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A latitudinal gradient in dimensionality of biodiversity Richard D. Stevens1 and J. Sebastián Tello2,3 1

Department of Natural Resources Management and the Museum of Texas Tech University, Lubbock TX 79409 2

Center for Conservation and Sustainable Development, Missouri Botanical Garden, P.O. Box 299, St. Louis, Missouri 63166, USA 3

Escuela de Biología, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076 y Roca, Apdo. 17-01-2184, Quito, Ecuador Corresponding author: Richard D. Stevens, Department of Natural Resources Management and the Museum of Texas Tech University, Lubbock TX 79409. Email:[email protected] Decision date: 05-Mar-2018 This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: [10.1111/ecog.03654].

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ABSTRACT Biodiversity is multifaceted and represents numerous dimensions expressing variation in richness and abundances of species, ecosystem functions, phylogenetic relationships, morphology, traits and interactions. Such dimensions are correlated to varying degrees and recent research has attempted to better understand behavior of such correlations. We define dimensionality of biodiversity as degree of redundancy in variation among multiple dimensions of biodiversity. One fundamental question regarding biodiversity is whether its dimensionality is spatially structured, also exhibiting geographic gradients. We examine if redundancy among dimensions of biodiversity changes latitudinally thereby contributing to increased tropical complexity. Geographic range maps of bats were overlaid on a 100 × 100 km grid of the New World to determine species composition of each cell. Species richness and three measures each of phylogenetic, functional and phenetic diversity were calculated. Dimensionality was estimated as evenness of eigenvalues generated from a principal components analysis (PCA) of multiple measures of biodiversity. High dimensionality is characterized by low correlations among biodiversity measures and high evenness of eigenvalues from PCA, whereas low dimensionality is characterized by high correlations and low evenness of eigenvalues. Latitudinal gradients of dimensionality were determined by regression analysis. Slope of the empirical relationship was compared to slopes generated from two null models that randomized the distribution of species. Dimensionality of biodiversity does indeed exhibit a latitudinal gradient, decreasing with increasing latitude. This empirical gradient was stronger than expected by the random distribution of species. Additionally, spatial variation in dimensionality of biodiversity could not be explained by a similar underlying


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pattern in variation of environmental conditions. Correlations among different dimensions of biodiversity vary spatially, and interpretations of such correlations should be geographically explicit. Mechanisms proposed to explain latitudinal gradients need not only account for gradients of biodiversity, but gradients in dimensionality as well. A gradient in dimensionality suggests that conservation strategies that rely on maximization of a single metric, such as species richness, might be of varying utility in different geographic contexts.

Keyword: dimensions of biodiversity, functional diversity, latitudinal gradient, phenetic diversity, phylogenetic diversity, taxonomic diversity


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Introduction For more than a century, ecologists, evolutionary biologists and biogeographers alike have sought to describe and understand broad scale patterns of biodiversity that characterize the world’s biota. Some of the most conspicuous and consistent patterns on earth are latitudinal gradients in biodiversity, in particular those observed for species richness. Indeed, number of species increases from the poles to the equator for most taxa, across most continents and oceans, and at most spatial and temporal scales (Rosenzweig 1995, Willig et al. 2013, Hillebrand, 2004). Recently, researchers have begun to characterize patterns in other forms of biodiversity involving ecological functions, evolutionary history, morphology/traits, and species interactions (Findley 1973, Martinez 1992, Webb 2000, Petchy and Gaston 2006). Patterns in these other forms of biodiversity are not as well understood as gradients in species richness. Nonetheless, like richness, other forms of biodiversity are not randomly distributed across space (Stevens et al. 2013). Instead, variation exhibits strong spatial structure at geographic scales, and some regions hold a disproportionate amount of the world’s biological diversity (Lamana et al. 2014, Silva and Brandoa 2014). For numerous reasons, from similar responses to underlying environmental gradients to

mathematical and statistical non-independences, multiple forms of biodiversity covary across space and time (Devictor et al. 2010, Meynard et al. 2011, Cisneros et al. 2014, Stevens and Tello 2014, Stevens and Gavilanez 2015). This co-variation among forms of diversity can be used to create powerful tests of effects of ecological and evolutionary mechanisms on spatial patterns of biodiversity (McGill 2003, Buckley et al. 2010, Stevens 2011), and can provide critical information about levels of anthropogenic threat and protection on species and ecosystems (Ceausu et al. 2015, Cisneros et al. 2015). Despite these potential important ‘This article is protected by copyright. All rights reserved.’

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theoretical and practical applications of studying biodiversity as a multidimensional phenomenon (Naeem et al. 2016), we are still just discovering how different dimensions are related to one another. Thus, one of the most fundamental questions for every examination of multiple forms of biodiversity is “how dimensional is the data set representing those multiple forms of biodiversity?” We define three important concepts for understanding dimensionality of biodiversity

(Figure 1). First, a dimension of biodiversity represents a unique conceptual form of diversity such as taxonomic, functional or phylogenetic diversity. This term is familiar to most ecologists and has been used for decades (Holloway and Stork 1991, Patterson 1994). A biodiversity measure is a numerical value calculated to express a particular dimension of biodiversity (e.g., species richness, Faith’s phylogenetic diversity or functional mean nearestneighbor distance). Finally, dimensionality of biodiversity refers to the degree of redundancy (co-variation) in spatial or temporal variation among multiple dimensions of biodiversity (Donohue et al. 2013). In this way, dimensionality quantifies how much each biodiversity measure represents an independent axis of variation. A low-dimensionality dataset would be composed of strongly correlated biodiversity measures (Figure 1). Hence, measures are redundant, variation in one measure would be a good surrogate for variation in others, and most multivariate variation could be summarized by only a few important orthogonal axes (as derived from a principal component analysis, for example). On the other hand, a highdimensionality dataset would contain biodiversity measures that are for the most part uncorrelated (Figure 1). Hence, measures are complementary, variation in one measure does not represent variation in others, and the majority of multivariate variation cannot be represented by a reduced set of derived axes (Stevens and Tello 2014).


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We still know little about dimensionality of spatial and temporal patterns of biodiversity.

Previous research has reported correlations among different dimensions of biodiversity (Devictor et al. 2010, Meynard et al. 2011, Cisneros et al. 2014, Stevens et al. 2006), implying low dimensionality at least from a spatial perspective. However, to our knowledge only two studies have explicitly quantified dimensionality of biodiversity and tested potential underlying mechanisms that may create such structure (Stevens and Tello 2014, Stevens and Gavilanez 2015). These two studies differ from those prior because they directly address redundancy of multiple dimension of biodiversity. Moreover, they demonstrated that dimensionality of biodiversity of Noctilionoid bats across the New World tends to be different than expected given underlying patterns of species richness and mathematical dependencies among measures, suggesting that ecological and evolutionary processes beyond those determining species richness gradients are needed to account for variation in other dimensions of biodiversity. Nonetheless, dimensionality studies are few, and underlying variation in evolutionary history of clades and environmental conditions of regions may create important differences in how biodiversity is expressed and distributed. Previous studies (Stevens and Tello (2014) and Stevens and Gavilanez (2015)) demonstrated that observed levels of dimensionality of biodiversity are different than random expectations based on a number of different null models, but we still don’t know how dimensionality and its deviations from random expectations might vary through space or time in any portion of the world. Thus, more research is needed to determine whether the results reported so far are a general characteristic of life on earth, or particular to the groups or regions that have been studied. Whether dimensionality (co-variation among dimensions of biodiversity) varies


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geographically or not is a fundamental question regarding the distribution of biodiversity that remains unanswered. Here, we use taxonomic, phylogenetic, functional and phenetic data to explore large-scale

geographic patterns of variation in dimensionality of biodiversity. Specifically, we address three hypotheses. First, many indices of biodiversity exhibit latitudinal gradients (Willig et al. 2003). This is the result of changes in species richness, as well as changes in the complexity of assemblage composition from tropical to temperate latitudes (Stevens et al. 2013). Accordingly, we examined the hypothesis that co-variation among biodiversity measures also changes with latitude and represents another manifestation of increases in complexity toward the equator. This hypothesis predicts that measures of biodiversity will be less correlated at low than at high latitudes, resulting in greater dimensionality of biodiversity in the tropics. Second, magnitude of many measures of biodiversity can increase with species richness for two reasons: a) an increase in the number of items being measured (species) generates more variance and 2) repeated co-occurrences of species can produce correlations among aggregated measures of community structure (as demonstrated by Hawkins et al. 2017). These effects alone, without influence of any biological mechanism, could create gradients in measures of biodiversity and ultimately their dimensionality. This second hypothesis predicts that any spatial variation in dimensionality of biodiversity is solely the product of variation in species richness and patterns of co-occurrence. Lastly, environmental conditions are strong predictors of geographic patterns in a number of different biodiversity measures in many groups of organisms (Field et al., 2009), including Neotropical bats (Tello and Stevens 2010). Thus, if (1) each measure of biodiversity responds to a different environmental gradient (e.g. richness correlates with temperature, but functional diversity with precipitation), and (2)


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environmental gradients are more correlated with each other in some regions than others (e.g. higher temperature-precipitation correlations in temperate than tropical regions), then spatial gradients in dimensionality of biodiversity could result from an underlying gradient of environmental dimensionality. This hypothesis predicts a positive relationship between dimensionality of biodiversity and dimensionality of environmental conditions.

Materials and Methods Measuring multiple dimensions of biodiversity Patterns of distribution and diversity of the bat super-family Noctilionoidea were characterized based on geographic range map overlaps of 133 species (Patterson et al. 2007, Tello and Stevens 2010). The continental New World was divided into 100 × 100 km grid cells (Figure 2), and species whose geographic range maps overlapped a particular cell were included in the list of species for that cell. We then computed 10 biodiversity measures representing taxonomic, functional, phylogenetic and phenetic dimensions of biodiversity. To represent taxonomic diversity, we simply calculated species richness per cell (Figure

2). To represent phylogenetic diversity, we used the noctilionoid portion of the mammal supertree of Bininda-Emonds et al. (2007). We calculated Faith’s phylogenetic diversity (PD, [Faith 1992]), phylogenetic species variability (PSV, [Helmus et al. 2007]) and phylogenetic species clustering (PSC, [Helmus et al. 2007]). PD represents the sum of branch lengths of all taxa within a grid cell. PSV reflects the distribution of pair-wise phylogenetic distances among species, while PSC measures the distribution of nearest-neighbor distances among species (Helmus et al. 2007). Measures of phylogenetic diversity were calculated using the R package PICANTE (Kembel et al. 2010). To represent functional diversity, we used the


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frequency distribution of species across six functional groups based on diet: aerial insectivores, frugivores, gleaning animalivores, nectarivores, piscivores and sanguinivores (Stevens et al. 2013). We then determined richness of functional groups per grid cell, diversity of functional groups based on Shannon’s index (Magurran and McGill 2011), and evenness of functional groups based on Camargo’s index (Camargo 1993). These measures characterize the diversity of pathways whereby bats move carbon, other nutrients, matter and energy through ecosystems. Finally, we characterized phenetic diversity based on 7 morphological variables (Stevens and Willig 1999): forearm length, greatest length of skull, condylobasal length, length of maxillary toothrow, breadth of post-orbital constriction, breadth of braincase, breadth across upper molars. Measures were based on the mean of 4 males and 4 females for most species. These morphological variables estimate overall body size as well as the size and shape of the cranium, an important trophic apparatus involved in mastication of food (see Stevens and Willig 1999 for details). Because morphological variables are log-normally distributed (LaBarbera 1989), we log-transformed values for each morphological measure and then estimated three measures of phenotypic diversity for each grid cell. Morphological volume was estimated as the product of the ranges of all morphological variables (Ricklefs and Travis 1980). Morphological variability was estimated by the standard deviation (STD) of the lengths of a minimum spanning tree joining all species in multidimensional space (Ricklefs and Travis 1980). Finally, phenetic clumping was estimated as average distance of a species to its nearest morphological neighbor (Stevens and Willig 1999). A plethora of biodiversity indices are now in existence (Magurran 2004), including

complimentary measures such as Hills numbers (Hill 1973, Chao et al. 2014) and sets based


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on Quadratic Entropy (Botta-Dukat 2005, Pavoine et al. 2005). We chose to focus on the indices employed here because they have formed the basis to our development of the concept of dimensionality of biodiversity (Stevens et al. 2013, Stevens and Tello 2014) and adopting some other set might detract from the clarity and consistency of this development. Nonetheless, the selection of diversity measures should not matter. To account for potential dependency of results based on the particular metrics selected, we ran additional analyses. First, we subsampled from the 10 measures of biodiversity used here a range of smaller subsets and reran analyses of dimensionality to determine whether the choice of particular indices affects conclusions drawn. These subsampled analyses always provided similar results as those based on all 10 measures (Stevens and Tello 2014). Second, we conducted additional analyses using an alternative set of biodiversity measures: species richness, mean phylogenetic distance, mean distance to nearest phylogenetic neighbor, standard deviation of distances to nearest phylogenetic neighbor, mean phenetic distance, mean distance to nearest phenetic neighbor, standard deviation of distances to nearest phenetic neighbor, as well as richness, diversity and evenness of functional groups. These alterative analyses led to identical conclusions regarding dimensionality of biodiversity (results not shown). Quantifying dimensionality of biodiversity Dimensionality describes redundancy and thus correlation among biodiversity measures across sites. Consequently, dimensionality is a matrix characteristic (i.e., rows equal geographic grid cells and columns represent measures of biodiversity). Although latitudinal gradients in diversity have often been examined using either square quadrats or latitudinal bands that vary in size longitudinally, they often yield qualitatively similar results (Willig and Selcer 1989, Willig and Sandlin 1991). Accordingly, to describe patterns of latitudinal ‘This article is protected by copyright. All rights reserved.’

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variation, dimensionality of biodiversity was calculated (as described below) for 42 latitudinal bands. A matrix for each band was formed by grouping two rows of grid cells (Figure 2) and their corresponding measures of biodiversity. Thus, each band had a latitudinal extent of 200 km. Bands of different dimensions have different numbers of cells and thus different sample sizes from which to conduct analyses. We chose bands of this particular dimension (2 rows by the number of columns that would fit longitudinally at that latitude) for our analyses so as to maximize the number of latitudinal bands for more powerful inferential tests (i.e., to maximize sample size). Nonetheless, assessment of patterns of biodiversity could be scaledependent (Lyons and Willig 2002). Analyses were also conducted on bands of other dimensions of 3, 4, 6, 7 or 12 rows of cells (divisors of 84, the total number of rows in the map; Figure 2). Results of analyses at larger scales were qualitatively similar and are presented among the Supplementary Material. To characterize dimensionality of biodiversity in each latitudinal band, we evaluated the

degree of redundancy (i.e., covariation) among the 10 biodiversity measures described above. To do this, we conducted a principal components analysis (PCA) on each latitudinal band based on a Pearson Product-Moment (PPM) correlation matrix. The average PPM coefficient was higher than the average Spearman-rank coefficient, suggesting that relationships among biodiversity measures were primarily linear (Sokal and Rohlf 1995). Analyses using either type of correlation matrix lead to identical conclusions (results not shown). Dimensionality in each latitudinal band was measured using Camargo’s evenness

(Camargo 1993) calculated on the magnitude of eigenvalues across axes derived from PCA (Figure 1). Evenness of eigenvalues characterized redundancy in the distribution of biodiversity. Low-dimensionality datasets contain strongly-correlated (redundant) ‘This article is protected by copyright. All rights reserved.’

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biodiversity measures. Consequently, the distribution of variation in biodiversity across principal components would be highly uneven: a few principal components would account for most of the multivariate variation, while most other principal components would represent only small fractions of variation (Figure 1). In contrast, highly dimensional datasets contain weakly-correlated (complementary) measures of biodiversity. In this case, variation would be more homogeneously distributed across principal components, and no principal component would account for a disproportionately large fraction of multivariate variation (Figure 1). In this context, high evenness of eigenvalues represents high dimensionality of biodiversity and low redundancy among measures. We found that evenness of eigenvalues was strongly correlated with other potential measures of dimensionality such as the mean absolute correlation among all pairs of biodiversity measures (Figure S2) or the determinant of the PPM correlation matrix (results not shown). Moreover, analyses using these alternative measures of dimensionality lead to identical conclusions, and are presented among the Supplementary Material. Latitudinal gradients in dimensionality of biodiversity To test our first hypothesis and quantify the empirical latitudinal gradient, we used linear ordinary least squares regression (Sokal and Rohlf 1995) to relate dimensionality of biodiversity (Camargo’s evenness or mean absolute correlations) to mean latitude per band. Because the area of latitudinal bands varied considerably due to variation in their longitudinal extents, we also included the number of cells per band as an additional independent variable in this regression model. A significant latitudinal effect would demonstrate a large-scale latitudinal gradient in dimensionality of biodiversity after controlling for differences in latitudinal bands in terms of area. ‘This article is protected by copyright. All rights reserved.’

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Often times when biodiversity gradients are related to environmental variables a

correction for spatial autocorrelation is made. Positive spatial autocorrelation in regression residuals can inflate the significance of the environmental predictors (Legendre 1993). In our analyses, however, we are interested in characterizing the spatial structure of dimensionality of biodiversity across latitudes, and not trying to understand the effect of an environmental variable that exhibits spatial variation. Because the only spatial dimension of interest for our analyses is latitude and this is a predictor of interest in our models, we do not need to correct for spatial autocorrelation. In fact, such a correction could lead us to an incorrect estimate of the effect of latitude in our regression models. Null model analyses to control for species richness and co-occurrence To test our second hypothesis and investigate whether latitudinal patterns in dimensionality of biodiversity result from gradients in species richness or the size and position of empirical geographic ranges (Figure 2), we compared empirical values of dimensionality per latitudinal band to dimensionality expected based on two null models. In these null models, number of species per cell was constrained to be identical to empirical data, but the geographic distribution of species (and hence their phylogenetic, phenetic and functional information) was randomized across space. Null model 1 used the “fixed sites and equiprobable species” (FiSi & EqSp) randomization algorithm described by Gotelli (2000). In this null model, species composition of each grid cell was the result of random sampling from a continentwide species pool. All species had the same probability of being assigned to a cell, and sampling stopped when the empirical value of richness in each cell was reached. In this way, null model 1 maintains underlying species richness gradients, but randomizes the sizes of species distributions (number of occupied cells) and destroys the position and cohesion of ‘This article is protected by copyright. All rights reserved.’

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empirical geographic ranges. Null model 2 uses a randomization algorithm that we termed the “range identity randomization” (Range ID Rand.), which is similar to the tip randomization algorithm used frequently in phylogenetic analyses (Helmus et al. 2007). The tip randomization algorithm reshuffles (i.e. permutes) the names of species associated with terminal positions in a phylogenetic tree (tips). Similarly, our range identity randomization algorithm reshuffles species names associated with geographic ranges. In this way, null model 2 controls not only for species richness gradients, but also for other realistic elements in the distribution of species such as size, cohesion, and relative position of geographic ranges as well as co-occurrence. In both null models, the geographic distribution of species is randomized, but each species maintains its phylogenetic position as well as its functional and phenetic traits. Each randomization algorithm was run 1,000 times. For each run, we (1) re-calculated

biodiversity measures and dimensionality as described above, and (2) regressed these null values of dimensionality against latitude and area of latitudinal bands. This produced frequency distributions of 1,000 null regression coefficients. We considered observed effects of latitude or area to be statistically significant if empirical regression coefficients were outside of the 95% most common values in the null distributions (i.e., beyond the 2.5% and 97.5% percentiles). Finally, we calculated standardized effect sizes for each latitudinal band. These values

reflect the degree of deviation of empirical dimensionality in a band from the values expected by either null model. Significant deviations from null model 1 suggest that species richness gradients are not enough to account for empirical values of dimensionality of biodiversity (Stevens and Tello 2014). Deviations from null model 2 would additionally indicate that there ‘This article is protected by copyright. All rights reserved.’

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are non-random spatial patterns in the distribution of phylogenetic, functional and phenetic dimensions of biodiversity. We regressed standardized effect sizes against latitude and area to examine if a latitudinal gradient in dimensionality of biodiversity remained even after accounting for species richness gradients (null models 1 & 2) and the empirical structure of geographic ranges (null model 2). Dimensionality of environmental conditions We were also interested in testing the hypothesis that geographic variation in dimensionality of biodiversity might reflect parallel gradients in the dimensionality (co-variation) of underlying environmental variables. Thus, for each latitudinal band, we calculated environmental dimensionality in a way equivalent to that used for the biodiversity data (see Quantifying dimensionality of biodiversity). Instead of biodiversity measures, we used 9 variables representing energy, environmental heterogeneity and climate seasonality within each cell on the map (Tello and Stevens 2010). Energy was represented by cell averages of net primary productivity (NPP), annual precipitation and mean annual temperature. Environmental heterogeneity was estimated by within-cell standard deviations of elevation, NPP, annual precipitation, and mean annual temperature. Seasonality was estimated by cell averages of monthly standard deviation of temperature and monthly coefficient of variation of precipitation (see [Tello and Stevens 2010] for details). Climate data were obtained from WorldClim at a spatial resolution of 30 arcseconds (~1km2; Hijmans et al. 2005). Net NPP data were obtained from Imhoff et al. (2004) at a resolution of 0.25 degrees. With these environmental data, we conducted a PCA on a correlation matrix in each latitudinal band. We then used the evenness of eigenvalues as a measure of dimensionality: high evenness indicates high environmental dimensionality and low correlations among environmental variables, ‘This article is protected by copyright. All rights reserved.’

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while low evenness corresponds to low environmental dimensionality and high correlations. To evaluate if dimensionality of biodiversity could result from environmental dimensionality we conducted a simple linear regression analysis (Sokal and Rohlf 1995). Finally, we incorporated these estimates of environmental dimensionality into regression models described above where biodiversity dimensionality was the response variable, and latitude, number of cells per band and environmental dimensionality were predictors.

Results Dimensionality of biodiversity (evenness of eigenvalues) decreased significantly with increasing latitude from tropical to temperate regions (Table 1; Figure 3A). For the most part, this pattern remains true regardless of the specific spatial scale of analysis (Table S1; Figures S3 & S4). The observed changes in dimensionality imply concomitant changes in the magnitude of correlation among diversity measures. Indeed, mean absolute correlation significantly increased with latitude ranging from around 0.35 near the equator to about 0.6 at higher latitudes (Figure S2A). According to null model expectations, weak but significant latitudinal gradients in

dimensionality of biodiversity can results solely from the observed spatial variation in species richness and the underlying structure of species ranges. Null dimensionality based on our simplest null model decreased as latitude increased (null model 1: FiSi & EqSp; Tables 1 & S1; Figure 3B). This indicates that even if assemblages where solely the result of random sampling from a continental species pool, dimensionality of biodiversity would decrease with latitude. This latitudinal gradient in mean null dimensionality is also produced by our more complex null model, where additional constraints of empirical species distributions are ‘This article is protected by copyright. All rights reserved.’

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maintained during data randomization (null model 2: Range ID Rand.; Tables 1 & S1; Figure 3E). This suggests that even if species distributions are random with respect to their phylogenetic position, functional group and phenotype, a latitudinal decrease in dimensionality of biodiversity is expected. Together, significant gradients in null dimensionality indicate that null models controlling for underlying structure in datasets need to be used to investigate more complex mechanisms underlying spatial patterns in dimensionality of biodiversity. Even though null models produce latitudinal gradients, these are not strong enough to

account for the empirical decrease in dimensionality of biodiversity from tropical to temperate regions. Indeed, the empirical regression coefficient for latitude was lower (more negative) than expected by either null model (Figure 3D & G). Moreover, standardized deviations from null model expectations (SESs) had significant negative relationships with latitude (Figure 3C&F; Table 1). Interestingly, dimensionality was consistently less than expected solely by the species richness gradient (null model 1; Figure 3C). On the other hand, dimensionality was greater than expected by the random distribution of species in the tropics, but it became less than expected in temperate regions (null model 2; Figure 3F). Results of null model analyses also were generally consistent across spatial scales (Table S1; Figures S3 & S4). Environmental dimensionality accounted for very little of the variation in

dimensionality of biodiversity (r2 = 0.045, P = 0.179; Figure 4). Unlike dimensionality of biodiversity, dimensionality of the environment exhibited no latitudinal gradient (Figure S5). Moreover, when environmental dimensionality was added to the regression models used to measure effects of latitude and band area this additional factor did not significantly improve the fit of any regression model. These results suggest that the latitudinal gradient in ‘This article is protected by copyright. All rights reserved.’

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dimensionality of biodiversity is not a simple result of an increase in dimensionality of underlying environmental gradients.

Discussion Geographical gradients in biodiversity are among the most pervasive and perplexing biological phenomena demanding scientific explanation. Despite centuries of research, we still do not fully understand underlying ecological and evolutionary mechanisms responsible for the uneven distribution of diversity at the global scale, and its aggregation in tropical regions (Willig et al. 2003, Gotelli et al. 2009). Most previous research, however, has focused narrowly on the study of taxonomic diversity, particularly species richness (Willig et al. 2003, Hillebrand 2004). Only recently, research has been broadened to take advantage of measures that represent functional, phenotypic, evolutionary and other important dimensions of biodiversity (Devictor et al. 2010, Meynard et al. 2011, Stevens et al. 2013, Cisneros et al. 2014). This approach promises to provide important insights into challenging questions about the assembly of local and regional assemblages, the distribution of species, and the formation of biodiversity gradients. However, the study of dimensionality of biodiversity remains in its infancy and even basic patterns await to be discovered. In previous work we have examined dimensionality of biodiversity for two different

geographic extents: the Neotropics (Stevens and Tello 2014) and the Atlantic Forest (Stevens and Gavilanes 2015). In both studies, we demonstrated that degree of dimensionality is different from random expectiations under a number of different null models. In this study, we show that dimensionality is not only different from random, but that it also varies across geography. In particular, we document for the first time a latitudinal gradient in the ‘This article is protected by copyright. All rights reserved.’

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dimensionality of biodiversity (Figures 3; Table 1) and show evidence that this latitudinal gradient in dimensionality is not the result of a latitudinal gradient in environmental dimensionality. Why is dimensionality of biodiversity higher in the tropics? To our knowledge, the

pattern we describe here is new, and theory or models have not yet been suggested to explicitly account for spatial gradients in dimensionality. A basic null hypothesis can be proposed, whereby these secondary diversity patterns (i.e., formed by relationships among individual biodiversity gradients) result from simple well-known structures in the distribution of diversity and species. Our null models embody two such null hypotheses. Null model 1 (FiSi & EqSp) created null patterns expected simply for the underlying gradient in species richness, while null model 2 (Range ID Rand.) produced expectations given the observed positions and sizes of species ranges. In both cases null expectations also contain potential effects of the empirical distribution of functional groups and phenotypic traits across the phylogeny. Our analyses, however, found that neither of these null models could account for the latitudinal decrease in dimensionality of biodiversity. This suggests that the geographical distribution of species with respect to their functions and phylogenetic positions is nonrandom, and that even after accounting for species richness gradients and other known elements of the distribution of species, dimensionality of biodiversity remains higher in the tropics than in temperate regions. Environmental conditions are strongly related to geographic patterns in individual

biodiversity measures in many groups of organisms (Field et al., 2009). Thus, if each measure of diversity responds to a different environmental gradient, and environmental conditions are less spatially correlated with one-another in the tropics, then that could explain the decline in ‘This article is protected by copyright. All rights reserved.’

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dimensionality of biodiversity with latitude. Our results, however, do not support this hypothesis either. The degree of spatial co-variation among environmental variables (environmental dimensionality) changes considerably among bands, but this variation in not related to either latitude or dimensionality of biodiversity (Figure 4 and S5). As a consequence, the latitudinal decline in dimensionality of biodiversity that we document in this study remains unexplained. Future research should test for effects of other ecological or evolutionary forces, as well as confirm the generality of our findings in other taxonomic groups and regions. Historical processes also shape patterns of biodiversity, and thus might contribute to

the observed latitudinal gradient in dimensionality. Substantive theory and more-limited but positive empirical evidence suggests that the tropics may be prolific accumulators of biodiversity. Indeed, from geologic perspectives based on fossils (Jablonski et al. 2006) to contemporary perspectives based on modern molecular phylogenies (Stephens and Wiens 2003, Wiens and Donoghue 2004, Stevens 2006), tropical species are often older and more variable in their age and phylogenetic position than temperate counterparts (Wier and Schluter, 2007). In Neotropical bats, tropical niche conservatism has likely contributed to these historical effects (Stevens 2011, Stevens 2006; Villalobos et al. 2013 but see Ramos Pereira and Palmeirim 2013). Noctilionoids cannot use torpor or hibernation to conserve energy during cold conditions (McNab 1969), and niche conservatism in this group is likely related to temperature seasonality. Under the highly seasonal conditions of temperate regions, noctilionoid assemblages are composed of distantly related species, likely the result of multiple invasions by generalist clades that can withstand harsher environments (Stevens et al. 2013, Jablonski et al. 2013). Indeed, noctilionoid species in temperate regions tend to (1) be


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less taxonomically redundant (often single representatives from a number of different subfamilies), and (2) have large geographic range sizes (often occurring in both North and South America). In contrast, under low seasonality conditions in the tropics, bat assemblages are composed of more closely related species (Stevens et al. 2013), which might result from continuous insitu diversification from a common ancestor. This disproportionate accumulation of newly-derived as well as old species in the tropics could create a form of variability that diminishes correlations and enhances the dimensionality of biodiversity. Testing historical mechanisms behind the observed gradient in dimensionality of biodiversity is beyond the scope of the current study, but developing models and tests for how evolution might have shaped this pattern would be an important advance. The complex multidimensionality of biodiversity creates challenges, but also provides

opportunities to understand the processes determining the distribution of species and the formation of gradients in biological diversity. Many potential mechanisms underlying large scale variation in species richness have accumulated over the past century of research (Willig et al. 2013, Pianka 1996, Rohde 1992). Scientists have been unable to reach consensus about what processes are most important, or what are their relative contributions to global patterns of biodiversity (Gotelli et al. 2009). A major difficulty has been that many mechanisms are similarly capable of recreating observed richness gradients (Willig et al. 2013). However, spatial variation in multiple dimensions of biodiversity creates inter-related patterns that result from the same biogeographic processes that control the distribution of species: speciation, extinction and geographic range dynamics. Thus, efficacy of competing processes could be identified based on the degree to which they account not only for the distribution of species richness, but also for gradients in other dimension of biodiversity (e.g. functional, phenetic,


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phylogenetic) and ultimately dimensionality of biodiversity. This logic can be used to create powerful tests for macroecological theory. This approach is already being used (Stevens et al. 2013, Villalobos and Rangel 2014), but needs to be expanded (Gotelli 2009). One particularly useful technique in this context is pattern-oriented modeling (Grimm et al. 2005), which simulates the behavior of multiple processes (e.g., niche conservatism, geographically biased diversification, energetic limits on richness) to predict system level properties (i.e. distribution of functional or phylogenetic diversity). We suggest that to be truly effective, pattern-oriented models should go beyond predicting primary diversity gradients. Indeed, successful macroecological theories should also be able to explain secondary patterns like the latitudinal gradient in dimensionality of biodiversity we document in our study. A latitudinal gradient in dimensionality also has substantial conservation implications.

Aside from being used to understand mechanisms underlying biodiversity gradients (Gaston 1996), richness has also been used to guide efforts for biodiversity management and conservation. Indeed, the design and implementation of protected natural areas often prioritizes maximizing the number of conserved species (Margules and Pressy 2000, Andelman and Willig 2002). However, protecting other dimensions of biodiversity, which can play important complementary roles in the functioning of ecosystems, may be of equal importance. A latitudinal gradient in dimensionality of biodiversity implies that the usefulness of any one measure of diversity to approximate the spatial distribution of others is dependent on geography. In temperate regions, where dimensionality of biodiversity is lowest, efforts to protect areas with the most species may lead to more predictable outcomes for the protection of other dimensions of biodiversity. In contrast, in the tropics, where dimensionality is highest, maximizing richness will do less to conserve functional, phylogenetic or other


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dimensions of biodiversity. Whether this possibility has had measurable effect is unclear. An important open question is whether protected areas chosen to maximize species richness in tropical regions are less effective than in temperate regions at conserving the multidimensionality of biodiversity.


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FIGURE LEGENDS

Figure 1. Conceptual differences in dimensionality of biodiversity among two regions or groups of taxa. Dimensionality refers to the degree of non-independence in the spatial or temporal variation among multiple measures of various dimensions of biodiversity. A lowdimensionality dataset would be composed of redundant (strongly correlated) biodiversity measures, and the variation in one measure would be a good surrogate for variation in others. This would produce low evenness in the magnitude of eigenvalues of a principal component analysis (PCA), whereby most multivariate variation could be summarized by only a few important derived orthogonal axes. In contrast, a high-dimensionality dataset contains complementary (mostly uncorrelated) biodiversity measures, and variation in one measure does not correspond to variation in others. Such a dataset would produce high evenness in the magnitude of eigenvalues of a PCA, suggesting that multivariate variation cannot be efficiently summarized by a reduced set of derived axes. The figure shows two contrasting datasets, each depicting co-variation in a pair of biodiversity measures. Results of PCAs are also shown, including direction of the derived axes (orange lines), as well as magnitudes of eigenvalues (bar graph).


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Figure 2. Geographical variation in species richness of noctilionoid bats across the New World. Richness was estimated as the number of geographic range overlaps in cells of 100 × 100 km. For each cell, we also calculated various measures representing functional, phenotypical and phylogenetic dimensions of biodiversity. Cells were grouped into latitudinal bands, and dimensionality of biodiversity was determined for each band. Bands varied in latitudinal width from 200 km (2 rows of cells) to 1,200 km (12 rows). Black cells contain only one species and were not included in analyses.


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Figure 3. Latitudinal gradients in dimensionality of biodiversity. A. Empirical dimensionality (Camargo’s evenness) decreases from the Equator towards temperate regions (Adj.R2 = 0.455; p < 0.001). The remainder of the top row presents results using the Fixed Sites & Equiprobable Species null model. The second row presents results using the Range Identity Randomization null model. B & F. Null dimensionality expected by both null models also decreases significantly with latitude. C & G. The latitudinal gradient remains when deviations of empirical from expected values are calculated (standardized effect sizes: SES). Note that these scatterplots show univariate relationships between dimensionality and latitude, while our regression models accounted additionally for a potential effect of area of latitudinal bands (Table 1; see also Figure S1 for partial regression plots). D & G. Finally, the regression coefficient of latitude is more negative than expected by the 1,000 repetitions of either null model (gray areas contain the 95% most common values of coefficients produced by the null models). In these analyses, latitudinal bands are formed by 2 rows of 100 x 100 km cells. Analyses using other spatial scales lead to similar conclusions (Table S1; Figures S3 and S4).


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Figure 4. Results from simple linear regression analysis evaluating the relationship between environmental dimensionality and dimensionality of biodiversity.


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Table Legend Table 1. Regression models relating dimensionality of biodiversity to latitude and area of latitudinal bands. Dimensionality was measured by Camargo’s evenness calculated on the distribution of eigenvalues produced by a principal components analysis (PCA). The PCA was based on a PPM correlation matrix. Regressions were fitted for empirical dimensionality values, as well as for the mean null values and standardized effect sizes (SES) produced by two null models: the Fixed Sites & Equiprobable Species null model (FiSi & EqSp) and the Range Identity Randomization null model (Range ID Rand.). Latitudinal bands were formed by 2 rows of 100 x 100 km grid cells (Figure 2). Analyses using other spatial scales lead to similar conclusions (Table S2; Figures S3 and S4). Significant coefficients are shown in bold italics.

Value

Intercept Null Model

Area (N of cells)

2 Adj.R

Coeff.

P

0.455

0.362