Confidently identifying the correct K value using the Δ K method: When does K = 2?

Populations delineated based on genetic data are commonly used for wildlife conservation and management. Many studies use the program structure combined with the Δ K method to identify the most probable number of populations ( K ). We recently found K  = 2 was identified more often when studies used Δ K compared to studies that did not. We suggested two reasons for this: hierarchical population structure leads to underestimation, or the Δ K method does not evaluate K  = 1 causing an overestimation. The present contribution aims to develop a better understanding of the limits of the method using one, two and three population simulations across migration scenarios. From these simulations we identified the “best K ” using model likelihood and Δ K . Our findings show that mean probability plots and Δ K are unable to resolve the correct number of populations once migration rate exceeds 0.005. We also found a strong bias towards selecting K  = 2 using the Δ K method. We used these data to identify the range of values where the Δ K statistic identifies a value of K that is not well supported. Finally, using the simulations and a review of empirical data, we found that the magnitude of Δ K corresponds to the level of divergence between populations. Based on our findings, we suggest researchers should use the Δ K method cautiously; they need to report all relevant data, including the magnitude of Δ K , and an estimate of connectivity for the research community to assess whether meaningful genetic structure exists within the context of management and conservation.