Journal
AMERICAN NATURALIST
Volume 178, Issue 3, Pages E48-E75Publisher
UNIV CHICAGO PRESS
DOI: 10.1086/661246
Keywords
Wolbachia; underdominance; population replacement; species invasions; critical propagule size; wave stopping
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Funding
- Foundation for the National Institutes of Health through the Grand Challenges in Global Health Initiative of the Bill and Melinda Gates Foundation
- National Science Foundation [DEB-0815145]
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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.
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