Sophia I Passy
email: sophia.passy@uta.edu.

Chad A Larson

Aurélien Jamoneau

William Budnick

Jani Heino

Thibault Leboucher

Juliette Tison-Rosebery

Janne Soininen5

Biogeographical patterns of species richness and abundance Distribution in stream diatoms are driven by climate and water chemistry

Keywords: climatic variability and tolerance, latitudinal diversity gradient, metabolic theory, more individuals hypothesis, nutrient enrichment, species-energy

This is the first inter-continental comparative assessment of diatom richness and species abundance distribution (SAD) along spatial, climatic, and water chemistry gradients using stream data from the US and Finland. We tested a number of hypotheses about the causes of variability in richness and by extension, the SAD, including the metabolic theory, the species-energy, the more individuals, the climatic variability, and the climatic tolerance hypotheses. We found no support for any of these concepts, given that the relationships of richness with explanatory variables were non-existent, weak or unexpected.

Diatom richness and the SAD responded more strongly to climatic variability, climatic extremes, and water chemistry, especially nutrient levels, than to mean temperature. A consequence of the weak energy dependence was a non-linear latitudinal gradient of richness in both countries, and a non-linear latitudinal gradient of the SAD in the US. The SAD was not entirely driven by richness but displayed distinct responses to spatial, climatic, and water chemistry factors, indicating that the environment had complementary effects on richness and the SAD. This emphasizes the utility of the SAD for ecological research-a notion that has been previously debated. Thus, we found sufficient support for the operation of multiple climate and water chemistry mechanisms in structuring diatom communities, which underscores their complex response to the environment and the necessity for novel predictive frameworks.

Introduction

The spatial variability in species richness along latitudinal, longitudinal, and elevational gradients has drawn a continued interest among ecologists for centuries, beginning with the works of Alexander von Humboldt and Carolus Linnaeus [START_REF] Pianka | Latitudinal gradients in species diversity: a review of concepts[END_REF][START_REF] Gaston | Global patterns in biodiversity[END_REF][START_REF] Willig | Latitudinal gradients of biodiversity: Pattern, process, scale, and synthesis[END_REF][START_REF] Rahbek | The role of spatial scale and the perception of large-scale species-richness patterns[END_REF][START_REF] Mittelbach | Evolution and the latitudinal diversity gradient: speciation, extinction and biogeography[END_REF]). There are numerous hypotheses about the nearly universal poleward decline in species richness with ecological and evolutionary rates, energy, and climatic favorability and stability emerging as important underlying factors. The elevation-richness relationship is more variable, most frequently conforming to a monotonically declining or a hump-shaped form, but there are some commonalities in the driving forces of the latitudinal and elevational gradients [START_REF] Rahbek | The role of spatial scale and the perception of large-scale species-richness patterns[END_REF]. Thus, warmer temperatures in tropical and low elevation regions shorten the generation times and accelerate the metabolic and mutation rates, leading to greater speciation [START_REF] Rohde | Latitudinal gradients in species-diversity: the search for the primary cause[END_REF][START_REF] Currie | Predictions and tests of climatebased hypotheses of broad-scale variation in taxonomic richness[END_REF][START_REF] Allen | Kinetic effects of temperature on rates of genetic divergence and speciation[END_REF]). These ideas were conceptualized within the framework of the Metabolic Theory of Ecology (MTE), which predicted species richness (S) as a function of temperature (T in Kelvin), according to the equation ln(S) = -EA/kT + I, where EA = activation energy with an expected value of about -0.65, k = Boltzmann constant (8.62 × 10 -5 eV K -1 ), and I = intercept [START_REF] Allen | Global biodiversity, biochemical kinetics, and the energetic-equivalence rule[END_REF][START_REF] Brown | Toward a metabolic theory of ecology[END_REF]).

The species-energy theory proposed that areas with greater total available energy, such as the tropics, have more diverse communities because they can support larger species populations with lower likelihood of extinction [START_REF] Wright | Species-energy theory: an extension of species-area theory[END_REF]. This theory is also known as the more individuals hypothesis (MIH), because larger species populations result in a greater total number of individuals [START_REF] Srivastava | Why more productive sites have more species: An experimental test of theory using tree-hole communities[END_REF]. The MIH predicts that richness scales positively with energy because richness is a function of the number of individuals, which is proportional to the available energy, i.e. communities are energylimited. Further elaboration of the species-energy theory recognized that temporal variability in energy may directly impact the richness of an area, given that periods of low energy are marked by higher extinction rates, and consequently, by a lower number of individuals. Thus, models that included total energy and energy variability explained the variability in bird and mammal species richness better than either energy variable alone [START_REF] Carrara | The species-energy theory: a role for energy variability[END_REF].

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

Finally, according to the climatic tolerance hypothesis, the tropics harbor greater richness because their more benign warm and humid conditions fall within the physiological tolerance of many more species compared to the cold and dry extra-tropical regions [START_REF] Currie | Predictions and tests of climatebased hypotheses of broad-scale variation in taxonomic richness[END_REF]). However, the latitudinal species patterns can be complicated by longitudinal effects, such as an east-west heterogeneity in rainfall, which is particularly distinct at mid-latitudes [START_REF] Terborgh | On the notion of favorableness in plant ecology[END_REF].

While the spatial variability of species richness has been extensively studied, we know substantially less about the spatial and environmental dependence of the species abundance distribution (SAD), defined here as the number of individuals across species in a community. In fact, due to a more theoretical and statistical emphasis in the study of the SAD over the past seventy years [START_REF] May | Patterns of species abundance and diversity[END_REF][START_REF] Mcgill | Species abundance distributions: Author-produced version of the article published in[END_REF][START_REF] Ulrich | A meta-analysis of species-abundance distributions[END_REF], the empirical latitudinal, longitudinal, and elevational patterns of the SAD and their underlying mechanisms, including environmental variability, have remained largely unknown.

It is possible that the latitudinal gradient of richness is paralleled by a corresponding gradient of the SAD. [START_REF] Brown | Why are there so many species in the tropics?[END_REF] suggested that as richness increases toward lower latitudes, the SAD may transition from a less even log linear (a few very abundant and some very rare species) to a more even curvilinear pattern (greater numbers of both intermediate and low abundance species) as a result of intensified enemy effects. There is evidence that the SADs of real forest communities do become less even at high latitudes when compared to neutrally assembled communities due to strong environmental filtering that favors only a few well-adapted species [START_REF] Qiao | A latitudinal gradient in tree community assembly processes evidenced in Chinese forests[END_REF]. However, there is no broad empirical support for a tendency in the SAD toward greater evenness and lognormality at low latitudes.

On the contrary, a recent study of forest trees showed the opposite trend-preponderance of less even logseries SADs at low latitudes but more even lognormal SADs at high latitudes, possibly as a result of overall greater dispersal in the tropics, and subsequent accumulation of rare species (Ulrich et al. 2016a).

A global study of dryland plant communities reported an overall prevalence of lognormal compared to log-series SADs, which was linked to environmental variability and stress but not to latitude (Ulrich et al. 2016b). There are even fewer and generally terrestrial studies of the SAD along elevational gradients,

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 which either have not reported any distinct patterns (Ulrich et al. 2016a;2016b) or shown a transition from log-series to lognormal SADs with altitude [START_REF] Arellano | The role of niche overlap, environmental heterogeneity, landscape roughness and productivity in shaping species abundance distributions along the Amazon-Andes gradient[END_REF]. Therefore, there is clearly a need for further research on the large-scale spatial patterns of the SAD, especially in aquatic ecosystems, which have been largely neglected in this context.

Our overall goal was to explore the large scale spatial patterns in diatom species richness and abundance distribution and determine if they are driven by the same environmental factors and whether these factors are climatic, including average temperature, seasonal and diurnal temperature fluctuation, and extreme temperatures, or water chemistry, i.e. nutrient levels, pH, and specific conductance.

Anthropogenic eutrophication is changing aquatic ecosystems globally by altering physico-chemistry, increasing primary production, and affecting species richness, composition and abundance with potentially strong ecological and evolutionary consequences [START_REF] Smith | Eutrophication science: where do we go from here?[END_REF][START_REF] Alexander | Does eutrophication-driven evolution change aquatic ecosystems?[END_REF]. A comprehensive review of the freshwater literature concluded that water chemistry variables were stronger predictors of diatom community structure than temperature [START_REF] Soininen | Environmental and spatial control of freshwater diatoms -A review[END_REF]. However, climatic factors outperformed water chemistry in predicting the distributions of individual diatom species across northern latitudes, e.g. Finland [START_REF] Pajunen | Climate is an important driver for stream diatom distributions[END_REF]. Therefore, the roles of climate vs. water chemistry and their interaction with spatial factors in defining diatom community properties are still unresolved and merit further research.

Here, we examined the shape of the SAD in freshwater diatom communities by calculating the We tested the following theories, hypotheses, and predictions. First, we tested whether ln(S) ~ -EA/kT with -EA between -0.6 and -0.7, as postulated by the MTE [START_REF] Brown | Toward a metabolic theory of ecology[END_REF]). We predicted that if this relationship holds, then parameter σ of the SAD would scale positively with EA/kT (σ ~

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 EA/kT), given that σ ~ -ln(S), as empirically shown for freshwater diatoms [START_REF] Passy | Abundance inequality in freshwater communities has an ecological origin[END_REF]. Second, we tested the predictions of the MIH that richness (S) increases with energy (here temperature, T) because S is a positive function of the number of individuals (N), which in turn, is proportional to the amount of energy [START_REF] Srivastava | Why more productive sites have more species: An experimental test of theory using tree-hole communities[END_REF]. However, since the effect of T on S is indirect through N, the expectation is that the correlations between T and N and N and S, would be equal to or greater than the correlation between T and S [START_REF] Currie | Predictions and tests of climatebased hypotheses of broad-scale variation in taxonomic richness[END_REF][START_REF] Carrara | The species-energy theory: a role for energy variability[END_REF]. Given the above consideration about the parameter σ-ln(S) relationship, we also predicted that if the MIH operates, parameter σ would scale negatively with T and N, i.e. communities would become more even (lower σ) at higher levels of available energy and higher numbers of individuals. Third, we extended our reasoning to the energy variability and climatic tolerance hypotheses and tested if seasonal (and diurnal) energy fluctuation and climatic harshness, respectively, decrease S, but increase parameter σ. Fourth, considering the strong impact of water chemistry on freshwater ecosystems, we predicted that climatic variables alone would be insufficient to describe the species richness and SAD patterns, but a combination of climatic and water chemistry factors would be required. For our objectives 1-4, we assumed that if the shape of the SAD is purely defined by richness, then parameter σ would respond to the same environmental predictors as richness and in a complementary way, e.g. parameter σ would show positive responses to predictors eliciting a negative response in richness and vice versa. However, if the SAD has unique environmental underpinning, parameter σ may display distinct environmental responses. Finally, we examined the spatial effects on richness and the SAD and how they constrained the community responses to climate and water chemistry to gain a deeper understanding of the causes of large scale community variability. macrophytes. Water chemistry, including total phosphorus, nitrate + nitrite, ammonia, pH, and specific conductance, was measured for the month of algal collection (Table A1). Samples were taken in July and August from 1993 to 2009 along a latitudinal range of 36 degrees, longitudinal range of 83 degrees, and elevational range of 2676 m. Climatic variables, including mean annual temperature (Tmean), temperature seasonality (standard deviation, TSD), mean diurnal temperature range (mean difference between monthly maximum and minimum temperatures, Tdiur), minimum temperature of the coldest month (Tmin), and maximum temperature of the warmest month (Tmax), were obtained from the WorldClim database [START_REF] Hijmans | Very high resolution interpolated climate surfaces for global land areas[END_REF]. Diatoms were identified in 590-700 cell counts and the total count was converted to total density (cells•cm -2 ).

Materials and Methods

Datasets

Finland. Data on climate (the same variables as in the US) and water chemistry, including total phosphorus, pH, and specific conductance, were available for 100 streams in Finland (fig. A1). Diatoms were sampled in July and August from 2001 to 2004 along a latitudinal range of 10 degrees, longitudinal range of 7 degrees, and elevational range of 302 m. Diatoms were identified in counts of about 500 cells.

Analysis of the species abundance distribution

Using count data, community SADs were fit with a Poisson lognormal distribution model, which is comparatively insensitive to sampling effort and performs equally well to other commonly used models [START_REF] Sӕther | Species diversity and community similarity in fluctuating environments: parametric approaches using species abundance distributions[END_REF][START_REF] Baldridge | An extensive comparison of speciesabundance distribution models[END_REF]. We estimated the standard deviation, parameter σ, with the poilog R-package [START_REF] Grøtan | poilog: Poisson lognormal and bivariate Poisson lognormal distribution[END_REF]. A comparison of the rank of the observed log likelihood with the log likelihood derived from 1000 bootstraps provided a goodness of fit (gof) metric. Values of gof between 0.05 and 0.95 indicate good fit. We also calculated the proportion of the species pool revealed by the sample, which represents the proportion of the total area of the fitted Poisson lognormal distribution.

We calculated the skewness () of the log2-transformed counts of individuals and the standard error of skewness (SES) as (6/n) 0.5 . Skewness is considered significant if the absolute value of the ratio /SES is greater than 2 (SYSTAT Software, Inc. 2009).

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

Theory testing

We performed a series of regression analyses to test the outlined theories and hypotheses. The metabolic theory was tested with model 1 (Tables 1,2) using ln(S) as a dependent variable. However, since the richness response to 1/kT can be curvilinear [START_REF] Algar | A test of Metabolic Theory as the mechanism underlying broad-scale species-richness gradients[END_REF], in a second model (model 2, Tables 1,2), we added a quadratic term. We further explored whether the predictions of the MTE can be extended to the SAD parameter σ, given its dependence on ln(S), and calculated models 1 and 2 for parameter σ as well (Tables 1,2).

Testing the more individuals hypothesis required several equations, including models 3 and 4

from Table 1 (the dependent variable was richness), and equation ( 1) below, which contained a quadratic term to account for potential nonlinearity in the density (N) response to mean temperature (Tmean). ln(N) = ln(Tmean) + ln(Tmean) 2

(1)

Our hypothesis that if the MIH operates, parameter σ would scale negatively with T and N, was tested with models 3 and 4 from Table 1. These ideas were tested only with the US dataset because it contained density data.

The climatic variability hypothesis, suggesting that variability in temperature would constrain richness, and consequently the SAD, was tested with model 5 from Tables 1 and2. The climatic tolerance hypothesis, implicating extreme temperatures as driving factors of community properties, was tested with model 6 from Tables 1 and2 for both richness and the SAD.

Additional models from Tables 1 and2 For the SAD, model 16 estimated the effect of richness on parameter σ. For each multiple regression model in Tables 1 and2, we performed backward selection of significant terms only to reduce redundancy and collinearity (Table A2). All models were compared using the Akaike Information

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

Criterion (AIC). Models with lower AIC provided better fits. Variance partitioning assessed to what extent the community responses to environmental factors were due to covariance of the environment with latitudinal, longitudinal, and elevational gradients. Specifically, we estimated how much of the variance explained by models 1-11 from Tables 1 and2 was contributed by covariance of the respective predictors in these models with the predictors in model 15. For the SAD, variance partitioning using models 1-15 also determined whether the response of parameter σ to the predictors (environmental and spatial) in these models was in fact driven by their covariance with richness (model 16). The response of skewness to climatic and water chemistry predictors was examined with multiple regressions using the backward stepping procedure. Variance partitioning and multiple regressions were performed with SYSTAT 13 (SYSTAT Software, Inc. 2009).

Results

In both the US and Finnish datasets, the Poisson lognormal model fit the abundance data well (0.36 ≤ gof ≤ 0.53). Parameter σ was a comparatively strong and negative function of ln-transformed richness (slope of -0.67 in the US, n = 669 and -0.83 in Finland, n = 100, P < 0.00001, Tables 1,2), i.e. rich communities had lower parameter σ and were thus more equitable. The relationship of ln-species richness with the Boltzmann temperature factor (1/kT) was not significant in the US and convex in Finland, inconsistent with the prediction of the MTE (Tables 1,2, models 1 and 2). Parameter σ exhibited a quadratic relationship with the Boltzmann temperature factor (more or less concave in both countries).

Thus, our expectation for opposing responses of ln-richness and parameter σ to 1/kT was not well supported.

In testing the species-energy and the MIH, we examined the relationships among richness, mean temperature, and density in the US dataset (Table 1, models 3 and 4). In contrast with the expectations of these hypotheses, richness displayed a U-shaped response to mean temperature (Table 1, fig. 1) and a marginally non-significant decline with density (slope = -0.64, R 2 = 0.01, p = 0.06, n = 669), while the density-mean temperature relationship was hump-shaped (lnN = 12.98 + 0.04Tmean -0.01Tmean 2 , R 2 =

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 0.04, P < 0.02, n = 667). Thus, richness was related weakly to mean temperature but not to density, indicating that the effect of temperature on richness was not due to a temperature dependence of density.

Parameter σ was weakly related to mean temperature (Table 1, fig. 2) and density (parameter σ = 1.86 + 0.03ln(N) 2 , R 2 = 0.03, P < 0.00005, n = 669), exhibiting a U-shaped response to both. In Finland, the greatest richness was observed at intermediate temperature and the lowest parameter σ, at the highest temperature (Table 2, figs 3, 4).

To test the role of climatic variability in defining community patterns, we examined the response of richness and parameter σ to seasonal and diurnal temperature fluctuation (Tables 1,2, model 5, figs 1-4). In the US and Finland, temperature variability provided a better fit for both variables than mean temperature, as indicated by their lower AIC. With the exception of parameter σ in Finland, diatom richness and abundance equitability exhibited non-linear responses to diurnal and/or seasonal temperature variability (Table A2).

The climatic tolerance hypothesis was tested using minimum (Tmin) and maximum temperatures (Tmax) as predictors of richness and parameter σ (Tables 1,2, model 6, figs 1-4). Contrary to the expectation of diminished richness at the low temperature extreme, richness was the highest at both ends of the Tmin gradient in the US and at lower Tmin in Finland. Maximum temperature had a notable effect (quadratic) on richness only in Finland. In the US, parameter σ exhibited low values (high equitability) at low Tmin and high Tmax levels. In Finland, parameter σ declined with both Tmin and Tmax. From all sets of climatic variables, extreme temperatures provided the best fit in Finland, while temperature variability outperformed the other variables in the US, as revealed by a comparison of their respective AIC (Tables 1,2, models 4-6). However, the model including all significant climatic variables (Table 1, model 7)

explained substantially greater amount of the variance in both richness and parameter σ, indicating that these community properties were products of multiple climatic influences.

In the US, all of the variance in richness and most of the variance in parameter σ explained by water chemistry was contributed by nutrient levels, which generally had a positive effect on richness and a negative effect on parameter σ ( We asked next if the behavior of richness and the SAD along climatic and water chemistry gradients (Tables 1,2, models 1-11) was driven by spatial variability of these gradients. To answer this question, we calculated the covariance of environmental variables (Tables 1,2 with space (i.e., spatially structured environment). In more complex models, including a combination of predictor sets, e.g. models 7, 10, and 11 (Tables 1,2), spatially structured environment explained only a portion of the variance. For parameter σ, which had a comparatively strong negative correlation with richness, we also assessed whether environment and space contributed to the explained variance independently of richness. Variance partitioning showed that in general, a substantial portion of the explained variance in parameter σ was captured by the environment and space after the richness effect was controlled for.

Skewness was positive in all communities in both the US and in Finland indicating a prevalence of common species. Of the skewness values, 50% were significant (/SES > 2) in the US and 71% in 3).

Discussion

We examined the behavior of both diatom richness and abundance distribution along environmental and spatial gradients in streams from two continents, testing a number of specific hypotheses. The response of richness to the Boltzmann temperature factor and mean temperature contradicted the MTE and the species-energy hypotheses, respectively, predicting a positive relationship (both hypotheses) with a specific rate of increase (MTE). Deviations from the predictions of the MTE were previously reported for both aquatic and terrestrial macroorganisms, where the richness-temperature relationship was found to be curvilinear, linear with a slope significantly different from predictions, or not significantly different from zero [START_REF] Algar | A test of Metabolic Theory as the mechanism underlying broad-scale species-richness gradients[END_REF][START_REF] Hawkins | A global evaluation of metabolic theory as an explanation for terrestrial species richness gradients[END_REF][START_REF] Pinel-Alloul | Large-scale geographic patterns of diversity and community structure of pelagic crustacean zooplankton in Canadian lakes[END_REF]. In microbes, including lake phytoplankton and soil bacteria, the richness response to temperature was also variable, following

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 respectively, a segmented [START_REF] Segura | Metabolic dependence of phytoplankton species richness[END_REF] or linear pattern, flatter than observed in macrobes [START_REF] Zhou | Temperature mediates continental-scale diversity of microbes in forest soils[END_REF]. A systematic analysis of multiple datasets across a broad range of terrestrial macroorganisms, testing the predictions of the MTE, found that the richness-temperature relationship was positive in datasets that included areas with colder winters but non-existent or negative in datasets from tropical, subtropical, and warm temperate regions [START_REF] Hawkins | A global evaluation of metabolic theory as an explanation for terrestrial species richness gradients[END_REF]. A review of the species-energy relationship noted that it is scale-dependent and transitions from unimodal at small scales to monotonically increasing at large scales [START_REF] Evans | Species-energy relationships at the macroecological scale: a review of the mechanisms[END_REF]. Here, the relationship of richness with the Boltzmann temperature factor and mean temperature was non-significant or weak in the US, but comparatively stronger and unimodal in Finland, even though both datasets covered regional to continental scales and included cold climate streams. The SAD response to the Boltzmann temperature factor and mean temperature was weak and U-shaped in the US, but stronger and monotonic in Finland,

where inequality (parameter σ) decreased with temperature.

The present results were also inconsistent with the more individuals hypothesis, which so far, has received mixed support [START_REF] Srivastava | Why more productive sites have more species: An experimental test of theory using tree-hole communities[END_REF][START_REF] Kaspari | Energy, density, and constraints to species richness: Ant assemblages along a productivity gradient[END_REF][START_REF] Mönkkönen | Energy availability, abundance, energy-use and species richness in forest bird communities: a test of the species-energy theory[END_REF][START_REF] Šímová | Global species-energy relationship in forest plots: role of abundance, temperature and species climatic tolerances[END_REF]). The hump-shaped behavior of density along the temperature gradient in the US dataset indicated that higher temperatures actually decrease the number of individuals, which is in stark contrast with the MIH prediction for a positive relationship. This pattern could be a consequence of intensified grazing at higher temperatures due to accelerated herbivore metabolic and consumption rates (O'Connor and Bruno 2009; West and Post 2016). Finally, the richness-density relationship was nonsignificant, indicating that the temperature effect on richness was not indirect through density. These findings suggest that i) the effect of temperature on both richness and the SAD is weak and may depend on latitude; ii) richness and the SAD may exhibit different and not necessarily complementary behavior along the temperature gradient; and iii) an overriding influence of factors other than temperature, given the non-linear density response to temperature.

Temperature variability and temperature extremes were better descriptors of both richness and parameter σ than mean temperature, but did not cause the responses predicted by the energy variability

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

and the climatic tolerance hypotheses, respectively. High richness was observed at both low and high seasonality in the US and high seasonality Finland in contrast with the energy variability hypothesis, which proposes that energy reduction during the cold seasons will lead to lower richness. This result can be partially explained from the perspective of coexistence theory, which postulates that temporal heterogeneity in resource supply increases biodiversity because it allows coexistence of species that alternate between dominance and persistence at different times [START_REF] Sommer | Comparison between steady state and non-steady state competition: experiments with natural phytoplankton[END_REF][START_REF] Tilman | The Maintenance of Species Richness in Plant Communities[END_REF].

In both the US and Finland, richness was high at the lowest minimum temperature, contrary to the expectation of the climatic tolerance hypothesis. It is possible that diatoms deviate from the expectation of this hypothesis because they inhabit the comparatively milder aquatic environment, less prone to extreme fluctuations. Conversely, in terrestrial habitats, where temperatures reach much greater extremes, the climatic tolerance hypothesis was supported (Šímová et al. 2011). Furthermore, low temperatures may favor diatoms over cyanobacteria [START_REF] Peterson | Temporal variation in enrichment effects during periphyton succession in a nitrogen-limited desert stream ecosystem[END_REF][START_REF] Van Der Grinten | Temperature-and light-dependent performance of the cyanobacterium Leptolyngbya foveolarum and the diatom Nitzschia perminuta in mixed biofilms[END_REF] or green algae [START_REF] Roberts | The role of periphyton during the recolonization of a shallow lake with submerged macrophytes[END_REF]; therefore, lower temperature minima and stronger temperature seasonality may prevent diatom exclusion and promote higher biodiversity of this algal group. High seasonality, low temperature minima, and low temperature maxima were also associated with the highest abundance equality (lowest parameter σ) in the US, which suggests more equitable resource partitioning. These results indicate that a decrease in the temporal variability of temperature and an increase in the temperature minima due to global warming [START_REF] Xu | Temperature and vegetation seasonality diminishment over northern lands[END_REF], can lead to lower biodiversity and abundance equitability in some stream diatoms.

Although climate had a stronger influence on both richness and parameter σ in the US and Finland, water chemistry captured a notable amount of variance. Nutrients explained 8-14% of the variance of richness and parameter σ, while specific conductance or pH added ≤5%, indicating that nutrient availability was a more important source of community variability, especially in the US dataset, which comprised primarily non-acidic steams. Richness was generally higher at intermediate or high nutrient values, while equality in the SAD increased with nutrients. An increase of diatom richness with nutrient supply has been previously documented and explained with the ability of more functional groups

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 (e.g., tolerant and sensitive to nutrient limitation) to coexist at high nutrients [START_REF] Passy | Continental diatom biodiversity in stream benthos declines as more nutrients become limiting[END_REF][START_REF] Soininen | Global patterns and drivers of species and trait composition in diatoms[END_REF]). Here, we further report that the SAD was also constrained by nutrient supply and in the US, it was even more responsive than richness. A recent study on the SAD of stream diatom communities, sampled across a land use gradient, revealed that their equitability increased (parameter σ decreased) with the transition from forest to agriculture and suggested that nutrient enrichment was responsible for this pattern [START_REF] Passy | Abundance inequality in freshwater communities has an ecological origin[END_REF]). In the present investigation we found support for this hypothesis and show that communities indeed became more even at higher nutrient supply across a broad range of latitudes.

Nevertheless, the best model for richness and parameter σ included both climatic and water chemistry variables. These variables explained substantial proportion of the variance in richness and parameter σ independently of space, indicating that the environment was an important determinant of community organization. While a combined effect of nutrients and temperature on microbial biodiversity has been reported before [START_REF] Soininen | Global patterns and drivers of species and trait composition in diatoms[END_REF][START_REF] Wang | Nutrient enrichment modifies temperature-biodiversity relationships in large-scale field experiments[END_REF]), this study is the first to demonstrate that nutrients and climate co-controlled the variability in the diatom SAD at a continental scale.

Skewness was positive in both datasets in contrast with a large body of literature, documenting negative skew as the dominant pattern [START_REF] Gregory | Explanations of commonness and rarity in British breeding birds: separating resource use and resource availability[END_REF][START_REF] Hubbell | The unified neutral theory of biodiversity and biogeography[END_REF][START_REF] Magurran | Explaining the excess of rare species in natural species abundance distributions[END_REF]. This discrepancy may be due to both sampling intensity and environmental influences.

Thus, when too few individuals are sampled, the left side of the SAD remains veiled and the right side exhibits a positive skew [START_REF] Mcgill | Does Mother Nature really prefer rare species or are log-left-skewed SADs a sampling artefact[END_REF]. Although in both datasets a comparatively large number of individuals was sampled following standard protocols, the proportion of species revealed by the sample had a median of 44-76%, indicating that some species remained veiled. However, skewness had detectable correlations with environmental factors (R 2 = 0.09-0.20), pointing to ecological constraints on the SAD symmetry as well. Skewness responded most strongly to temperature variability and pH in the US, while water chemistry and to a lesser extent temperature variability were the underlying factors in Finland. Thus, temperature variability proved to be a key driver of richness and the SAD, including its evenness and symmetry. Determining the mechanisms controlling the distribution of common species, i.e.

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

the SAD symmetry, has important practical implications, given that these species are primarily responsible for delivering ecosystem services [START_REF] Winfree | Abundance of common species, not species richness, drives delivery of a real-world ecosystem service[END_REF].

In both the US and Finland, diatom richness did not conform to the classical pattern of monotonic latitudinal decrease, consistent with prior diatom studies [START_REF] Passy | A distinct latitudinal gradient of diatom diversity is linked to resource supply[END_REF][START_REF] Soininen | Global patterns and drivers of species and trait composition in diatoms[END_REF]. These studies attributed the deviation from the classical pattern to the overriding effect of wetlands and their impact on micronutrient availability. Here the non-linear response of richness to latitude was associated with a nonlinear response of seasonality, which was one of the major predictors of richness. This suggests that temperature variability, in addition to micronutrient availability, may underlie the latitudinal richness distributions. The expectation for increased evenness in the SAD at low latitudes [START_REF] Brown | Why are there so many species in the tropics?[END_REF] was confirmed only in Finland, while in the US, the most equitable communities were observed at mid latitudes. The elevational response of richness-bimodal in the US but peaking at high elevations in Finland-did not follow the common monotonic decline or hump-shaped patterns. Admittedly, the elevational gradient in Finland was short and not sufficient to reveal the full variability in richness. The SAD was most even at intermediate elevations in the US and at lower elevations in Finland, but this response was weak. Thus, the latitudinal effects on diatom richness and the SAD became more prominent at high latitudes (Finland) compared to lower latitudes (the US). At high latitudes, elevation constrained richness as well, while the SAD remained weakly controlled by elevation across latitudes. These results can be explained with the generally weak correlation of richness and the SAD with mean temperature, which is a major covariate of both latitude and elevation. Notably, longitude had the strongest effect on the SAD in the US, explaining 19% of its variance. This finding may be due in part to the longitudinal dependence of total phosphorus with a peak at mid longitudes, where the SAD was most even (lowest parameter σ). Total phosphorus had virtually no relationships with either latitude or elevation. These finding reveal that richness and the SAD had unique responses to spatial variability, e.g. locations with low richness did not necessarily have low equality (high values of parameter σ). This means that richness and the SAD may have distinct environmental underpinning.

Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

Diatom richness and parameter σ were positively correlated, but this correlation did not underlie the responses of parameter σ to environmental and spatial variables, as indicated by variance partitioning.

In fact, the covariance of richness with these variables explained generally less than half of the SAD variance, implying that much of the SAD response was independent of richness. Furthermore, in the US, climate, water chemistry, and spatial models explained better the variance of parameter σ, while in Finland, the pattern was reversed and richness was explained better than parameter σ by the respective models. There were also differences in the environmental and spatial predictors that entered the regression models of richness and parameter σ (Table A2) as well as in the shape of the richness and parameter σ responses to common predictors (figs 1-4). For example, parameter σ displayed a monotonic decline with nutrients, while the richness response was non-linear, indicating that eutrophication has a differential effect on richness vs. abundance equality. The form of the SAD is strongly dependent on richness and total abundance (Locey and White 2013) and the usefulness of the SAD for ecological research has been questioned [START_REF] Yen | Is there an ecological basis for species abundance distributions?[END_REF], in part because of its dependence on richness. The results presented here demonstrate that the abiotic environment has distinct impacts on richness and the SAD, and that the shape of the SAD can be predicted by climatic and water chemistry variables, emphasizing the utility of the SAD in unravelling ecological mechanisms. Although we did not detect scaling relationships between temperature and the SAD, we encourage future research on organisms that are more temperature dependent than diatoms, to explore whether such relationships exist and thus add to the body of knowledge on the temperature effects on community organization.

Table 1. US diatoms. Regression models (Eqn) testing the responses of ln-transformed species richness, ln(S) (models 1, 2, and 15), species richness (models 3-15) and parameter σ (models 1-15) to environmental and spatial variables. Covariance of the selected predictors (X) in the respective model with i) the selected spatial variables in model 15 is given by X∩Spa and with ii) ln(S), by X∩ln(S).

Covariance was calculated only for significant X. Author-produced version of the article published in American Naturalit,192(5) Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

Table A1. Basic statistics of climatic, water chemistry and spatial variables included in the regression analyses (Tables 1,2). Tmean = mean annual temperature, TSD = temperature seasonality (standard deviation), Tdiur = mean diurnal temperature range, Tmin = minimum temperature of the coldest month, and Tmax = maximum temperature of the warmest month. Author-produced version of the article published in American Naturalit,192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

Variable

  standard deviation (parameter σ) of a Poisson lognormal distribution model and skewness. Parameter σ indicates how equitably abundances are distributed across abundance classes with lower values suggesting higher equitability. Skewness measures the symmetry of the SAD compared to a lognormal distribution. Negative values (left skew) indicate prevalence of rare species, while positive values (right skew), greater frequency of abundant species.

  were calculated in order to test the responses of richness and the SAD to climatic factors (model 7), nutrient (nitrogen and/or phosphorus) enrichment (model 8), overall water chemistry (model 9), climate and nutrient enrichment (model 10), and climate and overall water chemistry (model 11). The remaining models from Tables 1 and 2 determined the latitudinal (model 12), longitudinal (model 13), and elevational trends (model 14). Model 15 tested the overall spatial effect.

Finland.

  Skewness was either negatively (Pearson r = -0.21, P < 0.0001, the US) or non-significantly (Finland) related to richness. In both countries, skewness was positively correlated with parameter σ (Pearson r = 0.42-0.46, P < 0.0001), i.e. equitable communities were more symmetric with lower skewness and these communities tended to be rich in the US. Skewness increased at intermediate TSD and low pH in the US and at intermediate specific conductance and Tdiur but low total phosphorus in Finland (Table

  n = 669. AIC = Akaike Information Criterion. The AIC of the best environmental model is boldfaced. Tmean = mean annual temperature, TSD = temperature seasonality (standard deviation), Tdiur = mean diurnal temperature range, Tmin = minimum temperature of the coldest month, Tmax = maximum temperature of the warmest month, TP = total phosphorus, Cond = specific conductance, Lat = latitude, Long = longitude, Elev = elevation, and NS = non-significant.

Figure legend Figure 1 .

 legend1 Figure legend Figure 1. Relationships between richness and climatic (A-E), water chemistry (F-J), and spatial variables

Figure 2 .

 2 Figure 2. Relationships between parameter σ and climatic (A-E), water chemistry (F-J), and spatial

Figure 3 .

 3 Figure 3. Relationships between richness and climatic (A-E), water chemistry (F-H), and spatial variables

Figure 4 .

 4 Figure 4. Relationships between parameter σ and climatic (A-E), water chemistry (F-H), and spatial

Figure A1 .Figures

 A1 Figure A1. Map of the study streams in the US and Finland.

  Author-produced version of the article published in AmericanNaturalit, 192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830parameter σ model increased R 2 by only 3% (Tables1, A2, model 9). In Finland, richness showed a unimodal response to total phosphorus, while parameter σ exhibited a marginally non-significant Ushaped response (R 2 = 0.06, p = 0.053). Predictability of richness improved by 5% after including pH in the model (Table2, model 9). Notably, the effect of total phosphorus on parameter σ became significant and contributed 8% to the explained variance when the influence of specific conductance was accounted for in the full water chemistry model (Tables2, A2, model 9). The overall best environmental model included climatic and nutrient variables only in the US but climatic, nutrient, and water chemistry variables in Finland and explained 21-40% and 25-30% of the variance in richness and parameter σ,

Table

1

, models 8 and 9, figs 1, 2). Adding specific conductance to the respectively (Tables

1, 2

, A2, model 11). However, a model with climatic and nutrient variables only provided comparable fits in Finland (Tables

2, A2

, model 10).

The individual responses of richness and parameter σ to latitude, longitude, and elevation (Table

1

, models 12-14) were weaker in the US (2-19% explained variance) but stronger in Finland (5-22% explained variance). Although the spatial relationships were nonlinear, the richest communities in the US were found at lower latitudes and elevations, and at westernmost and intermediate longitudes. The most equitable communities (lowest parameter σ) in the US were observed at intermediate latitudes, longitudes, and elevations. In Finland, richness was the greatest at intermediate latitudes, extreme longitudes, and higher elevations, while parameter increased with latitude and responded unimodally to longitude and elevation. Nevertheless, the model including all spatial factors provided the best fit for both richness and parameter σ, capturing respectively 16-26% of the variance in the US and 18-24% in Finland (Tables

1, 2

, model 15).

  Author-produced version of the article published in AmericanNaturalit, 192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

	, models 1-11) with spatial
	predictors (Tables 1, 2, model 15) using variance partitioning. The amount of variance in richness and

parameter σ explained by individual predictor sets, e.g. mean temperature, temperature fluctuation, extreme temperature, nutrients, and water chemistry, was generally due to covariance of the environment

Table 2 .

 2 , 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 Author-produced version of the article published in American Naturalit, 192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 Finnish diatoms. Regression models (Eqn) testing the responses of ln-transformed species richness, ln(S) (models 1, 2, and 15), species richness (models 3-15) and parameter σ (models 1-15) to environmental and spatial variables. Covariance of the selected predictors (X) in the respective model with i) the selected spatial variables in model 15 is given by X∩Spa and with ii) ln(S), by X∩ln(S). n = 100. The AIC of the best environmental model is boldfaced. Abbreviations as in Table 1. -produced version of the article published in American Naturalit, 192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 Author-produced version of the article published in American Naturalit, 192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

		Author-produced version of the article published in American Naturalit, 192(5), 605-617
		The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830
			doi : 10.1086/699830
	Eqn Predictor set		Richness			SAD parameter σ
			AIC	R 2 X∩Spa	AIC	R 2	X∩Spa X∩ln(S)
	1	1/kT		NS			NS
	2	1/kT + (1/kT) 2		NS		1245	0.02	0.02	-0.01
	3	ln(N) + ln(N) 2		NS		1237	0.03	0.06	0.00
	4	Tmean + Tmean 2	5387	0.01	0.01	1245	0.02	0.02	-0.01
	5	TSD + TSD 2 + Tdiur + Tdiur 2	5331	0.09	0.08	1165	0.14	0.11	0.07
	6	Tmin + Tmin 2 + Tmax + Tmax 2	5351	0.07	0.05	1194	0.09	0.09	0.04
	7	Tmean + Tmean 2 + TSD + TSD 2 + Tdiur +	5299	0.15	0.07	1104	0.22	0.15	0.10
		Tdiur 2 + Tmin + Tmin 2 + Tmax + Tmax 2
	8	TP + TP 2 + NOx + NOx 2 + NH4 +	5323	0.11	0.07	1172	0.12	0.12	0.07
		NH4 2
	9	TP + TP 2 + NOx + NOx 2 + NH4 +	5323	0.11	0.07	1150	0.15	0.12	0.08
		NH4 2 + pH + pH 2 + Cond + Cond 2
		Tmean + Tmean 2 + TSD + TSD 2 + Tdiur +
	10	Tdiur 2 + Tmin + Tmin 2 + Tmax + Tmax 2 +	5259	0.21	0.10	1080	0.25	0.18	0.12
		TP + TP 2 + NOx + NOx 2 + NH4 +
		NH4 2
		Tmean + Tmean 2 + TSD + TSD 2 + Tdiur +
	11	Tdiur 2 + Tmin + Tmin 2 + Tmax + Tmax 2 +	5259	0.21	0.10	1080	0.25	0.18	0.12
		TP + TP 2 + NOx + NOx 2 + NH4 +
		NH4 2 + pH + pH 2 + Cond + Cond 2

Table 3 .

 3 Regression models of skewness in the US and Finland. Std. = standardized. Abbreviations as in

Table 1 .

 1 Author-produced version of the article published in AmericanNaturalit, 192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830

	Effect	Std. coefficient Standard error	t-value	p-value
	US, R 2 = 0.09, n = 669
	Constant	0.00	0.02	43.57	0.000000
	TSD	-0.11	0.01	-2.34	0.02
	TSD 2	-0.21	0.00	-4.92	0.000001
	Tdiur	-0.13	0.01	-2.93	0.003
	Tdiur 2	0.13	0.00	3.07	0.002
	NOx	-0.10	0.01	-2.65	0.01
	pH	-0.15	0.03	-3.71	0.0002
	Finland, R 2 = 0.20, n = 100
	Constant	0.00	0.05	20.88	0.000000
	Tdiur 2	-0.31	0.08	-2.54	0.013
	TP 2	0.31	0.04	2.71	0.008
	Cond 2	-0.33	0.07	-2.85	0.005

Table A2 .

 A2 Author-produced version of the article published in AmericanNaturalit, 192(5), 605-617 The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830 doi : 10.1086/699830 Significant variables (P < 0.05) included in models 1-15 from Tables 1 (US) and 2 (Finland).

		Author-produced version of the article published in American Naturalit, 192(5), 605-617
		The original publication is available at https://www.journals.uchicago.edu/doi/full/10.1086/699830
				doi : 10.1086/699830
	Total phosphorus (mg•L -1 ) + Tmax 2 + TP + NOx		0.00	0.19		0.02		0.03	0.04
	pH Abbreviations as in Table 1. + NH4		4.50	8.20		7.00		6.80	0.81
	Specific conductance (μS•cm -1 ) Lat + Lat 2 + Lat 3 Lat 2	9.40	277.00 Lat 2 + Lat 3		44.75	65.37 Lat 2 + Lat 3	59.24
	Tmean (°C) Long 2 + Long 3	-2.70 Long 2 + Long 3	5.00 Long + Long 2	-0.50	Long 2	0.28	2.03
	Eqn		US				Finland
	Tsd	Elev + Elev 3	Elev 2	6.93	10.19 Elev + Elev 2		9.52	Elev 2	9.29	0.80
		Richness	Parameter σ	Richness			Parameter σ
	Tdiur (°C) Lat + Long 2 +	6.50 Lat 3 + Long + Long 2	9.20		8.30		8.21	0.67
	1	NS	1/kT		NS			1/kT
	Tmin (°C) Long 3 + Elev 2 +	Minimum Maximum -21.30 -9.10 + Long 3 + Elev + Lat 2 + Long 2	Median -17.15	Mean -16.60 Lat 2 + Lat 3	SD 3.29
	2	NS	1/kT + (1/kT) 2	1/kT + (1/kT) 2		(1/kT) 2
	US Tmax (°C) Elev 3	Elev 2	14.80	21.00		18.75	18.78	1.66
	3	NS	ln(N) 2		-			-
	Latitude (degrees)		25.40	61.77		41.64	41.58	4.58
	4	Tmean 2	Tmean + Tmean 2	Tmean 2			Tmean
	Longitude (degrees)		-154.17	-70.74		-92.08	-95.63	16.48
			TSD + TSD 2 + Tdiur +
	Elevation (m) 5 TSD + TSD 2		57.00	2733.00 TSD + Tdiur + Tdiur 2 303.00	483.85 TSD + Tdiur	507.35
			Tdiur 2
	Total phosphorus (mg•L -1 )		0.002	3.40		0.07		0.16	0.31
		Tmin + Tmin 2 + Tmax	Tmin + Tmin 2 + Tmax +
	Nitrite + nitrate (mg•L -1 ) 6		0.01	13.95 Tmin + Tmax + Tmax 2 0.46	1.36 Tmin + Tmax 2	2.22
		+ Tmax 2	Tmax 2
	Ammonia (mg•L -1 )		0.002	5.80		0.03		0.06	0.25
		Tmean + Tmean 2 + TSD
	pH		2.95 TSD + TSD 2 + Tdiur +	9.60 TSD + Tdiur 2 + Tmin + 7.90	7.83 Tmean 2 + Tdiur + Tmin 2 + 0.56
	7	+ TSD 2 + Tdiur +
	Specific conductance (μS•cm -1 ) Tmin + Tmin 2 + Tmax 11.00	23595.65 Tmax + Tmax 2	476.00	539.10 Tmax 2	966.64
		Tdiur 2 + Tmin + Tmax
	Tmean (°C)		-0.80	23.70		9.60		9.86	3.59
	8	TP + TP 2 + NOx	TP + TP 2 + NOx	TP 2			NS
	Tsd			3.19	12.58		9.05		8.93	1.70
	9	TP + TP 2 + NOx	TP + Cond	TP 2 + pH 2			TP 2 + Cond 2
	Tdiur (°C)		7.80	19.60		12.10	12.54	1.86
		Tmean + TSD + TSD 2
	Tmin (°C)	-22.20 TSD + TSD 2 + Tdiur +	13.40		-9.40	-8.70	5.70
		+ Tdiur + Tmin + Tmax			Tmean + Tdiur + Tmin +	Tmean + TSD + Tdiur + Tmin
	Tmax (°C) 10	15.20 Tmin + Tmin 2 + Tmax +	36.30		29.20	29.35	2.87
		+ Tmax 2 + TP + NOx			Tmax 2 + TP 2			+ Tmax 2 + TP 2
	Finland	TP
		+ NH4
	Latitude (degrees)		60.27	70.06		66.26	65.91	2.81
			TSD + TSD 2 + Tdiur +
	Longitude (degrees) Tmean + TSD + TSD 2		23.28	30.44 Tmean + Tdiur + Tmin + 27.02	27.04 TSD + Tdiur 2 + Tmax 2 + TP 2.09
	11		Tmin + Tmin 2 + Tmax +
	Elevation (m) + Tdiur + Tmin + Tmax		18.00	320.00 Tmax 2 + TP 2 + pH 2 180.00	177.49 + Cond	81.91
			TP