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One central question in theoretical ecology concerns the factors that
make an ecosystem stable or unstable. One approach to this problem is to
model ecological communities as random systems. This means to draw
interaction coefficients at random from a specified distribution, and to
determine stability as a function of for example mean and variance. The
approach was pioneered by Robert May in the 1970s. May found that
increasing complexity would promote instability, leading him to ask what
the ‘devious strategies’ might be that nature uses to sustain stable
complex ecological communities. This sparked the so-called
diversity-stability debate, which continues to date.
In the language of physics the models proposed by May are disordered
systems, showing what is known as `frustration’ in spin glass physics.
For example, the resulting energy landscapes can be rugged, and the
number of marginally stable equilibria can be large. In this talk I will
summarise some of the contributions statistical physics has made to the
diversity-stability debate. In particular As one example, I will
describe how path integral methods and random-matrix theory can be used
to determine the stability of models of complex ecologies. I also will
discuss some of the challenges physicists and ecologists face in
interacting with one another at this cross-disciplinary interface.
References:
J. W. Baron, T. J. Jewell, C. Ryder, T. Galla, Eigenvalues of Random
Matrices with Generalized Correlations: A Path Integral Approach, Phys.
Rev. Lett. 128, 120601 (2022)
J. W. Baron, T. J. Jewell, C. Ryder, T. Galla, Breakdown of
Random-Matrix Universality in Persistent Lotka-Volterra Communities,
Phys. Rev. Lett. 130, 137401 (2023)
Tobias Galla
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)
https://sites.google.com/view/tobiasgalla/