Facets of functional diversity support niche‐based explanations for Australian biodiversity gradients

There is widespread support that species richness increases with the available energy of an ecosystem, but the mechanisms underlying this driver of biodiversity patterns remain elusive. We evaluated gradients of functional diversity to test whether the higher species richness of productive, structurally diverse environments is due to a greater range of niches being supported by the abiotic conditions present (environmental filtering), greater availability of biotic resource and habitat niches (more niches) or increasing functional similarity of species (niche packing).


| INTRODUC TI ON
Broad-scale biodiversity gradients, such as along latitude or productivity, are likely due to multiple drivers acting together, in different contexts, or on different taxa (e.g.Davies et al., 2007Davies et al., , 2011;;Gouveia et al., 2013;Skeels et al., 2020).Thus, we are unable to understand such gradients with continued efforts to identify a single unifying explanation (Hawkins, 2010;Kissling et al., 2012;Pavoine & Bonsall, 2011).Study of global and continental gradients may be informed by comparative regional analyses, parsing out relative contributions of separate mechanisms at particular positions on environmental gradients (Coops et al., 2018).For example, there is evidence that temperature and ambient energy drive species richness at high latitudes, while water energy (e.g.actual evapotranspiration, AET) becomes more important in less temperature-limited environments (Francis & Currie, 2003;Hawkins et al., 2003;Whittaker et al., 2007), and environmental heterogeneity may drive biodiversity gradients when energy is not limiting (Kerr & Packer, 1997; but see Stein et al., 2014).
Functional diversity approaches emphasize niche-based explanations of species richness gradients.Functional diversity is estimated from species traits (Cadotte et al., 2011;Petchey & Gaston, 2006), which are explicitly connected to niches-the conditions under which species can survive and reproduce (Hutchinson, 1957)-as they influence fitness (i.e.survival and reproduction) in particular environments (McGill et al., 2006;Violle et al., 2007).Niches determine the number of species that can (co-)exist in an ecosystem, based on their environmental tolerances and species interactions.
Trait-based measures of functional diversity can evaluate if broadscale biodiversity gradients are caused by such mechanisms as (1) environmental filtering, where biodiversity is limited to species with traits that are compatible with the environmental conditions (Cavender-Bares et al., 2009;Cornwell et al., 2006); (2) more niches, in which more species are supported in environments with greater environmental heterogeneity or structural diversity of vegetation (Culbert et al., 2013;MacArthur & MacArthur, 1961), and more roles to fill, such as additional trophic niches and ecological opportunity arising from species interactions (Schluter, 2016).In addition to the location of niches on environmental gradients, their width and overlap may drive biodiversity patterns, with (3) greater biodiversity possible from niche packing due to greater specialization (Belmaker et al., 2012;Forister et al., 2015;MacArthur & Levins, 1967;Mason et al., 2008;Pigot et al., 2016) or functional redundancy of species (Lamothe et al., 2018;Mouillot et al., 2014).However, (4) competitive exclusion may limit the co-occurrence of functionally similar species (Abrams, 1983;MacArthur & Levins, 1967).In contrast to the above mechanisms, the (5) more individuals hypothesis is neutral to species functions and niches, suggesting that productive areas have higher diversity because they can maintain a greater abundance of individuals (Wright, 1983).
Functional diversity is multi-faceted.Measures are based on a conceptualization of multi-dimensional functional space; each dimension is formed by a trait, and each species is plotted in this space based on its trait values (Laliberté & Legendre, 2010;Villéger et al., 2008).A range of metrics are used to summarize the range of functional traits spanned by an assemblage and the functional relatedness of the species (Ackerly & Cornwell, 2007;Mason et al., 2005Mason et al., , 2013;;Mouchet et al., 2010;Villéger et al., 2008).Studying a suite of functional diversity measures sensitive to distinct aspects of an assemblage's occupancy of functional space and with different expectations under distinct community assembly processes (Ackerly & Cornwell, 2007;Pavoine & Bonsall, 2011;Swenson & Weiser, 2014;Lamanna et al., 2014; Table 1) may support more comprehensive understanding of biodiversity gradients.
However, as with drivers of species richness gradients, the community assembly processes indicated by evaluations of functional traits are expected to vary with scale and with position on environmental gradients.Environmental filtering is expected to be most prevalent in harsh environments, with more niches and mechanisms influencing species co-occurrence, such as niche packing and competitive exclusion, operating in benign conditions (Kluge & Kessler, 2011;Seymour et al., 2015;Swenson & Weiser, 2014;Weiher & Keddy, 1995; Table 1).Regional variation in functional diversity gradients and their environmental associations has also been observed (Arnan et al., 2017;Floury et al., 2018;González-Maya et al., 2016).
The aim of this study is to use cross-scale evaluations of functional diversity gradients at regional and continental extents to productivity and vegetation height were less limiting, and in mammal assemblages, suggesting that biodiversity patterns scale differently for birds and mammals.

K E Y W O R D S
energy, environmental heterogeneity, functional biogeography, functional traits, spatial scale, species richness, vegetation structure explore niche-based explanations of Australian vertebrate biodiversity gradients.Extending from Coops et al. (2018), it uses structural equation models (SEMs) to evaluate measures of energy related to climatic harshness and resource availability, and environmental heterogeneity associated with vegetation structure as interrelated drivers of biodiversity.SEMs are a useful framework for evaluating causal hypotheses for macroecological patterns (Beck et al., 2012; and see, e.g., Byamungu et al., 2021;Santos et al., 2020;Skeels et al., 2020) and Coops et al. (2018) provide a valuable investigation into the hierarchy of drivers underlying Australian biodiversity gradients; however, its focus on species richness limited mechanistic understanding.Integrating recently compiled databases of ecological traits of birds and mammals (e.g.Kissling et al., 2014;Myhrvold et al., 2015;Wilman et al., 2014)

| MATERIAL S AND ME THODS
This study tested mechanistic explanations of regional and continental biodiversity gradients in Australia by (1) disaggregating species richness into complementary measures of functional diversity and (2) using structural equation modelling to explore the interrelated effects of climatic harshness (inversely related to AET), resource availability (gross primary productivity, GPP) and vegetation structure (tree height), allowing us to evaluate nichebased hypotheses related to harshness and environmental filtering, resource and habitat niche availability and niche packing (Table 1).

TA B L E 1
Complementary components of functional diversity that may be measured from the functional traits possessed by species within an ecological assemblage, and the hypothesized relationships between each facet of diversity and environmental driving variables related to aspects of energy availability (climatic harshness and resource availability) and environmental heterogeneity under different niche-based community assembly mechanisms.The names of hypothesized mechanisms are indicated in italics.

Species richness Total number of species in an assemblage
Positive relationships between species richness and actual evapotranspiration (AET, inversely related to climatic harshness), productivity (GPP, a proxy of resource availability) and vegetation height (a dimension of environmental heterogeneity) are commonly observed.Investigating underlying patterns of functional diversity may support inferences about the niche-based mechanisms driving these broad-scale species richness gradients

Functional richness
The range of functional traits contained by the species in an assemblage, assessed as the amount of space occupied by the assemblage when plotting the trait values of each species in an n-dimensional space formed when using the trait variables as axes, or a lower dimensional

Functional dispersion
The variability of functional traits contained by the species in an assemblage, assessed as the differences between species based on their traits, or the distances between pairs of species in functional trait space Functional dispersion will parallel increases in functional richness with the abiotic driver, AET, under environmental filtering and with the biotic drivers, GPP and vegetation height, under more niches.Niche packing is expected to cause reduced functional dispersion in environments supporting high biodiversity, and thus negative relationships between functional dispersion and AET, GPP and vegetation height.Competitive exclusion should cause increased functional dispersion in those high biodiversity environments, but requires data on actual community composition to assess

Functional evenness
The regularity of trait values contained by the species in an assemblage, assessed from the variability of functional differences between species Competitive exclusion is expected to cause increased functional evenness in high biodiversity environments (and thus positive relationships between functional evenness and AET, GPP and vegetation height), but requires data on actual community composition to assess.Niche packing may produce variable relationships with functional evenness and these gradients, depending on whether trait combinations tend to occur in discrete syndromes, or if they are dispersed throughout functional space.
Environmental filtering and more niches may produce negative gradients of evenness along the environmental drivers, if species are added to the edges of functional space Although vegetation structural complexity has both vertical and horizontal dimensions, and both are aspects of environmental heterogeneity that are expected to contribute to biodiversity gradients through the more niches mechanism, we are specifically interested in the contributions of vertical niche partitioning into habitat strata.Thus, we use tree height as our estimate of vegetation structure.

| Data
The assembled spatial datasets (Table 2) represent species distributions of Australian birds and mammals (modelled by Reside et al., 2013); climatic harshness and resource availability, which are both dimensions of the energy available in an ecosystem; vegetation structure and an environmental stratification used to evaluate differences in regional biodiversity gradients between regions (Metzger et al., 2013; Figure 1).
Species ecological traits were sourced from the EltonTraits 1.0 database of bird and mammal foraging traits (Wilman et al., 2014), which includes estimates of diet, foraging stratum, activity timing and body size in grams (Wilman et al., 2014).Diet variables provided a numeric estimate of the per cent importance of 10 resource categories.Foraging stratum was the per cent importance of seven canopy levels or substrates for birds, and a categorical variable coding four foraging strata for mammals (excluding marine strata).Activity cycle used binary variables coding diurnal versus nocturnal activity for birds, and diurnal, nocturnal and crepuscular activity for mammals.Our analyses weighted these traits such that diet, foraging stratum, activity period and body size were weighted equally despite differing numbers of component variables (i.e.individual traits were given a weight of 1/n, where n is the number of traits in that trait category).Although some traits were represented differently for birds and mammals, these discrepancies did not substantially influence estimates of functional diversity (Supplementary Information, SI).
Traits were linked to species distributions by species names.All species without a matching record in the trait database were evaluated for synonyms to reconcile the taxonomy.Overall, 598 bird species and 221 mammal species were analysed.

| Biodiversity metrics
Bird and mammal assemblages in each 10 km analysis pixel were produced by stacking species distributions.At each pixel, we calculated species richness (number of species) and three measures of functional diversity (Table 1) that were calculated from a matrix of the pairwise functional dissimilarities for all Australian species in the taxon.Species dissimilarities were calculated with the weighted Gower distance in the original trait space, rather than from an ordination.Although the Gower distance can be sensitive to the range of trait values in the species pool, for our sample of species, estimates of functional dissimilarity were highly correlated when calculated from the Australian or global species pool (Pearson r birds = 0.98, r mammals = 0.96).All functional diversity measures were estimated from presence/absence data, since estimates of abundance were unavailable.Functional dissimilarity and diversity were calculated in R 3.6.1 using the 'cluster' 2.1.0(Maechler et al., 2019) and 'vegan' 2.5.6 (Oksanen et al., 2019) packages.The three measures were: Functional richness, the total amount of trait space occupied, was calculated with a dendrogram-based measure of functional diversity (Petchey & Gaston, 2002).The functional dendrogram was produced by UPGMA clustering of the continental species pool.Functional richness is the sum of branch lengths connecting the species present in a given assemblage, and is mathematically related to species richness (Mason et al., 2013;Pavoine et al., 2013).
Functional dispersion, representing the variation of trait combinations between species, was calculated as the average pairwise dissimilarity between species in an assemblage.This measure is equivalent to Rao's Quadratic Entropy when calculated from presence/absence data, and is closely related to the dispersion index of Laliberté and Legendre (2010).
Finally, functional evenness, the regularity of species occurrences in trait space, was estimated from the deviations in branch lengths between a minimum spanning tree connecting the species in an assemblage in trait space and the branch lengths that would be expected under a perfectly even distribution of species (Villéger et al., 2008).It is standardized to range from 0 to 1, where 1 denotes perfect evenness.
These metrics span the three independent aspects of functional diversity (sensu Pavoine & Bonsall, 2011; Table 1).Although other metrics exist, they tend to be highly correlated with those chosen here, and are unlikely to alter our conclusions or contribute new insights.
To remove any variation in functional diversity that is due to gradients in species richness alone, we conducted all analyses on the residuals of the functional diversity metrics after accounting for species richness.Functional diversity-species richness relationships were determined with generalized additive models (GAMs; using package 'mgcv' 1.8.28;Wood, 2023) and residuals were inspected visually to confirm that the assumption of homogeneity of variances was met.

| Analyses
Analyses were performed on a stratified random sample of pixels to reduce impacts of spatial autocorrelation and ensure effective coverage of the environmental gradients across the continent and within each bioclimatic zone.For this sampling, the bioclimatic stratification (Table 2; Figure 1) was intersected with the Interim Biogeographic Regionalisation for Australia (Environment Australia, 2000) and 10% of the pixels in each combination of bioclimatic zone by ecoregion were randomly sampled.Although Coops et al. (2018) sampled only pixels containing forested vegetation (i.e.those with non-zero height estimates in the tree height dataset; Table 2), we imposed no such restrictions on the sample since forests are rare across much of Australia and may not be representative of many of the bioclimatic zones.
SEMs were developed using the 'SEM' 3.1.11R package (Fox et al., 2020) to evaluate the contributions of AET, GPP and tree height to each measure of biodiversity for birds and mammals.SEMs evaluate the support for causal hypotheses about hierarchical relationships between predictor variables and their relative importance to response variables, represented graphically in a path diagram (Grace et al., 2012(Grace et al., , 2014;;Shipley, 2000).We updated the path diagram evaluated by Gouveia et al. (2014) and Coops et al. (2018) to use as a starting point for our SEMs: This included AET as a predictor of tree height, and both of these as predictors of GPP (Figure 2).
Although either direction of the relationship between tree height and GPP is possible, at the temporal resolution of our datasets (Table 2), it is more likely that tree height influences GPP (with multi-layered canopies of taller vegetation yielding greater productivity) than vice versa.AET, tree height and GPP were specified as predictors of each diversity variable (Figure 2).These environmental variables may each be directly related to biodiversity since AET is inversely related to the climatic harshness of a system, GPP indicates resource availability and tree height can enable vertical niche partitioning.
Environmental predictor variables were log transformed and all variables were centred and scaled to unit variance prior to modelling so that the path coefficients, which estimate the strength of each relationship in the model, were comparable.Each SEM was iteratively updated to remove non-significant paths until the 'best' model, minimizing Akaike's information criterion (AIC), was achieved.Model goodness of fit was evaluated with the comparative fit index (CFI) and standardized root mean square residual (SRMR), which are less sensitive to sample size than χ 2 testing.CFI >0.9 or SRMR <0.08 indicate good model fit.
TA B L E 2 Descriptions of the datasets used in this project and their sources.

Species data
Species distributions Distribution maps of 221 mammal and 598 bird species generated by Reside et al. (2013) were used for this study.Distributions of species with sufficient (>5) occurrences were modelled at ~1 km resolution across Australia with the Maxent algorithm on the basis of bioclimatic variables summarizing temperature and rainfall derived from AWAP (Australian Water Availability Project) weather surfaces (Jones et al., 2009) and species occurrence records (excluding those outside of the bioregions known to be occupied by the species) in Australian biodiversity databases (Reside et al., 2013).Predictions were converted to binary maps of distributions using the thresholding rule that best represented the known range of the species and screened based on published species ranges and expert opinion (Reside et al., 2013).All of the published species distributions had adequate model accuracy (AUC, area under the ROC curve >0.7) or were judged to effectively represent the species distributions (n = 8 mammals) when screened against the known range (Reside et al., 2013).Species were considered to be present at the 10 km analysis resolution if 10% of the pixel's area was predicted to contain the species

Environmental predictor variables
Climatic harshness: Actual evapotranspiration (AET) AET estimates were derived from the AWAP outputs at 5 km resolution.AWAP modelled AET (in units of m) using a simple water balance model applied to input weather surfaces, remotely sensed estimates of incoming radiation and vegetation cover, and soils data (Raupach et al., 2009).Annual AET was averaged over the years 2005-2010.Upscaled to the 10 km analysis resolution with average-value resampling Resource availability: Gross primary productivity (GPP) Remotely sensed estimates of GPP were derived from the MODIS MOD17A3 collection 5 GPP product.MODIS GPP estimates the carbon fixed by vegetation (in units of kg C/m 2 ) at 1 km resolution based on the amount of incoming solar radiation, the fraction of radiation absorbed by vegetation and the efficiency with which vegetation fixes light energy into carbohydrates, modelled as a function of temperature and drought stress (Running et al., 1999(Running et al., , 2004;;Zhao et al., 2005).Annual estimates of GPP were averaged for the years 2005-2010.Upscaled to the 10 km analysis resolution with average-value resampling

Environmental heterogeneity: Tree height
Remotely sensed tree height estimates were determined from the global forest canopy height dataset of Simard et al. (2011).This dataset extrapolated point estimates of canopy height from the GLAS spaceborne LiDAR using environmental predictor variables (climate, topography, MODIS tree cover, etc.) to produce a continuous global map of forest height for the year 2005 at 1 km resolution.Upscaled to the 10 km analysis resolution with averagevalue resampling

Bioclimatic stratification
Global environmental stratification (GEnS) The continental study area was divided into bioclimatic zones using the GEnS stratification of Metzger et al. (2013), which developed a detailed, ~1 km resolution global environmental regionalization by clustering bioclimatic variables.Nine of the resulting bioclimatic zones are present in Australia with sufficient extent to evaluate regional biodiversity patterns.These zones largely divide Australia into latitudinal bands and may be insufficient to represent biogeographic patterns of vertebrates, which also show distinct biotic regions from east to west (Ebach et al., 2013).Thus, drawing on the results of Bein et al. (2020), we subdivided the six GEnS zones that spanned the longitudinal extent of Australia at the meridian of 134° E, giving a total of 15 zones (Figure 1).Upscaled to the 10 km analysis resolution with modal-value resampling Separate SEMs were constructed for birds and mammals and for the full continental extent and the regional extent of each bioclimatic zone.For each SEM, the dominant predictor of each diversity metric was identified as the one with the largest absolute path coefficient to that response variable.Co-dominant predictors were those with path coefficients within the 95% confidence interval of the dominant predictor.
Results in some bioclimatic zones were complicated by negative species richness gradients along the environmental predictors.Thus, to synthesize the regional results, we first determined whether the AET had strong positive relationships with GPP and tree height and was the dominant predictor of species richness for both taxa (Figure 3c,d) and for all functional diversity metrics for birds (Figure 3c).In contrast, GPP was the dominant predictor of all facets of mammal functional diversity (Figure 3d), which is consistent with the contrasting spatial patterns described for functional diversity of bird and mammal assemblages.In all cases, associations with the dominant predictor were strong and positive.

| Regional biodiversity gradients
At the regional level, relationships between biodiversity metrics and environmental predictors were variable (SI; Figure 4).The assessed Actual evapotranspiration (AET) was considered the underlying driver of the biotic gradient of tree height ('Height'), both AET and tree height were included as predictors of gross primary productivity (GPP) and all three of these environmental variables were specified as predictors of the four facets of biodiversity: species richness (SR), functional richness (FR), functional evenness (FE) and functional dispersion (FD).

FD
environmental variables tended to have limited explanatory power for functional diversity patterns within bioclimatic zones and SEM fit was generally only moderate (SI), suggesting that biodiversity gradients at the regional level are structured by additional drivers omitted by our analyses, or that the variables used in our study are imperfect surrogates of biodiversity, harshness, resource and habitat gradients.
The environmental variables that were the dominant predictors of functional diversity at the continental scale also tended to be important predictors within bioclimatic zones.AET was the dominant predictor of bird functional richness or dispersion in 7 of the 15 zones, and functional diversity gradients on AET tended to align with species richness gradients in these zones (i.e.environmental filtering; Figure 4a).However, GPP and tree height were nearly as important at structuring bird functional diversity, with dominant or co-dominant effects in six zones each (Figure 4b,c).As at the continental scale, GPP was the dominant or co-dominant predictor of mammal functional richness and dispersion in 9 of the 15 zones (Figure 4e), while there were important effects of tree height and AET in 5 and 4 zones respectively (Figure 4d,f).
For both taxa, regional gradients of functional richness and dispersion along tree height tended to counter species richness gradients, indicative of niche packing (Figure 4c,f).However, functional dispersion and species richness gradients aligned (more niches) in F I G U R E 3 Spatial patterns of facets of (a) bird and (b) mammal species ('Sp') richness and functional ('Fn') diversity across Australia and (c, d) results of the structural equation models (SEMs) of the associations of diversity metrics with climatic harshness (inversely related to actual evapotranspiration, AET), resource availability (gross primary productivity, GPP) and environmental heterogeneity (tree height).SEM structure corresponds to that illustrated in Figure 2, but, for clarity, all four biodiversity measures are grouped together in this representation, with a single path annotated by the estimated coefficients (±SE) for each of the four response variables; 'ns' indicates a path was removed during model refinement due to non-significance (p > 0.05).All paths retained in these models were highly significant (p < 0.001).Dominant or co-dominant drivers are indicated with bold text for the path coefficient.Explanatory power (R 2 ) for all endogenous variables and the goodness of model fit (estimated by the comparative fit index [CFI] and standardized root mean square residual [SRMR]) are also reported.FD, functional dispersion; FE, functional evenness; FR, functional richness; SR, species richness.zones with the lowest average tree height (Figure 4c,f).A similar pattern was observed along GPP, with niche packing as the prevailing mechanism in bioclimatic zones with higher average GPP (Figure 4b,e).However, evidence for the more niches mechanism was observed in more bioclimatic zones, across a greater portion of the GPP gradient, for birds (Figure 4b) than for mammals (Figure 4e).
In most cases, functional evenness gradients (when nontrivial) were in the same direction as those of functional richness and dispersion (Figure 4).This was especially the case in zones where niche expansion (environmental filtering or more niches) was the dominant pattern and in zones exhibiting niche packing along tree height (Figure 4f).In contrast, niche packing along GPP for mammals was accompanied by declines in functional evenness in some zones, but increased evenness in others (Figure 4e).

| DISCUSS ION
The investigated facets of biodiversity were environmentally structured at both continental and regional extents.However, relationships varied between facets of functional diversity, between environmental gradients and between scales, positions on environmental gradients and taxonomic groups, suggesting that different mechanisms structure the evaluated biodiversity gradients and underscoring that simple explanations are not applicable to broadscale biodiversity gradients.

| Continental biodiversity gradients
Both birds and mammals showed marked expansion of niche space along energy gradients at the continental extent (Figure 3c,d).
However, functional richness gradients for these taxa were structured by different energy variables, and thus different mechanisms (Table 1).
Environmental filtering was especially important to continental gradients of bird biodiversity, with AET having the strongest effects on all metrics of bird diversity (Figure 3c).With decreasing climatic harshness (increasing AET), bird species assemblages were more species rich and occupied more functional space, with species that were more evenly distributed in functional space and, on average, more functionally dissimilar from each other (Figure 3c).In contrast, mammal functional diversity gradients were decoupled from the continental species richness gradient along AET and primarily structured by GPP (Figure 3d), suggesting that the availability of resource niches explains mammal functional diversity gradients across Australia.
This difference between mammals and birds may be due to stark differences in their activity cycles.Nearly all (98.6%) of the mammal species studied were nocturnal, while nearly all birds (97.2%) were diurnal.Nocturnality allows animals to avoid thermal stress in hot, arid environments (Bennie et al., 2014;Levy et al., 2019).However, maintaining body temperatures during cold night-time conditions is energetically demanding (Levy et al., 2019) and may be unsustainable under resource limitations (Weyer et al., 2020).This may be why resource availability (GPP), not climatic harshness (AET), was the primary gradient structuring Australian mammal functional diversity gradients.Conversely, the diurnal activity of birds exposes them to the physically stressful daytime conditions that prevail across Australia (conditions to which Australian birds are adapted, Pacheco-Fuentes et al., 2022).Perhaps not surprisingly, then, climatic harshness was found to be the dominant predictor of bird diversity gradients.
Our finding that bird biodiversity gradients are structured by environmental filtering agrees with previous functional diversity research investigating long biodiversity gradients for birds (Byamungu et al., 2021;Devictor et al., 2010), as well as other taxa (e.g.plants: Andrew et al., 2021;Kluge & Kessler, 2011;Lamanna et al., 2014;Shiono et al., 2015;Swenson et al., 2012;freshwater fish: Schleuter et al., 2012), but contradicts Remeš and Harmáčková (2018)'s study of Australian bird assemblages.Environmental filtering has also been found to structure mammal biodiversity gradients (Dreiss et al., 2015), disagreeing with our results that the functional diversity of Australian mammal assemblages is more strongly structured by resource availability.However, the more resource niches hypothesis has generally not been assessed for broad biodiversity gradients.Resource availability does tend to be considered in investigations of steep elevation gradients, with mixed results (Byamungu et al., 2021;Ding et al., 2021;Hanz et al., 2019;Montaño-Centellas et al., 2021;Zhang et al., 2020).Our use of SEMs allowed us to detect this mechanism by parsing out the separate F I G U R E 4 Summary of the regional scale structural equation models (SEMs, see Supplementary Information for full model results) of facets of (a-c) bird and (d-f) mammal biodiversity along (a, d) climatic harshness (inversely related to actual evapotranspiration, AET), (b, e) resource availability (gross primary productivity, GPP) and (c, f) environmental heterogeneity (tree height) gradients.In each panel, bioclimatic zones (Figure 1) are positioned on the environmental gradient based on their mean value of this variable, and are included if the focal environmental variable is a (co-)dominant predictor of functional richness or dispersion gradients in the zone and the functional diversity gradient is not trivial (i.e.R 2 ≥ 0.1).The direction of the (co-)dominant effects of the focal environmental gradient on functional richness (FR), functional dispersion (FD) and functional evenness (FE) are indicated in bold; the direction of the species richness (SR) gradients are also indicated for comparison, but are italicized if the focal variable does not have a (co-)dominant effect on SR.The colour and placement of the region is based on whether the SR and FR or FD gradients align, consistent with niche expansion mechanisms (placed to the left of the axis and coloured yellow for environmental filtering or green, more niches), or are counter to each other, consistent with niche packing (bioclimatic zones to the right of the axis, coloured blue).*In these bioclimatic zones, FR and FD showed contradictory patterns.
Interpretations are based on FD, as it was modelled with higher R 2 .§ SR had a weak negative relationship with GPP in this zone.However, because it was negligible in comparison to the path coefficient for the dominant predictor of SR and to the FR gradient on GPP, this pattern is interpreted as most consistent with niche expansion mechanisms.
effects of GPP (Coops et al., 2018) rather than conflating them with the effects of environmental filtering by AET.We encourage further such studies so that the role of the more niches hypothesis is not overlooked.Alternatively, the distinct mechanisms associated with the two energy axes may be distinguished by dividing traits into groups related to resource acquisition or environmental tolerances and studying them separately (e.g.Floury et al., 2018;Ingram & Shurin, 2009;Kohli et al., 2021).
We found weak effects of tree height at the continental extent (Figure 3c,d), which is consistent with previous studies of environmental heterogeneity (e.g.Arnan et al., 2015;Fergnani & Ruggiero, 2017).
The limited support for effects of environmental heterogeneity at broad scales may be due to compounded effects of co-occurring processes (Feng et al., 2020).Our regional-scale analyses revealed contradictory mechanisms operating at different ends of the tree height gradient (below) that may cancel out when scaled up to the continental extent.Similarly, results may be obscured if different niche-based processes operate on different traits (Arnan et al., 2015;Ingram & Shurin, 2009;Shiono et al., 2015;Trisos et al., 2014).To partially mitigate this, multivariate estimates of functional diversity should be based on traits that are directly relevant to the function of interest (Cadotte et al., 2011;Petchey & Gaston, 2002).Although we were limited by the traits available within global databases, the resource and foraging strata traits we studied represent species niches related to resource use, including the vertical partitioning of resource use (Wilman et al., 2014).Therefore, we expect them to be appropriate to our evaluations of niche availability along resource (GPP) and tree height gradients at the continental and regional scales.
We found weak support for niche packing in diverse assemblages at the continental scale.Negative functional diversity gradients, indicative of niche packing, were never the dominant pattern.Instead, they were only observed along secondary gradients after accounting for the dominant effect of niche expansion mechanisms, and in cases where species richness and functional diversity were decoupled from each other and structured along different environmental gradients (Figure 3c,d).This contrasts with previous conclusions that niche packing is the dominant process behind long biodiversity gradients for birds (Pellissier et al., 2018;Pigot et al., 2016), mammals (Oliveira et al., 2016) and plants (Lamanna et al., 2014;Swenson & Weiser, 2014).These differences may be due to the different approaches used to assess niche packing.

| Regional biodiversity gradients
Biotic gradients contributed more to structuring regional functional diversity gradients than to continental patterns; thus, in many zones, functional diversity gradients were decoupled from species richness, which continued to largely be associated with AET (SI).Niche packing received stronger support at the regional scale than in the continental analyses and was especially prevalent in bioclimatic zones with higher GPP and taller vegetation.More niches contributed to functional diversity gradients in bioclimatic zones where resources (Figure 4b,e) and habitat niches (Figure 4c,f) were more limiting.This transition from niche expansion to niche packing in increasingly hospitable bioclimatic zones was observed for both taxa (Figure 4), and is consistent with Fox's guild assembly rule (Fox, 1987) and conclusions that niche expansion makes greater contributions to bird biodiversity gradients in abiotically harsh realms (Pellissier et al., 2018).
However, the relative importance of niche packing differed for birds and mammals, as did the position of the transition from niche expansion, especially when evaluating regional patterns along GPP: Niche expansion was the dominant mechanism for birds, occurring in zones with low-to-moderate GPP, with niche packing only observed in a single zone with relatively high GPP (Figure 4b).However, mammals exhibited the niche packing mechanism in many zones with moderate to high GPP, and niche expansion was only observed in the three least productive bioclimatic zones (Figure 4e).
The greater prevalence of niche packing at the regional extent for mammals than birds, despite an overall pattern of niche expansion at the continental scale for both, highlights differences in the spatial scaling of biodiversity patterns between these taxa.This may be due to the lower vagility of mammals than birds (Hillman et al., 2014).Vagility influences biogeographic patterns including species richness gradients (Moura et al., 2016), the locations of biogeographic boundaries and their drivers (Ficetola et al., 2021).
Consequently, mammals show greater biogeographic structuring than birds: there are more biotic regions for mammals than for birds (worldwide and in Australia; Holt et al., 2013), and mammal species are more likely to be restricted to a single region than are birds (Böhning-Gaese et al., 1998).Because of these constraints, regional species pools may be more restricted taxonomically and functionally for mammals than for birds, reducing the opportunity for niche expansion to structure regional biodiversity gradients.
Our functional evenness results provide further insights into different patterns of niche packing.Niche packing may lead to better filling of functional space and increased functional evenness.However, if traits do not vary independently, instead occurring in discrete 'syndromes' of viable trait combinations (Cooke et al., 2019), niche packing within the suitable trait syndromes may decrease functional evenness.Thus, it is not surprising that complex patterns of functional evenness have been reported (Pigot et al., 2016;Schleuter et al., 2012).We found that niche packing of mammal assemblages was often accompanied by gradients in functional evenness: All bioclimatic zones that showed niche packing along tree height had parallel reductions in functional evenness (Figure 4f), suggesting that new species were added to existing trait syndromes, perhaps corresponding to foraging strata.In contrast, when evaluating functional evenness patterns along GPP, niche packing reduced functional evenness in bioclimatic zones with low GPP, but increased functional evenness in more productive zones (Figure 4e).
Niche expansion may also influence functional evenness.If new species are added to the edges of functional space and have high functional uniqueness from the rest of the assemblage, functional evenness will be reduced (Ricklefs & Travis, 1980).However, we did not observe this effect.Instead, the functional evenness of bird assemblages paralleled increases in functional richness and dispersion in the bioclimatic zones that showed niche expansion with increasing GPP (Figure 4b).
As with the continental scale results, AET was more important for structuring functional diversity gradients for birds than for mammals at the regional scale and the dominant pattern in these zones continued to be of environmental filtering (Figure 4a).However, the direct effects of AET were weaker at regional than continental scales and AET was the dominant or co-dominant predictor in fewer than half of the bioclimatic zones.This corresponds to expectations and previous observations that environmental filtering is more important at the broad scale (e.g.Safi et al., 2011), while biotic drivers and other assembly processes gain importance at finer scales (Belmaker & Jetz, 2013;Trisos et al., 2014;Weiher & Keddy, 1995).
Moreover, we found little consistency in which bioclimatic zones showed important effects of AET aside from the notable result that the western portion of the warm, temperate and mesic zone exhibited patterns of niche packing for both taxa (Figure 4a,d).
The western warm, temperate and mesic zone was a notable outlier in a number of respects.In addition to exhibiting niche packing along AET, species assemblages in this zone showed declining species richness with AET (both birds and mammals) and tree height (birds), and generally no effect of GPP (SI).This zone is within the southwest Australian biodiversity hotspot, an area renowned for its floristic diversity and endemism despite the absence of features typically expected to generate such extraordinary diversity (Hopper & Gioia, 2004;Rix et al., 2014).Southwest Australia is an ancient, flat, infertile landscape neighbouring large deserts (Hopper, 2009;Rix et al., 2014).This has led to enormous speciation of plants, including adaptations to edaphic stress and radiations at the arid margins (Hopper, 2009).As a result, plant species richness in southwest Australia is lowest in the area of high rainfall (Hopper & Gioia, 2004), which parallels the negative species richness gradients we observed on AET for birds and mammals (Figure 4, SI).These taxa do not display similar endemicity or evolutionary histories to plants in southwestern Australia (Rix et al., 2014), but higher species richness on the edges of this zone may be due to contributions from the pool of arid zone species.Interestingly, we found that functional richness of birds and mammals increased with AET (Figure 4, SI), suggesting that climatic harshness limits functional diversity but not species richness in this zone.Thus, the gradients of bird and mammal species richness are underpinned by increased niche packing into the reduced functional space available at lower AET.

| Methodological limitations
The species assemblages we evaluated were generated by stacking species distribution model predictions, which may present several limitations to the study.First, the assemblages do not contain all Australian bird and mammal species, as species with fewer than five occurrence records were not modelled (Reside et al., 2013).The effects of missing species on estimates of functional diversity and their spatial gradients are unknown, and will depend on whether species rarity is associated with functional distinctiveness or redundancy (Jarzyna & Jetz, 2016).
There may also be concerns about the use of species distributions modelled from climatic predictor variables, given the strong climatic control of the energy and tree height variables evaluated in this study.However, we feel that this should not produce undue circularity: First, the functional diversity estimates will not be simple functions of the climate variables since they aggregate the potentially complex, idiosyncratic climatic associations of each species predicted to be present in an assemblage, in addition to their functional traits.Further, while the species distributions were modelled from simple temperature and precipitation variables (Reside et al., 2013), our energy and tree height variables aggregate the effects of both temperature and precipitation as well as the ecosystem's response (and see Coops et al., 2018).
Finally, stacked species distributions represent potential species assemblages, not actual communities (Cord et al., 2014;Ferrier & Guisan, 2006).As a result, they tend to overestimate species richness since the models may be missing additional limiting factors that prevent a species from occurring at a location (for instance, the species distribution models supporting our research only included climatic factors) and they do not account for other ecological processes, such as species interactions.Further research is needed to know if the patterns of niche packing that we observed occur within or between communities, and to evaluate the contributions of biotic interactions such as competitive exclusion to biodiversity gradients.Studies using real community composition data and analyses such as ours, as well as investigations into the contrast between turnover in species composition and functional traits (e.g.Cilleros et al., 2016;Messier et al., 2010), can help resolve how those community assembly mechanisms most explicitly related to species interactions scale up to broad-scale biodiversity gradients.

| CON CLUS IONS
This study evaluated the contributions of three ecological nichebased mechanisms to biodiversity gradients of Australian vertebrates, testing the environmental filtering, more niches and niche packing hypotheses with complementary axes of functional diversity, remotely sensed estimates of environmental gradients related to energy and vegetation structure and cross-scale investigations.
All three niche-based mechanisms contributed to biodiversity gradients, but the balance between them depended on scale, position on environmental gradients and taxonomic group.At the continental scale, the dominant pattern was of niche expansion with increasing energy, however, this was structured differently for birds and mammals.Environmental filtering by climatic harshness was the most supported explanation for Australian bird diversity gradients, while mammal assemblages exhibited the emergence of more niches with greater resource availability (GPP).The biotic gradients (GPP and tree height) and the niche packing mechanism were increasingly prominent predictors of functional diversity gradients at the regional scale.For both birds and mammals, there was a transition from more niches in arid zones at the extremes of the GPP and tree height gradients to niche packing in more benign zones.However, mammal assemblages were more frequently structured by niche packing than were birds, suggesting differences in the scaling of biodiversity gradients from the regional to the continental extent for these taxa.
Broad-scale biodiversity gradients have intrigued biogeographers for centuries, but have resisted conclusive explanations.There is extensive evidence that species richness increases with energy, productivity and environmental heterogeneity, and numerous hypotheses have been proposed to explain these patterns (reviewed by Field et al., 2009;Hawkins et al., 2003;Stein et al., 2014;Willig et al., 2003).Likewise, we found that species richness of Australian

CO N FLI C T O F I NTE R E S T S TATE M E NT
None.
with the framework of Coops et al. (2018) now allows us to evaluate the contributions of niche-based mechanisms of community assembly to broad-scale biodiversity gradients.
dominant and co-dominant patterns of functional richness and functional dispersion were aligned with the species richness gradient.Such alignment indicates that the addition of species is paralleled by increases in functional space relative to species richness, consistent with mechanisms of niche expansion (environmental filtering and more niches).Conversely, opposing gradients of species richness and functional richness or dispersion indicate niche packing.These interpretations were then ordered along the environmental gradients based on the average AET, GPP and tree height of each zone to highlight how the structuring of each aspect of biodiversity differed between zones and whether there were any systematic patterns to these differences.3| RE SULTS3.1 | Continental biodiversity gradientsBirds and mammals showed similar patterns of species richness across Australia, with high values in the northern tropics and the east coast forests and lowest species richness in the central deserts (Figure3a,b).However, birds showed markedly greater species richness and a wider band of high richness along the east coast.Despite these similarities, the spatial patterns of functional diversity, after accounting for species richness, were notably different between taxa (Figure3a,b).Bird functional diversity (Figure3a) peaked in northern Australia for all three metrics, especially in the Pilbara region of northwestern Australia and the Cape York Peninsula in north Queensland.There were additional areas of high functional richness in northeast Queensland, high functional dispersion in the Lake Eyre Basin in central Australia and high functional evenness in Tasmania.In contrast, mammal functional diversity (Figure3b) tended to be greatest in the south and east: There were large areas of high functional dispersion in eastern Australia, the Nullarbor Plain and southwestern Australia, while areas of high functional richness and evenness were more restricted to a narrow band along the east coast and the southern margin of the continent (including Tasmania) respectively.

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I G U R E 1 Environmental regionalization used to divide Australia into 15 bioclimatic zones.The bioclimatic zones were generated by intersecting the global environmental stratification (GEnS;Metzger et al., 2013) of climate regions with the meridian of 134°E longitude to reflect notable east-west distinctions in vertebrate community composition(Bein et al., 2020;Ebach et al., 2013).Preliminary path diagram for structural equation models of bird and mammal biodiversity.
bird and mammal assemblages tended to exhibit positive relationships with our abiotic and biotic energy variables and with tree height, a measure of environmental heterogeneity, especially when considering the dominant associations identified by our SEMs.However, our results emphasize that no single mechanism drives these broad-scale biodiversity gradients.We encourage further comparative, crossscale studies such as ours, and demonstrate that breaking biodiversity gradients into component parts, such as functional facets and spatial subdivisions based on an appropriate environmental regionalization, offers greater ability to identify the community assembly mechanisms contributing to biodiversity gradients and how their relative importance varies with ecological context.ACK N O WLE D G E M ENTSWe are grateful to Prof. Jeremy VanDerWal and Dr. Erin Graham from the James Cook University for access to the species distribution data modelled as part of the CliMAS project.No permits were required for this research.Open access publishing facilitated by Murdoch University, as part of the Wiley -Murdoch University agreement via the Council of Australian University Librarians.