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Information limitation and the dynamics of coupled ecological systems

Abstract

The dynamics of large ecological systems result from vast numbers of interactions between individual organisms. Here, we develop mathematical theory to show that the rate of such interactions is inherently limited by the ability of organisms to gain information about one another. This phenomenon, which we call ‘information limitation’, is likely to be widespread in real ecological systems and can dictate both the rates of ecological interactions and long-run dynamics of interacting populations. We show how information limitation leads to sigmoid interaction rate functions that can stabilize antagonistic interactions and destabilize mutualistic ones; as a species or type becomes rare, information on its whereabouts also becomes rare, weakening coupling with consumers, pathogens and mutualists. This can facilitate persistence of consumer–resource systems, alter the course of pathogen infections within a host and enhance the rates of oceanic productivity and carbon export. Our findings may shed light on phenomena in many living systems where information drives interactions.

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Fig. 1: Model setup, sensory signals and searcher motion in empirical systems.
Fig. 2: Information, motion and interaction rates.
Fig. 3: Population persistence and collapse in consumer–resource systems.
Fig. 4: Information limitation dictates qualitative dynamics in consumer–resource systems.
Fig. 5: Information limitation can destabilize mutualistic interactions.
Fig. 6: Sensory length scale drives dynamics and productivity.

Data availability

No data were generated in this study. Data in Fig. 1c were digitized from published studies19,20,5456. Chlorophyll data shown in Fig. 6b can be freely accessed via NOAA ERDDAP server (https://coastwatch.pfeg.noaa.gov/erddap).

Code availability

Simulations and ODE system solutions were conducted in the R environment (R Development Core Team). Code is available for download as Supplementary Software.

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Acknowledgements

We thank members of the Information in Ecology Workshop held at UBC, S. Munch, S. McKinley, R. Nisbet, M. O’Connor, D. Brumley, F. Carrara, S. Redner and M. Gil, for comments and suggestions. A.M.H. and B.T.M. were supported by NSF IOS grant no. 1855956. A.M.H. acknowledges Simons Foundation grant no. 395890.

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A.M.H. and B.T.M. designed the study, performed analyses and wrote the paper.

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Correspondence to Andrew M. Hein.

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Extended data

Extended Data Fig. 1 Shape of interaction rate functions is preserved under continuous variation in the degree of directed motion.

(a) Rate of drift toward target as a function of distance from the target for the two-state model described in the main text with l*=100 body lengths (black line), and for three alternative models in which drift rate toward the target is a saturating function of a signal that decays exponentially (purple), like a Gaussian (orange) or like an inverse-square power law (green) with distance from the target. Signal decay parameters were chosen so that the mean drift speed at distance 100 body lengths are equal for all models. Drift rate, H(l), is calculated as a saturating function of the signal to constrain searchers to a maximum drift speed: H(l)=−vmaxtanh(S(l)), where S(l) is the signal value at a distance l, from a target (see Supplementary Discussion for details). The hyperbolic tangent form is motivated by past work on signal-dependent taxis responses15,16; other saturating functions yield similar results. (b) Interaction rate computed by solving Eq. (1) using the drift rates shown in panel (a). (c) Per-capita interaction rates corresponding to interaction rates shown in panel (b). Note non-monotonic form similar to that shown in Fig. 2c of the Main Text. (d) Range of drift functions with different parameter values. Each curve is one parameterization of the exponential signal function shown in panel (b) with drift rate again given by H(l)=−vmaxtanh(S(l)). Dark colored curves indicate functions in which change in drift rate with distance from target is relatively slow, whereas lighter colors are drift rate functions with more abrupt transition from high to low drift rate as distance from target increases. (e) Per-capita encounter rate as a function of target density for the same curves shown in panel (d). Note that location and height of peak changes but qualitative shape of curve is preserved.

Extended Data Fig. 2 Interaction rates in random target landscapes.

(a) Interaction rate and per-capita interaction rate in a two-dimensional landscape with targets distributed according to a Poisson spatial process, (b) targets distributed according to a Poisson spatial process in which the length scale of sensory information, l*, differs for each target, and (c) targets distributed according to a Poisson spatial process where the searcher depletes targets as it moves through the environment. Points correspond to l* of 5 (squares), 10 (boxes), 20 (triangles), and 40 (diamonds) body lengths. For the simulation with variable l*, these values are averages. See Supplementary Discussion ‘Robustness to spatial arrangement, target variability, and target depletion’ for a description of simulations.

Extended Data Fig. 3 Analytic approximation of interaction rates in a random target landscape.

Per-capita interaction rates in a two-dimensional landscape with targets distributed according to a Poisson spatial process. Lines show analytic approximation (see Supplementary Discussion ‘Analytic approximation for interaction rate in a random target field’). Note that, while approximation overestimates per-capita rate at intermediate density, prediction at high and low densities is accurate, as is the predicted location of peak per-capita interaction rate.

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Hein, A.M., Martin, B.T. Information limitation and the dynamics of coupled ecological systems. Nat Ecol Evol 4, 82–90 (2020). https://doi.org/10.1038/s41559-019-1008-x

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