In combination with the microsatellite data, our mitochondrial findings are consistent with there being one species of Philornis on the islands from which we sampled. A population bottleneck was detected in the entire sample of individuals from the three islands, which is consistent with the pattern expected from an invasive, recently colonised species [4–6]. We report low genetic differentiation between island populations of the invasive avian parasite P. downsi on the Galápagos archipelago. Fly populations on Santa Cruz, Floreana, and Isabela showed strong evidence for high inter-island gene flow. However, low levels of divergence were detected between individuals from Floreana Island and those from Santa Cruz and Isabela when incorporating geographic sampling information. The molecular variance was mainly explained at the level of individuals, and not by island, which further demonstrates the low genetic differentiation between islands. Bayesian clustering analysis with geographic data assigned individuals to two genetic clusters, one comprising individuals from Santa Cruz and Isabela, and the second comprising all individuals from Floreana Island (Table 3, Figure 4). This might indicate that gene flow in P. downsi between Floreana and the other islands is restricted to some extent, or that this island underwent a distinct founding process. Pairwise F st between the three islands further indicated that flies on Floreana may be slightly genetically divergent from flies on the other two islands.
The Bayesian clustering method implemented in STRUCTURE is considered to be best able to infer correct individual assignments when genetic differentiation between populations is well defined . Furthermore, the ability to distinguish the source of an individual decreases under conditions of high dispersal and associated low genetic differentiation [51, 55]. The level of genetic differentiation (F st) between populations is found to be a useful predictor of the performance of assignment methods . In the current study, the inability of STRUCTURE to confidently assign individuals to any cluster with certainty may reflect the lack of power to do so due to the low genetic differentiation (i.e. F st) between sampling locations. Thus, we conclude there was an insufficient signal in the data to confidently assign individuals under the model of Pritchard et al. , despite reasonably high PI values across loci. Our results are therefore testament that taking the spatial context of individuals into account improved the efficiency of our analysis, as found by Fontaine et al. . Verifying the usefulness of STRUCTURE to assign individuals correctly where genetic differentiation is low and dispersal is common requires further study using empirical field data [51, 55].
The current study lacks genetic data from mainland P. downsi populations and data from all islands of the Galápagos where P. downsi occurs, which will be necessary for a detailed examination of founder effects, bottlenecks, introduction events and colonisation pathways. Thus, without knowing where P. downsi populations originally came from, or where they most recently arrived on the Galápagos archipelago, a comprehensive invasion history can not be constructed on a demographic or evolutionary scale [11, 56]. However, our findings lay the foundation for a more thorough understanding of the process of P. downsi invasion on the Galápagos archipelago. It is possible that P. downsi arrived on Ecuadorian cargo ships that were transporting fruit to the islands for human consumption [57, 58], while it is also suggested that the fly came with imported pigeons (discussed in ). Strong winds and air currents present during El Niño events on the Galápagos are believed to contribute to insect dispersal between islands , while transport of humans and materials is also suspected to aid inter-island insect dispersal. In four other invasive insect species, the dates of colonisation on each island suggest a wind-mediated southeast to northwest direction of colonisation across the islands . Such patterns remain unexplored for P. downsi.
Recently colonised invaders are often subject to a reduction in genetic variation and population bottlenecks because populations are not in genetic equilibrium [4–6]. We provide evidence for a population bottleneck in P. downsi across the three islands examined, which could be due to a small founding population, low immigration rates, or few introduction events [6, 61]. The low allelic diversity across loci and population bottleneck in P. downsi is further evidence for a small effective population size upon initial colonisation. However, the occurrence of multiple introductions can not be excluded, particularly in the absence of comparisons with potential source populations (e.g. from Ecuador, Trinidad, or Brazil) . Despite the presence of a population bottleneck and the (most likely related) low genetic diversity in P. downsi, the fly has clearly succeeded at establishing and spreading itself across the archipelago in high numbers.
Recently established species may persist at low and possibly undetectable numbers before becoming noticeably abundant and invasive years or decades later , which may reflect the lag time (i.e. the time between arrival and spread) observed in many species that become invasive . This scenario seems likely concerning the invasion of P. downsi on Galápagos because the fly was not detected in finch nests and identified until 1997 , despite the recent discovery of specimens found in collections made in 1964 [13, 17]. The parasite has since spread successfully and in high numbers across the archipelago (11 of 13 major islands) , indicating that any lag period that took place has passed. Yet it is unknown how recently each island was colonised and thus, whether particular island populations are undergoing a lag period that would favour the success of an immediate eradication effort (discussed in ).
Ecological [12, 28, 59] findings do not support the current existence of a lag period and indicate that P. downsi has spread successfully in at least 12 avian host species on the Galápagos Islands [12, 13]. In the current study, we provide evidence that the P. downsi population on Floreana Island has detectable levels of genetic differentiation when compared with two other island populations, which might be the result of a separate introduction event(s) or colonisation pattern. A wider geographic sample of locations across habitats and islands is needed to examine this more definitively in combination with a larger number of highly polymorphic genetic markers. However, it is clear that P. downsi populations generally have high connectivity between islands or high shared ancestry, although variation in population processes (e.g. rates of dispersal, colonisation histories) between particular islands may allow for low levels of inter-island genetic differentiation.
Absence of local genetic divergence
Local populations are expected to evolve adaptive differences in response to differing environmental conditions . The lack of genetic structure in P. downsi on the Galápagos archipelago may reflect the estimated short time period since the flies' introduction (~40 years ago)  such that populations have not yet diverged since colonisation. We document no genetic structure according to habitat type across islands, which implies high levels of fly dispersal between the two habitats. Across islands however, differences in host diversity and distribution, ecological variables, or colonisation history may result in genetic divergence due to genetic drift, as was evident from the low genetic differentiation we document on Floreana Island.
Fly populations may show rapid evolution with geographic cline, as shown by Huey et al.  who found increased wing length with latitude in Drosophila subobscura, just two decades after its introduction into North America. The evidence we present for high gene flow between habitats implies that morphological variation in P. downsi is unlikely, though other insect species on Galápagos show morphological variation and genetic differentiation between habitats and islands of the archipelago [56, 66, 67]. Clinal variation in morphology (and evidence for low dispersal) was also found for Bulimilus land snails on Galápagos  and Darwin's small ground finch .
Implications for control: the sterile insect technique (SIT)
The use of SIT to control P. downsi on the Galápagos Islands is perhaps the most appropriate method for eradicating an invasive fly within this ecologically fragile island ecosystem. SIT is a non-disruptive method as it does not introduce toxic or foreign chemicals into the environment, it is species specific, and does not introduce new genetic material into populations because the released organisms are not self-replicating [19, 69].
The effectiveness of SIT is affected by population genetic differentiation within the target species because the occurrence of undetected sub-species or strain differentiation across geographic populations can be detrimental to widespread sterile male release . Reinfestation of parasitic flies in SIT treated regions have been explained by genetic differentiation in the target species among allopatrically separated populations that may be experiencing reproductive isolation [e.g. ]. It is therefore of great advantage to use molecular genetic techniques for species characterisation and to examine population genetic structure prior to establishing large-scale sterile male release programs. We show that gene flow in P. downsi within and between three islands of the Galápagos is high, and unlikely to result in reproductive isolation. Thus, release of a single sterile strain of P. downsi could effectively suppress and eradicate the fly across the archipelago. Captive breeding experiments of adult P. downsi from multiple island populations are necessary to determine this with high confidence.