# The function-dominance correlation drives the direction and strength of biodiversity-ecosystem functioning relationships

Michael S. Crawford, Kathryn E. Barry, Adam T Clark, Caroline E Farrior, Jes Hines, Emma Ladouceur, Jeremy W Lichstein, Isabelle Maréchaux, Felix May, Akira S Mori, et al.

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## To cite this version:

Michael S. Crawford, Kathryn E. Barry, Adam T Clark, Caroline E Farrior, Jes Hines, et al. The function-dominance correlation drives the direction and strength of biodiversity-ecosystem functioning relationships. Ecology Letters, 2021, 24 (9), pp.1762-1775. 10.1111/ele.13776. hal-03269454

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# The function-dominance correlation drives the direction and strength of biodiversity-ecosystem functioning relationships

<figure><img src="image_3.png" /></figure>

Michael S. Crawford<fnref n="1" />,<fnref n="2" />,<fnref n="3" />* | Kathryn E. Barry<fnref n="1" />,<fnref n="4" />,<fnref n="5" />* | Adam T. Clark<fnref n="1" />,<fnref n="6" />,<fnref n="7" /> |

Caroline E. Farrior<fnref n="8" /> | Jes Hines<fnref n="1" />,<fnref n="9" /> | Emma Ladouceur<fnref n="1" />,<fnref n="6" />,<fnref n="10" /> | Jeremy W. Lichstein<fnref n="11" /> |

Isabelle Maréchaux<fnref n="12" />,<fnref n="13" /> | Felix May<fnref n="14" /> | Akira S. Mori<fnref n="15" /> | Björn Reineking<fnref n="16" /> |

Lindsay A. Turnbull<fnref n="17" /> | Christian Wirth<fnref n="1" />,<fnref n="4" />,<fnref n="16" />,<fnref n="18" /> | Nadja Rüger<fnref n="1" />,<fnref n="2" />,<fnref n="19" /> |

**Correspondence**

Michael S. Crawford, Transformation Pathways, Potsdam Institute for Climate Impact Research (PIK), Telegrafenberg, Potsdam 14412, Germany.

Email: mscrawfor@gmail.com

**Funding information**

Deutsche Forschungsgemeinschaft, Grant/ Award Number: FZT 118, RU 1536/3-1 and 202548816; German Centre for Integrative Biodiversity Research (iDiv), Grant/Award Number: 34600967, 34600900, 34600966 and 34600970; Agence National de la Recherche, Grant/Award Number: ANR- 10-LABX-0041 and ANR-10-LABX-25-01

Editor: Xavier Morin

**Abstract**

Community composition is a primary determinant of how biodiversity change influences ecosystem functioning and, therefore, the relationship between biodiversity and ecosystem functioning (BEF). We examine the consequences of community composition across six structurally realistic plant community models. We find that a positive correlation between species' functioning in monoculture versus their dominance in mixture with regard to a specific function (the "function-dominance correlation") generates a positive relationship between realised diversity and ecosystem functioning across species richness treatments. However, because realised diversity declines when few species dominate, a positive function-dominance correlation generates a negative relationship between realised diversity and ecosystem

<footnote n="1">¹German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Leipzig, Germany</footnote>

<footnote n="2">²Department of Economics, Institute of Empirical Economic Research, University of Leipzig, Leipzig, Germany</footnote>

<footnote n="3">³Department of Land-Use Management, Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany</footnote>

<footnote n="4">⁴Institute of Biology, University of Leipzig, Leipzig, Germany</footnote>

<footnote n="5">⁵Ecology and Biodiversity Group, Department of Biology, Utrecht University, Utrecht, Netherlands</footnote>

<footnote n="6">⁶Department of Physiological Diversity, Helmholtz Centre for Environmental Research (UFZ), Leipzig, Germany</footnote>

<footnote n="7">⁷Institute of Biology, University of Graz, Graz, Austria</footnote>

<footnote n="8">⁸Department of Integrative Biology, University of Texas at Austin, Austin, Texas, USA</footnote>

<footnote n="9">⁹University of Leipzig, Leipzig, Germany</footnote>

<footnote n="10">¹⁰Biodiversity Synthesis, Institute of Computer Science, Martin Luther University Halle-Wittenberg, Halle, Germany</footnote>

<footnote n="11">¹¹Department of Biology, University of Florida, Gainesville, Florida, USA</footnote>

<footnote n="12">¹²AMAP, University of Montpellier, CIRAD, CNRS, INRAE, Montpellier, IRD, France</footnote>

<footnote n="13">¹³Laboratoire Évolution et Diversité Biologique, UMR 5174 (CNRS/IRD/UPS), Toulouse Cedex, France</footnote>

<footnote n="14">¹⁴Institute of Biology, Freie Universität Berlin, Gartenhaus, Berlin, Germany</footnote>

<footnote n="15">¹⁵Graduate School of Environment and Information Sciences, Yokohama National University, Yokohama, Japan</footnote>

<footnote n="16">¹⁶University of Grenoble Alpes, INRAE, LESSEM, Grenoble, France</footnote>

<footnote n="17">¹⁷Department of Plant Sciences, University of Oxford, Oxford, UK</footnote>

<footnote n="18">¹⁸Max-Planck-Institute for Biogeochemistry, Jena, Germany</footnote>

<footnote n="19">¹⁹Smithsonian Tropical Research Institute, Balboa, Ancón, Panama</footnote>

<footnote>*Joint first authors.</footnote>

<footnote>This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>

<footnote>© 2021 The Authors. *Ecology Letters* published by John Wiley & Sons Ltd.</footnote>
functioning within species richness treatments. Removing seed inflow strength-
ens the link between the function-dominance correlation and BEF relationships
across species richness treatments but weakens it within them. These results sug-
gest that changes in species' identities in a local species pool may more strongly
affect ecosystem functioning than changes in species richness.

KEYWORDS

coexistence, community assembly, function–dominance correlation, model intercomparison, plant diversity, productivity, seed dispersal

INTRODUCTION

Anthropogenic environmental changes have led to dras-
tic global biodiversity loss (IPBES, 2019; MEA, 2005;
Newbold et al., 2015; Tittensor et al., 2014). The rate of
loss will likely accelerate in the coming decades (IPBES,
2019; Pereira et al., 2010; Pimm et al., 2014). Biodiversity
experiments demonstrate that the loss of randomly se-
lected species from controlled communities generally
decreases local ecosystem functioning (Tilman et al.,
2014). However, in natural systems, the effects of bio-
diversity change on ecosystem functioning and services
are context dependent. Even within a single ecosystem
type such as grasslands, there is significant divergence
in the direction (negative vs. positive; Meyer et al., 2018),
strength (Guerrero-Ramírez et al., 2017) and drivers
(Barry et al., 2019b) of biodiversity-ecosystem function-
ing (BEF) relationships. This variation is even greater
across ecosystem types (Duffy et al., 2017; van der Plas,
2019). Understanding this variability is therefore of crit-
ical importance to anticipating the impacts of biodiver-
sity change.

One likely cause of this variability is differences in
local-scale processes such as species interactions, which
influence community assembly and composition (Barry
et al., 2019a; Holt, 2013; Wright, 2002). Depending on
the nature and strength of local and regional community
assembly mechanisms, variation in these processes may
result in differences among BEF relationships across
ecosystems and scales (Leibold et al., 2017). In particu-
lar, when comparing communities that differ greatly in
species richness, those with high richness are more likely
to include species that produce high levels of ecosystem
functioning (e.g., biomass) through “sampling effects”
(Hooper et al., 2005; Huston, 1997), leading to positive
BEF relationships. Conversely, when comparing com-
munities with similar species richness, if a few dominant
species contribute disproportionately to functioning and
are able to supress their competitors, then communities
that include these dominant species will have low real-
ised diversity but high functioning, leading to negative
BEF relationships (Leibold et al., 2017, Figure 1a). We
refer to this characteristic pattern of contrasting BEF re-
lationships across communities as a “counter-gradient”
(Figure 1). This type of counter-gradient is often

associated with Simpson's paradox, which arises when
observed relationships vary across different subsets of
data (Simpson, 1951).

In addition to local processes related to species iden-
tity and dominance, regional processes such as seed
dispersal can affect community composition by main-
taining populations that would otherwise go extinct
(Leibold & Chase, 2018; Thompson & Gonzalez, 2016).
These regional-scale processes influence ecosystem func-
tioning independently of local-scale processes (Gonzalez
et al., 2020; Leibold & Chase, 2018; Thompson et al.,
2020). For example, if dispersal maintains populations
of species that are poorly locally adapted, then disper-
sal can weaken or lead to negative, BEF relationships
(Thompson et al., 2020). Alternatively, if species that
contribute strongly to ecosystem functioning are main-
tained by dispersal, then dispersal can lead to strong pos-
itive BEF relationships (Gonzalez et al., 2009; Shanafelt
et al., 2015; Thompson & Gonzalez, 2016; Thompson
et al., 2020).

Here, we consider six independently derived and val-
idated plant community models to explore the drivers
of variation in BEF relationships across local and re-
gional scales. We subjected these six models to a unified
set of simulation experiments: first, testing local effects
by varying initial diversity and composition and, sec-
ond, testing regional effects by simulating communi-
ties that included, or were isolated from, seed dispersal.
Although plant community models have been used in the
past to explore BEF relationships (Bohn & Huth, 2017;
Holzwarth et al., 2015; Maréchaux & Chave, 2017; Morin
et al., 2011), here, we consider a much wider variety of
models, systems (grasslands, forests and drylands) and
community assembly processes. This diversity of model-
ling approaches leads to a much wider range of resulting
BEF relationships, thereby better mirroring the context
dependence observed in natural systems.

We use this modelling experiment to test two hypoth-
eses. First, we hypothesise that context dependence in
BEF relationships observed across simulations can be
explained primarily by correlations between species'
ability to dominate in mixture ('dominance') versus their
baseline capacity to contribute to ecosystem functioning
in monoculture ('functioning'). We refer to this correla-
tion as the 'function-dominance correlation'. When the
<figure><img src="image_4.png" /><figcaption>**FIGURE 1** We hypothesise that the strength and direction of the relationship between the diversity of a community and its total biomass will depend on the function–dominance correlation of its species (c). Communities with a positive function–dominance correlation (a) will tend to be dominated by species that also generate significant functioning. When included in a mixture, these species will decrease biodiversity as they increase total biomass. Across species richness treatments, the likelihood of these species being incorporated into a community will increase, leading to a positive relationship between diversity and biomass. However, within species richness treatments, communities incorporating these dominant species will tend to have lower biodiversity—though more biomass—than communities in which they are absent. A negative function–dominance correlation (b) will lead to alternative diversity–biomass relationships, as they will tend to be dominated by species that provide little functioning. Across species richness treatments, this will lead to a negative relationship between diversity and biomass, as competitive—though low biomass—species are more likely to be incorporated into diverse mixtures. However, within species richness treatments, there will be a positive relationship between biomass and functioning as communities that lack these competitive species will subsequently contain higher diversity and biomass</figcaption></figure>

function–dominance correlation is positive, we expect to observe positive BEF relationships across communities that differ in species richness (due to positive sampling effects) versus negative BEF relationships across communities with similar richness (due to disproportionately strong contributions by dominant species; Figure 1a). Similarly, we expect to observe the opposite relationships when the function–dominance correlation is negative (due to negative sampling effects and disproportionately weak contributions from dominant species; Figure 1b). We refer to these two different scales of expected BEF relationships as across species richness treatments (black lines in Figure 1a and b) or within species richness treatments (coloured lines in Figure 1a and b).

Second, we hypothesise that reducing seed dispersal will increase the importance of the function–dominance correlation for BEF relationships, because seed dispersal decreases the relative abundance of the dominant species in our simulations. For example, if the function–dominance correlation is positive, lower

relative abundance of the dominant species resulting from seed dispersal will lead to a lower community functioning (Leibold et al., 2017). Thus, when the community is isolated from seed dispersal, relative abundance of the dominant species will increase, leading to increased ecosystem functioning while reducing realised diversity.

Consistent with our hypotheses, our results show that when the dominant species also contribute disproportionately to ecosystem functioning (i.e., positive function–dominance correlation), BEF relationships tend to be positive across communities with different species richness treatments and negative across communities within the same species richness treatment (i.e., a ‘positive counter-gradient’). Alternatively, BEF relationships tend to be weak or lead to a ‘negative counter-gradient’, when the function–dominance correlation is weak or negative, respectively. Further, the importance of the function–dominance correlation for BEF relationships across communities is higher in the absence of external seed input. Thus, the function–dominance correlation provides an
ecologically grounded and empirically tractable metric that appears to explain much of the context dependence observed across BEF relationships. This work therefore has major implications for how to apply BEF research to the problem of biodiversity change. In particular, if BEF relationships are determined by the function-dominance correlation, then changes in the identity of species in the local community, as is occurring in many communities worldwide (Blowes et al., 2019; Dornelas et al., 2014), may have larger impacts on ecosystem functioning than declines in species richness per se.

# MATERIALS AND METHODS

## Model descriptions

We included six published plant community models that cover a variety of ecosystems and model types, ranging from forests to succulent plants and from systems of differential equations to spatially explicit, individual-based models (Table 1). These capture key elements of their target systems and have been extensively analysed and documented in published literature (Clark et al., 2018; Maréchaux & Chave, 2017; May et al., 2009; Reineking et al., 2006; Rüger et al., 2020; Turnbull et al., 2013; Weiss et al., 2014). They support realistic levels of biodiversity, and the mechanisms driving coexistence are well understood.

Grass 1 (Clark et al., 2018) explores a trade-off between species' abilities to take up and retain resources versus to pre-empt other species from accessing resources. The model is designed to portray dynamics in a Minnesota tallgrass prairie and was parameterised from observations of three plant traits measured in experimental monocultures. Model dynamics are deterministic and allow for an arbitrarily large number of species to stably coexist, provided that their traits all fall within the correct regions of the trade-off space.

Grass 2 (Turnbull et al., 2013) is also designed to mimic dynamics in grassland plant communities and focuses on a classic trade-off between species relative growth rate and carrying capacity. The model explicitly considers effects of seasonal cycles. Fast-growing species can persist because they can rapidly exploit resources early in the growing season, before slower growing species become dominant. Again, this model is deterministic and allows arbitrarily large numbers of species to stably coexist.

Grass 3 (May et al., 2009; Weiss et al., 2014) explores trade-offs between asymmetric competition for light and susceptibility to grazing within central European managed grasslands. Competition is individual-based and spatially explicit. Given adequate belowground resources, larger, faster growing species dominate competition for light but are more vulnerable to grazing than their shorter, more stress-tolerant competitors. The resulting trade-off equalises fitness among competing

<table><caption>TABLE 1 Model descriptions</caption><thead><tr><th>Model ID</th><th>Study area</th><th>Model type</th><th>Spatial extent</th><th>Parameterization</th><th>Coexistence mechanisms</th><th>Literature</th></tr></thead><tbody><tr><td>Grass 1</td><td>Cedar Creek, Minnesota, USA</td><td>Ordinary differential equations</td><td>1 m<sup>2</sup></td><td>Field data</td><td>Trade-off between competitive ability for soil nitrate and nitrogen-use efficiency</td><td>Clark et al. (2018)</td></tr><tr><td>Grass 2</td><td>Temperate grasslands</td><td>Ordinary differential equations</td><td>1 m<sup>2</sup></td><td>Theoretical</td><td>Trade-off between rooting depth and resource uptake rate</td><td>Turnbull et al. (2013)</td></tr><tr><td>Grass 3</td><td>Central European grasslands</td><td>Individual-based, spatially explicit model</td><td>9 m<sup>2</sup></td><td>Field data (see Weiss et al., 2014)</td><td>Trait-driven niche and fitness differences defining competition above- and belowground; CNDD</td><td>May et al., (2009); Weiss et al. (2014)</td></tr><tr><td>Forest 1</td><td>Barro Colorado Island, Panama</td><td>Spatially implicit demographic cohort model</td><td>1 ha</td><td>Demographic trade-offs derived from forest inventory data</td><td>Demographic trade-offs; demography-driven niche differences within a vertical canopy gradient; external seed input</td><td>Rüger et al. (2020)</td></tr><tr><td>Forest 2</td><td>French Guiana</td><td>Individual-based, spatially explicit model</td><td>1 ha</td><td>Field data (functional traits)</td><td>Trait-driven among-species niche differences within a heterogeneous environment, both vertically (canopy gradient) and horizontally (gap dynamics); external seed input</td><td>Maréchaux and Chave (2017)</td></tr><tr><td>Dryland</td><td>Richtersveld, South Africa</td><td>Individual-based, spatially explicit model</td><td>25 m<sup>2</sup></td><td>Literature</td><td>Trade-offs between competition and storage ability for water, mediated through stochastic variation in water supply rate</td><td>Reineking et al. (2006)</td></tr></tbody></table>
species, and stable coexistence is realised through con-
specific negative density dependence that reduces the
fitness of individuals when surrounded by conspecific
neighbours.

Forest 1 (Rüger et al., 2020) is designed to simu-
late dynamics of a diverse tropical rainforest at Barro
Colorado Island, Panama, based on species demo-
graphic rates (growth, survival and recruitment). It ac-
counts for height-structured competition for light by
distinguishing four canopy layers. Canopy gaps are filled
by the tallest trees from lower canopy layers, regardless
of their horizontal position (perfect plasticity approxi-
mation; Purves et al., 2008). Tree species fall along two
demographic trade-offs: a growth-survival trade-off and
a stature-recruitment trade-off (Rüger et al., 2018). Here,
as in Rüger et al., (2020), the model is deterministic, and
stable coexistence within local communities relies on ex-
ternal seed inflow.

Forest 2 (Maréchaux & Chave, 2017) is an individual-
based and spatially explicit model of tropical forest
dynamics. It uses species-specific functional traits to pa-
rameterise tree physiological function and demographic
processes, according to relationships and trade-offs from
the literature. Individual trees compete for light within a
three-dimensional grid (1 m³ voxels), in which tree death
and gap formation create horizontal and vertical hetero-
geneity in light availability. Seed dispersal is spatially ex-
plicit and includes both local sources and external seed
inflow. Here, we used a model version without explicit
conspecific negative density dependence, so that stable
coexistence relies on external seed inflow.

Dryland (Reineking et al., 2006) is an individual-
based, stochastic model based on allocation trade-offs
and environmental heterogeneity. The model is param-
eterised for succulent communities in the Richtersveld,
South Africa (see Appendix S1: Model preparation).
Plants compete for water, and biomass allocation to
leaves, roots, water storage and seeds affects plant
growth, survival and reproduction. At high water supply
rates, species not investing in water storage outcompete
species investing in storage, which in turn persist lon-
ger under drought. Coexistence is partially maintained
by spatiotemporal heterogeneity in water supply. In the
present study, higher levels of local diversity were main-
tained via seed inflow.

Experimental design

For each model, a set of 64 species was selected by sam-
pling a functionally diverse assemblage from its species
pool. Depending on the model, this was achieved through
either sampling species from the underlying trade-off
surface (Grass 1, Grass 2 and Dryland) or by running
k-means clustering (k = 64) on the species pool (Grass 3,
Forest 1 and Forest 2). For each model, we implemented
an experimental design typical of BEF experiments

(sensu Roscher et al., 2004; Tilman et al., 1996), including
seven planted species richness treatments (1, 2, 4, 8, 16,
32 or 64 species) with 64 replicates each (except for the
64-species treatment with only one replicate). The one-
species treatment consisted of monocultures of each of
the 64 species, and the 2-32-species treatments were im-
plemented by randomly sampling (without replacement)
from the 64-species pool.

For each model, the 385 (6*64 + 1) experimental com-
munities were initialised with equal abundances of seeds
or seedlings for each planted species (depending on each
model's default settings) and run until stable abundance
distributions were achieved (hereafter 'equilibrium'; see
Appendix S1: Experimental design). Thus, due to their
slower dynamics, forest models were run significantly
longer than grassland and succulent models.

During this initial stage, seed inflow from the initial
species pool took place (with seed inflow). Seed inflow for
each species was constant and corresponded to average
internal seed production across all equilibrium monocul-
tures, divided by the number of species. This implemen-
tation generates equal numbers of saplings (forest models)
or equal seed biomass (grassland/dryland models) per
species per year and therefore buoys abundances of
poorly performing species. To explore the effect of isolat-
ing communities from their respective metacommunities,
in a second stage of the same duration, seed inflow was
stopped (without seed inflow). We measured diversity and
ecosystem functioning on the last time steps of each stage.

BEF relationships within models

For the results presented here, we use Shannon diversity to quantify community diversity. We do so because Shannon diversity incorporates information about both richness and evenness, and in several models, species abundances decline to very low levels rather than to zero (i.e., ‘asymptotic’ extinction). Thus, when species became functionally extinct, realised species richness remained unchanged. Note, however, that when analysed in terms of richness, our results are qualitatively similar (see Appendix S2). We also present results for two related ecosystem properties: (1) aboveground biomass (main results) and (2) net primary productivity (Appendix S3; results are identical to biomass for grassland models but not for dryland and forest models). To enable comparison between models with very different amounts of total biomass, we scaled the community biomass across all simulated communities to fall between 0 and 100.

Our analysis consisted of two steps. In the first step,
for each plant community model and seed inflow stage,
we fit a Bayesian linear regression between realised
Shannon diversity and biomass across planted spe-
cies richness levels to estimate the *across species rich-
ness treatment* BEF slope (black line in Figure 1; see
Appendix S1: Statistical methods). In the second step, we
fit independent Bayesian linear regressions within each
planted species richness level to quantify *within species
richness treatment* BEF slopes (coloured lines in Figure 1)
for each plant community model and seed inflow stage
(see Appendix S1: Statistical methods).

Regressions were fit using the Hamiltonian Monte Carlo (HMC) sampler Stan (Carpenter et al., 2017) through the ‘brms’ package (Bürkner, 2017) in R (R Core Team, 2019) using four chains, 2000 iterations (1000 as warm up), and Gaussian distributions for all models. We used weakly regularising default priors, and inspection of the HMC chains for each model showed excellent convergence, with R-hat values of 1.0 for all estimates. We used posterior predictive checks to visually inspect how well the statistical models reproduced the data (see Appendix S4).

Comparison across models

We quantified the function-dominance correlation for
each seed inflow stage separately. To do this, we boot-
strapped species' mixture biomasses (n = 2500) using the
32-species mixtures. Each bootstrap contained 2048 spe-
cies (32 species per mixture × 64 replicates) selected with
replacement. We then calculated the Pearson's correlation
between species' biomasses in monoculture ('function')
and their respective mixture biomasses ('dominance').
Note that like the 'selection effect' of Loreau and Hector
(2001), our correlation coefficient effectively summarises
overall effects of dominance on yield in mixture—that is,
it tests whether highly functioning species in monoculture
also tend to be highly functioning in mixture. We use this
metric, rather than the classic Loreau and Hector metric,
both for simplicity, and to avoid issues related to low or
zero monoculture biomass that can complicate the classic
Loreau and Hector metric (Clark et al., 2019).

We focused on the 32-species communities because they
encompass the highest initial diversity of any treatment
level beyond the single replicated 64-species treatment. We
then drew 2500 samples from the posterior distributions
of the within-treatment and across-treatment BEF slopes
of each model and regressed them against the function-
dominance correlations. Since both metrics are estimated
and thus incorporate error, we used Standard Major Axis
regression (lmodel2; Legendre, 2018).

RESULTS

Communities with seed inflow

In communities with seed inflow, community biomass
was positively correlated with realised Shannon diver-
sity across species richness treatments in five of the
six models (all except Forest 2). The most pronounced

positive relationships emerged from Grass 1, Grass
2 and Forest 1 (Figure 2). Within species richness
treatments, the slope of the relationship between re-
alised diversity and biomass was negative in four out
of the six models. This pattern was most pronounced
in Grass 1 and Forest 2. In Grass 2 and Forest 1, the
slope of the relationship between realised diversity
and biomass was negative within communities with
low species richness and became positive with increas-
ing species richness. In Grass 3 and Dryland, the slope
of the relationship between realised diversity and bi-
omass tended to be positive within species richness
treatments.

Consistent with our hypothesis, the effect of real-
ised diversity on community biomass was more positive
across species richness treatments (Figure 3) and more
negative within species richness treatments (Figure 4) in
models where the function-dominance correlation was
positive (cf. Figure 1). This relationship also emerged
when using realised species richness as a measure of
diversity rather than Shannon diversity (Appendix S2)
and productivity as a measure of ecosystem functioning
(Appendix S3).

Communities without seed inflow

After local communities were isolated from their meta-
community (by eliminating seed inflow), there was no
consistent pattern in how the slope of the relation-
ship between realised diversity and biomass changed
across species richness treatments (Figure 2). However,
within communities of the same species richness treat-
ment, the slope of the relationship between realised di-
versity and biomass often became more positive than
in simulations with seed inflow, for example, switching
from negative to positive (Grass 2 and Forest 2), be-
coming less negative (Grass 1) or becoming more posi-
tive (Dryland).

Eliminating seed inflow did not substantially alter
the function–dominance correlation, except for Forest
2, where this correlation changed from positive to neg-
ative (see Appendix S4). Consequently, the overall rela-
tionship between the function–dominance correlation
and the slope of the relationship between realised di-
versity and biomass across species richness treatments
became even more strongly positive (Figure 3). In con-
trast, within species richness treatments, the relation-
ship between the function–dominance correlation and
the slope of the relationship between realised diver-
sity and biomass tended to become weaker (Figure 4).
Similar results were obtained using productivity (rather
than biomass) as the measure of ecosystem functioning
(Appendix S3) or using realised species richness (rather
than realised Shannon diversity) as the measure of
community diversity (Appendix S2).
<figure><img src="image_5.png" /><figcaption>**FIGURE 2** The relationship between realised Shannon diversity and total community biomass for six plant community models. Points represent individual plant communities. Coloured lines refer to the relationships within species richness treatments, while the black lines refer to the relationship across species richness treatments. Ribbons represent the 95% credibility intervals of the model fits. Significant relationships (95% CI does not include 0) are shown with solid lines. Insignificant relationships are shown with dashed lines</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>FIGURE 3 The relationship between the function–dominance correlation and the slope of the BEF relationship across species richness treatments for six plant community models. Standard major axis regressions were run on each bootstrapped dataset (n = 2500), which each contained one function–dominance correlation paired with one posterior sample of the BEF slope per model. Ninety-five per cent confidence intervals for the mean where derived through nonparametric bootstrapping of the slope parameter (n = 1000)</figcaption></figure>

DISCUSSION

Biodiversity experiments have convincingly demonstrated the importance of biodiversity for ecosystem functioning. However, applying these findings to naturally assembled systems has proven challenging (van der Plas, 2019). We show that the sign and magnitude of BEF relationships both across species richness treatments (as traditionally reported for BEF experiments) and within species richness treatments can be predicted by the correlation between species' contribution to functioning and species' dominance in mixture (the 'function–dominance correlation'). When dominant species have a high capacity to provide ecosystem functioning, realised diversity and functioning are positively related across species richness treatments but negatively related within species richness treatments. Further, removing seed inflow strengthens the explanatory power of the function–dominance correlation across species richness treatments but weakens it within them. Importantly, our model intercomparison shows that these results are consistent for both biomass and net primary productivity, and across six different models that have been shown to accurately represent dynamics of grasslands, tropical forests and a dryland succulent community.

The function–dominance correlation mediates
BEF relationships

Relationships between realised Shannon diversity and
biomass were positive across species richness treatments
for five out of six models. This result is consistent with
many biodiversity experiments (reviewed by Tilman
et al., 2014). However, relationships between realised di-
versity and biomass were often negative within species
richness treatments, especially in models that had the
most positive relationships across species richness treat-
ments (i.e., Grass 1, Grass 2 and Forest 1). This negative

BEF relationship within species richness treatments is
also consistent with results from the Jena Experiment
(Leibold et al., 2017; Rychtecká et al., 2014) but has not,
to our knowledge, been tested elsewhere.

Our results show that this ‘counter-gradient’ can be ex-
plained by the function–dominance correlation. Where
this correlation is strong and positive (Grass 1, Grass 2
and Forest 1), BEF relationships across species richness
treatments were most positive, and BEF relationships
within species richness treatments were most negative. A
likely explanation is that communities with more species
are more likely to include dominant species that produce
high levels of ecosystem functioning through a ‘sampling
effect’ (Hooper et al., 2005; Huston, 1997). However,
within species richness treatments, these same dominant
and high-functioning species tend to displace poorly
performing species, potentially driving the negative re-
lationship between functioning and realised diversity.
Conversely, where the function–dominance correlation
is weak (Grass 3, Forest 2 and Dryland), the relationship
between realised diversity and biomass is weak or not
significant, both across species richness treatments and
within them.

This clear link between the function–dominance
correlation and BEF relationships emerged despite the
array of coexistence mechanisms and systems in our
models. Interestingly, the strength of the function–
dominance correlation was not related to mechanism
type, that is, resource partitioning (Grass 1, Grass 2
and Dryland), seed inflow (Forest 1 and Forest 2) or
conspecific negative density dependence (Grass 3).
However, strong local coexistence mechanisms like
resource partitioning (Dryland) and conspecific neg-
ative density dependence (Grass 3) increased the slope
of positive relationships between realised diversity and
ecosystem functioning within species richness treat-
ments. Grass 3, for example, is spatially explicit and
incorporates conspecific negative density dependence.
<figure><img src="image_7.png" /><figcaption>**FIGURE 4** The relationship between the function–dominance correlation and the slope of the BEF relationships within species richness treatments for six plant community models. Standard major axis regressions were run on each bootstrapped dataset (n = 2500), which each contained one function–dominance correlation paired with one posterior sample of the BEF slope per model and species richness treatment. Intervals indicate 95% confidence of the mean, derived through nonparametric bootstrapping of the slope parameter (n = 1000)</figcaption></figure>
Individuals surrounded by conspecifics perform more
poorly than individuals surrounded by heterospecif-
ics (May et al., 2009). Because individuals are more
likely to be surrounded by heterospecifics in commu-
nities with higher realised diversity, these more diverse
communities are also higher functioning. In higher
species richness treatments, effects of negative density
dependence are weak regardless of realised diversity,
and these effects disappear. Similarly, in Forest 1, BEF
relationships within species richness treatments are
negative at low species richness but become positive
at high species richness. In this model, more diverse
communities are likely to include several species of
similar competitive ability that are able to coexist. For
example, communities of ‘tall’ versus ‘slow’ species co-
exist because tall species maximise biomass in upper
canopy layers while slow species maximise biomass
in lower layers. Thus, at higher species richness lev-
els, species with these strategies partition the vertical
canopy gradient, leading to positive BEF relationships
within species richness treatments. In contrast, only
one of these strategies is likely to be represented in low
species richness treatments, in which case the highest
biomass occurs when one of these strategies dominates
resulting in low realised diversity.

Unlike the function-dominance correlation, the spe-
cific slope and sign of the relationship between realised
diversity and biomass varied with model structure both
between species richness treatments and within species
richness treatments. For example, the two tropical for-
est models show differing results. However, across model
types, study systems and community assembly mecha-
nisms, we were able to identify a common pattern: the
link between the function-dominance correlation and
the strength and direction of BEF relationships. Thus,
we expect that the function-dominance correlation
is relevant for understanding variation in the sign and
magnitude of BEF relationships across a wide variety of
systems.

The effect of removing seed inflow

One benefit of our modelling approach is our ability to
eliminate external dispersal (inflow). In BEF experi-
ments, although plots are weeded, it is usually not possi-
ble to distinguish whether new recruits of planted species
result from seeding treatments, dispersal from within the
plot or external seed dispersal. Thus, it is impossible to
fully isolate effects of local interactions from external
metacommunity processes. Although external seed in-
flow is thought to influence BEF relationships (Hooper
et al., 2005; Roscher et al., 2004), we found that com-
pletely removing seed inflow had little effect on BEF re-
lationships observed across species richness treatments,
which are the most commonly reported BEF relation-
ships in the literature.

However, within species richness treatments, the re-
lationship between realised diversity and biomass often
became more positive when seed inflow stopped (Grass
1, Grass 2, Forest 1, Forest 2 and Dryland). For example,
in Grass 2, the slope of the relationship between realised
diversity and biomass changed from negative (with seed
inflow) to positive (without seed inflow) within species
richness treatments. In this model, species are dominant
in mixture by having either a high carrying capacity or a
high growth rate (Turnbull et al., 2013). With seed inflow,
low-biomass species with high growth rates temporarily
prevent their slower competitors from accessing soil re-
sources. Consequently, higher functioning, slower grow-
ing species are unable to reach maximum size. Without
seed inflow, these high growth rate-low functioning
species decrease in relative abundance, and the remain-
ing species are better able to utilise available resources.
These processes combined result in a positive relation-
ship between realised diversity and biomass within spe-
cies richness treatments.

Although eliminating seed inflow had noticeable
effects on BEF relationships both across and within
species richness treatments, function-dominance cor-
relations remained largely unchanged with one excep-
tion. For Forest 2, the slope of the function-dominance
correlation changed from positive (with seed inflow)
to negative (without seed inflow). In this model, small,
low-biomass species disproportionately benefited from
removing seed inflow because they reach their reproduc-
tive size more rapidly than tall, high-biomass species.
Without seed inflow, these low-biomass species could
colonise more empty sites and reach a higher biomass in
mixture than tall species. This leads to a change in the
function-dominance correlation from positive with seed
inflow to slightly negative without seed inflow, which in
turn caused a reversal of the counter-gradient (negative
across species richness treatments and positive within
species richness treatments without seed inflow). This re-
versal reinforced the relationship between the function-
dominance correlation and the slope of the relationship
between realised diversity and biomass across species
richness treatments. This result, along with the Dryland
model without seed inflow, is the only example that we
know of a negative counter-gradient: a negative BEF re-
lationship across species richness treatments but positive
BEF relationships within species richness treatments.

Seed inflow in our models is limited to the original
species pool and assumes constant, uniform seed input
across species. While this approach is not realistic, our
results are consistent with findings from a recent meta-
analysis of seed addition experiments (Ladouceur et al.,
2020) which found that when dispersal limitation was
alleviated by seed addition, species richness increased
(also reviewed by Myers & Harms, 2009), while biomass
was relatively unaffected. Similarly, in our models, com-
munities generally had higher realised diversity with
seed inflow than without it, with biomass remaining
largely unaffected relative to changes in Shannon diversity (Appendix S5). Realised species richness was bolstered by seed inflow more than realised Shannon diversity, leading to a larger relative increase in the across-treatment slope once seed inflow was removed (Appendix S2). This strong response emerged because seed inflow was uniformly distributed and thus kept realised richness artificially high and reduced the importance of local competitive dynamics in driving communities' biomass and productivity.

## Applying our results to other functions and applications

Here, we focus on relationships between realised diversity and aboveground biomass/productivity. Aboveground biomass and productivity are good indicators for many other functions and services, such as root biomass, carbon storage/sequestration, harvestable volume for forests and ecosystem stability (Allan et al., 2013; Ratcliffe et al., 2017). We therefore expect that our results will hold for this set of functions. However, other functions such as aboveground and belowground decomposition, nutrient cycling, microbial biomass or resistance to climate extremes are not easily predicted by biomass or productivity. Although we would not expect the biomass-based function—dominance correlation to be informative for these functions, it may be that function—dominance correlations that are based on these other functions or related functions could still prove to be useful predictors. For example, in microbial systems, if a species comprises a large amount of microbial biomass in monoculture and also plays a dominant role in contributing a large amount of microbial biomass in mixture (positive function—dominance correlation for microbial biomass), then we would predict that the relationship between realised diversity and microbial biomass across species richness treatments would be strongly positive.

Function—dominance correlations may be an effective ecosystem assessment tool that could be adopted by applied ecologists interested in maintaining or restoring ecosystem health. Assessing function—dominance relationships with respect to species losses and gains may allow better prioritisation of management actions for conservation and more function-driven restoration (Ladouceur et al., 2021). Species loss and gain is commonly observed in many conservation areas, particularly those that lie within successional habitats such as old fields (Bourgeois et al., 2016; Walker et al., 2007). The function—dominance correlation, rather than species identity per se, may serve as an indicator of whether assisted community assembly (e.g., through replanting or re-seeding) would be effective at restoring additional ecosystem functioning (Isbell et al., 2019; Ladouceur et al., 2020). The function—dominance correlation may

serve as a community profile tool that allows assessment of ecosystem health and the success of management, conservation or restoration (sensu Matthews & Whittaker, 2015).

## CONCLUSIONS

Global biodiversity loss and local and regional biodiversity change are among humanity's most pressing concerns. The current consensus is that this change is likely to have devastating consequences on ecosystem functioning. However, our results suggest that diversity change will have the strongest impact on ecosystem functioning when dominant species provide the most function. If this is also found to be true in experiments and naturally assembled systems, it has important implications for biodiversity-ecosystem functioning research. Loss of—or change in—biodiversity may have smaller or larger effects on ecosystem functioning than currently predicted, depending on the species affected. If species that are lost are dominant and high functioning, we expect that their loss will cause declines in ecosystem functioning unless they are replaced by species that perform similarly well. Alternatively, if the species lost dominated the community while contributing little to functioning (e.g., by taking up space and pre-empting the establishment of higher-biomass species), the effect of biodiversity loss on ecosystem functioning may be positive even, while other effects of losing these species could be negative. For example, recent research indicates that tall, high-biomass tree species may be more prone to extinction future climate conditions than smaller or low-biomass species (McDowell et al., 2020), with negative consequences for ecosystem functioning (Aubry-Kientz et al., 2019; Rüger et al., 2020). Our results suggest that within these systems, ecosystem functioning may be likely to decline even if it is not reliant on species richness per se. Our results also suggest that isolation from seed sources may amplify the functional role of dominant species. This is particularly relevant in the context of land-use change, and the habitat fragmentation that follows it, which is currently regarded as the largest cause of biodiversity change globally (Intergovernmental Science-Policy Platform on Biodiversity & Ecosystem Services, 2019). By comparing the outputs from six well-understood models that span different ecosystem types and community assembly mechanisms, we were able to identify an emergent community metric—the function—dominance correlation—that drives variation in BEF relationships. This synthesis provides key information about how changes in community composition rather than biodiversity loss per se are likely to influence ecosystem functioning under global change.
ACKNOWLEDGEMENTS

This paper is a product of the SimNet workshop funded
by the FlexPool initiative (Grant 34600966)—the internal
funding mechanism of the German Centre for Integrative
Biodiversity Research (iDiv) Halle-Jena-Leipzig, a re-
search centre of the German Research Foundation
(DFG–FZT 118, 202548816). We are grateful to Volker
Grimm and Jonathan Chase for their helpful comments
throughout the planning and execution of this project.
KEB was funded by the iDiv FlexPool initiative (Grant
34600900). JL acknowledges sabbatical fellowship sup-
port from sDiv, the Synthesis Centre of iDiv (DFG–
FZT 118, 202548816). IM acknowledges funding from
‘Investissement d’Avenir’ managed by Agence National de
la Recherche (CEBA, ref. ANR-10-LABX-25-01; TULIP,
ref. ANR-10-LABX-0041). BR acknowledges funding
from EU FP7 ERA-NET Sumforest (Grant ANR-16-
SUMF-0002). NR acknowledges support by a research
grant from Deutsche Forschungsgemeinschaft DFG (RU
1536/3-1). MC and NR were supported by the iDiv flex-
pool initiative (Grants 34600967 and 34600970). Open
Access funding enabled and organized by Projekt DEAL.

AUTHOR CONTRIBUTIONS

This study was devised as a product of a collaborative
workshop attended by all authors. MC, NR, ATC, IM,
FM, BR and LAT designed the initial model intercom-
parison project with feedback from other authors. MC,
ATC, IM, CF and BR performed modelling experiments
on individual models and provided data and feedback
to MC. MC conducted model intercomparison analyses
with input from NR, KEB and ATC. KEB, MC, NR and
ATC wrote and revised initial drafts of the manuscript.
All authors contributed to the revision of the manuscript.

PEER REVIEW

The peer review history for this article is available at
https://publons.com/publon/10.1111/ele.13776.

OPEN RESEARCH BADGES

<figure><img src="image_8.png" /></figure>

This article has earned Open Data and Open Materials badges. Data and materials are available at: https://doi.org/10.5281/zenodo.4658931

DATA AVAILABILITY STATEMENT

All data, analyses and code for statistical analyses will
be uploaded to a public repository upon acceptance of
this paper for publication. All models are previously
published and archived.

ORCID

Michael S. Crawford https://orcid.
org/0000-0003-1282-400X
Kathryn E. Barry https://orcid.
org/0000-0001-6893-6479

Emma Ladouceur https://orcid.
org/0000-0002-4943-4358
Lindsay A. Turnbull https://orcid.
org/0000-0002-8035-2879
Nadja Rüger https://orcid.org/0000-0003-2371-4172

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## SUPPORTING INFORMATION

Additional supporting information may be found online
in the Supporting Information section.

**How to cite this article:** Crawford, M.S., Barry, K.E., Clark, A.T., Farrior, C.E., Hines, J., Ladouceur, E. et al. The function-dominance correlation drives the direction and strength of biodiversity-ecosystem functioning relationships. *Ecology Letters*, 2021;00:1–14. https://doi.org/10.1111/ele.13776