- Open Access
Unraveling the Temporal Dependence of Ecological Interaction Measures
PRX Life 4, 033001 – Published 1 July, 2026
DOI: https://doi.org/10.1103/8fb1-jmqh
Abstract
Identifying the network of species interactions is a fundamental step toward understanding ecosystem stability and biodiversity. However, the interpretability of empirical interaction measures remains a major challenge. Experimental estimates frequently exhibit puzzling temporal fluctuations, including sign shifts typically interpreted as transitions between competition and facilitation. Here, we analyze the temporal behavior of pairwise interaction measures to demonstrate that these fluctuations—and apparent shifts in ecological roles—can emerge intrinsically from standard population dynamics, without any underlying change in the actual ecological relationships. We show that inferred interactions are heavily distorted by experimental protocol choices, particularly the duration of observation and microbial growth constraints. By systematically evaluating interactions across timescales, we uncover a principled mechanism to mitigate these biases: short-term measurements reliably isolate direct, pairwise species couplings, whereas longer-term observations inevitably absorb indirect community feedbacks and systemic experimental constraints. By disentangling direct couplings from indirect network effects, our framework provides a robust, timescale-aware approach to interpreting empirical interaction matrices, offering critical quantitative guidance for experimental design and predictive ecosystem modeling.
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References (66)
- J. T. Wootton and M. Emmerson, Measurement of interaction strength in nature, Annu. Rev. Ecol. Evol. Syst. 36, 419 (2005).
- P. Yodzis, The indeterminacy of ecological interactions as perceived through perturbation experiments, Ecology 69, 508 (1988).
- A. Sanchez and J. Gore, Feedback between population and evolutionary dynamics determines the fate of social microbial populations, PLoS Biol. 11, e1001547 (2013).
- M. D. Bertness and R. Callaway, Positive interactions in communities, Trends Ecol. Evol. 9, 191 (1994).
- R. M. Callaway, R. W. Brooker, P. Choler, Z. Kikvidze, C. J. Lortie, R. Michalet, L. Paolini, F. I. Pugnaire, B. Newingham, E. T. Aschehoug, C. Armas, D. Kikodze, and B. J. Cook, Positive interactions among alpine plants increase with stress, Nature (London) 417, 844 (2002).
- S. Kéfi, M. van Baalen, M. Rietkerk, and M. Loreau, Evolution of local facilitation in arid ecosystems, Am. Nat. 172, E1 (2008).
- Q. He, M. D. Bertness, and A. H. Altieri, Global shifts towards positive species interactions with increasing environmental stress, Ecol. Lett. 16, 695 (2013).
- A. E. Adams, E. M. Besozzi, G. Shahrokhi, and M. A. Patten, A case for associational resistance: Apparent support for the stress gradient hypothesis varies with study system, Ecol. Lett. 25, 202 (2022).
- R. Díaz-Sierra, M. Rietkerk, M. Verwijmeren, and M. Baudena, Facilitation and competition deconstructed: A mechanistic modelling approach to the stress gradient hypothesis applied to drylands, Sci. Rep. 14, 2205 (2024).
- S. Azaele, S. Suweis, J. Grilli, I. Volkov, J. R. Banavar, and A. Maritan, Statistical mechanics of ecological systems: Neutral theory and beyond, Rev. Mod. Phys. 88, 035003 (2016).
- J. Grilli, Macroecological laws describe variation and diversity in microbial communities, Nat. Commun. 11, 4743 (2020).
- E. Ser-Giacomi, L. Zinger, S. Malviya, C. De Vargas, E. Karsenti, C. Bowler, and S. De Monte, Ubiquitous abundance distribution of non-dominant plankton across the global ocean, Nat. Ecol. Evol. 2, 1243 (2018).
- S. Allesina and S. Tang, The stability–complexity relationship at age 40: A random matrix perspective, Popul. Ecol. 57, 63 (2015).
- D. A. Kessler and N. M. Shnerb, Generalized model of island biodiversity, Phys. Rev. E 91, 042705 (2015).
- I. Akjouj, M. Barbier, M. Clenet, W. Hachem, M. Maïda, F. Massol, J. Najim, and V. C. Tran, Complex systems in ecology: A guided tour with large Lotka–Volterra models and random matrices, Proc. R. Soc. A 480, 20230284 (2024).
- S. Suweis, F. Ferraro, C. Grilletta, S. Azaele, and A. Maritan, Generalized Lotka-Volterra systems with time correlated stochastic interactions, Phys. Rev. Lett. 133, 167101 (2024).
- J. H. Lawton, Are there general laws in ecology? Oikos 84, 177 (1999).
- I. Volkov, J. R. Banavar, S. P. Hubbell, and A. Maritan, Inferring species interactions in tropical forests, Proc. Natl. Acad. Sci. USA 106, 13854 (2009).
- C. K. Fisher and P. Mehta, Identifying keystone species in the human gut microbiome from metagenomic timeseries using sparse linear regression, PLoS One 9, e102451 (2014).
- K. R. Foster and T. Bell, Competition, not cooperation, dominates interactions among culturable microbial species, Curr. Biol. 22, 1845 (2012).
- P. Daleo and O. Iribarne, Beyond competition: The stress gradient hypothesis tested in plant herbivore interactions, Ecology 90, 2368 (2009).
- M. A. Freilich, E. Wieters, B. R. Broitman, P. A. Marquet, and S. A. Navarrete, Species co-occurrence networks: Can they reveal trophic and non-trophic interactions in ecological communities? Ecology 99, 690 (2018).
- S. Hervías-Parejo, M. Cuevas-Blanco, L. Lacasa, A. Traveset, I. Donoso, R. Heleno, M. Nogales, S. Rodríguez-Echeverría, C. J. Melián, and V. M. Eguíluz, On the structure of species-function participation in multilayer ecological networks, Nat. Commun. 15, 8910 (2024).
- R. P. Seifert and F. H. Seifert, A community matrix analysis of Heliconia insect communities, Am. Nat. 110, 461 (1976).
- K. Faust and J. Raes, Microbial interactions: From networks to models, Nat. Rev. Microbiol. 10, 538 (2012).
- O. S. Venturelli, A. V. Carr, G. Fisher, R. H. Hsu, R. Lau, B. P. Bowen, S. Hromada, T. Northen, and A. P. Arkin, Deciphering microbial interactions in synthetic human gut microbiome communities, Mol. Syst. Biol. 14, MSB178157 (2018).
- A. Picot, S. Shibasaki, O. J. Meacock, and S. Mitri, Microbial interactions in theory and practice: When are measurements compatible with models? Curr. Opin. Microbiol. 75, 102354 (2023).
- J. Pasqualini, A. Maritan, A. Rinaldo, S. Facchin, E. Vincenzo Savarino, A. Altieri, and S. Suweis, Linking complex microbial interactions and dysbiosis through a disordered Lotka–Volterra model, eLife 14, RP105948 (2026).
- E. A. Bender, T. J. Case, and M. E. Gilpin, Perturbation experiments in community ecology: Theory and practice, Ecology 65, 1 (1984).
- M. S. Laska and J. T. Wootton, Theoretical concepts and empirical approaches to measuring interaction strength, Ecology 79, 461 (1998).
- S. H. Roxburgh and J. B. Wilson, Stability and coexistence in a lawn community: Experimental assessment of the stability of the actual community, Oikos 88, 409 (2000).
- J. L. Attayde and L.-A. A. Hansson, Press perturbation experiments and the indeterminacy of ecological interactions: Effects of taxonomic resolution and experimental duration, Oikos 92, 235 (2001).
- M. Novak, J. D. Yeakel, A. E. Noble, D. F. Doak, M. Emmerson, J. A. Estes, U. Jacob, M. T. Tinker, and J. T. Wootton, Characterizing species interactions to understand press perturbations: What is the community matrix? Annu. Rev. Ecol. Evol. Syst. 47, 409 (2016).
- C. Armas, S. Rodríguez-Echeverría, and F. I. Pugnaire, A field test of the stress-gradient hypothesis along an aridity gradient, J. Veg. Sci. 22, 818 (2011).
- P. Piccardi, B. Vessman, and S. Mitri, Toxicity drives facilitation between 4 bacterial species, Proc. Natl. Acad. Sci. USA 116, 15979 (2019).
- R. Di Martino, A. Picot, and S. Mitri, Oxidative stress changes interactions between 2 bacterial species from competitive to facilitative, PLoS Biol. 22, e3002482 (2024).
- J. B. Wilson and S. H. Roxburgh, Application of community matrix theory to plant competition data, Oikos 65, 343 (1992).
- B. A. Menge, Dection of direct versus indirect effects: Were experiments long enough? Am. Nat. 149, 801 (1997).
- S. Kéfi, E. L Berlow, E. A. Wieters, L. N. Joppa, S. A. Wood, U. Brose, and S. A. Navarrete, Network structure beyond food webs: Mapping non-trophic and trophic interactions on Chilean rocky shores, Ecology 96, 291 (2015).
- O. J. Meacock and S. Mitri, Environment-organism feedbacks drive changes in ecological interactions, Ecol. Lett. 28, e70027 (2025).
- U. Marconi, A. Puglisi, L. Rondoni, and A. Vulpiani, Fluctuation–dissipation: Response theory in statistical physics, Phys. Rep. 461, 111 (2008).
- A. Goyal, J. W. Rocks, and P. Mehta, Universal niche geometry governs the response of ecosystems to environmental perturbations, PRX Life 3, 013010 (2025).
- L. Pacciani-Mori, A. Giometto, S. Suweis, and A. Maritan, Dynamic metabolic adaptation can promote species coexistence in competitive microbial communities, PLoS Comput. Biol. 16, e1007896 (2020).
- M. E. Ritchie and D. Tilman, Predictions of species interactions from consumer-resource theory: Experimental tests with grasshoppers and plants, Oecologia 94, 516 (1993).
- R. MacArthur, Species packing and competitive equilibrium for many species, Theor. Popul. Biol. 1, 1 (1970).
- P. Chesson, Macarthur's consumer-resource model, Theor. Popul. Biol. 37, 26 (1990).
- G. M. Palamara, J. A. Capitán, and D. Alonso, The stochastic nature of functional responses, Entropy 23, 575 (2021).
- S. H. Strogatz, Nonlinear Dynamics and Chaos (CRC Press, Boca Raton, FL, 2018).
- Z. Neufeld and E. Hernández-García, Chemical and Biological Processes in Fluid Flows: A Dynamical Systems Approach (Imperial College Press, London, 2009).
- M. L. Rosenzweig, Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time, Science 171, 385 (1971).
- R. M. May, Limit cycles in predator-prey communities, Science 177, 900 (1972).
- R. T. Paine, Intertidal community structure, Oecologia 15, 93 (1974).
- J. E. Goldford, N. Lu, D. Bajić, S. Estrela, M. Tikhonov, A. Sanchez-Gorostiaga, D. Segrè, P. Mehta, and A. Sanchez, Emergent simplicity in microbial community assembly, Science 361, 469 (2018).
- N. J. Treloar, A. J. H. Fedorec, B. Ingalls, and C. P. Barnes, Deep reinforcement learning for the control of microbial co-cultures in bioreactors, PLoS Comput. Biol. 16, e1007783 (2020).
- K. Vetsigian, R. Jajoo, and R. Kishony, Structure and evolution of Streptomyces interaction networks in soil and in silico, PLoS Biol. 9, 10 (2011).
- E. Barter, A. Brechtel, B. Drossel, and T. Gross, A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics, Proc. R. Soc. A 477, 20200742 (2021).
- A. J. McKane and T. J. Newman, Predator-prey cycles from resonant amplification of demographic stochasticity, Phys. Rev. Lett. 94, 218102 (2005).
- S. Kéfi, E. L. Berlow, E. A. Wieters, S. A. Navarrete, O. L. Petchey, S. A. Wood, A. Boit, L. N. Joppa, K. D. Lafferty, R. J. Williams, N. D. Martinez, B. A. Menge, C. A. Blanchette, A. C. Iles, and U. Brose, More than a meal... integrating non-feeding interactions into food webs, Ecol. Lett. 15, 291 (2012).
- R. T. Paine, Food web complexity and species diversity, Am. Nat. 100, 65 (1966).
- J. T. Wootton, Predicting direct and indirect effects: An integrated approach using experiments and path analysis, Ecology 75, 151 (1994).
- A. R. Ives, B. Dennis, K. L. Cottingham, and S. R. Carpenter, Estimating community stability and ecological interactions from time-series data, Ecol. Monogr. 73, 301 (2003).
- F. C. Klebaner, Introduction to Stochastic Calculus with Applications (Imperial College Press, London, 2012).
- J. Aguilar, M. A Muñoz, and S. Azaele, Limits of inference in complex systems: When stochastic models become indistinguishable, Phys. Rev. X (to be published).
- I. M. Bomze, Lotka-Volterra equation and replicator dynamics: A two-dimensional classification, Biol. Cybern. 48, 201 (1983).
- I. M. Bomze, Lotka-Volterra equation and replicator dynamics: New issues in classification, Biol. Cybern. 72, 447 (1995).
- J. Aguilar, Unraveling the temporal dependence of ecological interaction measures, [codes and datasets] GitHub, 2026, https://github.com/jvrglr/Unraveling-the-temporal-dependence-of-ecological-interaction-measures