Wenying Shou

Ecological interactions are often mediated by feedbacks between organisms and their resource environments. Yet, how resource supply dynamics dictate collective dynamical phases of an ecosystem remains unclear. Here, we analyse a generalised consumer–resource model with non-reciprocal interactions to demonstrate that self-renewing versus externally-supplied resources yield fundamentally different dynamical phase diagrams. As interactions become increasingly non-reciprocal, ecosystems relying on self-renewing resources transition from stable dynamics to chaos and ultimately to infeasibility. By contrast, ecosystems with externally-supplied resources remain stable over a broader parameter range and transition to infeasibility without experiencing an intervening chaotic phase. Using the cavity method, we derive a unified stability condition applicable to a broad class of resource supply functions, explaining why externally-supplied resources can expand the stable region. We show that stability hinges crucially on the susceptibility of resources to perturbations, which depends strongly on their supply. Further, we show that external resource supply suppresses chaos in the unstable region by drastically reducing the susceptibility of resources closest to extinction. Our findings demonstrate that resource dynamics fundamentally reshape the accessible dynamical behaviours of an ecosystem, with implications for interpreting microbial community experiments.

As team science grows, so do ‘equal contribution’ designations, yet this information is routinely hidden or lost, creating inequity in recognition and crediting. We must fix this problem, now.

Correlation analyses using ecological time series can indicate phenomena such as interspecific interactions or an environmental factor that affects several populations. However, methodological choices in these analyses can significantly impact the results, potentially leading to spurious correlations or missed true associations. In this study, we explore how different decisions affect the performance of statistical tests for correlations between pairs of time series in simulated two-species ecosystems. We show that when performing nonparametric “surrogate data” tests, both the choice of statistic and the method of generating the null distribution can affect true positive and false positive rates. We also show how seemingly closely related methods of accounting for lagged correlation produce vastly different false positive rates. For methods that establish a null model by simulating the dynamics of one of the two species, we show that the choice of species simulated can influence test behavior. Additionally, we identify scenarios where the outcomes of analyses can be highly sensitive to the initial conditions of an ecosystem, even under simple mathematical models. Our results indicate the importance of thoughtful consideration and documentation of the statistical choices investigated here. To make this work broadly accessible, we include visual explanations of most methods tested in an appendix.

A fundamental paradox in ecology is the relationship between species diversity and ecosystem stability: May’s stability condition predicts that species diversity destabilises communities, yet many diverse ecosystems in nature are stable. Here, we show that this paradox can be resolved by explicitly considering resources, which May neglects. Specifically, May’s framework and the competitive exclusion principle jointly predict that resource diversity, which promotes species diversity, should destabilise communities. However, from computer simulations and analytical calculations using the finite-size cavity method, we find the opposite: resource diversity consistently generates stable, species-rich communities. Importantly, this stabilising effect disappears when resource dynamics is neglected (set to steady state). We also show that, contrary to the prevailing belief that interaction heterogeneity is always destabilising, different biological sources of heterogeneity have opposing effects on stability. Our work provides a solution to May’s paradox and demonstrates that resource dynamics are not just negligible background but are central drivers of ecosystem stability.

Microbial collectives can perform functions beyond the capability of individual members. Enhancing collective functions through artificial selection is, however, challenging. Here, we explore the ‘rafting-a-waterfall’ metaphor where achieving a target population composition depends on both target and initial compositions. Specifically, collectives comprising fast-growing (F) and slow-growing (S) individuals were grown for ‘maturation’ time, and the collective with S-frequency closest to the target value is chosen to ‘reproduce’ via inoculating offspring collectives. During collective maturation, intra-collective selection acts like a waterfall, relentlessly driving the S-frequency to lower values, while during collective reproduction, inter-collective selection resembles a rafter striving to reach the target frequency. Using simulations and analytical calculations, we show that intermediate target S frequencies are the most challenging, akin to a target within the vertical drop of a waterfall, rather than above or below it. This arises because intra-collective selection is the strongest at intermediate S-frequencies, which can overpower inter-collective selection. While achieving a low target S frequencies is consistently feasible, attaining high target S-frequencies requires an initially high S-frequency — much like a raft that can descend but not ascend a waterfall. As Newborn size increases, the region of achievable target frequency is reduced until no frequency is achievable. In contrast, the number of collectives under selection plays a less critical role. In scenarios involving more than two populations, the evolutionary trajectory must navigate entirely away from the metaphorical ‘waterfall drop.’ Our findings illustrate that the strength of intra-collective evolution is frequency-dependent, with implications in experimental planning.

Collectives, such as microbial communities, can perform functions beyond the capability of individual members. Enhancing these collective functions through artificial selection, however, presents significant challenges. Here, we explore the ‘rafting-a-waterfall’ phenomenon, a metaphor illustrating how the success in achieving a target population composition in microbial collectives depends on both the target characteristics and initial conditions. Specifically, collectives comprising fast-growing (F) and slow-growing (S) individuals were grown for a period of “maturation” time, and the collective with S-frequency closest to the target value is chosen to “reproduce” (inoculate) offspring collectives. Such collective selection is dictated by two opposing forces: during collective maturation, intra-collective selection acts like a waterfall, relentlessly driving the S-frequency to lower values, while during collective reproduction, inter-collective selection resembles a rafter striving to reach the target frequency. Due to this model structure, maintaining a target frequency requires the continued action of inter-collective selection. Using simulations and analytical calculations, we show that intermediate target S frequencies are the most challenging, akin to a target within the vertical drop of a waterfall, rather than above or below it. This arises because intra-collective selection is the strongest at intermediate S-frequencies, which can overpower inter-collective selection. While achieving low target S frequencies is consistently feasible, attaining high target S-frequencies requires an initially high S-frequency — much like a raft that can descend but not ascend a waterfall. The range of attainable target frequencies depends on the initial population size of the collectives: as the population size in Newborn collectives increases, the region of achievable target frequency is reduced until no frequency is achievable. In contrast, the number of collectives under selection plays a less critical role. In scenarios involving more than two populations, the evolutionary trajectory must navigate entirely away from the metaphorical ‘waterfall drop.’ Our findings illustrate that the strength of intra-collective evolution is frequency-dependent, with implications in experimental planning.

Correlation analyses using ecological time series can indicate phenomena such as interspecific interactions or an environmental factor that affects several populations. However, methodological choices in these analyses can significantly impact the results, potentially leading to spurious correlations or missed true associations. In this study, we explore how different decisions affect the performance of statistical tests for correlations between pairs of time series in simulated two-species ecosystems. We show that when performing nonparametric “surrogate data” tests, both the choice of statistic and the method of generating the null distribution can affect true positive and false positive rates. We also show how seemingly closely related methods of accounting for lagged correlation produce vastly different false positive rates. For methods that establish a null model by simulating the dynamics of one of the two species, we show that the choice of species simulated can influence test behavior. Additionally, we identify scenarios where the outcomes of analyses can be highly sensitive to the initial conditions of an ecosystem, even under simple mathematical models. Our results indicate the importance of thoughtful consideration and documentation of the statistical choices investigated here. To make this work broadly accessible, we include visual explanations of most methods tested in an appendix.

In disciplines from biology to climate science, a routine task is to compute a correlation between a pair of time series and determine whether the correlation is statistically significant (i.e., unlikely under the null hypothesis that the time series are independent). This problem is challenging because time series typically exhibit autocorrelation and thus cannot be properly analyzed with the standard iid-oriented statistical tests. Although there are well-known parametric tests for time series, these are designed for linear correlation statistics and thus not suitable for the increasingly popular nonlinear correlation statistics. There are also nonparametric tests that can be used with any correlation statistic, but for these, the conditions that guarantee correct false positive rates are either restrictive or unclear. Here, we describe the truncated time-shift (TTS) test, a nonparametric procedure to test for dependence between 2 time series. We prove that this test correctly controls the false positive rate as long as one of the time series is stationary, a minimally restrictive requirement among current tests. The TTS test is versatile because it can be used with any correlation statistic. Using synthetic data, we demonstrate that this test performs correctly even while other tests suffer high false positive rates. In simulation examples, simple guidelines for parameter choices allow high statistical power to be achieved with sufficient data. We apply the test to datasets from climatology, animal behavior, and microbiome science, verifying previously discovered dependence relationships and detecting additional relationships.