Highly pathogenic avian influenza (HPAI) outbreaks are devastating to poultry industries and pose a risk to human health. There is concern that demand for free-range poultry products could increase the number of HPAI outbreaks by increasing the potential for low pathogenic avian influenza (LPAI) introduction to commercial flocks. We formulate stochastic mathematical models to understand how poultry-housing (barn, free-range and caged) within the meat and layer sectors interacts with a continuous low-level risk of introduction from wild birds, heterogeneity in virus transmission rates and virus mutation probabilities, to affect the risk of HPAI emergence — at both the shed and industry scales. For H5 and H7 viruses, restricted mixing in caged systems, free-range outdoor access and, particularly, production cycle length significantly influence HPAI risk between sectors of the chicken production industry. Results demonstrate how delay between virus mutation and detection, ensuing from the short production cycle, large shed sizes and industry reporting requirements, could mean that HPAI emerges in meat-production sheds but is undetected with few birds affected. We also find that the Australian HPAI outbreak history appears to be better explained by low LPAI introduction rates and low mutation probabilities, rather than extremely rare introduction and relatively high mutation probabilities.