregularity (i.e., values closer to 2). However, abiotic drivers such as mixing of surface and groundwater beside streams could also create higher overall irregularity.

The normalized landscape shape index is also an aggregation metric and describes the ratio of the actual edge length of a landscape class to the hypothetical range of possible edge lengths for this landscape class, although note that this landscape index was one of the metrics shown by [START_REF] Frazier | Scope and its role in advancing a science of scaling in landscape ecology[END_REF] to be sensitive to variation in scope. This metric ranges from 0 if only one square patch is present to 1 for a maximally disaggregated (i.e., checkerboard) landscape. If geochemical processes were the only processes driving elemental distributions and they only operated at larger spatial grains, then we would expect the normalized landscape shape index to decrease from a value close to one to a value close to zero as spatial grain increases (Fig. 2b).

Meanwhile, if biotic ecosystem components such as demographic processes (e.g., aggregation and over-dispersion) were the only processes driving elemental distributions we may expect the normalized landscape shape index to increase from a value close to zero (clumping of species at small grain sizes) to a value close to one at large grain sizes.

Finally, for these analyses, the pixel size is 6207.943 m 2 and the ratio of extent to grain (i.e., scope sensu Frazier 2022) is 187,154 and 205,842 for Plum Point and Old Man's Pond respectively.

A Community Ecology of Elements in Practice: Proof of concept results and discussion

Proof of concept and stoichiometric distribution models

The white birch foliage StDMs explained between 13 and 42% of variation in the elemental responses for N, P, K, Mg, and Ca (see Table A1 and Fig. A2 -A6 in Supplementary

Information 1 for specific details on StDM model fits). The estimated percent nitrogen ranged from 1.90 to 3.67%, the percent phosphorus ranged from 0.16 to 0.42%, the percent potassium ranged from 0.24 to 1.61%, the percent calcium ranged from 0 to 0.62%, and the percent magnesium ranged from 0.03 to 0.24% for Plum Point. At Old Man!s Pond the estimated percentages were a little bit higher for all elements except phosphorous. Nitrogen ranged from 1.78 to 3.72%, the percent phosphorus ranged from 0.13 to 0.43%, the percent potassium ranged from 0.33 to 1.70%, the percent calcium ranged from 0.10 to 0.70%, and the percent magnesium ranged from 0.11 to 0.24% (see Supplementary Information 3 Fig. A9 for scaled elemental abundances in both study areas). These values are similar to patterns reported for other study areas on the island of Newfoundland [START_REF] Heckford | Spatially explicit correlates of plant functional traits inform landscape patterns of resource quality[END_REF].

Elemental dissimilarity indices across the landscape

In our proof of concept, we found that elemental dissimilarity increased with grain size, eventually reaching an asymptotic #landscape level dissimilarity" when the grain size kept increasing. The asymptote is the mean of the null model for our two study areas (Fig. 3). The observed increase in dissimilarity with spatial grain mimics relationships already observed for other components of biodiversity estimates. For example, species richness typically increases rapidly at local scales due to a) stochastic variation in species occupancy patterns among cells with more distant patches expected to demonstrate more differences in species composition (e.g.

gradient landscape of Fig. 2a); or b) increasing likelihood of sampling novel habitats as spatial grain increases (e.g., [START_REF] Whittaker | Evolution and measurement of species diversity[END_REF][START_REF] Harrison | Beta diversity on geographic gradients in Britain[END_REF][START_REF] Koleff | The relationships between local and regional species richness and spatial turnover[END_REF]. A variety of different environmental and organismal factors are hypothesized to drive species dissimilarity at various spatial scales ranging from habitat composition and structure at local scales to topology and dispersal limitation at regional scales (see Table 1 in [START_REF] Barton | The spatial scaling of beta diversity[END_REF] for more details).

Due to the way we carried out our analysis, it is unlikely that we are increasing the likelihood of sampling novel elements as spatial grain increases since all elements were found at every site.

Rather, one explanation for what we are observing is a predictable gradient of variation in elemental composition with more distant patches being more dissimilar: as the spatial grain of the analysis increases, we observe an increase in dissimilarity as more dissimilar patches are sampled (e.g., gradient in Fig. 2a vs. large checkerboard).

The trend we observe here between elemental dissimilarity and grain size suggests a similar change in environmental and organismal drivers with scale. For example, organism movement capacity affects species dissimilarity with species moving to track environmental gradients at fine spatial scales [START_REF] Kaspari | Salted roads and sodium limitation in a northern forest ant community[END_REF]. Thus, the rapid increase in elemental dissimilarity with grain size could be related to consumer species distribution and activity including demographic effects, abundance, and consumer movements as they distribute elements across the landscape.

Thus, the plateau at the asymptotic #landscape level dissimilarity" (Fig. 3) could be related to differences between large patches driven by landscape features such as aquatic-terrestrial boundaries, i.e., forest patch along the narrow lake on the southwest side of Old Man!s Pond (e.g.

McClain et al. 2003).

Our example is only one testable hypothesis. Alternate hypotheses could include variation in light availability, moisture, and plant competitors all of which could alter local elemental composition potentially causing a similar increase in dissimilarity at finer grain sizes.

Importantly, the dissimilarity in elements across the landscape can be a cause or a consequence of biodiversity, but in either case, theory on nutrient co-limitations and stoichiometry would suggest that greater elemental spatial turnover is indicative of greater biodiversity [START_REF] Elser | Organism Size, Life History, and N:P Stoichiometry[END_REF][START_REF] Chase | Ecological niches: linking classical and contemporary approaches[END_REF][START_REF] Harpole | Nutrient co-limitation of primary producer communities[END_REF]. For example, if elemental dissimilarity is very low with all elements equally abundant across the landscape, this should lead to biotic homogenization and the dominance by a few species (ones with lower R*, or equilibrium resource level, for the specific homogenous condition). While our study presents some first steps in tackling this question, further studies with species diversity data are needed to tease out these directional relationships. However, recent work suggests that high imbalance in stoichiometric ratios among connected patches (thus higher spatial turnover in elements) can lead to higher productivity at the meta-ecosystem scale because of spatial complementarity in limiting nutrients [START_REF] Pichon | Quality matters: stoichiometry of resources modulates spatial feedbacks in aquatic-terrestrial meta-ecosystems[END_REF].

Identifying hotspots and coldspots of elemental dissimilarity across the landscape

In our proof of concept, we demonstrate that at finer grains, the cells with higher local contributions to landscape dissimilarity (i.e., those that more unique than the average site) cluster together at both Plum Point and Old Man!s Pond as evidenced by the yellow patches present at grain size 500 m (Fig. 4). A grain size of 500 m corresponds to the scales at which organisms feeding on birch leaves are most active in their foraging -for example snowshoe hares have a home range of 0.027 -0.042 km 2 (Rizzuto et al. 2021) while moose have been shown to have daily movements between 0.5 km and 1.1 km depending on the season [START_REF] Hundertmark | Home range, dispersal and migration[END_REF].

Whether these patches of high contributions of dissimilarity are a consequence of biotic processes (e.g., foraging movements) or a cause of these biotic processes is unclear, and likely are the result of a complex feedback between abiotic and biotic processes. Large-bodied organisms can move an impressive amount of nutrients within and across ecosystems [START_REF] Schmitz | Animals and the zoogeochemistry of the carbon cycle[END_REF], which can lead to the expected succession of hotspots and coldspots in the landscape through source-sink dynamics (sensu [START_REF] Loreau | Unifying sources and sinks in ecology and E arth sciences[END_REF] for the extension of the source-sink concept to abiotic fluxes; [START_REF] Mcintyre | Fish distributions and nutrient cycling in streams: can fish create biogeochemical hotspots[END_REF][START_REF] Mcinturf | Vectors with autonomy: what distinguishes animal-mediated nutrient transport from abiotic vectors?[END_REF]. The clustering of cells with high local contributions to landscape dissimilarity at finer grain sizes could be indicative of these source-sink dynamics. Thus, the chain of cause and consequence generating the observed spatial variation in resource elements is being reconsidered in an exciting junction between biogeochemistry, ecosystem and community ecology.

As the grain size increases, however, the landscape becomes more homogenous with a greater number of cells exhibiting an intermediate level of uniqueness, and those cells that are most different are more diffuse across the landscape (Fig. 4). Only two larger patches of more unique cells are observed at a grain size of 5000 m for Plum Point. Meanwhile the more unique cells in both Plum Point and Old Man!s Pond seem to be concentrated around bodies of water at a grain size of 5000 m. One possible explanation for this is a shift in the driver of these hotpots/coldspots from biotic to abiotic drivers, such as landscape features, for example aquaticterrestrial boundaries. Likely, it represents a complex feedback between abiotic drivers, such as the mixing of surface and ground waters at the aquatic-terrestrial boundary converging chemically distinct flow paths [START_REF] Edwards | The hyporheic zone[END_REF], and biotic drivers, such as terrestrial ungulates foraging on aquatic plants (e.g. moose-aquatic plants relationship; [START_REF] Bump | Nutrient release from moose bioturbation in aquatic ecosystems[END_REF]. Future work can apply our method to more completely account for the stocks and flows of elements across scales including measuring the elemental footprints (or combination of nutrient stocks and effects of organisms on stocks) of soils, plants and small and large herbivores.

Identifying critical elements contributing to landscape uniqueness

In our proof of concept, we observed that in both Plum Point and Old Man!s Pond, potassium (K)

and calcium (Ca) are the most important contributors to dissimilarity. This is intriguing as many studies to date have been focused on the contributions of the three more abundant elements -Carbon, Nitrogen, and Phosphorus to biotic community structure and stability (e.g., [START_REF] Leroux | Predator-driven elemental cycling: The impact of predation and risk effects on ecosystem stoichiometry[END_REF][START_REF] Sterner | Ecological stoichiometry[END_REF][START_REF] Sentis | Stoichiometric constraints modulate temperature and nutrient effects on biomass distribution and community stability[END_REF]. Rather what this result suggests is that the distribution of these less abundant, but essential, elements may be just as important for community structure. Specifically, in both study areas K is more often the most important contributor (see Supplementary Information 3 Fig. A11; Fig. 5). In Plum Point, however, Ca becomes increasingly important as grain size increases, while K becomes less important. The converse occurs in Old Man!s Pond where K becomes increasingly more important, but appears to level off at 4000 m. Interestingly, Ca and K are inherently connected in plant nutrition whereby as Ca concentrations decrease, K concentrations increases due to luxury consumption of K and K antagonism whereby K occupies the majority of exchangeable ionic sites [START_REF] Wilkinson | Nutrient interactions in soil and plant nutrition[END_REF]. Moreover, it has been shown that Ca is generally taken up in amounts corresponding to availability rather than plant requirements [START_REF] Knecht | Terrestrial plants require nutrients in similar proportions[END_REF], perhaps explaining the different patterns in the two study areas. Our results highlight the importance of rarely measured elements such as K and Ca for structuring spatial dissimilarity in elements across spatial grains, a result that underscores the difficulties in multi-dimensional ratios given the controversy in ratio approaches for more elements than just N, P, and C [START_REF] Parent | The plant ionome revisited by the nutrient balance concept[END_REF].

There is a decline in mean core area with grain size for both elements in both study areas. The decline is especially pronounced for K in Plum Point (Fig. 5). The decline demonstrates that the landscape gets more homogeneous as grain size increases and occurs most precipitously for Ca in both Plum Point and Old Man!s Pond and then levels out at a grain size of 1500 m for both study areas. These declining trends are reflected in the normalized shape index plots where both elements become less aggregated as grain size increases. However, in the Plum Point study area there is a peak for both K and Ca at a grain size of 2000 m, after which the normalized landscape shape index declines. Elements at Plum Point are therefore least aggregated at grain size of 2000 m, and the landscape becomes more like a single square patch as grain size increases. At Old Man's Pond the normalized shape index reaches an asymptote for both K and Ca at a grain size of ~3000 m. Examining the perimeter area fractal dimension illustrates that, the shapes of elemental patches across the study area become more irregular as grain size increases, contrary to our earlier speculations. One explanation for this could be the increasing importance of abiotic drivers such as confluence of ground and surface waters at aquatic boundaries at larger grain sizes. Grain size contributes to increasing perimeter area fractal dimension irregularity in both study areas, but does appear to asymptote at a grain size of approximately 2000 m for Ca in both study areas. However, it should be noted that the two study areas have a different scope (ratio of range to extent) and [START_REF] Frazier | Scope and its role in advancing a science of scaling in landscape ecology[END_REF] showed that some metrics, including the landscape shape index, which we used here, is highly sensitive to variation in scope. Thus, comparisons between the two study areas may be artifacts of differences in scope.

Much research has determined that elements cluster in two distinct groups based on the competing needs to grow and maintain existing structure [START_REF] Ågren | Plant stoichiometry at different scales: element concentration patterns reflect environment more than genotype[END_REF][START_REF] Zhang | Leaf element concentrations of terrestrial plants across China are influenced by taxonomy and the environment[END_REF]. The first reflects plant growth rate and correlates with nitrogen and phosphorus concentrations -elements critical for the metabolism of nucleic acids and proteins [START_REF] Ågren | Plant stoichiometry at different scales: element concentration patterns reflect environment more than genotype[END_REF]. The second reflects maintaining plant structural components requires K, Ca, and Mg, that are critical for cell walls and might be more important for long-lived slow-growing plants [START_REF] Nakajima | Differential effect of calcium and magnesium on mechanical properties of pea stem cell walls[END_REF][START_REF] Maathuis | Physiological functions of mineral macronutrients[END_REF]. The structural elements appeared to be the most important drivers of elemental dissimilarity in white birch tissue across the landscape in our proof of concept. The ECBD metric does not tell us whether elemental importance is caused by low amounts or high amounts of these structural elements, however evidence suggests that K is rarely limiting and excess K availability can contribute to higher growth rates in plants [START_REF] Maathuis | Physiological functions of mineral macronutrients[END_REF]. Similarly, Ca is usually abundant in the lithosphere, however, Ca concentrations in plants can fall below a critical threshold in fast-growing tissues which can lead to diseases such as blossom end rot in tomatoes [START_REF] Maathuis | Physiological functions of mineral macronutrients[END_REF].

Notwithstanding current challenges in identifying the processes behind elemental importance, the fact remains that we can observe patterns in elemental importance. In meadow systems, studies have shown that in the absence of grazing by sheep, plants become more nutritious with greater concentrations of micronutrients such as Ca [START_REF] Marrs | Release from sheep-grazing appears to put some heart back into upland vegetation: A comparison of nutritional properties of plant species in long-term grazing experiments[END_REF]). In the boreal forest, moose are selective herbivores and could be selectively removing nutritious plants that relatively high in N and P in a similar fashion creating elemental coldspots [START_REF] Pastor | Spatial patterns in the moose-forest-soil ecosystem on Isle Royale, Michigan, USA[END_REF]. Indeed, the observed patterns in elemental importance should have a predictive influence over biodiversity simply because these patterns control the amount of co-limiting nutrients and their spatial turnover [START_REF] Marleau | Emergence of nutrient co-limitation through movement in stoichiometric meta-ecosystems[END_REF]. More specifically, the spatial heterogeneity in resource elements should relate to coexistence dynamics and community structure directly influencing the number of available niches. For example, studies have shown a correlation between plots containing tree species with calcium-rich detritus and a greater diversity and biomass of earthworms [START_REF] Reich | Linking litter calcium, earthworms and soil properties: a common garden test with 14 tree species[END_REF].

Perspectives

Our understanding of how and why chemical elemental concentrations change in space or across scales is currently very poor [START_REF] Kaspari | Biogeochemistry and Geographical Ecology: Embracing All Twenty-Five Elements Required to Build Organisms[END_REF], contributing to poor integration of empirical and theoretical metaecosystem research. The spatial distribution of resource elements, however, reflects element-specific feedbacks of passive abiotic and biotic processes, thus dissimilarity in resource elements may contain much of the information necessary to infer key characteristics of biotic communities, and the expected relationship between those characteristics and ecosystem function [START_REF] Wu | Testing biodiversityecosystem functioning relationship in the world's largest grassland: overview of the IMGRE project[END_REF]. Therefore, identifying spatial patterns in resource elements in the landscape may allow regional scale prediction of community structure, biodiversity, and ecosystem function. Moreover, the analysis of spatial patterns in the fundamental building blocks of all life -elements -can pave the way for greater integration of empirical and theoretical metaecosystem research. Such an integration would open significant new opportunities to finally develop a unified field of spatial ecology, from community to ecosystem and landscape level processes. Disentangling the drivers of these patterns is challenging, especially as the direction of causality is not always intuitive and often involves feedbacks between abiotic and biotic ecosystem components (see [START_REF] Ellis-Soto | A methodological roadmap to quantify animal-vectored spatial ecosystem subsidies[END_REF] for a guide to measuring the biotic component of spatial ecosystem subsidies). Here, we have presented a framework to explore spatial patterns in elemental distributions from foliage samples; however, the approach we present is timely as it corresponds with a time of recent growth in data on elemental composition of soil and diverse organisms across many different biomes. In this way, we provide ecologists with an additional and critical tool for describing ecosystems (see Table 1 for explicit predictions).

Dissimilarity of resource elements may be the result of or may affect food web structure. For instance, we know that elemental hotspots tend to appear at locations in the landscape rich in energy and material exchange (e.g., deep-sea hydrothermal vents), or where different chemical reactants are expected to meet (e.g., ecotone between terrestrial and aquatic ecosystems - et al. 2003;[START_REF] Bernhardt | Control points in ecosystems: moving beyond the hot spot hot moment concept[END_REF]. Different lines of evidence also suggest that organism movement can track those hotspots in the landscape [START_REF] Mcnaughton | Large mammals and process dynamics in African ecosystems[END_REF][START_REF] Leimgruber | Spatial patterns in relative primary productivity and gazelle migration in the Eastern Steppes of Mongolia[END_REF][START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF][START_REF] Balluffi-Fry | Quantity-quality trade-offs revealed using a multiscale test of herbivore resource selection on elemental landscapes[END_REF][START_REF] Kaspari | The seventh macronutrient: how sodium shortfall ramifies through populations, food webs and ecosystems[END_REF]. Recent conceptual and theoretical developments related to metaecosystem theory now challenge our current understanding by suggesting that organisms themselves, through their movement in the landscape and feeding interactions, could generate the emergence of those observed elemental hotspots in the landscape (i.e., zoogeochemistry; [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF][START_REF] Gounand | Meta-ecosystems 2.0: rooting the theory into the field[END_REF][START_REF] Schmitz | Animals and the zoogeochemistry of the carbon cycle[END_REF][START_REF] Mcinturf | Vectors with autonomy: what distinguishes animal-mediated nutrient transport from abiotic vectors?[END_REF]) and potentially diffuse the elemental hotspots generated by abiotic processes. The elemental dissimilarity approach presented here provides a way of measuring some of these elemental patterns across the landscape with the ECBD metric being particularly useful in teasing out the scale at which each element is most important for dissimilarity (see Table 1 for testable hypotheses).

McClain
More than that however, previous research has demonstrated how energy and nutrients in food webs generally come from different trophic pathways that vary in their resource quality and the speed at which energy and materials flow [START_REF] Rooney | Structural asymmetry and the stability of diverse food webs[END_REF]. Traditionally, stoichiometric analyses focus on ratios, which have proven useful to understand trophic interactions (e.g., [START_REF] Hall | Stoichiometrically explicit food webs: feedbacks between resource supply, elemental constraints, and species diversity[END_REF][START_REF] Leroux | Predator-driven elemental cycling: The impact of predation and risk effects on ecosystem stoichiometry[END_REF] and co-limitation in competitive communities (e.g., [START_REF] Harpole | Nutrient co-limitation of primary producer communities[END_REF][START_REF] Marleau | Emergence of nutrient co-limitation through movement in stoichiometric meta-ecosystems[END_REF]. In particular, these stoichiometric analyses that have focused on the C:N and C:P ratios of resources are a useful way to characterize these different trophic pathways as ecosystems with resources with high (low) C:N ratios tend to be less (more)

palatable for herbivores and this decreases (increases) the rate of materials flowing in this pathway [START_REF] Hall | Stoichiometry and planktonic grazer composition over gradients of light, nutrients, and predation risk[END_REF][START_REF] Shurin | All wet or dried up? Real differences between aquatic and terrestrial food webs[END_REF]. Our work, however, has demonstrated the role that some of the other less abundant essential elements (e.g. K and Ca) play in landscape elemental dissimilarity -potentially offering additional currencies to tease out some of these relationships. For example, whereas some top consumers focus on one energetic or material pathway, many consumers couple multiple pathways [START_REF] Rooney | A landscape theory for food web architecture[END_REF][START_REF] Ward | HSS revisited: multi-channel processes mediate trophic control across a productivity gradient[END_REF].

Indeed, this coupling of different energetic pathways is an important contributor to ecosystem stability [START_REF] Mccann | Trophic cascades and trophic trickles in pelagic food webs[END_REF][START_REF] Rooney | Structural asymmetry and the stability of diverse food webs[END_REF]. We hypothesize that, irrespective of the direction of causality, changes in the evenness or dissimilarity of element ratios should be reflected directly into the structure of biotic communities, providing a long-sought mechanistic link between community and ecosystem processes that can be measured directly in the field.

Thus, a community perspective on elemental resources holds promise to synthetize our understanding of biodiversity and ecosystem function across level of organization.

From an applied perspective, the majority of conservation planning focuses on the protection and restoration of species, populations or communities, despite a call towards #ecosystem-based management" in terrestrial, freshwater, and marine realms. We surmise that, in some cases, elemental hotspots may be important features to protect or restore. For example, natural sodium licks are critical sources of this limiting nutrient for many large ungulate communities in temperate and boreal forest ecosystems [START_REF] Kaspari | The seventh macronutrient: how sodium shortfall ramifies through populations, food webs and ecosystems[END_REF]. In many ways, a pivot towards considering elemental hotspots for conservation is akin to calls for considering species interactions [START_REF] Tylianakis | Conservation of species interaction networks[END_REF][START_REF] Harvey | Bridging ecology and conservation: from ecological networks to ecosystem function[END_REF]) -i.e., levels of biodiversity beyond the species that may be critical to maintain ecosystem functioning. We provide an analytical pipeline to begin identifying elemental hotspots across landscapes. Equally, however, we provide an analytical pipeline with the potential to identify areas to protect. For example, our analyses suggest several areas that stand out as hot/coldspots of elemental dissimilarity (e.g., the yellow patches present at grain size 500 m in Fig. 4). If future research demonstrates that these patterns in elemental dissimilarity are reflected in species diversity as we have hypothesized, then our analytical approach provides a tool to identify the specific areas (including area boundaries) to protect.

Geological processes and abiotic factors have historically been the point of focus for predicting elemental concentrations at local study sites, but recent works have shed light on the significance of biotic ecosystem components on elemental distribution [START_REF] Gounand | Meta-ecosystems 2.0: rooting the theory into the field[END_REF][START_REF] Schmitz | Animals and the zoogeochemistry of the carbon cycle[END_REF][START_REF] Mcinturf | Vectors with autonomy: what distinguishes animal-mediated nutrient transport from abiotic vectors?[END_REF][START_REF] Schmitz | Food webs and ecosystems: linking species interactions to the carbon cycle[END_REF][START_REF] Malhi | The role of large wild animals in climate change mitigation and adaptation[END_REF]. Biotic and abiotic processes affecting the distribution of elements are often interdependent. By integrating both perspectives, meta-ecosystem theory illustrates the intimate feedback between the biotic and abiotic components of ecosystems, and how patch-specific biotic (e.g., organismal dispersal) and abiotic (e.g., inorganic nutrient runoff) processes can lead to the emergence of regional scale phenomena [START_REF] Loreau | Meta-ecosystems: a theoretical framework for a spatial ecosystem ecology[END_REF][START_REF] Massol | Linking community and ecosystem dynamics through spatial ecology[END_REF][START_REF] Massol | How life-history traits affect ecosystem properties: effects of dispersal in meta-ecosystems[END_REF]. However, beyond theoretical and conceptual advancements, we are still missing a coherent empirical framework to i) study and analyse empirical patterns of elemental distribution in space and across spatial grains, and ii) to link those abiotic observations (including information on longer timescale abiotic drivers such as weathering of parent geological material) to the biotic component of ecosystems. We are optimistic that our community perspective on elemental resources helps develop an empirical framework initially to enhance our descriptions of ecosystems and understanding of how elemental distributions scale with spatial gradients across different ecosystem types (see Table 1). We feel that our work provides the foundation upon which future work can attempt to address (ii) -linking the abiotic observations to the biotic components, thus truly bridging these distinct ecosystem compartments.

Tables 807 Table 1. Testable hypotheses generated from our proof of concept. [START_REF] Leroux | Stoichiometric distribution models: ecological stoichiometry at the landscape extent[END_REF] for each of our five key elements from white birch foliage using three landscape covariates (normalized aspect, slope, and elevation) and three categorical landscape covariates (landcover, stand height, and dominant tree species) to predict stoichiometric composition for foliage in each cell. Then, we apply the macroecological spatial smoothing approach proposed by [START_REF] Patrick | The challenges that spatial context present for synthesizing community ecology across scales[END_REF] to resample and summarize local observations at increasingly large grain sizes to determine how community metrics (dissimilarity, local contribution to dissimilarity, and elemental contribution to dissimilarity) applied to elemental composition varied with spatial scale. We apply this approach to both the landscapes and a randomization, null model, of each landscape. Finally, we report how our three community metrics -dissimilarity in elemental composition, local contribution to dissimilarity, and elemental contribution to dissimilarity -vary with spatial scale.

Figure 1 .

 1 Figures 811

Figure 2 .

 2 Figure 2. Demonstration of how (a) dissimilarity changes with grain sizes for different

Acknowledgements

This paper came to fruition thanks to the RED-BIO group funded by the synthesis center CESAB of the French Foundation for Research on Biodiversity (FRB; www.fondationbiodiversite.fr) and the Canadian Institute of Ecology and Evolution (CIEE). "

The code required to replicate the analyses presented here is available on FigShare (https://figshare.com/s/64d154c3a8ec48784299) while the data required to replicate the analysis is available at Leroux, Shawn (2017): Stoichiometric distribution models: ecological stoichiometry at the landscape extent. figshare. Dataset. https://doi.org/10.6084/m9.figshare.4003482.v3 . AM coded the analysis to produce the results with contributions from EH, FM and NL. AM produced the final

that contribute more than average to beta-diversity, while red indicates sites that contribute less than average to beta-diversity. Note that a site can contribute more than average to beta-diversity by being either more nutrient-rich or nutrient-poor than the average site. See Fig. A1 in Supplementary Information 1 for map of study area locations.