Despite intensive and organized efforts to track species of high importance to humans, population censuses are often unable to detect small extant populations. For threatened or endangered species, this may result in conservative estimates of populations that bolster conservation efforts. However, for pests or non-native and potentially invasive species, failing to properly consider small, early-stage invasion populations can result in foregoing intervention strategies until populations are already established. Research on difficult-to-detect insect pests is critical to understanding the population dynamics of potentially harmful species before the negative effects of their full impact are realized. To address this latter issue, in this dissertation I utilize a highly unique dataset that has tracked non-native fruit fly (Diptera: Tephritidae) populations in California for over one hundred years to explore spatial statistical techniques that aid in detecting populations that are typically sub-detectable. In Chapter 1, I use spatial point pattern analysis with a variety of temporal treatments to confirm potential establishment signals of Bactrocera dorsalis (the oriental fruit fly) in the Los Angeles region of California. Building on this, Chapter 2 uses point pattern clustering metrics to determine which non-native tephritid species are likely already established in California and therefore pose a higher risk of invasion or outbreak. Finally, in Chapter 3, I explore which human and environmental factors drive B. dorsalis detections in California. Combined, these analyses reveal deeper dynamics of difficult-to-detect populations of non-native tephritid fruit flies and provide an approach for monitoring early-stage invasive species. Looking forward, these findings may inform best management practices as global climate change and globalization increase the likelihood of further problematic insect introductions worldwide.