Introduction

In light of global change and biodiversity loss, it is a key challenge to advance our understanding about ecosystem resilience and its relationship with diversity. Resilience is defined as the capacity of ecosystems to absorb changes in the environment without exhibiting large changes in ecosystem state (Holling 1973). Biodiversity among and within species may increase ecosystem resilience (Hughes & Stachowicz 2004; Isbell et al. 2015), when species (or genotypes) perform similar functions but respond differently to environmental change (Leary & Petchey 2009). Hence, a key aspect of diversity is variation in functional traits, i.e. the traits that determine how organisms respond to environmental change and affect ecosystem processes (Naeem & Wright 2003; Suding et al. 2008). Corresponding research has primarily focused on ecosystems with single equilibria (Yachi & Loreau 1999; Loreau & Mazancourt 2013), but was recently extended to ecosystems with alternative stable states (Dakos et al. 2019; Chaparro-Pedrazaet al. 2021). When such ecosystems experience a change in environmental conditions, higher biodiversity may prevent or delay the shift to an alternative ecosystem state (Figure 1; Chaparro-Pedrazaet al. 2021). Resilience is particularly crucial in these systems because shifts to alternative states often occur abruptly, are difficult to reverse, and can entail high costs when the ecosystem transitions to a state that is undesired for ecological and/or economic reasons (Scheffer et al. 1993; Foley et al. 2003; Diaz & Rosenberg 2008).
Ecosystems with alternative stable states are characterized by displaying two or more different states at identical external conditions (Fig. 1a). As an environmental driver increases gradually, the ecosystem shifts abruptly to an alternative state once a threshold, the tipping point, is passed, but recovers to its original state only at lower threshold conditions (Fig. 1a; Scheffer et al. 2001). Between these two threshold values, the state of the ecosystem depends on its history, a phenomenon termed hysteresis. A key mechanism behind hysteresis is positive feedback between organisms and their environment (Kéfi et al. 2016). For example, in shallow lakes submerged plants and phytoplankton can interact via mutual inhibition (a positive feedback), where macrophytes inhibit phytoplankton by consuming nutrients, while phytoplankton inhibit macrophytes by reducing water clarity (Kéfi et al. 2016). At intermediate nutrient concentrations, shallow lakes can thus be in a clear state dominated by submerged plants or in a turbid state dominated by phytoplankton, depending on which of these two functional groups dominated in the past (Scheffer et al. 1993).
Effects of diversity on the resilience of systems with alternative stable states were addressed conceptually (Dakos et al. 2019) and investigated with mathematical models of predator-prey systems (Ceulemans et al. 2019; Chaparro-Pedraza 2021; Wojcik et al. 2021) and shallow lakes (Chaparro-Pedraza et al. 2021). Two of these studies are particularly relevant here because they analyzed how trait change influences the position of tipping points along an environmental gradient (Chaparro-Pedraza 2021; Chaparro-Pedraza et al. 2021). Using three model systems (a population model, a predator-prey model, and a model of a shallow lake ecosystem), the authors report that trait change shifted the transition to an alternative state to a higher level of environmental stress (Chaparro-Pedraza 2021; Chaparro-Pedraza et al. 2021). In the shallow lake model system the shifts from a clear to turbid state and back from turbid to clear both occurred at higher nutrient loading when macrophytes varied in shade tolerance (Chaparro-Pedraza et al.2021). In this example, diversity was manipulated in one functional group. Yet, multiple functional groups may simultaneously be present, and the effect of diversity on ecosystem resilience may be different if more than one functional group varied in traits.
Studies on systems without alternative stable states have shown that simultaneous changes of diversity in multiple functional groups may lead to complex relationships between diversity and ecosystem processes (Thébault & Loreau 2003; Ceulemans et al. 2021). Specifically, diversity of one functional group can enhance (Eisenhauer et al.2012; Zhao et al. 2019), dampen (Bruno et al. 2008), or reverse (Thébault & Loreau 2003) the diversity effects of another functional group. These previous studies focused on trophic and facilitative interactions. It is unclear, however, how simultaneous versus independent changes of diversity play out when functional groups interact via mutual inhibition, an interaction that is characteristic of many ecosystems with alternative stable states (Kéfi et al. 2016; Bush et al. 2017).
Here we investigate how trait diversity in one, two, or three functional groups influences the resilience of ecosystems that have alternative stable states. We used a mathematical model developed by Bush et al. (2017) which describes abrupt oxic-anoxic regime shifts of aquatic ecosystems in response to changes in oxygen diffusivity. In this system, regime shifts are mediated by mutual inhibition of cyanobacteria and two types of sulfur bacteria (sulfate-reducing bacteria and phototrophic sulfur bacteria). The already published model (Bush et al. 2017) assumes no trait variation within each of the three functional groups, which is equivalent to there being only one strain in each functional group. We extended this model to include trait variation among multiple strains within each of the three groups of bacteria, and tested if the effect of diversity on resilience depends on (i) the amount of trait variation, and (ii) the combination of functional groups that contain variation. Increased resilience can be considered beneficial when it concerns the desired ecosystem state (oxic), but detrimental when it concerns the undesired state (anoxic). To describe our findings, we use the visualization framework illustrated in Figure 1 and terminology explained in Box 1.
We focused on a model that is simple enough to give generally applicable insights about the biodiversity-resilience relationship, but that is of sufficient complexity and realism to provide testable hypotheses for experiments and suggest novel approaches in ecosystem management. Moreover, by using a model of a specific ecosystem type, we may detect mechanisms that might be overlooked with simpler and more abstract models. We show that diversity can both enhance and reduce resilience depending on which and how many functional groups vary in traits, which illustrates the importance of considering multiple groups and their complex interactions.