One common form of reticulate evolution arises as a consequence of secondary contact between previously allopatric populations. Using extensive coalescent simulations, we describe the conditions for, and extent of, the introgression of genetic material into the genome of a colonizing population from an endemic population. The simulated coalescent histories are sampled from models that describe the evolution of entire chromosomes, thereby allowing the expected length of introgressed haplotypes to be estimated. The results indicate that our ability to identify reticulate evolution from genetic data is highly variable and depends critically upon the duration of the period of allopatry, the timing of the secondary contact event, as well as the sizes of the populations at the time of contact. One particularly interesting result arises when secondary contact occurs close to the time of a severe founder event, in this case, genetic introgression can be substantially more difficult to detect. However, if secondary contact occurs after such a founding event, when the range of the colonizing population increases, introgression is more readily detectable across the genome. This result may have important implications for our ability to detect introgression between ancestrally bottlenecked modern human populations and archaic hominin species, such as Neanderthals.