Maternally inherited Wolbachia transinfections are being introduced into natural mosquito populations to reduce the transmission of dengue, Zika and other arboviruses. Wolbachia-induced cytoplasmic incompatibility provides a frequency-dependent reproductive advantage to infected females that can spread transinfections within and among populations. However, because transinfections generally reduce host fitness, they tend to spread within populations only after their frequency exceeds a critical threshold. This produces bistability with stable equilibrium frequencies at both 0 and 1, analogous to the bistability produced by underdominance between alleles or karyotypes and by population dynamics under Allee effects. Here, we analyze how stochastic frequency variation produced by finite population size can facilitate the local spread of variants with bistable dynamics into areas where invasion is unexpected from deterministic models. Our exemplar is the establishment of wMel Wolbachia in the Aedes aegypti population of Pyramid Estates (PE), a small community in far north Queensland, Australia. In 2011, wMel was stably introduced into Gordonvale, separated from PE by barriers to Ae. aegypti dispersal. After nearly six years during which wMel was observed only at low frequencies in PE, corresponding to an apparent equilibrium between immigration and selection, wMel rose to fixation by 2018. Using analytic approximations and statistical analyses, we demonstrate that the observed fixation of wMel at PE is consistent with both stochastic transition past an unstable threshold frequency and deterministic transformation produced by steady immigration at a rate just above the threshold required for deterministic invasion. The indeterminacy results from a delicate balance of parameters needed to produce the delayed transition observed. Our analyses suggest that once Wolbachia transinfections are established locally through systematic introductions, stochastic “threshold crossing” is likely to only minimally enhance spatial spread, providing a local ratchet that slightly – but systematically – aids area-wide transformation of disease-vector populations in heterogeneous landscapes.

The file "collection_data_2018-08-14.cvs" contains the raw data on the Wolbachia infection frequencies in Aedes aegypti sampled in Pyramid Estates and Gordonvale up to August 2018. The individual rows are the results from individual traps together with their geographical location. The file "PE(data_for_Figs2,4&5).csv" contains the pooled data that are plotted in Figure 2 (with x-axis in days) and analyzed in Figures 4 and 5 (with the data represented as estimates of infection frequencies over discrete generations). The “dates” for the individual pooled samples used in Fig. 2 are the weighted arithmetic means of the sampling times within each temporal pooling period, with weights corresponding to sample sizes.

The methods are described in our text and in the references provided there, specifically Hoffmann et al. (2011, Nature 476:454-457), Schmidt et al. (2017, PLoS Biol. 15:e2001894) and Ryan et al. (2019, Gates Open Research 3:1547).