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Ordonez & Svenning – Glacial-interglacial legacies in functional diversity

Title: Geographic patterns in the ratio of realized to potential functional diversity are linked

to glacial-interglacial climate stability and accessibility

Running title: Glacial-interglacial legacies in functional diversity

Authors: Alejandro Ordonez1 and Jens-Christian Svenning1

1Section for Ecoinformatics and Biodiversity, Department of Bioscience, Aarhus University,

Ny Munkegade 114, DK-8000 Aarhus C, Denmark

Corresponding author: Alejandro Ordonez. Section for Ecoinformatics and Biodiversity,

Department of Bioscience, Aarhus University, Ny Munkegade 114, DK-8000 Aarhus C.,

Denmark. Email: [email protected]

Manuscript types: Research papers

Number of words in the abstract: 298/300

Number of words in the manuscript: 5233/5000 (Introduction through the Biosketch,

excluding abstract, references and figure legends)

Number of references: 49/50

Number of figures and tables: 4 Figures and 3 Tables [Total 7/8]

Author contributions. A.O. and J-C.S. developed the idea, analyzed the results and

contributed equally to writing the manuscript. A.O. compiled the datasets, developed and

performed the statistical modeling.

Key words: climatic anomalies, disequilibrium dynamics, functional traits, historical effects,

paleoclimate, time lags, Europe, Climate velocity, Last Glacial Maximum, functional traits

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ABSTRACT

Aim: Late Quaternary climate change can be an important determinant of large-scale species

richness patterns, but it is currently unknown if its effects also extend to functional diversity

(FD) and thus potentially ecosystem functioning. This study assessed whether deficits in

contemporary FD relative to expectations based on contemporary environmental regions and

species richness, are associated with glacial-interglacial climate stability and accessibility

from glacial refugia.

Location: Europe

Methods: Atlas data on distributions of plant species and functional trait information were

used to estimate functional richness (FRich) and dispersion (FDisp) for ~50×50 km grid cells

across Europe. Maximum expected FD was calculated using a both a quantile regression and

a null-model approach, with species richness and contemporary environmental regions as

constraints. Then, the proportion of the potential FD present in a grid cell – the realized-to-

potential FD ratio (R/P) – was estimated. Spatial autoregressive modeling with information-

theoretic multi-model selection was used to estimate the explanatory importance and

predictive ability of glacial-interglacial climate instability and accessibility to recolonization

from glacial refugia for R/P ratios.

Results: Minimum and median R/P ratios were 58% and 74% for FRich and 82% and 93% for

FDisp, showing that contemporary realized FD is often lower than expectations from species

richness and contemporary environmental regions. This deficit is significantly associated

with glacial-interglacial Quaternary climate change (FRich-R2: 0.52; FDisp-R2: 0.41). FRich and

FDisp R/P ratios high climatic instability (fast temperature and precipitation velocities) and

proximity to the major glacial temperate refuge regions (high accessibility).

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Main conclusions: Realized macro-scale FD patterns appear to be in moderate

disequilibrium with contemporary richness and environmental regions. Importantly, small

R/P ratios are associated with low glacial-interglacial climatic instability and proximity to

glacial refugia. These findings suggest that future climate change may elicit long-term

functional disequilibria and thus also have long-term consequences for ecosystem

functioning.

INTRODUCTION

Studies assessing the effects of climate on diversity have focused on evaluating how

contemporary or historical conditions shape species ranges (Svenning & Skov, 2007b;

Normand et al., 2011; Boucher-Lalonde et al., 2014) and species richness (Svenning & Skov,

2007a; Svenning et al., 2010; Boucher-Lalonde et al., 2014). A largely unexplored dimension

of the climate-diversity relation is the effect of historical climate on functional diversity

across large regions, despite the importance of functional diversity for community and

ecosystem functioning (Chapin III et al., 2000; Hooper et al., 2005). For the purpose of

clarity, we consider functional diversity (FD hereafter) as the overall range as well as the

dispersion of trait values in a region.

Evidence indicates that paleoclimatic changes have filtered regional species pools based on

climate-related traits (Brodribb & Hill, 2004; Svenning et al., 2010) and shaped dispersal trait

distribution patterns within and among continents (Normand et al., 2011; Kissling et al.,

2012), suggesting that there could also be effects on FD. Additionally, the relation between

species richness and the range in functional trait values (Cornwell et al., 2006; Laliberté &

Legendre, 2010) indicate that historical effects on species richness are likely, just for this

reason, to influence FD and any other correlate of richness. However, historical legacies in

species richness can be independent of past changes in species composition (Algar et al.,

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2011) and thereof break the richness-FD relation given that changes in the number of species

would not result in changes of the community mean, range or dispersion of trait values.

Either way, the existence and nature of long-lasting paleoclimatic effects on FD would have

significant implications for what to expect in terms of species, community and ecosystem

responses to future climatic changes (Chapin III et al., 2000; Hooper et al., 2005) and for the

development of traits-based approaches to forecast global vegetation functioning (Van

Bodegom et al., 2012).

Contemporary biotic, environmental and anthropogenic disturbances can affect the FD of a

community (Mouillot et al., 2013), restricting the occupied trait space (lower richness or

range) and reducing the deviation of species trait values from the community mean (lower

dispersion or variation). By analogy, paleoclimatic disturbances such as glaciations should

have also lowered the realized FD from its potential value based on contemporary

environmental regions and species’ richness. Assessing to what extent realized FD values

deviate from their potential maxima given current regional environment and species richness,

and the degree to which these deviations relate to historical disturbances offers a way to

quantify historical legacies in contemporary FD patterns.

We combine species’ distribution data with high-resolution contemporary and historical

environmental information to evaluate whether late-Quaternary climate has left a lasting

imprint on contemporary patterns of FD. Using the European flora as a study system and

building on Svenning et al. (2010)’s approach for species richness, we evaluated the FD

realized-to-potential ratio (R/P) of angiosperms in Europe as a way to determine the extent to

which historical climate has determined FD in the study region. We specifically evaluated the

idea that R/P ratios may be associated with late-Quaternary glacial-interglacial climate

change (measured as climate change velocity since the Last Glacial Maximum (LGM) ~

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21,000 years BP; Sandel et al., 2011) and/or accessibility to postglacial re-colonization from

glacial refugia (Normand et al., 2011) .

We expect that R/P ratios will decrease with faster climate velocities and larger distances to

glacial refugia. Our working hypothesis is that limited extinction pruning of the species pool

in climatically stable areas (slow velocity and high accessibility) promote species coexistence

and facilitate long-term species survival (Sandel et al., 2011), and allows higher rates of

immigration in the proximity of highly accessible areas (Normand et al., 2011). This in turn

would result in a more comprehensive sampling of the surviving regional trait pool

(increasing richness or range). It would also reduce functional dispersion, as species would

have more time for competition-driven filtering resulting in an even spacing among co-

occurring taxa and a loss of species with environmentally marginal trait combinations. In the

light of our findings, we also discuss the possible effects of historical factors on FD diversity

patterns in contemporary and future ecosystem functioning.

METHODS

Distribution data. We focused on the European flora because its current ecology and

historical distribution are relatively well understood (Ellenberg, 1988; Bennett et al., 1991),

making it an ideal system for critical interpretation of the historical legacies of glacial-

interglacial changes in macro-scale diversity patterns. We used plant species distribution data

from Atlas Florae Europaeae (Jalas & Suominen, 1994-1999), which maps the distribution of

European flora on an equal-area mapping unit of c. ~50km×50km (AFE grid cells). All cells

in the former Soviet Union were excluded due to the heterogeneous and sometimes limited

sampling effort in this region. All taxa below the species level were collapsed to the

corresponding species. The AFE covers approximately 20% of the plant species in Europe,

completely covering the clades treated so far. We only included angiosperms (n=3904

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species) in this study, excluding ferns, fern allies and gymnosperms to avoid possible

divergent effects on FD by including these phylogenetically distant groups.

Functional diversity estimation. Four eco-morphological traits associated to important plant

ecological strategies (Westoby et al., 2002; Chave et al., 2009) and the way plants respond to

environmental factors such as resources and disturbances (Lavorel & Garnier, 2002) were

used to estimate FD: specific leaf area (SLA, cm2*g-1), seed weight (SWT, mg), maximum

stem height (Hmax, m) and stem tissue density (WD, kg*m-3). SLA was used to represent the

trade-off between construction costs and carbon fixation (leaf economics spectrum; Wright et

al., 2004). SWT was used to represent a trade-off between seed size and seed production

(Moles & Westoby, 2006). Hmax was used to indicate the adult light niche (Moles et al.,

2009). WD was used to represent the trade-off between volumetric growth rates and mortality

rates or construction costs (wood economics spectrum; Chave et al., 2009). Trait values for

each taxon were initially determined using multiple published sources (Appendix S1).

Remaining missing values (SLA=80%, Hmax=69% SWT=54% and WD=15%) were filled

using a Multivariate Imputation Chained Equations approach (Buuren & Groothuis-

Oudshoorn, 2011). Before the analyses, all traits were log-transformed (as they were log-

normally distributed) and standardized (mean=0 and SD=1) to ensure that trait contribution to

FD metrics is scale independent.

We estimated two complementary FD metrics to describe grid level functional composition:

richness (Villéger et al., 2008) and dispersion (Laliberté & Legendre, 2010). Functional

richness (FRich) measures the range of the trait spectrum of the species pool based on the

multivariate trait space filled (volume) by the community as described by a multivariate

convex hull. In comparison, functional dispersion (FDisp) measures the spread of functional

types with respect to the functional space local center. While the FRich provided a measure of

the niche space occupied by co-occurring species, FDisp measured niche segregation among

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coexisting species. We also evaluated these moments for individual traits, defining trait

richness as the trait value range and functional dispersion as the standard deviation of the trait

values.

Realized-to-potential functional diversity ratio determinants. FD and species richness

(number of species per AFE grid cell) showed a significant relation (Fig. 1), as indicated by

Pearson correlations with Dutilleul et al. (1993) geographically effective degrees of freedom

(FRich-ρ=0.75 and FDisp-ρ=-0.16). Furthermore, the relation between species richness and FRich

or FDisp was consistent across environmentally distinct regions (Fig. 1). For this reason, we

used a combination of species richness and contemporary environmental regions to calculate

the expected maximum FD.

Two distinct methods are used to estimate the maximum potential FD based on species

richness and contemporary environmental regions for both multivariate and single traits:

Quantile regression and a null-community ensemble approach. These estimates represent the

expected FRich or FDisp if only contemporary species richness and regional environmental

conditions constrained FD, i.e., in the absence of historical influences. Based on this we

calculated realized-to-potential ratios in FD (R/P ratio) to represent how much of the possible

functional space and dispersion is actually currently realized.

First, we used an additive quantile regression smoothing approach with species richness and

Metzger et al. (2005)’s environmental regions of Europe as predictors. This approach

provided a regionally environmentally constrained estimate of FD on the basis of species

richness per AFE grid cell. Quantile regressions were fitted to estimate the 99% percentile

(τ=0.99) as it provides a conservative assessment of the expected maximum potential FD

limits due to the number of species and broad-scale cotemporary environmental conditions.

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After fitting this quantile regression model, we then projected it back to the study area to

estimate the maximum potential FD per AFE grid cell.

Second, we constructed 1000 null communities for each AFE grid cell by randomizing the

occurrence matrix, maintaining the original species richness, while restricting the pool of

species to be sampled to those within the same Metzger et al. (2005) environmental region.

This approach assumes that each species has an equal chance of occurring within each grid

cell contained within a given environmental region, so a deviation from this expectation can

be attributed to other factors beyond contemporary effects of species richness and regional

environmental conditions. We then proceeded to estimate the maximum FRich and FDisp for

each grid cell null community to get an estimate of highest potential FD per AFE grid cell.

Statistical analyses. We used spatial regressions with information-theoretic multi-model

selection to test the association between R/P ratios and historical predictors. Two types of

complementary variables (Appendix S1) were used to measure historical climatic instability

and postglacial accessibility to re-colonization: spatiotemporal rates of late-Quaternary

glacial-interglacial climate change (hereafter referred as climatic instability) and accessibility

to postglacial re-colonization from LGM refugia (hereafter referred only as accessibility).

While velocity represents the climatic instability of an AFE grid, accessibility represents how

easily each AFE grid could be reached by migration from glacial refugia.

Climatic instability was measured as mean annual temperature and precipitation change

velocities over the last 21,000 years (measured in km×decade-1 and caluclated as in Sandel et

al., 2011). Accessibility was measured as the inverse of the summed distance from each AFE

grid cell to all LGM refuge cells (measured in km-1 as in Svenning et al., 2010). Possible

glacial refugia were defined based on the minimum climatic requirements for cool-temperate

trees: GDD ≥800°C, mean temperature of the coldest month ≥-15°C, and summer

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precipitation ≥50 mm sensu Leroy and Arpe (2007). It is important to highlight that our

accessibility estimate is qualitatively similar to climatic analog-based estimates of climatic

refugia (Ohlemüller et al., 2012) and highly correlated to the mean of Normand et al.

(2011)’s species-specific accessibility estimates for 1016 European species of herbaceous and

woody plants using hind-casted species distribution models (Spearman’s ρ=0.92; pDutilleul-

corrected=0.001). Furthermore, Normand et al. (2011)’s study also estimated that a large fraction

of European species were likely displaced into refugia wholly or primarily located south of

the 46°N latitude during the LGM, supporting our usage of this area as refuge regions.

Spatial autoregressive (SAR) error models (autoregressive process only in the error term)

were used to describe the statistical relation between R/P ratios and historical predictors.

These have been demonstrated to the most reliable statistical specification regardless of the

process generating the spatial autocorrelation or the model selection criteria (Kissling & Carl,

2008). Neighborhood distances in the neighborhood structure were established using the

semi-variogram range, based on the residuals of an ordinary least squares (OLS) multiple-

regression with full set of predictors. The SAR modeling was used to examine the association

between historical climate and R/P ratios for both multivariate and single traits across all of

Europe. Similar analyses were done for the regions north and south of the 46oN latitude

separately, as these represent areas where species richness and distributions patterns have

shown to be associated with either dispersal limitation (Svenning & Skov, 2007b; Normand

et al., 2011) or ecological tolerance (mainly cold and drought; Leroy & Arpe, 2007). We

expect that R/P ratios in regions north of the 46oN latitude are smaller and show a stronger

association with historical predictors than areas south of this boundary.

We estimated SAR models for all possible combinations of the three historical predictors and

used information-theoretic model selection and multi-model inference to provide robust

estimates of their importance (Burnham & Anderson, 2002). We estimated Akaike weights

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(wAIC) calculated following Burnham and Anderson (2002). Relative importance of each

historical predictor was determined by summing the wAIC of all the models where the variable

of interest was included. Then, we determined the best fitting model, as the model with the

lowest ΔAIC (a measure of the probability that a given model was the best model for the

observed data within the set of candidate models). We also estimated model fit using

Nagelkerke’s (1991) pseudo-R2. Using this model, we further assessed which were the most

important historical predictor variables (contrast of regressions coefficients), considering both

their overall importance and their directional relation to the R/P ratios.

Contemporary climatic conditions could also modulate R/P ratios beyond their effects on

species richness. For this reason, all spatial regression analyses were also performed using

historical predictors and mean annual temperature and annual precipitation as predictors.

Contemporary predictors were selected due to it strong association diversity patterns in the

region (cf. Svenning & Skov, 2007b; Svenning & Skov, 2007a). These results are reported

in….

It is possible that the estimated effects of historical predictors on R/P ratios could simply

reflect spatial structure in the variables. We investigated this possibility using several

approaches. Firstly, we estimated how strong predictive power the historical variables confer

beyond the calibration region, using geographically independent validation. To do this, we

divided the study region in two (along the 10°E meridian) defining two training and testing

datasets (east training – west testing, and west training – east testing). Then we fitted a SAR

model on the training half of the data and then predicted the R/P ratios values in the testing

half. The predictive ability was determined as the Spearman correlation between predicted

and observed values in the test dataset. This approach allowed us to measure the predictive

ability of historical predictors and determine a possible causal link between R/P ratios and

historical climate.

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Secondly, as we found intercept-only SAR models to have high explanatory power for R/P

ratios in both FRich andf FDisp (see Results), we compared the explanatory power of intercept-

only SAR models fitted to the observed R/P ratios to those fitted on predicted to R/P ratios

using an ordinary least squares (OLS) multiple regression model. The implemented OLS

model was based on all supported historical variables as predictors. The predicted values

from this model by definition only depend on the historical variables; analyzing their pattern

using an intercept-only SAR model therefore tells us to what extent such historically-

determined variation may be captured by a purely spatial SAR.. Additionally, we partitioned

the variation resulting from sets of three OLS models that used either historical predictors,

space or both as predictor variables (Borcard et al., 1992). With this, we assessed the

individual and joint contributions of historical predictors, space as explanatory factors of R/P

ratios.

RESULTS

Realized functional richness (FRich) and dispersion (FDisp) estimates based on multiple-traits

(Fig. 2A, B) and single traits (Supplementary material S2) exhibited strong geographic

patterns. Areas of high FD were observed in regions with distinct contemporary

environmental conditions, notably areas with high topographic variability (e.g., the Pyrenees

and Alps), and high seasonality and annual precipitation (Scandinavia). Importantly, FD

values were higher in areas south of 46°N, the northernmost limit of the major glacial refugia

for temperate species (indicated by the dashed black line in Fig. 2), notably in Southern

Europe (with parts of the Iberian Peninsula as the main exception for FRich). FDisp also

achieved high values in some coastal areas of formerly glaciated areas of Scandinavia.

Furthermore, realized FD was lower than expected FD based on a random sampling of

species within the same environmental region (significantly lower FRich and FDisp in 75% and

79% of the evaluated AFE grid cells).

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These trends were much weaker for the potential FD, which exhibited a generalized smoother

south to north gradient in FRich, with just as high values in most of Central Europe as in

Southern Europe (Fig. 2C), and a generalized intermediate FDisp across all Europe with

pockets of high FDisp in the Mediterranean region (Iberian and Balkans Peninsula) and

Scandinavia (Fig. 2D). These quantile regressions based patterns were qualitatively

consistent with predictions based on null models (Appendix S2). For clarity, the primary

results discussed hereafter are based on quantile-regression based predictions of potential FD.

Results for the null model approach are presented as supplementary material (Appendix S2).

The R/P ratios ranged between 58% to 100% for FRich and 82% to 100% for FDisp (Fig. 2E, F).

Similarly, minimum R/P ratios in the range and variability of single-traits ranged between

30% and 80% (Appendix S2). Such relatively high R/P ratios are not unexpected given the

strong correlation between species richness on realized FD (see methods). Nevertheless, given

that realized FD levels were missing as much as 42 % or 18% of the potential maximum for

FRich and FDisp respectively, other factors besides richness and environmental regions may also

be of importance for current FD patterns.

Concerning the role of individual traits in driving R/P ratios, seed weight and wood density

were the traits with strongest support as possible determinants of FRich R/P ratios. Overall,

areas of large seed weight range deficit (lower seed sizes than expected) and stem density

range deficit (wood density is lower than expected) had the lowest FRich R/P ratios (SWT

R2NK: 0.51 WD R2

NK: 0.49). Meanwhile, stem height and seed weight were the traits with the

largest support as possible determinants of FDisp R/P ratios as areas of large deficits in stem

height (lower mean canopies than expected) and seed weight (lower seed sizes than expected)

trait variability had he lowest FDisp R/P ratios (Hmax R2NK: 0.597 SWT R2

NK: 0.58).

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As for realized FD, the dominant geographic pattern in R/P ratios was a contrast between

Southern and Northern Europe, with significant lower values in the latter (Fig. 3).

Geographic patterns of R/P ratios show Southern (including the Pyrenees) and Central

Europe as the areas with the highest R/P ratios for FRich (Fig. 2C) and FDisp (Fig. 2F).

Meanwhile, regions covered by the large northern ice sheets during the LGM showed the

lowest R/P ratios for FRich and FDisp (areas inside the red outline in Fig. 2C and F). The

similarity between FRich and FDisp R/P ratios in northern Europe and Scandinavia was not

surprising given the correlation between both components (FRich- FDisp: ρ=0.17, pDutilleul-

corrected<0.001).

Considering each historical climatic variable separately (single variable models in Table 1),

the R/P ratios showed negative associations to climatic instability (R/P ratios decreased as

velocity increase; Fig. 4A-B and D-E) and positive associations to postglacial accessibility

(R/P ratios increased with proximity to the main temperate glacial region; Fig. 4 C, F). If

contemporary factors (mean annual temperature and precipitation) were also evaluated

(Appendix S3), R/P ratios showed a negative association with mean annual temperature in

the case of FRich; and a positive associations to annual precipitation and mean annual

temperature in the case of FDisp. These associations were consistent, but weaker for single-

trait-based FD metrics with the exception of a negative effect of accessibility on SLA

dispersion (Appendix S2 and S3). Furthermore, the direction of the relation between historic

predictors and R/P ratios was similar in areas north (blue lines; Fig. 4) and south (orange

lines; Fig. 4) of the 46°N major temperate refuge boundary. This was also the case for annual

precipitation, but not mean annual temperature, where relations in areas south of the 46°N

boundary were flat and non-significant (Appendix S3).

ANCOVAS indicated that areas north of the 46°N glacial limit of climatic refugia had lower

ratios than those south of this limit (see also Fig. 3 and Appendix S3) and that the relation

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between R/P ratios and environmental factors differed between regions (Table 2), with the

FDisp relations with historical factors being noticeably weaker in Southern Europe (Fig. 4).

The different linear combinations of the three historical predictors produced R2NK greater or

equal to 0.5 for FRich or 0.4 FDisp (Table 1). These trends were consistent after including mean

annual temperature and annual precipitation as predictor variables (Appendix S3), showing

that including contemporary variables did not add predictor power. When summarized across

all models, statistical support (wAIC) for an effect of temperature instability was 1 and 0.999 in

the case of for FRich and FDisp, respectively, while that for accessibility was 0.935 of FRich and

0.999 for FDisp. The support for precipitation instability was much lower, with wAIC=0.656 for

FRich and wAIC=0.497 for FDisp. The importance of temperature instability and accessibility was

also observed after including mean annual temperature and annual precipitation as predictor

variables (Appendix S3). This was further supported by information-theoretic multi-model

inference as temperature instability wAIC was 1 for both FRich and FDisp, while accessibility wAIC

was 0.99 and 1 for FRich and FDisp respectively.

Information-theoretic multi-model inference showed differences in the most important

variables associated with R/P ratios for individual traits’ range and deviation (Appendix S2).

For trait ranges, temperature velocity highest relative importance score for SLA (wAIC=0.968),

SWT (wAIC=0.990) and Hmax (wAIC=1.0), while accessibility was the most important variable

for WD (wAIC=0.791). For trait dispersion, accessibility had the highest relative importance

score for SLA (wAIC=0.952), SWT (wAIC=1.0) and Hmax (wAIC=0.999), while precipitation

velocity was the most important variable for WD (wAIC=0.589).

For both FRich and FDisp a model explaining R/P ratios in terms of temperature velocity and

accessibility had the lowest ΔAIC and highest pseudo-R2 (Table 1). The model fit of this

model, measured as R2NK, was 0.521 for FRich or 0.413 FDisp (Table 3). Standardized

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coefficients from the best model showed the importance of both temperature instability and

accessibility, as well as an increase in R/P ratios with increasing climatic instability (negative

coefficient for temperature and precipitation velocity; Table 3) and increasing accessibility to

postglacial re-colonization (positive coefficient for accessibility; Table 3). When

contemporary and historical variables were both included as predictors, the model with the

lowest ΔAIC and highest pseudo-R2 for FRich included the full set of predictors, while for FDisp

it included annual mean temperature, annual precipitation, temperature instability and

accessibility (Appendix S3). Furthermore, the importance of contemporary and historical

variables in these models were comparable in terms of standardized coefficients (Appendix

S3).

The SAR model based on temperature velocity and accessibility had a high predictive ability

of R/P ratios as indicated by geographically independent validation. Models trained east of

10°E longitude accounted for 39,8% and 44,2% of the variation in FRich and FDisp of areas west

of this longitude, respectively, and models trained west of 10°E longitude accounted for

56,5% and 51,3% of the variation in FRich and FDisp in areas east of this longitude.

An intercept-only SAR model was not supported by information-theoretic model selection

when compared to models including climatic instability and/or accessibility (FRich: wAIC=0 and

FDisp: wAIC=0; Table 1). Still, it had relatively high explanatory power, just 1.9% for FRich and

1.4% of FDisp lower than the most supported model, i.e., with all three predictors. This was

also the case after including mean annual temperature and annual precipitation as predictor

variables (Appendix S3); indicating that the unexplained variability cannot be accounted by

including spatially autocorrelated contemporary predictors. This likely reflects how the SAR

model was able to capture much of the historical relations in the spatial error component.

Evidence for this was the very high predictive ability of intercept-only SAR models fitted to

R/P ratio predicted values from an OLS multiple regression using the historical predictors

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(R/P FRich R2NK= 0.89; R/P FDisp R2

NK= 0.94). Moreover, when observed R/P ratio explained

variation was partitioned using a OLS model into individual and shared components of

history and space, the shared contribution of both factors accounted for almost half of the

total explain variation (FRich: 15% and FDisp: 11%) and almost the same variability explained

by solely by history (FRich: 12% and FDisp: 10%) or space (FRich: 9% and FDisp: 8%) alone.

DISCUSSION

Our results suggest that plant assemblages in Europe often do not fully realize their potential

maximum FRich and FDisp, given contemporary regional environmental conditions and local

species richness, hence resulting in a “functional deficit” for regions across Europe. This

limited realization of the potential FD suggests that contemporary regional environment and

sampling of the regional species-pool are not the sole determinants of contemporary FD

patterns. This was further indicated by the importance of historical predictors as explanatory

variables of R/P ratios even after including contemporary environmental predictors.

Furthermore, we show that functional deficits in richness and dispersion are statistically

negatively related to Quaternary glacial-interglacial climate instability and positively related

to postglacial accessibility, suggesting functional disequilibria despite the last glaciation

ending ~11,500 years ago. These associations are consistent with the hypothesis that glacial

extinction dynamics and postglacial migration lags shown for European plants (Svenning &

Skov, 2007b; Normand et al., 2011) have an effects on plant FD and appear to supplement

the possible effects of random sampling from the current regional trait/species pool and local

habitat filtering by contemporary regional environmental factors.

Two possible factors might cause the estimated paleoclimate-related deficit on FD: 1) sorting

according to climatic tolerance by past climatic conditions (Svenning, 2003; Bhagwat &

Willis, 2008) and 2) postglacial migration lags (Normand et al., 2011) coupled to links

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between dispersal ability or immigration potential and plant traits (Bhagwat & Willis, 2008;

Nogués-Bravo et al., 2014). Glacial cooling or direct glaciation are likely to have removed

particular taxa or functional groups from a given area in non-random fashion depending on

their traits (e.g., via links to cold and drought tolerance; Svenning, 2003). It might have also

caused changes in species and community mean trait values depending on climatic historical

effects (e.g., glaciations filters could make species more cold-adapted than expected from the

current regional environment alone, by lowering/increasing the mean of some trait axis; e.g.,

Bhagwat & Willis, 2008). In comparison, migration lags are likely non-random with respect

to traits (Normand et al., 2011; Nogués-Bravo et al., 2014) and could explain the failure to

colonize climatically suitable areas as glacial cover receded and climate warmed since the

LGM.

The above factors are known to also influence broad-scale species richness patterns in Europe

(Svenning & Skov, 2007a; Fløjgaard et al., 2011), but also elsewhere (Blach-Overgaard et

al., 2013; Rakotoarinivo et al., 2013). These historical legacies on species richness could

potentially permeate to FRich and FDisp via the relations between FD and species richness. For

example, the lower realized than potential species richness shown in the European tree flora

by Svenning et al. (2010) is likely to have imposed an additional, indirect historical constraint

to the size and dispersion of the realized functional space of areas covered by ice during the

LGM.

The observed patterns in deviations in FD from their current potential are at least partially

consistent with differential impacts of the Quaternary glacial cooling in different parts of

Europe. The small R/P ratios in boreal areas may reflect both the slow and non-random

colonization from climatic refugia in Central and/or Eastern Europe (Leroy & Arpe, 2007;

Bhagwat & Willis, 2008) and the glacial climatic filtering of nearby boreal refuge regions.

Meanwhile, the small R/P ratios in the center of the Iberian Peninsula may reflect a failure to

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re-colonize after extirpation during Pleistocene glacial periods (Mijarra et al., 2009),

probably due to migratory barriers posed by the Pyrenees, the aridity in interior Iberian

Peninsula and the Mediterranean Sea (Svenning et al., 2008). In comparison, the otherwise

high R/P ratios in Southern Europe may be the result of more stable climate than in areas

further north and the high immigration possibilities into the region from LGM accessible

areas in the Italian and Balkan peninsulas (Medail & Diadema, 2009; Abellán & Svenning,

2014); resulting in the occurrence of relatively stable assemblages locally and/or regionally

over extended periods of time (Rodríguez, 2006) and may thereby reduced the effects on

LGM-present climatic variability on FD.

Intercept-only SAR models have high model fits, with only a small increase in explanatory

power when including only historical predictors or both contemporary and historical

predictors. This could be taken to indicate that associations with historical predictors, while

significant, are small enough to be negligible. However, several lines of evidence indicate

that such an interpretation would be misguided. Firstly, geographical independent validations

indicate that the estimated associations between R/P ratios and historical drivers have strong

predictive power beyond the calibration region. Perhaps more importantly, intercept-only

SAR models fitted not to the original R/P values, but to R/P values from OLS models with

historical predictors, have high explanatory power, meaning that the spatial error term in the

SAR models is capable of capturing much of a pattern determined by such spatially

structured variables. A reason for why much of the relations to the historical drivers are

captured in an intercept-only model is that they are broad-scale spatially structured variables,

as expected from the underlying mechanisms, such as large-scale migration dynamics (cf.

Bjorholm et al., 2006; Normand et al., 2011).

The estimated constraints on R/P ratios linked to glacial-interglacial climate instability and

accessibility suggest lags in climate tracking of >10,000 years. However, other spatially

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structured contemporary variables (namely temperature and precipitation) account for some

of the observed variability in R/P ratios even after the effects via species richness have been

considered. This points to a high potential for vegetation dynamics in response to future

climate change to also involve substantial disequilibria (Svenning & Sandel, 2013). This

disequilibrium will not just be in species distributions and species richness, but also in FD,

with likely consequences for ecosystem functioning due to changes in trait composition. Such

changes would occur directly via filtering of unsuitable traits or its absence due to migration

lags; and indirectly, via the effects on FD resulting from changes in species richness that

would reshuffle the local trait composition. Establishing the strength and prevalence of links

between FD and ecosystem functioning would help to predict how future changes in the later

as a result of legacies of contemporary environmental-changes on FD.

CONCLUSION

Our results suggest that realized macro-scale FD are often below the potential set by

contemporary environmental regions and species richness. The geographic patterns in these

deviations can be linked to glacial-interglacial climate change and postglacial accessibility.

Hence, glacial climatic sorting and lagged postglacial re-colonization appear to not only

affect species distributions (Normand et al., 2011) and species richness (Svenning et al.,

2010) in Europe, but also affect FD. As a result, plant assemblages realize less of their

potential FD where glacial cooling was strong and postglacial accessibility has been low.

These results point to the potential for long-term disequilibria in FD and highlight the need to

incorporate historical constraints on FD and the mechanisms driving them into predictive

models of future vegetation-related ecosystem functioning. This finding is important, as such

disequilibrium effects are likely to be much stronger over the much shorter (50-200 years)

time scales typically considered for future climate change (Svenning & Sandel, 2013). Future

studies should aim to evaluate the mechanisms and timescales of potential lags to provide a

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better understanding of the resistance and resilience of FD to future changes in climatic

conditions.

Acknowledgements. This article is a contribution of the HISTFUNC project (ERC Starting

Grant 310886 to J-C.S.). We thank the Atlas Florae Europaeae project for access to the

distribution data. The LEDA project and the Millennium seed database (Kew Botanical

garden) are acknowledged for contributing trait data. The authors thank David Curie, Jeremy

Kerr, Oliver Schweiger and Véronique Boucher-Lalonde for providing comments on earlier

versions of this manuscript.

Biosketch: Alejandro Ordonez and Jens-Christian Svenning are interested in understanding

how tolerance to past and current changes in climatic conditions, long-term migration lags

and lineage biogeography impose lasting legacies in species distribution and richness patterns

and shape contemporary functional diversity patterns and ecosystem functions.

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Additional references to data sources used in this study may be found in Appendix S1 at

[URL]. Results to complementary analyses may be found in Appendix S2 at [URL].

Additional information.

Supplementary material S1. Description of the trait imputation procedure and the

estimation of the maximum potential functional diversity

Supplementary material S2. Null model and single-traits based estimations of realized,

potential, and association between realized/potential functional diversity ratios with historical

climatic predictors.

Supplementary material S3. Association between realized/potential functional diversity

ratios with both contemporary and historical climatic predictors.

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Figure legends:

Figure 1. Changes in realized function al richness (top) and dispersion (bottom) as a function

of richness and broad scale environmental regions. Colors indicate Metzger et al. (2005)

environmental regions for Europe. Lines show the potential maximum FD estimated using a

quantile regression constrained on current regional environment and species richness (see

methods).

Figure 2. Realized (A, B) potential, (C, D) and realized/potential ratios (E, F) of plant

functional richness (left column) and dispersion (right column) per ~50×50km AFE grid cell

across Europe. Estimates of potential maximum functional diversity based on

environmentally constrained quantile regressions on species richness (see methods). The

thick-dashed black line indicates the boundary for the major Southern Europe glacial refuge

region (latitudes<46°N). Areas outlined in light grey solid lines indicate the maximum extent

(21000yrs ago ~LGM) of the Barents-Kara, British and Scandinavian ice-sheets.

Figure 3. Scatter plots of realized/potential ratios (R/P ratios, y-axis) of plant functional

richness (top row) and dispersion (bottom row) vs. late-Quaternary climate change in the

form of log-transformed annual mean temperature velocity (left column), log-transformed

total annual precipitation velocity (center column), and accessibility to postglacial re-

colonization (right column). Potential functional richness and dispersion estimated as in Fig,

1. Spatial autoregressive (SAR) model fits are presented for all Europe (black lines), and for

areas north (blue points and lines) and south (orange points and lines) of the boundary for the

major Southern Europe glacial refuge region (46°N). Model fits are presented in Table 1 and

A.

Figure 4. Scatter plots of realized/potential ratios (R/P ratios, y-axis) of plant functional

richness (top row) and dispersion (bottom row) vs. late-Quaternary climate change in the

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form of log-transformed annual mean temperature velocity (left column), log-transformed

total annual precipitation velocity (center column), and accessibility to postglacial re-

colonization (right column). Potential functional richness and dispersion estimated as in Fig,

1. Spatial autoregressive (SAR) model fits are presented for all Europe (black lines), and for

areas north (blue points and lines) and south (orange points and lines) of the boundary for the

major Southern Europe glacial refuge region (46°N). Model fits are presented in Table 1 and

2.

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Figure 1. Changes in realized function al richness (top) and dispersion (bottom) as a function of richness and environmental conditions. Colors indicate Metzger et al. (2005) environmental regions for Europe. Lines show the potential maximum FD estimated using a quantile regression constrained on current regional environment and species richness (see methods).

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Figure 2. Realized (A, B) potential, (C, D) and realized/potential ratios (E, F) of plant functional richness (left column) and dispersion (right column) per ~50×50km AFE grid cell across Europe. Estimates of potential maximum functional diversity based on environmentally constrained quantile regressions on species richness (see methods). The thick-dashed black line indicates the boundary for the major Southern Europe glacial refuge region (latitudes<46°N). Areas outlined in light red solid lines indicate the maximum extent (21000yrs ago ~LGM) of the Barents-Kara, British and Scandinavian ice-sheets.

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Figure 3. Contrast between areas north (white) and south (grey) of the 46oN latitude, a limit representing the areas where diversity and distributions patterns have shown to be associated with either dispersal limitation (northern regions) or ecological tolerance (southern regions). Contras between regions show significant differences for functional richness (T(1476)=-20.76, p < 0.001) and dispersion (T(1346)=-17.95, p < 0.001) with lower values in the northern regions.

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Figure 4. Scatter plots of realized/potential ratios (R/P ratios, y-axis) of plant functional richness (top row) and dispersion (bottom row) vs. late-Quaternary climate change in the form of log-transformed annual mean temperature velocity (left column), log-transformed total annual precipitation velocity (center column), and accessibility to postglacial re-colonization (right column). Potential functional richness and dispersion estimated as in Fig, 1. Spatial autoregressive (SAR) model fits are presented for all Europe (black lines), and for areas north (blue points and lines) and south (orange points and lines) of the boundary for the major Southern Europe glacial refuge region (46°N). Model fits are presented in Table 1 and 2.

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Table 1. Comparison of spatial autoregressive (SAR) models explaining the realized/potential functional diversity ratios of plant functional diversity (functional richness and functional diversity), based on individual and all pair-wise combinations of three historical climate instability variables. Models order along increasing ΔAIC. Potential functional diversity was calculated using quantile regressions on current regional environment and species richness (see Methods). Predictor variables are annual mean temperature velocity (AMTVEL; in km/decade), Total annual precipitation velocity (TAPVEL; in km/decade), and accessibility to postglacial re-colonization (ACC; in km-1).

Functional RichnessΔAIC wAIC R2

NK

AMTVEL-ACC 0.000 0.497 0.521AMTVEL-TAPVEL-ACC 0.007 0.496 0.521AMTVEL 9.847 0.004 0.518AMTVEL-TAPVEL 10.084 0.003 0.519ACC 68.007 0.000 0.504TAPVEL-ACC 69.439 0.000 0.505Intercept only 78.326 0.000 0.502TAPVEL 79.809 0.000 0.502

Functional DispersionΔAIC wAIC R2

NK

AMTVEL-ACC 0.000 0.503 0.413AMTVEL-TAPVEL-ACC 0.024 0.497 0.413AMTVEL 21.132 0.000 0.406AMTVEL-TAPVEL 21.141 0.000 0.407TAPVEL-ACC 21.616 0.000 0.406ACC 27.645 0.000 0.404TAPVEL 48.248 0.000 0.398Intercept only 54.119 0.000 0.396The table shows model rescaled Akaike’s Information Criterion (∆AIC), Akaike weights (wAIC, probability that the best model includes a given variable or variable combinations), and model fit based on Nagelkerke’s pseudo-R2 (R2

NK)

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Table 2. Analysis of covariance comparing R/P ratios in functional richness and dispersion between areas north and south of the boundary for the major Southern Europe glacial refuge region (latitudes<46°N). R/P ratios estimated as the proportion of the potential functional diversity (calculated using a environmentally constrained quantile regressions on species richness, see methods) currently observed on each AFE grid cell. Regressions coefficients, standard errors (in parenthesis) and p-values presented.

Functional RichnessTemperature

VelocityPrecipitation

velocityAccessibility

Coefficient P Coefficient P Coefficient P

Intercept 0.839(0.007) ***

0.829(0.012) ***

0.766(0.02) ***

Historical climate -0.0112(0.00250) ***

-0.0023(0.0026) NS

0.0059(0.0016) ***

North-South 0.0273(0.0091) ***

0.0369(0.018) *

0.152(0.0494) ***

North-South and Historical climate

-0.0136(0.0037) ***

0.0012(0.0042) NS

-0.0077(0.0028) ***

R2NK 0.524 0.504 0.504

AIC -6045 -5959 -6081k 6 6 6

LL 3028 2985 3046Moran’s I -0.004 NS -0.001 NS -0.001 NS

Functional Dispersion

Intercept 0.922(0.003) ***

0.903(0.005) ***

0.886(0.007) ***

Historical climate -0.0066(0.0012) ***

-0.0053(0.0012) ***

0.003(0.0001) ***

North-South 0.0193(0.004) ***

0.0409(0.008) ***

0.0732(0.0188) ***

North-South and Historical climate

0.0021(0.0018) NS

0.0056(0.002) ***

-0.0037(0.0011) ***

R2NK 0.412 0.407 0.404

AIC -8845 -8827 -9005k 6 6 6

LL 4428 4420 4508Moran’s I -0.014 NS -0.012 NS -0.008 NS

Explained model variance based on Nagelkerke’s pseudo-R2 (R2NK), Akaike’s Information Criterion (AIC),

number of free parameters (k), model log-likelihood (LL), and Moran’s I and its significance level as defined by permutation tests (n=1000 permutations). Significance levels: ***P < 0.001; **P < 0.01; *P < 0.05. NS not significant

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Table 3. Best spatial autoregressive models (SAR) explaining European plants realized/potential differences (R/P ratios) in multivariate functional richness and dispersion, as a function of historical climatic conditions. Predictor variables are annual mean temperature velocity (AMTVEL; in km/decade), Total annual precipitation velocity (TAPVEL; in km/decade), and accessibility to postglacial re-colonization (ACC; in km-1). Potential functional diversity calculated using an environmentally constrained quantile regression on species richness (see methods). Best model selected from all possible models explaining functional richness and dispersion on the bases of all possible lineal combinations of historical climatic variables (see Table 1 for ΔAIC measures). Both regressions coefficients and standardized coefficients (in parentheses) are presented, and if not value is included the variable was not selected in the best model.

Functional Richness Functional DispersionCoefficient P Coefficient P

(Intercept) 0.798 *** 0.899 ***AMTVEL -0.017 -0.005 ***

(-0.255) *** (-0.175)TAPVEL

ACC 0.004 *** 0.002 ***(0.257) (0.315)

R2NK 0.521 0.413

AIC -6034 -8849k 5 5LL 3022 4430Moran’s I -0.004 NS -0.014 NSExplained model variance based on Nagelkerke’s pseudo-R2 (R2

NK), Akaike’s Information Criterion (AIC), number of free parameters (k), model log-likelihood (LL), and Moran’s I and its significance level as defined by permutation tests (n=1000 permutations). Significance levels: ***P < 0.001; **P < 0.01; *P < 0.05. NS not significant.

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