A fundamental trade‐off among resilience, resistance, efficiency, and redundancy in tidal wetlands

Abstract

In an era of change, the survival and adaptability of ecosystems will be tested. An optimal ecosystem would be both resistant and resilient to negative disturbance but also efficient and redundant in its growth when given positive subsidies. However, initial evidence has suggested that these properties cannot all be maximized at the same time, and so we sought to quantitatively assess whether there are fundamental trade‐offs between them at the ecosystem level. To achieve this aim, we used a 250‐m resolution NASA MODIS dataset of gross primary productivity (GPP) to monitor 145,871 tidal wetland locations across the conterminous United States every 16 days from March 2000 to December 2020. We quantified the size and duration of the perturbation events in tidal wetland GPP (n = 13,754,386) and modeled their frequency distributions. Event sizes and recurrence intervals were exponentially distributed and event durations were closely modeled by an inverse power law. This scale‐free manner through which tidal wetlands dissipated perturbations to their GPP flux provided them with long‐term stability across a wide range of geography. We also found that a tidal wetland's positive event responses traded off between properties of efficiency and redundancy, its negative events traded off between resistance and resilience, and that all four properties were orthogonally related to one another. We then constructed a conceptual model to help understand the potential mechanism behind this four‐quadrant trade‐off. The trade‐off appeared to be driven by a feedback between the waiting time and magnitude of positive and negative events, the duration of their effects, and the environmental and physical constraints limiting an ecosystem's growth and productivity. In summary, we detail an emergent pattern of trade‐offs and constraints associated with how tidal wetland ecosystems respond to both positive and negative perturbations in carbon flux.

INTRODUCTION

In an era of changing and intensifying disturbance regimes, the performance of ecosystems will be tested. As disturbance regimes become increasingly extreme, insight into the current limits of ecosystems to withstand these pressures and sustain function is vital for predicting and managing their future trajectories. Ecosystems vary in their capacity to mitigate the negative effects of disturbances, such as damaging hurricanes or droughts, with some ecosystems better able to withstand and recover from these impacts than others (White & Jentsch, 2001). Ecosystems also vary in their capacity to assimilate beneficial energy inputs, such as from replenishing precipitation or nutrient subsidies (Castañeda‐Moya et al., 2020; Jentsch & White, 2019; Odum et al., 1979), with some ecosystems better able to survive and grow in suboptimal environments or when resources are limiting (Fath et al., 2004; Odum et al., 1995; Ulanowicz, 2009).

Resistance and resilience are two properties that can describe an ecosystem's response to negative disturbances (Curtin & Parker, 2014; Gunderson, 2000; Holling, 1973). Although these two terms have a wide variety of potential definitions (Ingrisch & Bahn, 2018; Martin‐Breen & Anderies, 2011; Quinlan et al., 2016), Pimm (1984) was the first to draw a quantitative distinction between them in the ecological literature. Several studies have since developed quantitative frameworks that infer resistance and resilience as emergent ecosystem properties, detectable through remote‐sensing imagery and long‐term ecological datasets (Angeler & Allen, 2016; Baho et al., 2017; Hogan et al., 2020). The prevailing measure of resistance is the effect size or magnitude of change in a response variable during a perturbation, while resilience is commonly measured as the amount of time required for the variable to return to an equilibrium following a perturbation (Holling, 1996). Across different systems, scales, and disparate response variables, ecologists have documented an apparent trade‐off between these two orthogonal quantities (Li et al., 2020; Miller & Chesson, 2009; Patrick et al., 2022). Evolutionary theory could potentially explain this pattern, as improving one property may come at a cost to the other (Allison, 2004; Bellingham et al., 1995; Thayne et al., 2021).

Similarly, efficiency and redundancy are properties that shape an ecosystem's ability to assimilate positive resource inputs into growth and productivity. Although these two terms have primarily been used by engineers when designing human and built environment systems (Chatterjee et al., 2022; Chatterjee & Layton, 2020; Dave & Layton, 2020), they have also been used by theoretical ecologists to describe the connectivity and complexity of ecological networks (Fath, 2015; Kharrazi et al., 2017; Ulanowicz et al., 2009). As a network or ecosystem receives new resource inputs, it can invest them into the construction of new components of ecosystem structure or into maintaining and reinforcing the connections and functional interactions among them (Fath et al., 2004; Odum, 1969). Quantitatively, an efficient system maximizes the component to connection ratio, while a redundant system minimizes it (Huang et al., 2024). Duplication of critical functions or components can enhance productivity and resilience to disturbances, but sustaining these redundancies requires additional energy and resources, which can strain the system, reduce overall efficiency, or increase its vulnerability to cascading failures (Inouye et al., 2021). Across both engineered and ecological systems, scientists have found that the long‐term productivity of a system is optimized within a “window of vitality” where efficiency and redundancy are balanced (Fath, 2015; Markolf et al., 2022; Ulanowicz et al., 2009).

Ecosystems are continually shaped by both positive resource pulses and negative disturbance events over time. By definition, the summary balance among individual positive and negative events, each of which occurs across a range of magnitudes, frequencies, and durations, can be considered an ecological equilibrium (Cuddington, 2001; Jentsch & White, 2019; White & Jentsch, 2001). Even an optimally balanced ecosystem would therefore need to be in a constant state of flux to maintain its equilibrium, perpetually compensating for these events through some mechanism. Potential trade‐offs and compromises imposed by physical constraints, outcomes of which are determined by the underlying structural components and functional connections that comprise an ecosystem, could provide such a mechanism. However, research in this area has been limited by the coarse scale and complexity of ecosystems, and the extensive sampling, long‐term data collection, and computing power required to capture variability and discern patterns that could reveal inherent constraints governing rare and common events alike. A big‐data, remote‐sensing approach could help in the search for such patterns.

Mixed aquatic–terrestrial ecosystems, such as tidal wetlands, are an ideal study candidate for detecting the signatures of physical constraints and trade‐offs at the ecosystem‐level because they experience a full spectrum of disturbances and energy subsidies, ranging from high‐intensity weather events to smaller scale tide and wave events (Odum et al., 1979, 1995). Such disturbances and subsidies can alter primary productivity and energy cascades through the ecosystem, and their effects can be diverse and heterogeneous across space and time (Turner et al., 1989). For example, a hurricane can physically destroy tidal wetland vegetation at one location, while also providing precipitation that enhances growth at another location (Chu et al., 2018). Tidal wetland productivity is also particularly sensitive to changes in the relative balance of freshwater versus saltwater inputs. Freshwater or nutrients added to the system can increase productivity, while waterlogged stress, saltwater intrusion, and hypersaline conditions may lead to dieback or changes in plant assemblages (Feher et al., 2017). Moreover, tidal wetlands are vitally important from a conservation standpoint, as they are among the most economically valuable ecosystems in the world due to their high productivity, storm buffering capacity, and ability to sequester carbon at rates up to one hundred times higher than terrestrial rainforests (Costanza et al., 1997; Mcleod et al., 2011). As atmospheric carbon dioxide concentrations and sea levels continue to rise globally, sustainable management of tidal wetland carbon fluxes and an improved understanding of their vulnerabilities to perturbation are urgently needed to conserve their critical role in climate regulation and coastal resilience.

We sought to uncover broad patterns in the dynamics of tidal wetland ecosystems by conducting a big‐data analysis of perturbations to their gross primary productivity (GPP), the rate at which energy and carbon are captured through photosynthesis. GPP integrates environmental conditions with biotic processes, making it a comprehensive summary metric for monitoring perturbations in ecosystem function over time and across diverse ecosystem types. Here, we developed a quantitative framework to detect and measure the frequency, magnitude, and duration of perturbations in tidal wetland GPP using a 21‐year satellite‐derived dataset spanning all tidal wetlands in the conterminous United States (CONUS). We expected these metrics to exhibit patterns and correlations that reflected constraints and trade‐offs among ecosystem properties of resistance, resilience, efficiency and redundancy, but also anticipated substantial variability in these metrics across all tidal wetlands nationwide.

METHODS

Tidal wetland GPP time series dataset

GPP (in units of grams of carbon assimilated per square meter per day) is a direct measure of the rate at which photosynthetically active biomass is able to capture solar energy used to sustain the carbon‐based organisms and processes that form an ecosystem (Feagin et al., 2020b; Odum, 1969). We used the MODIS (Moderate Resolution Imaging Spectroradiometer) MOD13Q1 tidal wetland GPP data product from the National Aeronautics and Space Administration (NASA) Oak Ridge National Laboratory (ORNL) to quantify the magnitude, duration, and frequency of perturbations to tidal wetland GPP over a 21‐year time period (Feagin et al., 2020a). This dataset provided daily averaged GPP estimates (in grams of carbon per square meter per day) at 250‐m resolution across the CONUS at 16‐day intervals from March 5, 2000 through December 2, 2020 (a total of 478 16‐day “epochs”). These 782,693 pixels contained the following tidal wetland ecosystem types: forested mangroves, herbaceous salt marshes, forested tidal freshwater swamps, and herbaceous tidal freshwater marshes.

GPP algorithm

Estimates of tidal wetland GPP for a given pixel and date were computed as a function of surface downwelling photosynthetically active radiation (PAR), surface air temperature, and Enhanced Vegetation Index (EVI) according to the following basic equation from Feagin et al. (2020b):

$$\text{GPP}=\mathrm{\epsilon }\times \text{iPAR}\times \text{fPAR}$$ (1)

where $\text{fPAR}$ is the amount of PAR intercepted by plant leaf surfaces (derived from NASA's MOD13Q1 EVI product), $\text{iPAR}$ is the incident PAR at the plant canopy (derived from relatively coarse meteorological datasets; Feagin et al., 2020a), and $\mathrm{\epsilon }$ is the plant light use efficiency (LUE), a multiplicative coefficient that describes the efficiency of converting light photons into biomass for a given plant type. LUE was a function of the minimum, maximum, and optimal temperatures at which a given plant type converts light into biomass, the actual temperature at the given time and location, light saturation, salinity, and $\text{fPAR}$, calculated using a unique Bayesian statistical framework (Barr et al., 2013).

GPP dataset curation

To maintain transparency and minimize reliance on heavily processed model inputs, we omitted EVI values flagged by NASA as spatially interpolated or assigned low quality assurance (QA) rankings. In cases of isolated missing values, we applied a conservative gap‐filling approach using the mean of the two flanking epochs, contingent on the availability of EVI for both dates at the given location. We then filtered this original dataset to only include pixels that contained 90% or greater tidal wetland class coverage, 90% or greater EVI reliability, and 90% or greater QA reliability (i.e., no clouds for at least one date of image capture during the 16‐day epoch, where the best image per epoch was used). This filtering reduced the number of pixels to 145,871 (about 19% of the original dataset), but ensured that the GPP estimates (n = 66,729,537) used in our analysis were obtained from pixels with the least amount of contamination from nontidal wetland land cover classes, and that estimates were QA‐filtered to avoid low‐reliability or overly processed inputs.

By omitting pixels with low tidal wetland coverage and QA reliability rankings, the refined GPP dataset may underrepresent fringing wetlands and overrepresent wetlands with greater vegetation coverage. Similarly, systems with large geographic areas (e.g., Louisiana Delta, Chesapeake Bay) may be overrepresented. Also, while GPP is a robust proxy for broader ecosystem function, it depicts a productivity‐centric view of ecosystem dynamics that may overlook structural variability and the critical components and processes influencing ecosystem function but not necessarily aboveground GPP. Nevertheless, pixel‐level estimates of average daily GPP revealed substantial spatial heterogeneity, with pronounced differences often observed between adjacent pixels (Figure 1), suggesting that each location represented a unique example of tidal wetland ecosystem dynamics.

FIGURE 1.

Average daily gross primary production (GPP) per location for the conterminous United States, March 5, 2000–December 2, 2020. At each of the 145,871 locations (250‐m spatial resolution), GPP estimates (in grams of carbon per square meter per day) were averaged across all available dates (16‐day temporal resolution; n = 478 dates). Map is drawn to scale but location dimensions have been enlarged to enhance their visibility; actual spatial resolution is finer than shown. Insets show magnified views of tidal wetlands south of New Orleans, LA on the Mississippi Bird's Foot and Lafourche Deltas.

Characterizing spatial variability in GPP and defining “locations”

To characterize the range of variability in tidal wetlands across the CONUS, we conducted a semi‐variogram analysis (Isaaks & Srivastava, 1989). This analysis revealed that inherent background variability (the nugget) accounted for about half of the total variance among pixels, and there was some spatial autocorrelation in GPP detected out to a range of about 40 to 50 km (Appendix S1: Figure S1). For comparison, previous work indicated that this distance was shorter (~12 km) for woody‐dominated tidal wetlands (Feagin et al., 2020b). This background variability and geographic patterning likely arise from the complex interplay among ecosystem components and processes, such as differences in elevation, plant species and community dynamics, accretion–erosion feedbacks, marine–terrestrial connectivity, sources and fluxes of nutrients and carbon (allochthonous riverine origin or autochthonous biomass production), water circulation patterns and flow rates, bounding slopes and tidal inundation periods, and subsidence–relative sea level effects. At larger spatial scales, finer patterns and variation may be lost or aggregated, while at finer scales, species composition differed from 1 m² to the next. Given this heterogeneity, and to preserve as much spatial detail as possible, our assumptions and conclusions were bound to describing variation in GPP at and above the scale of a 62,500‐m² pixel.

To move beyond the resolution‐dependent, sensor‐specific construct of a “pixel” and to better reflect the georeferenced continuity of the GPP time series, we define a “location” as a pixel‐sized spatial unit used in our analysis. While a pixel therefore represents the technical limitations of data collection, the term “location” emphasizes that each unit corresponds to specific coordinates on the Earth's surface. Importantly, “location” does not imply statistical or ecological independence, and the statistics used in our analysis were strictly descriptive in nature. We did not test for significant differences between categories (i.e., using t tests or ANOVA) or assume that locations were independent replicates. Still, we contend that the final GPP dataset captured the full spectrum of spatial variability inherent to tidal wetland ecosystems spanning diverse ecological and physical gradients.

Computing the GPP anomaly and defining perturbation “events”

We next computed the anomaly of GPP from each location's mean annual cycle, that is, the departure from the climatological average. By centering the data, the dominant background seasonal signal was filtered out, while signatures of unseasonably early or late green‐up and senescence events were retained. The GPP anomaly, $\mathrm{\beta }$, was quantified as the original GPP value on a given date $\mathrm{\alpha }$, minus the location's mean GPP on that date, μ:

$$\mathrm{\beta }=\mathrm{\alpha }-\mathrm{\mu }$$ (2)

where the mean GPP for a given date at a given location was the sum of all available $\mathrm{\alpha }$ values for that date in the study period (2000–2020) divided by the $n$ number measurements. This method was similarly applied for every date and location in the database.

A single discrete perturbation event was defined as when the GPP anomaly at a given location fell outside of one of its standard deviation (SD) (σ) boundaries for one or more consecutive dates. We initially investigated the behavior and frequency distributions of these events using various σ increments and found that the results were best represented using ±1 σ, because smaller perturbation events became harder to discern from one another at larger thresholds due to aliasing (see Appendix S1: Section S2). Variation beyond the σ boundaries signified that the location was perturbed beyond its normal operating range. These extreme GPP anomalies defined the dates of GPP perturbation “events,” while anomalies within the σ boundaries represented a location's regular variation.

This quantitative approach to defining perturbation events allowed the baseline conditions to be specified by location and date. It factored out differing “antecedent conditions” and seasonality effects that happened over the study period and across an array of environments and ecosystem types. Antecedent conditions describe the net environmental context of GPP prior to a perturbation (Hogan et al., 2020). For example, imagine an early‐season hurricane hit a tidal wetland within the context of an extreme yearlong drought; in that case, the GPP would already be abnormally low before the hurricane hit. The above procedure accounts for this context. We are thus looking for a return to the relative baseline condition for that location and time of the year during which recovery occurs—as opposed to returning to the exact same pre‐event GPP value or pre‐disturbance state (Dashti et al., 2024), which would have been an uncharacteristically low baseline due to the drought.

Measuring event effect size, return time, and waiting time

We then quantitatively assessed the effect size (E) or magnitude of each perturbation event (n = 13,754,386) as the maximum change in the GPP anomaly during the perturbation, the return time (R) as the amount of time elapsed from the start of the event until the GPP anomaly returned to the relative σ baseline boundaries of its mean annual cycle, and the event waiting time (WT) as the amount of time between successive negative or positive events (Figure 2). As defined by others (Hogan et al., 2020; Holling, 1996), −E and R provide measures of resistance and resilience to negative disturbances, respectively.

FIGURE 2.

Computing the gross primary production (GPP) anomaly, defining events, and measuring event E, R, and WT. GPP for the year 2008 for a salt marsh location in Texas is highlighted in blue, while GPP for all other years is gray. First, GPP estimates were transformed to GPP anomalies (in grams of carbon per square meter per day), that is, the distance from a location's mean annual cycle ±1 σ (vertical bars; see Equation 1). An event began on date x, reached a peak magnitude on date y, and returned to its baseline on date z. For each event, the effect size (±E) was measured as the maximum amount of change in the GPP anomaly, and the return time (R) was measured as the amount of time (16‐day epochs or days) the GPP anomaly exceeded its mean annual cycle ±1 σ. The waiting time (WT) between successive negative or positive events was measured as the amount of time elapsed between the end of one event and the start of the next event.

Within this framework, the WT between negative events also serves as a quantitative indicator of resistance, where shorter WTs reflect a reduced capacity to withstand negative perturbations. We expected locations with the highest resistance (i.e., longest negative event WT) to also display the lowest resilience (i.e., longest negative event R), based on the well‐established trade‐off between resistance and resilience observed across a wide range of contexts and scales (Li et al., 2020; Miller & Chesson, 2009; Patrick et al., 2022).

By contrast, a short WT between positive events implies a resource‐rich environment or frequent beneficial inputs, whereas a longer WT suggests limited resources and fewer opportunities for growth. Accordingly, efficient locations produce amplified or prolonged positive GPP perturbations, as reflected by high +E or R responses, whereas redundant locations display muted responses, indicating their superior buffering capacity.

The effect size of a perturbation event, E, was quantified following (Hogan et al., 2020; Patrick et al., 2022; Pimm et al., 2019) as

$$E={\mathrm{\beta }}_y-{\mathrm{\beta }}_x$$ (3)

where ${\mathrm{\beta }}_x$ is the GPP anomaly on date $x$ before the onset the perturbation (baseline condition in which the GPP anomaly has a magnitude of either less than +1 σ for positive events or greater than −1 σ for negative events), and ${\mathrm{\beta }}_y$ is the GPP anomaly on a later date $y$, when the magnitude of change in the GPP anomaly during the perturbation event was the largest.

The return time of an event, R, was quantified following (Hogan et al., 2020; Holling, 1996; Patrick et al., 2022), as the number of days between the date prior to the perturbation, $x,$ and date $z$, when the GPP anomaly returned to the baseline condition within its σ tolerance threshold:

$$R=z-x$$ (4)

The return tolerance was set between ${\mathrm{\mu }}_z\pm {\mathrm{\sigma }}_z$ where ${\mathrm{\sigma }}_z$ was the SD from the mean GPP for values that composed epoch $z$ at location. In practice, the use of the SD set an acceptable tolerance for the return to what one would normally expect for a given epoch.

The WT, or the event recurrence interval, was defined quantitatively as the amount of time (in epochs or days) between the end date of the first event (z ₁) and the start date of the next event (x ₂):

$$\mathit{\text{WT}}=x_2-z_1$$ (5)

Event frequency described either the total number of events a location experienced during the study period, or the average number of events a location experienced annually. Frequency and WT were inversely related; however, frequency summarized long‐term patterns while WT provided finer temporal resolution.

As an example, Hurricane Ike made landfall in Texas on September 13, 2008, destroying tidal wetland vegetation with sustained winds of 49 m s⁻¹ and prolonged salt water inundation that was caused by 4.9–6.1‐m storm surge (Figure 2). To obtain the GPP anomaly ${\mathrm{\beta }}_x$, we took the GPP on the prior epoch beginning August 28 and subtracted the average GPP for all August 28 estimates in the 2000–2020 time period. Then, to find R, we computed the anomaly for the post‐hurricane September 29 epoch to obtain ${\mathrm{\beta }}_{x+16}$ (i.e., the GPP dataset has 16‐day return intervals), and repeated the process until we reach date $z$, when ${\mathrm{\beta }}_z>{\mathrm{\mu }}_z-{\mathrm{\sigma }}_z$. We also recorded the maximum response on date $y$ to calculate the event's effect size (−E) using Equation (3). Finally, we solved Equations (4) and (5). However, in our actual analysis, we did not hand‐pick events like this and instead defined both negative and positive events quantitatively using a ±1 σ threshold tolerance.

Conceptually, this more objective process reduced sampling bias and allowed us to capture the entire spectrum of both externally and internally generated perturbations rather than just those that may be discernibly driven by discrete meteorological forcing events. We contend that this method can theoretically be applied to any multiyear time series dataset to define perturbation events and quantify their E and R, with potential to yield novel and synergistic discoveries relating system stability and resilience and unify researchers across disciplines with undisputed metrics of resilience.

Statistical analysis

All of the analyses were performed using the open‐source statistical program R version 4.2.1 and RStudio version 2023.06.2+561 (R Development Core Team, 2020). Databases and scripts can be accessed at Zenodo (Lerner, 2025). Return time histogram intervals were binned by epoch, and effect size histogram intervals were binned by 0.1 gC m⁻² day⁻¹. The fitdistrplus R package was used to fit parametric models to empirical effect size frequency distributions using maximum likelihood estimation (Delignette‐Muller & Dutang, 2015), and the best fitting models were determined by Akaike information criterion (AIC) score (see Appendix S1: Section S2).

RESULTS

Statistical properties of the tidal wetland GPP dataset

In total, our analysis was comprised of 66,729,537 independent GPP estimates (Figure 3a), across 145,871 pixel locations, averaging 4.72 ± 1.17 gC m⁻² day⁻¹ (Figure 3b). The GPP anomalies (departures from a location's mean annual cycle; Equation 2) were normally distributed around a location's mean annual cycle, and collectively (n = 66,729,537) their z‐scores roughly conformed to the Empirical (68‐95‐99.7%) Rule (Figure 3c). However, for anomalies larger than ±3 σ in magnitude (n = 116,744), negative anomalies were 3.15 times more common than positive ones. Nevertheless, GPP fluxes around their mean annual cycles were normally distributed for 87.7% of all epochs (n = 3,354,719 epochs in total, with 17–20 anomalies per epoch). However, the September 14th epoch exhibited twice that amount of non‐normality (Figure 3d), likely due to tropical storm events or other disturbances that caused physical damage or early plant senescence in some years. These non‐normally distributed epochs often contained outliers that signified the presence of the perturbation “events” that we were particularly interested in defining and analyzing, and so we did not transform or further standardize the data beyond calculating the GPP anomaly.

FIGURE 3.

Statistical properties of the tidal wetland gross primary production (GPP) dataset. (a) Histogram of GPP estimates spanning all locations and dates (n = 66,729,537 total estimates). Histogram bin color changes from yellow to green as GPP increases. (b) Histogram of average GPP for all tidal wetland locations across the continental United States (n = 145,871 locations). Histogram bin color changes from yellow to green for more productive locations. (c) GPP anomalies (n = 66,729,537) were normally distributed around their mean annual cycles (μ), roughly conforming to the Empirical (68‐95‐99.7%) Rule. (d) GPP anomalies were normally distributed around their mean annual cycles for 87.7% of 16‐day epochs (n = 3,354,719 total epochs); however, some epochs exhibited more non‐normal behavior than others. Each epoch contained between 15 and 21 GPP estimates, and normality was determined using Shapiro‐Wilks tests with alpha level 0.05.

Standardizing (e.g., z‐scoring) renders GPP dimensionless by centering values around each location's mean and scaling by its variance. Although this can reduce spatial variability and is sometimes necessary when comparing datasets with widely differing units or scales, it obscures the absolute magnitude of change in GPP, making it difficult to compare the actual scale of carbon flux across heterogeneous environments. For example, standardization could assign the same z‐score of +1 to anomalies of 0.5 and 3.0 gC m⁻² day⁻¹, masking important differences in carbon flux. Rather than directly transforming the data at the outset, we chose to control for GPP variability at a later stage of the analysis. This two‐tiered analytical approach preserved local heterogeneity and the original data structure, enabling variability to be addressed in a controlled manner without compromising interpretability or introducing bias from early‐stage transformations.

Statistical properties of GPP perturbation events

We found that large‐magnitude events were less common than small‐magnitude events and that the ±E frequency distribution was bimodal and asymmetric (Figure 4a) for negative events (n = 6,801,157) versus positive events (n = 6,953,229). Both negative and positive tails of the ±E distribution exhibited exponential decay spanning approximately four orders of magnitude. Within the family of exponential distributions, both tails were best fit by gamma distributions (according to lowest AIC score) with shape parameters (a = 1.34 and 1.71) and rate parameters (b = 0.96 and 1.40) for −E and +E, respectively (see Appendix S1: Figure S3). Regardless of the SD threshold that was chosen to define event occurrence, the shape and rate parameters of the best fit gamma distribution models rescaled in a predictable manner, for positive and negative effect sizes separately (Appendix S1: Figure S4). Overall, negative events were larger in magnitude and more variable than positive events, and this asymmetry became more pronounced at higher SD thresholds (Appendix S1: Figure S5), suggesting tidal wetlands were generally more susceptible to large losses in GPP than capable of realizing comparably large gains.

FIGURE 4.

Statistical properties of gross primary production (GPP) event metrics E, R, and WT. (a) Empirical frequency distributions for both negative (blue; n = 6,801,157) and positive (green; n = 6,953,229) event effect sizes (±E) were closely modeled by a two‐parameter gamma distribution. (b) Log–log plot of the empirical frequency distributions for both negative and positive perturbation event return times (R) were best fit by inverse power law functions, with power 2.00 for negative events and 2.52 for positive events. (c) Log‐linear plot of the exponentially distributed waiting times (WT) between successive negative and positive events. (d) Event effect size (±E) and return time (R) were linearly correlated for positive events, and for negative events this correlation was better fit by a logarithmic curve. Gray vertical bars represent the standard deviation (SD) from the mean ±E for each 16‐day interval in R.

Despite their vulnerability to severe disturbances at the interface of land and sea (Odum et al., 1995), tidal wetlands experienced slightly more positive than negative events (2.24 ± 0.35 and 2.19 ± 0.39 events per year, respectively), but negative events were slightly more extreme in their magnitude than positive events (−1.39 ± 1.33 vs. 1.22 ± 0.95 gC m⁻² day⁻¹, respectively). Yet, despite disproportionate negative and positive event magnitudes and frequencies, the net effect size of all positive and negative events averaged to nearly zero (−0.07 ± 1.74 gC m⁻² day⁻¹). A large SD pointed to strong short‐term positive or negative impacts in GPP, yet the mean suggested that there was minimal long‐term directional change in net GPP. This dynamic suggests a long‐term balance for tidal wetlands collectively in the CONUS over the 21‐year study period; however, net effect sizes were highly variable among locations (n = 145,871). Therefore, this balance appeared to be an ecosystem‐level property that strengthened at larger spatial scales.

For the return time of events, we found that long R were less frequent than short R, and this scaling closely followed an inverse power law function (with r ² = 0.96 and 0.97 for negative and positive events, respectively) spanning approximately four orders of magnitude for return times and seven orders of magnitude in the number of events (Figure 4b). The slopes of these inverse power laws were −2.00 (±0.05 SE) and −2.52 (±0.08 SE) for negative and positive events, respectively. The vast majority (90.4%) of return times were between 32 and 48 days in duration.

The longest positive event in our dataset was 2.28 years and the longest negative event was 3.02 years. The frequency distributions of return times were nearly identical for negative and positive events under 4 months; however, for return times longer than this, negative events were nearly tenfold more frequent than positive events. These longer negative events could be explained by the vulnerability of tidal wetlands to severe biomass‐altering disturbances, such as hurricanes and droughts. Recolonization or recovery from a severely degraded state can also be slow for some tidal wetland species (e.g., a mangrove forest damaged by a hurricane or freeze could require a long recovery time).

Moreover, the WTs (or recurrence intervals) between sequential negative or positive events were exponentially distributed (Figure 4c; r ² = 0.88 and 0.90, respectively). Exponentially distributed WTs are a defining feature of a Poisson process, which is commonly used to model the frequencies of natural phenomenon such as, earthquakes, hail, and heavy rainstorms. This suggested that GPP perturbations were generated stochastically with no temporal autocorrelation in event timing (Ayyub, 2014; Leadbetter et al., 2012), and events were therefore “memoryless.” In a memoryless system, the likelihood of an event remains relatively constant over time and was independent of its past events. This memoryless property suggested the timing of GPP perturbations may be strongly driven by stochastic forcings (e.g., weather and tide anomalies, nutrient pulses), in addition to pressures that can increase or decrease the likelihood of an event over time (e.g., stress, age, threshold behavior). In supporting work, we found that perturbation events in GPP were primarily driven by perturbations in vegetation canopy structure (EVI), and to a lesser extent, perturbations in air temperature or shortwave radiation (Appendix S1: Figure S6). While these frequency distributions suggested GPP perturbations were largely stochastic in origin, the magnitude and direction of perturbations appeared to be modulated by vegetation dynamics and feedbacks, indicating that biological structure played a key role in buffering or amplifying ecosystem GPP responses.

Furthermore, event effect size (E) and return time (R) were positively correlated, that is, larger magnitude events had longer return times on average (Figure 4d). For positive events, this covariation was best fit by a linear model and the correlation was relatively strong (r ² = 0.78), and for negative events, a logarithmic fit was more appropriate (r ² = 0.41). The asymptotic behavior for negative events around −4 gC m⁻² day⁻¹ suggested there was a catastrophic damage threshold, where any event exceeding this −E tipping point would have the maximum return time (R).

The patterns described above were revealed when all 145,871 pixel locations were viewed collectively at the continental scale. However, at finer spatial scales, locations exhibited a full range of effect size and return time responses. We sought to understand how E and R were statistically related to a location's performance (its average GPP during the study period), its event frequency (the average number of positive and negative events per year), and its recurrence interval of events (the average WT between two consecutive negative or positive events).

Patterns and trade‐offs at the location scale

We next explored how the responses of the 145,871 tidal wetland locations (250‐m resolution) created observable patterns within the range of the statistical frequency distributions and correlations previously described. Event effect size (E), duration (R), and WT varied strongly by location, even among wetlands of the same class and dominant vegetation type (Appendix S1: Figure S2). Given this spatial heterogeneity, consistent, generalizable patterns were difficult to detect across the landscape; however, these data and results can still provide a foundation for future targeted management or restoration efforts.

As tidal wetland locations became more productive on average, their ability to take advantage of positive events increased before reaching a plateau (Figure 5a), that is, average GPP and +E were positively correlated up to an average GPP of about 2 to 3 gC m⁻² day⁻¹. As their productivity increased, however, they also became more vulnerable to larger negative events in E. These trends appeared related to at least two physical constraints: (1) on average, a lower productivity ecosystem can gain or lose less carbon and energy than a higher productivity one, and (2) even the most severe negative events cannot drive productivity below zero.

FIGURE 5.

Patterns of variation in event metrics across tidal wetland locations. (a) Each plotted point represents the average negative and positive response of an individual tidal wetland location (n = 145,871). Locations became more vulnerable to larger negative events as their average gross primary production (GPP) increased. However, locations with the highest average GPP showed dampened responses to both positive and negative events. (b) Locations with longer waiting times (WTs) between events tended to have longer duration negative events and shorter duration positive events. Many locations with lower‐than‐average GPP (<4.72 gC m⁻² day⁻¹) had prolonged positive events, while locations with higher‐than‐average GPP did not. Conversely, many locations with higher‐than‐average GPP had prolonged negative events, while locations with lower‐than‐average GPP did not. (c) Locations with fewer than one positive event per year on average, those with higher‐than‐average GPP had small and short positive events, but those with below‐average GPP had larger and longer positive events. (d) Locations with more events on average tended to return to their mean annual cycle ±1 σ boundaries faster. Locations with less than one positive event per year showed two divergent outcomes: Either they had prolonged positive events (high R, shorter WT), or they quickly dissipated them (low R, longer WT). Black dotted line represents the expected R for a given WT (see Appendix S1: Section S4).

For tidal wetlands that were more productive than about 4 gC m⁻² day⁻¹ for positive events and 6 gC m⁻² day⁻¹ for negative events, these trends reversed, and responses to both positive and negative perturbations were dampened (Figure 5a), that is, average GPP and ±E became negatively correlated. This shift did not appear to be readily explainable by the physical constraints mentioned above.

Some locations did not experience a negative event for more than a year on average. Due to their scarcity of negative events, these locations were therefore considered highly resistant to negative events, and in particular, to small negative events. These highly resistant tidal wetlands had above‐average productivity likely because they had ample time between negative events to grow and develop. However, their negative events were strikingly large in magnitude on average when they eventually occurred (Figure 5a), and also took the longest to recover from (Figure 5b). In general, locations with the lowest frequency of negative events (those with the highest resistance) tended to also have the longest duration negative events (they were the least resilient). This trade‐off, that high resistance to perturbation was associated with a longer recovery time once impacted, has been demonstrated across a range of natural systems (Reed et al., 2024). Furthermore, these extremely resistant locations rarely if ever had an average GPP exceeding ~6.5 gC m⁻² day⁻¹, and therefore were unable to fully maximize their productivity.

The most productive and resilient locations in contrast (those with an average GPP >6.5 gC m⁻² day⁻¹) experienced at least one negative event per year on average, though the average −E of these events was relatively small and manageable compared to the highly resistant locations. Remarkably, these locations nearly always had an average −E below the catastrophic effect size damage threshold observed around −4 gC m⁻² day⁻¹ (see Figure 4d), and their average return times were never longer than about 2 months (Figure 5b). This is consistent with the common notion that system resilience entails more frequent failure, but the damage from these failures is minimal and rarely catastrophic (i.e., failure builds resilience). A strategy that maximized both resilience and productivity was uncommon though, as only about 3% of locations had an average GPP >6.5 gC m⁻² day⁻¹ (n = 4534), and just 0.5% of locations had an average GPP >7 gC m⁻² day⁻¹ (n = 696).

Notably, two divergent strategies emerged for locations that were starved of positive events (i.e., those with longer time to wait): (1) low productivity locations extended the benefits once received (they had long positive event return times) with a first bimodal peak expressed at ~3 gC m⁻² day⁻¹ (Figure 5b,c), and (2) high productivity locations quickly used them up as they had short positive event return times with a second peak at ~5.5 gC m⁻² day⁻¹ (Figure 5b,c). These divergent outcomes, for high‐ and low‐GPP locations, toggled depending on their effect size (Appendix S1: Figure S7) and return time (Figure 5b,c). This divergence was most pronounced in locations that experienced one or fewer positive events annually on average (Figure 5c).

Events were shorter in duration the more frequently they occurred (Figure 5d). Again, divergent outcomes for locations relatively starved for positive events (those with fewer than one event per year on average) appeared to be mediated by the average WT between events. Locations that waited more than about 1.5 years between positive events never had their positive events extended beyond 2 months. These locations had above‐average GPP (see Figure 5b), and presumably used the time between events to grow, develop, and stabilize (Fath et al., 2004). However, this growth inevitably decreased efficiency for processing any additional pulses or bursts of GPP and left the tidal wetlands susceptible to extremely damaging negative events (the bigger they were, the harder they fell). On the contrary, locations with below‐average GPP that experienced less than one positive event per year on average had the longest duration positive events on average, that is, they maximized their efficiency to ensure rare positive events were not wasted when they eventually occurred. When locations were not starved for positive events, the vast majority fell somewhere on a continuum between these two extremes, in an apparent “window of vitality” (Fath, 2015; Markolf et al., 2022; Zorach & Ulanowicz, 2003).

DISCUSSION

These findings suggest that (1) over two decades, negative and positive perturbations to tidal wetland carbon flux tended to offset one another at broader spatial scales, despite high local variability, (2) locations with below‐average GPP had the greatest efficiency for positive events and were the most resistant to small negative events, (3) locations with an average GPP greater than ~6.5 gC m⁻² day⁻¹ were the most resilient to negative events; however, they also endured at least one negative event per year on average, and (4) the optimal trade‐off between the ecosystem‐level properties of efficiency and redundancy for positive events, and resistance and resilience for negative events varied by location.

Decoupling event effect size (±E), return time (R), and WT provided unique insight into the dynamics of how these metrics interacted across tidal wetland locations. Relative frequency distributions of these event metrics indicated that perturbations in GPP were often initiated by stochastic processes but subsequently propagated or dampened by internal mechanisms and feedbacks. These processes yielded a bounded distribution of ±E that reflected the underlying physical limits of GPP gains and losses. Meanwhile, the scale‐invariance of R suggested that complex processes ranging from microbial nutrient cycling to geomorphological and climate dynamics operated and interacted across multiple scales to modulate tidal wetland growth and recovery.

The long‐term net balance of negative and positive event magnitudes should not be interpreted as stasis or an absence of change. Tidal wetlands in the CONUS and globally are undergoing rapid degradation and remain highly vulnerable to sea level rise, extreme disturbances, and chronic stressors that alter vegetation structure and disrupt hydrologic and sediment dynamics (Kirwan & Megonigal, 2013). Rather than indicating stasis, this long‐term balance may emerge from intrinsic resilience mechanisms that support resource renewal and functional recovery under sustained stress, such as succession, plant–soil interactions, and biogeochemical cycling (e.g., Fagherazzi et al., 2013; Morris et al., 2002; Wagner et al., 2017). A key component of this resilience was the inherent variability across spatial and temporal scales, which mitigated the risk of simultaneous functional collapse spanning vast areas (Odum et al., 1995). Alternatively, the observed balance may partly reflect statistical averaging across all locations or be a consequence of the symmetric thresholding approach used to define events and calculate ±E. However, pronounced negative skew in mean ±E when events were defined by higher σ thresholds indicated that the balance observed at the ±1 σ threshold was not simply a statistical or methodological artifact but instead reflected a meaningful emergent pattern of asymmetric negative and positive GPP responses.

These findings revealed a mechanism by which tidal wetlands were optimized in their collective GPP responses to a myriad of extraneous and confounding ecological factors. Deconstructing these innumerous factors into various latent variables was impractical and unfeasible at the temporal and spatial scale implemented in this study. Instead, a basic conceptual model is suggested that summarizes a general trade‐off governing tidal wetland ecosystem productivity and perturbation responses, deduced from and supported by the observed data themselves.

Conceptual model of trade‐off governing perturbation responses

We devised a conceptual model (Figure 6a) that incorporates empirical data with prevailing ecological theories of resilience (DeAngelis, 1980; Holling, 1973; Pimm, 1984), disturbance and succession (Jentsch & White, 2019; Odum, 1969; Pickett et al., 1989), and complexity (May, 1971; Peterson et al., 1998; Ulanowicz, 2009), to illustrate how productivity and resilience in tidal wetlands are constrained by physical limits and trade‐offs, and to describe how perturbations in productivity can reflect varying degrees of underlying stress and complexity. This conceptual model is not to be interpreted as a scientific mechanism, but rather the observation of general patterns of trade‐offs and constraints exhibited over two decades across tidal wetlands in the United States.

FIGURE 6.

Conceptual model of the trade‐off between efficiency and resistance, and redundancy and resilience in tidal wetlands. (a) Tidal wetlands tended to be either efficient and resistant, or redundant and resilient. Light and dark purple dashed lines represent the divergent strategies of an efficient and resistant ecosystem, and a redundant and resilient ecosystem, respectively. A theoretical representation of a simple ecosystem network assembly suggests connections (black lines) between system components (black dots) increase system complexity as stress decreases and gross primary production (GPP) increases. (b) Efficient and resistant locations (those with an average GPP less than 4.72 gC m⁻² day⁻¹; n = 65,819 locations) had larger (dotted line), longer lived (short‐dashed line), but less frequent (long‐dashed line) perturbation events relative to redundant and resilient locations (those with an average GPP greater than 4.72 gC m⁻² day⁻¹; n = 80,052 locations). WT, waiting time.

Here, ecosystem stress is defined as the degree to which suboptimal environmental conditions limit an ecosystem's capacity to sustain high productivity (Jones et al., 2021). In tidal wetlands, stress can be driven by multiple factors including temperature extremes, hydrologic deficits, poor soil drainage, high salinity, anoxia, and frequent physically disruptive events. Ecosystem complexity refers to the diversity and interconnectedness of biotic and abiotic components, processes, and feedbacks that collectively influence ecosystem structure and function.

We hypothesize that when a tidal wetland has low GPP and high stress, positive subsidies are absorbed to construct a simple linear network structure (Figure 6a, short‐dashed curve). This simple ecological network has few connections between its components and is maximally efficient at assimilating and distributing subsidies (Odum, 1988). Network nodes (Figure 6a, black dots) are theoretical representations of ecosystem components at a given point in time, such as resources, species, populations, communities, trophic levels, and functional groups and processes, while the connections and pairwise interactions between ecosystem components (Figure 6a, black lines linking the nodes) show that system complexity tends to increase when GPP is higher and stress is lower. The configurations of network nodes and linkages shown in this diagram illustrate a simplified hypothetical pathway by which a system may support greater productivity, resilience, and redundancy associated with increased species richness, trophic connectivity, and a broader range of ecological processes.

A simple, efficient, and resistant network structure appeared advantageous up to an optimum around 4.72 gC m⁻² day⁻¹, the average GPP of all locations. These low GPP locations were highly vulnerable to rare but damaging negative events, while concurrently, positive events were amplified and prolonged (see Figure 5a,b). To tolerate low resource availability or high stress, individual life history traits, population dynamics, and community structures favor strategies for utilizing ephemeral resources opportunistically (Yang et al., 2008). However, plants with traits that promote rapid regrowth and resistance to damage, such as higher lignin and lower protein levels, dormant or protected meristems, and storage organs (tap roots, stems, and tubers that contain essential nutrients) generally have lower growth rates under ideal conditions (Inouye et al., 2021). This inherent trade‐off limits maximum GPP and is illustrated in the conceptual diagram as a plateau in the efficiency–redundancy curve, where further increases in GPP are constrained even under low‐stress conditions.

When productivity exceeded 4.72 gC m⁻² day⁻¹ (the mean GPP for all locations), it became advantageous for tidal wetlands to support greater complexity and redundancy, which in turn reinforced both higher GPP and ecosystem‐level resilience (Figure 6a, long‐dashed curve). Functional and structural redundancy increases resilience by providing multiple pathways for ecosystem functions, such as GPP, to continue during recovery (Fath, 2015; Odum, 1969, 1988). These redundancies help stabilize an ecosystem by dampening large perturbations (Biggs et al., 2020). However, as more redundancy is introduced into an ecosystem, efficiency for positive events decreases, likely due to higher resource demands and increased competition (Inouye et al., 2021; Pimm & Lawton, 1977). In general, locations with above‐average GPP quickly dampened positive events, while locations with below‐average GPP magnified them.

To quantify the extent of this redundancy versus efficiency trade‐off, we compared the effect size, return time, and WT responses of locations with below‐ and above‐average GPP (Figure 6b), because the mean GPP of all locations (4.72 gC m⁻² day⁻¹) appeared to be an approximate tipping point from efficiency–resistance to redundancy–resilience (see Figure 5b,c). To account for variability in mean GPP, each location's mean response was normalized by its mean GPP. Locations with above‐average GPP had dampened responses that were on average about one‐third smaller in magnitude and shorter in duration compared to locations with below‐average GPP. A likely underlying mechanism was that positive events occurred about one‐third less frequently in efficient ecosystems compared to redundant ecosystems, and so the lower productivity ecosystems were pressured to amplify and prolong rare positive events when they finally occurred. These pressures weakened as positive events became more frequent and as GPP increased.

A simple and efficient network structure was resistant to minor negative perturbations; however, even the most resistant ecosystems could not protect against all perturbations. When they did occur in efficient and resistant locations, negative events were about one‐third larger in magnitude and one‐third longer in duration than those in redundant and resilient systems (Figure 6b), possibly because a single point of failure could jeopardize an entire simple, more linear network (Albert et al., 2000). Functional redundancy, whether achieved via biodiversity, a complex spatial trophic structure, or through temporal succession, is thus a hedge against the catastrophic loss of all future ecosystem productivity. As some have argued, complex and redundant ecosystems should generally bias towards resiliency (May, 1972; Pimm, 1984; Ulanowicz et al., 2009), as this is consistent with the insurance hypothesis (Huston, 1979; Naeem & Li, 1997; Walker, 1995), wherein the importance of maintaining ecosystem function every year outweighs the costs of maintaining a reserve of alternative traits or strategies that are maladaptive in off years. Tidal wetlands, and marine ecosystems more generally, also dissipate large‐scale disturbances and avoid catastrophic failure through the hydrodynamic transport of resources, which makes them more resilient but less resistant than terrestrial ecosystems (Odum et al., 1995; Patrick et al., 2022). Functionally redundant structure and mobile resources in a semiaquatic environment ensure that tidal wetland ecosystems, despite undergoing substantial reorganization, can quickly recover GPP after a disturbance.

These results suggest that the genesis of the fundamental trade‐off between an efficient versus redundant ecosystem for positive subsidies, and a resistant versus resilient ecosystem for negative disturbances, could be a function of the same underlying network structure, defined by the organisms and resources at a given location and time and their interactions and connectivity. Perturbation events shape these networks through time, and ecosystems feedback accordingly to optimize and balance this efficiency and resistance versus redundancy and resilience trade‐off. Furthermore, this trade‐off intensified when events were infrequent (<1 event/year) and produced locally divergent solutions in high versus low productivity tidal wetland ecosystems.

Human actions may work with or against these tidal wetland responses and their underlying structural dynamics. For example, an armored shoreline built to reduce negative disturbance on a landward tidal wetland should be expected to increase the WT between negative perturbation events—in other words, increase its resistance. Yet, according to the observed statistical distributions and correlations, an increased WT for negative disturbances is correlated with and predictive of a larger effect size and return time for the disturbances when they occur. At the same time, presumably the ecosystem will grow and gain GPP while continuing to receive positive subsidies behind the structure, creating more GPP to lose when a negative event does finally occur. Consequently, for this growing ecosystem to remain in thermodynamic equilibrium, it must dissipate the disturbing GPP flux through infrequent, yet increasingly catastrophic events.

It is important to recognize that no tidal wetland location in the United States over the past two decades maximized its productivity, resilience, resistance, efficiency, and redundancy all at the same time. Instead, these separately advantageous yet inherently conflicting ecosystem‐level properties traded off (e.g., resilience vs. resistance for negative events, and redundancy vs. efficiency for positive events), which suggested that tidal wetland ecosystems, and perhaps other biological and engineered systems in general, are shaped by these opposing priorities, compromises, and constraints. Evidence for this concept includes consistent statistical patterns and correlations among event effect size, return time, and WT metrics, along with locally adapted responses that revealed a fundamental trade‐off inherent to an ecosystem's structural and functional dynamics. These statistical patterns, correlations, and distributions therefore likely reflect a nonrandom, yet indeterminate conditioning, such that an ecosystem's internal components and functional processes continuously re‐optimize in response to the frequency and magnitude of its energy gains and losses.

AUTHOR CONTRIBUTIONS

Conceptualization: Joshua E. Lerner, Rusty A. Feagin, Thomas P. Huff, Astrid Layton, Raymond G. Najjar, Maria Herrmann, and Jose D. Fuentes. Methodology: Joshua E. Lerner, Rusty A. Feagin, Thomas P. Huff, Raymond G. Najjar, Maria Herrmann, and Jose D. Fuentes. Software: Joshua E. Lerner and Thomas P. Huff. Validation: Joshua E. Lerner, Rusty A. Feagin, Thomas P. Huff, Raymond G. Najjar, Maria Herrmann, and Jose D. Fuentes. Formal analysis: Joshua E. Lerner. Investigation: Joshua E. Lerner and Rusty A. Feagin. Data curation: Joshua E. Lerner, Rusty A. Feagin, and Thomas P. Huff. Writing–original draft preparation: Joshua E. Lerner and Rusty A. Feagin. Writing–review and editing: Joshua E. Lerner, Rusty A. Feagin, Thomas P. Huff, Astrid Layton, Raymond G. Najjar, Maria Herrmann, and Jose D. Fuentes. Visualization: Joshua E. Lerner and Rusty A. Feagin. Project administration: Joshua E. Lerner and Rusty A. Feagin. Funding acquisition: Rusty A. Feagin, Thomas P. Huff, Raymond G. Najjar, Maria Herrmann, and Jose D. Fuentes. Supervision: Rusty A. Feagin, Thomas P. Huff, Raymond G. Najjar, Maria Herrmann, and Jose D. Fuentes.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Supporting information

Appendix S1.

Lerner, Joshua E. , Feagin Rusty A., Huff Thomas P., Najjar Raymond G., Layton Astrid, Herrmann Maria, and Fuentes Jose D.. 2026. “A Fundamental Trade‐Off among Resilience, Resistance, Efficiency, and Redundancy in Tidal Wetlands.” Ecology 107(1): e70293. 10.1002/ecy.70293

DATA AVAILABILITY STATEMENT

Data and code (Lerner, 2025) are available in Zenodo at https://doi.org/10.5281/zenodo.17586378.