Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects

N.H. Barton, M. Turelli, American Naturalist 178 (2011) E48–E75.

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Journal Article | Published | English
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Abstract
Unlike unconditionally advantageous “Fisherian” variants that tend to spread throughout a species range once introduced anywhere, “bistable” variants, such as chromosome translocations, have two alternative stable frequencies, absence and (near) fixation. Analogous to populations with Allee effects, bistable variants tend to increase locally only once they become sufficiently common, and their spread depends on their rate of increase averaged over all frequencies. Several proposed manipulations of insect populations, such as using Wolbachia or “engineered underdominance” to suppress vector-borne diseases, produce bistable rather than Fisherian dynamics. We synthesize and extend theoretical analyses concerning three features of their spatial behavior: rate of spread, conditions to initiate spread from a localized introduction, and wave stopping caused by variation in population densities or dispersal rates. Unlike Fisherian variants, bistable variants tend to spread spatially only for particular parameter combinations and initial conditions. Wave initiation requires introduction over an extended region, while subsequent spatial spread is slower than for Fisherian waves and can easily be halted by local spatial inhomogeneities. We present several new results, including robust sufficient conditions to initiate (and stop) spread, using a one-parameter cubic approximation applicable to several models. The results have both basic and applied implications.
Publishing Year
Date Published
2011-09-01
Journal Title
American Naturalist
Volume
178
Issue
3
Page
E48 - E75
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Barton NH, Turelli M. Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects. American Naturalist. 2011;178(3):E48-E75. doi:10.1086/661246
Barton, N. H., & Turelli, M. (2011). Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects. American Naturalist, 178(3), E48–E75. https://doi.org/10.1086/661246
Barton, Nicholas H, and Michael Turelli. “Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects.” American Naturalist 178, no. 3 (2011): E48–75. https://doi.org/10.1086/661246.
N. H. Barton and M. Turelli, “Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects,” American Naturalist, vol. 178, no. 3, pp. E48–E75, 2011.
Barton NH, Turelli M. 2011. Spatial waves of advance with bistable dynamics: Cytoplasmic and genetic analogues of Allee effects. American Naturalist. 178(3), E48–E75.
Barton, Nicholas H., and Michael Turelli. “Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects.” American Naturalist, vol. 178, no. 3, University of Chicago Press, 2011, pp. E48–75, doi:10.1086/661246.
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