Interaction networks in persistent Lotka-Volterra communities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929312473546752 |
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| author | Poley, Lyle Galla, Tobias Baron, Joseph W. |
| author_facet | Poley, Lyle Galla, Tobias Baron, Joseph W. |
| contents | A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in a generalised Lotka-Volterra dynamical system. Beginning with a community of species interacting on a network with arbitrary degree distribution, we provide an analytical framework from which properties of the eventual `surviving community' can be derived. We find that highly-connected species are less likely to survive than their poorly connected counterparts, which skews the eventual degree distribution towards a preponderance of species with low degree, a pattern commonly observed in real ecosystems. Further, the average abundance of the neighbours of a species in the surviving community is lower than the community average (reminiscent of the famed friendship paradox). Finally, we show that correlations emerge between the connectivity of a species and its interactions with its neighbours. More precisely, we find that highly-connected species tend to benefit from their neighbours more than their neighbours benefit from them. These correlations are not present in the initial pool of species and are a result of the dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_08600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interaction networks in persistent Lotka-Volterra communities Poley, Lyle Galla, Tobias Baron, Joseph W. Populations and Evolution Disordered Systems and Neural Networks A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in a generalised Lotka-Volterra dynamical system. Beginning with a community of species interacting on a network with arbitrary degree distribution, we provide an analytical framework from which properties of the eventual `surviving community' can be derived. We find that highly-connected species are less likely to survive than their poorly connected counterparts, which skews the eventual degree distribution towards a preponderance of species with low degree, a pattern commonly observed in real ecosystems. Further, the average abundance of the neighbours of a species in the surviving community is lower than the community average (reminiscent of the famed friendship paradox). Finally, we show that correlations emerge between the connectivity of a species and its interactions with its neighbours. More precisely, we find that highly-connected species tend to benefit from their neighbours more than their neighbours benefit from them. These correlations are not present in the initial pool of species and are a result of the dynamics. |
| title | Interaction networks in persistent Lotka-Volterra communities |
| topic | Populations and Evolution Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2404.08600 |