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.