Measuring the Response Diversity of Ecological Communities Experiencing Multifarious Environmental Change

ABSTRACT

The diversity in organismal responses to environmental changes (i.e., response diversity) plays a crucial role in shaping community and ecosystem stability. However, existing measures of response diversity only consider a single environmental variable, whereas natural communities are commonly exposed to changes in multiple environmental variables simultaneously. Thus far, no approach exists to integrate multifarious environmental change and the measurement of response diversity. Here, we show how to consider and quantify response diversity in the context of multifarious environmental change, and in doing so introduce a distinction between response diversity to a defined or anticipated environmental change, and the response capacity to any possible set of (defined or undefined) future environmental changes. First, we describe and illustrate the concepts with empirical data. We reveal the role of the trajectory of environmental change in shaping response diversity when multiple environmental variables fluctuate over time. We show that, when the trajectory of the environmental change is undefined (i.e., there is no information or a priori expectation about how an environmental condition will change in future), we can quantify the response capacity of a community to any possible environmental change scenario. That is, we can estimate the capacity of a system to respond under a range of realistic or extreme environmental changes, with utility for predicting future responses to even multifarious environmental change. Finally, we investigate determinants of response diversity within a multifarious environmental change context. We identify factors such as the diversity of species responses to each environmental variable, the relative influence of different environmental variables and temporal means of environmental variable values as important determinants of response diversity. In doing so, we take an important step towards measuring and understanding the insurance capacity of ecological communities exposed to multifarious environmental change.

This study explores how response diversity—variability in species' responses to environmental changes—relates ecological stability under complex, multifactorial environmental shifts. The authors introduce a new approach to quantify response diversity considering multiple simultaneous environmental variables. They distinguish between response diversity to specific, anticipated changes and a broader measure of response capacity, which captures the potential of a community to adapt to any environmental changes. The findings provide insights into the factors influencing response diversity, advancing our understanding of the stabilising effects of biodiversity in the face of increasing environmental variability.

1. Introduction

Ecological stability, a multidimensional concept encompassing resistance, resilience, persistence, robustness and variability, has long been a central focus of ecological research, with particular emphasis on the temporal variability of ecosystem functions and their responses to environmental change (Donohue et al. 2013; Mccann 2000; Pimm 1984). There is a consensus that biodiversity dampens variability in aggregate community and ecosystem properties (Hautier et al. 2015; Isbell et al. 2015; Tilman, Isbell, and Cowles 2014; Yachi and Loreau 1999). This is because, in species‐rich communities, there is a higher chance that declines in abundance or performance (e.g., intrinsic growth rate) of one species may be compensated for by an increase in abundance or performance of another species (Yachi and Loreau 1999). Such dynamics have been named asynchronous and have been identified as a key driver of temporal stability across a range of systems (Craven et al. 2018; Gonzalez and Loreau 2009; Sasaki et al. 2019; White et al. 2023). Asynchronous dynamics are more likely to occur, even by chance, the greater the number of species that are present (Yachi and Loreau 1999), but especially so where species differ in their responses to environmental conditions (McCann 2016, Mori, Furukawa, and Sasaki 2013). This diversity of responses to environmental change has been termed response diversity (Elmqvist et al. 2003; Mori, Furukawa, and Sasaki 2013; Nyström 2006).

Despite a recent surge of interest in response diversity in ecology (Ross et al. 2023; Ross and Sasaki 2024; Ruiz‐Moreno, Emslie, and Connolly 2024; Sasaki et al. 2019), to date, there has been little exploration of response diversity in the context of multiple simultaneously changing (multifarious) environmental variables. This is despite differences in environmental tolerances among species resulting in low redundancy across environmental contexts, suggesting that response diversity is key to stability even when faced with multifarious environmental change (Mori, Furukawa, and Sasaki 2013). A recent review of the literature showed that among 46 studies identified that empirically measured response diversity, only three considered more than one environmental variable, but none of them proposed a method capable of accounting for potential nonadditivity in environmental effects on species responses (Ross et al. 2023). However, nonadditive effects of multiple environmental variables are common and have the potential to mediate the response to any individual stressor (Birk et al. 2020; Jackson et al. 2016), highlighting the need for a new approach able to consider interactions between environmental variables when quantifying response diversity.

Focusing on a single environmental variable may inaccurately represent human‐driven environmental change effects on species, communities and ecosystems (Jackson, Pawar, and Woodward 2021). When considering one environmental change variable, the diversity of species responses to that variable alone determines response diversity. However, when multiple environmental variables affect species responses, the diversity of species responses to each variable will jointly determine response diversity. Critically, we can imagine a scenario where species exhibit different amounts of response diversity to different environmental variables if species respond very differently from each other to one environmental variable, but respond similarly to another (Bray et al. 2019). Thus, the correlation between response diversity to each single environmental variable should strongly impact the response diversity to the two variables combined. Further, it is common for one environmental variable to have a larger (i.e., dominant) effect on species responses than others, thereby more greatly impacting community and ecosystem dynamics and stability (Birk et al. 2020; Morris et al. 2022). Finally, the (temporal) mean value of the environmental variables should drive the diversity of responses to those variables (Mori, Furukawa, and Sasaki 2013). For example, if the environment is fluctuating around extreme environmental conditions, more species are likely to be outside their range of environmental tolerances. This will, therefore, make species responses more similar, in turn, reducing response diversity. Extreme environmental fluctuations typically cause reductions in functioning, and thus instability, or reductions in population sizes through mortality, eventually resulting in species losses (Mouthon and Daufresne 2006). In contrast, when environmental variables fluctuate around intermediate values, higher response diversity may promote temporal stability of communities or functions.

Most empirical studies of response diversity have measured the diversity of responses to a known and specified direction and magnitude of environmental change (Bartomeus et al. 2013; Sasaki et al. 2019; Winfree and Kremen 2008). However, particularly when dealing with projections of future environmental change, we do not always know the magnitude of the expected environmental change and perhaps even have uncertainty about the trajectory of environmental change. This uncertainty increases when a greater number of environmental variables is considered. This hinders the quantification of response diversity when the environmental change a community will experience is undefined. Yet, the capacity of a community to respond to environmental change is contingent upon its intrinsic characteristics (i.e., species' traits; Suding et al. 2008). This suggests that response diversity should also be quantified without accounting explicitly for the environmental change to which the community could be exposed. This is an unexplored dimension of response diversity that captures the response capacity of a community to all possible environmental change scenarios in a defined environmental parameter space, and it more closely reflects the need to quantify the total insurance effect of biodiversity (Yachi and Loreau 1999).

Here, we address these issues. We (i) integrate response diversity and multifarious environmental change, (ii) explore and propose a new method for quantifying response diversity when there is little or no information about the environmental change context and (iii) investigate drivers of response diversity in a multifarious environmental change scenario. Building on work by Ross et al. (2023), we propose a way to quantify response diversity based on species response surfaces that can account for multiple environmental variables. We propose measures of response diversity designed for situations in which we only know about the boundaries of future environmental change, in contrast to when we know the precise trajectory of environmental change.

2. Materials and Methods

2.1. Quantifying Response Diversity in a Multifarious Environmental Change Context

The response diversity of a community can be measured as the diversity of species' responses to environmental change (McCann 2016; Mori, Furukawa, and Sasaki 2013). Ross et al. (2023) recently proposed characterising species' responses with the first derivative of their performance–environment function evaluated over an environmental gradient. A species' performance describes the success and fitness of a species measured through ecological and biological metrics such as its intrinsic rate of increase or biomass change along an environmental gradient. The method is based on fitting individual species' performance–environment relationships using generalised additive models (GAMs), then taking the first derivative of these relationships to identify the rate of change of species' performance curves along the environmental axis. The variation among first derivatives of different species (or individuals, populations, etc.) can then be used to quantify response diversity. The use of GAMs and the related first derivatives provide a flexible methodology to measure response diversity when species performance–environment relationships are linear or nonlinear (Ross et al. 2023). The variation in the first derivatives can then be quantified through two metrics that provide complementary information: response dissimilarity and response divergence. Response dissimilarity correlated poorly with the temporal stability of aggregate community properties using data from aquatic ciliates (Ross et al. 2023), so here we will focus on response divergence.

Response divergence accounts for whether performance–environment relationships differ in direction (positive or negative responses), and is calculated as:

$$\text{Divergence}=\frac{\left(\max \left[f^{\prime }\left(E\right)\right]-\min \left[f^{\prime }\left(E\right)\right]\right)-\left|\left|\max \left[f^{\prime }\left(E\right)\right]\right|-\left|\min \left[f^{\prime }\left(E\right)\right]\right|\right|}{\left(\max \left[f^{\prime }\left(E\right)\right]-\min \left[f^{\prime }\left(E\right)\right]\right)}$$ (1)

where $f^{\prime }\left(E\right)$ represents the first derivative of a performance–environment relationship, $f\left(E\right)$, at a particular environmental state, E. If the range of derivatives does not span zero, all species respond in the same direction to the environment (derivatives are either all positive or all negative). Hence, there is no diversity in direction of species responses, and the divergence value is zero. Conversely, when derivatives are perfectly symmetric around zero, divergence is maximum (=1). In intermediate cases, there needs to be at least one species decreasing while another is increasing (difference in the sign of the first derivatives) for divergence to be larger than zero. Response divergence values above zero are expected to be stabilising based on the insurance effect of biodiversity (Yachi and Loreau 1999).

This method and the associated metrics have been developed for quantifying response diversity in the context of a single environmental variable and cannot be directly applied to multifarious environmental change contexts. This is because, when species performances are determined by two, instead of one environmental variable, the performance curves modelling performance against each environmental variable separately now produce a performance surface modelling performance against two variables together. We represent this surface as $G=f\left(E_1,E_2\right)$, where $G$ is the growth rate (our measure of performance), $E_1$ is the first environmental variable, $E_2$ is the second environmental variable and f is a function describing the form of these relationships. The relationships can be linear or nonlinear and can include an interaction between E ₁ and E ₂.

We extended the above approach to account for two (and in principle more) environmental variables. Instead of calculating the first derivative (and measuring interspecific variation of these derivatives), we calculated the directional (first) derivative. A directional derivative is the slope on a performance surface at a particular location pointing in a particular direction. In an ecological context, the direction in which the directional derivatives are calculated will be dictated by the trajectory of the environmental change (the change in environmental conditions). For a step‐by‐step mathematical explanation of how to quantify directional derivatives, see Appendix S1.

The diversity of directional derivatives among species in a community calculated along a specified environmental change trajectory can then be quantified as response divergence. In this way, we can quantify response diversity in response to a defined trajectory of multifarious environmental change (i.e., when the temporal trajectory of each environmental variable is defined). We now describe the underlying principle to calculate response diversity in a multifarious environmental change context starting from individual species response surfaces; we apply our method to empirical data. We derived species response surfaces from a published study (Bestion, Schaum, and Yvon‐Durocher 2018) where the growth rates of five phytoplankton species were measured over 1 month at 13 phosphate concentrations and 6 temperatures, each with three replicates. The dataset is publicly available at: https://zenodo.org/records/1247453, and the code to reproduce our analysis with step‐by‐step explanation is available at https://github.com/FrancescoPola/response‐diversity‐multifarious‐environmental‐change (Polazzo 2024).

2.2. Response Diversity: Defined Trajectory of Environmental Change

To calculate response diversity, one needs information on the trajectory of the environmental change; that is, knowledge of how the environmental variables have changed or will change in future (Figure 1a,b).

FIGURE 1.

Calculation of directional derivatives of the growth rate of one species for a time series of environmental change. (a) Time series of temperature change. (b) Time series of phosphate concertation change. (c) Time series of temperature and phosphate concertation change overlayed on the performance surface of the phytoplankton species Ankistrodesmus nannoselene based on the species' growth rate. Sequential numbers in white boxes represent positions on the performance surface at time points corresponding to (a) for temperature and (b) for the phosphate concentration. Colours indicate the growth rate. (d) The time series of directional derivatives corresponding to the time series of environmental change in (a–c) and the species performance surface in (c). Note that in (d), the offset on the x‐axis is meant to show that the directional derivatives are calculated as we go from t = 1 to t = 2.

Since the empirical example presented here focused on measuring species response surfaces of a particular trait—which is normally done at constant environmental conditions—we simulated a time series of 10 timesteps where temperature and phosphate concentration change randomly within the values of the environmental variables used to measure the response surfaces. This allows plotting the trajectory of environmental change on a species' performance surface (Figure 1c) which provides a visual representation of the direction in which the directional derivatives are calculated when following the trajectory of environmental change (Figure 1d).

In a community context, one can calculate the directional derivative over time through the trajectory of the environmental change for each species individually. Next, by calculating response divergence among several species based on the variation in the directional derivatives within a community, one can quantify response diversity. Critically, our method does not assume stationarity in the time series describing the trajectory of environmental change, and can, thus, be applied to all types of environmental change trajectories including stochastic environmental fluctuations or directional trends as may be expected under climate change.

2.3. Response Capacity: Undefined Trajectory of Environmental Change

Now we analyse the case where we know how species respond to the environment (i.e., we have species response surfaces) but have no information about the trajectory of the environmental change. When the trajectory of the environmental change is undefined, we can calculate response diversity across all possible scenarios of environmental change to estimate the complete capacity of a community to respond to all possible changes in the environmental variables considered when measuring species response surfaces. We illustrate the principle using a hypothetical community of two species assembled from empirical data (Bestion, Schaum, and Yvon‐Durocher 2018): Ankistrodesmus nannoselene and Monoraphidium minutum.

Consider a single location on the performance surface of each species; this location corresponds to a specific set of environmental conditions (one x value and one y value). Since, in this example, we do not have a priori expectations about how each environmental variable will change, we can calculate the directional derivative for this specific location on the performance surface in many possible directions (Figure 2a,b). We can do this for multiple locations across the whole response surface (Figure 2c,d). Each point is an environmental location from which we calculate directional derivatives going in each of many different directions. Next, for each species, we consider one specific location and a specific direction. Then, we calculate the diversity—measured as response divergence—of the directional derivatives for that specific location and direction among species. We repeat the same process for all locations on the response surface and all directions of environmental changes. We then calculate the mean response divergence at each location (Figure 2e,f).

FIGURE 2.

Illustration of the principle underlying the calculation of response capacity. (a) and (b) show the response surfaces of Ankistrodesmus nannoselene and Monoraphidium minutum with one point on them from which directional derivatives extend in many possible directions. (c) and (d) The same species' response surfaces shown in (a) and (b), but in this case, there is a grid of points covering the whole surfaces. Response surfaces are shown in greyscale to better visualise directional derivatives. From each point, directional derivatives extend in many possible directions. In (e) and (f), considering the difficulties related to displaying multiple 3D performance surfaces, each having multiple points with directional derivatives extending in all possible directions, we focus here on representing only two species and nine points on each surface. For those points, we only display three directional derivatives to help visualise the calculation process, but note that computationally this is done for every possible combination of locations and directional derivatives.

Finally, response capacity can be summarised by taking the average across all environmental locations. The steps to calculate the response capacity of a system can be summarised as follows:

1. Calculate every ${\mathit{DD}}_{\mathit{sp},\mathit{loc},\mathit{dir}}$, that is, the directional derivative (DD) of each species (sp) in each location (loc) in each direction (dir).

2. Calculate ${\mathit{Div}}_{\mathit{loc},\mathit{dir}}=\mathit{Div}\left({\mathit{DD}}_{\mathit{sp},\mathit{loc},\mathit{dir}}\right)$, that is, the diversity (measured as divergence) of the directional derivatives for a given location and direction across species.

3. Calculate $\mathit{Div}=\frac{1}{n\mathit{loc}\times \mathit{dir}}\sum {\mathit{Div}}_{\mathit{loc},\mathit{dir}}$, that is, the average diversity (i.e., divergence) across locations ($n\mathit{loc}$ represents all the locations on the surface) and directions.

This calculation provides information about the response diversity of a community in all locations on the surface, which can be used to model the response capacity of a community to the whole set of environmental variables as represented on the response surface using GAMs (Figure 3a,b). In Figure 3, we calculated response diversity to all possible trajectories of environmental change at multiple locations of the environmental space delimited by the response surfaces of two hypothetical communities of three species. Community 1 was composed of A. nannoselene, M. minutum and Chlamydomonas moewusii, while Community 2 comprised A. nannoselene, Scenedesmus obliquus and Raphidocelis subcapitata. Differences in species response surfaces determine different values of response capacity under different environments (locations on the response surface). We then used GAMs to model response capacity over the whole environmental space. This allows us to compare how the response capacities of the two communities differ, and to ask where in the environmental parameter space one community is likely to have high response capacity, and thus is expected to maintain stable aggregate community properties within specific environmental limits.

FIGURE 3.

Response capacity calculated for two hypothetical communities. In each of (a) and (b) the predicted surfaces of response capacity of a community are shown. Regions with higher response capacity represent the environmental conditions under which the communities may be expected to maintain constant levels of aggregate community and ecosystem properties.

In this way, response diversity to many environmental change scenarios can be summarised in a single value capturing the total response capacity of the community (Figure 2); that is, the capacity of a community to respond to all possible changes in the multiple environmental variables used to measure the response surfaces. Response capacity, thus, provides a numerical quantification of the intrinsic insurance ability of a community in response to changes in these environmental variables (Yachi and Loreau 1999). Response capacity only depends on the performance–environment relationships of the species in a given community (Ross et al. 2023) and provides the first measurement of response diversity that is unrelated to the environmental context a community experiences.

2.4. Determinants of Response Diversity

In this section, we use simulations to explore how three features of species and their environments affect patterns of response diversity. First, we manipulated the relative importance of the two environmental variables (E ₁ and E ₂) on species responses. We simulated two cases: (i) one variable is dominant and has a larger effect on species responses than the other (Figure 4a upper panels); and (ii) both variables have an equal effect on species responses (Figure 4a lower panels). When the two environmental variables have equal relative importance, we expect that response diversity will be affected by features of performance curves for both variables (e.g., the amount of interspecific variation in species' environmental optima, specific environmental conditions under which a species achieves highest growth rate; Figure 4b). When there is a dominant environmental variable, we expect response diversity to be driven mainly by patterns in the responses to the dominant variable.

FIGURE 4.

Determinants of response diversity. In (a), the response of growth rate of one species to environmental variables E ₁ and E ₂ is shown. The panels on the left show the growth rate (y‐axis) of the species as a function of environmental variable E ₁ (x‐axis) with lines representing different levels of E ₂, colour‐coded accordingly. The variation in growth rate reflects the interaction between E ₁ and E ₂. Panels on the right side of (a) show the growth rate (y‐axis) as a function of environmental variable E ₂ (x‐axis), with lines colour‐coded based on the values of E ₁. (a) Highlights the dependence of growth rate on E2 while illustrating the impact of varying E ₁ levels. (a) A case where one environmental variable (E ₁) is dominant (upper panels), and for a case where the two variables have an equal effect (lower panels). (b) The concept of diversity in species responses together with the one of different means of one environmental variable. The three panels display three levels of response diversity with respect to E ₁ for a community of four species, that is, low response diversity (top panel), intermediate response diversity (middle panel) and high response diversity (bottom panel). The three different background colours in the panels show different means around which the environment fluctuates. (c) The amount of and correlation between diversity of species' responses to E ₁ and E ₂. The different panels illustrate different patterns of correlation in interspecific variation in E ₁ optima. Each coloured circle represents a species; the colour of the circle shows which community the species belongs to; the x‐ and y‐coordinate shows the E ₁ and E ₂ optima of that species. The top panel illustrates the no correlation treatment. All three communities have a fixed and rather low amount of variation in the position of the E2 optimum (y‐axis), whereas the variation in the position of the E ₁ optimum increases from low in community 1 (purple), to medium in community 2 (green), to high in community 3 (yellow). The intermediate panel illustrates the positive correlation treatment. Community 1 (purple) has low variation in the position of the optima for both E ₁ and E ₂, Community 2 (green) has intermediate variation in the position of optima for both E ₁ and E ₂. Community 3 (yellow) has high variation in the position of the optima for E ₁ and E ₂. Since the variation in the position of the optima gradually increases across the communities for both E ₁ and E ₂, this is the positive correlation treatment. The lower panel illustrates the negative correlation treatment. Community 1 has high variation in the position of the optima for E ₂, but low for E ₁. Community 2 has intermediate variation in the position of the optima for both E ₁ and E ₂, and Community 3 has high variation in the position of the optima for E ₁, but low for E ₂. Since, in this scenario, when variation in optima position for E ₂ is high, variation in optima position for E ₁ is low and vice versa, we call this the negative correlation treatment.

Second, we changed the correlation pattern in the diversity of species' responses to the two variables (Figure 4c). We simulated three cases, each with three communities of 10 species: (i) no correlation between species responses to the two environmental variables (communities had low, medium or high response diversity to one (E ₁), but medium response diversity to the other (E ₂), environmental variable; Figure 4c upper panel), (ii) positive correlation between environmental responses (communities had low, medium or high response diversity to both environmental conditions simultaneously (E ₁ and E ₂); Figure 4c middle panel) and (iii) negative correlation between environmental responses (communities with low response diversity to one environmental variable (E ₁ or E ₂) had high response diversity to the other, while the third had medium response diversity to both drivers; Figure 4c lower panel). We expect response diversity to be highest with positive correlation in response diversity to the two environments, as in this case, species should show the highest diversity in responses to both environmental variables. This should be especially so when both environments have equal relative importance (above).

Third, we manipulated the mean of each of the two environmental variables. We simulated three cases: (i) low mean environmental values, (ii) medium mean values and (iii) high mean values. We expect highest response diversity when the temporal mean of the environmental variables is at intermediate values with respect to the location of the species' performance curves (Figure 4b). That is, we expect highest response diversity when the response curves of some species have their optimum above the mean environmental condition, and some below the mean.

We analysed two determinants of response diversity that are only meaningful in a multifarious environmental change context (relative importance and correlation between species' environmental responses), and another that is important also in a single environmental variable scenario (mean environmental values). We chose these three potential determinants of response diversity because they have been previously identified as important and have good conceptual foundations (Laliberté et al. 2010; Mori, Furukawa, and Sasaki 2013; Ross et al. 2023). Additionally, they are testable in controlled empirical studies (Leary and Petchey 2009).

To test whether and how these factors determine response diversity, we simulated species growth rates under the influence of two environmental variables. For its widespread application and ease of implementation, we used the Eppley equation (Eppley 1972), though we recognise that numerous mathematical functions can be used to represent organismal response to changing environmental variables (Bernhardt et al. 2018; Kremer, Thomas, and Litchman 2017; Thomas et al. 2017). The Eppley equation captures the exponential relationship between maximum growth rate and temperature. This equation depicts typical features of organismal responses along a thermal gradient, such as an exponential increase in growth rate moving along the environmental gradient until reaching the maximum grow rate, and a sharp decline in growth rate beyond optimum. This pattern is often termed a thermal performance curve, where peak growth rate occurs within the biologically relevant temperature range for the organism (DeLong et al. 2018). Full explanation of simulations as well as code to reproduce the analysis is provided in the GitHub repository (https://github.com/FrancescoPola/response‐diversity‐multifarious‐environmental‐change/releases/tag/v3.0.0).

We simulated both additive and interactive environmental effects on species growth rates, but found no qualitative difference, so we report only the results of the additive effect (see GitHub for interactive effect details: https://github.com/FrancescoPola/response‐diversity‐multifarious‐environmental‐change/releases/tag/v3.0.0). We quantified response diversity as response divergence in all the simulations. The first two determinants of response diversity (variable dominance and correlation between the diversity of responses to the two variables) influenced both response diversity and response capacity. We report here only the results for response diversity. Results for response capacity largely mirrored those of response diversity for the first two determinants, and are reported in the file named ‘Creating the data for Response diversity in the context of multifarious environmental change’.

3. Results

3.1. Determinants of Response Diversity

Our simulations showed that when there was a dominant environmental variable—E ₁ in our simulations—response diversity always increased together with the diversity in responses to the dominant variable, with no effect of the correlation pattern in the diversity of species' responses to the two variables (Figure 5a–c). In this case, diversity in responses to the other environmental variable did not have any noticeable effect on response diversity. Indeed, when response diversity to the nondominant variable was high, but response diversity to the dominant variable was low, response diversity was overall low (Figure 5c, low E ₁ optimum diversity means high E ₂ optimum diversity, negative correlation). Hence, the correlation between diversity in responses to the two variables had little relevance when there was a dominant variable. However, the mean value around which the environmental variables fluctuated had a large impact on response diversity (Figure 5). The highest values of response diversity were always associated with communities exposed to environmental variables fluctuating around intermediate mean values (grey points in Figure 5).

FIGURE 5.

Effects of diversity in species' responses on response diversity measured as divergence. (a–c) How divergence changes in the different scenarios of correlation between E ₁ and E ₂ optimum diversity depending on the mean value of the environment in the case where E1 is the dominant variable. (d–f) How divergence changes in the different scenarios of correlation between E ₁ and E ₂ optimum diversity depending on the mean value of the environment in the case where E ₁ and E ₂ have an equal effect on species' growth rate. For all panels, small dots represent the divergence values measured for each community in our simulations, whereas the big dots are the mean values for each of the factor's levels.

When both environmental variables equally affected species growth rates, the diversity in responses to both variables had a large effect in determining response diversity, and so did the correlation pattern in the diversity of species' responses to the two variables (Figure 5d–f). When both environmental variables had an equal effect, having high diversity in responses to only one environmental variable was enough to produce high values of response diversity in the negative correlation scenario (Figure 5f). Again, the highest values of response diversity were found when the environmental variables fluctuated around intermediate mean values.

4. Discussion

4.1. Integrating Multifarious Environmental Change and Response Diversity

Response diversity has been proposed as a possible mechanism underlying the insurance effect of biodiversity, and thus as a key element stabilising community and ecosystem properties despite environmental fluctuations (Elmqvist et al. 2003; Mori, Furukawa, and Sasaki 2013; Ross and Sasaki 2024; Ruiz‐Moreno, Emslie, and Connolly 2024). However, there has been thus far no integration of response diversity in the context of multiple environmental stressors, limiting our ability to understand its relevance for real‐world ecosystems. Here, we began this integration and paved the way for future investigation looking at the contribution of response diversity in determining community and ecosystem stability in the face of multifarious environmental change.

Our method is based on species response surfaces. Although here we used species growth rate as the currency to quantify species response surfaces, any performance metric (e.g., carrying capacity) that describes the relationship between species and the environment can be used (Suding et al. 2008; Violle et al. 2007). Response diversity has been calculated as the multivariate dispersion of low‐level response traits (e.g., morphological traits; Bruno et al. 2016; Chillo, Anand, and Ojeda 2011; Schnabel et al. 2021). However, we advise against the use of low‐level traits without sufficient evidence of how such traits represent how species performance or functioning relates to the environment (De Bello et al. 2021; Violle et al. 2007). Without evidence that traits accurately characterise species' environmental responses, these traits are unlikely to mechanistically drive ecological stability (Ross et al. 2023).

Measuring species response surfaces, particularly when several variables are involved, can be logistically demanding. Recently, Collins, Whittaker, and Thomas (2022) suggested that experiments aiming to measure informative species response surfaces require at least five levels of each variable to construct meaningful surfaces. Still, scientists are increasingly recognising the importance of measuring species response surfaces for various traits. Such information can be used to gain mechanistic insights about community responses to multiple environmental variables (van Moorsel et al. 2023), and to aid in the development of predictive models describing species responses to environmental change (Collins, Whittaker, and Thomas 2022). As measurements of response surfaces continue in future, species response surfaces should hence become increasingly available (Bestion, Schaum, and Yvon‐Durocher 2018; Heinrichs et al. 2024).

Though measuring species response surfaces is typically easier using short‐lived species in the laboratory, recent studies have shown that response surfaces of relevant traits can be derived from field experiment (Brooks et al. 2023), and from time series of species responses spanning environmental gradients (Rogers and Munch 2020). Our proposed method for measuring response diversity from species' response surfaces is, therefore, applicable beyond simple laboratory experiments.

With increasing availability of response surface data, the methodological and conceptual extension of response diversity that we present here will help with understanding the role of response diversity in driving ecological stability in the face of multiple environmental variables and despite uncertainty surrounding scenarios of future environmental change. In turn, this may help to translate experimental results and theoretical advances into policy, due to the real‐world relevance of multifarious environmental change. Such information is critical because the temporal variability of aggregate properties plays a central role beyond ecology for economic systems, food production and other dimensions of human well‐being (Armsworth and Roughgarden 2003; Cardinale et al. 2012; Renard and Tilman 2019), and response diversity has been identified as a key mechanism for promoting sustainability (Walker et al. 2023).

4.2. Response Capacity as a Measure of the Adaptive Ability of a Community

Response diversity has commonly been calculated in response to some defined environmental change (Bartomeus et al. 2013; Laliberté et al. 2010; Ross et al. 2023). Measuring response diversity with respect to the environmental change a community experiences suggests that response diversity need not be an intrinsic property of a community, but that it depends on the extrinsic environmental context. Yet, the capacity of a community to respond to environmental change is ultimately determined by the suite of traits that characterise the species in the community (Elmqvist et al. 2003; Mori, Furukawa, and Sasaki 2013). We propose a way to calculate the response diversity of a community with respect to the environmental variables used to derive the response surfaces, but unrelated to the actual trajectory of environmental change experienced by the community. This new approach, which we call response capacity, can be used to systematically measure response diversity to any potential environmental change.

The applications of response capacity are potentially broad. Response capacity provides information about the regions of environmental variable space where a community can be expected to be stable, and where it can be expected to be unstable (Figure 3). By assembling experimental or artificial communities with the highest possible response capacity in specific portions of the environmental surface, with environmental variables fluctuating stochastically, response capacity may provide an operationalisable way to promote stable ecosystem functioning through time (Mori, Furukawa, and Sasaki 2013). Experimentally assembling communities with different response capacities may also be used to test various ecological questions. For example, communities assembled along a gradient of response capacity could be used to directly test the link between response diversity and temporal stability, providing new insight into mechanistic links between response diversity and temporal stability in a way that moves beyond the context dependence of specific environmental change scenarios.

We focused so far on how to calculate response capacity using species' entire performance surfaces. However, often we have a priori expectations regarding environmental change scenarios (e.g., 2° warming, higher nutrient load), rather than a totally naive trajectory of future environmental change (IPCC 2019). Any given environmental change scenario corresponds to a limited proportion of a response surface, so response capacity can be refined and calculated only for that area. This allows predicting how well a community may be “insured” against environmental change as represented under that specific environmental change scenario (Loreau et al. 2021). This approach should, therefore, facilitate specific predictions about response diversity and, in turn, ecological stability in response to anticipated future environmental change scenarios.

Finally, response capacity as discussed so far is derived from species response surfaces, which may or may not be measured for species in isolation. If surfaces are measured for species in isolation, those surfaces represent the fundamental response capacity of a community. The fundamental response capacity—as opposed to a realised response capacity which could be measured directly from a community of interacting species—does not account for the potential for species interactions to modify response surfaces (Ockendon et al. 2014), nor for eco‐evolutionary dynamics that may shift species responses (Fussmann, Loreau, and Abrams 2007). While these ideas have significant implications that future work should address, theoretical expectations and empirical evidence suggest that species responses to environmental change, particularly when such change is large, should play a larger role in shaping species responses than species interactions (Ives, Gross, and Klug 1999; Ives and Carpenter 2007; Ruiz‐Moreno, Emslie, and Connolly 2024). In this case, species response surfaces can provide realistic expectations about response capacity, regardless of whether they are measured in a community context or for species in isolation. Although most theoretical and empirical studies focus on species interactions within taxonomic groups or trophic levels, new theoretical evidence suggests that response diversity is also a major driver of stability in complex food webs (Danet et al. 2024). Empirical tests of these theoretical expectations are currently lacking, representing a clear avenue for future response diversity research.

4.3. On the Determinants of Response Diversity to Multifarious Environmental Change

Our work based on simulated species responses shows that, when there the influence of one environmental variable dominated, the response diversity to the dominant variable determined whether a community could achieve high response diversity. In these cases, the diversity of responses to the other variable(s) becomes secondary. Thus, in cases where one environmental variable dominates, response diversity largely behaves as it would to a single (dominant) variable. This is similar to recent meta‐analyses of freshwater systems, which found that net impacts of multiple environmental variables are usually best explained by the effect of the stronger variable alone (Birk et al. 2020; Morris et al. 2022). Hence, response diversity may be largely driven by the interspecific diversity in responses to a single, dominant, environmental variable in many real‐world systems (Bray et al. 2019). If dominant drivers are identified for particular organism groups, focusing only on the dominant drivers can save research effort when studying response diversity.

When environmental variables have the same influence on species responses, the correlation in response diversity between different environmental variables becomes pivotal for driving response diversity. Although variable dominance is common, at least in some systems (Bray et al. 2019; Morris et al. 2022), additive and synergistic interactions between environmental variables also occur (Birk et al. 2020; Crain, Kroeker, and Halpern 2008; Jackson et al. 2016). In these cases, diversity in responses to all environmental variables will modulate total response diversity.

Whether response diversity changes depending on features of the environmental variable for which response diversity is measured has been suggested as an important but little explored aspect of response diversity (Laliberté et al. 2010; Mori, Furukawa, and Sasaki 2013).

Response diversity was highest when the environmental variables fluctuated around intermediate mean values. When the environment was fluctuating around more extreme values, independently of whether it was doing so at the lower or higher end of an environmental gradient, response diversity was always lower than when environments fluctuated around intermediate values (Figure 5). Previous studies have concluded that environmental change can reduce both functional redundancy and response diversity because of species loss (Laliberté et al. 2010; Mori, Furukawa, and Sasaki 2013). Our study shows that even without losing species (we did not simulate species losses or gains), response diversity strongly depended on the values of the environmental variables. This appears to be the case independently of the correlation in diversity in species' responses to environmental variables. Indeed, even when interspecific diversity in species responses to both environmental variables was high, variables fluctuating around high or low mean values reduced response diversity compared to when the environment fluctuated around intermediate values.

Critically, Mori, Furukawa, and Sasaki (2013) suggested that if aiming to conserve an ecosystem's ability to deliver functions and services, the specific relationship between response diversity and anthropogenically driven environmental change is substantially more important than just measuring response diversity under unperturbed conditions. Here, we take a first step towards unveiling the mechanistic basis of the relationship linking response diversity to environmental change. We not only explore this relationship in general terms, but specifically in a multifarious environmental change context, which is widely recognised as the norm in real‐world systems in the Anthropocene (Bowler et al. 2020).

Numerous other determinants of response diversity could be conceived. For example, other features of species' performance–environment relationships (e.g., different shapes of species performance curves; cotolerance and antitolerance to multiple variables; Vinebrooke et al. 2004), and different scenarios of environmental change (e.g., different magnitudes of fluctuations in the environmental variables; different correlations in temporal change of the environmental variables, see Appendix S1: Section 6 Response diversity calculation) may affect response diversity. While investigating these and other factors would be informative, we wanted to explore determinants of responses that (i) have been previously identified as important, (ii) are mainly relevant for situations where more than one environmental variable influences species responses and (iii) can be empirically tested with relative ease.

5. Conclusions

We propose an empirically tractable method for quantifying response diversity in the context of multifarious environmental change that can be applied to experimental as well as observational studies. We showed how response diversity is measured when multiple environmental drivers are simultaneously changing depending on the trajectory of environmental change. Moreover, we proposed a way to calculate the response capacity of a system when the trajectory of the environmental change is undefined—that is, an estimate of the insurance capacity of a community under any possible environmental change scenarios (Yachi and Loreau 1999; Loreau et al. 2021). Finally, we explored the determinants of response diversity in a multifarious environmental change context. We showed how response diversity is determined by the diversity in species' responses to each environmental variable, as well as by the correlation in species responses to these drivers. We also found that response diversity strongly depends on the mean value around which the environment fluctuates, and on the effects of each environmental variable on species' traits. In sum, by extending the response diversity framework we make an important step towards understanding the insurance capacity of ecological communities in the Anthropocene in the face of unprecedented and multifarious environmental change.

Author Contributions

Francesco Polazzo: conceptualization, data curation, formal analysis, investigation, methodology, writing – original draft. Romana Limberger: data curation, writing – review and editing. Frank Pennekamp: conceptualization, investigation, writing – review and editing. Samuel R. P. ‐J. Ross: conceptualization, writing – review and editing. Gavin L. Simpson: formal analysis, writing – review and editing. Owen L. Petchey: conceptualization, data curation, formal analysis, funding acquisition, investigation, writing – original draft, writing – review and editing.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Appendix S1.

Appendix S2.

Data Availability Statement

Code and data to reproduce the analysis can be found on Github: https://github.com/FrancescoPola/response‐diversity‐multifarious‐environmental‐change/releases/tag/v4.0.0, and have been deposited in Zenodo with doi: 10.5281/zenodo.14065181. The original data used in this manuscript can be found at: https://zenodo.org/records/1247453.