Integrating multiple dimensions of ecological stability into a vulnerability framework

1. Ecological stability encompasses multiple dimensions of functional and composi - tional responses to environmental change. Though no single stability dimension used in isolation can fully reflect the overall response to environmental change, a common vulnerability assessment that integrates simultaneously across multi - ple stability components is highly desirable for ecological risk assessment. 2. We develop both functional and compositional counterparts of a novel, integra - tive metric of overall ecological vulnerability (OEV). We test the framework with data from a modularized experiment replicated in five lakes over two seasons, examining functional and compositional responses to both pulse and press dis - turbances across three trophic groups. OEV is measured as the area under the curve integrated over the entire observation period, with the curve delimiting the difference between the disturbance treatment and undisturbed parallel con - trols, expressed either as the log response ratio of biomass (functional OEV) or community dissimilarity index (compositional OEV). 3. Both, functional and compositional OEV correlated negatively with functional and compositional ‘resistance’, ‘temporal stability’ and ‘final/extent of recovery’ following both pulse and press disturbances, though less so with ‘resilience’ fol - lowing a pulse disturbance. We also found a positive correlation between func - tional and compositional OEV, which reveals the potential to also evaluate the intricate linkage between biodiversity and functional change.


| INTRODUC TI ON
Ecological stability is the general framework for understanding the inherent property of ecosystems to remain unchanged (Pimm, 1991).
Over the past decades, ecologists have developed many metrics to describe different aspects of stability such as resistance, engineering resilience, temporal stability and final recovery (Donohue et al., 2016;Kéfi et al., 2019;Hillebrand et al., 2018;Pimm, 1984).
However, most studies to date generally focus on describing one single stability component in response to one single disturbance type (Donohue et al., 2016).Recent findings have demonstrated that the ecological stability of a system is multidimensional, where different stability components are more or less correlated with one another (Donohue et al., 2013(Donohue et al., , 2016;;Hillebrand et al., 2018;Yang et al., 2019).
These findings suggest that no single component itself reflects the integrated stability of the entire system (Donohue et al., 2013;Yang et al., 2019).Furthermore, the effective dimensionality of stability that emerges from the strength of these relationships can vary depending on the type of disturbance (Donohue et al., 2013;Polazzo & Rico, 2021;Radchuk et al., 2019), the organisms or ecological properties affected (Kéfi et al., 2019) and the spatial and temporal context in which disturbances occur (Clark et al., 2021;Güelzow et al., 2017;Levin, 1992).Thus, it is becoming increasingly clear that a multidimensional analytical approach to the study of stability is needed to reduce the risk of underestimating the overall impact of disturbances.Such multidimensional approach is increasingly important in a world facing rapid and growing environmental change (IPCC, 2013;Millennium Ecosystem Assessment, 2005).
Each stability component is unique in the type of information it provides, and the study of stability cannot therefore be simplified to analysis of a single metric in isolation (Donohue et al., 2016;Ives & Carpenter, 2007;Pimm, 1991;Radchuk et al., 2019).Even so, the need to assess risks and prioritize management actions calls for an integrative measure that effectively captures multiple dimensions of stability in an overall vulnerability metric.Ideally, such a metric would allow comparison of the impact of different disturbances with different trajectories, such as pulse disturbances (changes with finite duration) and more consistent press disturbances.There is clear indication that both pulse (e.g.fires, floods, heat waves and storms; IPCC, 2013; Stockwell et al., 2020) and press (e.g.species loss, biological invasions, acidification; Donohue et al., 2016;IPBES, 2019) disturbances are becoming more frequent and intense across the globe.Even though pulse disturbances are temporally constrained, there is increasing evidence that they may be at least as important in driving long-term community dynamics compared to press disturbances (Jentsch et al., 2007;Lawson et al., 2015;Urrutia-Cordero et al., 2020) and can have long-lasting, persistent effects even after the disturbance per se has ended (Hillebrand et al., 2018).
To be fully operational, an integrative vulnerability metric should work not only for pulse and press perturbations, but also enable exploration and quantification of links between functional and compositional change.The links between functional and compositional change could, for example, be explored where it is possible to compute both functional and compositional counterparts of the same vulnerability metric, and examine their interrelationships (see,

K E Y W O R D S
biodiversity, communities, dimensionality, disturbances, ecological risk assessment, ecological stability, ecosystem management, vulnerability e.g. this principle used for other stability components in Hillebrand et al., 2018 andWhite et al., 2020).Understanding these interrelationships is important because biodiversity change in terms of species composition (i.e.compositional turnover) is a major mechanistic basis to explain the relationship between species richness and functional stability over time (Cleland, 2011).In contrast, it is less clear how biodiversity changes modulate stability components other than temporal variability (Ives & Carpenter, 2007).Recent results from mesocosm experiments testing the impacts of pulse disturbances revealed that multiple functional and compositional stability components may be coupled (Hillebrand et al., 2018).More generally, a recent meta-analysis spanning 508 field experiments globally distributed across marine, terrestrial and freshwater ecosystems found that functional recovery from pulse disturbances can be achieved with or without compositional recovery (Hillebrand & Kunze, 2020).
These results strongly indicate the need to integrate both functional and compositional responses in the study of the overall ecological vulnerability (OEV) of a system if we are to understand and predict the broader consequences of biodiversity change for ecosystems (Pimm et al., 2019).
Here, we develop an analytical framework that integrates multiple dimensions of stability for pulse and press disturbances into a single integrated metric, which we call OEV, from which we can quantify both its functional and compositional counterparts.We then test both functional and compositional counterparts of this metric by analysing the responses of three trophic groups of organisms (i.e.lake zoo-, phyto-and bacterioplankton) to the same pulse (presence of a planktivorous fish) and press (reduced light availability) treatments, both in isolation and combination, in 10 outdoor mesocosm experiments replicated across both space (five Scandinavian lakes) and time (two seasons).OEV was measured as the area under the curve integrated over the entire observation period, with the curve delimiting the difference between the disturbed treatment and parallel undisturbed controls under ambient conditions, expressed either as the log response ratio of biomass (functional OEV) or community similarity index (compositional OEV) between the disturbance treatment and the control (Table 1; Figure 1a-f).A major advantage of the framework is that it enables the quantification of OEV for both function and composition regardless of either disturbance or community type, while simultaneously integrating across multiple dimensions of stability.
We first assessed the capacity of OEV to integrate across multiple dimensions of stability to both pulse (resistance, resilience, temporal stability and final recovery) and press (rate of deviation, temporal stability and extent of recovery) disturbances (Table 1).We predict that both functional and compositional OEV correlate negatively with all of the measured functional and compositional stability metrics for pulse and press disturbances.We then investigated the functional consequences of biodiversity change by examining how compositional OEV relates to functional OEV across both pulse and press disturbances.Finally, we test the potential of our framework to reflect the overall functional and compositional vulnerability of each trophic group to pulse and press disturbances acting both in isolation and combination across all experiments.We thus exemplify the generality of the metric in the context of a modularized experiment across space and time, thus exposing it to considerable variation in local environmental conditions.

| Experimental data
We used data from a modularized lake mesocosm experiment done with the newly established SITES AquaNet infrastructure (see Urrutia-Cordero, Langvall, et al., 2021 for a detailed description of the infrastructure).The modularized experiment comprised of 10 individual experiments performed in five different lakes in Sweden over two seasons.Each experiment lasted 28 days.Five experiments (one in each lake) started in June 2017 (hereafter, 'Spring' experiments), and the remaining five in August 2017 ('Summer' experiments).The lakes (Feresjön, Bolmen, Erssjön, Erken and Stortjärn) span along a latitudinal and climatic gradient in Sweden, thus differing considerably in local environmental conditions such as temperature, nutrient status and humic content (Table S1).
Each experiment consisted of 16 mesocosms (polyethylene enclosures, 0.8 m diameter, 1.5 m height, 700 L volume; Cipax AB) filled with 550 L unfiltered water from the lake in which they were located.
The mesocosms were deployed under water (except the top 30 cm) using ropes attached to a jetfloat facility (Jetfloat International Gmbh).Each experiment comprised of four treatments, each replicated four times, resulting in 160 unique experimental units: (a) no experimental disturbance; (b) a pulse disturbance in the form of fish addition, where we added two juvenile crucian carp Carassius carassius (mean ± SD length: 5.77 ± 0.74 cm) to the mesocosms for the first 7 days of the experiment; (c) a press disturbance in the form of constant shading, where we placed a dark polyester mesh on top of the mesocosms reducing incoming light by approximately 50%; and (d) the pulse and press disturbances combined.We used a transient presence of a top consumer as pulse disturbance because small water bodies and lakes can experience fish colonization and extinction and/ or transient migratory patterns leading to sudden changes in fish predation pressure on zooplankton communities (Brönmark et al., 2014).
In addition, changing temperatures and heat waves directly affect predation and reproduction rates of planktivorous fishes, with subsequent cascading effects on lower trophic levels (Hansson et al., 2013;Jeppesen et al., 2014).The press disturbance aimed to mimic increased light limitation experienced by boreal and subarctic lakes as a result of increased precipitation and associated cloud cover from climate change (Weyhenmeyer et al., 2016).Furthermore, a reduction of light availability is one of the most important consequences of 'lake browning' from the discharge of terrestrially derived humic substances (Karlsson et al., 2009;Kritzberg et al., 2019).
We sampled each mesocosm six times, on days 1 (just before the experimental treatments were applied), 4, 7, 9, 14 and 28.We measured: (a) zooplankton biomass (function), using light TA B L E 1 Description and measurement of functional and compositional stability for both pulse and press disturbances.Measurement timing indicates when during the experiment each stability aspect was measured.

Overall ecological vulnerability
Resistance Final recovery

| Calculation of OEV
We quantified the OEV of a system to a pulse, press and the combination of both disturbances by measuring the area under the curve (AUC) over the entire time series of the functional log response ratio (functional OEV) or community similarity index (compositional OEV) between the disturbance treatment and the undisturbed control (Table 1; Figure 1a-f).We created plots for each mesocosm time series based on the log response ratio of biomass/abundance and community similarity index relative to mean control conditions (Figures S1-S3).To derive the log response ratio (LRR) from each mesocosm for functional OEV, we used the mean of the four replicated control functional values (total community biomass/abundance) as a benchmark for each sampling point , we predict greater OEV when both perturbations act in concert than separately (AUC red > AUC blue or AUC yellow).If pulse and press perturbations have opposing impacts on a function (h-i; phytoplankton and bacteria), we expect lower overall vulnerability when both disturbances act in concert than the sum of the two separately (AUC red < AUC blue + AUC yellow).For compositional responses, we expect greater overall vulnerability when both perturbations act in concert than separately (AUC red > AUC blue or AUC yellow) regardless of the trophic level (j-l)

| Calculation of individual stability components for pulse and press disturbances
We calculated multiple stability components for pulse disturbances following the analytical framework of Hillebrand et al. (2018), which we extended to also include the measurements of stability for press disturbances (Table 1; Figure 1).We calculated four stability components for each mesocosm that received a pulse disturbance (Table 1).
'Resistance' is the initial response to the pulse, and was calculated as the difference between the disturbed community and the control community at the sampling when the pulse disturbance ceased (i.e. at day 7).'Resilience' is the rate of recovery from the pulse disturbance, and was measured as the slope of the linear regression of the difference between the disturbed community and the control community after the pulse disturbance ceased (i.e. from sampling days 7 to 28).Linear regression was used due to the recovery trend being linearized based on the log-transformed response variable.
'Temporal stability' over the recovery trend was measured as the log (x + 1) of the inverse of the standard deviation of model residuals of the linear regression described above for resilience.'Final recovery' is the final measurable response to the disturbance, and was calculated as the difference between the disturbed community and the control community at the end of the experiment (i.e. at day 28).
For the press disturbance, we calculated three stability components (Table 1): rate of deviation over time, temporal stability over the deviation trend and extent of recovery.The rate of deviation over time and temporal stability over the deviation trend for press disturbances were measured in the same way as resilience and temporal stability for pulse disturbances, except that they are calculated from the commencement of the press disturbance (i.e. over the entire experimental period).Extent of recovery was measured for press disturbances in the same way as final recovery for pulse disturbances.
We restricted our analyses of the combined pulse and press disturbance treatment to stability components for pulse disturbances only because of constraints caused by linearizing the potential deviation trend induced by the press disturbance with the additional presence of a pulse disturbance.Including measurements from the combined pulse and press disturbance treatment in our analyses thus enabled us to explore whether the relationships between stability components for pulse disturbances and the OEV metric differed between systems with and without additional stress by press disturbances.

| Data analyses
We evaluated how OEV integrates multiple stability components for both pulse and press disturbances separately by exploring relationships between OEV and each stability component using Spearman rank correlations.We did this for both functional and compositional counterparts of OEV.We also used Spearman rank correlations to examine the relationships between functional and compositional OEV, and explore the functional consequences of biodiversity change within trophic groups of organisms.Functional stability components were standardized prior to analysis (  1).Unlike functional components, compositional stability components did not require prior standardization because they all integrate within the same scale from 0 to 1 (Table 1).
We tested the applicability of OEV to depict overall functional or compositional vulnerability of each of the organism groups to pulse or press disturbances, both in isolation and combination (Figure 1el).We used linear mixed models (LMMs) to test for disturbance effects across all experiments on the functional and compositional OEV of each trophic group.We included trophic group and experimental treatment (nested within community type) as fixed explanatory variables and lake and season (nested within lake) as random components in all models.For each LMM, we square root transformed the response variable (functional and compositional OEV) in order to achieve normality in the distribution of the residuals of the models after exploration with q-q plots.Having square root transformed OEV values also aided in visualizing patterns emerging in the correlation plots given the range in the original OEV values.All analyses were run with the 'lmer' function (package: lmerTesT) and figures were created with 'ggplot2' (Wickham, 2016) in R (version 4.0.0;R Core Team, 2020).

| Integration of multiple stability components into overall functional and compositional vulnerability
Both functional and compositional OEV showed a negative correlation with all stability components except for resilience following our pulse disturbance (Figure 2; Table S2).For functional aspects, we found similarly strong relationships between OEV and resistance, the rate of deviation for press disturbances, temporal stability and final/extent of recovery (Figure 2a; Table S2, p < 0.001 in all cases, −0.829 ≥ rho ≥ −0.542).For compositional aspects, correlations between OEV and both resistance and final/extent of recovery were similarly strong as for functional aspects (Figure 2; Table S2, for press disturbances (Figure 2; Table S2, p = 0.004, rho = −0.265)and temporal stability (Figure 2; Table S2, −0.438 ≥ rho ≥ −0.279).

| Linkages between functional and compositional vulnerability
The correlation between functional and compositional OEV was significant across all communities and all treatments (Figure 3; Table S3, p < 0.001 in all cases, 0.709 ≥ rho ≥ 0.530).We found, however, that high compositional OEV could be associated with either high or low functional OEV, whereas low compositional OEV was associated only with low values of functional OEV (Figure 3).
Correlations between functional and compositional aspects of OEV also varied among the biological communities under scrutiny, with significant positive correlations for all perturbed treatments in zooplankton communities (Figure 3; Table S3, p < 0.001 in all cases, 0.825 ≥ rho ≥ 0.503) compared to phytoplankton and bacterial communities (Figure 3; Table S3, almost no significant correlations).

| Overall functional and compositional vulnerability to pulse and press disturbances
Though OEV revealed a strong overall vulnerability for each of zoo-, phyto-and bacterioplankton communities in response to our experimental perturbations across all sites and seasons, we found differences in responses among the three trophic groups we examined (Table 2).Zooplankton displayed the strongest functional vulnerability across all disturbance types (pulse and press) followed by the phyto-and bacterioplankton (Figure 4; Table 2, p ≤ 0.001, larger negative estimate in Bact vs. Zoop than Phyto vs. Zoop).
Functional OEV to the pulse perturbation was greatest in the zooplankton, followed by the phytoplankton (Figure 4; Table 2, larger significant difference between the pulse treatment and control in zooplankton compared to phytoplankton), whereas the pulse perturbation had no effect on the functional OEV of the bacterioplankton (Figure 4; Table 2).For compositional OEV, zooplankton composition was most vulnerable, followed by that of bacterio-and phytoplankton (Figure 4; Table 2, larger significant difference between pulse treatment and control in zooplankton compared to bacteria and then phytoplankton).
The phytoplankton were functionally vulnerable to the press perturbation across all sites and seasons (Figure 4; Table 2, significant difference between the press treatment and control), whereas there were no significant effects on the functional vulnerability of the zoo-or bacterioplankton (Table 2).Moreover, our press perturbation had no effect on the compositional OEV of any of our focal trophic groups (Table 2).
Even though we did not see significant effects of our press perturbation on the functional vulnerability of zooplankton, the effects of the combined pulse and press perturbations were larger than those of the pulse perturbation in isolation (Figure 4; Table 2, larger significant difference between the combined pulse and press treatment and control compared to the significant difference between pulse treatment and control).We also found significant effects of the  2).
For compositional aspects, we also observed larger compositional vulnerability to the combined perturbations compared to the pulse and press perturbations in isolation (Figure 4; Table 2), despite no significant effects of shading in isolation in any community (Table 2).

| DISCUSS ION
Our study reveals several strengths of OEV as a potential management tool for ecological risk assessment.First, a critical advantage of using the OEV metric is its strong connection with a diverse range of stability components for both pulse and press disturbances.While some studies have employed an area under the curve approach to depict certain properties of stability (Todman et al., 2016;Zhang et al., 2010), none have actually evaluated how a metric such as OEV integrates across multiple stability components for both functional and compositional aspects.Functional and compositional OEV correlated negatively with their respective functional and compositional aspects of resistance, temporal stability and final/extent of recovery for pulse and/or press disturbances, but less so with resilience after a pulse.The observed inverse correlations are consistent with our predictions, and indicate that OEV acts as a robust and integrative metric of multiple dimensions of stability.Indeed, no other stability metric showed such strong relationships with other stability components (Figures S4 and S5).That OEV integrates across multiple dimensions of stability means that if either resistance, temporal stability or final/extent of recovery is low, the OEV of a system to a disturbance is consequently high and vice versa.While each stability component is unique in the type of information delivered (Kéfi et al., 2019) and no single stability metric can reveal the entire complexity of ecological stability (Hillebrand et al., 2018), these findings reveal that OEV integrates multiple dimensions of stability robustly and can thereby offer managers a straightforward and conceptually simple framework for assessing ecological risk.Though we test the applicability of our vulnerability framework in freshwater systems, OEV should also be a good candidate for other systems.However, its potential applicability across ecosystem realms needs to be investigated given that different ecological traits of organisms, as well as changing environmental contexts or disturbance types, have been shown to alter the effective dimensionality of ecological stability (Donohue et al., 2013(Donohue et al., , 2016;;Kéfi et al., 2019;Polazzo & Rico, 2021;Radchuk et al., 2019).
Though we did not find similarly strong correlations between the functional and compositional OEV with functional or compositional resilience from pulse disturbances compared to other stability metrics (Figure 2; Table S2), resilience and OEV were nonetheless interlinked.Communities with high resistance tend to show resilience values around 0, mainly because a community that is barely disturbed initially has little to recover from (Figures S4 and S5).Hence, stratifying the correlative analyses between OEV and resilience with ranks based on resistance values aids in removing the contribution of resistance to the apparent relationship between OEV and resilience.
On doing this, we found that communities that initially responded in similar ways to the disturbances (i.e.within the same ranks based on initial stability values) showed overall lower functional and compositional OEV with higher resilience (Figure S6).
Our results also show a strong positive relationship between overall compositional and functional vulnerability across all trophic groups.That is, the higher the compositional vulnerability, the greater the functional consequences (Figure 3; Table S3).Thus, OEV emerges as an effective tool to explore the functional consequences of biodiversity change.The trophic group comprising the fewest taxa (i.e. the zooplankton) drove the positive relationship between compositional and functional vulnerability (Figure 3; Table S3).In other words, in more diverse trophic groups (phyto-and bacterioplankton; Figure S7), functional stability (i.e.low functional vulnerability) can be achieved with or without compositional stability (Figure 3).
Although further evidence is needed to confirm the mechanism underpinning these patterns, it is likely that this was caused because more diverse communities generally hold higher functional redundancy, and thereby larger potential to experience compensatory dynamics among different taxa that stabilize biomass production at the community level (Allan et al., 2011;Gonzalez & Loreau, 2009).
The utility of the OEV metric is exemplified by results from our modularized experiment.Urrutia-Cordero, Langenheder, Although each analytical approach is different in the type of information provided, we show that an important advantage of using functional and compositional OEV as response variables (as shown in this study) is the possibility to also investigate the linkage between its functional and compositional counterparts, as well as with other stability metrics in a relatively straightforward way.
It is important to stress that OEV does not give the direction of the response, though this information can also be obtained.
For functional OEV, the difference between the area with positive sign and the area with negative sign from the LRR time series (Figures S1-S3) would be indicative of the direction of the response across the entire experimental period.For compositional OEV, one can take the initial dissimilarity values as a benchmark and do the same procedure by taking the area above and below that benchmark.Furthermore, our analytical framework should work not only for experimental settings, but also for ecological risk assessments based on natural observations when it is possible to obtain baselines derived from pre-disturbance conditions (Wright et al., 2015) or from comparable undisturbed whole ecosystems (Wilkinson et al., 2018).Our findings should, therefore, provoke discussions on which stability metrics should be measured and prioritized for ecological risk assessments.Understanding the connection of other known metrics with OEV can also help us reveal under which circumstances each of these other metrics best represent the OEV of a system.Generating such understanding is important because ecological risk assessments might need to rely on information provided by a stability metric that is simpler to measure over a time TA B L E 2 Results from LMM analyses evaluating the response of zoo-, phyto-and bacterioplankton communities to pulse and press disturbances captured by functional and compositional OEV across all experiments.The degree of variation explained by the fixed effects is indicated by m-R 2 , whereas c-R 2 stands for the total variation explained including both fixed and random effects.Black-bolded pvalues and black-bolded p-values in brackets denote significant effects of the explanatory variables at α = 0.05 and α = 0.1 respectively.Zoop = Zooplankton, Phyto = Phytoplankton and Bact = Bacterioplankton

4.
Our findings demonstrate that OEV comprises a robust framework to: (a) capture simultaneously multiple functional and compositional stability components, and (b) quantify the functional consequences of biodiversity change.Our results provide the basis for an overarching framework for quantifying the overall vulnerability of ecosystems to environmental change, opening new possibilities for ecological risk assessment and management. 5. Synthesis.Ecological stability comprises multiple dimensions that together encapsulate how ecosystems respond to environmental change.Considering these multiple aspects of stability simultaneously often poses a problem in environmental assessments, which frequently require overarching indicators of risk or vulnerability.While an analysis of multiple dimensions allows for deeper exploration of mechanisms, here we develop and test a new univariate indicator that integrates stability aspects under a broad range of disturbance regimes.Using a modularized experiment in Swedish lakes, we show that this integrative measure captures multiple stability dimensions reflecting compositional and functional vulnerability and their relationships between them.
b) phytoplankton biomass (function), derived from chlorophyll a analyses; (c) bacterial abundance (function), using flow cytometry; (d) zooplankton community composition (genus level), using light microscopy; and (e) phytoplankton and (f) bacterial community composition derived from 18S and 16S rRNA amplicon Illumina sequencing at the ASV level respectively.Because the original compositional dataset derived from 18S rRNA amplicon Illumina sequencing included eukaryotes other than phytoplankton, prior to our analyses we removed other taxa than phytoplankton from that dataset.See Urrutia-Cordero, Langenheder, et al. (2021) for further details on the methods during sampling and sample analyses and mesocosm performance.The study was approved by Uppsala animal ethics committee (permission number 5.8.18-03672/2017).

(
LRR = ln(treatment unit/control mean)).To estimate the variability within the control treatment, we ran the same calculations by comparing each control replicate value against the control mean within each sampling point (LRR = ln(control unit/control mean)).To derive compositional responses (for compositional OEV), we calculated the Bray-Curtis dissimilarity(Bray & Curtis, 1957) for each treatment mesocosm from the mean value compared to each of the four control replicates.Again, we did the same for each control replicate as mean dissimilarity to the other replicates to benchmark the variability within the control treatment without disturbances.Once we obtained these standardized time series based on the log response ratio and community dissimilarity index for each mesocosm (FiguresS1-S3), we calculated AUC using the 'pk.calc.auc'function from the pknca package(Denney et al., 2015) in R (version 4.0.0;R Core Team, 2020).For functional responses (functional OEV), a log response ratio of zero indicates no deviation from control conditions, thus the AUC is calculated with zero as a benchmark.For compositional responses (compositional OEV), dissimilarity values of 0 and 1 represent, respectively, a total compositional convergence or divergence relative to control conditions, thus AUC is also calculated with 0 as a benchmark (Figure1d-f).F I G U R E 1 Conceptual illustration of the measurement of overall ecological vulnerability (OEV) and its relationship with other stability components.(a-f) OEV is measured as the area under the curve (AUC) over the entire time series of the functional log response ratio (a-c) (functional OEV) or (d-f) community dissimilarity index (compositional OEV) a disturbed treatment and an undisturbed control.Yellow, blue and red backgrounds denote the AUC (light colours if positive responses, darker colours if negative) for pulse, press and combined pulse and press treatments respectively.The vertical black lines delimit the duration of the pulse disturbance (here, fish presence), whereas the dark grey background represents the duration of the press perturbation (here, shading).Other stability components are: RST = Resistance, FR = Final recovery, RSL = Resilience, TS rt = Temporal stability over recovery trend, RD = Rate of deviation, TS dt = Temporal stability over deviation trend and ER = Extent of recovery.(g-l) Expected responses of different trophic groups.If pulse and press disturbances have both a negative effect on a function (g; zooplankton) Bivariate relationships between each measured stability component and overall ecological vulnerability (OEV) to pulse and press perturbations for (upper panel) functional and (lower panel) compositional stability components.Each sample unit is a mesocosm replicate from one of the 10 experiments from the pulse (yellow), press (blue) and pulse and press (red) perturbation treatments.Circles = zooplankton, triangles = phytoplankton and squares = bacteria.For simplicity, we combined in the same plot data for resilience (RSL) for pulse perturbations and the rate of deviation (RD) for press perturbations (as both stability components represent rates of change over time), temporal stability over the recovery trend for pulse perturbations (TS rt ) and temporal stability over the deviation trend for press perturbations (TS dt ), and final recovery for pulse perturbations and extent of recovery for press perturbations combined pulse and press perturbation on the functional vulnerability of phytoplankton, which matched well the addition of the effects of the pulse and press perturbations in isolation (Figure4; Table

F
I G U R E 3 Relationship between the compositional and functional aspect of overall ecological vulnerability (OEV).Each sample unit is a mesocosm replicate from one of the 10 experiments from the pulse (yellow), press (blue) and combined pulse and press (red) perturbation treatments.Filled circles = zooplankton, open triangles = phytoplankton and open squares = bacteria.Please see Figure S8 for visualization of patterns separated for the three communities URRUTIA-CORDERO ET Al. et al. (2021) describe the outcome of the experiments in the form of the direct measured response variables for each taxonomic group (biomass/abundance and community turnover) and presents statistical analyses across sites and seasons.Urrutia-Cordero, Langenheder, et al. (2021) also extend on discussions on the observed response differences across disturbance types and communities.The modularized multitrophic structure of this experiment thus represents an ideal test case to illustrate how functional and compositional OEV could be applied to experiments if we want to compare different types of disturbances, different local ecosystems and different trophic groups.Specifically, we found strong differences in the overall vulnerability of zoo-, phyto-and bacterioplankton to both pulse and press disturbances across sites and seasons, with zooplankton communities being the most vulnerable community to the pulse disturbance and phytoplankton communities to the press disturbance.

Stability metrics for press perturbations Resilience Temporal stability over recovery trend Overall ecological vulnerability Extent of recovery Rate of deviation Temporal stability over deviation trend
i = intercept, t = time Table 1).Because initial functional responses to disturbances (resistance) can be positive or negative, either negative or positive functional resilience values can indicate functional recovery.For example, a positive slope over the recovery trend (i.e. a positive resilience value) indicates recovery only if the resistance value of the same mesocosm was negative, whereas a negative slope (i.e. a