TY  - JOUR
AU  - Ariman, Merve Kahraman
PY  - 2026
TI  - Topological characterization of ecological dynamics via persistent homology
JO  - AIMS Mathematics
SP  - 18122
EP  - 18147
VL  - 11
IS  - 6
AB  - Conventional linear methods provide valuable insights into ecological population dynamics but may not fully capture their underlying geometric complexity. We present a large-scale topological characterization of ecological population dynamics using persistent homology applied to 500 time series from the BioTIME database, spanning marine, terrestrial, and freshwater ecosystems. Time-delay embedding and Vietoris–Rips filtration yield two classes of topological invariants: Betti numbers        β    k  , which count persistent topological features, and persistence entropy        H    k  , which quantifies their distributional complexity. These invariants quantify multiscale cyclic organization in a manner that complements spectral and autoregressive approaches. Three principal components capture    92.6  % of topological variance, revealing that ecological attractor geometry is fundamentally low-dimensional. Realm membership explains less than    0.01  % of this variance, demonstrating that habitat type imposes negligible constraints on dynamical complexity relative to within-realm heterogeneity, a finding that challenges the widely assumed structuring role of environmental context. An exceptionally strong coupling (   ρ  =  0.989) between        β    k   and        H    k   reflects an information-theoretic bound        H    k    ≤      log    2    ⁡  (      β    k    ). These results support shared dynamical mechanisms, including density dependence, predator-prey interactions, and life history trade-offs, as primary determinants of attractor topology, and they establish persistent homology as a noise-robust complement to conventional methods for comparative ecological analysis.
UR  - https://doi.org/10.3934/math.2026737
DO  - 10.3934/math.2026737