Mingyu Luo

Theme 1: Frequency-domain analysis of population fluctuations 2019–present

Frequency-domain (spectral) analysis is a classic tool in time series analysis. My doctoral research extended it to ecological dynamics, first by examining how dispersal affects spatial synchrony at different timescales (Luo et al. 2021, Oikos), then by turning to competitive communities, where I tested theoretical predictions against grassland biodiversity experiments (Luo et al. 2025, Nature Ecology & Evolution). In that paper I derived a formula showing how frequency-domain patterns shape the statistics computed from finite-length time series, through weighted averaging. Together, these studies advance the frequency-domain theory of stochastic population dynamics and show that the timescale of observation can change ecological conclusions qualitatively, not merely add uncertainty, which matters for how ecological time series are interpreted.

Theme 2: Species coexistence in structured communities 2020–2022

Metapopulation theory gives simple mathematical criteria for when a population persists in a fragmented landscape; extended to two competing species, it yields the well-known competition–colonization trade-off. I took this further in two steps: fitting a long-term dataset of three competing Daphnia species with Bayesian methods, then deriving mathematical criteria for multispecies coexistence in fragmented landscapes (Luo et al. 2022, PNAS). The work brings together metacommunity theory, species coexistence theory, structural stability analysis, and Bayesian statistics.

Theme 3: Statistical model of food web structure 2021–2022

Food web structure shapes ecosystem dynamics, and body size is one of its main organizing principles: the allometric scaling of feeding relationships offers a quantitative handle on how energy flows through ecosystems. I developed a flexible probabilistic model that predicts foraging links from biotic factors (predator and prey body sizes) and abiotic drivers such as temperature. Fitting it to a global food web dataset with Bayesian methods and scalable MCMC algorithms, we showed how foraging patterns, including optimal prey–predator size ratios and feeding ranges, vary systematically with predator size and temperature across aquatic and terrestrial ecosystems (Li, Luo et al. 2023, Ecology Letters).

Theme 5: Theory of biodiversity and ecosystem functioning 2023–present

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 a new framework to integrate the effects of species traits (here, monoculture productivity) and their variation in the BEF relationship (in progress).

Theme 6: Coarse graining of ecological models 2024–present

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 preparation).

Theme 7: Theory of ecosystem sensitivity 2025–present

Sensitivity measures how ecosystem properties respond to environmental change and is closely connected to ecosystem resistance. Building on well-developed sensitivity theory, I further investigate its geometric properties and their connections to other stability measures in simple and complex systems (in preparation).