Functional redundancy of non‐volant small mammals increases in human‐modified habitats

Humans are rapidly altering natural habitats across much of the globe. Here we compared 264 globally distributed communities in natural and human‐modified habitats to detect changes in community richness and functional diversity with human influence.


| INTRODUC TI ON
Human activities are rapidly altering natural habitats across much of the globe, which makes it challenging to determine how these activities influence species and functional diversity in local communities (Blowes et al., 2019;Bogoni et al., 2018;Davidson et al., 2017;Newbold et al., 2018). Functional diversity, the range of functional traits found in ecological communities (Diaz & Cabido, 2001), has become central in biodiversity assessments as it can help reveal which ecological functions are lost with human influence (Brodie et al., 2021;Carmona et al., 2021;Cooke et al., 2019;Mouillot et al., 2013). Of particular interest for biodiversity assessments is functional redundancy, a facet of functional diversity that depicts how similar the species are regarding their functional traits (Mouillot et al., 2013). Functional redundancy can inform us on how many species and traits can be lost before communities lose functions (Carmona et al., 2021;Cooke et al., 2019), as well whether communities are gaining functionally common species through colonization (Mori et al., 2015;Newbold et al., 2018).
Biodiversity assessments are, however, hampered by globally idiosyncratic changes in local species richness and functional diversity with habitat alteration (Blowes et al., 2019;Dornelas et al., 2014).
These changes can occur between habitat types such as temperate or tropical forests (Blowes et al., 2019;Murphy & Romanuk, 2014; and subtropical forests or temperate grasslands (Corbelli et al., 2015). Idiosyncratic responses of local communities are partly expected because of compositional differences among larger biogeographical regions in which local habitats are embedded (Karger et al., 2016;Lessard et al., 2016). The composition of a local community results, to a large degree, from sorting the regionally available species pool which consists of those species that could potentially colonize and establish within a community (Cornell, & Harrison, 2014). This sorting is mediated by a combination of factors (also known as filters), such as species ability to disperse to and survive in a site given its environmental conditions (Karger et al., 2016;Lessard et al., 2016). Including the species pool into analysis of local community composition has the advantage that large regional differences, such as those between temperate and tropical forests, are already accounted for and the effects of local factors can be analysed in isolation (Karger et al., 2020).
An example of such local factors is the alteration of habitats due to human influence. Natural forests and grasslands (hereafter: natural habitats) are, for example, expected to have low rates of extinction and colonization with slow changes in species composition (Gibson et al., 2011;Newbold et al., 2018;Pfeifer et al., 2017) so that the potential SR and FD from the regional species pool are locally well represented (Figure 1). Natural habitats contain a set of often functionally unique species which are adapted to the specific local environment (Lessard et al., 2016;Newbold et al., 2018). When humans change the quality, size and connectivity of natural habitats, they also alter the local environment and trigger a re-assembly of communities from the available species pool (Dornelas et al., 2014;. This re-assembly can either decrease or increase SR depending on the rates of extinction and colonization (Jackson & Sax, 2010;Sax et al., 2005), as well either decrease or increase FD depending on whether species have the functional traits that allow to profit from modifications on habitats created by humans (Brodie et al., 2021;Carmona et al., 2021;Cooke et al., 2019;Mori et al., 2015;Newbold et al., 2018).
We aimed to assess how human influence alters local biodiversity by measuring the difference in observed species richness (∆SR) and functional diversity (∆FD) relative to their potential in the species pool. We estimated the potential SR and FD using the probabilistic species pool approach (Karger et al., 2016) where the probability of occurrence of each species present in the pool is a function of its dispersal ability and the site environmental suitability. We treated ∆FD as its standard deviation from a null ∆FD produced by a null model (i.e. ∆FD SES ), as needed to deal with the richness effect on FD (Oliveira et al., 2016), and with species with probabilities close to zero in the probabilistic species pool. Both ∆SR and ∆FD SES reach positive values when many species and traits present in the pool are absent in local communities, indicating a loss relative to community potential. We quantified variation in ∆SR and ∆FD SES under two perspectives: (1) comparing states of habitat modification (either human-modified or natural) and (2) comparing types of habitats (natural: natural forests, natural grasslands; modified: crop fields, clearcuts, tree plantations, grassland edges, forest edges). We expected higher ∆SR and ∆FD SES in modified than in natural habitats in both perspectives, as the loss of species adapted to natural conditions (the 'losers') and the colonization of species that profit under human influence (the 'winners') can increase the difference in observed and potential richness and functional diversity found in a site (Lewis et al., 2017). We then assessed the type of human influence on local communities and its geographical variation. To do so, we adapted the framework of Sax et al. (2005, see also Jackson & Sax, 2010 to incorporate the combinations of ∆SR and ∆FD SES -compared to the average ∆SR across all sites (global average) and ∆FD SES equal to zero (a null ∆FD), respectively-to distinguish four scenarios in which local communities could fit into ( Figure 1): • S1: ∆SR and ∆FD SES , for a given habitat, are lower than average ∆SR and zero, respectively, across habitats ( Figure 1). This indicates no local change in SR and FD so that potential SR and FD from the species pool are locally well represented. This result suggests that there has been limited local extinction and replacement as a result of human influence (Jackson & Sax, 2010;Sax et al., 2005).

K E Y W O R D S
anthropocene, functional hypervolume, habitat fragmentation, mammal dispersal, niche hypervolume, probabilistic species pool, regional species pool • S2: ∆SR is lower than average and ∆FD SES is higher than zero ( Figure 1). This indicates that local extinctions are counterbalanced by the immigrations so that ∆SR remains low (Dornelas et al., 2014). However, locally extinct species (the 'losers') are not replaced from a functional perspective. Instead, they are replaced by winner species with functions similar to those species that persist in a given habitat, leading to a reduction in functional diversity and increase in functional redundancy (Mori et al., 2015;Mouillot et al., 2013;Sobral et al., 2016).
• S3: ∆SR is higher than average and ∆FD SES is lower than zero ( Figure 1). This indicates a relative loss of species, but a gain in FD.
In this case, immigrants add functions to the local communities (e.g. granivores immigrating into crop fields in previously forested landscapes; Corbelli et al., 2015).
• S4: ∆SR and ∆FD SES are higher than average ∆SR and zero, respectively, across habitats ( Figure 1). This indicates deficits in both SR and FD. This is the worst-case scenario as local extinctions are not counterbalanced by immigration, resulting in large differences in observed relative to potential species richness and functional diversity (Bogoni et al., 2018;Carmona et al., 2021;Pfeifer et al., 2017).
Here, we assessed the influence of human habitat modification on 264 local communities of non-volant small mammals.
These communities are within the most common types of natural and modified habitats found in land (Newbold, Hudson, Arnell, et al., 2016;Newbold et al., 2018), and small mammals among the most functionally specialized and perhaps resilient organisms to human influence (Bovendorp et al., 2019;Flynn et al., 2009;Pfeifer et al., 2017; F I G U R E 1 Analytical framework used to analyse differences in natural vs. human-modified habitats with respect to loser (grey) and winner species (black). Each of the 264 observed communities has a potential species richness (SR) and functional diversity (FD) given by its local probabilistic species pool, which consists of all species that can disperse into a site (defined as a 2° grid cell) and persists there given the environmental conditions (from the niche models, species distribution modeling [SDMs]). Observed communities were assigned to either natural or human-modified habitats based on the state of human modification in which the field observation took place (see Section 2). Differences in observed to potential SR (∆SR), and differences in observed to potential FD (∆FD) between these habitat types were tested using an ANOVA with a subsequent Post-hoc Tukey honestly significant difference (HSD) test. Small mammal communities could show different scenarios (S1-S4) of ∆SR and ∆FD. These scenarios can be distinguished by comparing ∆SR and ∆FD to ΔSR and ΔFD SES = 0 and subsequently testing scenario prevalence using a Pearson's chi-squared test. The ΔFD SES = 0 depicts a ∆FD that is equal to the null ∆FD [Colour figure can be viewed at wileyonlinelibrary.com] Umetsu et al., 2008). As our communities are globally distributed, we could assess local variation in observed species richness and functional diversity while accounting for regional differences in the species pool.

| Study group and data
Non-volant small mammals are relatively well sampled across the globe, and have been used as a model group to test the effect of land-use changes on biodiversity (e.g. Fleming et al., 2014;Luza et al., 2019;Pfeifer et al., 2017;Umetsu et al., 2008). We The database of Luza et al. (2019) contributed with 90% of the data and PREDICTS with the remaining 10%. These databases were created to foster spatial assessments of biodiversity variation between natural and human-modified habitats (e.g. Newbold, Hudson, Arnell, et al., 2016;Newbold et al., 2018). In both databases, small mammal data were collected in paired patches of human-modified and natural habitats, mostly from Neotropics and Nearctic. Generally, the community data in spatially close habitats were collected in the same study. Data were accompanied by information of sampling effort (trap-nights) and sampling techniques (mostly live traps such as tomahawk, Sherman and pitfall traps), which allowed to standardize effort across databases. PREDICTS data were gathered directly with data owners, whereas Luza et al. (2019)

| Habitat classification into natural and humanmodified habitats
We analysed variation in ∆SR and ∆FD based on state of human modification (either natural or modified) and habitat type (two types of natural habitats, and five types of human-modified habitats). Types of natural habitats in our study comprised forests and grasslands, the most common natural habitats found in land. Natural forests were defined as forests with minimum disturbance, advanced secondary regeneration and remnants in landscapes with an alternative land use. Natural grasslands were native grasslands and savannas, generally grazed by domesticated ungulates, and remnants in landscapes with an alternative land use (Veldman et al., 2015). These habitats are assumed to reflect the structure of natural habitats and having a similar species composition as natural habitats (Gibson et al., 2011;Newbold et al., 2015). Types of human-modified habitats included tree plantations (monocultures of trees), clear-cuts (cleared land at an early stage of regeneration), crop fields (fields covered by soybean, hay, maize tillage, sugarcane, among others), artificial forest edges (edge between a natural forest and a human-modified habitat) and artificial grassland edges (edge between a natural grassland and a human-modified habitat).

| Species traits for functional diversity
We used body mass, litter size, gestation length, weaning age, sexual maturity age (days) and population density from Penone et al. (2016) to estimate functional diversity. These traits distinguish fast-from slow-life histories and specialized from generalized life styles among small mammal species (Davidson et al., 2017;Flynn et al., 2009;Penone et al., 2016). All traits had pairwise correlation <0.5 and were standardized to zero mean and unit variance before analysis.

| Delineating the local probabilistic species pool
The local probabilistic species pool (LPSP; sensu: Karger et al., 2016) provides a baseline to assess whether SR and FD are different from their potential. A LPSP considers the probability of occurrence of a global set of species into a site based on (1) species dispersal abilities (the dispersal pool) and (2) the match between a species environmental preference and environmental conditions at a given site (the environmental pool).

| Dispersal pool
The dispersal pool consists of all species from the global pool of 1112 non-volant small mammal species which are able to potentially reach a specific site. We calculated the dispersal pool based on the annual dispersal rate k. The parameter k was based on published data on natal dispersal distances-the period in which an individual is more likely to disperse (Whitmee, & Orme, 2013) and its generation length-the age at which an individual achieves half of its total reproductive output (Pacifici et al., 2013). As natal dispersal distances were available only for 49 species and six orders (Dasyuromorphia, Didelphimorphia, Diprotodontia, Eulipotyphla, Lagomorpha and Rodentia), we used data imputation based on a random forest (RF) algorithm (Stekhoven & Buehlmann, 2012). The RF algorithm provides a solution to estimate natal dispersal distances in face of uncertainty and lack of large amounts of data, as is the case of dispersal here (availability of data for 49 out of 3079 species with generation length data). This solution resulted in a linear relationship between body size and dispersal distance ( Figure S1.1), a similar relationship as found by Santini et al. (2013) using allometric equations to imputing missing data (see Appendix S1, Figure S1.1 for details on the imputation procedure). After imputing, we calculated k using natal dispersal distances and generation length for the 1112 species included in our analyses.
We used k to estimate the probability of dispersal of each species to the cell n (D n ) as: (Bischoff, 2005) where the exponent of species dispersal rate k during the time t defines the ability a species has to disperse from n to N cells (Karger et al., 2016). Dispersal was calculated starting from each grid cell of a species current range based on IUCN range maps (IUCN, 2017) for t = 40 years. However, because we imputed many estimates, we conducted a sensitivity analysis and recalculated the dispersal pool with three measures of k: (1) k = 0.04, which is the overall mean dispersal of all species, (2) k = 0.5 and (3) k = 1, which were among the most extreme dispersal values we found in our data (Appendix S1). We reported only analyses using pools based on species-specific dispersal k as sensitivity analysis returned qualitatively similar results. Species-specific dispersal kernels at 2° horizontal resolution were calculated using the disppool function, in the 'probpool' package in R (Koenig et al., 2018).

| Environmental species pool
We estimated species occurrence probability given climate conditions using species distribution modelling (Guisan, & Thuiller, 2005).
As predictors, we used mean annual temperature, standard deviation of annual temperature, mean annual precipitation and standard deviation of annual precipitation at a 0.5-degree grid cell from chelsa v1.2 (Karger et al., 2017). For presence-absence data, we used the IUCN range maps (IUCN, 2017). Absences were weighted so that the sum of the absences equals the sum of the presences. We used an ensemble of generalized linear models (Nelder, & Wedderburn, 1972), generalized additive models (Hastie, & Tibshirani, 1986), and RFs to estimate a species probability of occurrence E n in a given cell (n) (Thuiller et al., 2019). We used a 10-fold cross-validation of the models and calculated the area under curve (AUC) statistics, kappa statistics and true skills statistics (TSS) to evaluate model goodnessof-fit (Appendix S2, Table S2.1). Overall, 997 of 1112 species were included in the environment-based pool. The missing 115 species had no IUCN range maps, or had distributions too small to fit species distribution models. These 115 species without environmental probability scores were added into to the LPSP by assigning a value of 1, highly suitable, to locations where they have been observed.

| Observed relative to potential species richness (ΔSR) and functional diversity (ΔFD)
To estimate potential species richness (PSR) of the LPSP, we calculated the probabilistic species pool size index i DE for each site, using: The index is based on the sum of probabilities P of occurrence of all species s = 1 to S, considering the product of the probabilities for all species generated by x = 1 to X factors (dispersal (D n ) and environment (E n ) in the cell n) used to delineate the pool. The ΔSR of each site was calculated as ΔSR = PSR − LSR, being LSR the local species richness calculated as the sum of all species incidences in a site n. Positive values of ΔSR indicate loss of species so that potential SR is not locally well represented.
The potential functional diversity (PFD) of the community in site n (PFD n ) was estimated using the probability of occurrence and trait data of species s = 1 to S included in the respective LPSP. We estimated PFD using the n-dimensional hypervolume approach (Blonder et al., 2014; further details in Appendix S3, Table S3.1). Estimation of the local functional diversity (LFD) followed the same method used to estimate PFD, but now considering only the species found in the local communities. The ΔFD of each site was calculated as ΔFD = PFD − LFD. Positive values of ΔFD indicate loss of function so that potential FD is not locally well represented.
One important characteristic of the LPSP is that all 1112 nonvolant small mammal species we analysed are included in each LPSP.
Thus, if we assume that all 1112 species in the pool have some probability to occur in a community, the values of PFD would be equal across sites. However, many species will occur with probabilities close to zero as they are very unlikely to disperse and establish in sites distant from their current occurrence. To arrive at a binary classification needed to estimate an average pool hypervolume we ran, for each site, a probability-weighted sampling of the 1112 species, with sample size equal to i DE species. We used 100 sampling runs per site to obtain a null average PFD NULL and standard deviation ( PFD NULL ) of the potential functional diversity (PFD) to calculate the ΔFD (hereafter 'ΔFD SES ') for each site as follows: where ΔFD OBS is the observed difference between LFD and the PFD NULL , while ΔFD NULL is the average null difference between the null LFD-now produced by a probability-weighted sampling of size equal to local species richness (LSR)-and the PFD NULL ; ΔFD NULL is the standard deviation of ΔFD NULL across the 100 sampling runs. An observed ΔFD higher than the ΔFD NULL will produce positive values of ΔFD SES as a result of functional loss relative to community potential, whereas an observed ΔFD lower than the ΔFD NULL will produce negative values of ΔFD SES as a result of no functional loss relative to community potential.
Sampling effort might be an important source of uncertainty when assessing human influence on local richness and functional diversity.
We explored whether ΔSR and ΔFD SES were sensitive to different sampling effort by running analyses with three datasets based on sites sampled with >100, >500 and >1000 trap-nights.

| Distinguishing scenarios and testing their prevalence
To distinguish between the hypothetical scenarios S1-S4 (Figure 1), we defined a threshold to group sites into each of the four scenarios of human influence. To distinguish between S1 and S3, we used the global average ∆SR (ΔSR), as it represents the average difference in observed relative to potential SR across all studied communities. To distinguish between S2 and S4, we used ∆FD SES = 0, which depicts that the observed ∆FD is equal to the ΔFD NULL . As the grouping based on ΔSR and ∆FD SES = 0 is somewhat arbitrary, we conducted a sensitivity analysis where we defined thresholds along regular intervals of observed values of ∆SR and ∆FD SES (Appendix S5, Figures S5.1 and S5.2). After distinguishing scenarios, we tested differences in their frequency between natural and human-modified habitats using a Pearson's chi-squared analysis under a null assumption of equal number of sites across the combinations of scenarios and habitats. We ran this analysis using the chisq.test function in 'stats' package of R (R Core Team, 2020).

| Geographical variation in scenarios
To evaluate whether the prevalence of scenarios varied by biome, we assigned each site to one of the WWF biomes (Olson et al., 2001). We grouped biomes to show differences between temperate and tropical biomes, and forest-and grassland-like vegetation as (1) tropical forests: tropical and subtropical moist broadleaf forests, tropical and subtropical dry broadleaf forests; (2) temperate forests: boreal forests/taiga, Mediterranean forests, woodlands and scrub, temperate broadleaf and mixed forests, temperate conifer forests; (3) tropical grasslands: montane grasslands and shrublands, tropical and subtropical grasslands, savannas and shrublands; (4) temperate grasslands: temperate grasslands, savannas and shrublands. We used a Pearson's chi-squared analysis to identify significant differences among biomes and habitats in the number of sites assigned to each scenario.

| Testing differences between states of habitat modification and habitat types
Average ∆SR across natural habitat communities was 14.63 ± 8.28 species, and it was 10.98 ± 6.31 species across human-modified habitats; the global average of ∆SR was 13.12 ± 7.72 species. Average ∆FD SES across natural habitat communities was 0.58 ± 0.39 SDs, and it was 0.65 ± 0.41 SDs from the ΔFD NULL across human-modified habitats; the global average of ∆FD SES was 0.61 ± 0.40 SDs from the ΔFD NULL .
Analysis of variance showed a difference in observed relative to potential species richness (∆SR) between states of habitat modification. The ∆SR was 3.66 species higher in natural habitats when compared with human-modified habitats (F 1,262 = 15.08, p < 0.001, Figure 2; Figure S4.1). We found no difference in ∆FD SES between natural and human-modified habitats (F 1,262 = 1.62, Analysis of variance with post-hoc TukeyHSD test showed that habitat type influenced ∆SR (F 7, 256 = 116.2, p < 0.001). Forests and grassland had higher ∆SR than clear-cuts (Figure 3). We also found that habitat type influenced ∆FD SES (F 7, 256 = 100.1, p < 0.001).
TukeyHSD tests showed that clear-cuts and forest edges had higher ∆FD SES than crop fields (Figure 3)

| Testing the four scenarios of human influence
We found that scenarios 2 and 4 were the most common in our data.

| Geographical variation in scenarios
Pearson's chi-squared analysis showed a significant difference in scenarios among biomes (χ 2 = 93.09, df = 21, p-value ≤ 0.001). Scenarios 2 was prevalent in both human-modified and natural habitats of temperate forests, whereas scenario 4 was prevalent in both humanmodified and natural habitats of tropical forests (Table 2). While scenario 4 was common in natural temperate grasslands, scenario 2 was common in human-modified habitats of temperate grasslands (Table 2). Scenario 4 was prevalent in natural tropical grasslands.

| Sensitivity analysis
Our results were robust across sensitivity analyses considering unknown dispersal ability, differences in sampling effort or thresholds for grouping communities into scenarios. We estimated speciesspecific dispersal along a timeframe of 40 years, which marked the beginning of the green revolution period (Laurance et al., 2014).
Using this timeframe and dispersal data from literature (Whitmee, & Orme, 2013), we found very few non-volant small mammals able to disperse more than one degree over 40 years; overall, species have low dispersal rates (average of 184.66 ± 329.93 m/year; Appendix S1). Accordingly, studies of non-volant small mammals using other methods suggest that most of dispersion events occur at 100-500 m of a site (Bowman et al., 2002;Umetsu et al., 2008). Therefore, human influence along these 40 years likely promoted immigration only to the adjacent sites (Bovendorp et al., 2019;Umetsu et al., 2008).

| DISCUSS ION
Using ∆SR and ∆FD-which quantify how far communities are from their potential-we showed that human-modified habitats are closer to their potential richness than natural habitats. However, they are not closer to the functional diversity potential. Communities can undergo compositional changes while species richness is maintained, resulting in species replacement over space and time, and no systematic loss of richness (Blowes et al., 2019;Dornelas et al., 2014;Sax et al., 2005). We found a prominence of scenario 2 in humanmodified habitats-∆SR is lower than the global average of ∆SR, and ∆FD SES is higher than zero-depicting no change in richness but loss of functional diversity relative to community potential. However, we found S4 most prevalent in natural habitats-∆SR and ∆FD are both higher than global ∆SR average and zero, respectively-depicting loss of richness and functional diversity relative to community potential. We also found a variation of the most prevalent scenario across biomes, reinforcing that human influence on local community diversity shows geographical variation (Blowes et al., 2019;Brodie et al., 2021). These two main observations directly question whether a simple increase in species richness in human-modified habitats still contributes to ecosystem functioning and habitat intactness (sensu Newbold, Hudson, Arnell, et al., 2016;Steffen et al., 2015).
Changes in species composition, or even an increase in species richness with human influence, usually did not coincide with a similar change in functional diversity (Dornelas et al., 2014;Mouillot et al., 2013;Sax et al., 2005;Sobral et al., 2016). More specifically, such an accrual of species did not expand the functional hypervolume or F I G U R E 4 Geographical variation in the relationship between ∆SR and ∆FD SES . The top panel are maps of potential species richness and functional diversity (PFD, on square root scale) of the local probabilistic species pool (LPSP) at a resolution of 2 × 2-degree. Functional diversity is estimated by sampling i DE species from the LPSP based on their probability of occurrence. We repeated the procedure 100 times and then calculated an average potential hypervolume PFD for each grid cell. The unit of functional diversity, as measured by the n-dimensional hypervolume, is in standard deviations of transformed (centred and scaled) trait values, raised to the power of the number of traits. In the bottom panel, we present the studied sites with >1000 trap-nights and their respective scenario. FD, functional diversity; SR, species richness [Colour figure can be viewed at wileyonlinelibrary.com]

| Predominance of the scenarios in natural and human-modified habitats
The high prevalence of scenario 2 (71% of the cases) of no change in richness but loss of functional diversity relative to community potential could be explained by the intense and permanent management of human-modified habitats. Such a management often leads to local extinctions of 'loser' mammals: those with narrow range (Newbold et al., 2018), small litter size and slow life history (Carmona et al., 2021;Cooke et al., 2019;Flynn et al., 2009), and specialized diet (Brodie et al., 2021;Flynn et al., 2009;Hurst et al., 2014) and life habits (Fleming et al., 2014). For instance, species with litter size smaller than 2.25 individuals per litter/individual, and diet based on fish, fruit, seeds or nuts, might not persist with agriculture intensification and natural habitat loss (Brodie et al., 2021;Flynn et al., 2009;Hurst et al., 2014). Also, specialized digging mammals have been shown to decline under habitat loss and introduction of exotic species (Fleming et al., 2014). The loss of these unique community components is a global-wide process (e.g. Brodie et al., 2021;Carmona et al., 2021) that may hamper critical ecosystem processes such as the rate of predation, dispersal and recruitment of seeds, and the structure, dynamics and chemistry of soils (Bovendorp et al., 2019;Fleming et al., 2014;Flynn et al., 2009;Hurst et al., 2014;Santos-Filho et al., 2016). While these losers decline, generalists and widespread 'winner' species can increase in number without adding ecological functions (Newbold et al., 2018;Sobral et al., 2016).
Small mammals known to profit from human disturbances are usually terrestrial, small-sized, omnivores or insectivores, and prolific breeders under a wide range of environmental conditions (Castro, & Fernandez, 2004;Luza et al., 2015;Pfeifer et al., 2017), which may explain why scenario 2 is prevalent in most human-modified habitats. More than half (52%) of the sites with natural habitat showed high ΔSR and ΔFD, indicating that species richness and functional diversity are lower than their community potential. The prevalence of scenario 4 in natural habitats indicates that the local extinction of specialist and narrow-ranged 'losers' are not counterbalanced by generalist and widespread 'winner' small mammals (Newbold et al., 2018). There are two possible explanations for this result: (1) human influence in the surrounding landscape is influencing natural habitats, causing local extinctions and preventing compensatory immigrations (Bogoni et al., 2018;Bovendorp et al., 2019;Pfeifer et al., 2017); (2) the probabilistic species pool only includes dispersal and environmental filters, but neglects any potential biotic interactions (Karger et al., 2016;Lessard et al., 2016). For example, predator release in modified landscapes results in an increase in biomass of a few generalists which, in turn, leads to an increase in interspecific competition for limited resources and microhabitats (Bogoni et al., 2018;Bovendorp et al., 2019).
Scenarios which predict either a community under low rates of extinction and colonization (S1) or gains in functional diversity (S3) are almost absent in our data. It makes clear that human influence without changes in functional diversity is unlikely, and that a loss of functional diversity is the most likely outcome of human influence on non-volant small mammal communities.

| Differences between habitat types
Communities from human-modified habitats under intense management, such as clear-cuts and forest edges, showed the highest functional loss (observed ΔFD was higher than null ΔFD, producing positive ΔFD SES ). Clear-cuts, which result from forest logging and are rapidly transformed into crop fields, artificial pastures and tree monocultures (Laurance et al., 2014), presented a richness closer to the potential-lower ΔSR-than forests and grassland, and a functional diversity farther from their potential-higher ΔFD SES -than crop fields. A similar functional deficit was found for forest edges. Forest edges are often formed through forest loss and fragmentation (Pfeifer et al., 2017). As these edges are in close contact with the surrounding matrix, generally composed by environmentally and structurally contrasting habitats such as crop fields and artificial pastures, they differ in fundamental microhabitat conditions (e.g. temperature and humidity) relative to forest-core habitats (Castro, & Fernandez, 2004;Pfeifer et al., 2017). Edge formation has therefore promoted declines in abundance and local extinction of forest-core species while fostering the colonization of edge-tolerant, matrix-tolerant and gapcrossing species into edge habitats (Castro, & Fernandez, 2004;Umetsu et al., 2008). Consequently, communities from these severely disturbed habitats are well below their potential functional diversity.

| Geographical variation in scenarios
Rates of biodiversity change are heterogeneous across regions (Blowes et al., 2019;Brodie et al., 2021;Davidson et al., 2017;Dornelas et al., 2014). Temperate and tropical forest biomes that still maintain extensive areas of natural habitats (Newbold, Hudson, Arnell, et al., 2016) and are under slow rates of biotic change (Blowes et al., 2019) could present scenario 1, whereas temperate and tropical grasslands and savannas that are severely modified by humans (Newbold, Hudson, Arnell, et al., 2016;Veldman et al., 2015) and likely under fast rates of change could present scenario 4. We found a single prevalent scenario in the different states of human modification within a biome but variation in scenarios among biomes, except for temperate grasslands. The predominance of just one scenario per biome is expected due to its homogeneous species pool (Olson et al., 2001;Penone et al., 2016). However, more than one scenario can occur when the intensity of use and the degree of land-cover change compete with environmental filters in explaining regional biodiversity (Kehoe et al., 2017).
Scenario 2 of no change in richness but loss of functional diversity relative to community potential predominated in temperate forests, a biome under long-standing human influence (Blowes et al., 2019;Newbold, Hudson, Arnell, et al., 2016;Newbold et al., 2018;Song et al., 2018) and-as we did not observe richness loss-with enough time for species to adapt to novel conditions and immigrate into modified habitats (Newbold et al., 2018). Furthermore, biologic invasions are a major driver of local biodiversity change in temperate ecosystems (Murphy, & Romanuk, 2014). Although invaders competitively exclude local species in temperate forests, recent time-series analyses also show local gains of richness through immigration (e.g. Blowes et al., 2019). Our results add to this and show that such richness gains do not necessarily add functional diversity to non-volant small mammal communities from temperate forests.
Two scenarios predominated in the different states of human modification in temperate grasslands. This is globally the biome most influenced by humans as it is mechanistically easy to convert into other land uses, and is naturally suitable for cattle raising (Medan et al., 2011;Newbold, Hudson, Arnell, et al., 2016;Veldman et al., 2015). For instance, temperate grasslands are one of the regions presenting the highest agricultural yields in the world (Kehoe et al., 2017). Severe land-use change and landscape homogenization along the last centuries explain the predominance of scenario 2 in humanmodified habitats of temperate grasslands, such as crop fields. This scenario reveals the functionally redundant, depauperated community of small mammals occupying these habitats subjected to severe temporal variation in resource availability and microclimates due to the planting and harvesting of annual crops (Bilenca et al., 2007;Medan et al., 2011). In turn, the prevalence of scenario 4-richness and functional diversity loss-in natural grasslands of temperate regions can be explained by the too intensive grazing and burning regimes applied on grasslands used to cattle raising, which can be detrimental to the local biodiversity of these ecosystems (Andersen et al., 2012;Luza et al., 2015).
In turn, scenario 4 of richness and functional diversity loss relative to community potential predominated in tropical forests and grasslands, where human influence has been more recent but not less pervasive (Newbold, Hudson, Arnell, et al., 2016;Song et al., 2018). Habitat loss and harvesting (hunting and poaching) are the main causes of mammal population declines in the tropics (Bogoni et al., 2018;Brodie et al., 2021), with an extinction probability especially high for narrow ranged and functionally unique species that do not occur anywhere else (Brodie et al., 2021;Gibson et al., 2011;Newbold et al., 2018).
Furthermore, community and ecosystem impoverishment and biodiversity losses are expected in the coming decades whether actions to conserve tropical environments and species are not met (Brodie et al., 2021;Song et al., 2018).

| Shortfalls of SDMs and data
The probabilistic pools included in this study only account for ~33% of the global number of non-volant small mammal species.
The size of the LPSP, and also ΔSR and ΔFD SES , could therefore be underestimated (Karger et al., 2020). Omitting these species could bias our results towards the most optimistic scenario (S1), as we could omit severely threatened species experiencing human influence throughout their range (Newbold et al., 2018). We minimized these drawbacks by adding all species locally observed to the LPSP, including recently described and small-ranged species. Results suggest that such errors might be homogeneous over space, as neither scenario 1 predominate nor potential richness and functional diversity maps differ from existing ones (e.g. Oliveira et al., 2016). Finally, it is noteworthy that most data are from the Neotropics and Nearctic, while the Indo-Malay region and the eastern Palaearctic are underrepresented in the datasets we used here (Hudson et al., 2017;Luza et al., 2019). These regions have high richness and functional diversity of non-volant small mammals (Figure 4), and are currently under high rates of land-use change (Laurance et al., 2014;Song et al., 2018). As such, they are expected to behave like other tropical forest and grassland regions-that is, present the scenario S4 of richness and functional diversity loss relative to community potential-although data are needed to confirm this hypothesis.

| CON CLUS ION
Human modification of habitats can have multiple effects on species richness and functional diversity. For non-volant small mammal communities, a larger species richness in human-modified habitats did not result in larger functional diversity. Rather there seems to be an increase in functional redundancy, as the species which profit from human modification do not bring new functions into humanmodified habitats. An increase in species richness is often seen as a positive aspect, but if this increase in species richness did not coincide with an increase in ecological function, a higher species richness could instead weaken the capacity of habitats to withstand growing anthropogenic pressures, weakening ecosystem services and diminishing nature contribution to people.

ACK N OWLED G EM ENTS
ALL received a sandwich-doctorate fellowship from Brazilian and Cristian Dambros (UFSM) for the helpful comments during the conception of this study. We also thank the review done by Editor Fabricio Villalobos. Species distribution modelling was conducted on the Hyperion Supercomputer (WSL, Birmensdorf-CH). No permits were required to conduct this research.

CO N FLI C T O F I NTE R E S T
We have no conflict of interest to declare.

DATA AVA I L A B I L I T Y S TAT E M E N T
The community data of Luza et al. (2019)