Xueying Wang

Finished and ongoing work in ecology

Can the ecological Allee effect come from pure demographic stochasticity?

Ref: Xueying Wang and Nigel Goldenfeld. Demographic stochasticity gives rise to the Allee effect in predator-prey ecosystems. (Manuscript in preparation).

In my turbulence model, I highlighted the limiting effect of nutrient density ρ on organism growth. Specifically, when the nutrient population density ρ is small, it can slow down the growth of active organisms, even leading to a decline in the organism population if its growth rate becomes smaller than the decay rate. In the turbulence model, the nutrient density is the mean flow kinetic energy. Similar phenomena can be observed in many reallife, stochastic ecological systems where the growth of one organism depends on the population density of another. This phenomenon can be exemplified by an individual-level model of predator-prey dynamics, where a decline in prey density is always followed by a decrease in predator density of the same scale, resulting in a persistent oscillation, i.e., the quasi-cycle. While these dynamics may seem intuitive and straightforward, their origins are deeply rooted in the subtleties of demographic stochasticity.

In my work, I discovered that all ‘nutrient-limiting effects’ are lost in the deterministic approximation, indicating a stochastic origin of such effect. By analyzing its first-order approximation, the Langevin equation, a negative Ito drift emerges in the growth rate. This term is inversely proportional to the square root of ρ, indicating that its magnitude amplifies as the population diminishes. Such a phenomenon becomes dominant at low population densities ρ, leading to a decreasing population growth rate as ρ decreases. This behavior is similar to the phenomenon known as the Allee effect well-documented in ecology. The Allee effect describes a scenario where the growth rate of a population decreases at lower population densities ρ, characterized by a distinct curvature change in the growth rate function with respect to ρ. While the Allee effect is typically introduced via a nonlinear deterministic term, my findings indicate that the appearance of a similar effect can arise simply from the stochastic nature of ecological systems, without the need for any additional mechanistic explanations. A detailed and spatially-resolved explanation of this effect can be achieved through a field-theoretic analysis.

Ongoing work in neuroscience

Unlike their artificial analogs, biological networks exhibit spiking dynamics and transmission time delays. While these features add to the complexity of their dynamics, they significantly enhance the potential capabilities of the network. For instance, spiking dynamics enables the neurons to engage in temporally precise communication; it also allows the network to have “self-tuning” abilities through mechanisms such as spike-timing-dependent plasticity, etc. Such features underscore the innate ability of biological neuronal networks to self-organize. My research seeks to understand how emergent computational and cognitive functions arise in biological neuronal networks.

Dynamics of large-scale circulation in turbulent rotating Rayleigh-Bénard convection

In my undergraduate years, I worked on large-scale circulation dynamics in turbulent rotating Rayleigh-Bénard convection. My collaborators built the Rayleigh-Bénard convection cell on a slowly rotating plane and operated it in the parameter regime where the large-scale circulation shows up. They measured how the average azimuthal rotating speed of the large-scale circulation plane changes with the Rossby number. In the large Rossby number region, they discovered an unexpected growth of the relative retrograde azimuthal rotating speed of circulation plane with increasing Rossby number. Existing theories could not explain this phenomenon.

From the experimental data, we found out that the growth of relative retrograde rotation speed is caused by rare stochastic events like cessation and reversal of the circulation plane that are neglected by existing theories. During these rare events, the circulation plane rotates much faster than usual.

To quantitatively check how much the rare events contribute to the abnormal growth, we started from the idea of an early model and a revised theory based on it, where the system is described by two Langevin equations with additive white noise that captures the dynamics of the azimuthal angular motion and the strength of the circulation plane.

By decoupling the linear rotating component, we were able to reduce the model to an Ornstein-Uhlenbeck process-like form and further estimate theoretical values of frequencies of rare events and average azimuthal displacement per event at different Rossby number region. Based on these values, we calculated theoretically how much the rare events contribute to total relative rotation speed, which agrees very well with experimental values. Thus, our conjecture was confirmed, and the abnormal increase of rotation speed was explained -- the behavior of the large-scale circulation during those stochastic rare events are indeed the major cause of the unexpected growth in retrograde relative plain rotation speed.

We also estimated correction to previous models from Reynolds stress by fitting the probability distribution functions of plane rotation speed and circulation strength.

I did part of the theory and most of the data analysis for this project.