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 et al. 2016; Albert 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 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.
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 et al. 2019). However, in aboveground
terrestrial ecosystems herbivorous interactions are largely independent
of body masses (Valdovinos et al. 2022). Hence, we defined
herbivorous interactions to follow real world network properties (i.e.
connectance, nestedness, modularity; following Thébault & Fontaine
2010) and combined them with allometrically scaled carnivorous
interactions (following Schneider 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).
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, Bezansonet 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.
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
Hexp 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 Pi is the
productivity of plant species i.