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Improved foraging by switching between diffusion and advection: benefits from movement that depends on spatial context

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Abstract

Animals use different modes of movement at different times, in different locations, and on different scales. Incorporating such context dependence in mathematical models represents a substantial increase in complexity, but creates an opportunity to more fully integrate key biological features. Here, we consider the spatial dynamics of a population of foragers with two subunits. In one subunit, foragers move via diffusion (random search) whereas in the other, foragers move via advection (gradient-following search). Foragers switch back and forth between the subunits as functions of their spatial context (i.e., depending on whether they are inside or outside of a patch, or depending on whether or not they can detect a gradient in resource density). We consider a one-dimensional binary landscape of resource patches and non-habitat and gauge success in terms of how well the mobile foragers overlap with the distribution of resources. Actively switching between dispersal modes can sometimes greatly enhance this spatial overlap relative to the spatial overlap possible when foragers merely blend advection and diffusion modes at all times. Switching between movement modes is most beneficial when organism’s gradient-following abilities are weak compared to its overall capacity for movement, but switching can actually be quite detrimental for organisms that can rapidly follow resource gradients. An organism’s perceptual range plays a critical role in determining the conditions under which switching movement modes benefits versus disadvantages foragers as they seek out resources.

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Acknowledgments

We thank Jonathan Potts and one anonymous reviewer for helpful comments that improved the manuscript.

Funding

Funding from NSF ABI 1458748 (to WFF) and NSF DMS (1514752 (to RSC and CC) supported this work.

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Authors and Affiliations

  1. Department of Biology, University of Maryland, College Park, MD, 20742, USA

    William F. Fagan, Tyler Hoffman, Daisy Dahiya & Eliezer Gurarie

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA

    Robert Stephen Cantrell & Chris Cosner

Authors
  1. William F. Fagan
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  2. Tyler Hoffman
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  3. Daisy Dahiya
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  4. Eliezer Gurarie
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  5. Robert Stephen Cantrell
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Corresponding author

Correspondence to William F. Fagan.

Electronic supplementary material

Supplementary Figure 1

How foraging success depends on parameters that govern the switching between random search and gradient-following movement modes. In panel (a) we show the effect of α0 which determines the baseline rate of switching to random search mode (Eq. 7) and h1 which sets the threshold resource gradient for switching from random search mode to gradient following mode (Eq. 9). Other parameters are γ = 2,  D = 0.2,  R = 2,  α1 = 25, β0 = 2,  and β1 = 60. In panel (b) we show the interplay between switching parameter β0 which influences the rate of switching from random search mode to gradient following mode (Eq. 9) and the perceptual range R (Eqs. 4 and 5). Other parameters are γ = 0.5,  D = 0.5, α0 = 5,  α1 = 25,  h1 = 5,  and β1 = 60. (DOCX 151 kb)

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Fagan, W.F., Hoffman, T., Dahiya, D. et al. Improved foraging by switching between diffusion and advection: benefits from movement that depends on spatial context. Theor Ecol 13, 127–136 (2020). https://doi.org/10.1007/s12080-019-00434-w

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