Mingyu Luo

Theme 1: Frequency-domain analysis of population fluctuations (2019-)

Frequency-domain analysis, or spectral analysis, is a classic approach in time series analysis. My doctoral research expanded its application to ecological dynamics, first examining how dispersal affects spatial synchrony across different timescales (Luo et al. 2021 Oikos). Building on this foundation, I extended the approach to competitive communities and validated theoretical predictions using grassland biodiversity experiments (Luo et al. 2025 NEE). Crucially, in this work I derived a direct mathematical formula showing how frequency-domain patterns influence statistical outcomes in finite-length time series through weighted averaging. These works advance the frequency-domain theory of stochastic population dynamics and demonstrate that the timescale of ecological observations can cause qualitative shifts in outcomes—not merely increase uncertainty—with profound implications for interpreting ecological data.

Currently, I am developing ideas to integrate theories of ecological stabilities via spectral approaches (in progress).

Theme 2: Species coexistence in structured communities (2020-2022)

Metapopulation theory provides elegant mathematical criteria for population persistence in spatially fragmented landscapes. When extended to two-species metacommunities, this framework yields the famous competition-colonization trade-off. I advanced this theory by first fitting a long-term dataset of three competing Daphnia species using Bayesian approaches, then deriving mathematical criteria for multispecies coexistence in fragmented landscapes (Luo et al. 2022 PNAS). This work uniquely integrates metacommunity theory, species coexistence theory, structural stability analysis, and Bayesian statistics.

Theme 3: Statistical model of food web structure (2021-2022)

Food web structure fundamentally shapes ecosystem dynamics, with body size serving as a key organizing principle for predator-prey interactions. The allometric scaling of foraging relationships provides a quantitative framework for understanding how energy flows through ecosystems. I developed a flexible probabilistic model for predicting foraging links that incorporates both biotic factors (predator and prey body sizes) and abiotic drivers (such as temperature). Fitting this model to a global food web dataset using Bayesian approaches and modern scalable MCMC algorithms, we revealed how foraging patterns—including optimal prey-predator size ratios and feeding ranges—systematically vary with predator size and temperature across aquatic and terrestrial ecosystems (Li, Luo et al. 2023 Ecology Letters).

Theme 4: Ecosystem complexity, resilience, invariability, and productivity (2023-)

The complexity-stability debate represents one of ecology's most fundamental questions. Research has revealed that ecosystem complexity has opposing effects on two key stability measures: asymptotic resilience and temporal invariability. As the focus of my doctoral thesis, I used random matrix theory to derive analytical predictions for temporal invariability in complex ecosystems, providing a parallel to May's famous work on complexity-resilience relationships. Moving beyond classical random community matrix models, I am investigating the relationship between asymptotic resilience and temporal invariability under more realistic ecological scenarios. These results will help resolve the longstanding complexity-stability debate and clarify the relationships among different stability measures (Luo et al. in preparation).

Additionally, I am exploring theoretical connections between feasibility and stability in large random ecosystems, as well as correlations among entries of the community (Jacobian) matrix at equilibrium. This work aims to uncover fundamental relationships between ecosystem properties and identify the boundaries of classical theoretical frameworks, potentially revealing new organizing principles for complex ecological systems (in progress).

Theme 5: Theory of biodiversity and ecosystem functioning (2023-)

Biodiversity-ecosystem functioning (BEF) theory predicts that diversity enhances both productivity and stability (through portfolio and insurance effects). Drawing inspiration from mean-variance trade-offs in financial portfolio theory, I demonstrated that complex ecological communities may exhibit an analogous productivity-invariability trade-off. I have shown how this phenomenon emerges from species heterogeneity and am currently testing these predictions with empirical data (in progress).

Currently, I'm also developing new framework to integrate the effect of species trait (here monoculture productivity) and its variation in B-EF relationship (in progress).

Theme 6: Coarse graining of ecological models (2024-)

Complex ecological systems often contain dynamics across multiple scales, from individual interactions to ecosystem-level patterns. Coarse graining—a physics approach for systematically reducing model complexity while preserving essential dynamics—offers a powerful framework to bridge these scales and identify emergent properties. I have developed a theoretical framework for coarse graining ecological models. For locally linearized systems, I derived elegant mathematical criteria for exact coarse graining and proposed methods to quantify deviation from exact reducibility. I presented this work as a contributed oral presentation at the 2025 ESA meeting in Baltimore. Currently, I am organizing these theoretical results and applying them to realistic ecological models and empirical datasets (in progress).

Theme 7: Theory of ecosystem sensitivity (2025-)

Sensitivity measures how ecosystem properties response to environmental changes, connected to ecosystem resistence. Following the well-developed theory of senstivity. I further invesigate the geometrical properties and its connectance to other stability measurements in simple and complex systems (in progress).

Collaborative Research

I contribute mathematical and statistical expertise to diverse collaborative projects, often leading the mathematical modeling, numerical simulation, and statistical analysis components. My collaborations span remarkably diverse areas of ecology—from forest biomass accumulation and climate impacts to aquatic food web structure and Daphnia metacommunity—reflecting my commitment to applying quantitative approaches wherever they can advance ecological understanding. I actively seek collaborative opportunities in ecology, computational biology, and related fields. Whether building on my established research areas or venturing into uncharted territory, I'm particularly excited about collaborations that could open entirely new frontiers in ecological research, pushing the boundaries of what theoretical ecology can achieve.