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Interaction networks in persistent Lotka-Volterra communities (2404.08600v1)

Published 12 Apr 2024 in q-bio.PE and cond-mat.dis-nn

Abstract: 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.

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References (42)
  1. J. Grilli, Macroecological laws describe variation and diversity in microbial communities, Nature communications 11, 4743 (2020).
  2. W. R. Shoemaker, Á. Sánchez, and J. Grilli, Macroecological laws in experimental microbial communities, bioRxiv , 2023 (2023).
  3. J. H. Brown, Macroecology (University of Chicago Press, 1995).
  4. M. Pascual and J. A. Dunne, Ecological Networks: Linking Structure to Dynamics in Food Webs (Oxford University Press, USA, 2006).
  5. J. A. Dunne, R. J. Williams, and N. D. Martinez, Food-web structure and network theory: The role of connectance and size, Proceedings of the National Academy of Sciences 99, 12917 (2002a), https://www.pnas.org/content/99/20/12917.full.pdf .
  6. A.-M. Neutel, J. A. P. Heesterbeek, and P. C. de Ruiter, Stability in Real Food Webs: Weak Links in Long Loops, Science 296, 1120 (2002), 3076707 .
  7. M. Lurgi, D. Montoya, and J. M. Montoya, The effects of space and diversity of interaction types on the stability of complex ecological networks, Theoretical Ecology 9, 3 (2016).
  8. R. P. Rohr, S. Saavedra, and J. Bascompte, On the structural stability of mutualistic systems, Science 345, 1253497 (2014).
  9. J. A. Fuhrman, Microbial community structure and its functional implications, Nature 459, 193 (2009).
  10. J. E. Cohen, 13. Food Webs and Community Structure, in Perspectives in Ecological Theory, edited by J. Roughgarden, R. M. May, and S. A. Levin (Princeton University Press, 1989) pp. 181–202.
  11. J. E. Cohen, A stochastic theory of community food webs. VI. Heterogeneous alternatives to the cascade model, Theoretical Population Biology 37, 55 (1990).
  12. R. J. Williams and N. D. Martinez, Simple rules yield complex food webs, Nature 404, 180 (2000).
  13. R. J. Williams and N. D. Martinez, Stabilization of chaotic and non-permanent food-web dynamics, The European Physical Journal B 38, 297 (2004).
  14. S. Allesina, D. Alonso, and M. Pascual, A General Model for Food Web Structure, Science 320, 658 (2008).
  15. R. M. May, Will a Large Complex System be Stable?, Nature 238, 413 (1972).
  16. G. Barabás, M. J. Michalska-Smith, and S. Allesina, The Effect of Intra- and Interspecific Competition on Coexistence in Multispecies Communities, The American Naturalist 188, E1 (2016).
  17. J. Grilli, T. Rogers, and S. Allesina, Modularity and stability in ecological communities, Nature Communications 7, 12031 (2016).
  18. J. W. Baron, Eigenvalue spectra and stability of directed complex networks, Phys. Rev. E 106, 064302 (2022).
  19. T. Galla, Dynamically evolved community size and stability of random Lotka-Volterra ecosystems, EPL (Europhysics Letters) 123, 48004 (2018).
  20. G. Bunin, Interaction patterns and diversity in assembled ecological communities (2016).
  21. J. A. Dunne, R. J. Williams, and N. D. Martinez, Food-web structure and network theory: The role of connectance and size, Proceedings of the National Academy of Sciences 99, 12917 (2002b).
  22. B. Bollobás, A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs, European Journal of Combinatorics 1, 311 (1980).
  23. M. Newman, Networks (Oxford University Press, 2018).
  24. F. Chung and L. Lu, Connected Components in Random Graphs with Given Expected Degree Sequences, Annals of Combinatorics 6, 125 (2002).
  25. L. Poley, J. W. Baron, and T. Galla, Generalized Lotka-Volterra model with hierarchical interactions, Physical Review E 107, 024313 (2023b).
  26. E. Mallmin, A. Traulsen, and S. De Monte, Chaotic turnover of rare and abundant species in a strongly interacting model community, Proceedings of the National Academy of Sciences 121, e2312822121 (2024).
  27. G. Garcia Lorenzana and A. Altieri, Well-mixed lotka-volterra model with random strongly competitive interactions, Phys. Rev. E 105, 024307 (2022).
  28. M. Mézard, G. Parisi, and M. Virasoro, Spin Glass Theory and beyond: An Introduction to the Replica Method and Its Applications, Vol. 9 (World Scientific Publishing Company, London, 1987).
  29. C. De Dominicis, Dynamics as a substitute for replicas in systems with quenched random impurities, Physical Review B 18, 10.1103/PhysRevB.18.4913 (1978).
  30. H. Janssen, On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties, Zeitschrift für Physik B Condensed Matter 23, 377 (1976).
  31. M. Opper and S. Diederich, Phase transition and 1/f noise in a game dynamical model, Physical Review Letters 69, 1616 (1992).
  32. E. L. Sander, J. T. Wootton, and S. Allesina, Ecological network inference from long-term presence-absence data, Scientific reports 7, 7154 (2017).
  33. J. Camacho, R. Guimera, and L. A. N. Amaral, Analytical solution of a model for complex food webs, Physical Review E 65, 030901 (2002a), arxiv:cond-mat/0102127 .
  34. J. Camacho, R. Guimerà, and L. A. Nunes Amaral, Robust Patterns in Food Web Structure, Physical Review Letters 88, 228102 (2002b).
  35. L. Stone, D. Simberloff, and Y. Artzy-Randrup, Network motifs and their origins, PLOS Computational Biology 15, e1006749 (2019).
  36. D. B. Stouffer, J. Camacho, and L. A. N. Amaral, A robust measure of food web intervality, Proceedings of the National Academy of Sciences 103, 19015 (2006).
  37. C. J. Melián and J. Bascompte, Food web structure and habitat loss, Ecology Letters 5, 37 (2002).
  38. D. Garlaschelli and M. I. Loffredo, Patterns of link reciprocity in directed networks, Physical Review Letters 93, 268701 (2004), arxiv:cond-mat/0404521 .
  39. D. Garlaschelli, G. Caldarelli, and L. Pietronero, Universal scaling relations in food webs, Nature 423, 165 (2003).
  40. J. W. Baron, A path integral approach to sparse non-Hermitian random matrices (2023), arxiv:2308.13605 [cond-mat, q-bio] .
  41. J. E. Cohen, Derivatives of the spectral radius as a function of non-negative matrix elements, Mathematical Proceedings of the Cambridge Philosophical Society 83, 183 (1978).
  42. E. Deutsch and M. Neumann, Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix, Journal of Mathematical Analysis and Applications 102, 1 (1984).
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