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\begin{document}

\title{Animal movement and plant space-use drive plant diversity-productivity
relationships}



\author[1]{Georg Albert}%
\author[2]{Benoit Gauzens}%
\author[3]{Remo Ryser}%
\author[4]{Elisa Thébault}%
\author[5]{Shaopeng Wang}%
\author[6]{Ulrich Brose}%
\affil[1]{University of Göttingen}%
\affil[2]{iDiv}%
\affil[3]{German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig}%
\affil[4]{Bioemco - UMR 7618 (CNRS, UPMC, ENS, IRD, AgroParisTech)}%
\affil[5]{Peking University}%
\affil[6]{German Centre for Integrative Biodiversity Research Halle-Jena-Lepizig}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
Plant community productivity generally increases with biodiversity, but
the strength of this relationship exhibits strong empirical variation.
In meta-food-web simulations, we addressed if the spatial overlap in
plants' resource access and movement of animals can explain such
variability. We found that spatial overlap of plant resource access is a
prerequisite for positive diversity-productivity relationships, but
causes exploitative competition that can lead to competitive exclusion.
Movement of herbivores causes apparent competition among plants,
resulting in negative relationships. However, movement of larger top
predators integrates sub-food-webs composed of smaller species,
offsetting the negative effects of exploitative and apparent competition
and leading to strongly positive diversity-productivity relationships.
Overall, our results show that spatial overlap of plant resource access
and animal movement can greatly alter the strength and sign of such
relationships. In particular, the scaling of animal movement effects
opens new perspectives for linking landscape processes without effects
on biodiversity to productivity patterns.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

To quantify the impact of biodiversity loss on human well-being,
ecological research has measured biodiversity-ecosystem functioning
(BEF) relationships in experiments and in the field (Tilman \emph{et
al.} 2014; Duffy \emph{et al.} 2017). Even though the importance of
biodiversity for providing ecosystem functions is supported by
increasing empirical evidence, the quantitative relationships vary
remarkably across communities and sites (Cardinale \emph{et al.} 2007;
Duffy \emph{et al.} 2017; van der Plas 2019), calling for a systematic
understanding of the underlying mechanisms.

Many studies argue that complementarity in how plants use abiotic
resources is the main driving force behind positive plant
diversity-productivity relationships (Barry \emph{et al.} 2019).
However, the productivity of plants not only depends on how they access
and compete for resources, but is also strongly influenced by
interactions with herbivores and animals of higher trophic levels
(Schneider \emph{et al.} 2016; Barnes \emph{et al.} 2020; Albert\emph{et
al.} 2022). In addition, research on BEF relationships did not
systematically address the consequences of spatial structures such as
spatial heterogeneity in plant distribution and resource availability as
well as spatial integration by local and large-scale movement of
animals. While resource-based interactions between plants are spatial
processes constrained to a plant's immediate neighbourhood (Chesson
2000a), recent evidence draws attention to community assembly processes
that affect biodiversity maintenance in BEF experiments based on the
meta-community (Bannar-Martin \emph{et al.} 2018; Furey \emph{et
al.}2022), highlighting the importance of also considering processes at
larger spatial scales. This includes interactions of plants with animals
at higher trophic levels that integrate local effects over larger
spatial distances (McCann \emph{et al.} 2005; Ryser \emph{et al.} 2021).
Thus, this raises the question of how the interactions between animal-
and resource-based mechanisms and the different scales they are
associated with explain BEF patterns, such as the plant
diversity-productivity relationship, and their variance at the community
scale?

Traditionally, BEF research focuses on the relationship between plant
diversity and productivity emerging at the community level
(Cardinale\emph{et al.} 2007). Only recently, investigating the
implications of local interactions between plant individuals and their
immediate neighbours (hereafter: neighbourhood scale; Fig.1; Sapijanskas
\emph{et al.} 2013; Fichtner \emph{et al.} 2018) has started. At this
scale, individual plants access different parts of the total available
resources (e.g., the resource pools in the soil) depending on their
resource acquisition strategies (e.g., functional traits) and the
proportion of space they can access (e.g., spatial spread of their
roots). The latter adds a spatial component to plants' resource-use.
Reducing the spatial resource overlap between neighbouring plant
individuals (Fig. 1A) makes them complementary in their access to
resources as it reduces the strength of their competitive interactions
and thereby renders competitive exclusion less likely (Chesson 2000b).
While this spatial segregation of plants' resource-use facilitates
coexistence, it potentially imposes constraints on resource acquisition
and productivity. For example, if two plants have mostly complementary
resource requirements, they may benefit from having a spatial resource
overlap. These arguments suggest that an increased spatial resource
overlap could increase productivity at the community scale at the cost
of a higher likelihood of local competitive exclusion. As competitive
exclusion results in lower plant diversity, this can have negative
feedback on plant community productivity, calling for a more systematic
understanding of resource-mediated interactions between plants at the
neighbourhood scale and their importance for plant diversity-
productivity relationship.

While plants can interact through a local spatial resource overlap,
animal movement couples even distant plants, for instance when
herbivores move to switch resources. This movement of herbivores yields
apparent competition between plants (Fig. 1C, spatially-non nested),
which can impose strong negative effects on the productivity and
survival of the two resource plants (Holt 1977). At higher trophic
levels, populations of larger species such as top predators with large
home ranges (Tucker \emph{et al.} 2014; Hirt \emph{et al.} 2021) will
integrate energy fluxes across sub-food webs assembled from populations
of plants, herbivores and smaller consumers. This creates a spatially
nested food web structure with local food webs nested in the home range
of top predators (Fig. 1C). As a result, apparent competition emerges
among less mobile herbivores due to a shared, more mobile predator. This
spatial structure of natural food webs opposes the widespread classic
concepts that assume well-mixed and therefore spatially non-nested food
webs. Instead, the spatially nested food webs will display much higher
levels of complexity. Additionally, a spatial coupling of energy fluxes
from sub-food webs by top predators can have stabilizing effects
(McCann\emph{et al.} 2005). As food web stability also increases the
realized diversity of plants and eventually the productivity of plant
communities (Schneider \emph{et al.} 2016; Albert \emph{et al.} 2022),
spatially nested food web structures should also increase the
productivity of the plant community. Considering the strong impact
animals can have on plant community composition and functioning, the
consequences of representing food webs either as spatially nested or
non-nested could be substantial as they significantly differ in how they
couple individuals and populations.

Processes at different spatial scales, ranging from competition for
abiotic resources between neighbouring plants to apparent competition
and large-scale integration of food webs by top predators,
simultaneously affect functions within an ecosystem. Recent studies
emphasized the importance of integrating such processes that act at
different spatial scales in meta-communities (Furey \emph{et al.} 2022)
and meta-ecosystems (Gounand \emph{et al.} 2018), especially when
considering their implications for BEF relationships (Gonzalez \emph{et
al.} 2020; Furey \emph{et al.} 2022). Despite their importance for
community dynamics and functioning, the interactions among these
processes have yet to be explored. As a result, our mechanistic
understanding of how spatial interactions between plants via their
resources or through higher trophic levels affect community-level
functions is severely limited.

To address this issue, we introduce a spatially-explicit model of plant
individuals that can access local resource pools of their direct
neighbours. By integrating this plant-resource model with a
spatially-explicit food web model, we investigate how resource
competition and multi-trophic interactions interact across spatial
scales to shape diversity-productivity relationships in plant
communities. We hypothesize that, (1) positive diversity-productivity
relationships can only emerge when plants are able to interact through a
spatial resource overlap. Further, a spatially nested food web structure
will introduce processes at different spatial scales. We therefore
expect that (2) herbivore-induced apparent competition will have
negative effects on plant productivity, whereas (3) spatial integration
of sub-food webs by top predators should balance local dynamics and
increase apparent competition between herbivore populations, minimizing
competitive exclusion of plants and leading to an increase in their
diversity and productivity.

\section*{Methods}

{\label{methods}}

To investigate the effects of plant and animal space-use on plant
diversity-productivity relationships, we integrate both in a simulated
plant biodiversity experiment. We utilize a well-established model of
food web dynamics (Schneider \emph{et al.} 2016; Albert \emph{et
al.}2022), but implemented in a spatially-explicit context.
Specifically, instead of describing the dynamics of plant populations,
our model explicitly includes the spatial position of 64 evenly spaced
plant individuals and associated local resource pools (hereafter:
patch), arranged on an 8x8 grid with periodic boundary conditions. This
allows us to include local resource interactions between neighbouring
plants by manipulating their focus on using resources from their local
resource pools in relation to their neighbouring resource pools. Thus,
we can create a gradient of spatial overlap in resource access (`spatial
resource overlap') that ranges from no overlap to an even access to all
resource pools in the neighbourhood (Fig. 1A). Further, our model uses
two limiting plant resources. We assume that the access to both
resources has the same spatial constraints within a spatial resource
overlap scenario. However, we define resource requirements to differ
between plant species due to having different stoichiometries, allowing
for a complementarity in resource-use.

We additionally consider three scenarios of animal space-use (Fig. 1B).
First, we exclude animals to create a null model without their effects.
Second, in accordance with classic food-web models, we assume well-mixed
animal populations that can access all of their resource species
unconstrained (spatially non-nested food webs). Third, by constraining
the home range of animals based on their body mass, we create spatially
nested food webs in which larger species integrate multiple sub-food
webs, creating a nested food web structure (McCann \emph{et al.} 2005).
Despite a common meta-food web, the realized spatial topologies of
spatially nested and non-nested food webs can differ greatly (Fig. 1C).

While we use our model to investigate plant diversity-productivity
relationships at the community level, our proposed framework can be used
to assess, e.g., interactions between plant individuals or effects of
spatial heterogeneity in a multi-trophic context. It is therefore
flexible to generate further insights of the spatial processes in
complex food webs that drive ecosystems and their functioning.

\subsection*{Defining food web
topologies}

{\label{defining-food-web-topologies}}

In total, we analyse 20 different meta-food webs that were created to
mimic topologies of aboveground terrestrial ecosystems, where most BEF
experiments are conducted. In such ecosystems, carnivorous interactions
commonly follow allometric relationships, where larger predators consume
smaller prey species (Brose \emph{et al.} 2019). However, in aboveground
terrestrial ecosystems herbivorous interactions are largely independent
of body masses (Valdovinos \emph{et al.} 2022). Hence, we defined
herbivorous interactions to follow real world network properties (i.e.
connectance, nestedness, modularity; following Th\selectlanguage{ngerman}ébault \& Fontaine
2010) and combined them with allometrically scaled carnivorous
interactions (following Schneider \emph{et al.} 2016).

Each of 20 meta-food webs consists of 60 animal species with randomized
body masses, 16 plant species with dynamic body masses (i.e. they change
as plant individuals grow), and two limiting resources. To implement the
plant diversity treatment, we compare the complete 16-species plant
mixtures (i.e. 4 individuals per species, with random spatial
distributions) with their 16 monocultures (i.e. all 64 individuals of
the same species). Together with the plant (Fig. 1A) and animal
space-use treatments (Fig. 1B), we therefore investigate a total of
5,100 different trophic networks in a fully factorial design.

By defining local resource pools for each plant individual and allowing
plants to potentially support their own local food webs, our spatial
representation of the plant community most closely resembles forest
ecosystems. However, changing these assumptions by adapting the sizes of
animal home ranges and local resource pools allows for representing
other ecosystems as well. A detailed description of how we define
meta-food webs and represent them in space can be found in the
supplementary material (Supplementary 1-2).

\subsection*{Describing food web
dynamics}

{\label{describing-food-web-dynamics}}

To investigate how our treatments affect plant productivity and
diversity, we simulated food web dynamics using differential equations
that describe changes in animal, plant, and resource densities in
response to feeding interactions and metabolic processes. Specifically,
animals increase their biomass densities as they feed on other animals
or plants. Feeding rates are based on non-linear functional responses
that comprise capture coefficients, handling times, and interference
competition. Plant individuals increase their biomass based on
biomass-dependent growth rates, which are limited by the resource
availability. We assume a constant resource turnover. Densities of
resources, plants, and animals decrease as they are consumed. In
addition, plants and animals have metabolic demands that scale
allometrically. A detailed description of the model and its parameters
can be found in the supplementary material (Supplementary 3-4, Tab. S1).
Food web dynamics were calculated using Julia (version 1.6.1,
Bezanson\emph{et al.} 2017) and the DifferentialEquations package
(Rackauckas \& Nie 2017), utilizing a solving algorithm based on the
fourth-order Runge-Kutta method. The code used in this study is
available at https://github.com/GeorgAlbert/SpatialFoodWebBEF.

\subsection*{Measuring productivity and
diversity}

{\label{measuring-productivity-and-diversity}}

We measure plant productivity and diversity at the scale of plant
communities. We define plant productivity P of a community as the
resource uptake of all individuals of all plant species. To account for
cyclic dynamics at the end of simulations, we define plant productivity
as the average of productivity values obtained for the last 1,000
timesteps of our simulations. To capture plant diversity, we measure the
realized plant species richness (i.e. number of surviving plant species)
and plant density (i.e. number of surviving plants) at the end of the
simulation. Additionally, we calculate Shannon diversity
H\textsubscript{exp} to compare to species richness and thereby quantify
plant dominance patterns (Jost 2006) as\(H_{\exp}=\exp\left(-\sum_{i}{p_{i}\ln\left(p_{i}\right)}\right)\), with
\(p_{i}=\frac{P_{i}}{P}\) where P\textsubscript{i} is the productivity of plant
species i.

\section*{Results}

{\label{results}}

\subsection*{Plant diversity-productivity
relationships}

{\label{plant-diversity-productivity-relationships}}

To investigate the potential drivers behind plant diversity-productivity
relationships, we compare the effects of food-web and resource-use
scenarios (see Fig. 1) on productivity at both ends of the plant
diversity gradient. In monocultures without animals, we find that a
spatial overlap in plant resource access (`spatial resource overlap')
has no effect on productivity (Fig. 2, plant species richness of one;
Fig. S1A; green points). Instead, differences occur across the different
food-web scenarios. Specifically, monocultures without animals are the
most productive, closely followed by those embedded in spatially
non-nested food webs (dark blue points). In spatially nested food webs,
plant productivity of monocultures is the lowest on average but shows
the largest variation with a weakly positive response to an increased
spatial resource overlap (light blue points). We rarely found unviable
monocultures. The few examples we recorded were spread across all
resource-use scenarios and more common in spatially nested (93/1600)
than in spatially non-nested food webs (30/1600), and never occurred in
communities without animals. When focusing on monoculture productivity,
an interaction with neighbouring plants through a spatial resource
overlap therefore emerges as having little effect, rendering differences
in food web architecture as the main driver.

Our analyses reveal some striking effects of having a spatial resource
overlap on the diversity-productivity relationships in plant communities
without animals (Fig. 2, green lines). Without a spatial resource
overlap we find neutral relationships between productivity and species
richness (Fig. 2A). However, as soon as plants are able to access
resources of the neighbouring patches (i.e. with spatial resource
overlap), we find positive effects of plant diversity on productivity
that are similar across resource-use scenarios (Fig. 2B-E; Fig. S1B).
Taken together, these results suggest that a positive response of
productivity to species richness in plant communities without animals
requires a spatial resource overlap, but already small amounts of
spatial resource overlap (i.e. Fig. 2B) suffice to saturate these
relationships.

In spatially non-nested food webs, plant communities show a strong
decrease in productivity with increasing richness in most resource-use
scenarios (Fig. 2A-D; Fig. S1B; dark blue lines). Diversity-productivity
relationships are most negative when spatial resource overlap is
smallest (Fig. 2B). Across the gradient of resource-use scenarios, plant
monoculture productivity is constant (Fig. S1A), while it increases
considerably at higher plant species richness (Fig. 2B-E; Fig. S1B).
This culminates in neutral diversity-productivity relationships when
spatial resource overlap is maximized (Fig. 2E). Thus, in communities
with spatially non-nested food webs, a strong spatial resource overlap
with neighbouring plants has a positive effect on plant
diversity-productivity relationships.

In contrast, plant communities in spatially nested food webs display
positive diversity-productivity relationships in the majority of cases
(Fig. 2B-E, light blue line). We only find negative effects of plant
diversity on productivity when there is no spatial resource overlap
(Fig. 2A). However, productivity at both ends of the diversity gradient
displays large amounts of variation. As soon as plants have access to
resources of neighbouring patches (i.e. with spatial resource overlap),
productivity increases with diversity, reaching values with little
variation that are similar to those in plant communities without animals
(Fig. 2B-E). Together with having the lowest average productivity in
plant monocultures compared to all other food web scenarios (Fig. S1A),
this makes plant communities in spatially nested food webs exhibit the
most positive diversity-productivity relationships (Fig. 2B-E).

\subsection*{Plant community
composition}

{\label{plant-community-composition}}

Our prior results show that differences in the plant
diversity-productivity relationships are mainly driven by varying
productivity at the highest plant diversity levels (Fig. 2). To better
understand these differences between food-web and resource-use
scenarios, we investigated how plant community composition differs
between scenarios at the highest plant diversity level of 16 species.
Without a spatial resource overlap (i.e. spatial resource overlap at 0),
realized species richness, realized plant density, and Shannon diversity
display the highest values within each food web scenario considered
(Fig. 3). In communities without animals, the values are at their
absolute maximum (Fig. 3, green line). In spatially non-nested food
webs, the plant communities show a tendency towards lower values of
realized richness and density, and Shannon diversity is clearly lower,
indicating an increased heterogeneity in the plant community (Fig. 3,
light blue line). For spatially nested food webs, plant communities
display a slightly reduced plant species richness and density and have
the lowest Shannon diversity (Fig. 3, dark blue line). Thus, spatially
nested food webs support the least diverse plant communities when there
is no spatial resource overlap between neighbouring plants.

The compositional response of plant communities without animals to
increasing the spatial resource overlap between neighbouring plants
stands out as it displays a delayed but harsh drop for all three
compositional variables (Fig. 3, green lines). This leads to plant
communities that lose almost half of their plant individuals when
spatial resource overlap is highest (Fig. 3B), and includes the
extinction of slightly more than three species on average (Fig. 3A).
Since Shannon diversity decreases more than species richness (Fig.
3A\&C), an increased spatial resource overlap increases the
heterogeneity in the plant communities without animals. Taken together,
the effects of increasing the spatial resource overlap are most severe
for plant communities without animals.

Plant communities in spatially non-nested food webs follow very similar
patterns compared to communities without animals (Fig.3, dark blue
lines). However, the negative effects of increasing the spatial resource
overlap are less pronounced for plant richness and density, culminating
in about a quarter of plants and only about two species lost when the
spatial resource overlap was highest (Fig.3A\&B, dark blue lines).
Shannon diversity was generally lower than in communities without
animals, reaching the lowest values at maximum spatial resource overlap
compared to all other scenarios (Fig. 3C, dark blue line). When spatial
resource overlap is high, spatially non-nested food webs are therefore
enhancing differences between plant species more than any other
scenario.

Compared to the other food web scenarios, plant community composition in
spatially nested food webs show the weakest response to changes in
spatial resource overlap. Especially realized plant species richness,
which displays an average loss of only one species, was independent from
spatial resource overlap (Fig.3A, light blue line). Similar to spatially
non-nested food webs, only about a quarter of plants are lost when
spatial resource overlap is highest (Fig.3B, light blue line). Shannon
diversity again decreases with increasing spatial resource overlap but
ends up stabilizing over the last two steps of the spatial resource
overlap gradient (Fig.3C, light blue line). Overall, these findings
suggest that spatial resource overlap between neighbouring plants
matters the least in spatially nested food webs.

\section*{Discussion}

{\label{discussion}}

In our meta-food-web approach, we show that spatial processes related to
plant resource exploitation and animal movement strongly affect plant
diversity-productivity relationships. Positive relationships arise only
when plant resource access overlaps spatially (`spatial resource
overlap') at the cost of exploitative competition. Herbivore movement
introduces apparent competition between plants, which can reduce plant
productivity in diverse communities, yielding negative
diversity-productivity relationships. However, a realistic body mass
scaling of animal home range sizes moves apparent competition motifs up
the food chain. The reduced plant competition together with the spatial
integration of sub-food webs through the movement of top predators lead
to the most positive effects of plant diversity on productivity,
suggesting animal movement as a crucial driver of plant
diversity-productivity relationships.

\subsection*{Plant-resource
interactions}

{\label{plant-resource-interactions}}

A spatial resource overlap between neighbouring plants has two important
implications for plants. While it allows each plant to access a larger
share of resources available in the ecosystem, it also forces them to
engage in exploitative competition. In diverse plant communities,
however, plants will differ in their resource requirements and thus in
their competitive ability. Different resource requirements are usually
accompanied by low competition (Tilman \emph{et al.} 1997) and suggest a
stoichiometric complementarity between neighbouring plants
(González\emph{et al.} 2017) that is likely to have positive impacts on
plant productivity. We find this mirrored in our results, where, in the
absence of animals, even a weak spatial resource overlap is enough to
maximize productivity in diverse plant communities of species with
different resource requirements. Accessing small amounts of otherwise
inaccessible resources can therefore already suffice to lift resource
limitations, leading to positive diversity-productivity relationships
due to a stoichiometric complementarity.

Differences in competitive abilities across pairs of plant species are
rarely associated with such performance enhancements. Instead, they
should lead to local extinctions of the weaker competitor (Tilman 1982),
which we find mirrored in a loss of plants when the spatial resource
overlap increases. Surprisingly, this does not come at the cost of a
reduced productivity. Instead, plants with a competitive advantage,
either due to a higher efficiency in resource acquisition (i.e.
exploitative competition) or favourable multi-trophic interactions (i.e.
apparent competition), can maximize their resource uptake and thereby
increase their biomass (Wang \& Brose 2018). This has the positive side
effect of reducing energy requirements for metabolic processes relative
to their mass (Enquist \emph{et al.} 1998), contributing to a more
energy efficient plant community. Our findings suggest that this is
enough to counterbalance the loss of plants as well as the associated
diversity loss.

When plants have a spatial resource overlap, diversified resource
requirements create complementarity whereas selection
(\emph{sensu}Loreau 2000) due to competitive differences shift the
community to be more energy efficient (Wang \& Brose 2018), leading to
an optimized resource uptake in both cases. Consistent with our
hypothesis (H1), this increases productivity and leads to positive
diversity-productivity relationships. The consistency of those
relationships paired with the shifts in plant community composition
additionally implies that the contribution of complementarity and
selection processes to maximizing productivity varies depending on the
strength of the competitive interaction between plants.

\subsection*{Plant-animal interactions~}

{\label{plant-animal-interactions}}

When embedded in complex food webs, the response of plant productivity
to varying plant biodiversity is rooted in food-web topology. As the
number of plant species increases, there is an increasing number of
apparent competition motifs in which two plant species are coupled by a
shared herbivorous consumer population. In this motif, the plant species
with a higher resource acquisition efficiency achieves a higher biomass
density, leading to higher herbivore densities, which in turn has
negative top-down effects on other plant species with lower resource
acquisition efficiencies (Holt 1977). Accordingly, our simulations of
spatially non-nested food webs have shown that as plant species richness
increases, plant productivity decreases, which is, consistent with our
hypothesis (H2), reflected in negative diversity-productivity
relationships. However, when compared to scenarios without animals, the
added apparent competition does not foster competitive exclusion.
Instead, it seems to buffer some of the negative effects of an increased
exploitative competition (i.e. increased spatial resource overlap) as
more plant individuals and species are able to coexist when embedded in
a food web (see also Brose 2008; Albert \emph{et al.} 2022).

While the high levels of maintained plant individuals and species are
similar between spatially nested and non-nested food webs, the effects
of apparent competition on productivity are not. Specifically, our
simulations of spatial non-nested food webs assume a well-mixed system
without any differences in local biomass densities of animal species.
Ignoring such differences results in herbivore populations that can feed
simultaneously on different plants regardless of their location. In
nature, however, animal communities have a complex spatial organization
(e.g. Gonçalves-Souza \emph{et al.} 2015). While almost all animal
species move between resource patches, larger species travel longer
distances and have larger habitats (Tucker \emph{et al.} 2014;
Tamburello \emph{et al.} 2015; Hirt \emph{et al.} 2021). As a result,
meta-food webs have a structure in which smaller species from local food
webs are spatially integrated within the home ranges of larger species.
Apparent competition between plants in spatially nested food webs is
therefore spatially constrained depending on the home range size of the
herbivore. In addition, an increased amount of apparent competition
motifs between sub-populations of herbivores reduces their top-down
control on plants. Hence, instead of the negative plant
diversity-productivity relationships found in spatially non-nested food
webs, relationships in spatially nested food webs are the most positive,
peaking at levels similar to plant communities without animals.

Apart from the positive effects of an altered spatial topology (i.e.
effects of apparent competition) on diversity-productivity relationships
in spatially nested food webs, the spatial integration of sub-food webs
has additional dynamic benefits. In particular, biomass overshooting and
unstable dynamics leading to local extinctions are buffered in spatially
nested food webs by large top predators that stabilize biomass minima of
populations in the local food webs away from critically low values
(McCann \emph{et al.} 2005). This is reflected in the relatively stable
plant diversity of spatially nested food webs despite differences in the
spatial resource overlap of plants. Consistent with our hypothesis (H3),
we thus conclude that a spatial integration of sub-food webs associated
with spatially nested food webs has positive effects on plant
diversity-productivity relationships. The clear dynamic and topological
differences between spatially nested and non-nested food webs, which may
be negligible for biodiversity maintenance, can therefore have strong
implications for plant productivity, leading to vastly different plant
diversity-productivity relationships.

\subsection*{BEF: from multi-trophic to meta-food
webs}

{\label{bef-from-multi-trophic-to-meta-food-webs}}

BEF research has evolved from focusing on single functional groups (e.g.
plant communities) to the complex multi-trophic structure of natural
communities (e.g. Schuldt \emph{et al.} 2019; Barnes \emph{et al.} 2020;
Albert \emph{et al.} 2022). This development has shown that
multi-trophic interactions can facilitate plant coexistence and thereby
increase productivity. In our study, we extended this development by
applying meta-ecosystem (i.e. plant-resource exploitation bridges
between local habitats) and meta-food web approaches (i.e.
spatially-explicit structure of the food webs). Some of our results on
the effects of multi-trophic interactions differ significantly from
previous conclusions. While prior studies reported generally positive
effects of multi-trophic interactions on plant coexistence and
diversity-productivity relationships (Thébault \& Loreau 2003; Brose
2008; Albert \emph{et al.} 2022), we found that under the assumption of
spatially segregated plants (i.e. each plant inhabits its own local
habitat) this is not necessarily the case. Spatially non-nested animal
communities paired with spatially segregated plants instead result in
negative relationships, which finds an explanation in the systematic
increase in apparent competition motifs. In contrast, the spatially
nested structure of animal communities yields strongly positive
diversity-productivity relationships due to the positive effects of an
apparent competition shift~up the food chain (i.e. from between plants
to between herbivores) and the spatial integration of sub-food webs by
top predators.

By relaxing the classic assumption of well-mixed systems (e.g.
Schneider\emph{et al.} 2016; Albert \emph{et al.} 2022), we gained
accuracy in the description of the processes that drive ecosystems and
their functioning. The assumption of a well-mixed system is also at the
core of BEF research, as it usually compares the functioning of entire
communities of varying diversity. While this helped to identify
complementarity mechanisms as the main driver of positive BEF
relationships, it remains difficult to identify their concrete causes
(Barry \emph{et al.} 2019), which may be related to focusing on the
wrong spatial scale. Indeed, competition and the associated BEF
processes (i.e. complementarity and selection; Loreau 2000) act between
a few organisms and are thus spatially constrained. Our work
demonstrates that a multi-trophic investigation of spatially-explicit
plant-resource interactions additionally requires a spatially-explicit
consideration of the entire food web. Moreover, our simulations show
that the sign and strength of diversity-productivity relationships
depends on the joint effects of animal movement and spatial resource
overlap of plants. This renders the spatial organisation of
multi-trophic communities, which can vary across landscapes, an
important but often neglected aspect that can help to explain the
variation observed in empirical BEF relationships (Cardinale \emph{et
al.} 2007). Overall, our findings on diversity-productivity
relationships clearly demonstrate the importance of spatial community
structure and animal movement in driving BEF relationships in meta-food
webs.

\subsection*{Future directions}

{\label{future-directions}}

The development of accounting for spatial processes in BEF relationships
can be progressed in multiple ways. We have advanced this field in one
dimension by synthesizing spatially-explicit processes related to animal
foraging movement with spatially-explicit plant-resource exploitation.
Our model is flexible to also include other aspects of community
structure across spatial scales, including (1) local factors and species
traits influencing exploratory movement during foraging (Hirt \emph{et
al.} 2017), (2) neighbouring habitats coupled by lateral nutrient flows
in meta-ecosystems (Loreau \emph{et al.} 2003; Gounand \emph{et
al.}2018), (3) meso-scale landscape structures in community assembly
models (Bannar\selectlanguage{english}-Martin \emph{et al.} 2018; Saravia \emph{et al.} 2022),
including plant and animal dispersal (Ryser \emph{et al.} 2021), and (4)
biogeographic differences between species pools (e.g. of plants;
Sabatini \emph{et al.} 2022). In this vein, merging our
spatially-explicit meta-food web approach with food web assembly models
(Bauer \emph{et al.} 2022; Saravia \emph{et al.} 2022) offer a
particularly exciting avenue of future research as it allows to
understand how local spatial processes scale to the diversity and
ecosystem functioning patterns observed at larger spatial scales.

\subsection*{Conclusion}

{\label{conclusion}}

Despite its variability, the positive effects of diversity on
productivity in plant communities are a widely recognized pattern that
is consistent across ecosystems (Cardinale \emph{et al.} 2007). To date,
the most prominent among the proposed mechanisms driving these patterns
and their variability is complementarity in the resource-use of plants
(Barry \emph{et al.} 2019), which has more recently been supplemented by
multi-trophic complementarity (Poisot \emph{et al.} 2013; Albert\emph{et
al.} 2022). To better understand their differences, we explicitly
modelled the different spatial scales at which both mechanisms operate
in a simulated biodiversity experiment. We could show that a spatial
overlap in resource access between neighbouring plants is a fundamental
requirement for positive plant diversity-productivity relationships,
highlighting the tight association of exploitative competition with
resource-use complementarity and plant compositional shifts due to
selection. The realistic, spatially-explicit representation of meta-food
webs that integrate nested local sub-food webs stabilizes plant
coexistence and yields the strongest diversity-productivity
relationships we observe. Our modelling framework can serve as a
foundation to further enhance our mechanistic understanding of
multi-trophic processes in driving plant diversity-productivity
relationships. It provides a novel approach to managing biodiversity
while explicitly accounting for the spatial processes that underpin the
ecosystem functions that are the basis of our human society. Advancing
in this direction is therefore crucial for guiding conservation efforts
to maintain biodiversity and the functioning of ecosystems.

\section*{Acknowledgements}

{\label{acknowledgements}}

We thank the members of the EcoNetLab for helpful discussions. GA was
supported by the International Research Training Group TreeDi funded by
the German Research Foundation (DFG; GRK 2324/1 - 2018 (P9), 319936945).
ET was supported by the Agence Nationale de la Recherche
(ANR-17-CE32-0002/ECOSTAB). SW was supported by the National Natural
Science Foundation of China (31988102). GA, BG, RR and UB gratefully
acknowledge the support of iDiv funded by the German Research Foundation
(DFG--FZT 118, 202548816).

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\section*{Figure captions}

{\label{figure-captions}}

\textbf{Fig. 1:} Overview of the considered spatial processes of plant
and animal interactions within a plant community. (A) Differences in
plant space-use are captured by a gradient of spatial overlap in plant
resource access (`spatial resource overlap'), ranging from no overlap,
where each plant is limited to its own patch, accessing only its local
resource-pool and making exploitative competition impossible, to an even
overlap with plants in neighbouring patches, maximizing exploitative
competition. (B) We assume a home range size scaling with an animal's
body mass (left). To investigate its effect, we look at three scenarios
of animal space-use (right), one of which serves as a null model for
animal effects by excluding them entirely (`none'). Scenarios with
animals are either spatially non-nested, where animal populations are
assumed to be well-mixed, or spatially nested, where animal home range
sizes scale with their body mass. (C) When projecting them in space,
each of the three scenarios can lead to different realized trophic
interactions (right) despite a common meta-food web (left), illustrated
using a simple trophic chain. Note that spatially nested food webs can
also have similar interactions as spatially non-nested food webs
depending on which species interact.

\textbf{Fig. 2:} Plant diversity-productivity relationships for the
three food web scenarios considered, i.e. without food web (`none'),
with spatially nested food web (`nested`), and with spatially non-nested
food web (`non-nested'). Plant productivity is measured for the entire
community. (A-E) Effects of increasing the spatial overlap in plant
resource access (`spatial resource overlap'). Points show 50th
percentile (i.e. median); Error bars show 25th and 75th percentile.
Unviable monocultures not included.

\textbf{Fig. 3:} Effects of increasing the spatial overlap in plant
resource access (`spatial resource overlap') on plant community
composition in plant communities assembled from 16-species and in three
different food web scenarios, i.e. without food web (`none'), with
spatially nested food web (`nested`), and with spatially non-nested food
web (`non-nested'). Biodiversity is expressed in (A) realized species
richness, (B) realized plant density, and (C) Shannon diversity. Points
show 50th percentile (i.e. median); Error bars show 25th and 75th
percentile.

\section*{Figures}

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Fig. 1\selectlanguage{english}
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Fig. 2\selectlanguage{english}
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Fig.3

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